Magnetic Field Uniformity Across the GF 9-2 YSO, L1082C Dense Core, and GF 9 Filamentary Dark Cloud

SOFIA airborne observations of the GF 9-2 region using HAWC+ were obtained on the nights of 2016 December 13 and 14, at altitudes in excess of 12.5 km, for the SOFIA Cycle 4 program 04_0026. In the E-band (216 μm center wavelength, 43 μm bandwidth) polarimetry mode of HAWC+, the detector format consisted of two bolometer arrays of nominal pixel counts 32 × 40 and pixel projected dimensions of 9.33 arcsec per side. Each array was illuminated by an opposite sense of linear polarization from the polarization beam-splitter, with most sky directions simultaneously observed by pixels in both arrays. The pixel sampling was at half the diffraction-limited beamsize (18.2 arcsec FWHM) at this wavelength for the 2.5 m clear aperture of the SOFIA telescope. Observations were obtained using a chop–nod procedure, with identical chop and nod throws of 150 arcsec, tertiary chop frequency of 10 Hz, and telescope nod dwell time of 40 s. A 2 × 2 position dither, with motions equal to three pixels (27 arcsec), was combined with four half-wave-plate (HWP) position angles to enable polarimetry. A total integration time of one hour was achieved for the two observing nights.

The raw data were processed by the HAWC+ instrument team, including corrections for dead pixels and relative pixel gains as well as instrument and telescope intrinsic polarizations. The chops, nods, dithers, and HWP orientations were rectified, and the resulting images registered and averaged to produce "Level 4" (science-quality) data products. These included FITS images of total intensity (Stokes I), fractional polarization P, polarization PA, Stokes UI and Stokes QI, and all uncertainties. Initial examination of these images revealed high signal-to-noise-ratio (S/N) detection of total intensity in E band across much of the dense cloud core, but no significantly detected polarization at the native resolution of the detector pixels. The successful extraction of polarization from these data is described in Section 3.2.

Figure 2 shows black contours of the HAWC+ 216 μm total intensity overlaid on a 10 × 10 arcmin² NIR K-band image obtained with Mimir. The outer, magenta contour identifies the region where the HAWC+ intensity values are valid, with reduced S/N near the edges of that region due to the chop/nod/dither pattern placing fewer HAWC+ overlapping pixels toward those sky directions. The circles surrounding the brighter stars indicate Gaia (Gaia Collaboration et al. 2016) DR2 (Gaia Collaboration et al. 2018) matches (see Section 3.1), colored by distance bin.

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The contours show that the strongest thermal dust emission arises very near the YSO, with weaker resolved emission along two thin east and west arms and a wider southwest arm. The shape of the extended contour configuration is nearly identical to the distribution of C¹⁸O shown in Furuya et al. (2014a, their Figure 2, upper right). This indicates that the HAWC+ observations accurately reveal the locations of both the L1082C core and the GF 9-2 YSO, as well as the extent of the former.

Observations of NIR BSP were obtained using Mimir on the 1.8 m Perkins telescope, located in northern Arizona, in the H (1.6 μm) and K (2.2 μm) bands during several nights in 2011, 2013, 2014, 2015, and 2017. A total of 41 separate observations were obtained. Each observation consisted of images obtained through 16 HWP orientation angles for each of six sky-dither positions, for a total of 96 images. Exposure times per image were one of 2.3, 10, or 15 s. Images were evaluated for seeing and other effects, and observations using the same exposure times obtained during the same observing run were averaged to improve S/N and detection sensitivity. Total exposure times were 6.6 hr in the H band and 8.2 hr in the K band. Full details regarding Mimir polarimetry observations, data reduction, and data products are reported in Clemens et al. (2012a, 2012b).

A total of 856 stars in the Mimir FOV were contained in the final, merged H-band polarization stellar catalog. About 15% (125) of these stars were brighter than m_H = 15.2 mag, exhibited polarization S/N ("PS/N" ≡ P'/σ_P⁴ ) greater than 1.6 (i.e., σ_PA < 18°), and had P' values less than 4.5% (to avoid noise-driven false positives). Similarly, of 688 stars in the combined K-band polarization catalog, for magnitudes down to m_K = 14.3 there were 55 stars meeting the same PS/N criterion with P' less than 4%. Stars fainter than these two magnitude limits had PS/N values too small to yield reliable individual B-field orientations, but were able to be combined to yield useful average properties, as described in the following section.

Key quantities for the 860 stars with measured H- or K-band polarization values are reported in Table 1. There, stellar coordinates, H-band and K-band photometric and polarimetric values, 2MASS (Skrutskie et al. 2006) photometry, WISE (Wright et al. 2010) W1- and W2-Band (4.5 μm, equivalent to M-band) photometry, and Gaia DR2 (Gaia Collaboration et al. 2016, 2018) g-band photometry and parallaxes, as well as all associated uncertainties, where available for each star, are presented.

Table 1.  Photometry, Polarimetry, and Parallaxes for GF 9/L1082C Field Stars

		Mimir Values/Uncertainties
No.	R.A./Decl.	H	${P}_{H}^{{\prime} }$	PAH	QH	UH	K	${P}_{K}^{{\prime} }$	PAK	QK	UK
	(°)	(mag)	(%)	(°)	(%)	(%)	(mag)	(%)	(°)	(%)	(%)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
056	312.71671	11:929	2.393	143.0	0.659	−2.303	11.680	1.297	135.5	0.023	−1.310
	60.33037	0:001	0.109	1.3	0.114	0.108	0.006	0.185	4.1	0.139	0.185
154	312.75253	13:836	1.927	124.1	−0.752	−1.886	13.554	2.089	116.8	−1.326	−1.797
	60.28807	0:005	0.638	9.5	0.631	0.639	0.007	0.788	10.8	0.799	0.782
237	312.78150	15:426	3.908	138.4	0.547	−4.584	15.183	4.170	152.2	3.102	−4.517
	60.34538	0:017	2.458	18.0	2.359	2.459	0.034	3.555	24.4	2.872	3.835
320	312.81297	9:781	1.377	145.8	0.509	−1.281	9.436	0.713	138.0	0.075	−0.712
	60.34628	0:000	0.055	1.1	0.050	0.055	0.001	0.064	2.6	0.055	0.064
816	313.01130	7:890	3.957	123.4	−1.585	−3.705	7.393	0.919	107.6	−0.762	−0.540
	60.37427	0:001	0.759	5.5	0.858	0.740	0.001	0.163	5.1	0.166	0.155

2MASS Values/Unc.			WISE Values/Unc.		Gaia DR2 Values/Unc.
J	H	K	W1	W2	g	π	Notes
(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mas)	⋯
(13)	(14)	(15)	(16)	(17)	(18)	(19)	(20)
12.868	12.006	11.753	11.621	11.622	15.779	0.366	⋯
0.024	0.026	0.020	0.023	0.020	0.001	0.038	⋯
14.576	13.836	13.595	13.450	13.469	17.683	0.420	⋯
0.036	0.039	0.034	0.024	0.027	0.001	0.117	⋯
16.117	15.571	15.120	14.882	14.862	19.111	0.692	⋯
0.100	0.142	0.140	0.028	0.044	0.003	0.261	⋯
10.982	9.821	9.520	9.333	9.429	14.479	0.121	⋯
0.022	0.026	0.022	0.022	0.020	0.000	0.038	⋯
7.715	7.556	7.510	7.309	7.450	8.518	3.407	⋯
0.018	0.053	0.021	0.033	0.020	0.000	0.028	⋯

Note. This is a shortened and selective version of the full table that is available in electronic form, with the rows shown here chosen to span the range of H-band magnitudes for stars having complete matches to K, WISE, and Gaia values.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Within the Mimir FOV, a total of 723 stars were contained in Gaia DR2. These were matched to entries in the H-band combined polarization catalog, using a 0.7 arcsec radius window, resulting in 610 matches. Plots of H-band P' versus parallax and (H − M) stellar color⁵ versus parallax revealed that very few stars in the FOV are closer than 300 pc. Stepwise increases in these quantities in plots versus distance for other dark clouds arise because cloud thicknesses are much smaller than the distances to the clouds, which helps to localize the effects of reddening and polarization by the dust contained in such clouds (e.g., Figure 13 of Santos et al. 2017). No strong steps were present in the plots of P' and reddening versus Gaia distance for the GF 9 field stars. Additionally, as both of those quantities depend on dust column density, and the available directions to the stars whose light passes through the dark clouds being studied are largely stochastic, the steps seen in those other clouds are often less than dramatic and the functional forms of the steps are unknown. This has left interpretations of such plots, for the purpose of assigning dark cloud distances, rather subjective.

Based on the uniformity of the B-field orientations in Section 3.3, a similar step change in PA might be equally definitive and simpler to model. Fifty-one stars were found to have values of parallax plus uncertainty in parallax greater than 2.0 mas. These stars were selected as having some reasonable likelihood of being located closer than 500 pc, a value greater than the maximum of the previous distance estimates for GF 9. In the left panel of Figure 3, the NIR PAs measured for H (in blue) and K (in green) are plotted versus Gaia DR2 parallaxes for those stars.

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A stepwise change in PA was sought using a Metropolis–Hastings Markov Chain Monte Carlo (MCMC) approach. The model consisted of two uniform PA values plus a transition parallax value. Priors were uniform in PA from 60° to 240° and uniform in parallax between 1 and 100 mas. Seventeen of the stars had measured PA values with uncertainties in both H and K under 60°, so those PA values were combined for each of those stars, using inverse variance weighting, to avoid double counting the stars. Thirty-four stars only had either H- or K-band PA uncertainties meeting that criterion, and so did not need to have their PA values averaged over wavelength. A couple of the brightest stars tended to dominate the initial MCMC results, so an additional 4° was added in quadrature to all PA uncertainties to reduce that effect and permit more stars to contribute to the combined fit. Uncertainties in both the parallax and PA quantities were incorporated via Gaussian likelihoods, with the parallax likelihood split between the two model PA values at the transition parallax. As noted in Table 1, four stars were rejected from inclusion in this fitting due to nonphysical combinations of low polarizations with large distances, oddly blue (g − H) colors,⁶ or strongly non-Serkowski (Serkowski et al. 1975; Wilking et al. 1980) ratios of ${P}_{H}/{P}_{K}$ (which would imply polarization processes that were not based on normal interstellar medium dust dichroism). Whether these represent unresolved binaries or hot stars with intrinsic polarizations is beyond the scope of this work.

After 500,000 steps, the MCMC routine established the stable findings shown as the corner plot in the right panel of Figure 3. It favors an initial PA of 180° ± 8° that transitions to a final PA of 130° ± 2° at a parallax of 3.71 ± 0.14 mas. None of the quantities exhibit significant covariance, as indicated by the round two-dimensional Gaussian-looking distributions shown in Figure 3 (right panel). The values are indicated as the orange line in the left panel of the plot (with uncertainty ranges indicated by the dotted orange lines).

The abrupt PA change at 270 ± 10 pc was adopted as the distance to the GF 9 cloud, the L1082C core, and the GF 9-2 YSO. Post facto weak changes in the plots of (H − M) with parallax and ${P}_{H}^{{\prime} }$ with parallax were noticed at about the same parallax of 3.7 mas. This correspondence is good evidence that the distance to the cloud has been revealed via the PA step.

Of the 610 H-band matching Gaia DR2 stars, only four with parallax S/N > 2 have parallaxes greater than 3.71 mas, while 253 (98%) are more distant. Hence, the NIR BSP stars, which have a high correspondence to Gaia DR2 stars, are located behind the GF 9 cloud and are ideal probes of the B field threading the dust in the cloud and dense core. Additionally, NIR color, ${P}_{H}^{{\prime} }$, and PA all show an absence of step changes for distances beyond 270 pc. That is, the layer dust (and embedded B field) associated with GF 9 appears to be the only dust layer along these lines of sight (L ∼ 97° and B ∼ 10°).

The extended 216 μm thermal dust emission from the L1082C dense core beyond the centrally bright GF 9-2 YSO is very weak, with the resolved arm intensities shown in Figure 2 being only ∼40 MJy sr⁻¹ above nearby background regions. Smoothing to coarser angular resolution than the HAWC+ pixel size was necessary to boost S/N and enable polarization detections, similar to that applied to SCUPOL (Greaves et al. 2003) observations reprocessing as described in Clemens et al. (2016). Smoothing was performed on the Stokes UI and QI maps, weighted both by the variances in their pixel uncertainty values and by a Gaussian kernel of FWHM equal to four HAWC+ pixels. Instead of using a regular grid of central positions for the Gaussian smoothing, the intensity image (Figure 2) was used as a guide for discrete synthetic-aperture placements, starting at the YSO position and working along the arms seen in FIR emission. The Gaussian kernel sizes and center placements of the apertures were varied to find the maximum number of independent apertures that exhibited PS/N > 1.6. The resulting aperture-averaged Stokes UI, QI , and I values were used to compute the polarization P, its uncertainty σ_P, the corrected P', position angles PA and BPA,⁷ and the uncertainty in position angle.

The four-pixel FWHM case returned 6 synthetic apertures that met the PS/N criterion and 11 that did not. The convolved HAWC+ polarization properties for these 17 apertures are listed in Table 2 and displayed in Figure 4. Interestingly, five of the six detected apertures show inferred B-field orientations that are very close to those found for NIR BSP stars probing nearby directions.

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There is a remarkable uniformity and agreement of the plane-of-sky B-field orientation BPAs seen in Figure 4, as revealed by SOFIA HAWC+ and by Mimir polarimetry. The overall BPA is about 135°, which appears to be parallel to the 216 μm intensity-traced northwest arm, but is mostly perpendicular to the eastern arm and to the southwestern arm.

A rough estimate of the mean column densities for each arm was developed by examining the (H − M) reddening to stars located behind the two arms. For six stars in or near the northeastern arm, their mean (H − M) is 0.66 mag, though significantly increasingly red for the stars nearest the dense core. The two stars in the southeastern arm that are closest to the three SOFIA position detections exhibit a mean (H − M) of 1.0 mag. With typical reddening to molecular hydrogen column density conversions, and correcting for the intrinsic colors of the stars, the northeastern arm has a column density in the range 3–4 × 10²¹ H₂ cm⁻² and the southeastern arm is higher, at about 7–8 × 10²¹ H₂ cm⁻². Thus, the BPA being parallel to the elongation of the less dense northeastern arm and perpendicular to the more dense southeastern arm follows trends seen for filamentary clouds elsewhere (Myers 2009; Li et al. 2013; Planck Collaboration et al. 2016b) for these column densities.

The mean orientation of the BPA is generally perpendicular to much of the large-scale dark arc of the GF 9 cloud seen in Figure 1. The North Galactic Pole direction is at PA 3084, which makes the revealed B field for the L1082C dense core in GF 9 nearly perpendicular to the Galactic disk.

The degrees of B-field uniformity and agreement were probed by comparing the BPAs versus offset from the YSO position for these FIR and NIR data sets. In addition, the 0.77 μm (I-band) BSP of Poidevin & Bastien (2006) and the Planck 353 GHz (850 μm) TEP, both of which span much larger FOVs, were included in the comparison. All of these data points were selected subject to a position angle uncertainty criterion of less than 25°. After selection, two different weighted fits of BPA versus offset were performed. These data, and the fits, are shown as Figure 5.

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In that figure, the TEP position offsets have been added in quadrature with half of their FWHM beamsizes, to indicate their effective beam-averaged offsets from the YSO position. Symbol color identifies the data set, as listed in the legend in the upper left. Some key physical offset values are marked and listed just above the lower axis.

Fits of two different forms for BPA versus offset were performed, one was linear in BPA and offset, the other was a power-law relation. In the figure, the black dashed line represents the linear fit of the full set of BPAs versus offset, weighted by the variances of their uncertainties, as

$$\begin{eqnarray}&&{\mathrm{BPA}}_{\deg }=(134.9\pm 0.3)-(4.6\pm 0.2)\times {r}_{\mathrm{pc}},\end{eqnarray} \tag{ 1 }$$

where BPA_deg is the B-field equatorial orientation angle measured in degrees and r_pc is the radial offset measured in parsecs. The gray dashed line represents the power-law fit:

$$\begin{eqnarray}&&{\mathrm{BPA}}_{\deg }=(153.6\pm 0.6){r}_{\mathrm{pc}}^{(-0.024\pm 0.003)}.\end{eqnarray} \tag{ 2 }$$

The weak slopes for both of these fits, less than 5° per pc for the linear fit, confirms the high degree of uniformity of the mean BPA across two orders of magnitude of physical offset.

There are some deviations away from the uniform mean B field. Some are seen in Figure 5 as the scatter off the mean, by up to about 25° for the farthest offset Mimir and I-band data. In Figure 4, the blue H-band Mimir vectors show small PA undulations along the mean field when traversing from the lower left to the upper right. Additionally, one SOFIA HAWC+ position shows an extreme departure from all other SOFIA BPAs and from the local Mimir BPAs.

This last BPA departure could be an early indication of changes in the local B-field direction driven by dense core collapse onto the envelope surrounding a YSO disk. Alternatively, it could be due to the disruption caused by the weak outflow from the YSO, which itself shows some elongation to the northeast (PA ∼ 45°; Furuya et al. 2014b), the same as the PA of the line connecting the YSO to that SOFIA position. Faint emission is seen in Spitzer IRAC images to ∼35 arcsec southwest of the YSO (along PA ∼ 225°). If this emission represents the extent of the other outflow lobe, the lack of SOFIA HAWC+ detection in this area could be explained by disrupted or tangled B-field lines.

The examination for rotation of BPA with wavelength was performed in two ways. The first was a nonquantitative examination of the data presented in Figure 5. In that figure, there is a slight tendency for the HAWC+ points to exhibit greater BPA values while the Planck values are lesser. However, there is no strong progression of BPA with wavelength that stands out at any radial offset. The figure also shows that because the different polarization probes each span limited radial offset zones, detailed quantitative comparisons that use the full data set for each wavelength will introduce a spatial bias, since there is no single zone sampled by all wavebands.

Nevertheless, in the second examination method, weighted-average BPA values were formed for the data set at each wavelength, using a common criterion that each data set utilized only elements for which the BPA uncertainties were less than 25°. This resulted in sample sizes of 73 stars for the I band, 183 stars for the H band, 115 stars for the K band, six positions for HAWC+ 216 μm, and 115 positions for Planck 353 GHz out to about 05 offset from the YSO. The mean BPA values, and propagated uncertainties, are shown in Figure 6 as colored triangles and vertical error bars. All six SOFIA BPAs were used, including the one that significantly departs from the other five. If only the five are used, the SOFIA data point moves down on the plot by 10°. Also, some of the Planck data correspond to offsets that are quite far from the YSO position, so even a weak change in BPA with location will affect the utility of inclusion of the Planck data with the SOFIA and stellar data for the purpose of finding a wavelength dependence.

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Least-squares fits to the run of BPA with wavelength were performed; one was linear with wavelength and one was a power law of wavelength. The fit functions and parameters returned were

$$\begin{eqnarray}&&{\mathrm{BPA}}_{\deg }=(129.7\pm 0.2)-(16.0\pm 0.7)\times {10}^{-3}\times {\lambda }_{\mu {\rm{m}}}\end{eqnarray} \tag{ 3 }$$

and

$$\begin{eqnarray}&&{\mathrm{BPA}}_{\deg }=(129.72\pm 0.10)\times {\lambda }_{\mu {\rm{m}}}^{(-0.012\pm 0.002)},\end{eqnarray} \tag{ 4 }$$

where BPA_deg is the B-field orientation angle in degrees and λ_μm is the wavelength measured in microns. While these fits do, formally, report BPA rotations with wavelength, the rotation amounts are quite small, amounting to less than 15° over the entire wavelength range. In contrast to the BPA rotation with wavelength (and/or position) identified by Jones (2003) and Poidevin & Bastien (2006) for the L1082C core in GF 9, Figures 4 and 6 show negligible BPA rotation with either wavelength or position.