The Various Kinematics of Dwarf Irregular Galaxies in Nearby Groups ...

THE ASTRONOMICAL JOURNAL, 120 : 3027È3059, 2000 December ( 2000. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE VARIOUS KINEMATICS OF DWARF IRREGULAR GALAXIES IN NEARBY GROUPS AND THEIR DARK MATTER DISTRIBUTIONS STE PHANIE COü TE Canadian Gemini Office, Herzberg Institute of Astrophysics, National Research Council of Canada, 5071 West Saanich Road, Victoria, BC, Canada, V9E 2E7 ; Stephanie.Cote=hia.nrc.ca

CLAUDE CARIGNAN Departement de Physique and Observatoire du Mont Megantic, Universite de Montreal, C.P. 6128, Succ. Centre Ville, Montreal, Quebec, Canada, H3C 3J7 ; claude=cena.astro.umontreal.ca

AND KENNETH C. FREEMAN Mount Stromlo Observatory, P.M.B. Weston Creek, ACT 2611, Australia ; kcf=msokcf.anu.edu.au Received 1999 October 20 ; accepted 2000 August 24

ABSTRACT Eight dwarf irregular galaxies, in the two nearby groups of galaxies Sculptor and Centaurus A (at 2.5 Mpc and 3.5 Mpc), have been imaged in neutral hydrogen (H I) with the Australia Telescope and the Very Large Array. These galaxies have absolute magnitudes ranging from M \ [15.7 to [11.3. Yet they are mostly rotationally supported, with maximum velocities going from B19 to 67 km s~1. Multicomponent mass models have been Ðtted to the rotation curves to investigate the properties of their dark matter halos and the scaling laws of dark matter halo parameters. Dwarf galaxies have, on average, a higher dark to luminous mass ratio, as well as higher dark halo central densities than spiral galaxies. They have a larger dispersion of their dark matter properties both in terms of their total dark matter amount and of their dark halo parameters, compared to spiral galaxies. It is therefore very difficult to predict a dwarf galaxy rotation curve shape based only on its optical properties. Dwarfs are not well Ðtted by cold dark matter (CDM) halos of the type proposed by Navarro, Frenk, & White, even for "CDM models with ) as low as 0.3. For two of our dwarfs we also have Ha rotation curves conÐrm0 the discrepancy with the CDM models cannot be attributed to beam-smearing ing the H I velocities, so e†ects. Key words : dark matter È galaxies : dwarf È galaxies : kinematics and dynamics 1.

INTRODUCTION

variety of spiral and dwarf galaxies rotation curves (e.g., Begeman 1987 ; Broeils 1992). One can then inspect how the dark halo properties vary from galaxy to galaxy. Many years ago Tinsley (1981) already suggested that bluer galaxies appear to have a higher total mass-to-light ratio (based on global mass estimates from H I proÐles widths). Kormendy (1987) inspected these scaling laws closely using the model Ðts to the H I rotation curves available, Ðnding that not only the dark to luminous mass ratio increases for lower luminosity galaxies but also that their dark halos are more centrally concentrated (note that the central density is the best constrained parameter in these models). This so far has been conÐrmed by studies of more extreme dwarfs (e.g., DDO 154 ; Carignan & Freeman 1988), as well as more recently in the bigger sample of van Zee et al. (1997) for dwarfs with [18.4 º M º [13.7. Because the dark halo B shape of the rotation curve (for parameters determine the example, its compactness and steepness) there is a directly observed relation between the shapes of rotation curves and the galaxy luminosities. This has led Persic, Salucci, & Stel (1996) to construct, from a set of more than 700 optical rotation curves, a universal rotation curve (URC), dependent only on the luminosity of the galaxy to determine its curveÏs shape at any radius and usable down to M \ B [17.5. But there has been no investigation into extrapolating the form to dwarf galaxies. It is in any case probably too simplistic even for normal spirals since Verheijen (1997), for example, Ðnds for his sample of 22 spiral galaxies that about one-third do not follow the URC. In this paper the H I kinematics of eight nearby dwarf

The strongest evidence for dark matter in galaxies comes from extended neutral hydrogen (H I) rotation curves, and especially among all the galaxy types from those of dwarf irregular (dIrr) galaxies. These systems are literally dominated by dark matter, their luminous matter usually bringing only a minor dynamical contribution. From their extended H I distribution one can derive rotation curves to large galactocentric radii, probing very far out into the dark halo potential. For these reasons the dark matter halo parameters can be more tightly constrained. By studying all the way down to the most extreme low-mass dIrrÏs, one hopes to get a better handle on the dark halo scaling laws, the goal being to study possible correlations between dark halo properties and galaxy morphological types. The structure of the dark matter halos can be inspected by subtracting the luminous and gaseous mass dynamical contribution from the observed velocities of the rotation curves. This involves setting a mass-to-light ratio (M/L ) B* for the disk population to obtain the stellar surface densities from the luminosity proÐle. This (M/L ) is in most cases B * enough to have not well determined unless one is fortunate resolved stellar population studies for the galaxy or vertical stellar velocity dispersion information. One way to alleviate the problem of this extra free parameter to Ðt is to assume a ““ maximum disk ÏÏ by Ðtting the maximal (M/L ) allowed * by the observed velocities, therefore providing aBlower limit to the amount of dark matter. This approach has been widely used and, by modeling the dark halo with a simple nonsingular isothermal sphere, good Ðts were obtained for a 3027

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COŒTEŠ, CARIGNAN, & FREEMAN

Vol. 120

TABLE 1 OPTICAL PARAMETERS OF THE SELECTED DWARFS (from Coüte et al. 2001)

Name UGCA 442 . . . . . . . . . SDIG . . . . . . . . . . . . . . . NGC 625 . . . . . . . . . . ESO 245-G05 . . . . . . ESO 381-G20 . . . . . . DDO 161 . . . . . . . . . . ESO 444-G84 . . . . . . ESO 325-G11 . . . . . .

R.A. and Decl. (1950) 23 00 01 01 12 13 13 13

41 05 32 42 43 00 34 42

10, 41, 56, 58, 18, 38, 32, 01,

[32 [34 [41 [43 [33 [17 [27 [41

13 51 41 50 33 09 47 36

58 24 24 33 54 14 30 30

M

B [13.8 [11.3 [15.7 [15.0 [13.9 [14.9 [12.7 [13.8

B[R

k B (mag arcsec~2)

a~1 (kpc)

0.49 0.74 0.82 0.22 0.56 0.52 0.36 0.7

22.2 23.3 20.3 22.6 22.9 21.8 23.1 24.0

0.43 0.22 0.42 0.38 0.62 0.7 0.24 1.2

NOTE.ÈUnits of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds.

galaxies is presented, as well as, when appropriate, a mass model from their rotation curve. The dIrrÏs of our sample are all dwarf members of two nearby groups of galaxies outside the Local Group, Sculptor at 2.5 Mpc and Centaurus A at 3.5 Mpc. Our Parkes H I survey detected three dozen dwarf members in these two groups (see Coüte et al. 1997 for a detailed description). Eight objects among the most gas-rich ones, with a range of absolute magnitude M B from [15.7 to [11.3, were selected for kinematical studies. Some of their optical parameters are listed in Table 1. After reviewing the data gathering and reductions, the H I analysis is discussed in ° 3, followed by the mass models in ° 4, while ° 5 discusses the various results. 2.

OBSERVATIONS AND REDUCTIONS

2.1. Radio Data The observations were carried out with the Australia Telescope Compact Array (ATCA) between 1991 November and 1992 October, with di†erent conÐgurations to improve the uv coverage, and with the Very Large Array (VLA) in B/C and C/D conÐgurations in 1992 February and June. The observational parameters are summarized in Table 2. At the ATCA the correlator was set to a 8 MHz bandwidth with 512 channels, giving a channel separation

of 3.3 km s~1, while for the VLA observations a 1.56 MHz bandwidth with 128 channels was used, with on-line Hanning smoothing, for a channel separation of 2.6 km s~1. A description of the VLA instrument can be found in Napier, Thompson, & Ekers (1983), and information on the AT in the Australia Telescope Compact Array UserÏs Guide (Duncan et al. 1997). The calibrations and reductions were performed with the NRAO software package AIPS. The absolute Ñux calibration was determined by observing 1934[638 or 0407[658 at the ATCA (Ñux densities of 16.19 and 15.51 Jy, respectively), and 3C 48 or 1328]307 at the VLA (16.06 and 14.87 Jy). The standard AIPS procedures were followed for the calibration, described in detail in the Analysis of ATCA Data guide (Killeen 1994). The uv data were inspected, and bad visibility points were edited out. In particular some of the observations carried out during the day su†ered from solar interference in the shortest baselines, for which the a†ected data had to be carefully removed. After applying calibration and bandpass corrections to each uv database, the continuum emission was subtracted in the visibility domain using channels free of line emission (van Langevelde & Cotton 1990). None of our galaxies showed associated continuum emission. For the ATCA data

TABLE 2 OBSERVING LOG FOR THE AT AND VLA DATA

Source

Date

Array

t int (hr)

Central Velocity or Frequency (km s~1 or MHz)

UGCA 442 . . . . . . . . .

1991 Dec 2 1992 Sep 4 1992 Feb 2 1992 Feb 7 1992 Feb 2 1992 Jun 15 1992 Jan 31 1992 Sep 4 1992 Oct 1 1992 Feb 13 1992 Jun 22 1992 Feb 5 1992 Jun 22 1992 Jan 31 1992 Sep 4 1992 Oct 5 1991 Nov 29 1992 Sep 4 1992 Oct 5

AT 1.5C AT 750D VLA B/C VLA B/C VLA B/C VLA C/D AT 3.0D AT 750D AT 375 VLA B/C VLA C/D VLA B/C VLA C/D AT 3.0D AT 750D AT 375 AT 1.5C AT 750D AT 375

11 0.5 0.6 4 3 2 11 0.5 1.5 4 2 4 2 9.5 2 1.5 12 1.5 1

1419 1419 200 200 400 400 1417 1417 1417 600 600 750 750 1417 1417 1417 1417 1417 1417

SDIG . . . . . . . . . . . . . . . NGC 625 . . . . . . . . . . ESO 245-G05 . . . . . .

ESO 381-G20 . . . . . . DDO 161 . . . . . . . . . . ESO 444-G84 . . . . . .

ESO 325-G11 . . . . . .

Beam (arcsec ] arcsec)

rms (mJy beam~1)

40 ] 40

5.6

13 ] 13

5.7

15 ] 15

3.5

17 ] 17

4.5

13 ] 13

1.7

13 ] 13

2.0

22 ] 22

5.7

30 ] 30

4.6

No. 6, 2000

KINEMATICS OF DWARF IRREGULAR GALAXIES

(observed at a Ðxed frequency, with no on-line Doppler tracking), every database had to get aligned in velocity to correct for the e†ects of EarthÏs motions. Only then were all the uv databases of an object concatenated together into a single database used for the mapping. Two sets of maps were produced for each galaxy, one with uniform weighting and one with natural weighting and smoothed to lower resolution. No extra smoothing was applied in velocity when mapping, as we wanted to preserve the best possible velocity resolution to inspect the velocity proÐles. These two sets of maps were CLEANed (Schwab 1984) well into the noise, by monitoring the total cleaned Ñux as a function of the total number of CLEAN components recovered, and Ðnally were restored with a circular symmetric Gaussian beam. These maps were then corrected for the beam response of the antennae to rectify for attenuation away from the center of the primary beam. No H I emission was detected from other galaxies within the primary beam and through the bandwidth observed other than the intended source and Galactic emission around zero redshift. Moment maps were obtained from each data cube by analyzing intensity proÐles at each R.A.-decl. position through the cube (i.e., along the velocity axis). Zerothmoment (which gives the integrated total H I column density), Ðrst-moment (the intensity-weighted velocity), and second-moment (the velocity dispersion) maps were produced, using Hanning smoothing in velocity and Gaussian smoothing spatially. To check on these moment analysis results, velocity proÐles (of the high-resolution uniformweighting cube) of each galaxy were inspected at each R.A.decl. pixel, and single Gaussians were Ðtted to produce another set of total intensity, velocity, and velocity dispersion maps (with XGAUS).

3029

of view of [email protected] diameter, Ðtted with a Tektronix CCD of 1024 ] 1024 24 km pixels, with 1 e~ ADU~1 gain and 12 e~ pixel~1 readout noise. At least two exposures of 900 s in R and three in B and I were taken for each object. The Ha spectroscopy observations were carried out in 1991 April and November with the Double Beam Spectrograph (DBS) on the MSSSO 2.3 m telescope. The long slit is about 6@ and was set to a width of 2A, positioned along the major axis of the object. The detector used was a photoncounting array with a spatial resolution of 0A. 67 pixel~1. We used a 1200 G mm~1 grating covering a spectral range of 6450È6750 A in the red, at 0.4 A pixel~1 (18 km s~1 at Ha). 3.

H I ANALYSIS

3.1. H I Distribution H I column density maps (mostly from the low-resolution cubes) are shown in Figure 1, superposed on optical images. Table 3 gives the integrated H I masses for our eight galaxies as derived from our channel maps, which are very comparable with our Parkes values (Coüte et al. 1997). Also listed in the table are the H I diameters, measured at a column density of 1 M pc~2. The H I envelopes are in every case much more _extended than the optical galaxy, with an average D /D of 2.3, typical for such late-type 25 optical diameter, deÐned at a B systems (where D H Iis the 25 surface brightness level of 25 mag arcsec~2 ). Van Zee et al. (1997) Ðnd a slightly higher median D /D of 2.6 for their H I dwarf 25 galaxies, and sample of low surface brightness (LSB) indeed there is a hint in our sample that the lower surface brightness objects have higher D /D . I 25 smooth and rather The H I distributions look in Hgeneral symmetric, with minor spurs. In these dwarfs that mostly do not have clear optical nuclei, one Ðnds that the H I peaks are not necessarily positioned at the optical centers, and sometimes double or multiple H I peaks are found. In the case of ESO 245-G005, the narrowband imaging of Miller (1996) shows that many of these H I peaks agree well with the main H I regions. The smoothness of these H I distributions is actually surprising, considering that at high resolution the H I envelopes of some nearby galaxies exhibit an amazing display of structures as H I shells, holes and bubbles, which are presumed to have been created by stellar winds and supernovae explosions. More than 30 holes seen in Ho II (Puche et al. 1992) have diameters of more than 500 pc.

2.2. Optical Data The surface photometry data and Ha rotation curves that will be used later on for the mass models are described in detail in Coüte, Carignan, & Freeman (2001) ; we brieÑy review here their origins. Broadband imaging was carried out on the dwarfs through Bessell B, R, and I Ðlters (these are very close to the Cousins system). The observations were acquired between 1991 April and 1992 October with the MSSSO 2.3 m telescope. The f/18 Nasmyth focus using the Imager gave a Ðeld

TABLE 3 H I PROPERTIES OF OUR SAMPLE OF DWARFS

Galaxy (1)

V sys (km s~1) (2)

SPAT (deg) (3)

SiT (deg) (4)

p HI (km s~1) (5)

M HI (106 M ) _ (6)

D HI (arcmin) (7)

V max (km s~1) (8)

R max (kpc) (9)

R 25 (kpc) (10)

UGCA 442 . . . . . . . . . SDIG . . . . . . . . . . . . . . . NGC 625 . . . . . . . . . . ESO 245-G05 . . . . . . ESO 381-G20 . . . . . . DDO 161 . . . . . . . . . . ESO 444-G84 . . . . . . ESO 325-G11 . . . . . .

266 220 406 397 589 737 588 549

228 ^ 2 298 ^ 2

64 ^ 7 42 ^ 23

6.9 2.1 4.8 10.3 5.4 9.8 4.2 5.0

3.64 1.23

54 ^ 10 57 ^ 6 70 ^ 10 32 ^ 6 52 ^ 5

87 5.6 45 206 102 300 71 90

57.8 19.3

88 ^ 8 311 ^ 1 293 ^ 7 104 ^ 14 310 ^ 3

8.4 4.8 9.8 5.3 8.7 9.3 8.0 6.9

47.7 50.5 67.5 63.1 43.1

3.78 3.74 6.25 3.23 3.47

1.1 0.3 1.8 1.2 1.2 2.1 0.76 1.1

NOTES.ÈCol. (2) : Systemic velocity. Col. (3) : Position angle of the H I distribution. Col. (4) : Its inclination. Col. (5) : Velocity dispersion in H I. Col. (6) : Total mass of H I assuming a distance of 2.5 Mpc for Sculptor galaxies and 3.5 Mpc for the Centaurus A ones. Col. (7) : H I diameter at the 1 M pc~2 level. Col. (8) : Corrected maximum rotation velocity. Col. (9) : Maximum radius (for the rotation _ of k \ 25 mag arcsec~2 curve). Col. (10) : Radius at a level B

FIG. 1.ÈH I column density maps and H I velocity Ðelds overlaid on SRC enlarged prints, for UGCA 442. Contour levels are at 0.63 ( \ 3 p), 1.26, 2.52, 5.03, 10.06, 15.10, and 20.13 ] 1020 atoms cm~2. For the velocity Ðeld the isovelocity contour interval is 10 km s~1. Same for SDIG. Contour levels are at 0.50 ( \ 3 p), 1.0, 2.0, 3.0, 4.0, 5.0, and 6.0 ] 1020 atoms cm~2. Same for NGC 625. Contour levels are at 0.15 ( \ 3 p), 0.29, 0.59, 1.17, 2.35, 3.52, 4.69, and 5.87 ] 1020 atoms cm~2. The velocity Ðeld shown here is from the high-resolution (uniform weighting) cube. Same for ESO 245-G005, with contour levels of 0.39 ( \ 3 p), 0.77, 1.54, 3.08, 4.62, 6.16, and 7.7 ] 1020 atoms cm~2. The velocity Ðeld is the high-resolution one. Same for ESO 381-G020, with contour levels of 0.31 ( \ 3 p), 0.62, 1.23, 2.45, 4.91, 7.36, 9.81, and 12.27 ] 1020 atoms cm~2. Same for DDO 161, with contour levels of 0.27 ( \ 3 p), 0.54, 1.07, 2.14, 4.27, 8.55, 12.82, 17.09, and 21.37 ] 1020 atoms cm~2. Same for ESO 444-G084, with contour levels of 0.24 ( \ 3 p), 0.49, 0.98, 1.95, 3.9, 7.79, 11.69, and 15.59 ] 1020 atoms cm~2. Same for ESO 325-G011, with contour levels of 0.73 ( \ 3 p), 1.45, 2.91, 4.37, 5.82, 7.28, 8.74, 10.20, and 11.64 ] 1020 atoms cm~2.

3030

FIG. 1.ÈContinued

3031

FIG. 1.ÈContinued

3032

FIG. 1.ÈContinued

3033

FIG. 1.ÈContinued

3034

FIG. 1.ÈContinued

3035

FIG. 1.ÈContinued


3037

FIG. 1.ÈContinued

With our resolution (less than 255 pc for all galaxies, except UGCA 442, for which it is 485 pc), such holes should be easily detectable. Their rarity in our dwarfs is even more surprising considering that all our galaxies, with the exception of SDIG, have been detected in Ha (Skillman, Coüte, & Miller 2000) and seem to have had recent or current star

formation activities. It should be stressed though that our sample was selected from the H I richest dwarfs among all dwarf members of the Sculptor and Centaurus A groups, and one could imagine that it could bias against galaxies with a lot of recent active star formation, which presumably would have depleted them of some H I.

3038

COŒTEŠ, CARIGNAN, & FREEMAN 3.2. H I Kinematics

The radial velocity Ðelds (from the moment analysis), are shown in Figure 1, overlaid on SERC prints. In the presence of radial motions, outÑows, or other complex velocity structures in the gas disks, the velocity proÐles could in fact be double-peaked or multipeaked, and for these reasons care was taken to inspect each velocity proÐle pixel per pixel and to compare the moment maps with those obtained by single-Gaussian Ðts (with XGAUS). Especially for the velocity dispersion maps, the moment results can be deceptive by producing too low dispersions if one is not careful in setting the cuto† Ñux threshold, because channels below this threshold are deleted and this can generate narrower proÐles in regions of fainter signal. In some cases, notably SDIG, ESO 245-G005 and especially NGC 625, several peaks were indeed present, at least in some regions, but we did not attempt multi-Gaussian Ðttings, as clearly better resolution and higher signal-tonoise ratio data would be necessary. For our Ðve other dwarfs the velocity proÐles are dominated by a single peak in intensity, and the moment maps agree well with the XGAUS results. The moment velocity dispersion maps do not show the pathological signature of higher dispersions in regions of higher H I column densities (in fact, for the objects for which Ha imaging is available, it appears that the high dispersion regions do not necessarily correspond to the H II regions either as might have been expected ; see Skillman et al. 2000). The moment maps results will therefore be adopted for the rest of the discussion. Rotation curves were obtained by Ðtting a tilted-ring model to the velocity Ðelds (Begeman 1987). This consists of an iterative process in which the velocity Ðeld is partitioned into concentric rings, a beamwidth in size, and in each ring six kinematical parameters are Ðtted to the observed radial velocities (the kinematical center, systemic velocity, inclination, position angle, and rotation velocity). Because the position angle and inclination are free to vary from one ring to the next, this enables one to model successfully warps in galactic disks, since it is observed that most H I disks are warped. For the initial values of the kinematical parameters, one uses estimated values from the global proÐle (for the systemic velocity), from optical data (for the center), or from ellipses Ðtting to the H I distribution (for the inclination and position angle). The radial velocities in each annulus are weighted with o cos h o , and points inside a given angle from the minor axis (here typically 20¡È30¡) are completely discarded (to avoid large deprojection errors). The center and the systemic velocity are the Ðrst parameters to be determined and are then Ðxed to a constant value for all rings. The orientation parameters like the inclination and the position angle, as well as the rotation velocity, are then Ðtted in each ring. The best tool to check the validity of the derived rotation curve is to analyze the residual velocity Ðeld, which is the di†erence between the true observed radial velocities and the radial velocities modeled by using the Ðtted kinematical parameters. Systematic residual patterns will clearly diagnose which parameter(s) is (are) at fault. A new rotation curve can then be derived with these adjusted parameters, until the user is satisÐed of the s2 of the Ðt and of the residual velocity map. For the Ðnal rotation curve the orientation parameters are Ðxed to some average values, with only the rotation velocity being free to vary (see Fig. 2).

Vol. 120

This method is assuming of course that the H I is distributed in inÐnitely thin rings. This is most probably not the case, and in the presence of a thick H I disk, or Ñaring of the H I disk at large galactocentric radii, one will be sampling in a given line of sight several parts of the galaxy with di†erent velocities, creating skewed velocity proÐles. Our data are not suitable for such a study of the proÐles skewness in detail, but Olling (1995, 1996) has done some careful modeling to estimate the e†ect of Ñaring on the observed velocity Ðelds and rotation curves. It is expected to be more important in dwarf galaxies because the Ñaring is proportional to the ratio of the velocity dispersion to the rotation velocity, which will be higher for dwarfs. But when the velocity dispersion drops with radius then the thickness might not increase and may even stay Ñat. To limit the e†ect of possible Ñaring on the rotation parameters, much more weight was put on the points close to the major axis for the tiltedring analysis, and the points around the minor axis were eliminated because the e†ect of Ñaring will be much less severe near the major axis (see the diagram in Olling & van Gorkom 1992). Before these rotation curves can be used for the dynamical analysis to follow, one must Ðrst consider and evaluate some corrections to be applied to these derived velocities. First of all let us consider the beam-smearing correction, due to the fact that the radio beams are quite large and when the velocity gradient is steep as in the very inner parts of the rotation curve, where the H I surface densities are higher, the derived velocity as averaged over the whole beam will be lower. It is usually recommended to start worrying about beam-smearing e†ects when R /b \ 6 (Bosma HO and b is the 1978), where R is the Holmberg radius HO FWHM of the synthesized beam, and estimates of the beam-smearing corrections can be obtained through model data cubes (Begeman 1989 ; Broeils 1992). But the velocity gradients in the inner parts of dwarfs are not as steep as in normal galaxies (i.e., dwarfsÏ rotation curves rise slowly), and their H I radial proÐles are often Ñat in the innermost parts, thus reducing the beam-smearing e†ects. For ESO 444-G084, which has from all our objects the worst sampling (with R /b \ 3.4), these corrections were estimated HO2.5 km s~1 in the rising part, based on de to be less than Blok & McGaugh (1997) models. However, van den Bosch et al. (2000) have reexamined a sample of these de Blok & McGaugh (1997) LSBs and calculate more substantial beam-smearing corrections, conÐrmed by the Ha velocities obtained for Ðve of these LSBs by Swaters, Madore, & Trewhella (2000). But these LSBs H I rotation curves were of lower resolution than the ones for our dwarfs, and besides for two of our objects we have obtained Ha velocities in the rising part of the curves which match extremely well their H I velocities, showing that beam-smearing corrections were not underestimated. Another correction to be applied to the rotation velocities is the asymmetric drift correction, because of the pressure term induced from the velocity dispersion of the gas. This correction should be particularly important in dwarf galaxies which have low maximum rotation velocities and so their velocity dispersion might represent a considerable percentage of V . The method followed is presented in Skillman et al. max (1987). We used the Meurer et al. (1996) formulation which is more general as it does not assume a constant velocity dispersion with radius :

No. 6, 2000


3039

80 (a)

(c)

230

60 225

Halo

220 90

40 (b)

80

70

20 HI

60

Stars 50 0

1

2

3

4

0 0

1

2

3

4

Radius (kpc)

30 (a)

(c)

300

295

20

290 80

(b)

60

10

40

20

0

0.5

1

1.5

0 0

0.5

1

1.5

Radius (kpc)

FIG. 2.ÈPosition angle (a) and inclination (b) vs. radius from the tilted-rings Ðts to the velocity Ðelds. The lines show the adopted values used to derive the Ðnal H I rotation curves (c). Also shown is their best-Ðt mass model (if one was Ðtted), with the contributions from the stellar disk, H I disk, and dark halo traced separately. Velocities obtained from H I are in Ðlled circles, and those from Ha in open circles.

Lu L ln & V 2 \ V 2 [ 2u [ u2 , c o L ln r L ln r

(1)

where V is the corrected velocity, V is the observed one, u c o gas surface density. is the velocity dispersion, and & is the The corrected velocities are higher than the observed ones by up to 4 km s~1. These Ðnal corrected rotation curves are plotted in Figure 2. The errors at each point were calculated from half the di†erence between the velocities on each side (receding vs. approaching) of the galaxy, or from the formal errors given by the least-squares Ðts, whichever were the highest.

Because the asymmetric drift corrections are uncertain to about 25% (Lake & Skillman 1989), this uncertainty was also incorporated in the plotted errors. In the case of UGCA 442 and DDO 161, the H I rotation curves were combined with the Ha velocities obtained from long-slit spectra obtained at the Siding Spring 2.3 m telescope (Coüte et al. 2001), which extend to almost 1 kpc. As expected for such systems, the rotation curves are seen to be slowly rising, however the Ñat part is reached in all cases, with V ranging from 19 to 67 km s~1. As for the max velocity dispersions they are mostly uniform throughout the H I envelopes with average values of D8 km s~1, which is

3040


Vol. 120

60 (a)

100

(c)

80

40 60

80

(b)

60

20

40

20

0

1

2

3

4

0

5

0

1

2

3

4

5

Radius (kpc)

60

315

(a)

(c) 310

Halo

305

40

300 80 (b) 70

20

Stars

60

HI

50

40

30 0

1

2

3

0

4

0

1

2

3

4

Radius (kpc)

FIG. 2.ÈContinued

similar to what is found in face-on giant spirals where p D 8È12 km s~1 (Shostak & van der Kruit 1984). The V values of our dwarfs are several times higher than their p,max so they are mainly supported by rotation rather than being pressure-supported, even for our lower luminosity object (at M \ [11.3), allowing us to build multicomponent mass B models. 4.

MASS MODELS

The mass models to be applied to our objects, described in detail in Carignan (1985), calculate the potential at each radius directly from the surface brightness distribution for the stellar component, the surface density distribution for the H I component, and the adopted density distribution for the dark halo.

The stellar mass distribution is obtained by using the luminosity proÐles derived in Coüte et al. (2001). Because dwarfs do not have central spheroidal bulges, these proÐles show the presence of only an exponential disk, for which the stellar mass surface density can be obtained by multiplying the light proÐles by a constant mass-to-light ratio (M/L ) . B* This is the only free parameter for modeling this component and sets the amplitude of the stellar contribution. It is preferable to use the red luminosity proÐle because it is more representative of the old stellar component which contributes the most to the total stellar mass. Consequently the I luminosity proÐles were used for the modeling, except for UGCA 442 for which the B proÐle extends much farther out (the B and I proÐles are very similar in any case, with comparable scale lengths). The surface density is then integrated to predict the rotation curve (see Carignan 1985).

No. 6, 2000


3041

80 (c)

(a)

300

295

Halo

60 290

285

280

40

90

(b)

80 70

HI

20 60

Stars 50 40 0

2

4

6

0

8

0

2

4

6

8

Radius (kpc)

130

80

(a)

(c)

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FIG. 2.ÈContinued

Especially in dwarf galaxies, the gas component is far from being negligible, as in fact it is in some cases a larger contributor to the visible mass than the stellar disk itself. The gas mass distribution is obtained from the H I radial surface density proÐles derived above, assuming that the H I is optically thin. The total mass of the gas is then taken to be 4/3 times the amount of H I present, to account for the amount of primordial helium associated with the H I. No molecular gas mass is taken into account. The H I surface density proÐles that will be used are the high-resolution ones at small radius, combined with the low-resolution ones at large radius. The latter ones extend much farther and so are invaluable in tracing the gas mass distribution as far out as possible. Because the thickness of the gas layer in the

direction perpendicular to the equatorial plane has only a rather small inÑuence on the total Ðnal mass distribution, we have not tried here to Ðt it. Lake & Skillman (1989), for example, have calculated that for a scale height of 200 pc the model rotation curves are lower by only 2% compared to a model with 100 pc. For the dark halo an isothermal sphere (Carignan 1985) is used. It has two free parameters : the core radius r , and c the one-dimensional velocity dispersion p. The central density o is given by 0 9p2 o \ . (2) 0 4nGr c Although viewed by some as archaic, this model is still the

3042

COŒTEŠ, CARIGNAN, & FREEMAN 60 (a)

310

(c)

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Halo 60

(b)

Stars

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Radius (kpc)

FIG. 2.ÈContinued

one generating the best Ðts (lowest s2) compared to others. For example, for the 22 rotation curves of the Ursa Major cluster galaxies, Verheijen (1997) obtained better Ðts even with the pseudo-isothermal model than with a Hernquist proÐle. As for the CDM halos of Navarro, Frenk, & White (1996b), they will be compared below. Our complete mass model has therefore three free parameters, which have to be Ðtted using our one observed rotation curve, and so there will not be of course a unique [(M/L ) , r , p] solution Ðtting within the errors. The more B * is cthe rotation curve, the better one can hope to extended constrain these parameters. Also combining the H I rotation velocities with higher resolution optical (Ha) rotation velocities in the inner parts helps better constraining (M/L ) . The values of (M/L ) Ðtted to H I rotation curves can beB *substantially a†ected Bby* beam-smearing in the inner parts of the curves (see Blais-Ouellette et al. 1999). As mentioned above, dwarf galaxies should su†er less from this, and in any case for our dwarfs the H I data are of relatively high spatial resolution, and besides a few of them have Ha rotation curves as well. One approach is ““ the best-Ðt method,ÏÏ which consists in Ðnding the minimum s2 to the Ðt ; another one is the ““ maximum-disk method,ÏÏ which maximizes the contribution of the stellar disk by Ðtting the largest (M/L ) allowed by the rotation curve. This might B *larger normal galaxies where the light seems make sense in to dominate in the inner parts, as it might be the case in the Milky Way (Sackett 1997). Bottema (1993, 1997) Ðnds though from the observed stellar velocities in normal galaxies that the disk rotation is on average only 63% of the maximum rotation. For dwarf galaxies the dark matter halo is often seen to be dominant even in the rising part of the rotation curve (Coüte, Carignan, & Sancisi 1991), i.e., even with maximum disks it is not possible for the disk rotation to account for most of the maximum rotation. Here maximum-disk Ðts were also performed on our dwarfs, since this provides at least lower limit results on the dark halo masses. In any case because of the small contribution of the stellar material to the overall mass in dwarfs, the

exact value of (M/L ) does not have much impact on the Ðnal halo results. B * The mass models are illustrated in Figure 2, with the results recorded in Table 4, while Figure 3 shows the gas radial surface density distributions. Comments on individual galaxiesÏ kinematics and mass models can be found in the Appendix. 5.

RESULTS

5.1. Maximum V elocities of Dwarf Galaxies The maximum velocities derived for six of our dwarfs (excluding NGC 625 which was not modeled and ESO 245G005 for which the rotation curve does not extend far enough) are plotted against their total magnitudes in Figure 4 below, along with a compilation of all the galaxies found in the literature (most of them cited in Broeils 1992) which have been carefully analyzed with tilted-ring Ðts to a complete gas velocity Ðeld, listed all in the legend. Despite the sparsity of points this shows a clear trend, which is the basis of the Tully-Fisher relation, with the low-luminosity dwarfs following the relation set by the most luminous spirals, although with a strong Ñattening of the slope at the faint end (this will be discussed in detail in a forthcoming paper). But the majority of dwarfs all the way down to M \ [14 B clearly have still considerable maximum rotation velocities. Only at extreme low luminosities where the Local Group dIrrÏs lie does the smooth trend seem to break up. Some of it is likely due to underestimating the V of the Local Group max (1993), for which objects observed by Lo, Sargent, & Young the high-resolution imaging missed some of the extended low surface brightness gas. The few dwarfs which have been reobserved at Arecibo by Ho†man, Lewis, & Salpeter (1995) indeed reveal much more rotation than the Lo et al. data (see the detailed discussion in Skillman 1995). Nevertheless it is around M \ [13 where the trend falls apart that we B start to Ðnd systems with misaligned H I kinematics such as SDIG, GR 8, Sextans A, etc., while brighter dwarfs around M \ [14, such as DDO 154, still show normal rotation. B

Best-Ðt Max-disk Best-Ðt Max-disk Best-Ðt Max-disk Best-Ðt Max-disk Best-Ðt Max-disk

(2)

1.3 2.7 2.3 2.8 0.9 1.2 4.6 6.5 4.0 5.0

(M/L ) B* (M /L ) _ _ (3) 0.67 1.4 2.28 2.78 2.07 2.76 1.50 2.12 5.24 6.56

M * (108 M ) _ (4) 1.1 1.1 1.24 1.24 4.1 4.1 0.69 0.69 1.01 1.01

M gas (108 M ) _ (5) 1.7 1.9 2.4 3.1 3.3 3.5 1.5 1.7 2.8 4.2

r c (kpc) (6) 35 35 31 34 41 41 39.5 40 22.5 25.0

p (km s~1) (7) 0.071 0.057 0.028 0.020 0.026 0.023 0.116 0.092 0.011 0.006

o 0 (M pc~3) _ (8)

DARK HALO

0.041 0.036 0.020 0.016 0.015 0.014 0.103 0.084 0.009 0.005

o halo (M pc~3) _ (9) 3.1 1.7 0.9 0.6 2.0 1.6 0.5 0.3 0.3 0.1

M /M dark lum (10)

AT R

10.0 10.2 5.8 5.7 5.3 5.3 7.8 9.3 6.4 6.8

(M/L ) B dyn (11)

25

0.38 0.39 0.35 0.34 1.07 1.05 0.10 0.12 0.24 0.25

M tot (109 M ) _ (12)

0.005 0.005 0.004 0.005 0.003 0.003 0.008 0.009 0.003 0.003

o halo (M pc~3) _ (13)

14.2 9.8 5.1 4.6 9.3 8.2 12.9 10.0 1.2 0.8

M /M dark lum (14)

52.0 52.1 21.7 22.5 27.6 27.3 93.5 94.8 10.6 10.6

(M/L ) B dyn (15)

AT R (last point) max

2.69 2.69 2.15 2.23 6.35 6.28 3.06 3.10 1.38 1.39

M tot (109 M ) _ (16)

NOTES.ÈLuminous disk parameters : Col. (3) : Mass-to-light ratio of the stellar disk. Col. (4) : Total mass in stars. Col. (5) : Total mass in gas. Dark halo parameters : Col. (6) : Core radius. Col. (7) : Velocity dispersion. Col. (8) : Central density. At the optical radius R : Col. (9) : Density of the dark halo. Col. (10) : The dark-to-luminous mass ratio. Col. (11) : The total mass-to-light ratio. Col. (12) : The total mass. 25 At R : Col. (13 ) : Density of the halo. Col. (14) : The dark-to-luminous mass ratio. Col. (15) : The total mass-to-light ratio. Col. (16) : The total mass. max

ESO 325-G11 . . .

ESO 444-G84 . . .

DDO 161 . . . . . . .

ESO 381-G20 . . .

UGCA 442 . . . . . .

GALAXY (1)

LUMINOUS DISK

TABLE 4 MASS MODELS RESULTS

3044


At this point the rotation has become so small that random motions starts to contribute a relatively important part of the dynamical support, and eventually at smaller rotation the gas distribution is no longer a thin disk but has pu†ed up, which can foster a preferred axis of rotation away from the optical axis. 5.2. H I Radial ProÐles Using the orientation parameters derived from the velocity Ðeld analysis, integrating these total H I distributions along ellipses we produced H I radial surface density distributions for our objects (Fig. 3). These radial proÐles are scaled by 4/3 to account for the presence of primordial helium and by the cosine of the inclination angle for depro-

Vol. 120

jection, where the optical inclination values were used for the peculiar galaxies NGC 625 and ESO 245-G005. 5.2.1. Gas Surface Densities L evels

Cayatte et al. (1994) have produced averaged H I radial proÐles for each Hubble type between S0 and Sdm, using a sample of 84 undisturbed galaxies observed by Warmels (1988) and Broeils (1992), and showed that average H I surface densities peak for Sc and Scd, decreasing again for later types. Comparing our gas surface density proÐles with those of van Zee et al. (1997), who have a sample of six LSB dwarfs and four normal dwarfs, half of our dwarfs (ESO 381-G020, DDO 161, ESO 444-G084, and UGCA 442) have higher surface densities than any of their normal dwarfs (averaged over 0.5 R because of the e†ect of the HI 6

20

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100

12

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6 8

4

6

4

2 2

0

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600

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FIG. 3.ÈGas radial surface density distributions. The dotted lines shows the critical density for star formation (following Kennicutt 1989).

No. 6, 2000


3045

30 15

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150

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250

FIG. 3.ÈContinued

higher resolution for our sample, where R is the H I radius HI measured at a column density of 1 M pc~2). It should be _ kept in mind though that our dwarf sample was selected among the objects with the highest H I Ñuxes among all the Sculptor and Centaurus A group dwarf members (Coüte et al. 1997), and so perhaps it is not surprising to Ðnd higher surface densities than in more ““ typical ÏÏ dwarfs, although high gas surface densities do not necessarily correlate with higher total H I mass ; for example the LSBs of de Blok et al. (1996) have H I surface densities about a factor of D3 lower than in normal late-type galaxies, despite having higher M /L ratios than normal galaxies. Here there are no H I Bbetween gas surface densities and optical surface trends brightness for our eight dwarfs ; neither are there any with their absolute blue magnitudes or with their degree of iso-

lation in the groups. The two objects with the lowest surface densities are NGC 625 and SDIG, which happen to be respectively the galaxies with the highest and lowest central surface brightness among this sample (Coüte et al. 2001), and the highest and lowest current star formation as judged from their Ha emission (Skillman et al. 2000 ; see also Heisler et al. 1997). Obviously the gas surface densities play an important role in regulating the star formation processes, and the state of these two galaxies could be explained by depletion of the gas from the recent bout of star formation in the case of NGC 625 and inhibition of star formation because of a low surface density below some critical threshold for SDIG. The peak H I surface density of DDO 161 is unusually large, reaching almost 21 M pc~2, the highest in our _

3046


Vol. 120

FIG. 4.ÈAbsolute B magnitude vs. s the log of the maximum rotation velocity, for galaxies with full kinematical information (H I velocity Ðelds), from Broeils (1992), Ho†man et al. (1995), Lo et al. (1993), Skillman et al. (1987, 1988), Pickering et al. (1997), and van Zee et al. (1997). Our dwarfs are indicated by Ðlled circles.

tor galaxies there are already Ha and [O III] maps for UGCA 442 and ESO 245-G005 (Miller 1996), and both are harboring several H II regions. NGC 625 is also particularly active. However in this case it is not possible to derive a reliable rotation curve which is needed for the calculation of the critical threshold. Possibly the choice of a \ 0.67 crit derived for spirals might not be suitable for dwarfs, as for example Hunter & Plummer (1996) Ðnd a \ 0.3 for crit Sextans A. More likely it is the azimuthally averaging of the proÐles which washes out local H I maxima peaking above the critical thresholds. Indeed in UGCA 442 the brightest H II region is located at proximity to the H I peak, and similarly in E245-G005, the three main Ha-emitting regions are each in the vicinity of H I peaks. This has been noticed in numerous galaxies and in dwarfs too, as in the sample of van Zee et al. (1997). The issue of the spatial resolution on the H I peaks values (discussed above) is thus of prime importance if one wishes to determine the critical thresholds properly. Higher resolution H I mappings for a large number of dwarfs will be required before the validity of the Kennicutt (1989) dynamical criterion can be assessed, compared to thresholds based on simple critical column densities such as the ones proposed by Gallagher & Hunter (1984) and Skillman et al. (1987) (5 ] 1020 and 1021 atoms cm~2, respectively).

sample and certainly much above the average for its type according to Cayatte et al. (1994). First, the errors on this value are ^7.8 M pc~2 because of the uncertainty in the inclination (with i _in the range 70¡ ^ 10¡, the deprojection corrections on the radial proÐle are important). Second, these peak values are evidently dependent on the spatial resolution of the H I mapping, and DDO 161Ïs H I map has indeed the highest resolution of our sample, with 0.22 kpc beam~1. Local Group dwarfs, for example, that have been mapped by Lo et al. (1993) at similar high resolution also have H I peaks above 20 s (CVndwA, at 0.42 kpc beam~1, has an H I peak of 32 M pc~2, the same as DDO 187 at _ 0.34 kpc beam~1). Furthermore it is possible that DDO 161 is devoid of molecular gas, so that its total gas surface density has a normal value. No attempts were made here to add the molecular gas mass to our H I (plus He) gas surface densities because of the large uncertainties in the H to H I ratios for late-type and dwarf galaxies. It is thought 2that the molecular mass is roughly 0.06 times the H I mass in Sm and irregulars (Young 1993), 10 times lower than in earlytype objects. But most probably the conversion factor from the detected CO column density to the H column density increases for decreasing metallicity and is 2therefore difficult to extrapolate for such metal-poor systems (Wilson 1995). In Figure 3 are plotted for all the dwarfs the critical densities for star formation, using the dynamical criterion of Kennicutt (1989). This was based on ToomreÏs (1964) idea that below a certain critical surface density of gas a rotating self-gravitating disk should be stable against density perturbations leading to star formation. We calculated these using the velocity dispersions and gradients of the rotation curves derived above and with the stability parameter a \ 0.67 (as found in Kennicutt 1989). None of our dwarfscritseem to have gas densities exceeding their respective critical thresholds. In the case of the Centaurus A dwarfs an Ha imaging survey is in progress, but it is already clear that all of them will reveal sites of active star formation since their spectra all had generous Ha lines (Coüte et al. 1997). For the Sculp-

The shapes of the proÐles generally follow very closely the typical surface density distributions of the Cayatte et al. (1994) Sdm galaxies, with a Ñatter proÐle within R followed by an exponential decline. Taylor et al. (1994)25 found that their Ðve H II galaxies have steep (sharply peaked) H I proÐles in contrast to the Ñatter proÐles of the LSB galaxies. Certainly van Zee et al. (1997) and de Blok et al. (1996) samples of LSB galaxies also all have rather Ñat proÐles. This is mostly because their surface densities, even in the inner galactic regions, are all lying below the critical threshold for star formation. At very large radius, around the Holmberg radius, all our H I radial proÐles show a marked Ñattening o†, declining slower than exponentially. This has been noticed for other dwarfs and irregulars by Ho†man et al. (1993), who conjecture that the fallo† for the total hydrogen column density is more like a power law and thus argue that these large extended gas disks may account for the reported lowredshift Lya absorption features seen in QSO spectra. Because of the high space density of these Lya lines, it has often been suggested that dwarf galaxies may contribute signiÐcantly to their cross sections (see, e.g., Maloney 1992 ; Shull, Stocke, & Penton 1996). But beyond gas density levels of a few times 1019 atoms cm~2, the H I column in disk galaxies falls o† sharply (e.g., NGC 3198 ; van Gorkom 1991). This truncation probably corresponds to the H I ] H II transition as the hydrogen becomes ionized by the extragalactic UV radiation Ðeld (predicted by Sunyaev 1969 ; see also Maloney 1993). Since the shape of the gas (neutral]ionized) distribution beyond the sharp cuto† is unknown (and its variation from one type of galaxy to another as well), the contribution from dwarf galaxies compared to normal ones to the Lya lines numbers can only be vaguely estimated. But at least the H I cross sections (i.e., before the cuto†) can be compared. Our H I data extend down to a few times 1019 atoms cm~2 in the best cases, and at these levels we can estimate roughly that a typical nearby

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5.2.2. Shape of the Gas ProÐles and Gas Cross Sections

No. 6, 2000


dwarf would o†er a cross section of D26 arcmin2 in H I, just by averaging on the H I sizes of all our mapped objects. Assuming that the rest of the dwarfs in each group (Coüte et al. 1997) which were detected at Parkes but not mapped in H I have similar properties, the total dwarf cross section in Sculptor and Centaurus A would be D855 arcmin2 at the current level of a few times 1019 atoms cm~2. This is most probably an overestimate because the smallest dwarfs should not have as large H I envelopes as the dwarfs selected for mapping. Nevertheless this does not match the contribution of normal galaxies in those groups by far : in Sculptor, NGC 55 alone covers 450 arcmin2, which is more than all the Sculptor dwarfsÏ area put together, and there are several other gas-rich spirals in the group (NGC 247, NGC 7793, NGC 300, and NGC 253) ; in Centaurus A too, M83 alone has an extremely extended H I distribution (Rogstad et al. 1974), which covers about 900 arcmin2. So the dwarfs represent at most approximately 15% of the total H I cross section in the groups. This is similar to the conclusions reached by Szomoru et al. (1994) from their H I mappings of 12 Ðelds in the Perseus-Pisces supercluster and foreground void, where they found that H I dwarfs contribute 12% at most of the total H I cross section. At a level of 1014 atoms cm~2 (at which Lya absorption lines are routinely detected), it is unlikely that the sum of the dwarfsÏ gas coverage will exceed that of the main members, even if the dwarfsÏ radial H I proÐles are expected to Ñatten o† more drastically. Roughly, despite the large number of gas-rich dwarfs in our groups, the normal galaxies will be o†ering a larger cross section for Lya absorption in the spectra of QSOs than the dwarfs will. 5.3. Properties of Dark Halos 5.3.1. Overall Properties

The results of the mass models show that there are undoubtedly large amounts of dark matter in dwarfs. In all cases the dark matter halo is the most massive component in these galaxies, accounting for at least 54% and up to more than 92% of their total mass (out to the last measured point of their rotation curves). They are deÐnitely dark halo dominated. In the rising part of the rotation curve, except for ESO 325-G011, the dark halo is already the major dynamical contributor, and the stellar disk is not selfgravitating. This is also the case for other dwarfs such as DDO 154 (Carignan & Freeman 1988), DDO 127 (J. Kormendy 1996, private communication), DDO 170 (Lake, Schommer, & van Gorkom 1990), as well as the majority of the van Zee et al. (1997) dwarf sample in which the dark matter component dominates in the inner regions. Even the gas component is sometimes dynamically more important than the stellar disk, as in DDO 161, or UGCA 442, which has twice as much mass in H I than in stars. For our objects the stellar disk (M/L ) ranges between 1.2 and 6.5 (in the maximum-disk cases),B *similar to the range covered by van Zee et al. (1997) dwarfs (0.6È6). From population synthesis models, only the lower range of these values should be expected for dwarf galaxies, and so the dark matter masses that we have obtained here are probably only lower limits ; the dark mass in dwarfs could be even higher. While the halo parameters r and p are reasonably well constrained in our models, this cis not true for the stellar disk (M/L ) . B *a However, since the total stellar mass in these galaxies is minor component of their total mass, even when using the maximum-disk (M/L ) value, this uncertainty in (M/L ) B* B*

3047

has little impact on the determination of the total galaxy masses or even their total mass-to-light ratios. One can see in Table 4 that the total masses and mass-to-light ratios obtained from the maximum-disk models and the best-Ðt models are very similar. These mass-to-light ratios, calculated at the last point of the rotation curves, range from 10 up to more than 93, which is close to the ratios found for small groups of galaxies (e.g., Huchra & Geller 1982). 5.3.2. Correlations with Halo Parameters

Let us now look at how the derived dark halo masses correlate with other properties. For the purpose of comparing with our dwarfs, a selected sample of galaxies (Table 5) was collated from the literature (mainly from Broeils 1992, with the addition of more recent studies) for which detailed mass decomposition had been performed using similar isothermal sphere models Ðts, on extended rotation curves (reaching at least 7a~1 ; see below). In many previous studies the dark matter masses and luminous masses of the galaxies, and their ratios M /M , were calculated at lum at the last point of di†erent radii in each galaxy,dark usually each rotation curve. In late types this last point is more likely to be at a larger radius compared to the optical scale length than in early types as their H I is so much more extended. We should look at these values at a particular set radius to make more meaningful comparisons between galaxies, for example, at a few times the stellar disk scale length a~1. Figure 5 shows the M /M ratios at 7a~1 versus lum the absolute magnitude (a) ;dark the maximum velocity of the rotation curve (b) ; the disk scale length a~1 (c) ; the color B[R (d) ; the gas richness M /L (e) ; and the central B H I studies of these trends surface brightness k ( f). Earlier B (Carignan & Freeman 1988 ; Kormendy 1990) suggested that M /M gets signiÐcantly larger for galaxies at the dark end.lumBroeils (1992) sees a clear correlation for low-mass M /M to increase with decreasing maximum velocity. darknormal lum spirals M /M is not far from 1, which was For darkago lum pointed out many years by Bahcall & Casertano (1985), for example, but it is known to be a function of luminosity (see, e.g., Persic & Salucci 1988, 1990). However, with our sample of dwarfs, the obvious increase in dispersion among the low-mass dwarfs is more striking than this trend. Although on average there is indeed an increase of M /M for lower luminosity galaxies, some of these dark have lum the same ratios as normal galaxies. This objects increased dispersion is conÐrmed by a study of a larger sample of dwarfs recently completed by Swaters (1999). It can be argued though that the radius 7a~1 may not be an adequate reference radius for dwarfs. The stellar disk is so unimportant in these systems, in which even the gas component can be more massive, and therefore a~1 is not necessarily representative of the baryonic scale length for a dwarf. For this reason baryonic scale lengths were estimated for each galaxy. First the gas scale length h~1 was corrected for the beam size b. The baryonic scale length was obtained by averaging this corrected gas scale length with the optical disk scale length a~1, but with respective weights depending on the galaxyÏs H I mass to stellar mass ratio : h

bar

\

M M * gas ] a~1 ] ] h~1 , cor M ]M M ]M * gas * gas

(3)

where h~1 \ J(h~1)2 [ b2 . cor

(4)

Mb,i B [18.62 [18.3 [21.7 [19.2 [16.45 [22.8 [15.9 [18.95 [19.88 [21.9 [20.0 [18.62 [13.81 [18.77 [15.15 [21.4 [17.51 [16.5 [17.36 [21.6 [21.4

1.61 4.5 12.0 1.9 1.3 13.0 1.3 2.2 2.3 5.4 2.0 2.6 0.5 5.8 1.7 11.4 1.4 1.6 1.7 8.3 4.5

a~1 (kpc)

1.6 15.5 2.5 3.3 5.1 8.0 2.5 3.9 1.4 6.4 3.4 12.4 3.8 4.7 3.0 10.5 5.1

2.2 8.9 13.1

h bar (kpc)

22.0 21.9 24.0 21.9 21.5 21.5

21.5 23.3 21.9 20.7 22.3 22.0 23.2 21.4 21.1 20.3 20.5 21.6 23.2 23.0

k B (mag arcsec~2) 87 102 222 115 90 298 79 136 323 214 201 157 48 222 66 273 92 85 121 266 241

V max (km s~1)

1.7

1.25

1.22 0.89

1.25 1.02 1.5 0.71 1.46 1.11 0.64 1.57

0.74 0.76 1.39 0.91

B[R /L HI 0.3 1.8 0.5 1.1 0.5 0.3 2.9 0.6 0.4 0.5 0.2 0.8 4.8 0.5 5.4 0.72 1.4 3.0 0.5 0.75 0.71

M

4.2 2.0 0.7 1.0 1.3 1.5 4.4 1.7 9.6 1.3 6.9 0.7 2.7 1.0 1.1

1.5

M /M at 7a~1 d l 3.5 0.8

34.6 3.4 4.8 119.5 103

1.2 3.1 0.7 0.4

8.7 21.6 24.8 3.2 10.9 3.0 10.1

5.5 44.9

8.7 4.5 74

r c (kpc)

0.8

2.0 0.3 0.9 1.0 1.4 8.0 1.3

2.1 1.7

M /M at 4.5 h d l bar 3.3 0.9 0.6

0.0016 0.030 0.0006 0.0017

0.001

0.011 0.009 0.0018 0.051 0.009 0.015 0.005

0.017 0.0013

o 0 pc~3) _ 0.007 0.0095 0.0003 (M

1 2 3 3 4 5 3 1, 6 1, 6 3 6 1, 6 7 1, 6 1, 8 3 9 2 1, 6 3 3, 6

References

NOTE.ÈModeled galaxies with rotation curves reaching at least 7a~1 and/or 4.5 h . bar REFERENCES.È(1) Puche & Carignan 1991 ; (2) de Blok & McGaugh 1997 ; (3) Broeils 1992 ; (4) Carignan et al. 1988 ; (5) Roelfsema & Allen 1985 ; (6) Begeman 1987 ; (7) Carignan & Beaulieu 1989 ; (8) Lake et al. 1990 ; (9) Coüte et al. 1991.

N55 . . . . . . U1230 . . . N801 . . . . N1003 . . . U2259 . . . U2885 . . . N1560 . . . N2403 . . . N2841 . . . N2998 . . . N2903 . . . N3198 . . . D154 . . . . N5033 . . . D170 . . . . N5533 . . . N5585 . . . F583-1 . . . N6503 . . . N6674 . . . N7331 . . .

Galaxy

TABLE 5 PARAMETERS OF THE COMPARISON SAMPLE OF GALAXIES


3049

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12

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0 0.5 1 1.5 0 5 10 15 0

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6 20

25

B-R FIG. 5.ÈRatio of dark to luminous mass at a radius of 7a~1, vs. the absolute magnitude, the maximum rotation velocity (km s~1), the optical scale length (kpc), the color (B[R), the gas richness (M /L ), and the central B surface brightness ( mag arcsec~2). The open circles are for our dwarfs, while the Ðlled _ _ ones are from the comparison sample of galaxies of Table 5.

The resulting sample of galaxies with rotation curves reaching at least 4.5h is essentially the same as previously bar that do not reach this radius, although (minus four galaxies three others not previously included now qualify ; see Table 5). Figure 6 shows M /M estimated at 4.5h . Again, it dark lum is clear that the ratios are higher on average forbarsmall lowluminosity galaxies, but the large dispersion of dark matter properties among dwarfs is still present. The galaxy with the most extreme dark matter properties is still DDO 154, with M /M [ 8. But it is not an exceptional dwarf ; some of lum have M /M close to this value. Note that ourdark galaxies when estimating Mdark /Mlum at 4.5h , the low surface dark the lum same range bar of values as the brightness galaxies have normal galaxies, while they have been thought to be more dark matter rich from M /M estimated at a few times dark a~1. lum This may be caused by the optical disk scale lengths LSBÏs Ñatter luminosity proÐles, which means that at 7a~1, for example, one is sampling further out into their dark halo. Here the dark matter richness does not correlate at all with the surface brightness k . In Figure 7 the ratio of gas B

mass to dark matter mass is shown, as a function of magnitude and maximum rotation velocity. While de Blok & McGaugh (1997) hint at a trend of increasing gas-richness for slower rotating galaxies, here M /M stays near the gas about dark 7 magnitudes, same values over the whole range of and similarly over the complete range of V , with values max at the last mostly between 1% and 15% (when calculated point of the rotation curve). Looking now at the dark matter halo parameters, Figure 8 shows the central dark halo density for our dwarfs compared to the previous sample, where only galaxies with data reaching to at least 4.5h are considered. This is important since extended rotation bar curves are essential for constraining these dark matter parameters (see, e.g., Lake & Feinswog 1989). It is often argued that these trends are highly modeldependent (see the maximum-disk vs. Bottema disk trends of de Blok & McGaugh 1997), but the modelsÏ discrepancies (variations of [30% in the parameter values) largely disappear when considering only reliable extended rotation curves. While Kormendy (1990) advocates an increasing

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KINEMATICS OF DWARF IRREGULAR GALAXIES central dark halo density for lower luminosity galaxies, it is clear that it is mostly an increased dispersion in the values of o that is found for galaxies with lower luminosity and 0 lower V (which are typically smaller and bluer too on max average). The overall trend does conÐrm the Kormendy relations, in the sense that, on average, the lower luminosity galaxies have a more centrally dense dark halo. But this large dispersion seems to indicate that similar galaxies (meaning those with similar optical properties) can have diverse dark matter halos with fairly di†erent properties. Within the same ranges of luminosity (or V ) for dwarf max galaxies, dark halos have central densities varying by a factor of 10 ! In fact early-type dwarfs, for which a global M/L can be estimated from velocity dispersions, seem to have much lower dispersion in their amount of dark matter as a function of luminosity ; Mateo (1998) Ðnds a relation log M/L \ 2.5 ] 107/(L /L ) for the Local Group dSphÏs. _ Interestingly, for the dIrrÏs, the surface brightness of the galaxy seems to be irrelevant. This is the only galaxy property plotted in Figure 8 that does not show a trend with

3051

the dark halo parameters. However, the range of surface brightness in our sample is narrow (unfortunately most of the de Blok & McGaugh 1997 LSBs could not be included since their rotation curves are not sampled very far out in terms of h ). The same trends are found for the core radius r (Fig. 9),barwhere smaller (and bluer) galaxies of low lumic nosity and V have smaller core radii (i.e., have more conmax centrated dark halos). But by normalizing the core radius with a characteristic radius of the galaxy (R here), which 25 is needed to eliminate the size bias (larger galaxies being larger in every aspect), most of the trends vanish into scatter diagrams (Fig. 10). Athanassoula, Bosma, & Papaioannou (1987), using a larger sample of galaxies modeled di†erently, found a trend of increasing R /R with morphological c 25 types (when averaging over all galaxies of a given type). This suggested that the halos of early-type galaxies are more concentrated than those of late types. One must keep in mind though that while R is a good reference radius for 25 early-type galaxies, it is probably not fully justiÐed to use it for dIrrÏs as pointed out above.

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COŒTEŠ, CARIGNAN, & FREEMAN 5.3.3. Implications

These trends have important implications for galaxy formation scenarios. Indeed, Navarro, Frenk, & White (1996b, hereafter NFW) have predicted from N-body simulations that CDM halos should follow a universal structure proÐle in which there is a strong correlation between the mass of a halo and its concentration (the exact form of this relation depends on the chosen cosmogony). Normal galaxies can be made consistent with their ) \ 1 (SCDM) predictions by 0 scaling the (M/L ) of the disk with luminosity. But dwarf B* galaxies are good test cases for these predictions because their baryonic material is less signiÐcant dynamically so their observed rotation curve represents the dark matter mass more closely. Their predicted CDM halos are more concentrated because in hierarchical clustering scenarios low-mass systems collapse earlier than more massive systems. This means their halos are denser because the mean density of the universe at the time of collapse is higher. Figure 11 shows the SCDM NFW best-Ðtting halos (minimum s2) to our sample of dwarf galaxy rotation curves. The Ðtted parameters for the CDM halos are the concentration index c and V , the velocity at the radius 200 is 200 ] o , with an within which the mean density crit adopted H \ 75 km s~1 Mpc~1 (these two parameters are 0 correlated for any given cosmological model, and for these Ðts the relation of c as a function of V compatible with 200 Frenk, & White SCDM was used, as described in Navarro, 1997). For these Ðts the gas contribution has been removed from the observed rotation velocities in order to isolate the dark matter mass. The stellar disk contribution should also be removed, but that would imply Ðxing an uncertain (M/L ) for the stars, so it is here neglected. This means the B *actually ““ maximum halo ÏÏ Ðts because presumably Ðts are (M/L ) D 0. This should make it easier to Ðt highly conB * NFW halos. But despite this, it is clear that centrated SCDM halos are mostly not compatible with observed rotation curves : the SCDM halos are substantially more concentrated than what is inferred from observations. This problem was originally pointed out by Moore (1994) for four dwarf galaxies. A possible explanation, then proposed by Navarro, Eke, & Frenk (1996a), is that early bursts of star formation could expel a large fraction of the baryonic material in dwarfs, signiÐcantly altering the central regions. However, the parameters used to model these events are not totally realistic. Furthermore, low surface brightness galaxies, which can have quite large scale lengths and be massive objects, are also observed to be less concentrated than their simulated halos (McGaugh & de Blok 1998 ; Pickering et al. 1997). Since they do not have the shallow potentials of dwarfs, it is more difficult to create baryonic outÑows to solve their concentration problem. Navarro (1996, 1998) has proposed, meanwhile, that lower concentration halos, compatible with the observed curves of dwarfs and LSBs, can be produced by low ) Ñat CDM 0 models, with ) \ 0.3 and " \ 0.7. Figure 12 illustrates the 0 results of ““ maximum-halo ÏÏ Ðts to our rotation curves as well as those of other H IÈmapped galaxies, as collated by Pickering et al. (1997), with V and c free (not restricted to 200in Fig. 11 Ðts). For these SCDM compatible values as ““ maximum-halo ÏÏ Ðts, the baryonic components of the galaxies (gas and stars) were neglected in order to Ðt the maximal CDM halo possible. This allows one to obtain an

upper limit on the concentration index ; i.e., the most likely to approach the high value needed to be consistent with SCDM. In other words, this maximal value of c indicates what is the highest ) possible so that model and data 0 agree. Despite this, the Ðts results show that even the fashionable ) \ 0.3 and " \ 0.7 case can not produce low 0 enough concentration halos for many dwarfs and LSBs. A bigger problem is that for many objects, as shown by McGaugh & de Blok (1998), it is simply not possible at all to get a good Ðt. While the SCDM halos are too concentrated, the "CDM ones have asymptotic velocities unsuitably far o†. Furthermore, McGaugh & de Blok (1998) point out that one does not have the freedom to Ðt c and V 200 freely (as was done for Fig. 12). These two parameters are linked by the choice of cosmogony [once the cosmological parameters, such as ) or P(k) the shape of the power spectrum, are decided], and there is simply no plausible cosmology that can predict c and V values needed to Ðt many 200 above, van den Bosch et al. dwarfs and LSBs. As mentioned (2000) have shown that by reevaluating the beam-smearing corrections on some LSBs, H I rotation curves these can be reconciled with the steeper proÐles needed by CDM models. This cannot be the case, though, for our dwarf galaxiesÏ curves, for example, because in two objects we have optical Ha velocities that conÐrm the H I data, so the discrepancies with the CDM models cannot be due to beam-smearing e†ects. The NFW proÐles therefore fail to provide satisfying Ðts to a large number of galaxies, not only the Milky Way (Navarro & Steinmetz 2000). Moreover, new high-resolution simulations of dark matter halos by Moore et al. (1999) (with each halo containing [106 particles while the previous simulations so far used 5000È 20,000 particles per halo) are found to have steeper central density proÐles than the NFW proÐle. These fail to reproduce observed rotation curves even more convincingly. In summary these results show a larger range of dark halo properties for dwarf galaxies, as compared to the proposed universality of normal galaxiesÏ rotation curves. This implies that dwarfs with otherwise similar properties can have very di†erent fractions of dark matter. There is also a large diversity seen in the star formation histories of dwarfs (see, e.g., Grebel 1998). Perhaps this is not surprising considering all the di†erent possible origins of dwarf galaxies. Dwarf galaxy formation can occur by collapse of the lower density peaks (e.g., Dekel & Silk 1986) but also in the tidal tails of some more recent mergers (Duc & Mirabel 1999). This diversity in origin would imply furthermore that dwarf dark matter halos could possibly be made up of a di†erent mixture of dark matter Ñavors, such as di†erent fractions of baryonic to nonbaryonic dark matter. One still needs a good dose of skepticism though toward the present dark matter models with respect to the unknown contribution of the luminous matter (i.e., maximum-disk or not ?). However, much better constrained mass models will soon be possible in the nearby galaxies for which detailed resolved stellar photometry is possible, yielding a better estimate of the (M/L ) to use in the models. These will be necessary to pin * downB precisely the trends in the dark halo parameters of dwarfs. In particular it would possible to detect if the scatter in the dark halo parameters for dIrrÏs could actually be due to a bimodal distribution in the properties of dIrrÏs, with tidal dwarfs as one class and ““ normal ÏÏ ones as the other. Tidal dwarf galaxies, formed from material tidally pulled

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FIG. 12.ÈResults of NFW Ðts (not restricted to SCDM) to maximal halos (i.e., neglecting the light and gas mass this time to allow the largest concentration possible approaching the SCDM value). Despite this some dwarf galaxies and LSBs Ðts are too concentrated even for ) \ 0.3 halos. Data are from Begeman (1987), Broeils (1992), Carignan 0et al. (1988), Carignan & Beaulieu (1989), Carignan & Puche (1990), Coüte et al. (1991), de Blok et al. (1996), Lake et al. (1990), Meurer et al. (1996), Pickering et al. (1997), Puche et al. (1990), and Puche et al. (1991).

out from interacting systems, are expected, according to numerical simulations (Barnes & Hernquist 1992 ; Elmegreen, Kaufman, & Thomasson 1993), to have a much lower dark matter content. The large scatter seen for the halo central densities (o ) would be due to one population of 0 ““ normal ÏÏ dIrrÏ s with high o and another one of tidal 0 on the other hand, have a dwarfs with low o . Since dSphÏs, 0 smaller scatter in their dark matter properties (Mateo 1998) and large halo central densities, this would imply that only ““ normal ÏÏ dIrrÏs might evolve into dSphÏs, while tidal dwarfs would not, perhaps because a large number of them would eventually be tidally disrupted by their parent galaxy. This would be analogous to the disruption of the young globular clusters forming in mergers : they have a power-law luminosity function with lots of faint clusters, while the old globular cluster systems have a Gaussian luminosity function with few faint clusters, the faint ones having probably been disrupted through mass loss by stellar evolution (see, e.g., Zepf et al. 1999). In the case of our sample, the dwarf with the lowest dark matter content and lowest o (ESO 325-G011) is indeed the one the closest to 0 A, the most massive galaxy in the group, Centaurus although only projected separations are available at this point. One way to recognize tidal dwarfs seems to be through their metallicity : Duc & Mirabel (1994) for example found that the tidal dwarfs of Arp 105 have higher metallicity than dIrrÏs of the same luminosity, more comparable to outer parts of spirals. Work is in progress to get metallicities for our nearby Sculptor and Centaurus A dwarfs (Skillman et al. 2000). 5.4. Surface Densities in Dwarf Galaxies Another possible clue about the nature of dark matter comes from the fact that in most spiral galaxies, the ratio of

the H I surface densities to dark matter surface densities (& /& ) is seen to stay remarkably constant (Bosma H I DM 1978), even out to large radii (Carignan et al. 1990), while it is not at all the case for the stellar densities. This has been used as an argument for a strong coupling between the H I gas and the dark matter, hinting that the dark matter is not dissipationless and therefore has possibly a baryonic nature. One can then model the rotation curves using a scaled-up version of the H I dynamical contribution (i.e., varying the gas mass) rather than a dark matter halo, and obtain reasonable Ðts, sometimes even better ones : Broeils (1992) illustrates this very well in the case of NGC 1560, for which a better Ðt is obtained by modeling the rotation curve with only the stellar disk and a boosted H I component (scaled up by a factor of about 2.5). In DDO 154, H I surface densities need to be multiplied by a factor of 8.7 to get a passable agreement with the rotation curve (Carignan & Purton 1998). There are some ways of making these scalings physically meaningful : one is by arguing that the H I mass increase corresponds to a distance increase (because the H I mass depends on the square of the distance), and another one is to decrease the H I spin temperature, which means that the actual H I column density is much di†erent than the one that would be inferred from the observed brightness temperature. The Ðrst method of distance increase is unlikely because several studied galaxies have their distance well determined by diverse distance estimators, such as Cepheids, and in many cases, the increase in distance that would be required is so large (by a factor of 10 or more in some cases) that it can be ruled out. The second way is to invoke that large masses of H I are invisible at 21 cm because of a decreased H I spin temperature. However, one would need an explanation for why these optically thick cold H I clouds would stay shielded from UV radiation. Corbelli & Salpeter (1993) calculate for a range of models estimating heat inputs to the H I in low pressure environments (even as far out as outer disks) that the spin temperature is always ? 3 K. Also these clouds need to be very dense (for a low covering factor) so one need to explain why no star formation takes place (Silk 1994). Clumpuscules of cold gas are known to exist in spiral galaxies, but so far Dickey & Brinks (1993) Ðnd from H I absorption toward a few background continuum sources in three galaxies that later type ScÏs seem to have a lower fraction of cold H I than SbÏs, while the trend should go in the opposite direction since dark matter dominates more and more the mass for lower luminosity galaxies. Also, there are some galaxies that do not show a constant ratio of gas surface densities to dark matter surface densities, for which the scaled-up gas component will consequently not do the trick. In fact most of the dwarfs in our sample do not : the ratio of H I to dark matter surface densities starts dropping appreciably at roughly the Holmberg radius. Figure 13 compares the ratios & /& and * DM were & /& for the Ðve dwarfs from our sample which H I DM mass-modeled (where here the & were obtained by inteDMdistribution of our isograting the dark matter spherical thermal sphere model). For example in the case of DDO 161, for which R D 3 kpc, & /& drops by at least a HO H I found DM for our other four factor of 10, and similar factors are dwarfs. The error bars include the possible e†ects from warps, within the ranges of inclinations and position angles allowed by the residual Ðelds (see Appendix) and have been

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cut o† at the radii where dilution e†ects might start (i.e., at large radii if the H I is asymmetric, the lower value of & HI would simply be due to diluting a small patch of H I within a large empty ellipse). Many spirals have H I radial proÐles measured out to a larger number of a~1, and down to similar column densities, than some of our dwarfs but exhibit a remarkably Ñat & /& ; only a few do show a H I DM decline. On the other hand, not all dwarfs have declining ratios of gas to dark matter surface densities ; a few dwarfs have a ratio of densities staying fairly constant out to the outermost radii (for example, DDO 154 ; Carignan & Purton 1998). Once again this shows the diversity allowed among galaxies even of the same morphological type, which is possibly a reÑection of the diversity of their dark matter halo make-ups. 6.

SUMMARY

In summary, we have presented aperture synthesis observations at the AT and the VLA of eight selected gas-rich dwarfs in Sculptor and Centaurus A. Their H I distributions are very extended with respect to the optical galaxies, as is normally the case in late morphological types, reaching here on average more than two Holmberg radii R . Dwarfs at the periphery of the groups do not have moreHO extended H I envelopes than those near the massive members. These main members o†er a wider cross section in H I than all the dwarfs despite the large number of these. Among the eight dwarfs studied, Ðve of them have normal kinematics, of an inclined rotating disk, for which a rotation curve can be derived by Ðtting tilted rings to the velocity Ðeld. But three objects have the H I gas rotating around a di†erent axis than the optical major axis. SDIG, a very low luminosity dwarf at Mb,i \ [11.3, is very similar to GR 8 B kinematically, being another example of transition object between the brighter dwarfs that are mostly supported by rotation, and the faintest dwarfs dominated by random motions and pressure supported. For NGC 625 and ESO 245-G005, two of our brightest dwarfs at Mb,i \ [15.65 B and [15.03, it is conjectured that the peculiar kinematics is probably due to past interactions that have perturbed the H I distributions and kinematics. In NGC 625, the H I is rotating around the major axis, but its distribution is still elongated along the optical major axis direction (unlike the situation in polar rings). In ESO 245-G005, the H I axis is misaligned by about 60¡ from the optical isophotal major axis and by about 30¡ from the optical bar. By modeling the mass distribution of the Ðve (wellbehaved) dwarf galaxies using a stellar disk]H I disk]dark matter halo decomposition, we have found that dwarf irregular galaxies are dark matter dominated. The dark matter halos of our dwarfs account for 54% up to 92% of their total mass (inside R ). In most cases the dark halo max is the major dynamical contributor already in the rising part of the rotation curve, and sometimes even the H I disk is more massive than the stellar disk, as in UGCA 442 and DDO 161.

Vol. 120

Contrary to what is found in most normal spirals, the ratios of H I to dark matter surface densities are no longer constant at large galactocentric radii. One can no longer Ðt scaled-up H I disks instead of dark halos to explain the rotation curves, since at large radii there is no longer a strong coupling between the H I gas and the dark matter. Our mass model results show that, when comparing galaxy properties at a set baryonic reference radius in galaxies with extended rotation curves, our lower luminosity galaxies have, on average, higher total mass-to-light ratios, and their dark halos, on average, have higher central densities (along the Kormendy 1990 correlations). But more noticeably there is an increased dispersion among the dark matter properties of dwarf galaxies, in terms of dark matter amount as well as for the dark halo parameters. Within the same range of luminosity dwarf galaxies can have halos with central densities varying by a factor of 10. Consequently any type of unifying scheme (e.g., the URC) will fail to predict adequately the rotation curves of dwarf galaxies based only on their optical properties. These dwarf rotation curves are also difficult to Ðt with the CDM model curves of Navarro et al. (1996a) which are too concentrated. Even a low ) \ 0.3 and " \ 0.7 "CDM model does not produce 0 low enough concentration halos to suit many of the dwarfs and LSBs. Since dwarf galaxies of otherwise similar properties can have largely di†erent fractions of dark matter and dark halos with di†erent structures, it is then very probable that the dark halos are a composite of di†erent dark matter types (baryonic as well as nonbaryonic) and that every galaxy can have its own relative amounts of dark ingredients. This conclusion holds whatever is assumed about the stellar mass-to-light ratios (M/L ) of our dwarfs. B* The data acquisition as well as some of the analysis presented here were part of a Ph.D. thesis submitted to Mount Stromlo Observatory, Australian National University. It is a pleasure to thank Bruno Binggeli, Evan Skillman, and Jacqueline van Gorkom for their extensive and interesting comments on the dissertation manuscript. Dennis Crabtree is thanked for his careful reading of a draft. Thanks to E. S. and J. H. for their relentless encouragements to Ðnish this paper. We are also grateful to an anonymous referee for his/her remarks which helped to improve some aspects of the paper. The Australia Telescope is funded by the Commonwealth of Australia as a National Facility which is operated in association with the Division of Radiophysics by CSIRO. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Financial support for part of this work was provided to SC by an Australian National University Postgraduate Scholarship and by Fonds FCAR Quebec. C. C. acknowledges Ðnancial support from NSERC and Fonds FCAR.

No. 6, 2000


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APPENDIX COMMENTS ON INDIVIDUAL GALAXIES UGCA 442.ÈIn the mass models its disk (M/L ) is not well constrained, as expected because the stellar disk has such a B* small overall dynamical contribution, but the dark halo parameters r and p are reasonably well constrained, and the best-Ðt c and maximum disk models output very similar dark halo parameters. These models show that UGCA 442 is clearly an exceptional galaxy : more than 90% of its mass is nonluminous, and its total M/L reaches above 50. SDIG.ÈIts velocity Ðeld appears to be that of a very face-on system with no Bparticular strong warp. However, one has to realize that the optical major axis is at a position angle of 30¡.3, while the H I kinematic major axis is here at 118¡, i.e., almost 90¡ o†. In other words, the gas seems to be rotating about the optical major axis rather than the minor axis as in normal spirals and dwarfs. The individual velocity proÐles are complex, though, with the presence of several components : the Gaussian Ðts and the moment velocity Ðeld results agree well in the central regions but less so at large galactocentric radii. Such misalignments between kinematical and optical axes are not unheard of. Sextans A has a kinematical axis 40¡ o† from the optical axis (Skillman et al. 1988). NGC 5253, one of the low-luminosity late-type spirals of the Centaurus A group, shows rotation around its major optical axis (Kobulnicky & Skillman 1995). The most similar case to SDIG is probably GR 8, a dwarf at the outskirts of the Local Group in the same magnitude range (M \ [11.32 for SDIG and [10.58 for GR 8). It has B a rotation axis parallel to the optical major axis (Carignan et al. 1990). Because of their unusual kinematics it is not possible to carry out detailed multicomponent mass models on these systems ; however, with a few assumptions Carignan et al. (1990) were able to derive a global dynamical mass for GR 8, and a similar analysis for SDIG will be presented in a forthcoming paper. Meanwhile some estimates of the rotation velocities can be derived by applying the tilted-ring analysis as if the H I lies in a Ñat rotating disk. Perhaps surprisingly it is found that the dynamical center agrees exactly with the optical one. With the inclination Ðxed to its optical value of 42¡, one obtains a maximum velocity of 19 km s~1 . NGC 625.ÈAs for SDIG, the large-scale rotation is around the major axis rather than the minor axis (although many proÐles are multi-peaked here again). But NGC 625 does not share many similarities with either SDIG or GR 8 other than that, since it is much brighter at M \ [15.65, with colors typical of a Scd with (B[R) \ 0.89 and (B[I) \ 1.27 (Coüte et al. 2001) but a morphology curiouslyBreminiscent of a S0 system. It also has strong emission lines like a blue compact dwarf (Skillman et al. 2000). Has NGC 625 been seriously disturbed by a close interaction or a merger event ? It is at the periphery of the Sculptor group (see Coüte et al. 1997), and far enough (almost 3¡ \ 130 kpc) from the nearest galaxy, the dwarf ESO 245-G005, that a recent close encounter between these two objects is unlikely to be the cause. Several H I clouds are known to lie in the Sculptor group region (Haynes & Roberts 1979), so possibly NGC 625 has recently encountered and accreted such a cloud. But from the Ha spectra of Marlowe et al. (1997), it appears that the ionized gas follows quite complex orbits (not matching the H I ones), reinforcing the view that NGC 625 is seriously disturbed, and has most probably su†ered a major merger event rather than just being a case of bad digestion of an H I cloud. Because of its kinematical complexities it was not possible to obtain a rotation curve let alone a mass model. ESO 245-G005.ÈIts H I kinematical axis is here again departing from the optical major axis, although less drastically than for the previous two galaxies. The photometry of Miller (1994) and Coüte (1995) shows an underlying exponential disk of position angle of 144¡ and inclination of 37¡, with a strong bar at a position angle of 115¡. The best results from the tilted-ring Ðts to the H I gives a position angle of 88¡^8¡, for an inclination of 54¡^10¡. The large errors quoted here on these orientation parameters reÑect the range of possible tilted-ring solutions yielding acceptable velocity residuals. The resulting rotation curve is still rising out to the last measured velocity reaching 43 km s~1, and seemingly not showing any sign of Ñattening. This is not surprising since the maximum rotation of a dwarf of this luminosity is expected to be around 60 km s~1. From spectrophotometric data of eight H II regions Miller (1996) Ðnds a strong abundance gradient along the bar, which is unusual in a barred Magellanic galaxy. It is possible that some H I cloud of a di†erent metallicity has been accreted in an otherwise normal dwarf galaxy, or that the whole object is the product of a recent merger, with not yet a good global mixing of the heavy elements throughout the system. No mass model was carried out on ESO 245-G005 because of its uncertain kinematics. ESO 381-G020.ÈAlthough it is of the same luminosity class as UGCA 442, it is not as dark matter dominated as the latter. For UGCA 442 the dark halo contribution starts to dominate in the rising part of the rotation curve even for the maximumdisk model. But here for ESO 381-G020, the stellar disk is clearly the main contributor in the inner parts and dominates the gas contribution at all radii, in the maximum-disk as well as in the best-Ðt model. The dark to luminous mass ratio nevertheless means an impressive amount of 80% of dark matter in that system at the last measured point. The total mass-tolight ratio still reaches about 20, which is much more than what is seen in late-type spirals in general (Broeils 1992). DDO 161.ÈDDO 161 is, optically, close to edge-on with i \ 80, so deriving reliable orientation parameters is not opt su†er from the intrinsic assumption in the model that the straightforward. The parameters obtained from the tilted-ring Ðts gas disk is an inÐnitely thin disk, since for this galaxy we are presumably starting to resolve the thickness of the disk. Consequently it was attempted to Ðx these parameters to their optical values, but in that case the velocity residuals obtained were clearly unacceptable, showing the pathological pattern of opposite positive and negative residuals zones. This pattern is seemingly caused by a wrongly determined inclination according to the residual diagnostic models of Warner, Wright, & Baldwin (1973), for example. Another possibility is that the pattern is due to a strong Ñaring of the H I disk, which could produce a similar signature in the residuals. But to model this properly, the way it was done for NGC 4244 for example (Olling 1995), would require much more sensitive data. The best tilted-ring solutions are obtained for a position angle of [67¡ ^ 7¡ and inclination 70¡ ^ 10¡, the large errors thus reÑecting the range of parameter values producing acceptable residuals.

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In the mass model the stellar component is found to dominate only in a very small inner region, overall the gas is almost twice as massive, and at the last point of the rotation curve dark matter represents 90% of the mass. The total mass-to-light ratio rises to more than 25, which makes DDO 161 an extremely dark matterÈrich dwarf galaxy. ESO 444-G084.ÈThe H I distribution is extremely extended, staying rather symmetric, but from a glance at the velocity Ðeld, it is obvious that the H I is severely warped : the position angle varies signiÐcantly from roughly 120¡ to 85¡ outward. From all our dwarfs it has the most extended rotation curve, in terms of optical scale lengths (i.e., R \ 13.6a~1). But despite max this the parameters are not well constrained, especially its mass-to-light ratio for the stellar disk (M/L ) . The stellar mass B* clearly dominates the other components only in the very inner parts (\1 kpc), with a (M/L ) º 4.6. This ratio is higher than B * what is found among our other dwarfs and those in the literature, even though ESO 444-G084 is just as blue as these, and according to population synthesis models, (M/L ) should be less than 1. Nevertheless our models still give very high dark to B* luminous mass ratio, which translates into a total of more than 90% of dark mass at the last measurement. The total mass-tolight ratio reaches a record number above 90, which is even more than for DDO 154. And the central density o of the halo 0 reaches a striking value of around 0.1 M pc~3, which is the densest dark halo ever derived for a dIrr, perhaps not _ surprisingly as ESO 444-G084 is the lowest luminosity galaxy so far for which a multicomponent mass model has been Ðtted. ESO 325-G011.ÈFrom all the dwarfs in our sample it is the object with the shortest rotation curve in terms of disk scale lengths (R \ 2.9a~1 only), so not surprisingly the parameters are the least well-constrained of all the models. 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