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4 Discussion

4.1 Properties of the detected galaxies

We derived a number of global properties for the 33 galaxies with reliable detections in our HI line survey based on the available pointed HI data, including our own new results. These are listed in Table 5. The values for the observed linewidths and the heliocentric velocity are the means from all individual pointed observations listed in Table 4. The inclination, i, is derived straight from the cosine of the ratio of the optical minor and major axis diameters, and the profile widths W50 and W20 were corrected to $W_{50}^{\rm cor}$ and $W_{20}^{\rm cor}$, respectively, using this inclination. The HI mass and blue absolute magnitude, MB, were as a first approximation computed straight from the observed velocity and a Hubble constant of H0=100 km s-1 Mpc-1. We furthermore assumed that all apparent magnitudes listed in Table 2 were measured in the B band.

The survey region lies quite close in the sky to the Virgo cluster. This is illustrated in Fig. 3 which shows the Nançay survey region in Supergalactic coordinates, with the positions of the galaxies detected in HI as well as the apex of the Virgocentric flow field, M 87. The proximity of our survey region to the Virgo overdensity motivated us to calculate distances to our galaxies using the POTENT program (Bertschinger et al. 1990), hence corrected for Virgocentric infall.

\includegraphics [width=8.5cm]{}\end{figure} Figure 3: Location of the detected galaxies in Supergalactic coordinates. The survey area is bounded by solid lines; the beginning R.A. at 11.5$^{\rm h}$ and ending R.A. at 15$^{\rm h}$ are marked. The star symbol at the lower left indicates the position of $\rm Virgo~A = M~87$

The POTENT corrections are based on the overall underlying density field deduced from flow fields out to velocities of 5000 kms-1. A comparison of the correction with a pure Virgocentric infall model (cf., Kraan-Korteweg 1986) confirms that the main perturbation of the velocity field within our survey region is due Virgocentric infall. More local density fluctuations or a Great Attractor component (at an angular distance of $\approx 77$$^\circ$) have little impact on the velocities.

The "absolute'' corrections to the observed velocity due the Virgo overdensity vary depending on velocity and angular distance from the Virgo cluster. But the effects on global properties such as magnitudes and luminosities and HI masses can be quite significant, particularly for low velocity galaxies at small angular distance from the apex of the streaming motion (Kraan-Korteweg 1986).

The velocities corrected for streaming motions, absolute magnitudes and HI masses based on POTENT distances are also listed in Table 5. The corrections in velocity reach values of nearly a factor of 2, the respective corrections in absolute magnitudes of $0\hbox{$.\!\!^{\rm m}$}6$ and the logarithm of the HI masses of up to 0.6 dex.

In Fig. 4 the measured velocity width is plotted as a function of HI mass. There is a well known trend (a sort of HI Tully-Fisher Relation) that larger ${M}_{\rm HI}$ masses are strongly correlated with higher rotation speeds (cf., Briggs & Rao 1993). Figure 4 displays HI masses based on observed velocities as well as HI masses corrected for Virgocentric flow using the POTENT program (solid respectively open circles) including the shifts in galaxy masses due to the perturbed velocity field. The drawn line indicates an upper bound to the velocity width, based on disc galaxies that are viewed edge-on; galaxies falling far below the line are viewed more face-on.

\includegraphics [width=8.5cm]{}\end{figure} Figure 4: Log of velocity width (50%) as a function of HI mass, ${M}_{\rm HI}$, for the confirmed detections. The line is a boundary to the HI mass versus line-width relation derived from a much larger sample of galaxies (Briggs & Rao 1993), $\Delta V = 0.35 (M_{\rm HI}/M_{\odot})^{1/3}$ km s-1. HI masses computed using distance $d=V_{\rm hel}/H_0$ are marked by solid dots. Open circles mark masses corrected to POTENT distances to compensate for Virgocentric flow, and the arrows indicate the masses for galaxies with independent distance measures as referenced in the text

A surprise that appeared in Fig. 4 is that one galaxy, UGC 7131, from our Nançay survey lies above the usual bound for velocity width, even after correction for Virgocentric infall.

Subsequently, new measurements of distance using resolved stellar populations were released for four of our galaxies (Karachentsev & Drozdovsky 1998; Marakova et al. 1998). This includes UGC 7131, which was found to lie at a distance d>14 Mpc, i.e., considerably further than indicated from the observed velocity listed in Table 5 ($V_{\rm hel} = 251~\mbox{\rm km\,s$^{-1}$}$) or for flow motions corrected velocity ($V^{\rm POT} =
487~\mbox{\rm km\,s$^{-1}$}$). However, with this new independent distance estimate UGC 7131 does fall within the HI mass range expected for its linewidth.

Its morphology as evident on the sky survey plates does not indicate a morphology earlier than the galaxy type listed in Table 2a, Sdm, for which one could expect a higher HI mass in agreement with its new determination (cf., shift in Fig. 4). It has a slight comet-like structure not atypical for BCD galaxies. On the other hand, the deep CDD-image in Markarova et al. (1998, their Fig. 3) finds UGC 7131 to be unresolved and amorph, which does confirm the larger distance and is not consistent with a nearby (low-velocity) galaxy.

Interestingly enough, the angular distance is a dominant parameter on the infall pattern. UGC 7131 has a very small angular distance from the Virgo cluster, i.e., only 19 degrees. If it were at a slightly smaller angle, and depending on the model parameters for the Virgocentric model, the solution for the distance would become triple valued: typically with one solution at low distance, one just in front of the Virgo cluster distance, and one beyond the Virgo cluster distance (cf., Fig. 3 in Kraan-Korteweg 1986). Although the angular distance (from the Virgo cluster core) within which we find triple solutions does depend on the infall parameters such as the decleration at the location of the Local group, none of the models with currently accepted flow field parameters suggests a triple solution for galaxies with observed velocities as low as the one measured for UGC 7131, except if the density profile within the Virgo supercluster were considerably steeper than usually assumed.

With the exception of the observed velocity, all further indications about UGC 7131 support the considerably larger distance -- even its distribution in redshift space. The locations of the HI-selected galaxies are shown in a cone diagram in Fig. 5 with heliocentric velocity as radial coordinate, where POTENT distances are drawn as contours. An arrow indicates the revision with regard to the location of UGC 7131. It is clear from this display that UGC 7131 is not a member of the nearby CVn I group, nor of the more distant CVn II group, but most likely is a member of the Coma I group. (Since our distances and survey volumes have been computed using H0= 100 km s-1 Mpc-1 for convenience, the distances for these four galaxies were adjusted to our scale, assuming that they are correct in a system with H0=75 km s-1 Mpc-1.)

\includegraphics [width=8.5cm]{}\end{figure} Figure 5: Cone diagram showing the relative locations of the detected galaxies as a function of R.A. and heliocentric velocity in km s-1. Long dashes show contours of constant distance computed using POTENT (Bertschinger et al. 1990) to compensate for Virgocentric flow. The arrow indicates the revised distance for UGC 7131 (Karachentsev & Drozdovsky 1998)

Assuming that both the observed velocity and the revised distance to UGC 7131 are correct, this can only be combined if this galaxy resides in a triple solution region of the Virgocentric flow pattern, implying that our current knowledge of the density field within the Local Supercluster and the induced flow motions are not yet well established. On the positive side, this example demonstrates that independent distance derivations of fairly local galaxies, close in the sky to the Virgo cluster, can teach us considerably more about the density field and the flow patterns within the Local Supercluster.

4.2 Comparison with the Fisher-Tully catalog of nearby galaxies

A convenient plot for comparing relative sensitivities of different surveys, such as the Fisher-Tully Catalog of Nearby (late-type) Galaxies (Fisher & Tully 1981b) and the more recent LSB galaxy catalogues (Schombert et al. 1997; Sprayberry et al. 1996) is shown in Fig. 6. Here, the distance to each galaxy is plotted as a function of its HI mass. Briggs (1997a) showed that there is a sharp sensitivity boundary to the Fisher-Tully catalog, indicated by the diagonal dashed line in Fig. 6, and that the newer surveys for LSB galaxies add no substantial number of objects to the region where Fisher-Tully is sensitive. The new objects lie predominantly above the F-T line. A crucial test provided by the new Nançay survey, is to cover a large area of sky at a sensitivity matched to the Fisher-Tully sensitivity, to determine whether their catalog is indeed complete. The result shown in Fig. 6 is that the Nançay survey finds galaxies both within the F-T zone and above it. All the galaxies that we detected within the F-T intended "zone of completeness'' (below their sensitivity line and within $10 \,h^{-1}$ Mpc) were already included in the F-T Catalog. One notable galaxy that was not included in the F-T Catalog, NGC 4203, lies well within the F-T zone of sensitivity; it is classified as Hubble type S0 and therefore was not included in Fisher and Tullys' source list of late-type galaxies. We conclude that the F-T Catalog is remarkably complete in this region for late-type galaxies, and that the biggest incompleteness that may arise when their catalog is used for measuring the HI content of the nearby Universe is that the F-T Catalog may be lacking the occasional, rare early-type galaxy with substantial HI.

\includegraphics [width=8.5cm]{}\end{figure} Figure 6: Distance to each of the detected galaxies plotted as a function of HI mass, ${M}_{\rm HI}$. Plus symbols indicate objects detected by Fisher & Tully (1981b); solid dots are for objects that were not. The arrow indicates the shift implied for the revised distance to the galaxy UGC 7131 (Makarova et al. 1998). A diagonal line indicates the sensitivity attained by the Fisher-Tully Catalog (1981b), as estimated by Briggs (1997a). The cross-hatched band indicates the range of the $4~\sigma$ level, depending on the coordinates of the galaxies relative to the centre of the survey strip

4.3 The H I mass function

The distribution of HI masses is rather homogeneous with a mean of log(${M}_{\rm HI}$) = 8.4 for observed velocities - and of log(${M}_{\rm HI}$) = 8.7 for POTENT corrected HI masses. An HI mass function can be estimated in a straightforward way for our Nançay sample. The precision of this computation will be low for several reasons: The total number of galaxies is low. There are no masses below $M_{\rm HI}\approx 3{\ }10^7\, M_{\odot}$.The volume scanned is small, and it cannot be argued that the sample is drawn from a volume that is respresentative of the general population, in either HI properties or in the average number density. However, the calculation is a useful illustration of the vulnerability of these types of calculation to small number statistics and distance uncertainties.

We show four different derivations of the HI mass function in Fig. 7. First, we calculated the number density of galaxies by computing distances, HI masses, and sensitivity volumes based on heliocentric velocities $V_{\rm hel}/H_0$. The mass functions are binned into half-decade bins, but scaled to give number of objects per decade. The value for each decade is computed from the sum $\Sigma 1/V_{\rm max}$, where $V_{\rm max}$ is the volume of the survey in which a galaxy with the properties ${M}_{\rm HI}$ and $\Delta V$could have been detected. The values of $1/V_{\rm max}$ are plotted for all galaxies as dots. The points representing the number density of objects of mass ${M}_{\rm HI}$ are plotted per bin at the average ${M}_{\rm HI}$ for the galaxies included in that bin, so that, for example, the two highest mass bins, which have only one galaxy each, are plotted close to each other as upper limits. It is notable that the galaxy UGC 7131 causes a very steeply rising tail in the top panel, because is is treated in this calculation as a very nearby, but low mass object. Placed at a greater, more appropriate distance, it becomes more massive, and it is added to other galaxies of greater velocity width and higher HI mass in the higher mass bins.

\includegraphics [width=7cm]{}\end{figure} Figure 7: HI mass function for the Canes Venatici survey volume, normalized to number of objects per decade of mass. Error bars represent Poisson statistics for the present sample after binning. The smooth solid curve is the analytic form derived by Zwaan et al. (1997) with a slope of $\alpha=-1.2$, the grey line has a slope of $\alpha=-1.4$(Banks et al. 1998). The bottom panel shows the result restricted to the CVn-group regions (< 1200 kms-1) where the dashed curve represents the Zwaan et al. HI mass function multiplied by a factor of 4.5. The dotted line gives an indication of the volume probed as a function of mass (see right vertical axis); the points give $1/V_{\rm max}$ for each of the galaxies in the sample, taking into account the different velocity widths

An improved calculation based on the POTENT distances is displayed in the second panel. In the third panel, the four galaxies with independent distance measurements have been plotted according to their revised distances. In the 4th panel we have restricted our sample to include only the overdense foreground region which includes the CVn and Coma groups, i.e., the volume within $V_{\rm hel} < 1200$ kms-1 and about 1/2 the R.A. coverage (about half the solid angle). Big galaxies can be detected throughout the volume we surveyed, but little galaxies can be detected only in the front part of our volume. The volume normalization factors, which are used to compute the mass function, are sensitivity limited for the small masses in the front part of our survey volume only. For the large masses, the $V_{\rm max}$'s include the whole volume, including the volume where the numbers of galaxies are much less. Hence, when restricting the "survey volume'' we get a fairer comparison of the number of little galaxies to the number of big ones.

In all four panels the solid line represents the HI mass function with a slope of $\alpha=-1.2$ as derived by Zwaan et al. (1997) from the Arecibo blind HI driftscan survey, whereas the grey line represents an HI mass function with a slope of $\alpha=-1.4$ as deduced by Banks et al. (1998) for a similar but more sensitive survey in the CenA-group region.

In the first three panels, the steeper slope seems to be in closer agreement with the survey results than the more shallow HI mass function with $\alpha=-1.2$.However, as argued above, the small masses are over-represented in comparison to the large masses if we regard the full Nançay survey region. This leads to a slope that is too steep for the faint end. Restricting our volume to the dense foreground region including "only'' the CVn and Coma groups, we find that the Zwaan et al. HI mass function with a scaling factor of 4.5 to acount for the local overdensity (dashed line in the bottom panel) gives an excellent fit to the data.

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