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The Astrophysical Journal, 531:L107­L110, 2000 March 10
2000. The American Astronomical Society. All rights reser ved. Printed in U.S.A.

HIGH-RESOLUTION ROTATION CURVES OF LOW SURFACE BRIGHTNESS GALAXIES R. A. Swaters,1 B. F. Madore,2 and M. Trewhella
3

Received 1999 November 10; accepted 2000 January 14; published 2000 February 11

ABSTRACT High-resolution Ha rotation cur ves are presented for five low surface brightness galaxies. These Ha rotation cur ves have shapes different from those previously derived from H i obser vations, probably because of the higher spatial resolution of the Ha obser vations. The Ha rotation cur ves rise more steeply in the inner parts than the H i rotation cur ves, and they reach a flat part beyond about two disk scale lengths. With radii expressed in optical disk scale lengths, the rotation cur ves of the low surface brightness galaxies presented here and those of the high surface brightness galaxies have almost identical shapes. Mass modeling shows that the contribution of the stellar component to the rotation cur ves may be scaled to explain most of the inner parts of the rotation cur ves, albeit with high stellar mass-to-light ratios. On the other hand, well-fitting mass models can also be obtained with lower contributions of the stellar disk. These obser vations suggest that the luminous mass density and the total mass density are coupled in the inner parts of these galaxies. Subject headings: galaxies: halos -- galaxies: kinematics and dynamics -- galaxies: structure
1. INTRODUCTION

The rotation cur ves of high surface brightness (HSB) spiral galaxies rise fairly steeply to reach an extended, approximately flat part, well within the optical disk (Bosma 1978, 1981a, 1981b; Rubin, Ford, & Thonnard 1978, 1980). The discover y that the rotation cur ves of these galaxies are more or less flat out to 1 or 2 Holmberg radii has been one of the key pieces of evidence for the existence of dark matter outside the optical disk (see also van Albada et al. 1985). Within the optical disk, the obser ved rotation cur ves can in most cases be explained by the stellar components alone (Kalnajs 1983; Kent 1986). The rotation cur ves of so-called low surface brightness (LSB) galaxies have been studied only recently (de Blok, McGaugh, & van der Hulst 1996, hereafter BMH; see also Pickering et al. 1997). These rotation cur ves, derived from H i obser vations, were found to rise more slowly than those of HSB galaxies of the same luminosity, if the radii are measured in kiloparsecs. At the outermost measured point, they were often still rising. McGaugh & de Blok (1998) noted that, with radii expressed in disk scale lengths, the rotation cur ve shapes of LSB and HSB galaxies become more similar but not necessarily identical. Based on the mass modeling of these H i rotation cur ves, de Blok & McGaugh (1997, hereafter BM) concluded that LSB galaxies were dominated by dark matter and that the contribution of the stellar disk to the rotation cur ve, even if scaled to its maximum possible value, could not explain the obser ved rotation cur ve in the inner parts. The H i rotation cur ves of LSB galaxies have received a great deal of attention because they provide additional constraints on theories of galaxy formation and evolution and of dark halo structure (e.g., Dalcanton, Spergel, & Summers 1997; Mihos, McGaugh, & de Blok 1997; Hernandez & Gilmore 1998; Kravtsov et al. 1998; McGaugh & de Blok 1998). Unfortunately, most of the galaxies studied in BMH and BM are
1 Kapteyn Astronomical Institute, University of Groningen, Postbus 800, Groningen, 9700 AV, Netherlands; and Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, DC 20015-1305. 2 Carnegie Obser vatories, 813 Santa Barbara Street, Pasadena, CA 911011292; and NASA/IPAC Extragalactic Database, California Institute of Technology, Pasadena CA 91125. 3 Infrared Processing and Analysis Center, MS 100-22, 770 South Wilson Avenue, California Institute of Technology, Pasadena CA 91125.

only poorly resolved, making their results sensitive to the effects of beam smearing. For five of the galaxies in their sample, high-resolution Ha rotation cur ves, which have been obtained in order to eliminate beam smearing and to investigate the rotation cur ve shapes in the inner parts of LSB galaxies, are presented in this Letter.
2. SAMPLE, OBSERVATIONS, AND DATA REDUCTION

The galaxies presented here were selected from the sample of LSB galaxies of BMH. The only galaxies chosen were those that satisfied the criteria given in BM to define their useful rotation cur ves. An over view of the properties of the galaxies is given in Table 1, which lists the name of the galaxy (col. [1]), the adopted distance in megaparsecs for H0 = 75 km s 1 Mpc 1 (col. [2]), the central surface brightness in units of mag arcsec 2 (col. [3]), the disk scale length in kiloparsecs (col. [4]), the inclination angle (col. [5]), the position angle (col. [6]), the absolute magnitude (col. [7]), and the systemic velocity (col. [8]). The obser vations were carried out at the Palomar Observator y with the 200 Hale telescope4 on 1998 November 20. The FWHM velocity resolution was 54 km s 1, and the pixel size in the spatial direction was 0 . 5. Each galaxy spectrum consisted of a single 1800 s exposure. The slit was oriented along the major axis, at the position angle derived by BMH (see Table 1). Despite their low surface brightnesses, all galaxies showed up clearly on the slit-viewing monitor. The slit could therefore be accurately aligned with the center of the galaxy by eye. The data were reduced using standard procedures in IRAF, and the resulting Ha position-velocity diagrams are presented in Figure 1.
3. THE HIGH-RESOLUTION ROTATION CURVES

To derive the rotation cur ves, we started by making Gaussian fits to the line profiles at each position along the major axis in order to obtain the radial velocities. These fits and their errors are overlaid on the Ha position-velocity diagram in Figure 1. The positions of the galaxy centers were determined from the
4 The Palomar 200 telescope is operated in a joint agreement among the California Institute of Technology, the Jet Propulsion Laborator y, and Cornell University.

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Fig. 1.--Ha position-velocity diagrams for the five LSB galaxies, binned to 1 . Contour levels are at 2, 2, 4, 8, 16, 24, and 32 times the rms noise. The dots with error bars give the radial velocities with the formal errors as derived from Gaussian fits to the velocity profiles. The solid lines represent the rotation cur ves, derived as described in § 3. The vertical dotted line indicates the galaxy center; the horizontal dotted lines denote the heliocentric systemic velocities.

Fig. 2.--The high-resolution Ha rotation cur ves ( filled circles, solid lines) and the H i rotation cur ves from BMH (open circles, dotted lines). The horizontal bar shows the FWHM beam size of the H i obser vations.

peak of the continuum light along the slit. All galaxies were sufficiently bright to allow us to determine the position of the center along the slit with an accuracy of better than 1 . To obtain a larger radial coverage of the rotation cur ves, the Ha data were combined with the H i data presented in BMH. To this end, the derived Ha velocities were plotted on the H i position-velocity diagrams. Both sets of data were found to agree well with each other if the effects of beam smearing on the H i data are taken into account (see Swaters 1999). Therefore, we have used the H i data to determine rotation velocities beyond the radii where we found Ha emission. Note

that in most cases, the H i extends only a little beyond the Ha. Next, the rotation cur ves derived for the approaching and the receding sides were combined. The Ha points were sampled ever y 2 and the H i points ever y 7 . 5 (approximately two points per beam). The errors on the rotation velocities were estimated from the differences between the two sides and the uncertainties in the derived velocities. We will refer to these rotation cur ves as the high-resolution rotation cur ves (HRCs). The derived HRCs are shown in Figure 2 together with the H i rotation cur ves presented in BM. Probably because BM did not correct for beam smearing, the H i rotation cur ves systematically underestimate the inner slopes of the rotation cur ves, especially for F568-V1 and F574-1. Both these galaxies have a central depression in the H i distribution, as can be seen in the H i maps presented in BMH. The spatial smearing of H i from larger radii into the obser ved central depression leads

TABLE 1 Properties of the Galaxiesa Name (1) F563-V2 ...... F568-1 ........ F568-3 ........ F568-V1 ...... F574-1 ........
a b c

D (Mpc) (2) 61 85 77 80 96

mB 0 (mag arcsec 2) (3) 22.1 23.8 23.1 23.3 23.3

h (kpc) (4) 2.1 5.3 4.0 3.2 4.3

i (deg) (5) 29 26 40 40 65

P.A. (deg) (6) 148 13 169 136 90c

MB (mag) (7) 18.2 18.1 18.3 17.9 18.4

vsysb
(km s 1) (8) 4310 6524 5911 5769 6889 4 6 3 7 6

Data from BMH and BM. This Letter. Derived from the optical image in BMH.


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Fig. 3.--Mass models fitted to the HRCs. The top panels give maximum disk fits; the bottom panels give fits with a stellar mass-to-light ratio of zero. The dotted line represents the contribution of the stellar disk to the rotation cur ve, the dashed line represents the contribution of the gas, the long-dashed line represents the dark halo, and the solid line represents the total model rotation cur ve. For F568-1, the dot-dashed line represents the contribution of the central component to the rotation cur ve.

to an apparent solid-body­like rotation cur ve, in particular for the highly inclined galaxy F574-1.
4. MASS MODELING

For the mass modeling presented here, we have used the same parameters for the thickness of the gaseous and stellar disks as BM have used. The stellar disk was assumed to have a vertical sech2 distribution, with a scale height z 0 = h /6. R-band light profiles, presented in de Blok, van der Hulst, & Bothun (1995) and BMH, were used to calculate the contribution of the stellar disk to the rotation cur ve. The H i was assumed to reside in an infinitely thin disk. The only difference with the mass models presented in BM is that we have decomposed the light profile of F568-1 into a disk and a central component and have fitted these components to the rotation cur ve separately. In the other galaxies, no significant central component is present. For the dark matter component, a pseudoisothermal halo was used, following BM, which has a rotation cur ve given by

v2 lo (r ) = 4pGr 0 rc2 1 ha

[

rc r a r cta n r rc

()]

,

where rc is the halo core radius and r 0 is the central density. One of the major uncertainties in fitting mass models to
TABLE 2 Mass Model Parameters Maximum Disk Name F563-V2a ...... F568-1b ........ F568-3 ........ F568-V1 ....... F574-1 ........
a b

No Disk rc (kpc) 0.94 1.5 2.5 1.2 1.5 r0 (M, pc 3) 0.283 0.181 0.048 0.188 0.092

U (M,/LR, ,) 5.4 17.2 1.5 9.3 3.7

rc (kpc) ) ) 3.0 6.7 3.4

r0 (M, pc 3) ) ) 0.027 0.005 0.003

No R-band data are available; mass modeling is based on B-band data. For F568-1, a central component was fitted separately, which has U, bulge = 14.4 in the maximum disk fit.

rotation cur ves, in the absence of an independent measurement of the stellar mass-to-light ratio U , is the uncertainty in the contribution of the stellar disk to the rotation cur ve. However, lower and upper limits on U, and hence on the dark matter content, can be obtained by assuming that the contribution of the stellar disk to the rotation cur ve is either minimal or maximal. In the maximum disk mass models, the contribution of the stellar disk to the rotation cur ve is scaled to explain most of the inner parts of the rotation cur ve. The resulting rotation cur ve fits are shown in the top panels of Figure 3. What immediately strikes the eye is that, in contrast to the findings of BM, the inner parts of the rotation cur ves can be explained almost entirely by the contribution of the stellar disk in all of these LSB galaxies, with the exception of F568-3. The dark halo parameters (see Table 2) are ill-defined for most galaxies in our sample because most of the HRCs do not extend to large radii. Nonetheless, it is clear that in these maximum disk fits, the contribution of the dark halo will only become important outside the optical disk, as is also the case for HSB galaxies. The required stellar mass-to-light ratios for the maximum disk fits (listed in Table 2) may be high, up to 17 in the R band. Most of these are well outside the range of what current population synthesis models predict (e.g., Worthey 1994). If these high values of U are to be explained solely by a stellar population, the stellar content and the processes of star formation in LSB galaxies need to be ver y different from those in HSB galaxies. Alternatively, these high mass-to-light ratios may indicate the presence of an additional bar yonic component that is associated with the disk, as has been suggested by, e.g., Pfenniger, Combes, & Martinet (1994). On the other hand, the fact that the stellar disk can be scaled to explain the obser ved rotation cur ve may simply reflect the possibility that luminous and dark masses have similar distributions within the optical galaxy. The other extreme for the contribution of the stellar disk to the rotation cur ve is to assume that its contribution is negligible. The dark halo parameters for this minimum disk fit are listed in Table 2. High central densities of dark matter and small core


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radii are required to explain the obser ved steep rise in the HRCs. From Figure 3, it is clear that the minimum disk mass models fit the rotation cur ves just as well as the maximum disk models do. In fact, a good fit can be obtained with any massto-light ratio lower than the maximum disk mass-to-light ratio, demonstrating that the degeneracy that exists in the mass modeling for HSB galaxies (e.g., van Albada et al. 1985) also exists for LSB galaxies. Irrespective of the contribution of the stellar disk to the rotation cur ve, the similarity between the shapes of the obser ved rotation cur ves and those of the stellar disks implies that the total mass density and the luminous mass density are coupled within the region of the optical disk.
5. DISCUSSION

The HRCs derived for the LSB galaxies rise steeply in the inner parts and reach a flat part beyond about two disk scale lengths, as is found for HSB galaxies. In Figure 4, the rotation cur ves for LSB galaxies (dotted lines) are compared with those of three typical late-type HSB galaxies from Begeman (1987), NGC 2403, NGC 3198, and NGC 6503. All the galaxies in Figure 4 have no bulges, or only weak ones. In the top panel of Figure 4, the radii are given in kiloparsecs. In these units, the rotation cur ves of LSB galaxies rise more slowly than those of HSB galaxies, indicating that these galaxies not only have lower central surface brightnesses but also lower central mass densities, as was found by de Blok & McGaugh (1996) as well. A different picture emerges in the bottom panel of Figure 4, in which the rotation cur ves are scaled by their optical disk scale lengths and normalized to the velocity at two disk scale lengths. The normalization probably does not introduce systematic effects because the maximum difference in absolute magnitude between the galaxies in Figure 4 is only 1.5 mag. With radii expressed in disk scale lengths, the rotation cur ves of the LSB galaxies presented here and those of HSB galaxies have almost identical shapes. This is consistent with the concept of a "universal rotation cur ve" (Persic, Salucci, & Stel 1996; see also Rubin et al. 1985). The similarity between the LSB and HSB rotation cur ve shapes suggests that rotation cur ve shapes are linked to the distribution of light in the stellar disks, independent of central disk surface brightness. Although such a link is most easily understood if the stellar disks are close to maximal, independent of surface brightness, the required high mass-to-light ratios

Fig. 4.--Rotation cur ves of the five LSB galaxies (dotted lines) compared with the rotation cur ves of three typical late-type HSB spiral galaxies from Begeman (1987): NGC 2403 (MB = 19.3), NGC 3198 (MB = 19.4), and NGC 6503 (MB = 18.7). In the top panel, the rotation cur ves are expressed in kiloparsecs; in the bottom panel, the rotation cur ves are scaled with their scale lengths and normalized with the rotation velocity at two disk scale lengths.

seem to favor a picture in which LSB galaxies are dominated by dark matter within the optical disk and HSB galaxies more by the stellar disk. The relative contribution of the stellar disk to the rotation cur ve may change continuously from LSB to HSB, or perhaps LSB and HSB galaxies constitute discrete galaxy families, as has been suggested by Tully & Verheijen (1997). We thank Roelof Bottema for valuable discussions and Er win de Blok for making available the H i data and for useful comments. R. A. S. thanks IPAC for its hospitality during his visits, which were funded in part by a grant to B. F. M. as part of the NASA Long-Term Space Astrophysics Program.

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