Metallicity Structure in the Milky Way Disk Revealed by Galactic H ii Regions

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Published 2019 December 16 © 2019. The American Astronomical Society. All rights reserved.
, , Citation Trey V. Wenger et al 2019 ApJ 887 114 DOI 10.3847/1538-4357/ab53d3

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0004-637X/887/2/114

Abstract

The metallicity structure of the Milky Way disk stems from the chemodynamical evolutionary history of the Galaxy. We use the National Radio Astronomy Observatory Karl G. Jansky Very Large Array to observe ∼8–10 GHz hydrogen radio recombination line and radio-continuum emission toward 82 Galactic H ii regions. We use these data to derive the electron temperatures and metallicities for these nebulae. Since collisionally excited lines from metals (e.g., oxygen, nitrogen) are the dominant cooling mechanism in H ii regions, the nebular metallicity can be inferred from the electron temperature. Including previous single-dish studies, there are now 167 nebulae with radio-determined electron temperature and either parallax or kinematic distance determinations. The interferometric electron temperatures are systematically 10% larger than those found in previous single-dish studies, likely due to incorrect data analysis strategies, optical depth effects, and/or the observation of different gas by the interferometer. By combining the interferometer and single-dish samples, we find an oxygen abundance gradient across the Milky Way disk with a slope of −0.052 ± 0.004 dex kpc−1. We also find significant azimuthal structure in the metallicity distribution. The slope of the oxygen gradient varies by a factor of ∼2 when Galactocentric azimuths near ∼30° are compared with those near ∼100°. This azimuthal structure is consistent with simulations of Galactic chemodynamical evolution influenced by spiral arms.

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1. Introduction

The present-day chemical structure of the Milky Way disk is an important constraint on models of Galactic chemodynamical evolution (e.g., Chiappini et al. 2003; Minchev et al. 2014, 2018; Snaith et al. 2015). Radial metallicity gradients, for example, are found in both the Milky Way and other spiral galaxies in studies using collisionally excited lines in ionized star-forming regions (e.g., Searle 1971; Shaver et al. 1983) and stellar abundances (e.g., Bovy et al. 2014; Hayden et al. 2014). These gradients reveal the history of star formation, stellar migration, and chemical enrichment by stars across galactic disks (Minchev et al. 2018). Stellar and gaseous tracers provide complementary information about the chemodynamical history of the Galaxy. The chemical abundances of stars represent the enrichment of the interstellar medium (ISM) when the stars were born, whereas the abundances of gaseous tracers represent the end product of billions of years of stellar evolution and ISM enrichment.

Evidence for azimuthal variations in galactic radial metallicity gradients is observed in both the Milky Way (e.g., Balser et al. 2015, hereafter B15) and other galaxies (e.g., Sánchez-Menguiano et al. 2016, 2017; Ho et al. 2017, 2018). Azimuthal abundance variations in the Milky Way are identified in multiple elements and tracers, such as the oxygen abundances of H ii regions (e.g., B15) and the iron abundances of Cepheids (e.g., Luck et al. 2006; Pedicelli et al. 2009). Such variations are not expected in an old and well-mixed galaxy (Balser et al. 2011), and chemodynamical models of galaxies typically assume axisymmetric metallicity gradients (e.g., Chiappini et al. 2003). Azimuthal variations may be caused by streaming motions and radial migration induced by galactic bars (Di Matteo et al. 2013), spiral arms (Grand et al. 2016; Ho et al. 2017; Mollá et al. 2019b; Spitoni et al. 2019), and/or perturbations from minor galaxy interactions (Bird et al. 2012).

Here we expand the Galactic H ii region metallicity surveys of Quireza et al. (2006b), Balser et al. (2011), and B15 to create a more complete map of metallicity structure in the Milky Way disk and to search for evidence of azimuthal variations in the Galactic radial metallicity gradient. H ii regions are the sites of recent high-mass star formation. These nebulae are an ideal tracer of Galactic metallicity structure because (1) they live for ≲10 Myr, and they therefore reveal the current enrichment of the ISM; (2) their distances can be derived accurately using maser parallax measurements (e.g., Reid et al. 2014) or kinematic techniques (e.g., Wenger et al. 2018); and (3) their metallicities are easily derived using optical and infrared collisionally excited lines or inferred from the nebular electron temperatures. The radio recombination line (RRL) and radio-continuum emission from H ii regions are an extinction-free diagnostic of the nebular electron temperature (Mezger & Henderson 1967), which is empirically related to the H ii region metallicity (Shaver et al. 1983). Radio wavelength observations of H ii regions can reveal metallicity structure across the Milky Way disk due to the lack of dust extinction.

The local thermodynamic equilibrium (LTE) electron temperature of an ionized gas can be derived from the RRL-to-continuum brightness ratio when the nebula is optically thin (B15). The electron temperature surveys of Galactic H ii regions by B15, Balser et al. (2011), and Quireza et al. (2006b) used single-dish telescopes. Although these instruments are extremely sensitive to faint RRL emission, they are not ideal for measuring accurate RRL-to-continuum brightness ratios because of the uncertainties in the continuum brightnesses. The single-dish continuum brightness of an H ii region is measured by scanning the telescope across the source in multiple directions. Then, a baseline fit to the diffuse background continuum emission is removed. The accuracy of the radio-continuum brightness is limited by the ability to accurately remove this diffuse component.

An interferometer is the ideal tool for measuring the RRL-to-continuum brightness ratio of Galactic H ii regions. By their nature, interferometers are not sensitive to large scale, diffuse emission, such as the nonthermal radio-continuum emission that permeates the Galactic plane. We measure the total continuum flux density of nebulae more accurately with an interferometer than with a single-dish telescope if the angular size of the source is smaller than the largest angular scale of the telescope. Too, interferometer data can be constructed as a high angular resolution image or data cube. These images and cubes reduce source confusion and can provide maps of electron temperature variations across a resolved nebula. Finally, interferometers like the National Radio Astronomy Observatory (NRAO) Karl G. Jansky Very Large Array (VLA) simultaneously measure both radio-continuum and RRL emission. Any systematic calibration or weather issues affecting the data will be removed in the RRL-to-continuum flux ratio.

We use the VLA to derive the nebular electron temperatures and metallicities of Galactic H ii regions across the Milky Way disk. A subset of these nebulae overlap with previous single-dish surveys, which allows us to compare the interferometer-derived electron temperatures with those derived from single-dish observations.

2. Target Sample

Recent RRL surveys have more than doubled the number of known Galactic H ii regions (Bania et al. 2010, 2012; Anderson et al. 2014, 2015a, 2015b, 2018; Wenger et al. 2019). The Widefield Infrared Survey Explorer (WISE) Catalog of Galactic H ii Regions (hereafter, WISE Catalog) contains the infrared and radio properties of more than 2000 known nebulae (Anderson et al. 2014). To derive accurate electron temperatures, we require the subset of WISE Catalog nebulae observable by the VLA. Our selection criteria are nebulae with (1) a single RRL velocity component, (2) a maser parallax measurement or an accurate kinematic distance, and (3) a predicted RRL flux density >1.7 mJy beam−1.

When this survey began, the WISE Catalog contained RRL measurements of ∼1200 unique Galactic H ii regions. Many of these nebulae are clustered in H ii region groups or complexes, and a single-dish observation will see the combined emission from multiple discrete sources. These star-forming complexes are the source of ionizing photons, which may leak out into and ionize the diffuse ISM. In these cases, the RRL spectrum of the H ii region will show multiple velocity components from either multiple discrete H ii regions or a mix of H ii regions and diffuse ionized gas. The presence of spectrally confused, or blended, RRL components will limit our ability to derive the nebular RRL flux density accurately. Therefore, we remove ∼100 nebulae with multiple velocity component RRLs in the WISE Catalog.

In order to study Galactic metallicity structure, accurate distances to tracers are needed. Therefore, we further limit the WISE Catalog sample to those nebulae with published maser parallax measurements and/or accurate kinematic distances. We adopt the kinematic distance uncertainty model of Anderson et al. (2012) to estimate the accuracy of kinematic distances in the WISE Catalog. Because we aim to generate a Galactocentric map of the Milky Way metallicity structure, we require kinematic distance accuracies such that the uncertainty in the Galactocentric radius is σR < 2 kpc and the uncertainty in Galactocentric azimuth is σθ < 20°. Out of our sample of ∼1100 single-velocity RRL component nebulae, 107 have an associated maser parallax measurement and 364 have a kinematic distance meeting these accuracy thresholds. This brings our total sample of H ii regions to 471 nebulae.

Finally, we identify the subset of this sample with previously measured RRL flux densities bright enough to be detected by the VLA in a 10 minute observation. The point-source sensitivity of the VLA with this integration time is ∼2 mJy beam−1 per 31.25 kHz channel at ∼9 GHz. By smoothing the spectra to 5 km s−1 resolution and averaging seven RRL transitions, we estimate a spectral rms noise of ∼0.3 mJy beam−1 per channel. We thus require our sample of H ii regions to have a predicted 9 GHz RRL flux density greater than five times this sensitivity limit, ∼1.7 mJy beam−1.

All previously measured RRL flux densities of northern sky H ii regions in the WISE catalog were made with single-dish telescopes around ∼9 GHz. We first scale the observed RRL brightness temperatures to exactly 9 GHz assuming the RRL brightness temperature is proportional to the RRL frequency (B15). We convert these scaled RRL brightness temperatures to point-source flux densities assuming telescope gains of ∼2 K Jy−1 for the Green Bank Observatory (GBO) Green Bank Telescope (GBT; Balser et al. 2011), ∼0.27 K Jy−1 for the NRAO 140 Foot Telescope (hereafter, 140 Foot; Balser et al. 2016), and ∼5 K Jy−1 for the Arecibo Observatory (Bania et al. 2012). Any source with a predicted 9 GHz RRL flux density SL,9 GHz > 1.7 mJy beam−1 fulfills our sensitivity criterion. This threshold removes only 10 nebulae from our sample, bringing the total number of observable H ii regions to 461.

The VLA is not sensitive to emission on scales larger than ∼145'' in the D (most compact) configuration at ∼9 GHz. If we assume that the radio size of an H ii region is approximately one-half of the infrared size (e.g., Bihr et al. 2016), then 30% of the H ii regions in our sample have radio diameters greater than this largest angular scale. Our observations will not be sensitive to these angularly large nebulae if their emission is uniform on such large spatial scales. We expect to detect clumpy emission within these large H ii regions, however, so we do not use any size restriction when defining our sample.

Finally, we select our observing targets from this sample of 461 nebulae to maximize our coverage of the Galactic disk. We divide the Galaxy into 120 bins of size 12° in Galactocentric azimuth, over the azimuth range −30° to 150°, and 2 kpc in Galactocentric radius, up to 18 kpc. Using the maser parallax distance, when available, or the WISE Catalog kinematic distance to compute the Galactocentric radii and azimuths of the nebulae, we identify the two brightest and most compact H ii regions in each bin. Some bins only have one (or zero) nebulae that meet our distance accuracy and predicted RRL flux density requirements. Figure 1 shows the Galactocentric positions of the 128 H ii regions we select using these criteria as well as the 20 nebulae observed in the pilot survey. One H ii region, G032.272-0.226, is observed in both the pilot survey and main survey. Of the 120 position bins, 78 (65%) contain at least one H ii region that meets our selection criteria.

Figure 1.

Figure 1. Galactocentric positions and Milky Way disk coverage of the VLA survey H ii regions. The Galactic Center is the black point at the origin and the Sun is the black point 8.34 kpc in the direction θ = 0°. The colored points are the H ii regions in the pilot survey (blue) and main survey (red). The Galactic disk is divided into 120 bins of size 12° in Galactocentric azimuth, over the azimuth range −30° to 150°, and 2 kpc in Galactocentric radius, up to 18 kpc. Bins that contain at least one nebulae are colored light gray, whereas empty bins are dark gray.

Standard image High-resolution image

Our final H ii region target catalog contains 147 unique nebulae. Table 1 lists information about these H ii regions: the WISE Catalog name; the VLA project in which it was observed (13A-030 is the pilot survey and 15B-178 is the main survey); the WISE infrared position; the WISE infrared radius, RIR; the estimated 9 GHz RRL flux density, S9 GHz,L; the telescope and reference for the previous RRL detection; the previously measured RRL-to-continuum brightness ratio, SL/SC, and derived electron temperature, Te; and the reference for the RRL-to-continuum brightness ratio and electron temperature.

Table 1.  Survey Targets

Field Project R.A. Decl. RIR S9 GHz,L Telescopea RRL SL/SC Te Te
    J2000 J2000 (arcsec) (mJy   Authorb   (K) Authorc
    (hh:mm:ss) (dd:mm:ss)   beam−1)          
G005.883−0.399 15B-178 18:00:31.5 −24:04:18.9 22.35 844.15 ± 5.77 140 Foot Q06a
G009.598+0.199 15B-178 18:06:11.1 −20:32:36.5 34.09 226.92 ± 20.00 140 Foot L89
G010.596−0.381 15B-178 18:10:24.6 −19:57:08.4 60.00 586.69 ± 4.23 140 Foot Q06a 0.0686 ± 0.0006 9810 ± 90 Q06b;B15
G012.804−0.207 15B-178 18:14:15.0 −17:55:56.4 21.15 3034.62 ± 23.85 140 Foot Q06a 0.0808 ± 0.0007 7620 ± 100 Q06b;B15
G013.880+0.285 15B-178 18:14:35.7 −16:45:09.7 144.31 587.42 ± 5.00 140 Foot Q06a 0.1210 ± 0.0012 6960 ± 80 Q06b;B15
G015.212+0.167 15B-178 18:17:40.0 −15:38:13.8 176.72 10.95 ± 0.11 GBT A15b
G017.336−0.146 15B-178 18:22:57.2 −13:54:41.0 102.77 6.70 ± 0.18 GBT A11
G017.928−0.677 15B-178 18:26:01.7 −13:38:14.6 164.84 13.00 ± 0.30 GBT A11
G018.584+0.344 15B-178 18:23:34.9 −12:34:48.7 42.50 14.00 ± 0.28 GBT A11
G019.030+0.423 15B-178 18:24:09.0 −12:08:53.0 77.79 4.05 ± 0.38 GBT A11
G019.716−0.261 15B-178 18:27:56.0 −11:51:39.4 58.90 14.80 ± 0.27 GBT A15b
G019.728−0.113 15B-178 18:27:25.2 −11:46:55.1 42.50 7.70 ± 0.20 GBT A11
G020.227+0.110 15B-178 18:27:33.8 −11:14:11.4 71.07 5.25 ± 0.12 GBT A11
G020.363−0.014 15B-178 18:28:16.1 −11:10:25.6 42.50 10.90 ± 0.24 GBT A11
G021.386−0.255 15B-178 18:31:04.0 −10:22:43.4 57.60 15.65 ± 0.14 GBT A11
G021.603−0.169 15B-178 18:31:10.0 −10:08:48.4 31.87 4.10 ± 0.20 GBT A15b
G023.041−0.399 15B-178 18:34:41.3 −8:58:37.1 151.85 65.35 ± 0.66 GBT A11
G023.423−0.216 15B-178 18:34:44.5 −8:33:10.9 96.79 816.54 ± 3.65 140 Foot Q06a 0.1162 ± 0.0008 6500 ± 55 Q06b;B15
G023.661−0.252 15B-178 18:35:18.9 −8:21:34.2 56.59 24.30 ± 0.23 GBT A11
G023.787+0.223 15B-178 18:33:50.6 −8:01:42.3 189.71 146.15 ± 22.69 140 Foot L89
G024.185+0.211 15B-178 18:34:37.6 −7:40:51.3 178.07 176.92 ± 16.15 140 Foot L89
G024.724−0.084 15B-178 18:36:41.1 −7:20:16.7 254.14 253.85 ± 26.92 140 Foot L89
G024.728+0.159 15B-178 18:35:49.5 −7:13:20.1 75.57 42.20 ± 0.25 GBT A11
G024.734+0.087 15B-178 18:36:05.6 −7:15:01.3 85.58 93.95 ± 0.50 GBT A11
G025.397+0.033 15B-178 18:37:30.8 −6:41:08.8 39.69 88.46 ± 10.38 140 Foot L89
G025.398+0.562 15B-178 18:35:37.4 −6:26:34.0 42.50 23.25 ± 0.15 GBT A11
G025.477+0.040 15B-178 18:37:38.2 −6:36:45.1 42.50 4.60 ± 0.20 GBT A11
G026.597−0.024 15B-178 18:39:55.9 −5:38:45.0 26.61 16.65 ± 0.25 GBT A15a
G027.210+0.282 15B-178 18:39:58.0 −4:57:39.4 42.50 6.00 ± 0.17 GBT A15b
G027.562+0.084 13A-030 18:41:19.3 −4:44:21.4 42.50 22.60 ± 0.15 GBT A11 0.1601 ± 0.0021 5827 ± 94 B11;B15
G028.320+1.243 15B-178 18:38:34.9 −3:32:04.8 60.00 2.25 ± 0.10 GBT A15b
G028.451+0.001 15B-178 18:43:14.9 −3:59:11.0 28.70 9.20 ± 0.20 GBT A15b
G028.581+0.145 15B-178 18:42:58.4 −3:48:18.8 42.50 6.75 ± 0.10 GBT A11
G029.019+0.165 15B-178 18:43:42.1 −3:24:19.3 106.80 14.35 ± 0.19 GBT A11
G029.770+0.219 15B-178 18:44:53.2 −2:42:49.6 42.50 7.60 ± 0.10 GBT A11
G029.816+2.225 15B-178 18:37:49.6 −1:45:17.9 168.83 9.25 ± 0.16 GBT A15b
G029.956−0.020 15B-178 18:46:04.5 −2:39:25.2 94.36 896.81 ± 3.69 140 Foot Q06a 0.0992 ± 0.0064 6510 ± 90 Q06b;B15
G030.211+0.428 15B-178 18:44:56.7 −2:13:30.7 37.11 2.75 ± 0.20 GBT A15b
G031.269+0.064 15B-178 18:48:10.6 −1:27:00.7 24.84 92.31 ± 10.38 140 Foot L89
G031.274+0.485 13A-030 18:46:41.9 −1:15:43.8 83.38 4.15 ± 0.10 GBT A11 0.0944 ± 0.0042 8690 ± 462 B11;B15
G031.577+0.103 15B-178 18:48:35.9 −1:09:28.0 117.27 80.77 ± 8.46 140 Foot L89
G032.030+0.048 15B-178 18:49:37.2 +0:46:47.7 42.50 6.35 ± 0.13 GBT A11
G032.272−0.226 13A-030 18:51:02.3 +0:41:25.4 42.50 32.90 ± 0.14 GBT A11 0.0889 ± 0.0008 8238 ± 104 B11;B15
G032.272−0.226 15B-178 18:51:02.3 +0:41:25.4 42.50 32.90 ± 0.14 GBT A11 0.0889 ± 0.0008 8238 ± 104 B11;B15
G032.733+0.209 13A-030 18:50:19.9 +0:04:54.3 42.50 11.95 ± 0.27 GBT A11 0.1638 ± 0.0037 5856 ± 156 B11;B15
G032.876−0.423 13A-030 18:52:50.7 +0:14:57.6 126.62 15.20 ± 0.32 GBT A11 0.1817 ± 0.0043 6074 ± 176 B11;B15
G032.928+0.607 13A-030 18:49:16.4 +0:16:22.3 65.68 25.60 ± 0.09 GBT A11 0.0680 ± 0.0006 9843 ± 170 B11;B15
G032.976−0.334 13A-030 18:52:44.0 +0:06:31.4 131.80 12.50 ± 0.20 GBT A11 0.1485 ± 0.0040 6411 ± 207 B11;B15
G033.643−0.229 15B-178 18:53:32.9 +0:31:44.7 42.50 3.35 ± 0.16 GBT A11
G034.041+0.053 13A-030 18:53:16.4 +1:00:40.2 42.50 19.45 ± 0.20 GBT A11 0.1384 ± 0.0021 6105 ± 120 B11;B15
G034.133+0.471 13A- 030 18:51:57.1 +1:17:01.3 42.50 58.55 ± 0.18 GBT A11 0.1021 ± 0.0005 7655 ± 63 B11;B15
G034.686+0.068 13A-030 18:54:23.8 +1:35:31.5 42.50 21.75 ± 0.15 GBT A11 0.1492 ± 0.0026 5335 ± 112 B11;B15
G035.126−0.755 15B-178 18:58:07.6 +1:36:30.0 169.39 36.85 ± 0.26 GBT A15b
G035.948−0.149 15B-178 18:57:28.4 +2:37:01.0 42.50 3.35 ± 0.21 GBT A11
G036.918+0.482 15B-178 18:56:59.9 +3:46:04.5 29.02 6.25 ± 0.17 GBT A11
G037.445−0.212 15B-178 19:00:26.2 +3:55:11.2 124.08 17.35 ± 0.15 GBT A11
G037.469−0.105 15B-178 19:00:05.9 +3:59:22.0 41.03 5.14 ± 0.10 Arecibo B12
G038.550+0.163 13A-030 19:01:07.7 +5:04:22.6 42.50 15.50 ± 0.20 GBT A11 0.1008 ± 0.0016 8216 ± 167 B11;B15
G038.643−0.227 15B-178 19:02:41.5 +4:58:37.5 42.50 5.30 ± 0.09 GBT A11
G038.651+0.087 13A-030 19:01:35.3 +5:07:43.9 42.50 8.70 ± 0.07 GBT A11 0.0738 ± 0.0015 9428 ± 245 B11;B15
G038.738−0.140 15B-178 19:02:33.4 +5:06:05.0 105.52 9.75 ± 0.10 GBT A11
G038.840+0.497 13A-030 19:00:28.5 +5:28:58.5 84.39 7.45 ± 0.07 GBT A11 0.0734 ± 0.0020 9221 ± 317 B11;B15
G038.875+0.308 13A-030 19:01:12.5 +5:25:41.8 42.50 27.05 ± 0.12 GBT A11 0.0822 ± 0.0008 8384 ± 116 B11;B15
G039.183−1.422 15B-178 19:07:56.9 +4:54:31.2 60.00 4.95 ± 0.16 GBT A15b
G039.196+0.224 15B-178 19:02:05.8 +5:40:32.2 60.00 2.32 ± 0.10 Arecibo B12
G039.869+0.645 13A-030 19:01:49.3 +6:27:45.5 68.19 10.80 ± 0.09 GBT A11 0.0708 ± 0.0013 9373 ± 214 B11;B15
G041.750+0.034 15B-178 19:07:29.9 +7:51:27.3 121.00 2.90 ± 0.10 GBT A15b
G041.762+1.479 15B-178 19:02:19.9 +8:31:54.0 268.99 2.35 ± 0.09 GBT A15b
G043.149+0.028 15B-178 19:10:07.7 +9:05:47.0 35.18 3129.19 ± 10.23 140 Foot Q06a
G043.240+0.131 15B-178 19:09:55.7 +9:13:28.1 42.50 5.40 ± 0.17 GBT A11
G043.432+0.521 13A-030 19:08:54.1 +9:34:22.2 74.33 11.25 ± 0.15 GBT A11 0.1021 ± 0.0019 8338 ± 198 B11;B15
G043.523−0.648 15B-178 19:13:15.5 +9:06:54.0 88.57 2.20 ± 0.18 GBT A11
G043.818+0.393 13A-030 19:10:03.7 +9:51:31.6 108.26 14.80 ± 0.09 GBT A11 0.0781 ± 0.0013 8802 ± 196 B11;B15
G043.818+0.395 15B-178 19:10:03.7 +9:51:31.6 108.26 14.80 ± 0.09 GBT A11 0.0781 ± 0.0013 8802 ± 196 B11;B15
G043.968+0.993 15B-178 19:08:11.3 +10:16:04.7 50.84 5.55 ± 0.25 GBT A15b
G044.417+0.536 13A-030 19:10:41.0 +10:27:22.6 84.69 6.55 ± 0.08 GBT A11 0.0926 ± 0.0026 8492 ± 299 B11;B15
G044.501+0.335 13A-030 19:11:34.3 +10:26:07.5 50.65 24.25 ± 0.12 GBT A11 0.1017 ± 0.0017 8350 ± 153 B11;B15
G045.197+0.738 13A-030 19:11:24.5 +11:14:28.3 80.49 9.35 ± 0.10 GBT A11 0.0556 ± 0.0010 10841 ± 245 B11;B15
G045.391−0.725 15B-178 19:17:03.7 +10:43:57.9 191.48 26.50 ± 0.26 GBT A11
G046.173+0.533 15B-178 19:14:00.4 +12:00:39.7 60.00 2.04 ± 0.04 Arecibo B12
G048.719+1.147 15B-178 19:16:38.2 +14:32:58.9 82.92 6.30 ± 0.32 GBT A15b
G049.399−0.490 15B-178 19:23:55.6 +14:22:54.6 51.68 68.15 ± 0.23 GBT A11
G049.690−0.166 15B-178 19:23:19.0 +14:47:29.5 178.62 76.92 ± 7.69 140 Foot L96
G050.032+0.605 15B-178 19:21:09.8 +15:27:24.2 139.55 5.50 ± 0.20 GBT A15b
G052.001+1.602 15B-178 19:21:21.4 +17:39:45.1 49.60 2.00 ± 0.07 GBT A15b
G052.098+1.042 15B-178 19:23:37.1 +17:29:01.8 122.52 38.40 ± 0.17 GBT A11
G052.160+0.708 15B-178 19:24:58.5 +17:22:49.6 67.26 7.00 ± 0.20 GBT A11
G052.256+0.702 15B-178 19:25:11.2 +17:27:43.9 120.73 5.30 ± 0.08 Arecibo B12
G054.093+1.748 15B-178 19:24:58.5 +19:34:32.6 81.06 2.60 ± 0.10 GBT A15b
G054.490+0.930 15B-178 19:28:49.9 +19:32:08.0 245.76 4.95 ± 0.09 GBT A11
G054.490+1.579 15B-178 19:26:24.4 +19:50:41.1 87.52 3.50 ± 0.10 GBT A15b
G055.114+2.422 15B-178 19:24:29.9 +20:47:33.2 146.16 28.75 ± 0.17 GBT A15b 0.0423 ± 0.0003 13126 ± 144 B11;B15
G059.796+0.241 15B-178 19:42:32.9 +23:50:02.4 159.46 53.38 ± 0.41 GBT B11 0.0975 ± 0.0008 9068 ± 120 B11;B15
G060.592+1.572 15B-178 19:39:11.2 +25:10:59.4 126.28 13.05 ± 0.13 GBT A15b
G061.431+2.081 15B-178 19:39:02.7 +26:09:52.0 143.57 3.65 ± 0.17 GBT A15b
G061.720+0.863 15B-178 19:44:23.6 +25:48:44.2 72.00 9.30 ± 0.10 GBT A11
G062.577+2.389 15B-178 19:40:21.9 +27:18:45.9 141.52 31.60 ± 0.18 GBT A15b
G068.144+0.915 15B-178 19:59:09.7 +31:21:32.3 160.08 23.91 ± 0.27 GBT B11 0.0697 ± 0.0009 10834 ± 207 B11;B15
G070.280+1.583 15B-178 20:01:47.8 +33:31:33.4 53.06 328.08 ± 1.75 GBT B11
G070.673+1.190 15B-178 20:04:24.0 +33:38:59.2 120.63 2.65 ± 0.13 GBT A15b
G070.765+1.820 15B-178 20:02:03.9 +34:03:47.8 86.97 12.10 ± 0.14 GBT A15b
G071.150+0.397 15B-178 20:08:50.5 +33:37:30.8 144.06 33.75 ± 0.10 GBT A15b
G073.878+1.023 15B-178 20:13:34.7 +36:15:00.4 71.21 7.80 ± 0.10 GBT A15b
G074.155+1.646 15B-178 20:11:45.0 +36:49:26.5 95.39 3.70 ± 0.11 GBT A15b
G074.753+0.912 15B-178 20:16:27.5 +36:54:57.7 91.43 6.40 ± 0.12 GBT A15b
G075.175−0.593 15B-178 20:23:50.1 +36:24:39.5 306.78 8.80 ± 0.14 GBT A15b
G075.768+0.344 15B-178 20:21:41.2 +37:26:02.9 197.80 273.60 ± 0.56 GBT B11 0.0790 ± 0.0004 8590 ± 47 B11;B15
G078.174−0.550 15B-178 20:32:30.2 +38:52:15.1 160.63 10.20 ± 0.15 GBT A15b
G078.886+0.709 15B-178 20:29:24.7 +40:11:18.7 174.84 9.75 ± 0.23 GBT A15b
G080.191+0.534 15B-178 20:34:13.7 +41:08:14.5 53.88 4.85 ± 0.12 GBT A15b
G091.113+1.580 15B-178 21:09:36.0 +50:13:22.5 278.16 37.75 ± 0.17 GBT A15b
G093.518+2.611 15B-178 21:15:22.5 +52:40:39.6 107.51 4.45 ± 0.16 GBT A15b
G094.263−0.414 15B-178 21:32:32.7 +51:02:19.3 100.14 2.10 ± 0.10 GBT A15b
G096.289+2.593 15B-178 21:28:42.4 +54:37:05.8 193.20 23.60 ± 0.11 GBT A15b 0.0570 ± 0.0009 11039 ± 314 B11;B15
G096.434+1.324 15B-178 21:35:20.3 +53:47:14.1 91.59 5.05 ± 0.14 GBT A15b
G097.444+3.083 15B-178 21:32:14.7 +55:45:52.4 95.94 2.00 ± 0.18 GBT A15b
G097.515+3.173 15B-178 21:32:10.8 +55:52:44.6 122.86 33.60 ± 0.18 GBT A15b
G101.016+2.590 15B-178 21:54:19.5 +57:43:06.4 101.64 3.40 ± 0.18 GBT A15b
G104.700+2.784 15B-178 22:16:25.9 +60:03:01.8 102.78 6.25 ± 0.18 GBT A15b
G109.104−0.347 15B-178 22:59:09.0 +59:28:36.7 95.34 6.00 ± 0.12 GBT A15b
G111.802+0.526 15B-178 23:16:32.4 +61:19:49.6 96.95 5.10 ± 0.20 GBT A15b
G118.276+2.490 15B-178 00:07:14.9 +64:57:44.9 239.84 2.35 ± 0.17 GBT A15b
G118.592+2.828 15B-178 00:09:40.8 +65:20:50.2 161.64 3.30 ± 0.18 GBT A15b
G124.637+2.535 15B-178 01:07:47.3 +65:21:12.5 165.16 18.30 ± 0.21 GBT A15b 0.0576 ± 0.0012 10758 ± 288 B11;B15
G125.092+0.778 15B-178 01:10:51.9 +63:34:06.7 136.99 2.85 ± 0.17 GBT A15b
G135.188+2.701 15B-178 02:42:24.6 +62:54:07.3 142.05 6.05 ± 0.12 GBT A15b
G136.119+2.118 15B-178 02:47:33.7 +61:58:48.1 127.23 3.30 ± 0.13 GBT A15b
G136.884+0.911 15B-178 02:48:55.9 +60:33:38.8 805.95 69.23 ± 8.08 140 Foot L89 0.0995 ± 0.0025 8204 ± 257 B11;B15
G141.084−1.063 15B-178 03:10:16.0 +56:50:04.3 249.15 7.80 ± 0.12 GBT A15b
G148.474+1.982 15B-178 04:05:41.7 +54:54:55.2 104.17 2.55 ± 0.14 GBT A15b
G150.859−1.115 15B-178 04:03:50.6 +51:00:57.9 123.28 2.85 ± 0.13 GBT A15b
G154.646+2.438 15B-178 04:36:48.8 +50:52:42.5 370.38 25.02 ± 0.33 GBT B11 0.0673 ± 0.0009 9734 ± 175 B11;B15
G189.830+0.417 15B-178 06:08:58.1 +20:38:29.2 199.15 82.62 ± 1.35 140 Foot Q06a
G192.638−0.008 15B-178 06:13:07.5 +17:58:33.5 174.27 52.91 ± 0.44 GBT B11 0.0971 ± 0.0010 8833 ± 107 B11;B15
G196.448−1.673 15B-178 06:14:37.3 +13:50:02.6 302.50 30.80 ± 0.37 GBT B11 0.0773 ± 0.0010 9945 ± 164 B11;B15
G201.535+1.597 15B-178 06:36:11.8 +10:51:56.8 790.64 12.79 ± 0.26 GBT B11 0.0713 ± 0.0015 10063 ± 283 B11;B15
G212.021−1.309 15B-178 06:45:07.1 +0:12:49.8 1075.77 50.00 ± 5.38 140 Foot L96
G218.737+1.850 15B-178 07:08:39.2 −4:18:55.1 215.23 35.22 ± 0.28 GBT B11 0.0509 ± 0.0005 14578 ± 195 B11;B15
G224.158+1.213 15B-178 07:16:29.0 −9:24:51.3 558.98 8.35 ± 0.12 GBT A15b
G227.760−0.127 15B-178 07:18:30.6 −13:13:29.4 324.34 7.54 ± 0.09 GBT B11 0.0485 ± 0.0007 12495 ± 249 B11;B15
G231.481−4.401 15B-178 07:09:54.3 −18:29:53.7 511.74 21.11 ± 0.49 GBT B11 0.1011 ± 0.0024 9098 ± 286 B11;B15
G233.753−0.193 15B-178 07:30:04.6 −18:32:03.8 311.06 27.16 ± 0.41 GBT B11 0.0822 ± 0.0015 9482 ± 209 B11;B15
G243.244+0.406 15B-178 07:52:42.5 −26:29:00.1 941.61 49.06 ± 0.47 GBT B11 0.0764 ± 0.0012 10220 ± 110 Q06b;B15
G253.694−0.414 15B-178 08:15:34.9 −35:45:30.3 1540.80 42.31 ± 4.23 140 Foot L89
G341.207−0.232 15B-178 16:52:20.7 −44:28:06.8 58.11 90.60 ± 0.45 GBT A15b
G348.691−0.826 15B-178 17:19:06.6 −38:51:37.7 1328.28 3132.27 ± 13.38 140 Foot Q06a
G351.246+0.673 15B-178 17:20:17.7 −35:54:29.2 131.55 2251.35 ± 7.73 140 Foot Q06a 0.0896 ± 0.0006 8560 ± 70 Q06b;B15
G351.311+0.663 15B-178 17:20:31.2 −35:51:37.7 119.03 3356.38 ± 10.69 140 Foot Q06a

Notes.

aOriginal RRL detection telescope. bOriginal RRL detection reference. cRRL-to-continuum flux ratio measurement and electron temperature derivation reference

References. L89, Lockman (1989); L96, Lockman et al. (1996); Q06a, Quireza et al. (2006a); Q06b, Quireza et al. (2006b); A11, Anderson et al. (2011); B11, Balser et al. (2011); B12, Bania et al. (2012); A15a, Anderson et al. (2015a); A15b, Anderson et al. (2015b); B15, Balser et al. (2015).

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3. Observations and Data Reduction

We used the VLA to simultaneously observe radio-continuum and RRL emission toward our sample of 147 Galactic H ii regions. The data were acquired in the most compact (D) antenna configuration as part of two projects: the pilot survey (13A-030; 5 hr) in Feb and Apr 2013, and the main survey (15B-178; 30 hr) in Oct and Nov 2015. A summary of the observations is in Table 2.

Table 2.  Observation Summary

  13A-030 15B-178
Dates 2013 Feb and Apr 2015 Oct and Nov
Observing Time (hr) 5 30
H ii Region Targets 20 128
Primary Calibrators 3C286 3C286, 3C48
Secondary Calibrators J1733−1304, J1822−0938 J0019+7327, J0102+5824
  J1824+1044, J1922+1530 J0244+6228, J0349+4609
    J0358+5606, J0625+1440
    J0653−0625, J0735−1735
    J0804−2749, J1604−4441
    J1744−3116, J1820−2528
    J1822v0938, J1824+1044
    J1922+1530, J1924+3329
    J1925+2106, J2007+4029
    J2025+3343, J2137+5101
    J2137+5101
    J2148+6107

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The VLA X-band receiver covers the frequency range ∼8–12 GHz. We used the Wideband Interferometric Digital ARchitecture (WIDAR) correlator in the 8-bit sampler mode to simultaneously measure ∼8–10 GHz radio-continuum emission and eight hydrogen RRL transitions in both linear polarizations. The continuum data were measured by 16 low spectral resolution spectral windows (hereafter, continuum windows) covering 7.8–8.9 GHz and 9–10 GHz continuously. The RRL spectra were measured by eight high-spectral resolution (31.25 kHz) spectral windows (hereafter, spectral line windows), each with 16 MHz of frequency coverage. There are only seven Hα RRL transitions in this frequency range (H87α to H93α), so we tuned one of the spectral line windows to H109β. The native velocity resolution ranges from 0.9 km s−1 at H87α to 1.2 km s−1 at H93α, with a velocity coverage ranging from 488 km s−1 to 600 km s−1 for these transitions, respectively. In one observing session of the pilot survey, the spectral line window for H88α was mistuned, so we exclude that spectral window from these analyses. Table 3 lists the following properties for each spectral window: the center frequency, νcenter; the bandwidth; the number of channels; the channel width, Δν; the targeted RRL transition; and the RRL rest frequency, νRRL.

Table 3.  Correlator Setup

Window νcenter Bandwidth Channels Δν RRL νRRL
  (MHz) (MHz)   (kHz)   (MHz)
0 7949.3 128 128 1000
1 8049.1 128 128 1000
2 8049.1 16 512 31.25 H93α 8045.605
3 8205.3 128 128 1000
4 8333.3 128 128 1000
5 8313.0 16 512 31.25 H92α 8309.385
6 8461.3 128 128 1000
7 8589.3 128 128 1000
8 8588.5 16 512 31.25 H91α 8584.823
9 8717.3 128 128 1000
10 8845.3 128 128 1000
11 8876.4 16 512 31.25 H90α 8872.571
12 9082.3 128 128 1000
13 9210.3 128 128 1000
14 9177.3 16 512 1000 H89α 9173.323
15 9338.3 128 128 1000
16 9466.3 128 128 1000
17 9491.9 16 512 31.25 H88α 9487.824
18 9594.3 128 128 1000
19 9722.3 128 128 1000
20 9850.3 128 128 1000
21a 9821.1 16 512 31.25 H87α 9816.867
22 9887.3 16 512 31.25 H109β 9883.083
23 9978.3 128 128 1000

Note.

aSpectral window 21 was mistuned for one observing session in 13A-030.

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Our targets are clustered into 12 observing sessions based on position, with ∼10 H ii regions per group. Every observing session begins with a ∼15 minute integration on a primary calibrator, which is used for the absolute flux, delay, and bandpass calibration, followed by a ∼10 minute integration on a secondary calibrator located near the H ii region science targets, which is used for the complex gain calibration. These calibrators are listed in Table 2. We observe each science target for 10–15 minutes to reach the necessary spectral sensitivity, then we return to the secondary calibrator for ∼5 more minutes. During each observing session, we repeat this process for each science target.

We use the Wenger Interferometry Software Package (WISP) to calibrate, reduce, and analyze these data (Wenger 2018). WISP is a Python wrapper for the Common Astronomy Software Applications package (CASA; McMullin et al. 2007). Although WISP was developed to reduce Australia Telescope Compact Array data for the Southern H ii Region Discovery Survey (Wenger et al. 2019), its modular framework can be applied to any radio interferometric data set. We follow the Wenger et al. (2019) data reduction process, which we briefly describe here.

3.1. Calibration

The WISP calibration pipeline derives calibration solution tables using the calibrator source data, flags radio frequency interference (RFI) and other bad data, and applies the calibration solutions to the science target data. We inspect both the calibration solutions and calibrated data to assess the quality of the calibration solutions and to manually flag bad data that was missed by the WISP automatic flagging routines. The most common issues we flag are (1) antennas with poor calibration solutions, (2) broad-frequency RFI that contaminates an entire spectral window, and (3) shadowed antennas. In rare cases, RFI can compromise nearly one-half of all of our spectral windows.

3.2. Imaging

We use the WISP imaging pipeline to automatically generate and clean images from the calibrated visibility data. We begin by regridding all of the data to a common kinematic local standard of rest (LSR) velocity frame with a channel width ΔvLSR = 1.2 km s−1. Using the TCLEAN task in CASA, we generate several images and data cubes: (1) a multi-scale, multifrequency synthesis (MS-MFS) continuum image of the combined continuum spectral windows, (2) an MS-MFS image of each continuum and spectral line window, and (3) a multi-scale data cube of each spectral line window. Following the strategy of Wenger et al. (2019), we use CLEAN masks from each spectral line window MS-MFS image to CLEAN the data cube for that spectral window.

Many of our observed H ii regions are spatially resolved. We increase our surface brightness sensitivity to resolved emission by uv-tapering our visibilities when generating images. This process, however, reduces our point-source sensitivity and worsens our angular resolution. Therefore, we generate both non-tapered and uv-tapered images/data cubes for each field. The latter are tapered to a synthesized half-power beamwidth (HPBW) of 15'', which is about twice the native VLA resolution at X band.

4. Data Analysis

The data analysis process for this survey closely follows the Wenger et al. (2019) strategy. Because multiple nebulae may be observed in a single VLA pointing, we first identify unique WISE Catalog sources in each 8–10 GHz MS-MFS continuum image. Emission is associated with the WISE Catalog nebulae as long as the peak continuum brightness pixel is within a circle centered on the WISE Catalog position with a radius equal to the WISE Catalog infrared radius. We manually locate these peak continuum brightness pixels for each nebula with detected radio-continuum emission.

Unlike Wenger et al. (2019), we wish to derive the total fluxes of extended sources in addition to their peak fluxes. We use a watershed segmentation algorithm to identify the pixels associated with the manually identified continuum peaks in our images and data cubes. This algorithm considers an image as a three-dimensional topological surface, where the image brightness corresponds to the "depth" of the surface. The algorithm identifies the basins that would be filled by flooding the surface from a given starting point (see Bertrand 2005). In cases where multiple starting points will flood the same basin (i.e., in confused fields), the algorithm divides the basin into separate regions for each flooding source. Hereafter, we will use "watershed region" to describe the regions identified by the watershed segmentation algorithm.

We set the manually identified continuum brightness peak locations as the flooding sources for the watershed segmentation algorithm. Using the MS-MFS images clipped at five times the spatial rms noise, we run the algorithm to identify the watershed regions associated with each continuum source. Figure 2 shows an example region identified by this algorithm. We use the clipped continuum images to avoid low-brightness noise spikes in the watershed regions, but, as a result, we also miss faint emission associated with the nebulae. Therefore, our total continuum fluxes are systematically underestimated, especially for faint sources.

Figure 2.

Figure 2. Watershed regions in a ∼2 GHz combined MS-MFS continuum image. This field is centered on G019.728−0.113 and contains three WISE Catalog H ii regions. The black contours are at 5, 10, 20, and 50 times the spatial rms noise (∼0.6 mJy beam−1 at the field center), and the yellow dashed circles represent the position and infrared radii of the WISE Catalog nebulae. The manually identified peak continuum brightness pixels are indicated by the colored plus symbols, and the watershed regions by the colored contours. These regions were created using the MS-MFS image clipped at five times the spatial rms noise to avoid including noise spikes in the watershed regions. These nebulae are examples of continuum quality factors (QF) A, B, and C, as indicated in the legend (see Section 5.1).

Standard image High-resolution image

For each continuum source we measure the brightness and total flux at the location of the peak brightness and within the watershed region, respectively. The uncertainty of the peak continuum brightness is derived as the spatial rms of the CLEAN residual image divided by the VLA primary beam response at the peak continuum brightness position. To compute the uncertainty on the total continuum flux, we must consider that the spatial noise in an interferometric image is correlated on the scale of the synthesized beam. The variance in the sum of the brightnesses of N pixels within a region is

Equation (1)

where σi is the spatial rms of the CLEAN residual image divided by the VLA primary beam response at the position of the ith pixel, ρij is the correlation coefficient between the ith and jth pixels, and the sums are taken over all N pixels within the region. We use the two-dimensional Gaussian synthesized beam to define the correlation coefficient:

Equation (2)

where

Δx and Δy are the angular separations between the ith and jth pixels in the east–west and north–south directions, respectively, and θmaj, θmin, and ϕ are the synthesized beam major axis, minor axis, and north-through-east position angle, respectively. In the simple case where σi ≃ σj ≃ σ (i.e., the noise is constant across the source), Equation (1) reduces to

Equation (3)

where Nbeam is the number of synthesized beams contained within the region. Many of our sources are extended or located near the edge of the primary beam, such that the primary beam response and noise varies across the source. Therefore, we use Equation (1) to derive the total continuum flux uncertainties.

We maximize our sensitivity to the faint RRL emission by averaging each observed Hnα RRL transition and both polarizations. This average spectrum is denoted by $\langle \mathrm{Hn}\alpha \rangle $. For non-tapered images, we extract spectra from each line spectral window data cube at the location of the peak continuum brightness. The $\langle \mathrm{Hn}\alpha \rangle $ spectrum is computed as the weighted average of the individual RRL transitions. The weights are given by ${w}_{i}={S}_{C,i}/{\mathrm{rms}}_{i}^{2}$ where SC,i is the continuum brightness and rmsi is the spectral rms noise of the ith spectral window, both measured in the line-free region of the spectrum. For uv-tapered images, we spatially smooth the data cubes to a common beam size, then extract the spectra and compute the $\langle \mathrm{Hn}\alpha \rangle $ spectrum in the same fashion.

The total RRL emission within the watershed regions is extracted from the data cubes differently than for the peak position. For each pixel in the region, we measure the median continuum brightness in the line-free region of the spectrum, SC,i. Then we sum each pixel's spectrum, SL,i, weighted by the median continuum brightness in that pixel. The final extracted spectrum for this spectral window is normalized by the ratio of the median non-weighted sum and median weighted sum:

Equation (4)

This complicated procedure correctly weights the final spectrum by the continuum level in each pixels' spectra, thereby maximizing the signal-to-noise ratio of the RRL and ensuring that the final spectrum has the correct flux density. The watershed region $\langle \mathrm{Hn}\alpha \rangle $ spectrum is then computed using the same weighted average of the individual RRL transitions as for the peak positions.

Finally, we measure the $\langle \mathrm{Hn}\alpha \rangle $ RRL properties. We first identify the line-free regions of the spectrum to estimate the spectral rms noise and to fit and remove a third-order polynomial baseline. Then we fit a Gaussian to the baseline-subtracted spectrum and measure the RRL brightness, the FWHM line width, and the LSR velocity.

5. Results

5.1. VLA Data Products

Our goal is to derive an accurate nebular electron temperature for as many of the observed Galactic H ii regions as possible. Given that some of these nebulae will be extremely faint, spatially resolved, and/or in confusing fields, no single data analysis method will work for each nebula. For each source, we therefore employ a suite of different analysis methods and then we pick the combination of non-tapered or uv-tapered images and peak position $\langle \mathrm{Hn}\alpha \rangle $ or watershed region $\langle \mathrm{Hn}\alpha \rangle $ spectra that maximizes our RRL sensitivity and minimizes our electron temperature uncertainty.

We detect radio-continuum emission in 88 (59%) of the 148 observed fields. This low detection rate is a result of the relatively poor surface brightness sensitivity of the VLA. Many of the fields, however, contain multiple WISE Catalog H ii regions and/or H ii region candidates. We detect radio-continuum emission toward 114 known or candidate H ii regions. Table 4 lists the measured radio-continuum properties of these nebulae: the WISE Catalog source name; the MS-MFS synthesized frequency of the combined continuum spectral windows, νC; the peak continuum flux density, ${S}_{C}^{{\rm{P}}};$ a quality factor (QF) for the peak flux density, ${\mathrm{QF}}_{C}^{{\rm{P}}};$ a column indicating whether the peak flux density was measured using the non-tapered (N) or uv-tapered (Y) image; the total flux density within the watershed region, ${S}_{C}^{{\rm{T}}};$ a QF for the total flux density, ${\mathrm{QF}}_{C}^{{\rm{T}}};$ and a column indicating whether the peak flux density was measured using the non-tapered or uv-tapered image. The MS-MFS synthesized frequency varies slightly for each field due to differences in data flagging. We select either non-tapered or uv-tapered based on which gives the smallest fractional uncertainty in the final electron temperature derivation (if the source also has a RRL detection), or which has the smallest fractional uncertainty in the continuum flux density. For resolved nebulae, the uv-tapered images typically have a smaller fractional electron temperature or continuum flux density uncertainty.

Table 4.  Continuum Data Products

Name νC ${S}_{C}^{{\rm{P}}}$ ${\mathrm{QF}}_{C}^{{\rm{P}}}$ TaperPa ${S}_{C}^{{\rm{T}}}$ ${\mathrm{QF}}_{C}^{{\rm{T}}}$ TaperPa
  (MHz) (mJy beam−1)     (mJy)    
G005.885−00.393 8962.2 4516.01 ± 13.31 A N 5254.49 ± 35.45 A N
G010.596−00.381 8962.2 395.02 ± 6.66 A Y 907.08 ± 18.66 A Y
G013.880+00.285 8962.2 1696.64 ± 3.26 A Y 3368.06 ± 10.64 B N
G017.336−00.146 8962.1 10.91 ± 0.29 B Y 51.38 ± 0.84 B N
G017.928−00.677 8962.1 14.48 ± 0.37 B Y 57.76 ± 1.07 B N
G018.584+00.344 8962.1 22.53 ± 0.82 A Y 46.79 ± 1.20 A N
G018.630+00.309 8962.1 13.01 ± 4.37 C Y 0.04 ± 0.18 C N
G019.677−00.134 8962.1 163.19 ± 3.36 C Y 469.63 ± 7.10 C N
G019.728−00.113 8962.1 24.23 ± 0.40 A N 27.24 ± 0.68 A N
G019.754−00.129 8962.1 46.45 ± 0.59 B N 45.73 ± 1.01 B N
G020.227+00.110 8962.1 8.61 ± 0.13 B Y 41.72 ± 0.36 B N
G020.363−00.014 8962.1 50.30 ± 0.09 A N 58.28 ± 0.23 A N
G020.387−00.018 8962.1 8.58 ± 0.16 B Y 26.85 ± 0.46 B Y
G021.386−00.255 8962.1 122.94 ± 0.12 A N 136.88 ± 0.45 A N
G021.596−00.161 8962.2 5.70 ± 0.16 A N 6.77 ± 0.26 A N
G021.603−00.169 8962.2 19.32 ± 0.15 A N 27.62 ± 0.34 A N
G023.661−00.252 8962.2 30.11 ± 0.46 B Y 152.51 ± 1.16 B N
G024.153+00.163 8962.2 10.94 ± 1.62 C N 4.60 ± 1.14 C N
G024.166+00.250 8962.2 16.56 ± 0.79 B N 17.44 ± 1.11 B N
G024.195+00.242 8962.2 9.77 ± 0.57 B N 47.78 ± 1.69 B N
G024.713−00.125 8962.2 32.51 ± 2.11 C N 138.58 ± 5.73 C N
G025.397+00.033 8962.2 229.49 ± 0.56 B N 494.08 ± 2.57 B N
G025.398+00.562 8962.1 203.74 ± 0.36 A Y 221.10 ± 1.21 A N
G025.401+00.021 8962.2 54.54 ± 0.60 B N 150.97 ± 1.87 B N
G027.562+00.084 8898.2 47.71 ± 0.23 A N 111.74 ± 0.71 A N
G028.320+01.243 8962.1 21.17 ± 0.04 A N 30.22 ± 0.11 A N
G028.438+00.014 8962.2 4.01 ± 0.35 A N 11.73 ± 0.74 A N
G028.451+00.001 8962.2 36.09 ± 0.30 A N 84.81 ± 1.30 A N
G028.581+00.145 8962.2 25.87 ± 0.18 A N 39.68 ± 0.41 A N
G029.770+00.219 8962.2 35.40 ± 0.16 A N 72.53 ± 0.45 A N
G029.956−00.020 8962.2 1770.38 ± 4.48 A N 4299.65 ± 22.54 A N
G030.211+00.428 8962.2 15.61 ± 0.04 A N 25.81 ± 0.12 A N
G031.269+00.064 8962.2 2.70 ± 0.34 A N 1.00 ± 0.22 A N
G031.279+00.061 8962.2 125.29 ± 0.35 A N 306.72 ± 1.15 A N
G031.580+00.074 8962.2 13.41 ± 0.21 B N 15.17 ± 0.38 B N
G032.030+00.048 8962.2 17.10 ± 0.19 A N 25.83 ± 0.40 A N
G032.057+00.077 8962.2 13.36 ± 1.03 C Y 94.17 ± 2.13 C N
G032.272−00.226 8962.2 147.87 ± 0.18 A N 330.84 ± 0.75 A N
G032.928+00.606 8898.2 173.86 ± 0.27 A N 336.64 ± 1.38 A N
G033.643−00.229 8962.2 6.37 ± 0.09 A Y 10.85 ± 0.15 A N
G034.041+00.052 8962.2 25.97 ± 0.48 A Y 83.27 ± 1.08 A N
G034.089+00.438 8962.2 34.42 ± 2.87 C N 83.68 ± 7.38 C Y
G034.133+00.471 8962.2 378.58 ± 1.10 A Y 517.00 ± 2.35 A N
G034.686+00.068 8962.2 55.42 ± 0.60 A Y 107.24 ± 0.95 A N
G035.126−00.755 8962.2 123.85 ± 0.43 A Y 241.91 ± 0.71 A N
G035.948−00.149 8962.2 12.05 ± 0.03 A N 26.66 ± 0.08 A N
G036.870+00.462 8962.2 3.03 ± 0.31 C N 9.77 ± 0.67 C N
G036.877+00.498 8962.2 1.22 ± 0.17 C N 1.90 ± 0.22 C N
G036.918+00.482 8962.2 6.21 ± 0.08 A N 7.56 ± 0.15 A N
G038.550+00.163 8962.2 54.11 ± 0.25 A N 122.86 ± 0.77 A N
G038.643−00.227 8962.3 18.70 ± 0.05 A N 24.79 ± 0.18 A N
G038.652+00.087 8962.2 19.77 ± 0.24 A N 49.91 ± 0.96 A N
G038.840+00.495 8962.2 4.49 ± 0.09 B N 84.27 ± 0.66 B N
G038.875+00.308 8962.2 279.04 ± 0.43 A N 320.84 ± 1.04 A N
G039.183−01.422 8962.3 20.75 ± 0.15 A Y 57.82 ± 0.30 A N
G039.196+00.224 8962.3 62.54 ± 0.06 A N 67.11 ± 0.19 A N
G039.213+00.202 8962.3 5.13 ± 0.09 B N 5.85 ± 0.16 B N
G039.864+00.645 8962.3 67.52 ± 0.51 A Y 103.48 ± 0.79 A N
G043.146+00.013 8962.3 1434.45 ± 126.49 B Y 1427.47 ± 158.00 B Y
G043.165−00.031 8962.3 2330.17 ± 78.58 C N 3341.55 ± 144.37 C N
G043.168+00.019 8962.3 332.86 ± 17.06 B N 600.24 ± 31.78 B N
G043.170−00.004 8962.3 4331.44 ± 149.88 B Y 11158.53 ± 398.42 B Y
G043.432+00.516 8962.3 11.08 ± 0.35 B Y 82.31 ± 0.83 B N
G043.523−00.648 8962.3 5.84 ± 0.04 A Y 13.22 ± 0.09 A N
G043.818+00.395 8962.3 21.54 ± 0.97 B Y 94.69 ± 1.89 B N
G043.968+00.993 8962.2 47.26 ± 0.07 A N 49.81 ± 0.20 A N
G043.999+00.978 8962.2 22.23 ± 0.22 C N 25.05 ± 0.42 C N
G044.501+00.332 8962.3 21.92 ± 1.24 B Y 135.68 ± 2.23 B N
G044.503+00.349 8962.3 7.16 ± 0.36 A N 8.58 ± 0.54 A N
G045.197+00.740 8962.3 7.76 ± 0.18 B N 140.36 ± 1.42 B N
G048.719+01.147 8962.4 37.12 ± 0.10 A Y 69.80 ± 0.29 A N
G049.399−00.490 8962.4 166.98 ± 7.12 A Y 232.47 ± 8.75 A N
G052.098+01.042 8962.3 287.77 ± 0.50 A Y 432.07 ± 0.89 A N
G052.232+00.735 8962.4 68.65 ± 4.32 C Y 162.56 ± 5.42 C N
G054.093+01.748 8962.3 18.84 ± 0.03 A Y 34.60 ± 0.08 A Y
G054.490+01.579 8962.3 24.30 ± 0.06 A Y 44.24 ± 0.13 A N
G054.543+01.560 8962.3 3.73 ± 0.26 C Y 3.52 ± 0.21 C N
G055.114+02.422 8962.3 138.55 ± 1.25 A Y 618.76 ± 2.79 B N
G060.592+01.572 8962.3 55.66 ± 0.22 A Y 166.35 ± 0.51 A N
G061.720+00.863 8962.7 90.28 ± 0.16 A N 97.51 ± 0.38 A N
G062.577+02.389 8962.7 51.31 ± 0.28 B N 359.10 ± 1.71 B N
G068.144+00.915 8962.7 42.25 ± 1.61 B Y 302.02 ± 4.24 B N
G070.280+01.583 8962.6 542.61 ± 15.70 A Y 1930.78 ± 37.24 A N
G070.293+01.599 8962.6 3550.27 ± 9.03 A N 5690.67 ± 39.20 A N
G070.304+01.595 8962.6 245.05 ± 9.37 A N 1829.40 ± 41.28 A N
G070.329+01.589 8962.6 1067.39 ± 23.78 B N 2670.68 ± 65.51 B N
G070.673+01.190 8962.6 260.40 ± 0.72 A Y 407.26 ± 1.43 A N
G070.765+01.820 8962.6 28.79 ± 0.52 A Y 173.85 ± 1.36 B N
G071.150+00.397 8962.7 208.43 ± 0.25 A N 392.62 ± 0.92 A N
G073.878+01.023 8962.6 75.77 ± 0.09 A N 120.61 ± 0.26 A N
G074.155+01.646 8962.6 10.25 ± 0.04 A N 37.97 ± 0.21 A N
G074.753+00.912 8962.6 55.70 ± 0.07 A N 74.69 ± 0.20 A N
G075.768+00.344 8962.6 1059.58 ± 10.20 A Y 4104.53 ± 20.67 B N
G078.114−00.550 8962.6 14.17 ± 3.03 C Y 0.04 ± 0.10 C N
G078.174−00.550 8962.6 4.21 ± 0.19 B N 23.01 ± 0.72 B N
G078.886+00.709 8962.6 83.02 ± 0.08 A N 110.14 ± 0.25 A N
G080.191+00.534 8962.6 5.14 ± 0.09 A N 40.72 ± 0.45 A N
G094.263−00.414 8963.1 4.40 ± 0.04 B Y 18.73 ± 0.14 B N
G096.289+02.593 8963.1 27.93 ± 0.32 B N 442.24 ± 2.68 B N
G096.434+01.324 8963.1 23.34 ± 0.10 A N 36.94 ± 0.25 A N
G097.515+03.173 8963.1 131.05 ± 0.65 A Y 508.47 ± 1.73 B N
G097.528+03.184 8963.1 41.23 ± 0.29 A N 49.32 ± 0.55 A N
G101.016+02.590 8963.0 17.71 ± 0.06 A Y 21.24 ± 0.14 A N
G104.700+02.784 8963.0 9.00 ± 0.17 A Y 39.99 ± 0.36 A N
G109.104−00.347 8963.0 7.10 ± 0.07 A N 19.36 ± 0.20 A N
G124.637+02.535 8963.4 252.56 ± 0.20 A N 293.16 ± 0.62 A N
G125.092+00.778 8963.5 6.70 ± 0.02 A Y 20.65 ± 0.07 B N
G135.188+02.701 8963.4 19.82 ± 0.09 A Y 65.47 ± 0.18 B N
G141.084−01.063 8963.8 12.17 ± 0.19 A Y 62.35 ± 0.37 B N
G150.859−01.115 8963.8 11.73 ± 0.10 A Y 18.02 ± 0.15 A N
G196.448−01.673 8964.0 10.93 ± 0.47 B N 350.13 ± 4.13 B N
G218.737+01.850 8964.1 202.41 ± 0.69 A Y 554.43 ± 1.73 A N
G351.246+00.673 8962.2 7191.06 ± 24.43 A Y 11722.85 ± 66.92 A N
G351.311+00.663 8962.2 2809.89 ± 29.27 A Y 5561.39 ± 64.30 A N

Note.

a"N" if non-tapered image measurement; "Y" if uv-tapered image measurement.

Download table as:  ASCIITypeset images: 1 2

The QF is a qualitative assessment of the accuracy of the continuum flux measurement. QF A detections are isolated, unresolved, and near the center of the primary beam, QF B detections are slightly resolved, in crowded fields, and/or are located off center from the primary beam, QF C detections are well-resolved, in very crowded fields, and/or are located near the edge of the primary beam. Any continuum sources that are confused/blended are assigned QF D. These nebulae are excluded from the tables and all subsequent analysis since we are unable to measure their continuum fluxes accurately. The three nebulae in Figure 2 are examples of each continuum QF: G019.728−00.113 is a QF A detection, G019.754−00.129 is a QF B detection because it is off center, and G019.677−00.134 is a QF C detection because it is resolved and near the edge of the primary beam.

We detect $\langle \mathrm{Hn}\alpha \rangle $ RRL emission toward 82 (72%) of our 114 continuum sources. All RRL detections are toward previously known H ii regions. Figure 3 shows representative $\langle \mathrm{Hn}\alpha \rangle $ RRL detections with different signal-to-noise ratios. Our typical spectral rms noise is ∼1 mJy beam−1, about three times greater than what we estimated using the VLA sensitivity calculator. This decease in sensitivity is likely due to RFI that compromised entire spectral line spectral windows. We may be able to further increase our spectral line sensitivity by self-calibration.

Figure 3.

Figure 3. Representative $\langle \mathrm{Hn}\alpha \rangle $ stacked spectra. The spectra for G010.596−00.381 (top left), G071.150+00.397 (top right), G124.637+02.535 (bottom left), and G073.878+01.023 (bottom right) span the range of typical RRL detection signal-to-noise ratios. The black histogram is the data, the red curve is the Gaussian fit with parameters listed in the legend, and the magenta curve is the fit residuals. These spectra were extracted from the non-tapered data cubes at the location of the peak continuum brightness.

Standard image High-resolution image

Table 5 lists the measured $\langle \mathrm{Hn}\alpha \rangle $ RRL properties of our detections: the WISE Catalog source name; the weighted average frequency of the $\langle \mathrm{Hn}\alpha \rangle $ spectrum, νL, where the weights are the same as those used to average the individual RRL transitions (see Section 4); the amplitude of the Gaussian fit to the spectrum extracted from the location of peak continuum brightness, ${S}_{L}^{{\rm{P}}};$ the spectral rms at this position, rmsP; the center LSR velocity of the fitted Gaussian, ${v}_{\mathrm{LSR}}^{{\rm{P}}};$ the FWHM line width of the fitted Gaussian, ΔVP; a column indicating whether the spectrum was extracted from the non-tapered (N) or uv-tapered (Y) image; the amplitude of the Gaussian fit to the spectrum summed within the watershed region, ${S}_{L}^{{\rm{T}}};$ the spectral rms in this region, rmsT; the center LSR velocity of the fitted Gaussian, ${v}_{\mathrm{LSR}}^{{\rm{T}}};$ the FWHM line width of the fitted Gaussian, ΔVT; and a column indicating whether the spectrum was extracted from the non-tapered or uv-tapered image. As before, we use either the non-tapered or uv-tapered image, depending on which gives the smallest fractional uncertainty in the derived electron temperature. Unlike B15, we do not assign QFs to our RRL detections. Our spectral baselines are always flat and well modeled by a third-order polynomial, therefore, no qualitative assessment is necessary. Two nebulae, G005.885−00.393 and G070.293+01.599, are excluded from Table 5 because they have blended, non-Gaussian line profiles.

Table 5.  RRL Data Products

Name νL ${S}_{L}^{{\rm{P}}}$ rmsP ${v}_{\mathrm{LSR}}^{{\rm{P}}}$ ΔVP TaperPa ${S}_{L}^{{\rm{T}}}$ rmsT ${v}_{\mathrm{LSR}}^{{\rm{T}}}$ ΔVT TaperTa
  (MHz) (mJy (mJy (km s−1) (km s−1)   (mJy) (mJy) (km s−1) (km s−1)  
    beam−1) beam−1)                
G009.612+00.205 8862.2 5.53 ± 0.39 1.19 2.5 ± 0.8 22.2 ± 1.9 N 2.71 ± 0.08 0.24 3.2 ± 0.3 22.1 ± 0.8 N
G009.613+00.200 8786.3 81.07 ± 0.67 1.97 4.0 ± 0.1 20.4 ± 0.2 Y 133.99 ± 1.12 3.29 3.8 ± 0.1 20.5 ± 0.2 N
G010.596−00.381 8816.4 59.07 ± 0.60 1.87 1.1 ± 0.1 23.3 ± 0.3 Y 107.40 ± 0.98 3.06 1.1 ± 0.1 23.1 ± 0.2 Y
G010.621−00.380 8789.6 80.22 ± 0.52 1.67 −0.5 ± 0.1 24.8 ± 0.2 N 3.61 ± 0.03 0.10 −0.7 ± 0.1 24.9 ± 0.2 N
G010.623−00.385 8737.2 175.69 ± 1.08 4.12 1.1 ± 0.1 35.0 ± 0.2 Y 182.71 ± 0.99 4.03 0.9 ± 0.1 39.9 ± 0.2 N
G012.805−00.196 8779.1 1097.15 ± 3.02 11.78 36.3 ± 0.0 36.4 ± 0.1 Y 2079.31 ± 5.80 22.02 36.7 ± 0.0 34.5 ± 0.1 Y
G012.813−00.200 8767.2 199.79 ± 1.44 4.85 30.2 ± 0.1 27.2 ± 0.2 N 74.74 ± 0.65 2.20 30.4 ± 0.1 27.7 ± 0.3 N
G013.880+00.285 8806.2 267.42 ± 0.64 1.90 52.4 ± 0.0 21.5 ± 0.1 Y 530.66 ± 1.35 4.06 52.0 ± 0.0 21.6 ± 0.1 Y
G017.928−00.677 8738.1 10.52 ± 1.04 3.06 38.4 ± 1.0 21.1 ± 2.5 Y
G018.584+00.344 8806.1 3.57 ± 0.35 1.09 14.4 ± 1.2 24.1 ± 3.0 Y 7.58 ± 0.60 1.80 14.3 ± 0.9 22.2 ± 2.1 Y
G019.677−00.134 8595.3 18.57 ± 1.27 4.14 54.7 ± 0.9 27.0 ± 2.4 Y 50.04 ± 2.52 8.33 55.6 ± 0.7 26.6 ± 1.6 N
G019.728−00.113 8883.1 4.09 ± 0.34 1.08 53.6 ± 1.0 25.3 ± 2.5 Y 3.29 ± 0.25 0.81 52.9 ± 0.9 25.0 ± 2.3 N
G020.363−00.014 8832.6 7.16 ± 0.32 0.98 55.1 ± 0.5 22.3 ± 1.2 N 7.90 ± 0.34 1.05 55.5 ± 0.5 22.5 ± 1.1 N
G021.603−00.169 8886.8 2.67 ± 0.30 0.87 −4.9 ± 1.3 23.0 ± 3.8 Y
G023.661−00.252 8885.9 5.28 ± 0.34 1.03 66.5 ± 0.7 22.2 ± 1.7 Y 26.59 ± 1.08 3.17 67.2 ± 0.4 20.5 ± 1.0 Y
G024.195+00.242 8819.2 3.38 ± 0.50 1.53 33.0 ± 1.8 24.3 ± 4.8 Y 3.52 ± 0.55 1.72 31.9 ± 1.9 25.1 ± 5.0 N
G025.397+00.033 8826.1 20.71 ± 0.28 0.94 −14.0 ± 0.2 28.0 ± 0.4 N 35.95 ± 0.56 1.88 −14.0 ± 0.2 27.3 ± 0.5 N
G025.398+00.562 8775.9 15.47 ± 0.27 0.98 11.7 ± 0.3 32.0 ± 0.6 Y 15.69 ± 0.29 1.07 11.5 ± 0.3 31.3 ± 0.7 N
G025.401+00.021 8867.2 10.30 ± 0.55 1.73 −10.7 ± 0.6 24.3 ± 1.5 Y 12.38 ± 0.51 1.54 −10.2 ± 0.4 22.4 ± 1.1 N
G026.597−00.024 8892.9 7.09 ± 0.21 0.80 17.3 ± 0.5 34.6 ± 1.2 N 15.57 ± 0.51 1.78 18.6 ± 0.5 30.0 ± 1.1 Y
G027.562+00.084 8542.6 15.65 ± 0.53 1.55 88.2 ± 0.3 20.4 ± 0.8 Y 18.08 ± 0.59 1.74 88.2 ± 0.3 20.8 ± 0.8 N
G028.320+01.243 8893.2 1.77 ± 0.26 0.65 −40.5 ± 1.1 15.0 ± 2.7 N 1.76 ± 0.30 0.86 −39.6 ± 4.5 34.1 ± 21.9 N
G028.451+00.001 8840.4 5.07 ± 0.32 1.10 −7.2 ± 0.9 28.7 ± 2.2 Y 5.96 ± 0.36 1.20 −6.9 ± 0.8 27.2 ± 1.9 N
G028.581+00.145 8860.3 2.84 ± 0.24 0.76 −13.1 ± 1.0 24.4 ± 2.5 N 3.58 ± 0.28 0.94 −13.0 ± 1.0 26.9 ± 2.6 N
G029.770+00.219 8778.8 5.85 ± 0.38 1.15 −30.9 ± 0.7 21.6 ± 1.7 Y 7.10 ± 0.47 1.39 −30.9 ± 0.7 21.4 ± 1.6 N
G030.211+00.428 8715.8 2.83 ± 0.37 0.97 −10.8 ± 1.1 16.6 ± 2.6 Y 3.00 ± 0.38 1.02 −11.5 ± 1.1 17.6 ± 2.6 N
G031.580+00.074 8828.1 3.51 ± 0.46 1.04 100.4 ± 0.8 12.0 ± 1.8 N 3.27 ± 0.39 0.93 100.8 ± 0.8 13.5 ± 1.9 N
G032.030+00.048 8848.2 5.13 ± 0.39 0.99 89.8 ± 0.6 15.3 ± 1.3 Y 4.81 ± 0.31 0.80 90.3 ± 0.5 16.1 ± 1.2 N
G032.272−00.226 8819.0 21.61 ± 0.40 1.32 22.9 ± 0.2 26.5 ± 0.6 Y 27.01 ± 0.49 1.63 22.9 ± 0.2 26.9 ± 0.6 N
G032.928+00.606 8590.7 13.70 ± 0.29 1.00 −37.9 ± 0.3 28.9 ± 0.7 N 20.89 ± 0.49 1.63 −38.2 ± 0.3 26.9 ± 0.7 N
G034.041+00.052 8776.4 4.10 ± 0.40 1.26 36.9 ± 1.1 23.6 ± 2.7 Y 12.60 ± 0.91 2.80 37.7 ± 0.8 22.7 ± 1.9 Y
G034.133+00.471 8801.3 42.46 ± 0.44 1.41 36.1 ± 0.1 24.6 ± 0.3 Y 56.32 ± 0.58 1.86 36.1 ± 0.1 24.6 ± 0.3 N
G034.686+00.068 8724.2 7.06 ± 0.37 1.15 50.5 ± 0.6 23.8 ± 1.4 Y 14.29 ± 0.63 1.94 50.4 ± 0.5 22.4 ± 1.1 Y
G035.126−00.755 8814.3 17.99 ± 0.40 1.17 35.0 ± 0.2 20.0 ± 0.5 Y 34.45 ± 0.71 2.05 35.3 ± 0.2 19.9 ± 0.5 N
G035.948−00.149 8872.5 1.87 ± 0.24 0.74 51.4 ± 1.4 22.6 ± 3.6 N 3.15 ± 0.41 1.19 49.3 ± 1.4 21.0 ± 3.6 N
G038.550+00.163 8758.9 11.79 ± 0.37 1.18 27.6 ± 0.4 23.7 ± 0.9 Y 14.88 ± 0.46 1.46 27.7 ± 0.4 23.8 ± 0.9 N
G038.643−00.227 8762.5 2.70 ± 0.41 1.12 69.4 ± 1.4 18.5 ± 3.5 Y 3.81 ± 0.64 1.61 68.4 ± 1.3 15.6 ± 3.3 Y
G038.840+00.495 8764.1 7.57 ± 0.98 2.80 −42.8 ± 1.3 20.3 ± 3.2 Y
G038.875+00.308 8808.9 25.36 ± 0.26 0.89 −13.4 ± 0.1 27.8 ± 0.3 N 27.91 ± 0.31 1.07 −13.8 ± 0.2 28.3 ± 0.4 N
G039.196+00.224 8787.5 4.51 ± 0.24 0.84 −21.7 ± 0.8 28.7 ± 1.9 N 4.88 ± 0.27 0.95 −21.1 ± 0.8 29.2 ± 2.0 N
G039.864+00.645 8738.8 5.21 ± 0.34 1.14 −41.3 ± 0.9 27.3 ± 2.1 Y 8.57 ± 0.51 1.72 −42.0 ± 0.8 27.6 ± 2.0 N
G043.146+00.013 8708.1 134.45 ± 0.75 2.67 8.7 ± 0.1 30.2 ± 0.2 Y 101.01 ± 0.52 1.86 8.5 ± 0.1 31.1 ± 0.2 Y
G043.151+00.011 8695.6 62.31 ± 0.51 1.84 5.8 ± 0.1 31.8 ± 0.3 N 48.52 ± 0.35 1.27 6.0 ± 0.1 31.9 ± 0.3 N
G043.162+00.005 8768.7 42.28 ± 0.66 2.22 6.5 ± 0.2 27.0 ± 0.5 N 15.82 ± 0.21 0.70 6.2 ± 0.2 27.1 ± 0.4 N
G043.165−00.031 8665.8 154.87 ± 2.24 8.99 6.8 ± 0.3 38.8 ± 0.7 N 128.59 ± 1.59 6.41 7.5 ± 0.2 39.0 ± 0.6 N
G043.168+00.019 8762.5 46.09 ± 0.53 1.69 9.9 ± 0.1 24.1 ± 0.3 N 20.67 ± 0.22 0.70 9.8 ± 0.1 24.1 ± 0.3 N
G043.170−00.004 8670.2 223.40 ± 0.87 3.38 7.8 ± 0.1 36.0 ± 0.2 Y 851.52 ± 2.80 10.04 4.5 ± 0.0 30.7 ± 0.1 Y
G043.175+00.025 8739.0 40.65 ± 0.58 2.02 14.9 ± 0.2 28.7 ± 0.5 N 22.55 ± 0.27 0.95 14.9 ± 0.2 29.6 ± 0.4 N
G043.432+00.516 8896.0 6.81 ± 0.97 2.92 −11.8 ± 1.8 25.1 ± 5.6 Y
G043.818+00.395 8881.8 8.70 ± 0.60 2.11 −8.5 ± 1.0 31.0 ± 2.6 Y
G043.968+00.993 8789.7 3.87 ± 0.24 0.87 −25.5 ± 1.0 31.9 ± 2.5 N 3.92 ± 0.26 0.94 −25.4 ± 1.0 31.2 ± 2.6 N
G044.501+00.332 8806.0 2.80 ± 0.29 0.85 −41.6 ± 1.1 22.0 ± 2.8 Y 6.46 ± 0.37 1.05 −43.4 ± 0.5 19.7 ± 1.3 Y
G048.719+01.147 8828.4 3.70 ± 0.32 1.05 −25.6 ± 1.1 26.5 ± 2.8 Y 6.51 ± 0.55 1.79 −25.9 ± 1.1 26.6 ± 2.8 N
G049.399−00.490 8880.6 21.50 ± 0.43 1.34 62.7 ± 0.2 22.7 ± 0.5 Y 24.46 ± 0.40 1.28 61.5 ± 0.2 24.1 ± 0.5 Y
G052.098+01.042 8835.7 24.43 ± 0.33 1.15 37.5 ± 0.2 29.3 ± 0.5 Y 36.72 ± 0.47 1.63 37.3 ± 0.2 28.7 ± 0.4 N
G052.232+00.735 8756.0 5.54 ± 0.90 2.72 −1.1 ± 2.2 26.2 ± 6.9 Y 19.84 ± 1.48 4.37 −2.3 ± 0.8 20.8 ± 1.8 Y
G055.114+02.422 8859.8 6.60 ± 0.30 1.08 −73.6 ± 0.7 32.8 ± 1.8 Y 29.62 ± 0.78 2.87 −74.8 ± 0.4 32.6 ± 1.0 Y
G060.592+01.572 8864.6 3.93 ± 0.32 1.05 −50.2 ± 1.1 27.2 ± 2.7 Y 11.25 ± 0.76 2.50 −48.5 ± 0.9 26.8 ± 2.2 Y
G061.720+00.863 8808.8 7.00 ± 0.67 2.11 −69.6 ± 1.2 25.9 ± 3.3 N 7.39 ± 0.78 2.42 −68.4 ± 1.3 24.5 ± 3.3 N
G062.577+02.389 8747.3 8.53 ± 0.98 2.95 −71.2 ± 1.3 22.3 ± 3.2 Y 24.80 ± 2.49 7.44 −72.0 ± 1.1 22.0 ± 2.7 Y
G070.280+01.583 8782.7 49.01 ± 0.86 2.68 −23.6 ± 0.2 23.4 ± 0.5 Y 186.56 ± 1.83 5.95 −25.1 ± 0.1 25.3 ± 0.3 Y
G070.304+01.595 8763.0 72.95 ± 1.10 3.53 −18.2 ± 0.2 24.5 ± 0.4 Y 51.50 ± 0.84 2.63 −17.6 ± 0.2 23.4 ± 0.4 N
G070.329+01.589 8694.4 157.24 ± 2.52 8.96 −18.4 ± 0.2 30.4 ± 0.6 Y 123.82 ± 1.89 6.77 −17.8 ± 0.2 30.6 ± 0.5 N
G070.765+01.820 8843.3 13.56 ± 1.53 4.85 −78.1 ± 1.4 24.9 ± 3.4 N
G071.150+00.397 8783.3 34.14 ± 0.49 1.56 −12.2 ± 0.2 24.2 ± 0.4 Y 38.36 ± 0.62 1.99 −12.2 ± 0.2 24.6 ± 0.5 Y
G073.878+01.023 8815.2 6.24 ± 0.32 1.12 −49.5 ± 0.7 29.6 ± 1.8 N 8.50 ± 0.41 1.47 −50.3 ± 0.7 30.8 ± 1.8 N
G074.155+01.646 8798.0 4.15 ± 0.46 1.18 −32.2 ± 0.9 15.9 ± 2.0 Y 5.86 ± 0.74 1.88 −31.6 ± 1.0 15.7 ± 2.3 Y
G074.753+00.912 8840.0 5.45 ± 0.33 1.04 −48.9 ± 0.7 23.7 ± 1.7 N 6.42 ± 0.37 1.25 −49.6 ± 0.8 27.9 ± 1.9 N
G075.768+00.344 8789.4 100.01 ± 0.64 2.09 −8.6 ± 0.1 25.5 ± 0.2 Y 364.25 ± 1.98 6.65 −8.7 ± 0.1 27.0 ± 0.2 Y
G078.886+00.709 8821.1 12.24 ± 0.37 1.04 −1.9 ± 0.3 19.1 ± 0.7 N 15.90 ± 0.46 1.31 −1.9 ± 0.3 19.5 ± 0.7 N
G096.289+02.593 8873.2 4.36 ± 0.29 0.97 −87.5 ± 0.9 26.8 ± 2.1 Y 27.37 ± 0.93 3.18 −97.7 ± 0.5 28.3 ± 1.1 Y
G096.434+01.324 8856.1 3.89 ± 0.28 0.85 −77.8 ± 0.8 21.8 ± 1.9 Y 4.08 ± 0.29 0.88 −77.9 ± 0.8 21.8 ± 1.8 N
G097.515+03.173 8865.1 9.56 ± 0.29 1.00 −76.8 ± 0.4 28.0 ± 1.0 Y 35.06 ± 0.79 2.72 −74.4 ± 0.3 28.2 ± 0.7 Y
G097.528+03.184 8901.3 4.34 ± 0.26 0.79 −71.6 ± 0.7 23.1 ± 1.6 N 4.55 ± 0.25 0.79 −72.0 ± 0.7 24.1 ± 1.6 N
G101.016+02.590 8896.8 2.57 ± 0.36 0.92 −70.2 ± 1.1 16.3 ± 2.7 Y 2.85 ± 0.38 1.00 −70.2 ± 1.1 16.8 ± 2.7 N
G109.104−00.347 8852.5 2.98 ± 0.29 0.90 −44.1 ± 1.1 22.7 ± 2.6 Y 3.60 ± 0.34 1.09 −44.4 ± 1.2 25.7 ± 2.9 N
G124.637+02.535 8817.1 16.81 ± 0.27 0.96 −77.5 ± 0.2 30.5 ± 0.6 N 18.35 ± 0.33 1.18 −77.6 ± 0.3 30.7 ± 0.6 N
G135.188+02.701 8974.4 2.61 ± 0.37 1.06 −73.2 ± 1.4 19.9 ± 3.3 Y 6.42 ± 0.88 2.59 −72.2 ± 2.8 31.9 ± 12.6 Y
G141.084−01.063 8853.2 8.50 ± 1.15 3.15 −25.2 ± 1.3 18.8 ± 3.2 Y
G196.448−01.673 8872.6 4.71 ± 0.37 1.08 10.9 ± 0.8 20.8 ± 1.9 Y 27.00 ± 0.98 3.00 12.5 ± 0.4 22.6 ± 0.9 Y
G351.246+00.673 8789.9 851.65 ± 2.69 8.64 −0.4 ± 0.0 24.7 ± 0.1 Y 1474.38 ± 3.93 12.75 −0.1 ± 0.0 25.1 ± 0.1 Y
G351.311+00.663 8839.3 356.60 ± 1.81 5.76 −6.9 ± 0.1 24.2 ± 0.1 Y 774.71 ± 2.46 7.79 −6.2 ± 0.0 24.1 ± 0.1 Y

Note.

a"N" if non-tapered image measurement; "Y" if uv-tapered image measurement.

Download table as:  ASCIITypeset images: 1 2

5.2. Electron Temperatures

Thermal bremsstrahlung (free–free) emission is the primary source of H ii region radio-continuum emission. Its intensity depends on the plasma electron temperature, the plasma electron density, and the stellar ionizing photon rate. The free–free opacity of an H ii region in LTE is well-approximated by

Equation (5)

where Te is the plasma electron temperature, EM is the emission measure, and ν is the frequency (Mezger & Henderson 1967). The emission measure is the integral of the squared electron number density, ne2, along the line-of-sight path through the nebula: $\mathrm{EM}=\int {n}_{e}^{2}\,{dl}$. An optically thin H ii region has a continuum brightness temperature TC ≃ τCTe. Without an independent determination of the emission measure, we are unable to use the continuum emission alone to derive the nebular electron temperature.

The RRL intensity and line width reveal the physical characteristics of an H ii region. The line center opacity of an H ii region in LTE is approximated by

Equation (6)

where Δν is the full-width half-maximum (FWHM) line width in frequency units (Kardashev 1959; Mezger & Hoglund 1967). Similar to the continuum, we need an independent measurement of the emission measure in order to use the RRL properties to derive the electron temperature.

The typical hydrogen RRL line width for Galactic H ii regions is ∼25 km s−1 (Wenger et al. 2019). There are four physical effects that contribute to the RRL FWHM line width: (1) intrinsic broadening, due to the uncertainty principle; (2) collisional broadening, due to the collisions of the emitting atoms; (3) thermal Doppler broadening, due to the Maxwellian velocity distribution of emitting atoms in the plasma; and (4) nonthermal Doppler broadening. Of these, thermal and nonthermal Doppler broadening are the most significant contributors to the width of RRLs. The nonthermal (i.e., turbulent) components can only be constrained with additional information. RRL line width measurements for nebular plasma atoms other than hydrogen are needed, since atoms with different masses have different Maxwellian velocity distributions. Alternatively, the thermal contribution to the RRL line width can be determined by deriving the plasma temperature.

We derive the nebular electron temperature from the RRL-to-continuum brightness ratio. For an H ii region in LTE that is optically thin to both continuum and RRL emission, the ratio of the radio-continuum brightness temperature to the RRL peak brightness temperature is equal to the ratio of the continuum opacity to the line center opacity. This ratio is independent of the emission measure. A complete derivation of the electron temperature equation is in the Appendix. For RRLs near H90α, assuming the continuum and RRL emission originate in the same volume of gas, we find

Equation (7)

where νL is the RRL frequency, SC is the continuum flux density, SL is the RRL center flux density, ΔV is the RRL FWHM line width in velocity units, and y+ is the ratio of the number density of singly ionized helium to hydrogen.

We use Equation (7) to derive the electron temperatures of the 72 nebulae in our sample with a VLA $\langle \mathrm{Hn}\alpha \rangle $ RRL detection and a continuum QF A, B, or C. We only detect helium RRLs in a few, bright sources, so we assume y+ = 0.08 for all VLA detections, following Balser et al. (2011) and B15. Equation (7) is only weakly dependent on y+. A 10% increase from y+ = 0.08 results in a mere 0.6% increase in Te. We do not consider uncertainties in y+ in the subsequent analyses because the electron temperature uncertainties are typically much greater than 0.6%. Furthermore, we assume non-LTE effects and collisional broadening are negligible at these frequencies (see Balser et al. 1999). The RRL flux density, RRL FWHM line width, and continuum flux density are measured in the $\langle \mathrm{Hn}\alpha \rangle $ stacked spectrum, and the RRL frequency is the weighted average frequency of the individual RRL transitions. Again, the frequency weights are the same as those used to average the individual RRL transitions (see Section 4). In the Appendix, we show that this strategy can produce accurate electron temperatures.

Table 6 lists the WISE Catalog source name, the telescope used for the observation, the measured RRL-to-continuum flux ratios, the RRL FWHM line widths, and the derived electron temperatures for the B15 single dish and our VLA H ii region samples. This table only lists the highest quality electron temperature derivations; we remove all QF D sources from the B15 and VLA samples. The electron temperature uncertainties are computed by propagating the RRL-to-continuum flux ratio and FWHM line width uncertainties through Equation (7). For VLA sources, the "Type" column indicates whether the position of peak continuum brightness (P) or watershed region (T) is used to measure the RRL-to-continuum flux ratio. The "Taper" column identifies which data cube is used (N for non-tapered and Y for uv-tapered). We select the combination of "Type" and "Taper" that minimizes the fractional uncertainty in the derived electron temperature. In cases where the same source is detected in multiple surveys, we only list the VLA values, if available. If the source is not observed or detected in the VLA survey, we list the GBT values. If the source is not in the VLA survey nor the GBT survey, we list the 140 Foot values. Table 6 also includes information about the H ii region distances, which is discussed in Section 5.4.

Table 6.  H ii Region Distances and Properties

Name Telescope SL/SC ΔV Te Typea Taperb d R Distancec Distance
      (km s−1) (K)     (kpc) (kpc) Method Reference
G000.666−00.036 140 Foot 0.0569 ± 0.0033 40.5 ± 0.4 8170 ± 180 ${7.59}_{-0.65}^{+0.84}$ ${0.21}_{-0.11}^{+0.91}$ P R09c
G001.125−00.106 140 Foot 0.1070 ± 0.0018 24.5 ± 0.2 7130 ± 70 d d K
G003.266−00.061 140 Foot 0.0978 ± 0.0100 25.3 ± 0.4 7440 ± 280 d d K
G005.900−00.431 140 Foot 0.0691 ± 0.0006 22.5 ± 0.2 11130 ± 170 ${2.99}_{-0.20}^{+0.17}$ ${5.38}_{-0.16}^{+0.19}$ P S14
G005.987−01.191 140 Foot 0.0840 ± 0.0008 26.5 ± 0.2 8180 ± 70 d d K
G008.137+00.232 140 Foot 0.1019 ± 0.0007 25.4 ± 0.1 7090 ± 60 d d K
G010.160−00.350 140 Foot 0.0911 ± 0.0005 31.2 ± 0.2 6830 ± 30 d d K
G010.308−00.150 140 Foot 0.0874 ± 0.0005 31.6 ± 0.2 6800 ± 40 d d K
G010.596−00.381 VLA 0.1506 ± 0.0015 23.1 ± 0.2 5704 ± 72 T Y ${4.87}_{-0.44}^{+0.55}$ ${3.64}_{-0.48}^{+0.42}$ P Sa14
G012.804−00.207 140 Foot 0.0808 ± 0.0007 30.7 ± 0.3 7620 ± 100 ${2.83}_{-0.28}^{+0.38}$ ${5.61}_{-0.35}^{+0.26}$ P I13
G013.880+00.285 VLA 0.1568 ± 0.0004 21.5 ± 0.1 5848 ± 19 P Y ${3.79}_{-0.26}^{+0.49}$ ${4.61}_{-0.31}^{+0.39}$ P S14
G015.097−00.729 140 Foot 0.0938 ± 0.0008 35.3 ± 0.3 5720 ± 60 ${1.94}_{-0.10}^{+0.16}$ ${6.49}_{-0.15}^{+0.09}$ P X11
G016.993+00.873 140 Foot 0.0928 ± 0.0006 23.6 ± 0.1 6890 ± 60 ${2.38}_{-0.24}^{+0.27}$ ${6.10}_{-0.30}^{+0.22}$ K
G017.928−00.677 VLA 0.1461 ± 0.0158 21.1 ± 2.5 6269 ± 877 T Y ${12.65}_{-0.37}^{+0.37}$ ${5.41}_{-0.31}^{+0.23}$ K
G018.144−00.281 140 Foot 0.1052 ± 0.0008 25.2 ± 0.2 7180 ± 70 ${4.00}_{-0.30}^{+0.36}$ ${4.68}_{-0.26}^{+0.28}$ K
G018.584+00.344 VLA 0.1547 ± 0.0135 22.2 ± 2.1 5712 ± 645 T Y ${14.36}_{-0.39}^{+0.42}$ ${7.02}_{-0.31}^{+0.25}$ K
G018.669+01.965 140 Foot 0.0907 ± 0.0006 28.4 ± 0.2 7210 ± 60 ${2.42}_{-0.25}^{+0.25}$ ${6.08}_{-0.25}^{+0.27}$ K
G019.064−00.282 140 Foot 0.2916 ± 0.0052 25.2 ± 0.3 5440 ± 70 ${4.44}_{-0.29}^{+0.39}$ ${4.37}_{-0.27}^{+0.25}$ K
G019.677−00.134 VLA 0.1166 ± 0.0063 26.6 ± 1.6 6141 ± 429 T N ${11.66}_{-0.36}^{+0.43}$ ${4.75}_{-0.27}^{+0.29}$ K
G019.728−00.113 VLA 0.1363 ± 0.0115 25.0 ± 2.3 5813 ± 629 T N ${11.89}_{-0.43}^{+0.36}$ ${4.89}_{-0.25}^{+0.28}$ K
G020.363−00.014 VLA 0.1416 ± 0.0067 22.5 ± 1.1 6150 ± 367 T N ${11.68}_{-0.40}^{+0.40}$ ${4.86}_{-0.29}^{+0.24}$ K
G020.728−00.105 140 Foot 0.1249 ± 0.0035 26.5 ± 0.1 5590 ± 90 ${11.74}_{-0.48}^{+0.32}$ ${4.91}_{-0.31}^{+0.23}$ K
G021.603−00.169 VLA 0.1039 ± 0.0121 23.0 ± 3.8 7959 ± 1399 P Y ${16.03}_{-0.49}^{+0.53}$ ${8.81}_{-0.42}^{+0.42}$ K
G023.423−00.216 140 Foot 0.1162 ± 0.0008 24.3 ± 0.1 6500 ± 55 ${5.55}_{-0.87}^{+1.37}$ ${3.42}_{-0.11}^{+0.71}$ P B09
G023.661−00.252 VLA 0.1737 ± 0.0079 20.5 ± 1.0 5583 ± 318 T Y ${10.98}_{-0.44}^{+0.41}$ ${4.76}_{-0.31}^{+0.23}$ K
G023.713+00.175 140 Foot 0.1027 ± 0.0015 26.8 ± 0.4 6840 ± 110 ${7.63}_{-0.15}^{+0.16}$ ${3.62}_{-0.19}^{+0.27}$ K
G024.195+00.242 VLA 0.1190 ± 0.0187 24.3 ± 4.8 6692 ± 1465 P Y d ${6.17}_{-0.23}^{+0.29}$ K
G024.456+00.489 140 Foot 0.1020 ± 0.0008 29.2 ± 0.5 6370 ± 80 ${7.56}_{-0.23}^{+0.23}$ ${3.80}_{-0.21}^{+0.28}$ K
G024.844+00.093 140 Foot 0.1326 ± 0.0012 24.9 ± 0.2 5860 ± 90 ${7.48}_{-0.23}^{+0.23}$ ${3.72}_{-0.18}^{+0.19}$ K
G025.382−00.151 140 Foot 0.0974 ± 0.0027 25.6 ± 0.1 7460 ± 70 ${3.71}_{-0.25}^{+0.40}$ ${5.20}_{-0.29}^{+0.22}$ K
G025.397+00.033 VLA 0.0853 ± 0.0012 28.0 ± 0.4 7893 ± 142 P N ${16.40}_{-0.47}^{+0.66}$ ${9.53}_{-0.38}^{+0.55}$ K
G025.398+00.562 VLA 0.0774 ± 0.0014 32.0 ± 0.6 7610 ± 177 P Y ${14.11}_{-0.36}^{+0.41}$ ${7.49}_{-0.28}^{+0.28}$ K
G025.401+00.021 VLA 0.1074 ± 0.0046 22.4 ± 1.1 7871 ± 438 T N ${16.00}_{-0.44}^{+0.59}$ ${9.25}_{-0.44}^{+0.38}$ K
G025.867+00.118 140 Foot 0.1189 ± 0.0016 27.3 ± 0.4 6120 ± 100 ${7.53}_{-0.18}^{+0.13}$ ${3.80}_{-0.16}^{+0.17}$ K
G027.562+00.084 VLA 0.1594 ± 0.0057 20.8 ± 0.8 5765 ± 261 T N ${9.65}_{-0.58}^{+0.50}$ ${4.43}_{-0.25}^{+0.26}$ K
G028.320+01.243 VLA 0.0819 ± 0.0125 15.0 ± 2.7 14189 ± 2932 P N ${19.42}_{-0.98}^{+1.15}$ ${12.63}_{-0.83}^{+1.05}$ K
G028.451+00.001 VLA 0.0923 ± 0.0058 27.2 ± 1.9 7576 ± 629 T N ${15.25}_{-0.46}^{+0.50}$ ${8.87}_{-0.38}^{+0.38}$ K
G028.581+00.145 VLA 0.0946 ± 0.0079 26.9 ± 2.6 7490 ± 837 T N ${15.83}_{-0.59}^{+0.55}$ ${9.38}_{-0.45}^{+0.45}$ K
G028.746+03.458 GBT 0.1106 ± 0.0007 21.0 ± 0.1 8399 ± 73 ${14.79}_{-0.54}^{+0.36}$ ${8.45}_{-0.38}^{+0.30}$ K
G029.770+00.219 VLA 0.1029 ± 0.0071 21.4 ± 1.6 8465 ± 755 T N ${17.46}_{-0.60}^{+0.93}$ ${11.00}_{-0.47}^{+0.87}$ K
G029.956−00.020 140 Foot 0.0992 ± 0.0064 29.8 ± 0.1 6510 ± 90 ${5.14}_{-0.45}^{+0.65}$ ${4.61}_{-0.24}^{+0.21}$ P Z14
G030.211+00.428 VLA 0.1263 ± 0.0168 17.6 ± 2.6 8355 ± 1446 T N ${15.46}_{-0.59}^{+0.47}$ ${9.28}_{-0.49}^{+0.34}$ K
G030.758−00.047 GBT 0.0908 ± 0.0003 33.5 ± 0.1 6567 ± 30 ${7.20}_{-0.17}^{+0.11}$ ${4.63}_{-0.22}^{+0.22}$ K
G031.268+00.478 GBT 0.0944 ± 0.0042 23.2 ± 1.0 8690 ± 462 ${14.75}_{-0.45}^{+0.49}$ ${8.77}_{-0.34}^{+0.39}$ K
G031.580+00.074 VLA 0.2544 ± 0.0357 13.5 ± 1.9 5769 ± 992 T N ${4.67}_{-0.59}^{+0.88}$ ${4.97}_{-0.41}^{+0.23}$ P Z14
G032.030+00.048 VLA 0.2159 ± 0.0159 16.1 ± 1.2 5720 ± 519 T N ${5.16}_{-0.21}^{+0.24}$ ${4.81}_{-0.09}^{+0.08}$ P S14
G032.272−00.226 VLA 0.0850 ± 0.0016 26.9 ± 0.6 8207 ± 200 T N ${12.52}_{-0.34}^{+0.40}$ ${7.04}_{-0.22}^{+0.28}$ K
G032.733+00.209 GBT 0.1638 ± 0.0037 21.0 ± 0.4 5856 ± 156 ${12.88}_{-0.35}^{+0.40}$ ${7.39}_{-0.25}^{+0.30}$ K
G032.800+00.190 GBT 0.0750 ± 0.0004 29.5 ± 0.1 8625 ± 49 ${13.01}_{-0.44}^{+0.33}$ ${7.50}_{-0.29}^{+0.27}$ K
G032.870−00.427 GBT 0.1817 ± 0.0043 18.2 ± 0.4 6074 ± 176 ${10.99}_{-0.45}^{+0.34}$ ${6.03}_{-0.28}^{+0.20}$ K
G032.928+00.606 VLA 0.0723 ± 0.0016 28.9 ± 0.7 8641 ± 244 P N ${17.66}_{-0.79}^{+0.91}$ ${11.51}_{-0.59}^{+0.91}$ K
G032.982−00.338 GBT 0.1485 ± 0.0040 20.9 ± 0.5 6411 ± 207 ${10.91}_{-0.39}^{+0.39}$ ${5.99}_{-0.24}^{+0.26}$ K
G034.041+00.052 VLA 0.1489 ± 0.0119 22.7 ± 1.9 5809 ± 591 T Y ${11.48}_{-0.43}^{+0.32}$ ${6.52}_{-0.26}^{+0.22}$ K
G034.133+00.471 VLA 0.1140 ± 0.0013 24.6 ± 0.3 6858 ± 96 T N ${11.55}_{-0.40}^{+0.32}$ ${6.59}_{-0.27}^{+0.21}$ K
G034.256+00.136 GBT 0.0999 ± 0.0006 24.4 ± 0.1 8084 ± 55 ${3.29}_{-0.38}^{+0.30}$ ${5.96}_{-0.26}^{+0.21}$ K
G034.686+00.068 VLA 0.1232 ± 0.0058 22.4 ± 1.1 6876 ± 418 T Y ${10.59}_{-0.37}^{+0.43}$ ${6.03}_{-0.22}^{+0.25}$ K
G035.126−00.755 VLA 0.1428 ± 0.0032 19.9 ± 0.5 6793 ± 193 T N ${2.24}_{-0.31}^{+0.27}$ ${6.62}_{-0.23}^{+0.26}$ K
G035.197−01.756 GBT 0.0947 ± 0.0005 23.6 ± 0.0 8603 ± 40 ${3.20}_{-0.49}^{+0.49}$ ${6.00}_{-0.30}^{+0.28}$ P Z09
G035.948−00.149 VLA 0.1419 ± 0.0202 22.6 ± 3.6 6148 ± 1143 P N ${3.15}_{-0.36}^{+0.36}$ ${6.10}_{-0.28}^{+0.21}$ K
G037.754+00.560 GBT 0.1170 ± 0.0028 23.4 ± 0.8 7163 ± 246 ${11.99}_{-0.34}^{+0.40}$ ${7.43}_{-0.24}^{+0.28}$ K
G038.550+00.163 VLA 0.1149 ± 0.0038 23.8 ± 0.9 7019 ± 299 T N ${11.29}_{-0.42}^{+0.34}$ ${7.05}_{-0.26}^{+0.24}$ K
G038.643−00.227 VLA 0.1262 ± 0.0204 18.5 ± 3.5 7992 ± 1725 P Y ${6.51}_{-0.13}^{+0.14}$ ${5.62}_{-0.23}^{+0.22}$ K
G038.652+00.087 GBT 0.0738 ± 0.0015 27.0 ± 0.6 9428 ± 245 ${16.66}_{-0.85}^{+0.79}$ ${11.35}_{-0.63}^{+0.74}$ K
G038.840+00.495 VLA 0.0900 ± 0.0120 20.3 ± 3.2 9919 ± 1792 T Y ${16.74}_{-0.76}^{+0.95}$ ${11.48}_{-0.66}^{+0.83}$ K
G038.875+00.308 VLA 0.0882 ± 0.0009 27.8 ± 0.3 7719 ± 107 P N ${14.06}_{-0.57}^{+0.46}$ ${9.16}_{-0.38}^{+0.38}$ K
G039.196+00.224 VLA 0.0726 ± 0.0041 28.7 ± 1.9 8853 ± 658 P N ${14.56}_{-0.56}^{+0.60}$ ${9.67}_{-0.42}^{+0.49}$ K
G039.728−00.396 GBT 0.0874 ± 0.0020 25.7 ± 0.7 8503 ± 255 ${9.18}_{-0.46}^{+0.50}$ ${6.00}_{-0.22}^{+0.24}$ K
G039.864+00.645 VLA 0.0780 ± 0.0048 27.6 ± 2.0 8606 ± 707 T N ${16.52}_{-0.89}^{+0.72}$ ${11.37}_{-0.69}^{+0.69}$ K
G040.503+02.537 GBT 0.1074 ± 0.0006 22.4 ± 0.1 8223 ± 55 ${1.41}_{-0.32}^{+0.30}$ ${7.35}_{-0.28}^{+0.24}$ K
G043.146+00.013 VLA 0.0868 ± 0.0005 31.1 ± 0.2 6942 ± 48 T Y ${11.59}_{-0.42}^{+0.45}$ ${7.91}_{-0.27}^{+0.31}$ K
G043.165−00.031 VLA 0.0542 ± 0.0007 39.0 ± 0.6 8648 ± 144 T N ${11.05}_{-0.90}^{+0.90}$ ${7.47}_{-0.48}^{+0.68}$ P Z13
G043.168+00.019 VLA 0.1280 ± 0.0015 24.1 ± 0.3 6282 ± 92 T N ${10.94}_{-0.77}^{+0.98}$ ${7.45}_{-0.48}^{+0.67}$ P Z13
G043.170−00.004 VLA 0.0768 ± 0.0003 30.7 ± 0.1 7876 ± 35 T Y ${11.11}_{-0.98}^{+0.83}$ ${7.60}_{-0.64}^{+0.54}$ P Z13
G043.432+00.516 VLA 0.0930 ± 0.0138 25.1 ± 5.6 8119 ± 1883 T Y ${12.93}_{-0.46}^{+0.58}$ ${8.95}_{-0.38}^{+0.41}$ K
G043.818+00.395 VLA 0.0788 ± 0.0056 31.0 ± 2.6 7806 ± 750 T Y ${12.59}_{-0.42}^{+0.57}$ ${8.74}_{-0.29}^{+0.44}$ K
G043.968+00.993 VLA 0.0822 ± 0.0054 31.9 ± 2.5 7255 ± 647 P N ${13.88}_{-0.53}^{+0.66}$ ${9.79}_{-0.46}^{+0.53}$ K
G044.418+00.535 GBT 0.0926 ± 0.0026 24.3 ± 0.7 8492 ± 299 ${16.93}_{-1.06}^{+0.92}$ ${12.41}_{-0.92}^{+0.86}$ K
G044.501+00.332 VLA 0.1064 ± 0.0063 19.7 ± 1.3 9044 ± 694 T Y ${15.38}_{-0.70}^{+0.88}$ ${11.11}_{-0.60}^{+0.70}$ K
G045.197+00.740 GBT 0.0556 ± 0.0010 30.5 ± 0.6 10841 ± 245 ${14.50}_{-0.54}^{+0.83}$ ${10.45}_{-0.44}^{+0.64}$ K
G045.453+00.044 GBT 0.0871 ± 0.0007 27.6 ± 0.1 8026 ± 63 ${8.11}_{-1.10}^{+1.43}$ ${6.26}_{-0.31}^{+0.57}$ P W14
G046.495−00.241 140 Foot 0.1989 ± 0.0071 20.1 ± 0.2 4860 ± 80 ${5.71}_{-0.08}^{+0.16}$ ${6.27}_{-0.19}^{+0.21}$ K
G048.719+01.147 VLA 0.0943 ± 0.0083 26.6 ± 2.8 7606 ± 900 T N ${12.90}_{-0.59}^{+0.63}$ ${9.70}_{-0.45}^{+0.45}$ K
G048.922−00.285 140 Foot 0.0805 ± 0.0005 26.7 ± 0.2 8440 ± 60 ${5.27}_{-0.19}^{+0.22}$ ${6.29}_{-0.00}^{+0.01}$ P W14
G049.002−00.303 140 Foot 0.1859 ± 0.0017 24.4 ± 0.2 8170 ± 50 ${5.30}_{-0.21}^{+0.20}$ ${6.30}_{-0.00}^{+0.01}$ P W14
G049.201−00.365 140 Foot 0.0650 ± 0.0003 30.3 ± 0.1 9070 ± 70 ${5.31}_{-0.22}^{+0.18}$ ${6.31}_{-0.00}^{+0.01}$ P W14
G049.384−00.298 140 Foot 0.0786 ± 0.0006 31.6 ± 0.3 8585 ± 65 ${5.43}_{-0.10}^{+0.11}$ ${6.37}_{-0.11}^{+0.19}$ K
G049.399−00.490 VLA 0.1167 ± 0.0021 24.1 ± 0.5 6675 ± 151 T Y ${5.34}_{-0.26}^{+0.36}$ ${6.33}_{-0.00}^{+0.01}$ P W14
G049.489−00.378 GBT 0.0903 ± 0.0003 30.2 ± 0.0 7166 ± 25 ${5.42}_{-0.10}^{+0.11}$ ${6.46}_{-0.15}^{+0.19}$ K
G052.098+01.042 VLA 0.0854 ± 0.0011 28.7 ± 0.4 7725 ± 134 T N ${3.53}_{-0.82}^{+1.36}$ ${6.77}_{-0.19}^{+0.19}$ P O10
G052.232+00.735 VLA 0.1083 ± 0.0085 20.8 ± 1.8 8258 ± 841 T Y ${10.47}_{-0.59}^{+0.42}$ ${8.44}_{-0.32}^{+0.32}$ K
G052.766+00.333 GBT 0.0841 ± 0.0011 25.4 ± 0.4 8970 ± 186 ${9.24}_{-0.37}^{+0.55}$ ${7.84}_{-0.23}^{+0.33}$ K
G055.114+02.422 VLA 0.0484 ± 0.0013 32.6 ± 1.0 11357 ± 409 T Y ${16.12}_{-1.07}^{+1.23}$ ${13.24}_{-0.92}^{+1.13}$ K
G059.796+00.241 GBT 0.0975 ± 0.0008 21.8 ± 0.2 9068 ± 120 ${8.79}_{-0.65}^{+0.48}$ ${8.51}_{-0.34}^{+0.32}$ K
G060.592+01.572 VLA 0.0692 ± 0.0048 26.8 ± 2.2 9883 ± 922 T Y ${12.14}_{-0.86}^{+0.75}$ ${10.86}_{-0.66}^{+0.53}$ K
G060.881−00.135 GBT 0.1229 ± 0.0010 21.2 ± 0.2 7463 ± 77 ${4.06}_{-0.09}^{+0.08}$ ${7.66}_{-0.22}^{+0.31}$ K
G061.473+00.094 GBT 0.0846 ± 0.0004 26.0 ± 0.1 8857 ± 43 ${3.99}_{-0.09}^{+0.07}$ ${7.52}_{-0.22}^{+0.19}$ K
G061.720+00.863 VLA 0.0777 ± 0.0076 25.9 ± 3.3 9170 ± 1282 P N ${13.96}_{-1.11}^{+0.96}$ ${12.38}_{-0.91}^{+0.85}$ K
G062.577+02.389 VLA 0.0766 ± 0.0079 22.0 ± 2.7 10626 ± 1470 T Y ${13.97}_{-1.12}^{+0.96}$ ${12.57}_{-0.92}^{+0.79}$ K
G063.164+00.449 GBT 0.0994 ± 0.0011 25.1 ± 0.1 7760 ± 90 ${3.76}_{-0.07}^{+0.08}$ ${7.78}_{-0.25}^{+0.25}$ K
G064.130−00.475 GBT 0.0973 ± 0.0005 23.9 ± 0.1 8452 ± 58 ${3.64}_{-0.07}^{+0.08}$ ${7.66}_{-0.21}^{+0.19}$ K
G068.144+00.915 GBT 0.0697 ± 0.0009 24.7 ± 0.3 10834 ± 207 ${11.92}_{-0.98}^{+0.90}$ ${11.53}_{-0.53}^{+0.88}$ K
G069.922+01.511 GBT 0.0712 ± 0.0003 27.0 ± 0.1 9703 ± 50 ${11.56}_{-1.04}^{+0.88}$ ${11.69}_{-0.79}^{+0.61}$ K
G070.280+01.583 VLA 0.0901 ± 0.0009 25.3 ± 0.3 8214 ± 109 T Y ${7.92}_{-0.63}^{+0.78}$ ${9.37}_{-0.41}^{+0.41}$ K
G070.293+01.599 GBT 0.0505 ± 0.0005 37.0 ± 0.2 10297 ± 121 ${7.96}_{-0.69}^{+0.69}$ ${9.36}_{-0.37}^{+0.43}$ K
G070.304+01.595 VLA 0.0992 ± 0.0017 23.4 ± 0.4 8211 ± 182 T N ${7.36}_{-0.71}^{+0.65}$ ${8.95}_{-0.26}^{+0.48}$ K
G070.329+01.589 VLA 0.0745 ± 0.0012 30.6 ± 0.5 8244 ± 170 T N ${7.35}_{-0.69}^{+0.69}$ ${9.03}_{-0.35}^{+0.40}$ K
G070.765+01.820 VLA 0.0896 ± 0.0105 24.9 ± 3.4 8412 ± 1317 T N ${12.68}_{-1.19}^{+1.02}$ ${12.65}_{-0.90}^{+0.83}$ K
G071.150+00.397 VLA 0.1035 ± 0.0016 24.2 ± 0.4 7551 ± 147 P Y ${6.56}_{-0.58}^{+0.81}$ ${8.85}_{-0.39}^{+0.30}$ K
G073.878+01.023 VLA 0.0744 ± 0.0037 30.8 ± 1.8 8177 ± 545 T N ${9.10}_{-0.63}^{+1.03}$ ${10.52}_{-0.46}^{+0.66}$ K
G074.155+01.646 VLA 0.1929 ± 0.0238 15.9 ± 2.0 6327 ± 980 P Y ${7.68}_{-0.75}^{+0.75}$ ${9.68}_{-0.46}^{+0.46}$ K
G074.753+00.912 VLA 0.0923 ± 0.0056 27.9 ± 1.9 7386 ± 592 T N ${9.03}_{-0.80}^{+0.86}$ ${10.52}_{-0.53}^{+0.61}$ K
G075.768+00.344 VLA 0.0900 ± 0.0005 27.0 ± 0.2 7743 ± 57 T Y ${3.49}_{-0.28}^{+0.28}$ ${8.20}_{-0.05}^{+0.05}$ P A11
G075.842+00.404 GBT 0.0751 ± 0.0003 30.5 ± 0.1 8363 ± 32 ${3.73}_{-0.39}^{+0.52}$ ${8.26}_{-0.08}^{+0.11}$ P R12
G076.155−00.286 GBT 0.0651 ± 0.0005 30.9 ± 0.2 9498 ± 119 ${7.13}_{-0.72}^{+0.72}$ ${9.66}_{-0.51}^{+0.36}$ K
G076.384−00.621 GBT 0.0407 ± 0.0002 42.0 ± 0.2 11245 ± 92 ${1.28}_{-0.08}^{+0.11}$ ${8.13}_{-0.01}^{+0.01}$ P X13
G078.032+00.606 GBT 0.0832 ± 0.0005 27.2 ± 0.2 8567 ± 86 ${1.51}_{-0.09}^{+0.07}$ ${8.16}_{-0.00}^{+0.00}$ P R12
G078.147+01.820 GBT 0.0910 ± 0.0008 24.6 ± 0.2 8596 ± 107 ${1.51}_{-0.10}^{+0.07}$ ${8.16}_{-0.00}^{+0.00}$ P R12
G078.886+00.709 VLA 0.1525 ± 0.0048 19.5 ± 0.7 6530 ± 260 T N ${3.31}_{-0.27}^{+0.29}$ ${8.35}_{-0.05}^{+0.06}$ P R12
G079.270+02.488 GBT 0.1161 ± 0.0021 20.8 ± 0.6 7977 ± 222 ${1.50}_{-0.09}^{+0.08}$ ${8.20}_{-0.00}^{+0.00}$ P R12
G079.293+01.296 GBT 0.0729 ± 0.0007 30.0 ± 0.1 8693 ± 86 ${7.22}_{-0.80}^{+0.85}$ ${9.90}_{-0.42}^{+0.55}$ K
G080.350+00.718 GBT 0.0699 ± 0.0007 26.5 ± 0.3 10250 ± 155 ${9.31}_{-0.89}^{+1.03}$ ${11.46}_{-0.68}^{+0.68}$ K
G080.362+01.212 GBT 0.1058 ± 0.0030 23.0 ± 0.7 7921 ± 294 ${1.62}_{-0.08}^{+0.06}$ ${8.21}_{-0.00}^{+0.00}$ P R12
G080.938−00.129 GBT 0.0774 ± 0.0004 28.7 ± 0.1 8853 ± 62 ${1.49}_{-0.07}^{+0.09}$ ${8.24}_{-0.00}^{+0.00}$ P R12
G081.681+00.540 GBT 0.0608 ± 0.0002 35.9 ± 0.1 8829 ± 36 ${1.49}_{-0.08}^{+0.09}$ ${8.26}_{-0.00}^{+0.00}$ P R12
G082.566+00.362 GBT 0.1038 ± 0.0011 23.4 ± 0.2 8030 ± 128 ${1.49}_{-0.06}^{+0.10}$ ${8.28}_{-0.00}^{+0.00}$ P R12
G083.792+03.269 GBT 0.0943 ± 0.0012 23.1 ± 0.3 8643 ± 184 ${1.49}_{-0.08}^{+0.09}$ ${8.31}_{-0.01}^{+0.01}$ P R12
G085.241+00.021 GBT 0.0799 ± 0.0011 26.9 ± 0.3 8824 ± 177 ${5.93}_{-0.86}^{+0.70}$ ${9.76}_{-0.44}^{+0.44}$ K
G092.920+02.823 140 Foot 0.1308 ± 0.0028 24.8 ± 0.5 10840 ± 270 ${7.08}_{-0.89}^{+1.03}$ ${11.31}_{-0.69}^{+0.65}$ K
G096.289+02.593 VLA 0.0634 ± 0.0022 28.3 ± 1.1 10169 ± 464 T Y ${10.13}_{-1.22}^{+1.53}$ ${13.76}_{-0.87}^{+1.31}$ K
G096.434+01.324 VLA 0.1125 ± 0.0085 21.8 ± 1.8 7745 ± 762 T N ${8.50}_{-1.40}^{+0.70}$ ${12.44}_{-0.95}^{+0.65}$ K
G097.515+03.173 VLA 0.0711 ± 0.0017 28.2 ± 0.7 9226 ± 281 T Y ${7.27}_{-0.82}^{+1.10}$ ${11.78}_{-0.64}^{+0.78}$ P H15
G097.528+03.184 VLA 0.1029 ± 0.0060 24.1 ± 1.6 7726 ± 584 T N ${7.26}_{-0.89}^{+1.12}$ ${11.76}_{-0.63}^{+0.81}$ P H15
G101.016+02.590 VLA 0.1510 ± 0.0218 16.8 ± 2.7 7600 ± 1434 T N ${6.87}_{-0.89}^{+1.09}$ ${11.80}_{-0.69}^{+0.79}$ K
G108.191+00.586 GBT 0.0759 ± 0.0004 25.8 ± 0.1 9590 ± 59 ${4.25}_{-0.46}^{+0.62}$ ${10.48}_{-0.33}^{+0.40}$ P C14
G108.375−01.056 GBT 0.0806 ± 0.0009 26.1 ± 0.3 8992 ± 131 ${5.01}_{-0.88}^{+0.77}$ ${10.98}_{-0.59}^{+0.64}$ K
G108.764−00.952 GBT 0.0706 ± 0.0004 29.6 ± 0.2 9404 ± 81 ${4.54}_{-0.74}^{+0.86}$ ${10.61}_{-0.43}^{+0.71}$ K
G109.104−00.347 VLA 0.1998 ± 0.0222 25.7 ± 2.9 4061 ± 554 T N ${4.05}_{-0.85}^{+0.69}$ ${10.31}_{-0.49}^{+0.57}$ K
G110.099+00.042 GBT 0.0543 ± 0.0003 38.0 ± 0.2 9240 ± 75 ${4.56}_{-0.82}^{+0.76}$ ${10.75}_{-0.58}^{+0.58}$ K
G111.558+00.804 GBT 0.0829 ± 0.0005 27.1 ± 0.1 8483 ± 51 ${2.62}_{-0.10}^{+0.15}$ ${9.62}_{-0.06}^{+0.09}$ P M09
G111.612+00.371 GBT 0.0885 ± 0.0005 26.8 ± 0.1 8428 ± 68 ${5.99}_{-1.04}^{+0.85}$ ${11.92}_{-0.79}^{+0.68}$ K
G112.212+00.229 GBT 0.0777 ± 0.0008 28.8 ± 0.2 8641 ± 118 ${3.62}_{-0.60}^{+0.93}$ ${10.28}_{-0.44}^{+0.66}$ K
G115.785−01.561 GBT 0.0806 ± 0.0017 26.8 ± 0.6 8794 ± 242 ${3.56}_{-0.68}^{+0.79}$ ${10.40}_{-0.50}^{+0.59}$ K
G118.345+04.856 140 Foot 0.0911 ± 0.0193 20.7 ± 0.3 9540 ± 1050 ${0.56}_{-0.42}^{+0.53}$ ${8.66}_{-0.28}^{+0.32}$ K
G124.637+02.535 VLA 0.0659 ± 0.0011 30.5 ± 0.6 9181 ± 198 P N ${7.31}_{-1.47}^{+0.90}$ ${13.44}_{-0.86}^{+1.22}$ K
G124.894+00.323 GBT 0.0781 ± 0.0031 27.0 ± 1.2 8975 ± 460 ${3.22}_{-0.65}^{+0.71}$ ${10.50}_{-0.47}^{+0.65}$ K
G128.772+02.009 GBT 0.0854 ± 0.0028 20.9 ± 0.7 10361 ± 427 ${8.51}_{-1.14}^{+1.82}$ ${15.14}_{-1.09}^{+1.64}$ K
G132.156−00.729 GBT 0.0769 ± 0.0006 24.9 ± 0.2 9785 ± 123 ${4.83}_{-0.90}^{+0.96}$ ${12.09}_{-0.74}^{+0.86}$ K
G133.712+01.221 GBT 0.0760 ± 0.0003 27.7 ± 0.0 8977 ± 38 ${1.95}_{-0.04}^{+0.04}$ ${9.79}_{-0.03}^{+0.03}$ P X06;H06
G133.781+01.428 GBT 0.0785 ± 0.0005 27.5 ± 0.1 8752 ± 74 ${1.94}_{-0.03}^{+0.05}$ ${9.79}_{-0.02}^{+0.04}$ P X06;H06
G135.188+02.701 VLA 0.1347 ± 0.0204 19.9 ± 3.3 7259 ± 1414 P Y ${7.37}_{-1.26}^{+1.36}$ ${14.52}_{-1.18}^{+1.27}$ K
G136.884+00.911 GBT 0.0995 ± 0.0025 23.5 ± 0.6 8204 ± 257 ${1.95}_{-0.04}^{+0.04}$ ${9.86}_{-0.03}^{+0.03}$ P X06;H06
G138.494+01.634 GBT 0.0969 ± 0.0014 23.8 ± 0.3 8302 ± 131 ${2.87}_{-0.58}^{+0.72}$ ${10.75}_{-0.61}^{+0.56}$ K
G141.084−01.063 VLA 0.1400 ± 0.0203 18.8 ± 3.2 7300 ± 1431 T Y ${1.99}_{-0.49}^{+0.61}$ ${10.04}_{-0.57}^{+0.46}$ K
G150.596−00.955 GBT 0.0671 ± 0.0005 27.8 ± 0.1 10016 ± 83 ${2.74}_{-0.65}^{+0.56}$ ${10.77}_{-0.63}^{+0.59}$ K
G151.609−00.233 GBT 0.0543 ± 0.0004 31.7 ± 0.2 10795 ± 98 ${7.00}_{-1.25}^{+1.44}$ ${14.75}_{-1.10}^{+1.56}$ K
G154.646+02.438 GBT 0.0673 ± 0.0009 28.6 ± 0.4 9734 ± 175 ${4.39}_{-0.79}^{+1.05}$ ${12.33}_{-0.67}^{+1.17}$ K
G155.372+02.613 GBT 0.0703 ± 0.0013 25.6 ± 0.5 10253 ± 309 ${6.65}_{-1.26}^{+1.36}$ ${14.76}_{-1.30}^{+1.30}$ K
G169.180−00.905 GBT 0.0872 ± 0.0013 23.1 ± 0.4 9345 ± 179 d d K
G173.599+02.803 GBT 0.1060 ± 0.0013 20.9 ± 0.3 8612 ± 137 d d K
G173.937+00.298 GBT 0.0935 ± 0.0014 23.0 ± 0.3 8829 ± 158 d d K
G192.638−00.008 GBT 0.0971 ± 0.0010 22.1 ± 0.2 8833 ± 107 ${1.58}_{-0.06}^{+0.08}$ ${9.89}_{-0.06}^{+0.08}$ P R10
G196.448−01.673 VLA 0.0928 ± 0.0035 22.6 ± 0.9 8884 ± 435 T Y ${5.23}_{-0.33}^{+0.41}$ ${13.44}_{-0.32}^{+0.40}$ P H07
G209.037−19.377 GBT 0.0878 ± 0.0007 26.1 ± 0.0 8322 ± 55 ${0.41}_{-0.00}^{+0.01}$ ${8.70}_{-0.00}^{+0.01}$ P S07;M07;K08
G213.076−02.213 GBT 0.0564 ± 0.0006 28.6 ± 0.3 11343 ± 162 ${6.58}_{-1.27}^{+1.27}$ ${14.27}_{-1.15}^{+1.23}$ K
G213.703−12.601 GBT 0.0750 ± 0.0004 29.8 ± 0.1 8986 ± 65 ${0.80}_{-0.34}^{+0.42}$ ${9.01}_{-0.33}^{+0.42}$ K
G218.737+01.850 GBT 0.0702 ± 0.0007 24.6 ± 0.3 10671 ± 143 ${5.39}_{-1.11}^{+0.89}$ ${12.99}_{-1.00}^{+0.86}$ K
G220.524−02.759 GBT 0.0473 ± 0.0021 31.8 ± 1.7 12037 ± 725 ${7.62}_{-1.35}^{+1.47}$ ${14.92}_{-1.31}^{+1.42}$ K
G225.470−02.587 GBT 0.1141 ± 0.0020 22.6 ± 0.4 7537 ± 158 ${0.09}_{-0.08}^{+0.43}$ ${8.56}_{-0.24}^{+0.28}$ K
G227.760−00.127 GBT 0.0485 ± 0.0007 28.9 ± 0.4 12495 ± 249 ${4.33}_{-0.84}^{+0.84}$ ${11.73}_{-0.72}^{+0.72}$ K
G231.481−04.401 GBT 0.1011 ± 0.0024 20.5 ± 0.6 9098 ± 286 ${4.49}_{-0.85}^{+0.79}$ ${11.60}_{-0.68}^{+0.73}$ K
G233.753−00.193 GBT 0.0822 ± 0.0015 24.1 ± 0.4 9482 ± 209 ${2.68}_{-0.63}^{+0.67}$ ${10.13}_{-0.46}^{+0.54}$ K
G243.244+00.406 GBT 0.0793 ± 0.0014 22.3 ± 0.2 10477 ± 214 ${4.09}_{-0.60}^{+0.98}$ ${10.84}_{-0.52}^{+0.73}$ K
G345.284+01.463 140 Foot 0.0891 ± 0.0006 24.1 ± 0.2 8530 ± 640 d d K
G345.410−00.953 140 Foot 0.1036 ± 0.0004 26.3 ± 0.1 6960 ± 50 d d K
G348.249−00.971 140 Foot 0.0918 ± 0.0005 28.2 ± 0.2 6610 ± 100 d d K
G348.710−01.044 140 Foot 0.1067 ± 0.0008 24.6 ± 0.2 7150 ± 90 ${3.32}_{-0.27}^{+0.34}$ ${5.12}_{-0.32}^{+0.25}$ P W12
G351.130+00.449 140 Foot 0.1272 ± 0.0015 22.1 ± 0.2 6650 ± 70 d d K
G351.170+00.704 140 Foot 0.1283 ± 0.0009 25.9 ± 0.1 5610 ± 20 d d K
G351.246+00.673 VLA 0.1131 ± 0.0003 25.1 ± 0.1 6772 ± 24 T Y ${1.31}_{-0.12}^{+0.15}$ ${7.05}_{-0.15}^{+0.12}$ P W14
G351.311+00.663 VLA 0.1301 ± 0.0004 24.1 ± 0.1 6230 ± 27 T Y ${1.32}_{-0.12}^{+0.16}$ ${7.04}_{-0.15}^{+0.12}$ P W14
G351.367+00.640 140 Foot 0.1151 ± 0.0012 23.9 ± 0.1 6840 ± 40 ${1.31}_{-0.12}^{+0.16}$ ${7.05}_{-0.17}^{+0.11}$ P W14
G351.472−00.458 140 Foot 0.1067 ± 0.0012 23.3 ± 0.5 7460 ± 120 d d K
G351.646−01.252 140 Foot 0.0848 ± 0.0005 28.1 ± 0.1 7620 ± 30 d d K
G351.688−01.169 140 Foot 0.1029 ± 0.0006 23.6 ± 0.1 7560 ± 90 d d K
G352.597−00.188 140 Foot 0.1172 ± 0.0025 20.9 ± 0.9 7560 ± 240 d d K
G353.038+00.581 140 Foot 0.1040 ± 0.0012 28.6 ± 0.1 6250 ± 30 d d K
G353.092+00.857 140 Foot 0.2296 ± 0.0024 28.7 ± 0.1 5630 ± 40 d d K
G353.195+00.910 140 Foot 0.0826 ± 0.0006 30.8 ± 0.2 7100 ± 40 d d K
G353.408−00.381 140 Foot 0.0912 ± 0.0008 24.0 ± 0.2 8480 ± 60 d d K

Notes.

a"P" if measured at the location of peak continuum brightness; "T" if measured within the watershed segmentation region b"N" if non-tapered image measurement; "Y" if uv-tapered image measurement c"K" for Monte Carlo kinematic distance; "P" for parallax distance dKinematic distances are unreliable in the direction of the Galactic center and anti-center

References. A11, Ando et al. (2011); B09, Brunthaler et al. (2009); C14, Choi et al. (2014); H06, Hachisuka et al. (2006); H07, Honma et al. (2007); H15, Hachisuka et al. (2015); I13, Immer et al. (2013); K08, Kim et al. (2008); M07, Menten et al. (2007); M09, Moscadelli et al. (2009); O10, Oh et al. (2010); RD09, Roman-Duval et al. (2009); R09a, Reid et al. (2009a); R09c, Reid et al. (2009b); R10, Rygl et al. (2010); R12, Rygl et al. (2012); S07, Sandstrom et al. (2007); S10, Sato et al. (2010); S14, Sato et al. (2014); Sa14, Sanna et al. (2014); U12, Urquhart et al. (2012); W12, Wu et al. (2012); W14, Wu et al. (2014); X06, Xu et al. (2006); X11, Xu et al. (2011); X13, Xu et al. (2013); Z09, Zhang et al. (2009); Z13, Zhang et al. (2013); Z14, Zhang et al. (2014).

Download table as:  ASCIITypeset images: 1 2 3 4 5

In total, there are now 189 Galactic H ii regions with accurate electron temperature determinations. This is an increase of 99 nebulae (110%) over the B15 sample. A fraction of these nebulae have inaccurate distances, however, and cannot be used to investigate Galactic metallicity structure.

5.3. Comparison with Single Dish

Our sample combines measurements from three telescopes: the 140 Foot, the GBT, and the VLA. Each of these telescopes may be affected by systematics that lead to discrepancies between the derived electron temperatures because each is sampling a different volume of gas within and surrounding the H ii regions. For example, diffuse foreground and background emission may affect the single-dish observations, but such extended emission is filtered out by the VLA. In principle, there may be differences between the different single-dish measurements as well. Balser et al. (2011) find no significant difference between the derived electron temperatures for 16 nebulae observed by both the 140 Foot and the GBT. Here we compare the single-dish and VLA observations of 22 nebulae in common between the B15 single-dish catalog and our VLA catalog.

We first compare the fitted LSR velocity of these nebulae. The top panel of Figure 4 shows the difference between the single-dish RRL LSR velocity and that measured by the VLA for the 22 nebulae observed by the VLA and either the GBT or the 140 Foot. Here and in all subsequent analyses, we use the "best" combination of non-tapered or uv-tapered data cubes and continuum peak brightness location or watershed region for spectral extraction. "Best" means the combination of tapering and spectral extraction technique that minimizes the fractional uncertainty in the derived electron temperature. The single-dish and VLA LSR velocities are in good agreement, with a weighted mean difference of −0.09 ± 0.34 km s−1 (the error here is the uncertainty of the mean), a median difference of −1.28 km s−1, and a standard deviation of 1.59 km s−1. Throughout these analyses, we use the reciprocal variances of the fitted Gaussian parameters as the weights in the averages.

Figure 4.

Figure 4. Difference between single-dish and VLA RRL LSR velocities (top) and ratio of single-dish to VLA RRL FWHM line widths (bottom) as a function of the VLA values for 22 nebulae also observed by the GBT (squares) or 140 Foot (circles). We use the "best" VLA images and spectral extraction technique, which minimizes the fractional uncertainty of the derived electron temperature. The weighted mean LSR velocity difference is −0.09 ± 0.34 km s−1 and the weighted mean FWHM line width ratio is 0.99 ± 0.02, where the weights are the reciprocal variances in the differences or ratios derived from the fitted Gaussian parameter uncertainties.

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Next, we compare the single-dish and VLA RRL FWHMs. The bottom panel of Figure 4 shows the ratio of the single-dish RRL line width to that measured by the VLA for the overlapping nebulae. The weighted mean of the line width ratios is 0.99 ± 0.02, the median ratio is 1.03, and the standard deviation is 0.10. For the narrowest RRLs, the VLA line widths are ∼5%–10% smaller than those measured by the single-dish telescopes. This trend is likely due to the fact that the VLA is probing a denser and less turbulent component of the nebulae.

Finally, we compare the measured RRL-to-continuum brightness ratios and derived electron temperatures between the single-dish and VLA surveys. Figure 5 shows the ratio of the single-dish and VLA measured RRL-to-continuum flux ratios (top) and electron temperatures (bottom). The single-dish RRL-to-continuum brightness ratios are systematically ∼10% less than the VLA brightness ratios. The weighted mean of these ratios is 0.86 ± 0.03 with a median of 0.90 and a standard deviation of 0.12. Consequently, the single-dish electron temperatures are ∼10% greater than the VLA electron temperatures. The weighted mean of the electron temperature ratios is 1.12 ± 0.03 with a median of 1.10 and a standard deviation of 0.12.

Figure 5.

Figure 5. Ratio of single-dish to VLA RRL-to-continuum brightness ratios (top) and electron temperatures (bottom) as a function of the VLA values for the same nebulae as in Figure 4. The weighted mean ratio of the single-dish and VLA RRL-to-continuum brightness ratios is 0.86 ± 0.03 and the weighted mean electron temperature ratio is 1.12 ± 0.03, where the weights are the reciprocal variances in the ratios derived from the fitted Gaussian parameter uncertainties.

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The cause of the systematic difference between the single-dish and VLA RRL-to-continuum brightness ratios and electron temperatures is unclear. The difference may be due to a problem with the derivation of the RRL-to-continuum brightness ratio or perhaps due to a fundamental difference in the RRL and/or continuum emission measured by the different telescopes. We know that there are a few issues with how the single-dish RRL-to-continuum ratios are derived. B15 measured the continuum flux densities of their nebulae at νC = 8556 MHz, whereas the average frequency of their observed RRL transitions is $\langle {\nu }_{L}\rangle =8902\,\mathrm{MHz}$. In the Appendix, we show that the B15 strategy overestimates the true electron temperature by ∼6%. Furthermore, we do not scale the single-dish and VLA RRL-to-continuum brightness ratios to a common frequency because each survey observed similar RRL transitions. The typical VLA $\langle \mathrm{Hn}\alpha \rangle $ weighted frequency is within 2% of the B15 average RRL frequency. Neither of these two effects can fully explain the observed 10% difference between the single-dish and VLA RRL-to-continuum brightness ratios.

There are several factors that might affect the measured continuum and/or RRL flux densities: the single-dish continuum flux densities are uncertain due to poor continuum background subtraction; the single-dish telescopes are not pointed at the center of the continuum source during the RRL observation; the VLA is not sensitive to extended emission associated with the H ii region; and/or the VLA is seeing more optically thick gas. (1) The continuum flux densities are the largest source of uncertainty in the single-dish electron temperature derivation (see B15). If the continuum background level is poorly constrained, then the single-dish continuum flux densities will be inaccurate. We limit our analysis to high-continuum QF single-dish nebulae, however, so these problems should be minimal. Furthermore, random errors in the single-dish continuum background levels would not cause the observed systematic difference in single-dish versus interferometric electron temperatures. (2) The single-dish RRL spectra must be measured at the location of the peak continuum brightness. If the telescope is not pointed properly, then the RRL flux densities will be underestimated. This is also not a likely explanation for the discrepancy because B15 peaked on source for their RRL observations. (3) The VLA is not sensitive to diffuse emission. If the source of such emission has a different density and/or temperature, the VLA electron temperatures will differ from the single-dish values. (4) Finally, the nebulae may be optically thick, and/or the compact emission visible to the VLA is more optically thick than the diffuse emission missed by the VLA. Optical depth effects such as these would lead to an underestimation of the VLA continuum flux densities and electron temperatures. Some or all of these issues may be contributing to the remaining 4% discrepancy between the single-dish and VLA RRL-to-continuum brightness ratios.

We wish to use as much data as possible to constrain the metallicity structure of the Galactic disk. Therefore, in subsequent analyses that combine the single-dish and VLA electron temperatures, we multiply the single-dish electron temperatures by 0.9 to accommodate the systematic offset between the VLA and single-dish data.

5.4. Distances

Distances to Galactic H ii regions are derived in three main ways: (1) spectrophotometrically, (2) geometrically, and (3) kinematically. Spectrophotometric distances are only available for optically unobscured nebulae. Since most of the nebulae in our sample are very distant with lines of sight passing through the Galactic plane, we do not consider spectrophotometric distances in this analysis. The extremely fine angular resolution provided by very long baseline interferometry (VLBI) is used to measure the parallaxes and proper motions of masers associated with high-mass star-forming regions (e.g., Reid & Honma 2014). Several hundred maser parallax measurements have been made as part of the Bar and Spiral Structure Legacy (BeSSeL) Survey,8 the Japanese VLBI Exploration of Radio Astrometry (VERA),9 and various European VLBI Network (EVN)10 projects. The vast majority of Galactic H ii regions, however, lack parallax measurements. We must therefore rely on kinematic techniques to derive the distances to nebulae without a geometric distance determination.

Of the 189 Galactic H ii regions in our sample with accurate electron temperature determinations, 46 (24%) have a maser parallax measurement. As in Wenger et al. (2018), we derive the parallax distance and distance uncertainties by Monte Carlo resampling the measured parallax within its uncertainties. We generate 5000 samples of the parallax distance, then we fit a kernel density estimator (KDE) to the distance distribution to calculate a probability distribution function (PDF). The peak of the PDF is the derived parallax distance, and the width of the PDF characterizes the parallax distance uncertainty (see Wenger et al. 2018).

Kinematic distances are computed by measuring the line-of-sight velocity of an object and assuming that object follows some Galactic rotation model (GRM). We use the Wenger et al. (2018) Monte Carlo kinematic distance method and the Reid et al. (2014) GRM to derive the kinematic distances to our sample of Galactic H ii regions. This method computes the distances and distance uncertainties by resampling the observed LSR velocities, the solar motion parameters, which define the LSR, and the GRM parameters to determine the kinematic distance PDFs. Wenger et al. (2018) find that the Monte Carlo kinematic distances are reasonably accurate when compared to the parallax distances for a sample of 75 Galactic high-mass star-forming regions. The median difference between the kinematic and parallax distances for these nebulae is 17% (0.42 kpc).

Within the Solar circle, there exists a kinematic distance ambiguity (KDA). An axisymmetric GRM yields the same LSR velocity at two distances, and additional information must be used to break this degeneracy. The WISE Catalog lists the KDA resolutions (KDAR) for a subset of the known Galactic H ii regions. As in Wenger et al. (2018), we use the WISE Catalog KDARs for nebulae with LSR velocities farther than 20 km s−1 from the tangent point velocity. All nebulae within 20 km s−1 of the tangent point velocity are assigned to the tangent point distance.

Due to line-of-sight velocity crowding, kinematic distances are inaccurate in the direction of the Galactic center and anti-center. Following Wenger et al. (2018), we remove all kinematic distance nebulae located within the zones −15° <  < 15° and 160° <  < 200°. After removing these nebulae, we are left with 121 Galactic H ii regions with kinematic distances. Our final catalog contains 167 nebulae with accurate electron temperatures and either a parallax (46) or kinematic (121) distance. Table 6 lists the relevant distance parameters for each nebulae: the heliocentric distance d; the Galactocentric radius, R; the distance method ("P" for parallax and "K" for kinematic); and the maser parallax observation reference, if any. Nebulae with accurate electron temperatures, without a parallax measurement, and in the direction of the Galactic center/anti-center are also included in this table for completeness. These nebulae are, however, excluded from all subsequent analyses.

5.5. Metallicity Structure

H ii region electron temperatures are a proxy for their nebular metallicities (e.g., Churchwell & Walmsley 1975). The H ii region electron temperature structure across the Galactic disk thus reveals structure in metallicity. Shaver et al. (1983) derived an empirical relationship between H ii region metallicities, determined using optical collisionally excited lines to derive the oxygen and hydrogen column densities, and electron temperatures, determined from RRLs:

Equation (8)

where Te is the nebular electron temperature.

We begin our investigation of Galactic chemical structure by measuring the radial electron temperature and metallicity gradients. Figure 6 shows the nebular electron temperature and metallicity gradients using the electron temperatures and Galactocentric radii from Table 6 and metallicities derived using Equation (8). The metallicity uncertainties are determined by propagating the electron temperature uncertainties through Equation (8). We use a robust least-squares routine to fit a linear model to both distributions. The least-squares fit is robust because we dampen the effect of outliers by minimizing a "soft" loss function, $\rho (z)=\sqrt{1+{z}^{2}}-1$, where z is the squared residuals. This routine does not consider the uncertainties of the data because (1) there are uncertainties in both the dependent and independent variables and (2) the Galactocentric radius uncertainties are asymmetric. Nonetheless, the best-fit linear model to the nebular electron temperature distribution is Te/K = (4345 ± 68) + (374 ± 12)R/kpc, and the best fit for the nebular metallicity distribution is 12+log10(O/H) = (9.148 ± 0.038) − (0.054 ± 0.004)R/kpc. Within the errors, these gradients are consistent with the gradients found by B15 using their "best" distances and Green Bank sample: Te/K ∝ (402 ± 33)R/kpc and 12 + log10(O/H) ∝ (−0.058 ± 0.004)R/kpc.

Figure 6.

Figure 6. The nominal radial electron temperature (top) and metallicity (bottom) gradients. The abscissa error bars are the 1σ uncertainties in the parallax or kinematic distances derived from our Monte Carlo distance analysis, and the ordinate error bars are the 1σ uncertainties in the electron temperature or metallicity derived from the continuum and RRL uncertainties. The lines are the robust least-squares linear model fits to the data as defined in the legends.

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A simple least-squares fitting method cannot account for asymmetric uncertainties in both the abscissas (i.e., Galactocentric radii) and the ordinates (i.e., electron temperatures). Therefore, we estimate the true variance of the linear model by Monte Carlo resampling the data 1000 times. The electron temperatures are drawn from a Gaussian distribution centered at the derived electron temperature and with a width equal to the derived electron temperature uncertainty. The Galactocentric radii are drawn from the parallax or kinematic distance PDFs. For each realization of the data, we fit a robust least-squares linear model. Similar to the Monte Carlo kinematic distance method in Wenger et al. (2018), we estimate the most likely linear model parameters by fitting a KDE to the PDFs of each model parameter. The peak of this KDE is the most likely parameter, and the 1σ confidence interval is derived from the bounds of the PDF such that (1) the PDF evaluated at the lower bound is equal to the PDF evaluated at the upper bound and (2) the integral of the normalized PDF between the bounds is 68.3%. Figures 7 and 8 show, respectively, the most likely linear model parameters derived from this Monte Carlo method and the covariance between the model parameters for the electron temperature and metallicity gradients. The most likely fits are ${T}_{e}/{\rm{K}}={4493}_{-188}^{+156}+{359}_{-18}^{+22}\,R/{\rm{kpc}}$ and $12+{{\rm{log}}}_{10}({\rm{O}}/{\rm{H}})={9.130}_{-0.030}^{+0.034}-{0.052}_{-0.004}^{+0.004}\,R/{\rm{kpc}}$. These gradients are within 1σ of the nominal least-squares values, and the asymmetric uncertainties are more accurate given the uncertainties in the derived electron temperatures and distances.

Figure 7.

Figure 7. The most likely electron temperature gradient determined by Monte Carlo resampling the derived electron temperatures and Galactocentric radii. The top panel shows the data and the most likely linear model (black line) as defined in the legend. The error bars are the same as in Figure 6. The shaded region represents the range of fits from 1000 Monte Carlo realizations of the data. The bottom panel shows the covariances between the linear model parameters (slope, with units of K kpc−1, and intercept, with units of K). The histograms are the PDFs of the Monte Carlo fit parameters, and the black curves are KDE fits to the PDFs. The solid lines are the peaks of the PDFs (the most likely fit parameters), and the dotted lines represent the 1σ confidence intervals. The dashed lines are the nominal values of the fit parameters derived from the robust least-squares fit to the data (i.e., without Monte Carlo resampling, as in Figure 6).

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Figure 8.

Figure 8. Same as Figure 7 for the radial metallicity gradient. The most likely linear model is defined in the legend. The covariance slope has units of dex kpc−1 and the intercept has units of dex.

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To visualize the variations in nebular electron temperature in the Galactic disk, we use kriging to spatially interpolate between discrete nebulae (see also B15). The kriging method computes the average semivariance of the data as a function of the spatial separation between the data points. The average semivariance is measured in many separation bins, known as "lags," and the semivariogram (average semivariance as a function of lag) is fitted with a model. The expected value of the data at any position is derived from this semivariogram model (see Feigelson & Babu 2012).

We compute the nominal kriging map of nebular electron temperatures using the Table 6 electron temperatures and distances. Figure 9 shows this electron temperature map, where we use a linear semivariogram model to interpolate between the discrete H ii region positions. The top panel is the kriging result and the bottom panel is the standard deviation of the kriging interpolation. This standard deviation map characterizes the intrinsic scatter of the data across the Galactic disk. The H ii region points are colored by their electron temperature to highlight the differences between the actual nebular electron temperature and the interpolated value at that position. Figure 10 shows the same kriging results with a linear semivariogram model for the H ii region metallicities. Qualitatively, these figures are similar to the electron temperature and metallicity maps in B15. It is clear from these figures that the radial gradients have a strong dependence on Galactocentric azimuth.

Figure 9.

Figure 9. Kriging map of nebular electron temperatures. The top panel shows the kriging interpolation in a face-on view of the Galactic disk. The points are the H ii regions in our sample, colored by their derived electron temperatures. The bottom panel shows the kriging standard deviation. The Galactic Center is located at the origin and the Sun is located at the red cross. The dashed circles are 4, 8, 12, 16, and 20 kpc in radius. White areas are outside R = 20 kpc or have data values beyond the range shown on the color bar.

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Figure 10.

Figure 10. Same as Figure 9 for the nebular metallicities.

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These kriging results consider neither the uncertainties in the nebular electron temperatures and metallicities nor the H ii region distance uncertainties. We estimate the most likely kriging map of nebular electron temperatures and metallicities using a Monte Carlo technique in the same way as we determined the most likely radial gradients. We Monte Carlo resample the data within their uncertainties 1000 times, and, for each realization of the data, we generate a kriging map. At each pixel of the kriging map, we construct a PDF of the interpolation values, fit a KDE, and locate the peak and bounds of the KDE. The peak is the most likely kriging value at that position, and the bounds represent the 1σ confidence interval, as before.

Figures 11 and 12 show the most likely kriging interpolation map, most likely standard deviation map, and the upper and lower 1σ confidence interval bound maps for the nebular electron temperatures and metallicities, respectively. The qualitative structure in the Monte Carlo kriging interpolation maps is similar to that in the nominal kriging maps, though the 1σ confidence interval bound maps reveal where the kriging interpolation is ill constrained. For most of the Galactic disk, the most likely kriging values have 1σ bounds ≲500 K in electron temperature and ≲0.8 dex in metallicity. These uncertainties are significantly less than the most likely kriging standard deviations of ∼1000 K and ∼0.25 dex, which suggests that the intrinsic scatter in the nebular electron temperatures and metallicities exceeds the formal uncertainties.

Figure 11.

Figure 11. Most likely kriging map of nebular electron temperatures determined by Monte Carlo resampling the derived electron temperatures and distances. Shown are the most likely kriging interpolation values (top left), most likely kriging standard deviation values (top right), lower 1σ bounds (bottom left), and upper 1σ bounds (bottom right) on the kriging interpolation confidence intervals. The features in each plot are the same as in Figure 9.

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Figure 12.

Figure 12. Same as Figure 11 for the nebular metallicities.

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6. Discussion

The radial gradient is the most prominent feature in the metallicity structure of the Galactic disk. Our Monte Carlo analysis of nebular metallicities results in a most likely H ii region oxygen gradient of −0.052 ± 0.004 dex kpc−1. Mollá et al. (2019a) list the oxygen abundance gradients derived from a variety of tracers (see their Table 2). The derived gradients range from about −0.05 dex kpc−1 for H ii regions and Cepheids to about 0 dex kpc−1 for old stellar populations. Our H ii region oxygen gradient is consistent with those found using Cepheids (e.g., −0.0529 ± 0.0083 dex kpc−1 from Korotin et al. 2014), other H ii region samples (e.g., −0.0525 ± 0.0189 dex kpc−1 from Fernández-Martín et al. 2017), and the Mollá et al. (2019a) binned H ii region sample (−0.048 ± 0.005 dex kpc−1).

The large variance in the measured radial metallicity gradients of different tracers is likely due to two primary effects: (1) changes in the metallicity gradient with time and (2) dynamical evolution of stellar populations. The radial gradient as traced by stars is flatter at larger heights above the Galactic midplane (Cheng et al. 2012; Anders et al. 2017). There is evidence that the stellar metallicity gradient also flattens in the inner galaxy (Hayden et al. 2015). These stellar populations are likely older, and thus their metallicity gradient reflects that of a younger Galaxy. Radial migration also plays an important role in stellar metallicity gradients (Sellwood & Binney 2002). The dynamical influence of non-axisymmetric features, like spiral arms and bars, can cause stars to migrate from their birth locations. Some studies have found that radial migration significantly affects the observed stellar metallicity gradients (e.g., Minchev et al. 2013, 2014), whereas others find only an increase in the stellar metallicity dispersion at all Galactocentric radii (e.g., Grand et al. 2014). These effects should have little impact on the H ii region metallicity gradient because these nebulae are very young (≲10 Myr) compared to the dynamical timescale of the Galaxy (∼250 Myr). For example, Grand et al. (2014) use a chemodynamical simulation of a Milky Way-size galaxy to show that, over time, the gas metallicity maintains a low dispersion at all radii, whereas the dispersion of the stellar metallicity increases due to radial migration.

Evidence for azimuthal variations in the radial electron temperature and metallicity gradients has been found in the Milky Way (e.g., B15) and other galaxies (e.g., Ho et al. 2017). Here we expand upon the B15 analysis by using a larger sample of Galactic H ii regions and a more accurate kinematic distance derivation technique. Evidence for azimuthal structure is already apparent in Figures 912, and here we test the statistical significance of these azimuthal variations.

To quantify the azimuthal structure in the nebular electron temperature and metallicity radial gradients, we divide the Galaxy into azimuthal bins and compute the radial gradients within each bin. Following B15, we use bins of size 30° in Galactocentric azimuth centered every 5° from −50° to 200°. Using the nebulae in each bin, we make a robust least-squares linear fit to their derived electron temperatures and metallicities as a function of their Galactocentric radii. Figure 13 shows the best-fit linear model slopes as a function of Galactocentric azimuth for the nebular electron temperature and metallicity gradients. Unlike B15, we do not exclude bins with only a few nebulae, nor those with nebulae spanning a small range of Galactocentric radii. The uncertainties in these bins will be correctly determined in the subsequent Monte Carlo analysis. In this simple least-squares analysis, however, the best-fit parameters and their uncertainties are unreliable in sparsely populated bins, such as those below ∼0° and above ∼120°. Nonetheless, we find a similar structure in the electron temperature and metallicity gradient slopes as found by B15. The electron temperature and metallicity slopes vary by a factor of 2 and 3, respectively, between Galactocentric azimuths of ∼20° and ∼100°. These variations are slightly less in magnitude than those found by B15, probably because of our much larger sample size near 100° in Galactocentric azimuth.

Figure 13.

Figure 13. Nominal variations in the radial electron temperature (top) and metallicity (bottom) gradients as a function of Galactocentric azimuth. The Galaxy is divided into 30° bins spaced every 5° in Galactocentric azimuth. The points are the slopes of the robust least-squares linear model fit to the data in each bin, and the error bars are the 1σ uncertainties in the fitted slopes. Bins below ∼0° and above ∼120° are sparsely populated and their slopes are unreliable.

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Multiple sources of uncertainty affect the apparent azimuthal variations shown in Figure 13. These sources include the derived electron temperature uncertainties and the distance uncertainties, which affect both the derived Galactocentric radii and azimuths of the nebulae. To better quantify these sources of uncertainty and to test the statistical significance of the apparent azimuthal variations, we perform yet another Monte Carlo analysis. We Monte Carlo resample the nebular electron temperatures, metallicities, and distances to generate 1000 realizations of the data. As before, the electron temperatures and metallicities are drawn from a Gaussian distribution, whereas the distances are drawn from the parallax or kinematic distance PDFs. For each realization of the data, we fit the radial gradients in each of the several Galactocentric azimuth bins. Finally, we fit a KDE to the linear model parameter PDFs to estimate the most likely parameters and their confidence intervals.

Figure 14 shows the most likely electron temperature and metallicity gradients from our Monte Carlo analysis. The most obvious difference between this and the nominal gradients in Figure 13 is the larger error bars. This Monte Carlo analysis properly accounts for the uncertainties in both the nebular electron temperatures/metallicities and distances, so these error bars more accurately reflect the uncertainties in the gradients within each azimuth bin. Despite the larger uncertainties, the azimuthal variations in the radial gradients remain statistically significant. The electron temperature gradient ranges from ∼250 K kpc−1 at ∼30° to ∼500 K kpc−1 at ∼100°, a factor of ∼2 increase, and the metallicity gradient ranges from about −0.035 dex kpc−1 to about −0.075 dex kpc−1 over the same range, a factor of ∼2 decrease.

Figure 14.

Figure 14. Same as Figure 13 for the most likely gradients derived from our Monte Carlo analysis. The error bars are the 1σ confidence intervals on the most likely slopes.

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The derived electron temperatures and metallicities are the largest source of error in the radial gradient determinations. Figure 15 shows the radial metallicity gradients in each Galactocentric azimuth bin where we Monte Carlo resample only the metallicity (top) or only the distances (bottom). The gradient uncertainties are a factor of ∼2 larger when we resample only the metallicities.

Figure 15.

Figure 15. Same as the metallicity gradients in Figure 14, except we only Monte Carlo resample the derived metallicities (top) or distances (bottom).

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The azimuthal variations in the metallicity gradient are predicted by some simulations (Di Matteo et al. 2013; Grand et al. 2016). Grand et al. (2016), for example, find azimuthal metallicity structure in the young, thin disk stellar population of a cosmological simulation of a Milky Way analog. The azimuthal variations are induced by the non-axisymmetric peculiar motions near spiral arms, which drives radial migration and a redistribution of metals. The magnitude of the azimuthal variations is ∼0.1 dex in their simulation. If such stellar azimuthal metallicity structure is persistent over long periods of time, the enrichment of the ISM by these stars might explain the observed azimuthal structure in the HII region metallicity distribution. Di Matteo et al. (2013) find a similar magnitude of variation in metallicities as traced by old stars in an N-body simulation. In Figure 16, we show the residuals of the electron temperature and metallicity Monte Carlo kriging maps after subtracting the most likely radial gradients. Excluding the Galactic center and edge of the map, the magnitude of variation in the metallicity residual map is ∼0.1 dex, which is consistent with the Grand et al. (2016) simulation. In the first quadrant, the residual structure between R ∼ 6 kpc and ∼12 kpc is qualitatively similar to the simulated residuals in Grand et al. (2016) and may be evidence for spiral arm induced radial migration in the Milky Way.

Figure 16.

Figure 16. Most likely electron temperature (top) and metallicity (bottom) Kriging map residuals. The residuals are determined by subtracting the most likely gradient from the Monte Carlo Kriging maps. The features in each plot are the same as in Figure 9.

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Recent two-dimensional chemical evolution models also predict azimuthal structure in the gas-phase oxygen abundance. For example, Spitoni et al. (2019) find that density fluctuations due to spiral arms produce oxygen abundance variations on the order of ∼0.1 dex, with the most azimuthal structure apparent at and beyond the corotation radius. The magnitude of these abundance fluctuations decreases with time as the model galaxy becomes well-mixed. This model does not consider stellar migration and enrichment, which, according to the Grand et al. (2016) simulation, are likely important factors. Mollá et al. (2019b) use a 2D chemical evolution code applied to a Milky Way analog to conclude that spiral arms only marginally alter the azimuthal metallicity structure. Their model predicts present-day oxygen abundance variations of ∼0.03 dex increasing to ∼0.1 dex in the outer Galaxy. The oxygen abundance variations are more significant within 1–2 Gyr after spiral arms are introduced in their model.

The nebulae in this study cover only about one-half of the Galactic disk. The Southern H ii Region Discovery Survey (SHRDS; Wenger et al. 2019) is finding hundreds of new H ii regions in the third and fourth Galactic quadrants, and the SHRDS interferometric observations will allow for accurate electron temperature and metallicity derivations. In a future work, we will combine these northern sky nebulae with newly discovered southern sky H ii regions to create a map of H ii region metallicities across the entire Galactic disk. We will use this map to test the chemodynamical evolution simulations by searching for evidence of metallicity structure associated with spiral arms, the Galactic bar, and/or other components of the Milky Way.

7. Summary

We use the VLA to measure the ∼8–10 GHz RRL and radio-continuum flux densities of 82 Galactic H ii regions. We derive the RRL-to-continuum brightness ratio, electron temperature, and metallicity of these nebulae. Including previous single-dish observations, the catalog of Galactic H ii regions with accurate electron temperatures and distances now contains 167 nebulae spanning Galactocentric radii 4–16 kpc and azimuths −20° to 140°.

The distances to Galactic H ii regions are the largest source of uncertainty in previous studies using these nebulae to trace Galactic metallicity structure (e.g., B15). Maser parallax distances have been determined for 46 of our nebulae. For the remainder, we use a novel Monte Carlo kinematic distance technique to determine distances (Wenger et al. 2018). Both the kinematic distances and distance uncertainties to the nebulae in our sample are more accurate than in the B15 study. In this work, the RRL-to-continuum brightness ratio uncertainties are about twice as important as the distance uncertainties.

Using a Monte Carlo analysis, we derive the most likely Milky Way radial electron temperature and metallicity gradients as ${T}_{e}/{\rm{K}}={4493}_{-188}^{+156}+{359}_{-18}^{+22}\,R/{\rm{kpc}}$ and $12+{{\rm{log}}}_{10}({\rm{O}}/{\rm{H}})\,={9.130}_{-0.030}^{+0.034}-{0.052}_{-0.004}^{+0.004}\,R/{\rm{kpc}}$, respectively. This metallicity gradient is consistent with previous H ii region studies (e.g., B15) and young stellar tracers, such as Cepheids (e.g., Korotin et al. 2014). We generate maps of the electron temperature and metallicity structure of the Galactic disk using a Monte Carlo kriging analysis. These maps reveal significant azimuthal variations in the Galaxy's metallicity structure. The radial metallicity gradient varies by a factor of ∼2 (∼0.04 dex kpc−1) between Galactocentric azimuths of ∼30° and ∼100°. We find non-axisymmetric spatial metallicity variations on the order of ∼0.1 dex, which is consistent with the Grand et al. (2016) chemodynamical simulation. These variations may be evidence for radial migration and metal mixing induced by the Milky Way's spiral arms.

The Southern H ii Region Discovery Survey (Wenger et al. 2019) will add hundreds of nebulae with electron temperature and metallicity derivations to the third and fourth Galactic quadrants. With H ii region coverage across the entire Galactic disk, we will investigate the association between the Milky Way's metallicity structure and the locations of spiral arms. Such structure is a test of chemodynamical simulations and can be directly compared to extragalactic systems.

We thank the anonymous reviewer for their constructive feedback on this manuscript. T.V.W. is supported by the NSF through the Grote Reber Fellowship Program administered by Associated Universities, Inc./National Radio Astronomy Observatory, the D.N. Batten Foundation Fellowship from the Jefferson Scholars Foundation, the Mars Foundation Fellowship from the Achievement Rewards for College Scientists Foundation, and the Virginia Space Grant Consortium. L.D.A. is supported in part by NSF grant AST-1516021. T.M.B. is supported in part by NSF grant AST-1714688.

The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

Facility: VLA. -

Software: Astropy (Astropy Collaboration et al. 2013), CASA (McMullin et al. 2007), KDUtils (Wenger et al. 2017), Matplotlib (Hunter 2007), NumPy & SciPy (van der Walt et al. 2011), PyKrige (Murphy 2014), Python (https://www.python.org/), WISP (Wenger 2018).

Appendix: Electron Temperature Derivations

Here we derive the relationship between the nebular electron temperature, hydrogen radio recombination line (RRL) brightness, and radio-continuum brightness of an H ii region. This derivation relies on several assumptions: (1) the nebula is homogeneous, isothermal, and in LTE; (2) the nebula is optically thin in both radio-continuum and RRL emission; (3) the nebula is composed solely of ionized hydrogen and singly ionized helium; and (4) the RRL and continuum brightness are measured with the same telescope in the Raleigh–Jeans limit.

The free–free radio-continuum absorption coefficient of an isothermal plasma is

Equation (9)

where Te is the electron temperature, ν is the observed frequency, ni is the ion number density, and ne is the electron number density (Oster 1961). Altenhoff et al. (1960) approximate the absorption coefficient as

Equation (10)

which is accurate within 10% for 100 MHz < ν < 35 GHz and 5000 K < Te < 12000 K (Mezger & Henderson 1967). The free–free optical depth is the integral of this absorption coefficient along the line of sight, ${\tau }_{C}(\nu )=\int {k}_{C}(\nu ){dl}$. In a homogeneous medium with line-of-sight depth l, the optical depth simplifies to τC(ν) = kCl.

The LTE hydrogen RRL absorption coefficient for the transition from principle quantum state m to n is

Equation (11)

where νL is the RRL rest frequency, χn is the energy required to ionize the atom from state n, fnm is the oscillator strength of the m to n transition, ϕν(ν) is the normalized line profile with inverse frequency units, np is the hydrogen number density, h is the Planck constant, k is the Boltzmann constant, e is the electron charge, me is the electron mass, and c is the speed of light (Brocklehurst & Seaton 1972; Balser 1995). The Rydberg formula determines the transition frequency between state m and n:

Equation (12)

where Z is the effective nuclear charge and R is the Rydberg constant. For hydrogen, Z = 1 and $R={R}_{\infty }(1-{m}_{e}/{m}_{p})$, where ${R}_{\infty }$ is the Rydberg constant for an infinite mass and mp is the proton mass. If we let Δn = m − n, then the hydrogen transition frequencies are

Equation (13)

For the low Δn transitions in the radio regime (e.g., H109α), Δn ≪ n and

Equation (14)

Substituting these frequencies into Equation (11), and assuming that we are observing in the Rayleigh–Jeans limit χn ≪ kTe, the LTE RRL absorption coefficient becomes

Equation (15)

Evaluating the constants and moving to astrophysically relevant units, this equation becomes

Equation (16)

The RRL optical depth is the integral of this absorption coefficient along the line of sight, which is ${\tau }_{L}^{* }(\nu )={k}_{L}^{* }(\nu )l$ for a homogeneous medium.

In an optically thin medium in LTE, the specific intensity of some emission with optical depth τ is Iν ≃ Bν(T)τ, where Bν(T) is the Planck function at some temperature T. Assuming the RRL and continuum emission originate in the same volume of homogeneous, isothermal gas with electron temperature, Te, the RRL-to-continuum specific intensity ratio at νL is

Equation (17)

For a Gaussian line profile with FWHM line width Δν,

Equation (18)

and

Equation (19)

Using Equation (19) in (17), we find

Equation (20)

If the nebulae is composed of only hydrogen and singly ionized helium, then

Equation (21)

where ${n}_{{\mathrm{He}}^{+}}$ is the singly ionized helium number density and ${y}^{+}\equiv {n}_{{{\rm{He}}}^{+}}/{n}_{p}$ is the ratio of singly ionized helium to hydrogen by number. We use the Doppler equation to convert the FWHM line width from frequency to velocity units:

Equation (22)

where ΔV is the FWHM line width in velocity units. The RRL-to-continuum specific intensity ratio at νL is thus

Equation (23)

The expression (fnmΔn/n) is not a strong function of n for Δn = 1 hydrogen RRLs. For example, (fnmΔn/n) = 0.19435, 0.19395, and 0.19363 for Δn = 1 and n = 80, 90, and 100, respectively, using the oscillator strengths from Menzel (1968). This variation is less than 0.3% across these H transitions, so we adopt the H90α oscillator strength to simplify the RRL-to-continuum specific intensity equation as

Equation (24)

Solving for the electron temperature, we find

Equation (25)

A.1. Single-dish Observations

Single-dish telescopes measure intensity in units of antenna temperature, TA. In the absence of atmospheric attenuation, the antenna temperature is related to the brightness temperature distribution, TB(θ), by

Equation (26)

where ηb is the telescope beam efficiency, Ωb is the telescope main beam solid angle, f(θ) is the telescope beam pattern, and the integral is the convolution of the source brightness distribution with the telescope beam (Mezger & Henderson 1967). For a Gaussian beam with HPBW θb, the beam pattern is $f(\theta )=\exp [-4\mathrm{ln}(2){\theta }^{2}/{\theta }_{b}^{2}]$ and the beam solid angle is ${{\rm{\Omega }}}_{b}=2\pi {\int }_{0}^{\infty }f(\theta )\theta \,d\theta =\pi {\theta }_{b}^{2}/(4\mathrm{ln}2)$. Similarly, if the source brightness distribution is Gaussian with amplitude TB and half-power width θs, then the source brightness temperature distribution is ${T}_{B}(\theta )={T}_{B}\exp [-4\mathrm{ln}(2){\theta }^{2}/{\theta }_{s}^{2}]$. In astronomy, θ is typically very small, $\sin \theta \simeq \theta $, and the integral in Equation (26) is

Equation (27)

where we use ${\int }_{0}^{\infty }x\,\exp (-{{ax}}^{2}){dx}=1/(2a)$. The antenna temperature is thus

Equation (28)

For a resolved source, θs ≫ θb and TA ≃ ηbTB. For an unresolved source, θs ≪ θb and ${T}_{A}\simeq {\eta }_{b}{T}_{B}({\theta }_{s}^{2}/{\theta }_{b}^{2})$.

Brightness temperature is defined as

Equation (29)

where Iν is the specific intensity. For an optically thin medium, Iν = Bν(T)τ, where T is the blackbody temperature of the emission and τ is the optical depth. In the Rayleigh–Jeans limit, the brightness temperature is simply

Equation (30)

Substituting Equation (30) into (28), we find

Equation (31)

If the RRL and continuum antenna temperatures are measured with the same telescope and at the same frequency, and if both sources of emission originate from the same volume of homogeneous and isothermal gas with electron temperature Te, Equation (24) is trivially

Equation (32)

where TC(νL) and TL(νL) are the continuum and RRL antenna temperatures measured at the RRL frequency νL, respectively. Equation (25) becomes

Equation (33)

A.2. Averaging Single-dish RRLs

In Galactic H ii region surveys, we average multiple RRL transitions to increase the RRL signal-to-noise ratio. Each RRL transition is an independent measurement of the nebular electron temperature, so the electron temperature derived from many RRL-to-continuum antenna temperature measurements is

Equation (34)

assuming that adjacent RRL transitions have similar FWHM line widths in velocity units (e.g., Balser et al. 2011). Previous single-dish RRL studies have used different strategies for averaging RRL transitions. Balser et al. (2011, 2015), for example, scale each RRL antenna temperature to account for the variations in telescope beam size with frequency, then average the rescaled RRL spectra. They measure the continuum antenna temperature at one frequency within the RRL frequency range, then take the ratio of the average RRL antenna temperatures to this continuum temperature. This strategy is an approximation to Equation (34).

Here we compute the difference between the true electron temperature and the Balser et al. (2011, 2015) approximation using multiple RRL transitions. From Equation (34), the factor we need to derive is

Equation (35)

where Te ∝ Xtrue and Xtrue is the only variable in Equation (34) that depends on the RRL transition. Balser et al. (2011, 2015) approximate this factor as

Equation (36)

where νC is the observed continuum frequency and ${T}_{L}^{* }({\nu }_{L})$ is the RRL antenna temperature corrected for the variation of telescope beam size with frequency. They rescale the observed RRL antenna temperature, TL(νL), using

Equation (37)

where θb is the HPBW at νL, and ${\theta }_{b}^{* }$ is the HPBW at νC, and θs is the half-power width of the source. The observed source brightness distribution is the convolution of the actual source brightness and the telescope beam. With the assumption that the telescope beam and source brightness distribution are Gaussian, the convolution is also a Gaussian with half-power width ${\theta }_{o}^{2}={\theta }_{s}^{2}+{\theta }_{b}^{2}$. Balser et al. (2011, 2015) measure the source half-power width at νC, which is ${({\theta }_{o}^{* })}^{2}={\theta }_{s}^{2}+{({\theta }_{b}^{* })}^{2}$. The true, deconvolved source size is ${\theta }_{s}^{2}={({\theta }_{o}^{* })}^{2}-{({\theta }_{b}^{* })}^{2}$, and the rescaled antenna temperature in terms of observables is

Equation (38)

For a point source, ${({\theta }_{o}^{* })}^{2}\simeq {({\theta }_{b}^{* })}^{2}$ and ${T}_{L}^{* }({\nu }_{L})\simeq {T}_{L}({\nu }_{L}){[{\theta }_{b}^{2}/({\theta }_{b}^{* })}^{2}]$, whereas if the source is very resolved, ${({\theta }_{o}^{* })}^{2}\,\gg {({\theta }_{b}^{* })}^{2}$ and ${T}_{L}^{* }({\nu }_{L})\simeq {T}_{L}({\nu }_{L})$.

Using Equations (16), (19), and (22), the line center LTE optical depth of the ith RRL transition is

Equation (39)

where we have assumed ${\tau }_{L,i}^{* }=\int {k}_{L,i}^{* }\,{dl}={k}_{L,i}^{* }l$ for a homogeneous medium with an LTE absorption coefficient ${k}_{L,i}^{* }$ and a line-of-sight depth l. The antenna temperature of this transition is

Equation (40)

and the rescaled RRL antenna temperature is

Equation (41)

The average rescaled RRL antenna temperature of several RRL transitions is

Equation (42)

assuming that the RRLs have similar FWHM line widths in velocity units.

From Equation (10), the continuum optical depth at frequency νC is

Equation (43)

where, again, we have assumed that the medium is homogeneous. The continuum antenna temperature is

Equation (44)

Substituting Equations (42) and (44) into the Balser et al. (2011, 2015) approximation of X, we find

Equation (45)

The ratio of the X approximation and Xtrue is

Equation (46)

As a sanity check on this expression, if the RRL and continuum antenna temperatures are measured at only one RRL frequency, then ${\nu }_{C}={\nu }_{L}=\langle {\nu }_{L}\rangle $ and this ratio is unity. Balser et al. (2015) measured the continuum antenna temperature at νC = 8.556 GHz and the RRL antenna temperature for 6 H transitions (H87α to H93α, excluding H90α). The average RRL frequency is $\langle {\nu }_{L}\rangle =8.903\,\mathrm{GHz}$, but Balser et al. (2015) use $\langle {\nu }_{L}\rangle =9\,\mathrm{GHz}$. With these values, the X ratio is

Equation (47)

Therefore, Balser et al. (2015) and other studies that average the same RRL transitions and observe the same continuum frequency will overestimate the derived electron temperatures by ∼5.7%.

Quireza et al. (2006a, 2006b) use different RRL transitions and calibration strategies to derive electron temperatures. In their C ii survey, they observe H91α and H92α. They assume both transitions have the same antenna temperature in the bright H ii region W3, and they use this assumption to calibrate H92α relative to H91α. From Equation (40), this calibration factor is

Equation (48)

W3 is unresolved in their survey, so ${\theta }_{s}^{2}+{\theta }_{b}^{2}\simeq {\theta }_{b}^{2}$. Using ${\theta }_{b}^{2}\propto {\nu }^{-2}$ for a Gaussian beam, this factor becomes

Equation (49)

Therefore, the average RRL antenna temperature in their surveys is

Equation (50)

The continuum antenna temperature at νC is given by Equation (44), and the Quireza et al. (2006a, 2006b) X is

Equation (51)

The ratio of this X approximation to Xtrue is

Equation (52)

Quireza et al. (2006a, 2006b) did not account for the variation in telescope beam size in their analysis. Therefore, their ratio X/Xtrue has a dependence on the source size. In the limit that the source is unresolved at all frequencies, ${\theta }_{s}^{2}\ll {\theta }_{b}^{2}$. For Gaussian beams with θ2ν−2, the ratio in this limit becomes

Equation (53)

Using the RRL frequencies, νC = 8.665 GHz, and $\langle {\nu }_{L}\rangle \,={\nu }_{{\rm{H}}91\alpha }$, which is what Quireza et al. (2006a, 2006b) use, we find

Equation (54)

For unresolved sources, Quireza et al. (2006a, 2006b) correctly calculate the electron temperatures in their C ii survey. In the resolved case, ${\theta }_{s}^{2}\gg {\theta }_{b}^{2}$ and

Equation (55)

Therefore, the Quireza et al. (2006b) electron temperatures for the C ii survey nebulae are underestimated by up to 5% depending on the source morphology.

In their 3He survey, Quireza et al. (2006a, 2006b) only observe the H91α transition. The X ratio for this survey is simpler:

Equation (56)

with limits

Equation (57)

and

Equation (58)

Quireza et al. (2006b) underestimate their electron temperatures by up to 2% in their 3He survey.

In Table 7, we list the X/Xtrue factors for the Quireza et al. (2006a, 2006b), Balser et al. (2011), and B15 single-dish studies. For each survey, we list the author; the observed RRL transitions; the observed continuum frequency; the average RRL frequency they used in the electron temperature equation; and the X/Xtrue factor.

Table 7.  Single-dish Electron Temperature Corrections

Author RRLs νC $\langle {\nu }_{L}\rangle $ a X/Xtrue
    GHz GHz  
Quireza et al. (2006a, 2006b) C ii Survey H91α;H92α 8.665 8.585 0.956 to 1.0
Quireza et al. (2006a, 2006b) 3He Survey H91α 8.665 8.585 0.983 to 1.0
Balser et al. (2011, 2015) H87α to H93α 8.665 9.0 1.057

Note.

aAverage RRL frequency used by the author, which is not the actual average RRL frequency.

Download table as:  ASCIITypeset image

A.3. Interferometer Observations

Interferometers measure intensity in units of flux density per synthesized beam, S, which is related to brightness temperature, TB, by the Rayleigh–Jeans law:

Equation (59)

If the RRL and continuum flux densities are measured at the same frequency, with the same telescope, and with the same synthesized beam size, the RRL-to-continuum flux density ratio and electron temperature are given by Equations (24) and (25), respectively, where IC is the continuum flux density and IL is the RRL flux density.

A.4. Averaging Interferometer RRLs

An important difference between interferometric observations and single-dish observations is that interferometers measure the RRL and continuum emission simultaneously. At each RRL frequency, we measure the RRL flux density and continuum flux density with the same synthesized beam. If the source is homogeneous and isothermal, we can ignore all effects of the varying beam size.

In our VLA survey analysis, we extract spectra from our data cubes in two ways: from the pixel of brightest continuum emission, such that the spectrum has units of flux density per beam, or from the sum of all pixels within a region, such that the spectrum has units of flux density. We average these spectra weighted by the continuum brightness and rms noise in the line-free regions, so our interferometric X factor is

Equation (60)

where SC and SL are the continuum and RRL brightness or flux density, respectively, and $\langle {\rangle }^{* }$ indicates a weighted average. If we assume that the spectral rms noise is the same in each RRL transition, then the weighted average values are simply

Equation (61)

Equation (62)

Equation (63)

From Equations (10) and (59), the continuum brightness at the ith RRL frequency is

Equation (64)

for a homogeneous nebula with depth l. The RRL frequency is the only factor that depends on RRL transition, so

Equation (65)

and

Equation (66)

Using Equations (16) and (59), the LTE brightness of the ith RRL is

Equation (67)

for a homogeneous medium with depth l. The average RRL brightness is

Equation (68)

The average RRL frequency is

Equation (69)

so the interferometric X approximation simplifies to

Equation (70)

The ratio of this approximation to Xtrue is

Equation (71)

We observe the seven RRL transitions from H87α to H93α. Our X factor ratio is thus

Equation (72)

Our strategy for averaging multiple RRL transitions to compute electron temperatures is accurate.

Footnotes

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10.3847/1538-4357/ab53d3