THE STELLAR AND GAS KINEMATICS OF THE LITTLE THINGS DWARF IRREGULAR GALAXY NGC 1569

2.1.1. Observations

We observed NGC 1569 with the Kitt Peak National Observatory (KPNO¹²) Mayall 4 m telescope with the Echelle spectrograph for three nights in 2008 February and five nights in 2008 November. The sky conditions for the 2008 February observing run were moderate with only a few cirrus clouds interfering sporadically throughout the run. The moon was in a waning crescent phase and was separated by more than 180° from NGC 1569. The weather conditions for the 2008 November observing run were superb with nearly photometric conditions throughout the five nights; however, the moon passed through third quarter during the second night of our run but was separated from NGC 1569 by more than 60°.

Table 2 lists the observation log. In order to place the slit, we identified the center of the galaxy and position angle (P.A.) of the major axis from isointensity contours on our V-band image. We observed at four P.A.s, all centered on the morphological center of the galaxy: the major axis (P.A. = 121°), the minor axis (P.A. = 31°), and ±45° from the major axis. Figure 2 shows the HST¹³ V-band, O iii λ5007, Hβ, and Hα filter composite image of NGC 1569 taken with the Advanced Camera for Surveys and the Wide Field Planetary Camera 2 instruments (bottom panel) with the slit positions superimposed.

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Table 2. Optical Spectroscopic Observations of NGC 1569 Taken with the KPNO 4 m + Echelle Spectrograph in 2008

UT Date	P.A.a	Ngalb	Tgal(s)c	Nskyd	Tsky(s)e	Nspecf	NRVg
Obs.
Mg Ib spectral region
02/01	Major axis (121°)	5	9000	5	9000	7	4
02/02	Major axis (121°)	5	9000	5	7393	9	5+1
02/03	Minor axis (31°)	4	7200	4	5673	4	11+1
11/19	+45° from major axis (166°)	8	13,800	7	12,000	4	5
11/20	−45° from major axis (76°)	3	5400	2	3600	2	6+1
11/21	−45° from major axis (76°)	8	14,400	8	13,860	6	9
11/22	−45° from major axis (76°)	5	9000	5	8841	3	10
	Major axis (121°)	3	5400	3	5400	4	10
O iii λ5007 observations
11/23	Major axis (121°)	3	4800	3	1800	95	NA
11/23	Minor axis (31°)	3	1800	1	600		NA

Notes. ^aPosition angle observed. ^bNumber of galaxy exposures co-added into a single spectrum. ^cTotal integration time, in seconds, on galaxy. ^dNumber of sky exposures co-added into a single spectrum. ^eTotal integration time, in seconds, on sky. ^fNumber of one-dimensional spectra extracted. ^gNumber of radial velocity standard stars used in cross-correlation function. The "+1" is in reference to the solar spectrum, from twilight flats, used as a radial velocity standard star.

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We converted the Echelle into a two-dimensional, long-slit spectrograph by replacing the cross-disperser with a mirror flat. This permitted the isolation of a single order and produced a 3' long slit. In order to maximize throughput, while maintaining high spectral resolution, we opened the slit to a width of 25. For the stellar kinematic data, we targeted the prominent Mg Ib stellar absorption features at wavelengths 5183.6 Å, 5172.7 Å, and 5167.3 Å, by isolating order 10 for the 316°–63° Echelle using the post-slit filter KP 1433. This filter has a central wavelength of 5204 Å and an FWHM of 276 Å. The free spectral range of the Echelle was 517 Å centered at 5170 Å, but for the Tektronix 2048 × 2048 CCD that we used, only 286 Å fit across the chip. We used the "fast UV" camera along with pre-slit filter GG 495. The prominent Mg Ib stellar absorption features were easily detected. There are no telluric features in the spectral region we observed.

For our spectral range, this setup provided an FWHM = 0.38 Å as measured from the central lines of Th–Ar comparison lamp exposures, giving a velocity resolution of ∼22 km s⁻¹. This corresponds to a velocity dispersion, σ, of ∼9 km s⁻¹. We achieved an angular pixel scale of about 12 pixel⁻¹, after binning by 2 pixels in the cross-dispersion direction, and a final spectral pixel scale of 0.14 Å pixel⁻¹.

For each observing run, we moved a single radial velocity standard star in 30'' steps along the slit and used these data to trace the cross-dispersion curvature of the slit on the CCD. We averaged 10 dome flats from each night to determine pixel-to-pixel variations in the detector. Also, we took twilight sky exposures that were used to correct for illumination variations. The rotator on the Echelle was set to the desired P.A. before observations began, and we generally used one P.A. during a night.

Each night we observed a series of radial velocity standard stars. These Milky Way stars were selected to have a range of spectral types (F, G, and K) and luminosity classes (III–V) to provide a varied spectral stellar library for the cross-correlation analysis. Table 3 lists the standard stars used in the cross-correlation. We observed some of the same stars from night to night and run to run to minimize and identify systematic offsets. There were no trends identified over our narrow wavelength region between the radial velocity standard star spectral types or classes.

Table 3. Radial Velocity Standard Stars Used for Cross-correlation

HD	Apparent	Metallicity	Spectral	R.A. (J2000)	Decl. (J2000)	Vhelioa	σV	Texp	UT Date
No.	Magnitude, V	Fe_H	Type and Class	(hh:mm:ss)	(°:':'')	(km s−1)	(km s−1)	(s)	Obs. (2008)
8779	6.41	−0.401	K0 IV	01:26:53.5	−00:21:18	−5.0	0.5	36	02/03
9138	4.84	−0.372	K4 III	01:30:37.9	+06:11:15	+35.4	0.5	7	02/03
								10	11/22
12029	7.44	...	K2 III	01:59:11.2	+29:25:16	+38.6	0.5	90	11/22
22484	4.28	−0.102	F9 IV–V	03:37:18.5	+00:25:41	+27.9	0.1	5	02/01
								5	02/02
								5	02/03
								5	11/22
23169	8.50	...	G2 V	03:44:23.9	+25:45:06	+13.3	0.2	240	02/03
26162	5.50	−0.023	K1 III	04:09:39.8	+19:37:52	+23.9	0.6	15	02/01
32963	7.60	0.083	G5 IV	05:08:27.3	+26:20:18	−63.1	0.4	80	02/02
								80	11/21
65583	6.97	−0.562	G8 V	08:01:03.6	+29:11:09	+12.5	0.4	60	11/19
								75	11/22
65934	7.70	...	G8 III	08:02:42.1	+26:36:49	+35.0	0.3	90	11/22
66141	4.39	−0.302	K2 IIIb Fe-0.5	08:02:42.5	+02:18:39	+70.9	0.3	10	11/22
75935	8.46	...	G8 V	08:54:20.3	+26:52:50	−18.9	0.3	170	11/21
90861	6.88	...	K2 III	10:30:22.2	+28:32:15	+36.3	0.4	60	11/21
92588	6.26	−0.101	K1 IV	10:41:50.1	−01:47:11	+42.8	0.1	35	11/19
								40	11/22
102494	7.48	−0.264	G9 IVw...	11:48:22.8	+27:17:36	−22.9	0.3	90	11/22
122693	8.11	...	F8 V	14:03:15.6	+24:31:14	−6.3	0.2	170	02/03
126053	6.27	−0.452	G1 V	14:23:41.4	+01:12:08	−18.5	0.4	35	02/02
								35	02/03
132737	7.64	...	K0 III	15:00:14.4	+27:07:37	−24.1	0.3	80	02/01
								80	02/02
								80	02/03
136202	5.06	−0.082	F8 III–IV	15:19:44.9	+01:44:01	+53.5	0.2	24	02/03
144579	6.66	−0.693	G8 IV	16:05:14.4	+39:08:02	−60.0	0.3	35	02/01
								35	02/03
145001	5.00	−0.265	G5 III	16:08:27.6	+17:01:29	−9.5	0.2	10	02/02
								10	02/03
154417	6.01	−0.046	F8.5 IV–V	17:05:42.8	+00:41:26	−17.4	0.3	20	02/03
182572	5.16	−0.373	G7 IV Hδ 1	19:25:22.5	+11:57:47	−100.5	0.4	24	11/20
								24	11/21
187691	5.11	0.077	F8 V	19:51:26.1	+10:26:15	+0.1	0.3	24	11/19
								24	11/21
194071	7.80	...	G8 III	20:22:58.8	+28:16:26	−9.8	0.1	90	11/20
203638	5.41	0.025	K0 III	21:24:38.4	−20:48:55	+21.9	0.1	15	11/20
								24	11/21
212493	4.79	...	K0 III	22:28:17.3	+04:44:19	+54.3	0.3	7	11/19
								7	11/21
								10	11/22
213014	7.45	...	G9 III	22:28:36.3	+17:18:25	−39.7	0.0	75	11/19
213947	6.88	...	K2	22:35:00.6	+26:38:32	+16.7	0.3	40	11/21
222368	4.13	−0.152	F7 V	23:40:23.3	+05:40:21	+5.3	0.2	5	11/20
								5	11/22
223311	6.07	...	K4 III	23:48:58.7	−06:20:00	−20.4	0.1	20	11/20
								30	11/21

Notes. ^aHeliocentric radial velocities. All data in table, except for metallicity and the last column, come from the United States Nautical Almanac Office (2008). Metallicities are listed, where available, and references are given below. References. (1) Soubiran et al. (2008); (2) Randich et al. (1999); (3) Cenarro et al. (2007); (4) Yoss & Griffin (1997); (5) McWilliam (1990); (6) Chen et al. (2000); (7) Fuhrmann (1998).

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For NGC 1569, we took 1800 s exposures after first verifying the telescope pointing by offsetting from a nearby foreground star before each exposure. To ensure proper sky subtraction after each galaxy exposure, we observed a nearby dark region of sky for 1800 s. In some cases, the sky exposures were scaled by a constant to correct for differing sky conditions. Following every star, galaxy, or sky exposure, we took Th–Ar comparison lamp exposures in order to acquire accurate wavelength calibration as a function of time and position. For each P.A., we took five to seven exposures on the galaxy, which we co-added for a total integration time of 2.5–3.5 hr, during a single night.

2.1.2. Data Reductions

All data reductions were accomplished using the Image Reduction and Analysis Facility (IRAF¹⁴). We fit the overscan to all images in order to remove the electronic pedestal, and corrected for pixel-to-pixel variations using dome flats taken each night (ccdproc). We trimmed the two-dimensional flats so that the steep drop-off of light toward the edges would not complicate the normalization function.

The wavelength solution was modeled by fitting the comparison lamp exposures independently for each spectrum each night. For a given night, the wavelength solutions were stable to within a tenth of an angstrom. Because we observed comparison lamp exposures before every spectrum, our wavelength solutions were robust. Thus, we were able to place all images on the same wavelength scale for each observing run (longslit, identify, reidentify, fitcoords). We used the radial velocity standard star that was moved spatially along the slit to map out the distortion along rows of constant position, and then we used the comparison lamp exposures to trace the distortion along columns of constant wavelength. These fitting procedures produced coordinate maps that were then applied to every respective object exposure (transform). Next, we applied a slit function that corrected for the minor illumination drop-off at the edges of the slit in the cross-dispersion direction. This was achieved by combining the twilight flats from a single night and fitting a two-dimensional function to the illumination pattern along bins of summed columns in the cross-dispersion direction (illum).

Before combining the spectra, we ensured proper galaxy alignment by overplotting the spectra and matching the peak flux in individual images. If necessary, a pixel shift was applied to align peaks. Galaxy images from a single night with the same P.A. were combined into a single spectrum with an algorithm to reject cosmic rays (imcombine). The same combining process, without the shifting procedure, was applied to the sky images. Finally, we subtracted the co-added sky image from the co-added galaxy image while taking care to scale the combined sky image, when needed, to correct for differing exposure times and sky conditions. Figure 3 shows the co-added galaxy spectrum of the major axis of NGC 1569 before and after sky subtraction.

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2.2.1. Observations and Data Reductions

A different post-slit filter (KP 1547) was used for the ionized gas, but otherwise, the telescope setup was unchanged. The KP 1547 filter has a central wavelength of about 5015 Å and an FWHM of 27 Å, and was used for targeting the O iii λ5007 emission feature. We observed both the major and minor axes. We took dome flats, twilight flats, and stepped one radial velocity standard star along the slit spatially to correct for the slit distortion and to find the center of the slit in the same fashion as for the other filter, described previously.

Additionally, we took Th–Ar comparison lamp exposures after all object images for accurate wavelength calibration. We observed three galaxy and three sky positions for the major axis P.A., and three galaxy positions for the minor axis. However, due to threatening clouds during the course of the night, we were only able to observe one sky image for the minor axis. The sky image was scaled to compensate for the large difference in exposure time. Despite the difficulties, the brightness of the O iii emission line made it possible to obtain high signal-to-noise (S/N) emission line spectra. We followed the same data reduction procedure as for the stellar spectral data. Figure 4 shows the fully reduced, two-dimensional, co-added, O iii λ5007 emission spectrum for the major and minor axes of NGC 1569.

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The LITTLE THINGS project retrieved the calibrated H i line uv-data from THINGS but improved upon the quality of the THINGS data products by applying a multi-scale cleaning algorithm implemented in the AIPS task imagr (see, e.g., Cornwell 2008; Rich et al. 2008; Greisen et al. 2009). Instead of approximating all structures as a sum of point sources, this algorithm iteratively fits Gaussians to four angular scales of 135'', 45'', 15'', and 0'', respectively. The multi-scale cleaning algorithm produces a single data cube in which all observed angular frequencies are properly represented and with near uniform (Gaussian) noise statistics, which is a great advantage over standard cleaning methods. A beam size of 771 × 704 (with a P.A. of 165) and a spectral resolution of 2.6 km s⁻¹ were achieved.

In order to separate noise from real galaxy emission, we used the Natural-weighted cube and smoothed it to a 25'' × 25'' (convl) beam. We blanked this smoothed cube twice, first for all pixels below 2.5σ of the rms of the smoothed cube (blank), and then again by hand for any additional emission that was clearly noise. This final, blanked cube became the master for the cubes with smaller beam sizes and was used as a conditional transfer. For a comprehensive review of our mapping procedure, please see Hunter et al. (2012).

The half-power beam width (HPBW) of the primary beam is 32', but the largest angular scale of emission that is expected to be recovered by the interferometer is ∼15', which is determined by the D array. Any smooth structure larger than ∼15' will be invisible to the interferometer. This was useful in removing foreground Milky Way H i emission, which has velocities that partly overlap with some of the velocities encountered in NGC 1569. In essence, the interferometer is blind for emission from the Milky Way, and will only register its small-scale structure, which is still considerably more extended than that of NGC 1569. The multi-scale cleaning algorithm was able to model this Milky Way emission sufficiently well so emission from NGC 1569 could be isolated from the rest using the blanking method described above. A more in-depth discussion of Milky Way confusion with NGC 1569 is discussed in our upcoming paper describing the map made with the Robert C. Byrd Green Bank Telescope (GBT; M. Johnson, in preparation, hereafter Paper II).

Figure 5 shows the LITTLE THINGS integrated flux map. This image shows tenuous emission to the south and northeast of the galaxy that are imaged for the first time. Although faint, this low-level, extended emission was confirmed in follow-up observations with the GBT and will be discussed in Paper II.

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3.1.1. Extracting One-dimensional Spectra

We extracted one-dimensional stellar spectra from the two-dimensional spectra of NGC 1569 (scopy). It was necessary to sum over a series of consecutive rows in the cross-dispersion direction during spectral extraction in order to increase the S/N. In the portion of the spectrum that contains the brightest light, from radii 0'' to −25'' (west of center) measured from the center of the galaxy, which is also where the SSCs reside (shown in Figure 6), we summed over five rows, 61 of the major axis. For the regions of the galaxy that have a lower light concentration, from radii 17'' to 0'' (east of center), we summed over 10 rows of the major axis, 122. To avoid diluting the true stellar velocities and velocity dispersions, we never summed over more than 122, which, at a distance of 3.36 Mpc (Grocholski et al. 2008), corresponds to 195 pc.

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Figure 7 shows three, one-dimensional galaxy spectra and one stellar template spectrum for comparison. The top and third panels were the result of summing over 122 in the cross-dispersion direction along the major axis of NGC 1569 and the second panel summed over 61. These three spectra show the range of S/N for our galaxy spectra and all of our spectra used in the cross-correlation method (CCM) had an S/N above ∼5. The bottom panel shows HD 132737, a K0 III template star for comparison. All of the standard stars had S/N above ∼50, usually near 90, although this was difficult to measure due to the lack of line-free continuum (see the bottom panel of Figure 7).

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We extracted one-dimensional spectra of the radial velocity standard stars using apall (see, e.g., the bottom panel of Figure 7). We identified the center of the peak emission in each star and fit the background using the spatial regions of the slit that contain no stellar data. In some cases, we used the twilight sky exposures to extract a solar spectrum, which was used in the CCM as a G2 V radial velocity standard star. Table 2 identifies the nights that utilized these solar spectra by the +1 added to the number of standard star spectra in Column 9. Once one-dimensional spectra were extracted, we added into the header of each star the V_helio radial velocities from the United States Nautical Almanac Office (2008). These spectra of radial velocity standard stars are the templates that were used in the CCM. We fit a cubic spline function to the continuum in the spectra of the galaxy and the template stars (continuum). The slit width of 25 may have caused small telescope tracking errors for some of the template stars because the seeing on most nights was around 12. However, the exposure times for the standard stars were short, less than a minute for a large portion (see Table 3), so tracking errors do not a play a large role in the total error budget.

3.1.2. Cross-correlation Method

We cross-correlated the template stars with each other to test the CCM and to check the observed stars' velocities, which was within a few percent of the stars' known velocities in most cases (fxcor). The one-dimensional spectra from the galaxy were cross-correlated with the stellar templates observed during the same night. We only performed cross-correlations of the stars with stars and stars with galaxy spectra that were obtained on the same night in order to minimize the uncertainties in the observational setup, such as varying P.A.s. The heliocentric radial velocities and velocity dispersions of the stars in NGC 1569 were determined, for each spectrum, by fitting a single Gaussian curve to the peak of the CCM. We did not explore the possibility of asymmetric Gaussian profiles as the quality of our data was not good enough for accurate analysis. We made the assumption that the stars in NGC 1569 are virialized and the Gaussian profiles are symmetric. We excluded regions around emission line features in order to avoid internal galaxy emission or residuals due to atmospheric emission lines that were not completely removed during the sky subtraction step (see the top image of Figure 3, which shows residual sky emission lines around 5196.8 Å and 5199.1 Å, and the top panel of Figure 7).

We cross-correlated each template star with each galaxy position and averaged the V_helio values by weighting them by the standard deviations of the different template spectra, thus determining the V_helio values at each galaxy radius. By weighting the V_helio values in this manner, an ill-fitting template would not contribute as much to the resulting V_helio of the galaxy spectra as a good-fitting template. Also, we observed no trend between stellar spectral types or classes when determining a "good-fitting" versus an "ill-fitting" template in the CCM; S/N dominated the quality of the fit.

To determine the intrinsic velocity dispersions of the stars, σ_obs, in NGC 1569 as a function of radius, we employ the definition of a Gaussian and correct for instrumental broadening using the following equation:

$$\begin{equation} \sigma _{\rm obs} = \frac{\sqrt{{\rm FWHM_{{\rm obs}}}^2-{\rm FWHM_{{\rm instr}}}^2}}{{2.35}}. \end{equation} \tag{ 1 }$$

We determine the inherent, average instrumental FWHM, FWHM_instr = 35 km s⁻¹, by cross-correlating the template stars from a single night with each other. The intrinsic broadening of a single star should be unresolved, so the FWHM_instr of the cross-correlation of the template stars with each other represents the instrumental signature. Although the spectral types and classes of the radial velocity standard stars span a range, our usable wavelength region is only ∼150 Å, and thus cross-correlations of the stars between differing spectral types did not create variations in the resulting FWHM_instr or FWHM_obs above their respective standard deviations.

3.2.1. Extracting One-dimensional Spectra

3.2.2. Multiple Gaussian Decomposition

Figure 8 shows an example of a single extracted spectrum of the O iii λ5007 emission feature taken from the major axis. It is evident that there are three distinct, bright peaks over a total width of 4.1 Å, or, ∼176 km s⁻¹. We disentangled these blended features with multiple Gaussian components (splot). The three velocities obtained for the brightest three peaks in Figure 8 are −133.9, −84.2, and −31.5 km s⁻¹ spanning a range of over 100 km s⁻¹ at a distance of −132 from the center of the galaxy along the major axis. This fitting procedure was repeated for each spectrum extracted along the cross-dispersion axis.

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3.3.1. Tilted Ring Models

3.3.2. The Bulk Velocity Field

NGC 1569 shows a dominance of non-circular and random motions as seen in the intensity-weighted mean velocity field in Figure 9. The blue features across NGC 1569 show H i gas with motions that are non-circular and do not follow the bulk motion of the galaxy disk. A "typical" rotating disk generally displays a grading scale of isovelocity contours with blueshifted (relative to the systemic motion) H i on one side and redshifted H i on the opposite side. The systemic velocity of the system separates the two halves. This is not what is observed in Figure 9. Nevertheless, we were able to apply the method developed by Oh et al. (2008) to extract bulk rotation from chaotic systems like NGC 1569.

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An iterative double Gaussian deconvolution procedure was used to separate velocities of H i clouds superimposed upon the bulk motion at a given position in the H i data cube. The deconvolution program uses only the H i intensities that are above 2σ in the bulk velocity field. This limits the extracted velocity fields to the inner, concentrated H i disk. The red outline in Figure 9 roughly identifies the region over which we extract the bulk velocity field. At each position within this region, if there are two distinct Gaussian peaks detected above 2σ, then the velocities of the central wavelengths of each respective peak are compared to a model velocity field. The velocity closest to the model velocity field is assigned to a bulk motion map while the outlying velocity is assigned to one of two non-circular velocity maps. The $\it {strong}$ non-circular velocity map contains all velocities that are derived from Gaussian peaks that have a $\it {higher}$ intensity than the bulk motion velocity, whereas the reverse is true for the $\it {weak}$ non-circular velocity map.

Figure 10 shows (a) the final bulk velocity map, (b) the strong non-circular velocity map, (c) the weak non-circular velocity map, and (d) the strong non-circular velocity superimposed on the weak non-circular velocity map. The black oval in each panel of Figure 10 identifies an H i cloud that has systemic motions significantly deviating from the bulk motion of the galaxy. In fact, this cloud is virtually absent in the bulk velocity field (see panel (a) in Figure 10). Stil & Israel (2002) first detected this H i cloud and describe it as "high velocity cloud 3 (HV3)." This cloud is discussed in more detail in Section 5. In Section 4.3, we derive the H i rotation curve using the two-dimensional bulk velocity field and the tilted ring model.

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Figure 11 shows position–velocity (P-V) graphs, where the positive positions are in the eastern direction. The error bar in the radial direction represents the angular area of the slit over which the velocities were determined. We used the weighted average of the minor axis velocity points to determine a systemic velocity, V_sys, of −82 ± 7 km s⁻¹, which is denoted by the horizontal solid line in Figure 11. This value is consistent with H i studies such as Reakes (1980), V_sys = −77 ± 1 km s⁻¹, and de Vaucouleurs et al. (1991), V_sys = −89 ± 5 km s⁻¹. But it is inconsistent with the value obtained by Schneider et al. (1992), V_sys = −104 ± 4 km s⁻¹, who state that the H i flux used to derive the velocity is confused with foreground Galactic emission.

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We used the four P.A.s to constrain the inclination and line of nodes. The de-projection was derived by the following formula obtained from V. Rubin (2009, private communication):

$$\begin{equation} V_{\rm obs} - V_{\rm sys} = \frac{V({\rm R})\sin (i)\cos (\eta - \theta)}{[\sec ^2 (i) - \tan ^2 (i)\cos ^2(\eta - \theta)]^{1/2}}. \end{equation} \tag{ 2 }$$

Here, i is the inclination of the disk, η is the P.A. of the observed point in the plane of the sky, θ is measured north through east to the receding major axis, which is the P.A. of the major axis (line of nodes), V_obs is the observed line-of-sight radial velocity, V_sys is the systemic velocity, and V(R) is the rotational velocity. Although the velocities of the stars are quite irregular, we were still able to constrain the inclination of the disk to i ≈ 60° ± 10° and the major axis ${\rm {\rm P.A.}} \approx 120\mbox{$^\circ $}\pm 8\mbox{$^\circ $}$ using a least-squares fit. Both of these estimates agree well with the H i results (see Table 1). Furthermore, Figure 12 shows P-V diagrams of the stars plotted with H i intensity contours. These plots demonstrate the kinematic similarity between the stars and H i, as the stars follow the H i in all four P.A.s. The stellar velocity dispersions are shown in Figure 13 for each of the four P.A.s. The average of the velocity dispersion, 〈σ_obs〉, weighted by the uncertainty of each point, for all four P.A.s is 21 ± 4 km s⁻¹.

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In order to disentangle σ_R, σ_z, and σ_ϕ from σ_obs, we use the following relation from Gerssen et al. (1997):

$$\begin{equation} \sigma _{\rm obs}^2 = \big[\sigma _{\rm R}^2\ \sin ^2(\eta - \theta) + \sigma _{\rm \phi }^2\cos ^2(\eta - \theta)\big] \sin ^2i + \sigma _{\rm z}^2 \cos ^2i. \end{equation} \tag{ 3 }$$

Here, η is the intrinsic angle within the plane of the galaxy, θ is the receding major axis P.A., and i is the inclination of disk. Since the H i and stars are well matched (see Section 4.2), from here on we use the better determined inclination of i = 69° ± 7° and major axis P.A. of 1225 from the H i kinematics. Since we have only a few points along each intermediate P.A., i.e., ±45° from the major axis, we focus on the major axis, where η = θ and thus, σ_R does not contribute to σ_obs. Following Swaters (1999), we make the assumption that the stellar velocity dispersion in the stars follows the Milky Way properties observed for stars near the Sun. Therefore, σ_obs = σ_z for the major axis.

Swaters (1999) found a relation between integrated M_B of a galaxy and the central vertical velocity dispersion:

$$\begin{equation} \log \sigma _z = -0.15M_{\rm B} - 1.27. \end{equation} \tag{ 4 }$$

This relation predicts a σ_z of 21 km s⁻¹ for NGC 1569, which is equal to our observed value of 21 ± 4 km s⁻¹. NGC 1569 agrees well with the overall trend observed in spiral galaxies, i.e., lower luminosity systems have lower velocity dispersions.

Figure 14 shows the decomposed line-of-sight radial velocities of the ionized gas for the major axis and has the stellar and H i velocities overplotted for comparison. The H i velocities in this figure come from a P-V slice through the major axis of the H i data cube with a sampling width of 8'', equal to the FWHM of the H i beam. There was no deconvolution done to produce these H i velocities; they are simply the observed velocities along the major axis P.A. The velocities of the O iii ionized gas match the velocities of Hα along the major axis observed by Tomita et al. (1994, see their Figure 3).

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In Figure 14, we observe two forms of ionized gas: high-velocity gas and low-velocity gas. The low-velocity ionized gas has velocities that match the H i and stellar velocities and is likely associated with H ii regions, or the remnants thereof, leftover from recent star formation. The high-velocity ionized gas at a radius of −20'' has the signature of an expanding shell as identified by the solid red outline in Figure 14. This expanding shell has an expansion velocity of ∼70 km s⁻¹. The stellar velocities overplotted in Figure 14 perfectly match the velocities of the low velocity gas (∼ +10 km s⁻¹) at the center of the expanding gas shell (R ∼ −20''). These low velocities of the ionized gas also coincide with the bulk motion of the H i gas. Curiously, this agreement extends to the peculiar dip to lower velocities at the western edge of the red oval outline. This agreement in velocity (stars and O iii) shown by the black arrow in Figure 14 is presumably from H ii regions connected with particularly bright stars. Within this expanding shell, there is only one H i velocity point. The absence of H i in this region is due to an H i hole blown out by SSC A (Israel & van Driel 1990). SSCs A and B reside at radii −22'' and −12'', respectively. Due to the lack of H i and the matching stellar and low-velocity ionized gas in the expanding shell region, even including peculiar motions, we conclude that our stellar spectra are dominated by a young, luminous stellar population that are ionizing nearby gas leftover from the star formation process. At the same time these young, luminous stars, mostly from SSC A, created the expanding shell from winds and supernova explosions during the most recent star formation episode. This expanding shell was also observed and discussed by Westmoquette et al. (2007a, 2007b), who also observed both the low- and high-velocity ionized gas.

The high-velocity ionized gas seen everywhere else is likely the result from outflow from the recent starburst activity (Westmoquette 2007a, 2007b). We also see evidence of galactic wind at radii greater than +0''. Because of the exponential drop in stellar light, the integrated emission from the stars was too faint to extract stellar kinematic information in our optical spectra beyond a radius of ±30''. Thus, no stellar velocity information is known in the region of the high-velocity ionized gas at radii greater than +30''.

The low-velocity ionized gas centered at R = +15'' in Figure 14 also shows matching stellar and gas velocities. This region, however, has more H i than the expanding shell centered at −20''. It is not as obvious here as for the expanding shell centered at R = −20'', but it is possible that the stellar spectra around R = +15'' are also dominated by young, luminous stars because they too follow the velocities of the low velocity ionized gas and H i.

Studies of H ii regions of NGC 1569 (Greve et al. 1996; Hunter et al. 1993; Waller 1991; Götz 1990; Young et al. 1984) show that there is star formation in the region at R = +50'', but it is not as intense as the western side of the galaxy where the SSCs reside. Again, we note that the velocities of the ionized H ii regions (low velocity gas) and H i agree well in this area.

Figure 15 shows the observed rotation curve. We find a maximum rotational velocity, V_rot, of 33 ± 10 km s⁻¹, which was calculated from the average of the last nine data points in Figure 15. The uncertainty is dominated by the rapid drop in S/N in the bulk velocity field beyond a radius of 2.2 kpc. Within the errors, Figure 15 shows a rising, solid body-type rotation curve, which at best reaches the usual flat part at radii >2.2 kpc.

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Figure 16 shows a velocity dispersion map of the bulk (main) velocity component only. The average H i velocity dispersion is high, $\langle \sigma _{{\rm H\,\mathsc{i}}}\rangle$ = 10 km s⁻¹, compared to the observed rotation speed, V_rot = 33 ± 10 km s⁻¹. Because of the high H i velocity dispersions in NGC 1569, we correct the observed rotation velocities for asymmetric drift in the same manner as Oh et al. (2011), and derive the curve shown by the filled circles in Figure 17. The maximum rotation velocity determined from H i increased from the observed V_rot = 33 km s⁻¹ to V_max = 50 km s⁻¹ after the asymmetric drift correction was applied.

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The upper left panel in Figure 12 displays the observed radial velocity of gas (contours) and integrated stars (points) as a function of position along the slit that passes through the major axis. This P-V diagram shows "forbidden" H i motion in the upper right quadrant between −40 and −70 km s⁻¹ at around a distance of −06 from the galaxy center, as identified by the black oval. We define "forbidden" H i as motion that does not follow the ordered rotation. Along the major axis in Figure 12, we show a black curve that traces the average velocities of the H i contours from 0' to 2', which is the region of the diagram that follows the ordered motion of the H i gas. This black curve is then reflected through the origin to show what the expected ordered motion should be from −2' to 0'. At some positions between distances of 0' and −05 from the galaxy center, the stellar velocities follow the velocity trend of the forbidden motion, whereas at other positions around −04, the stellar velocities follow the ordered rotation of the H i disk.

Could the gas and stars be showing evidence of counter-rotation? If this were the case, then we would expect H i contours in the lower left quadrant of all the panels of Figure 12, which we do not observe. Therefore, we identify the forbidden H i motion as the northeastern tip of the NCM cloud identified in Figure 1 and by the black oval in Figure 10. The major axis, P.A. = 122° (shown in Figure 1 and by the black line throughout Figure 10), slices through the tip of the NCM cloud. The velocities of this cloud in the strong non-circular velocity map, panel (b) of Figure 10, match the velocities of the contours of the forbidden H i in Figure 12. The NCM cloud has similar velocity structure and position as HV3 in Stil & Israel (2002). We conclude that the stars and gas are not counter-rotating but there is evidence of a kinematic disturbance.

When the stellar velocities are laid on top of an optical image, we can physically see the areas in the galaxy that correspond to observed stellar kinematic features. Figure 6 shows the HST image in gray scale. Red and blue ovals are superimposed on the picture, representing the positions of the extracted spectra along the major axis. The length of each oval represents the angular area of the slit that we summed, while the width of the ovals represents the 25 slit width. Red and blue ovals represent redshifted and blueshifted V_helio radial velocities, respectively, relative to the systemic velocity of NGC 1569. Each of the ovals is representative of independent data points from spectra taken on different nights. Therefore, there are some redshifted and blueshifted velocities shown at the same positions. The green "X" marks the center of the slit and the center of the galaxy.

In the region west of SSC A, the overall rotation of the stars is actually redshifted, which is seen from the dominance of red ovals in Figure 6. The locations of the blue ovals that reside to the west of SSC A correspond to a distance of −27'' from the galaxy center. If this location is compared with the velocity dispersion plot of the stars for the major axis P.A. (top left panel) in Figure 13, the velocity dispersion is larger by ∼10 km s⁻¹ from the average stellar velocity dispersion. The increase in stellar velocity dispersion in this region is consistent with secondary star formation that formed out of the surrounding material that was shocked by the expanding shell discussed in Section 4.2. Therefore, these peculiar kinematics observed in the stars are likely from light composed mostly of young, luminous stars in NGC 1569.

In the optical HST image of NGC 1569, shown in the right image of Figure 1, we can observe Hα streamers, which are material likely trapped in the outflow, extending to the northeast and southwest from the SSC region, as indicated by the arrows. Also, there is a large Hα hole where the SSCs reside, also identified in Figure 1. We estimate the projected surface area of this hole to be about 0.2 kpc² at the distance of NGC 1569. Figure 12 also shows a hole in the H i in all four P.A.s. It is centered around 04 in the major axis P.A. and around 01 in the remaining three P.A.s in Figure 12 (see Israel & van Driel 1990). It is in this hole that we observe the disturbed stellar kinematics. These features are likely evidence of outflow from mechanical energy input from stellar winds and supernova remnants from the collection of massive stars in the SSCs. Large amounts of X-ray emission coming from this region (Ott et al. 2005a) are consistent with this interpretation.

We explore the three-dimensional shape of NGC 1569 using our kinematic measure, V_max/σ_z. For this relationship, we use the asymmetric drift corrected V_max from our H i analysis. Because we want the maximum velocity of the baryons that are responding to the total gravitational potential in the galaxy, it is necessary to correct for radial pressures in the gas that can artificially mask the true maximum rotation speed. We derived an asymmetric drift corrected V_max of 50 ± 10 km s⁻¹ from the H i analysis, discussed in Section 4.3, and we use σ_z of 21 ± 4 km s⁻¹ from the stellar kinematics, discussed in Section 4.1. We follow the same reasoning as Hunter et al. (2005) for our decision to use σ_z in our V/σ relation. We determine a V_max/σ_z = 2.4 ± 0.7. This is indicative of a thick distribution of young stars that dominate our spectra. As a reminder, this result assumes that the stars are in a virailized disk and that the Gaussian profiles are symmetric. Our stellar template spectra span a range of classes and types from F-type main sequence to K-type supergiants and thus, cover a range of stellar ages. Our observed galaxy spectra are a mix of all the stars in the galaxy but are dominated by the brightest stars, which are the younger stellar population. There may be a thin distribution of older stars that our spectra simply were not sensitive to and perhaps the disk is thicker in the region of SSC A than in the center of the galaxy. The increase in velocity dispersion and decrease in rotation speed around SSC A are consistent with velocities of stars that formed from shocked gas surrounding the observed expanding shell in the region of SSC A, as discussed above. Overall, the disk of NGC 1569 appears to be thick compared to spiral galaxies.

Here, we compare the H i morphology and velocity fields with our deep Hα image of NGC 1569 and the HST image. The left image of Figure 1 shows the contoured integrated H i map. This image displays tenuous emission, detected for the first time, extending to the south of the galaxy disk in a teardrop shape, and to the northeast; black ovals outline this emission. Also identified in this image are two features to the east labeled as "H i Companion" and "H i Bridge" identified by Stil & Israel (1998) and Mühle et al. (2005). Stil & Israel conclude that these features are indicative of a low-mass H i companion to NGC 1569. Our data detect this H i cloud, which can also be easily seen in Figures 5 and 9 at around α = 04:32:15, δ = +64:49:00. The extended H i emission, circled in Figure 1, and the two features identified by Stil & Israel (1998) as evidence of a possible low-mass H i companion, may be related to each other and show evidence of a recent interaction or merger with NGC 1569. We discuss these claims further in Paper II where we present results from deep GBT H i mapping around NGC 1569 and three of its nearest neighbors.

Figure 18 shows our deep Hα image with the contoured integrated H i map overlaid so that we can compare the morphologies. What is interesting here is that there is a UD H i cloud to the west that is at the edge of the optical galaxy in the same region where we observe the disturbed stellar kinematics. This H i cloud is nearly 50 M_☉ pc⁻² more dense than the surrounding medium and if there is molecular gas, the column density could be much larger.

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In Figure 18, we also observe two smaller, dense H i clouds on the opposite side, east of the optical galaxy. Possibly, there was one continuous, dense H i structure that connected these two dense H i clouds with the UD H i cloud. The most concentrated stellar light is in between these dense H i clouds where the SSCs reside, which suggests that the stars in this region formed out of the dense H i ridge that used to connect these clouds. The trigger for the starburst could have come from the impact of the infalling NCM H i cloud, shown in Figure 10 and identified by the blue oval in Figure 18, that compressed the interstellar medium of NGC 1569 and caused the dense H i ridge to collapse. It is more likely that the NCM cloud is infalling into the galaxy, rather than outflowing, because there is evidence of shocked gas near the impact area of the NCM cloud as seen in the continuum maps by Kepley et al. (2010, see their Figure 12).

We see in Figure 18 that, in general, the H i density is more concentrated to the north of the SSCs than it is to the south, as shown by the blue arrows and contour levels. There is a slight H i depression in the contour levels right above SSC A as indicated in Figure 18, possibly created by the outflow of the gas. This figure also shows the approximate location and projected size of two giant molecular clouds (GMCs) identified by Taylor et al. (1999, see Figures 3 and 4). These GMCs lie between the UD H i cloud and the SSCs and are at the tip of the NCM H i cloud. The region between the UD H i cloud and the SSCs that contains the GMCs is the most probable area for the next generation of star formation. McQuinn et al. (2010) suggest that the starburst episode in NGC 1569 is ongoing and started roughly 500 Myr ago.

Also in Figure 18 are streamer-like, arced Hα features, which trace H ii regions, toward the south and north. The high-density H i in the north and the visible Hα features in the south could be the results of the projection effects from the inclination of the galaxy. The X-ray emission is less absorbed to the south, according to Ott et al. (2005a), indicating that the north side of the galaxy is pointed toward us, and thus closer than the south side, assuming that the emission is escaping in the z-direction. Hα arcs and streamers extend nearly all the way through the H i disk in the southern direction of the disk. Similarly, the H i gas appears more dense in the northern half of the disk because there is more gas along the line of sight than there is in the southern half of NGC 1569.

Figure 18 also shows a strong Hα chimney to the north (Hunter et al. 1993; Mühle et al. 2005; Westmoquette et al. 2008). The H i depression noted in Figure 18 shows the escape route for the Hα emission (Mühle et al. 2005; Westmoquette et al. 2008). Magnetic field lines found by Kepley et al. (2010) may be following the outflow of the gas in this region and are channeling cosmic ray electrons out of the disk. Although the H i is more concentrated to the north, due to the projection effect of the inclined disk, the intense stellar winds from the starburst are able to penetrate all the way through the H i disk in the northern half of the galaxy, too. Tenuous Hα emission to the northeast of the optical galaxy stretches all the way through the H i disk just as it does in the southern part of the galaxy.

Westmoquette et al. (2008) discuss the kinematics of the Hα emission and suggest that "blowout," defined here as gas escaping the gravitational potential of the galaxy, from stellar feedback from the massive stars created in the starburst, is not yet occurring due to decreasing ionized gas velocities at the edges of the expanding Hα shells seen near SSC A. If we assume that the total mass of NGC 1569 is equal to our dynamical mass of 1 × 10⁹ M_☉ (discussed in Section 6.3), then the escape speed is ∼70 km s⁻¹ at a radius of 2.2 kpc. According to Figure 14, the ionized gas we observe with our O iii spectra shows high velocity gas in excess of 70 km s⁻¹ indicating that perhaps some of the gas is in the process of being expelled from the galaxy in a blowout. Ott et al. (2005b) also suggest that NGC 1569 is in the process of losing about 5 × 10⁶ M_☉ of hot gas, corrected for our distance. However, Ott et al. argue that in order for gas to escape completely from a galaxy, it must be moving at supersonic velocities when it hits the cool surrounding gas at one scale length. We observe tenuous H i stretching nearly 12 kpc south of the galaxy that is likely associated with tidal filaments (Paper II), so the hot gas may cool and fall back onto the disk of NGC 1569 when it hits this cold, neutral gas. Thus, it is not clear if this hot gas will actually escape the galaxy.

Figure 19 shows the H i intensity-weighted velocity contours, with the extended H i trimmed, superimposed over a low-contrast Hα image. In the region around the Hα image, we observe a butterfly shape in the H i. The western wing of the butterfly has velocities that are blueshifted relative to the systemic velocity, as seen by the blue and purple contours, whereas the eastern butterfly wing has redshifted velocities, as seen by the orange and red contours and are identified in Figure 19. The location of the UD cloud (solid black oval) and NCM cloud from Figure 10 (dashed black oval) are also indicated. The velocity structure of the NCM cloud appears different in Figure 19 than in Figure 10 because we are observing the intensity-weighted velocity field instead of the deconvolved velocity structure. The possible "H i Companion" and "H i Bridge" discussed by Stil & Israel (1998) are seen as purple contours and do not follow the rotation of the rest of the galaxy. Again, we surmise that these features are most likely remnants from a past interaction.

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To the south of the Hα image in Figure 19, we see a cavity in the H i. This cavity is likely carved out by ultraviolet photons, winds, and explosions from the massive stars in the starburst. X-ray emission fills the cavity (Martin et al. 2002; Ott et al. 2005a). Furthermore, Figure 19 shows that the spectacular Hα tail, known as the "western arm" from Hodge (1974), that extends to the southwest of the optical galaxy is, in fact, the lit-up edge of the UD H i cloud. This western arm was previously believed to have been associated with the strong NCM cloud created from outflow due to the apparent spatial overlap of the two features (Waller 1991; Martin 1998). However, Stil & Israel (2002) argue that the Hα tail is, in fact, from infall rather than outflow and that these structures are connected to the H i bridge. Similarly, Mühle et al. (2005) argue that H i gas is being accreted onto NGC 1569 and Ott et al. (2005a) also see the Hα tail emitting soft X-rays. Infalling H i gas is a likely scenario, especially since we can see tenuous H i emission to the south and northeast of NGC 1569, which has the same radial velocities as the H i bridge. Because the tenuous H i gas to the south is spread over such a large region of space, ∼92 kpc², and evidence of interaction is observed in our GBT data, which we report in an upcoming paper, the origin of this tenuous gas, H i companion, H i bridge and Hα tail coming from outflow from the starburst is unlikely. We conclude that these features are the result of a recent interaction, which caused the NCM cloud to infall and compress a dense ridge that stretched across the entire optical disk, creating a global starburst which created the SSCs, and left behind what is now the UD H i cloud.

We see that the velocities of the UD cloud are fairly constant, but according to Figure 16, the velocity dispersions at this location are high compared to the average. Thus, we observe that the UD H i cloud is kinematically warm because of its high velocity dispersion. Perhaps this dense H i region to the west of the optical disk will be the location of a future star formation episode, provided the gas kinematically cools over time.

We use the spectral energy distribution (SED) fitting procedure from Zhang et al. (2012) to model the stellar mass and our results are presented in Figure 20. Briefly speaking, the Hubble time is logarithmically divided into six independent age bins, and the star formation rate (SFR) in each age bin is assumed to be constant. A library consisting of ∼4 × 10⁶ different star formation histories is created by changing the relative star formation intensity among the six age bins. In addition, the metallicities and internal dust extinction are also free parameters when creating the library. The usually adopted two-component (e.g., exponential plus bursts) SED modeling method can introduce a bias in the estimation of parameters (Zhang et al. 2012). We use Johnson's U-, B-, and V-band, Hα, Two Micron All Sky Survey (2MASS) J-, H-, and K_s-band, and Spitzer 3.6 μm photometry data in the SED fit. In the inner regions (radii <1.3 kpc) of NGC 1569, we do not use the 3.6 μm data because the starburst emission in these inner regions is expected to have significant contributions from hot dust (Zhang et al. 2010). In the outer regions (radii >1.3 kpc), we use all data except the 2MASS data because they are too shallow to properly model the outer disk. Instead of looking for the best-fitting parameter, we use the Bayesian technique to find the most probable estimates of parameters by constructing a probability density function and the corresponding cumulative distribution function for each parameter, and the confidence interval is defined as the central 68% of the cumulative distribution function. Any possible degeneracies between different parameters are reflected in the confidence intervals.

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The right panel of Figure 20 shows the cumulative summed stellar mass as a function of radius. The profile approaches the horizontal asymptote at a mass of 2.8 × 10⁸ M_☉, giving the total stellar mass of NGC 1569. The left panel of Figure 20 shows the surface density mass profile, corrected for inclination. We see that the stellar mass density profile follows a broken or double exponential. For these data, we make no assumptions about disk scale height or constant mass-to-light ratio. When we compare a de Vaucouleur's R^1/4 profile to the surface mass density in Figure 20, it is clear that it does not fit the data as well as a double exponential profile.

To see how the R^1/4 profile compares to the more traditional surface brightness profile, we plot our 3.6 μm photometry surface brightness in Figure 21. We observe a marginally better fit by the double exponential profile over the R^1/4 profile. We see that the R^1/4 profile overestimates the surface brightness in the center and underestimates it at ∼0.5 kpc. We conclude that the surface brightness, as well as mass profile of NGC 1569, is best fitted as a double or broken exponential disk.

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In Figure 21, there is a break in the exponential profile around 1.3 kpc where it becomes flatter. This surface brightness profile is a Type III "antitruncated" profile, as described by Erwin et al. (2005). A Type III profile is ascribed to disk flaring in the outer disk in M94 by Herrmann & Ciardullo (2009). They attribute this characteristic to a recent interaction or merger. If this type of surface brightness profile is generally indicative of a flared disk resulting from an interaction or merger, then this would be additional evidence for an outside influence on NGC 1569.

To check the validity of our derived stellar surface mass density profile, we turn to our observed stellar kinematics. From Swaters (1999 and references therein), we use the relationship between vertical stellar velocity dispersion, σ_z, and stellar surface mass density, Σ(R):

$$\begin{equation} \sigma _z = \sqrt{\pi G z_o \Sigma (R)}. \end{equation} \tag{ 5 }$$

Here, z_o is the vertical scale height, which we assume is constant in this relationship and is defined as twice the exponential scale height, z_o = 2h_z. We also assume a vertical sech² scale-height distribution for the stellar component with the empirical relationship h/z_o = 5 (van der Kruit & Searle 1981), where h and z_o are the disk scale length and scale height, respectively. From an exponential disk fit to the inner part of the 3.6 μm surface brightness profile, we derive a scale length, h, of 1.54 kpc, giving a scale height, z_o, of 0.31 kpc for NGC 1569.

Figure 22 shows our observed stellar velocity dispersions, plotted so that all radii are positive, along with the model velocity dispersion profile derived from Equation (5). In Figure 22, there is general agreement between the observed and predicted stellar velocity dispersions in the center; however, the observed stellar velocity dispersions appear to increase as a function of radius, which is opposite of what is expected. This anomaly can be explained as an isolated area where the stars have a higher dispersion because they are the stars formed in the expanding shell described in Section 4.2. These high dispersion stellar velocities coincide with the peculiar dip, identified by the black arrow, at the edge of the expanding shell in Figure 14 (R = −27''⇒0.5 kpc). We do not know how the stars act beyond ∼0.5 kpc, as our spectra do not probe past this radius, so we cannot definitively determine what happens beyond this increase.

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We used the stellar surface density profile, determined from the SED fitting, to model the expected rotation velocities of the stars (rotmod), assuming that the total mass of the galaxy comes from the stars. The results for this model, corrected for inclination, are shown by the asterisk symbols in Figure 17. This graph shows that in the inner 1 kpc, half of the observable stellar disk of NGC 1569, the gravitational potential is dominated by the observed stellar mass.

The total H i mass of NGC 1569, summed over the integrated H i map, Figure 5, is 2.3 × 10⁸ M_☉. To calculate the expected velocity of the gas as a function of radius, we use the H i mass surface density profile. We assume an axisymmetric, infinitely thin disk comprised entirely of gas and an inclination of 69° ± 7° (see Oh et al. 2011 for more details). The model H i velocities as a function of radius are shown by the triangle symbols in Figure 17. The maximum rotation velocity of the model H i rotation curve is 18 km s⁻¹, less than half of the asymmetric drift corrected V_max (filled circles).

NGC 1569 also contains molecular hydrogen (H₂). According to Israel (1988), the amount of H₂ in NGC 1569 as a whole is about 5 × 10⁷ M_☉ corrected to a 3.36 Mpc distance. This produces the ratio $M_{\rm H_2}/M_{{\rm H\,\mathsc{i}}}$ = 0.2 over the galaxy. The estimate of the total H₂ is an approximation, though, because Israel determined the total H₂ mass by scaling the results derived by Young et al. (1984) for the central 50'' of the galaxy. Also, the CO to H₂ conversion factor used by Israel is potentially dependent on metallicity, and NGC 1569 has a low metallicity. However, the scaled mass agrees with Obreschkow & Rawlings (2009) who find an H₂ mass of ∼2 × 10⁷ M_☉, corrected for a distance of 3.36 Mpc. In either case, these estimates suggest that the total amount of H₂ is on the order of 10% of the total baryonic mass (stars + gas) in NGC 1569.

In the previous sections, we have modeled the contributions to the rotation curve of NGC 1569 due to stars and gas. Here, we explore the dark matter content in NGC 1569 by assuming that the observed, asymmetric drift corrected, rotation represents motion under the total gravitational potential of the system. Using our V_max = 50 km s⁻¹, we calculate a dynamical mass, M_dyn, of 1.3 × 10⁹ M_☉ within a radius of 2.2 kpc, using the following equation:

$$\begin{equation} M_{\rm dyn}(R) = \frac{V_{\rm max}^2\ R}{G}, \end{equation} \tag{ 6 }$$

where V_max is the maximum rotation speed determined from the asymmetric drift corrected rotation curve, and R is the radius where V_max is measured. We determine an H i mass and a stellar mass inside a radius of 2.2 kpc of 1.7 × 10⁸ M_☉ and 2.5 × 10⁸ M_☉, respectively. To account for helium, we scale the H i mass by a factor of 1.36 (de Blok et al. 2008), and achieve a total baryonic mass of 4.8 × 10⁸ M_☉. Subtracting this from the dynamical mass, we are left with only 8.2 × 10⁸ M_☉ of missing, dark matter within a radius of 2.2 kpc.

There are, however, a number of uncertainties in the dark matter determination. The most important uncertainty is that we assume that we have found the turnover radius and, hence, the maximum rotation, V_max, of NGC 1569. However, the S/N is low in the region where the turnover radius occurs. If the true maximum rotation speed of the galaxy is actually higher, then our calculation of dynamical mass, along with the deduced dark matter mass in the central region of NGC 1569, will be underestimated. Another uncertainty comes from the fact that these calculations use a V_max derived under the assumption that the inclination of the H i disk is 69° ± 7°, as determined from the tilted ring model. If a V_max of 50 km s⁻¹ is correct, then NGC 1569 has a low dark matter content inside the visible disk, which is unlike most other dwarf galaxies studied (e.g., Oh et al. 2011; Sawala et al. 2011; Walker et al. 2009).

To see the effect of such a low dark matter content, we examine the dark matter fraction, γ_dm(M_DM/M_tot), as a function of radius using the following equation given in Oh et al. (2011):

$$\begin{equation} \gamma _{\rm dm}(R) = \frac{M_{\rm DM}}{M_{\rm tot}} = \frac{V_{\rm rot}(R)^2 - V_{\rm star}(R)^2 - V_{\rm gas}(R)^2}{V_{\rm rot}(R)^2}, \end{equation} \tag{ 7 }$$

where V_rot is the rotation velocity corrected for asymmetric drift derived from H i, V_star is the stellar rotation velocity assuming all the mass is in the stars determined from the SED fitting, and V_gas is the gas rotation velocity determined from the H i surface density assuming Newtonian dynamics. Figure 23 shows the fraction of dark matter as a function of radius. The average values in the inner 1 kpc are zero, within the errors, due to the dominance of the stars. However, in the outer region, beyond 1.25 kpc, the fraction of dark matter has an average of ∼0.5, which is below the average of 0.7 found for a sample of seven dwarf galaxies by Oh et al. We see here that the stars account for all of the dynamical mass within a radius of ∼1 kpc—no dark matter is needed within this radius. Thus, NGC 1569 appears to be dark matter deficient in the inner disk compared to other dwarfs.

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In ΛCDM, the dark matter halos hosting galaxies have an approximately universal shape that follows a concentration–mass relation (e.g., Bullock et al. 2001; Prada et al. 2012). Hence, CDM halos are a one-parameter family, typically parameterized by mass within the virialized extent (M_vir) or maximum circular velocity (V_max). Adding the assumption that there is a monotonic mapping of dark matter halo mass to galaxy luminosity (e.g., the brightest galaxies are hosted by the most massive dark matter halos), a galaxy's dark matter halo can be uniquely determined from its luminosity using the technique of abundance matching (Kravtsov et al. 2004; Vale & Ostriker 2004; Conroy & Wechsler 2009). Here, abundance matching is performed, as described in detail in Tollerud et al. (2011a), using the halo V_max function from the Millenium II simulation (Boylan-Kolchin et al. 2009) and the r-band galaxy luminosity functions of Blanton et al. (2005). The r-band absolute magnitude for NGC 1569 (M_r = −17.6) is determined from the SED fit described in Section 6.1, and this is used to infer that the halo of NGC 1569 has V_max = 95 km s⁻¹. This implies M_vir ≈ 1.6 × 10¹¹ M_☉, and the virial extent of the halo is R_vir ≈ 140 kpc.

With these values for the total mass of NGC 1569's dark matter halo, the concentration–mass relation implies a unique shape for the halo profile. As outlined in Tollerud et al. (2011b), the halo shape is parameterized using a Navarro et al. (1997, NFW) halo profile and the shape parameters are assigned so that the halo falls on the median of the concentration–mass relation. Figure 24 shows the NFW density profile as a function of radius for NGC 1569. The resulting circular velocity profile is given as the solid line in Figure 25. Figure 17 shows the inner region of the NFW profile, solid line, compared to the modeled gas and stellar masses.

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As is clear from Figure 17, the stellar mass is close to the expected dark matter mass in the inner 1 kpc, and the uncertain effect of the baryons on the dark matter halo should be significant here. Thus, it is ambiguous whether or not the dominance of the baryons in the inner 1 kpc implies a halo profile inconsistent with ΛCDM, or simply that the baryonic mass of the galaxy is altering the shape of the dark matter halo in the region where the dark matter does not dominate the gravitational forces.

By R ∼ 2 kpc, however, the ΛCDM prediction lies within the error bars of the measured rotation curve. If the model is correct, the hint of a turnover in the rotation curve that we see is likely to be an artifact of low S/N, as the rotation curve implied by this halo profile does not peak until R ≈ 20 kpc, far beyond the baryonic extent of the galaxy. Additionally, it implies that in a global sense, NGC 1569 is not dark matter deficient because at a radius of ∼2 kpc, the rotation curve is consistent with ΛCDM predictions.

• 1.  
  A systemic velocity, V_sys, of −82 ± 7 km s⁻¹ was determined from averaging the heliocentric radial velocities of the stars along the minor axis.
• 2.  
  NGC 1569 has a stellar kinematic major axis equal to the morphological major axis at a P.A., measured east from north, of 121°.
• 3.  
  The stars and gas kinematically follow each other.
• 4.  
  NGC 1569 has an average stellar velocity dispersion of 〈σ_z〉 = 21 ± 4 km s⁻¹ and a kinematic measure, V_max/σ_z = 2.4 ± 0.7, which is suggestive of a thick disk.
• 5.  
  The stellar velocity dispersion increases from 21 ± 4 km s⁻¹ to 33 ± 9 km s⁻¹ in the region of the SSCs at a radius of ∼+0.5 kpc from the galaxy center, which is consistent with velocities of stars that formed in shocked gas in the expanding shell around SSC A. The region in the vicinity of the SSCs is a disturbed part of the disk.
• 6.  
  NGC 1569 follows the observed trend of σ_z – M_B in large spiral galaxies (Swaters 1999).
• 7.  
  The 3.6 μm light profile of NGC 1569 follows a double exponential disk better than a de Vaucouleurs's R^1/4 profile. The light profile is shallower in the outer disk than in the inner disk.

• 1.  
  Multiple velocity components are observed in the spectra as a result of mechanical energy input from the starburst.
• 2.  
  There is one expanding shell observed from the high-velocity ionized gas seen along the major axis and indications for outflow.
• 3.  
  The stellar velocities match low-velocity ionized and H i gas and are likely produced by the stars that caused the expanding shell (high velocity gas) observed on the western side of the disk.

• 1.  
  Extended H i emission to the south and north of NGC 1569 was imaged for the first time.
• 2.  
  NGC 1569 shows a dominance of non-circular velocities across the H i disk as seen in the intensity-weighted velocity field.
• 3.  
  An NCM H i cloud was observed and appears to be impacting NGC 1569 at the eastern edge of a dense H i cloud that lies west of the SSCs, as determined from a double Gaussian decomposition method that was successfully applied to our H i data.
• 4.  
  We suggest that the impact from the NCM H i cloud caused the dense ridge in the center of the disk to become unstable, thus creating the starburst and enabling the formation of the SSCs.

• 1.  
  The disturbed stellar kinematics correspond to the region west of SSC A.
• 2.  
  A "butterfly" shape in the H i gas morphology is observed, likely caused from outflow from the starburst. Gas is escaping from the body of the butterfly, perpendicular to the stellar and gas disks.

• 1.  
  A total stellar mass of 2.8 × 10⁸ M_☉ was determined from a new SED fit and a total gas mass, including helium and metals, of 2.3 × 10⁸ M_☉ was determined.
• 2.  
  A dynamical mass of 1.1 × 10⁹ M_☉ was calculated from the V_max = 50 km s⁻¹ at a radius of 2.2 kpc.
• 3.  
  The stars dominate the gravitational potential in the inner 1 kpc of the H i disk.
• 4.  
  The derived rotation curve from the H i kinematics compared to the modeled H i rotation from the surface mass density and the modeled stellar rotation shows that only a small amount, 80% of the baryonic mass, is needed in dark matter. This is unlike typical dwarf galaxies.
• 5.  
  The rotation of the stars and gas seem to agree with an NFW profile at a radius of ∼2 kpc.
• 6.  
  The NFW model predicts a virial mass of 1.6 × 10¹¹ M_☉ and gives a virial radius of 22 kpc, well beyond the radius where baryonic material is detected.