3 Results and discussion

   
3.1 Results

Figure 1: Integrated HI emission maps of SBS1543+593. The QSO position is marked by a cross in all panels. See Sect. 2 for a discussion of the conversion to atoms cm-2. A)  $39\arcsec \times 39\arcsec$ resolution. The contours are 0.03, 0.045, 0.06, 0.09, 0.12, 0.18, 0.24, 0.36, 0.48, 0.72 and 0.85 Jy Beam-1 km s-1. A $3\sigma$ feature, 2 channels wide, would have an integrated flux of 0.07 Jy Beam-1 km s-1. B)  $29\arcsec \times 25\arcsec$ resolution. The contours are 0.045, 0.06, 0.09, 0.12, 0.18, 0.24, 0.36 and 0.45 Jy Beam-1 km s-1. A $3\sigma$ feature, 2 channels wide, would have an integrated flux of 0.06 Jy Beam-1 km s-1. C)  $12\arcsec \times 11\arcsec$ resolution. The contours are 0.03, 0.045, 0.06, 0.09, 0.12 and 0.22 Jy Beam-1 km s-1. A $3\sigma$ feature, 2 channels wide, would have an integrated flux of 0.045 Jy Beam-1 km s-1. D) Integrated HI 21cm emission profile for SBS 1543+593. The profile is derived from the GMRT observations, using the $29\arcsec \times 25\arcsec$ resolution data. The spectrum has been smoothed to a resolution of $\sim$10 km s-1.

Figure 1 shows maps of the integrated HI emission (obtained using the AIPS task MOMNT) at the three different resolutions discussed above. The QSO position is marked by a cross in all three maps. The centre of the optical galaxy is very close to the QSO position; the QSO is located only $2.4\arcsec$ NNE of the galaxy centre (Reimers & Hagen 1998). The low resolution map shows that the HI distribution is asymmetric, with the peak emission displaced to the south-east of the galaxy centre. The higher resolution maps show clearly that the HI distribution is concentrated in a ring-like structure, with HI emission actually being depressed at the centre of the galaxy. The HI ring is coincident with the faint spiral arms seen in the optical images (Reimers & Hagen 1998; Bowen et al. 2001a). Many of the irregular patches of emission seen in the HST image (Bowen et al. 2001a) also appear to be associated with peaks of HI emission. The HI concentration at $15^{\rm h}44^{\rm m}20^{\rm s} ~ , ~ 59^{\rm d}12\arcmin 09\arcsec$ corresponds to the HII region whose spectrum is given in Reimers & Hagen (1998). The velocity we measure at the location of this HII region is $2855\pm 6$ km s^-1. In addition to the inner HI ring, there are also spurs in the HI emission (see Figs. 1B and 1C) towards the north and south; these may mark the beginning of faint outer spiral arms.

Figure 2: A) The velocity field of SBS 1543+593 derived from the $29\arcsec \times 25\arcsec$ resolution cube. The velocity contours go from 2830 km s-1 to 2900 km s-1 and are spaced 5 km s-1 apart. Note that the contours are straight on the approaching (lower velocity) side and curved on the receding (higher velocity) side. The QSO position (which is only 2.25$\arcsec$ from the optical centre of the galaxy) is marked with a cross. B) The rotation curve derived from the velocity field shown in  A). The curve for the approaching side is marked by stars, and for the receding side by open pentagons. The rotation curve for the approaching side can be seen to rise approximately linearly, while that for the receding side flattens out.

Measurement of the integrated flux corresponding to weak extended line emission can be a non-trivial problem (see, for example, Jörsäter & van Moorsel 1995; Rupen 1999). However, as a rule of thumb (apart from serious zero spacing problems), deeply cleaned images give a fairly reliable estimate of the total flux. The integrated fluxes that we get from the cleaned $39\arcsec \times 39\arcsec$ and $29\arcsec \times 25\arcsec$ data cubes are $4.0\pm 0.4$ Jy km s^-1 and $3.6\pm 0.4$ Jy km s^-1. These are in excellent agreement with the single dish measurement of $4.0\pm 0.4$ Jy km s^-1 (Bowen et al. 2001b). From the area of the clean beam in these two low resolution images, the conversion from 1 Jy Beam^-1 km s^-1 to atoms cm^-2 is $7.3\times 10^{20}$ atoms cm^-2 and $1.5\times 10^{21}$ atoms cm^-2 respectively. Since the highest resolution map (Fig. 1C) is uncleaned, there is no obvious way to convert the units from Jy Beam^-1 to Jy. If one simply uses the area of the best fit Gaussian to the main lobe of the dirty beam to convert from Jy Beam^-1 to Jy, one gets a total flux of $\sim$4.4 Jy km s^-1. This must be an overestimate, since it is clear from Fig. 1C that a considerable fraction of the smooth emission seen in Fig. 1A has been resolved out but the estimated flux in the higher resolution image is higher than that in the lower resolution ones. Given this problem in scaling for the highest resolution image, we estimate the column density at the QSO position only from the two lower resolution maps. The column densities are $5.9\times 10^{20}$ atoms cm^-2 and $4.9 \times 10^{20}$ atoms cm^-2 for the $39\arcsec \times 39\arcsec$ and the $29\arcsec \times 25\arcsec$ resolutions, respectively. The integrated emission profile of SBS 1543+593, as derived from the $29\arcsec \times 25\arcsec$ resolution data (smoothed to a velocity resolution of 10 km s^-1), is shown in Fig. 1D. The systemic velocity as measured from the profile is $2862\pm 10$ km s^-1. This agrees (within the errors of the two measurements) with the velocity of $2868\pm2$ km s^-1 measured from the Bonn spectrum by Bowen et al. (2001a).

The velocity field of SBS 1543+593 (derived using the AIPS task MOMNT on the $29\arcsec \times 25\arcsec$ resolution cube) is shown in Fig. 2A. The iso-velocity contours are asymmetric; they are straight on the approaching side and curved on the receding side. This type of velocity field has been dubbed "kinematically lopsided'' (Swaters et al. 1999). As noted earlier, the galaxy is also morphologically lopsided. The rotation curve was derived separately for the approaching and receding sides using the AIPS task GAL. During these fits, the galaxy centre was kept fixed at the optical centre. The systemic velocity was kept fixed at the value of 2870 km s^-1, the inclination at $50^{\rm o}$ and the position angle (of the receding half of the major axis, measured east of north) at $-16\degr$ (all of which were obtained from an initial global fit to the velocity field). The inclination and the position angle are in good agreement with our estimates from the optical image presented in Reimers & Hagen (1998).

The derived rotation curves are shown in Fig. 2B. As expected from the iso-velocity contours, the rotation curve is almost linear on the approaching side, while it tends to flatten out on the receding side. The maximum (inclination corrected) rotation speed in SBS 1543+593 is $\sim$45 km s^-1. The rotation curve can be measured out to a radius of $\sim$$60\arcsec$, corresponding to a linear distance of 11 kpc. The implied dynamical mass is then $M_{\rm dyn} \sim 5 \times 10^9$ $M_\odot$.

   
3.2 Discussion

The flux that we measure for SBS 1543+593 corresponds to a total HI mass of $1.4 \pm 0.14\times 10^9$ $M_\odot$, in excellent agreement with the single dish measurement of Bowen et al. (2001b). This is thus the third DLA whose HI mass is significantly less than that of an L_* spiral. Besides these, the galaxy NGC 4203 (which lies in front of the QSO Ton 1480, and is likely to be a DLA; Miller et al. 1999) has also been found to have a low HI mass. Thus, all low redshift DLAs (or candidate DLAs) for which HI emission observations have been attempted have masses less than that of an L_* spiral.

The derived HI masses are also considerably less than the $M_{\rm HI}^*$ ($\sim$ $7 \times 10^{9}$ $M_\odot$) obtained from Schecter function fits to the HI mass function determined in blind HI surveys (Zwaan et al. 1997; Rosenberg & Schneider 2001). It also follows from these mass functions that large galaxies make the major contribution to the local HI mass density. However, in order to determine the contribution of galaxies of different HI masses to the cross-section for DLA absorption, one also needs to know the typical sizes of their HI disks. Rao & Turnshek (1998) deduced, based on determinations of the typical sizes of HI disks made by Rao (1994), that bright spiral galaxies make the major contribution to the z=0 cross-section for DLA absorption. However, more recent determinations of the HI size and mass distribution of galaxies indicate that the cross-section for DLA absorption is, in fact, not dominated by large spiral galaxies (Rosenberg & Schneider 2001; Zwaan et al. 2001), and that a sample of low redshift DLAs should contain a large variety of galaxy types. This is consistent with the optical and HI observations of low z DLAs.

It would be interesting to compare the velocity profiles of low ionization metal lines in the HS 1543+5921 spectrum with the large scale kinematics of SBS 1543+593. Unfortunately, high velocity resolution optical/UV observations are as yet not available for this system. We note, however, that the systemic velocity that we obtain for SBS 1543+593 is in excellent agreement with the value of $2868\pm2$ km s^-1 obtained from the single dish HI profile (Bowen et al. 2001b). Further, the velocity obtained in our observations ($2855\pm 6$ km s^-1) for the gas coincident with the HII region (for which an optical emission spectrum exists) is in reasonable agreement with that obtained in the optical ($\sim$2700 km s^-1; Reimers & Hagen 1998), given the poor resolution (18 angstroms, i.e. $\sim$1000 km s^-1) of the optical spectrum. Similarly, the velocity we obtain at the QSO location is $\sim$ $2870 \pm 10$ km s^-1, which agrees within the error bars with the velocity of 2700 km s^-1 obtained from the Ly$-\alpha$ line (Bowen et al. 2001a), given the large uncertainty ($\sim$200-300 km s^-1) in the latter measurement (Bowen et al. 2001b). A high resolution low ionization metal line absorption spectrum of the QSO (and of Ton 1480, which lies behind NGC 4203) would provide interesting spot checks of the reliability in using such absorption lines to probe large scale gas kinematics of the absorbing galaxies (see, for example, Prochaska & Wolfe 1997; Prochaska & Wolfe 1998).

It is also interesting to compare the HI column density as obtained from the Ly-$\alpha$ spectrum with that obtained from the 21 cm emission. The comparison is, however, complicated by the comparatively large size of the GMRT synthesized beam. At a distance of 38 Mpc, $29\arcsec$ corresponds to a linear size of $\sim$5.3 kpc. Given this great disparity in the transverse sizes covered by the HI and UV measurements, the column density of $5 \times 10^{20}$ atoms cm^-2 obtained from the 21 cm map is in reasonable agreement with the estimate of $2.2\times10^{20}$ atoms cm^-2 obtained from the Lyman-$\alpha$ profile.

Comparisons of DLA samples with samples of galaxies selected by blind HI emission are complicated by issues of optical extinction. It has long been suggested that DLA samples could be seriously biased against high HI column density systems, because such absorbers would contain enough dust to substantially dim the background QSO (e.g. Heisler & Ostriker 1988; Fall & Pei 1993; Pei et al. 1999). Deep optical observations of a radio selected sample of QSOs however suggest that such biases may be modest (Ellison et al. 2001). It is curious (but, of course, not statistically significant, particularly given the fact that optical depth effects may be less important in LSB galaxies than in normal spirals) that the QSO HS 1543+5921 lies behind a region of low local HI column density in SBS 1543+593. Interestingly, an inspection of the HI maps of the S0 galaxy NGC 4203 presented by van Driel et al. (1988) shows that Ton 1480 also lies behind a region of low column density. Unfortunately, testing the above bias would require 21cm mapping of a statistically significant number of DLAs which is, alas, a task for the next generation radio telescope.

Acknowledgements

The GMRT observations presented in this paper would not have been possible without the many years of dedicated effort put in by the GMRT staff to build the telescope. The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. Useful discussions with R. Nityananda are gratefully acknowledged. We also thank the referee, E. Brinks, for several comments which improved both the readability and the content of this paper.