A&A 429, 439-447 (2005)
DOI: 10.1051/0004-6361:20041678

Completing H I observations of galaxies in the Virgo cluster

G. Gavazzi¹ - A. Boselli² - W. van Driel³ - K. O'Neil⁴

1 - Universitá degli Studi di Milano-Bicocca, Piazza delle scienze 3, 20126 Milano, Italy
2 - Laboratoire d'Astrophysique de Marseille, BP8, Traverse du Siphon, 13376 Marseille, France
3 - Observatoire de Paris, Section de Meudon, GEPI, CNRS UMR 8111 and Université Paris 7, 5 place Jules Janssen, 92195 Meudon Cedex, France
4 - NRAO, PO Box 2, Green Bank, WV 24944, USA

Received 16 July 2004 / Accepted 2 September 2004

Abstract
High sensitivity (rms noise $\sim$0.5 mJy) 21-cm H  I line observations were made of 33 galaxies in the Virgo cluster, using the refurbished Arecibo telescope, which resulted in the detection of 12 objects. These data, combined with the measurements available from the literature, provide the first set of H  I data that is complete for all 355 late-type (Sa-Im-BCD) galaxies in the Virgo cluster with $m_{\rm p}\leq 18.0$ mag. The Virgo cluster H  I mass function (HIMF) that was derived for this optically selected galaxy sample is in agreement with the HIMF derived for the Virgo cluster from the blind HIJASS H  I survey and is inconsistent with the Field HIMF. This indicates that both in this rich cluster and in the general field, neutral hydrogen is primarily associated with late-type galaxies, with marginal contributions from early-type galaxies and isolated H  I clouds. The inconsistency between the cluster and the field HIMF derives primarily from the difference in the optical luminosity function of late-type galaxies in the two environments, combined with the HI deficiency that is known to occur in galaxies in rich clusters.

Key words: galaxies: distances and redshifts - galaxies: general - galaxies: ISM - galaxies: clusters: individual Virgo - radio lines: galaxies

1 Introduction

Seen from a 25 year perspective, H  I observations of galaxies have provided us with some of the most powerful diagnostics of the role of the environment in regulating the evolution of late-type galaxies in the local Universe. This includes the definition of the "H  I deficiency'' parameter that measures the lack of gas in individual cluster galaxies with respect to their "undisturbed'' counterparts in the field (e.g. Haynes & Giovanelli 1984; Solanes et al. 2001, and references therein). It is well established that spiral galaxies in rich clusters which have a normal optical morphology have systematically positive H  I deficiency parameters, i.e. a significantly reduced H  I content (e.g. Haynes et al. 1984). The pattern of H  I deficiency found in spiral galaxies that are members of rich, X-ray luminous clusters was interpreted as due to the dynamical interaction of the galaxy ISM with the hot cluster IGM (e.g. ram-pressure (Gunn & Gott 1972), viscous stripping (Nulsen 1982), thermal evaporation (Cowie & Songaila 1977) or to the tidal interaction with nearby companions (Merritt 1983) and/or with the cluster potential well (Byrd & Valtonen 1990; Moore et al. 1996)). Since the H  I deficiency parameter indicates if a particular galaxy has already passed through the densest cluster region, it is perhaps the most valuable environmental indicator, as it provides a clear signature of a galaxy's membership of a rich cluster.

The Virgo cluster, due to its proximity to us (17 Mpc), has received the most attention in H  I studies. Various works (e.g. Chamaraux et al. 1980; Helou et al. 1981; Haynes & Giovanelli 1986; Hoffman et al. 1989b, 2003) provided evidence for the presence in the Virgo cluster of a mixture of galaxies with extreme H  I deficiencies and galaxies with normal H  I contents. This, in conjunction with distance estimates from the Tully-Fisher (1977) relation, provided circumstantial evidence for significant infall onto the Virgo cluster (Tully & Shaya 1984; Gavazzi et al. 1999b, 2002). In addition to these single-dish studies of their global H  I  properties, the detailed mapping of Virgo cluster galaxies with radio synthesis telescopes (e.g., Warmels 1986; Cayatte et al. 1990) provided evidence that H  I ablation occurs outside-in, producing a spatial truncation of the H  I disks (Cayatte et al. 1994).

Practically all H  I studies of Virgo galaxies were carried out by pointed observations of individual, optically selected galaxies. Conversely, the first blind H  I survey of a $4^{\circ}\times 8^{\circ}$ area of the Virgo cluster with the 76 m Jodrell Bank multibeam instrument (Davies et al. 2004) resulted in the detection of 2 isolated H  I clouds, besides that of 27 previously catalogued galaxies above the survey's H  I mass limit of $5\times 10^7 ~M_\odot$ for a galaxy with a 50 km s^-1 linewidth. A higher sensitivity, full-cluster blind H  I survey of the Virgo cluster is planned for 2005-2006 with the ALFA multibeam system at Arecibo (http://alfa.naic.edu/). In preparation for this survey we decided to complete with the present single-beam Arecibo system the pointed observations of late-type (Sa-Im-BCD) galaxies with $m_{\rm p}\leq 18.0$ mag in the Virgo cluster area. Here we report on the results of these observations which, in conjunction with the previously available H  I data-set, enable us to review the properties of galaxies in this cluster as obtained from optically selected H  I observations.

The selection of the cluster targets for H  I observations is described in Sect. 2, the observations and the data reduction are presented in Sect. 3 and the results in Sect. 4. A discussion of the H  I mass function, as derived from a complete optically selected sample is given in Sect. 5 and the conclusions are presented in Sect. 6.

Figure 1: The Virgo cluster region considered in the present analysis. The dashed broken line represents the boundary of the VCC catalog and the rectangle the area covered by the HIJASS blind HI survey. Superposed are the X-ray contours from ROSAT (Böhringer et al. 1994). All 355 late-type (Sa-Im-BCD) members of the Virgo cluster with $m_{\rm p}\leq 18.0$ are shown divided into H  I detected (296) and undetected (59). Large symbols refer to objects observed in this work.

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2 Sample selection

All data on the Virgo cluster galaxies are collected and made available worldwide via the "Goldmine'' WWW site (http://Goldmine.mib.infn.it; see Gavazzi et al. 2003). The H  I completeness of the database is remarkable: the majority ($\sim$80%) of disk (Sa-Im-BCD) galaxies with $m_{\rm p}\leq 18.0$ mag belonging to the Virgo cluster has been detected in H  I and for most of the remaining galaxies significant upper limits are available. The present work is aimed at completing the data on this optically selected sample with high sensitivity ( $rms \sim 0.5$ mJy) H  I observations. Our selection criterion includes all 355 disk (Sa-Im-BCD) galaxies with $m_{\rm p}\leq 18.0$ mag that are members, i.e. their measured redshift is in the interval -500<V<3000 km s^-1, or bona-fide members of the Virgo cluster, i.e. 26 objects without a direct redshift measurement, that have been classified as belonging to the cluster according to the surface brightness criterion used by Binggeli et al. (1985) in the compilation of the Virgo Cluster Catalog (VCC hereafter), and that were subsequently assigned to a particular Virgo sub-cloud by Gavazzi et al. (1999b), using a positional criterion. We include in the target sample all (14) VCC galaxies meeting the above optical selection criterion that were not observed previously in H  I  namely: VCC 1, 99, 227, 256, 275, 315, 517, 528, 531, 675, 679, 1237, 1358 and 1597. Moreover we targeted the 19 undetected VCC galaxies that were observed previously with an rms noise level of 0.7 mJy or higher, namely: VCC 48, 222, 323, 341, 358, 362, 524, 666, 802, 1086, 1121, 1189, 1196, 1287, 1377, 1435, 1448, 1885 and 1970.

A map of the Virgo cluster region is shown in Fig. 1 where all (355) galaxies meeting the above selection criterion are shown with the contours of the X-ray emission from the cluster measured by ROSAT (Böhringer et al. 1994) superimposed. Including the measurements obtained for this work, all galaxies have been surveyed in H  I  with 296 detections and 59 upper limits.

3 Observations

Using the refurbished 305-m Arecibo Gregorian radio telescope we observed 57 galaxies in the Virgo cluster and Coma supercluster (see Sect. 2) in February 2004, for a total of 28 h observing time. Data were taken with the L-Band Wide receiver, using nine-level sampling with two of the 2048 lag subcorrelators set to each polarization channel. All observations were taken using the position-switching technique, with the blank sky (or OFF) observation taken for the same length of time, and over the same portion of the telescope dish as was used for the on-source (ON) observation. Each 5 min+5 min ON+OFF pair was followed by a 10s ON+OFF observation of a well-calibrated noise diode. The overlaps between both sub-correlators with the same polarization allowed a contiguous velocity search range while ensuring an adequate, wide coverage in velocity. The velocity search range was -1000 to 8500 km s^-1. The velocity resolution was 2.6 km s^-1. The instrument's HPBW at 21 cm is $3'~\hspace{-1.7mm}.\hspace{.0mm}5$$~\times~$ $3'~\hspace{-1.7mm}.\hspace{.0mm}1$ and the pointing accuracy is about 15''. The pointing positions used are the optical center positions of the target galaxies listed in Table 1. Calibration corrections are good to within 10% (and often much better), see the discussion of the errors involved in O'Neil (2004).

Using standard IDL data reduction software available at Arecibo, corrections were applied for the variations in the gain and system temperature with zenith angle and azimuth. A baseline of order one to three was fitted to the data, excluding those velocity ranges with H  I line emission or radio frequency interference (RFI). The velocities were corrected to the heliocentric system, using the optical convention, and the polarizations were averaged. All data were boxcar smoothed to a velocity resolution of 12.9 km s^-1 for further analysis. For all spectra the rms noise level was determined and for the detected objects the central line velocity, the line widths at, respectively, the 50% and 20% level of the peak, and the integrated line flux were determined. No flux correction for source to beam size was applied because the optical extent of all detected targets does not significantly exceed the Arecibo beam.

4 Results

In order to identify sources whose H  I detections could have been confused by nearby galaxies, we queried the NED, HyperLeda and Goldmine databases and inspected DSS images over a region of 10' radius surrounding the central position of each source, given the telescope's sidelobe pattern. Quoted values are weighted averages from the HyperLeda database, unless otherwise indicated.

The H  I spectra of both the clearly and the marginally detected galaxies are shown in Fig. 2 and the global H  I line parameters are listed in Table 1. These are directly measured values; no corrections have been applied to them for, e.g., instrumental resolution.

	Figure 2: H  I spectra of the tentatively detected galaxies in the Virgo cluster.
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Table 1 is organized as follows:

-

Col. 1: Obj. is the galaxy designation;

-

Cols. 2-3: (J2000) celestial coordinates;

-

Col. 4: the heliocentric optical recessional velocity (in km s^-1);

-

Col. 5: the rms dispersion in the baseline (mJy);

-

Col. 6: $S\!_{\rm p}$ is the peak flux of the detected line (mJy);

-

Col. 7: $V_{\rm HI}$ is the heliocentric central radial velocity of a line profile (in km s^-1), in the optical convention, with its estimated uncertainty (see below);

-

Cols. 8-9: W₅₀ and W₂₀ are the line widths at 50% and 20% of peak maximum, respectively, (km s^-1);

-

Col. 10: $I_{\rm HI}$ is the integrated line flux (Jy km s^-1), with its estimated uncertainty (see below);

-

Col. 11: A quality flag to the spectra is given, where Q=1 stands for high signal-to-noise, double horned profiles, Q=2 for high signal-to-noise, single horned profiles, and Q=3, 4 for low signal-to-noise profiles whose measured line parameters are not reliable.

We estimated the uncertainties $\sigma_{V_{\rm HI}}$ (km s^-1) in $V_{\rm HI}$ and $\sigma_{I_{\rm HI}}$ (Jy km s^-1) in  $I_{\rm HI}$ following Schneider et al. (1986, 1990), as:

$$\sigma_{V_{\rm HI}} = 1.5(W_{20}-W_{50})X^{-1}$$ (1)

and

$$\sigma_{I_{\rm HI}} = 2(1.2W_{20}/R)^{0.5}R\sigma = 7.9(W_{20})^{0.5}\sigma$$ (2)

where $I_{\rm HI}$ is the integrated line flux (Jy km s^-1), R is the instrumental resolution (12.9 km s^-1), and X is the signal-to-noise ratio of a spectrum, i.e. the ratio of the peak flux density $S\!_{\rm p}$ and $\sigma$, the rms dispersion in the baseline (Jy).

The uncertainty in the W₂₀ and W₅₀ line widths is expected to be 2 and 3 times $\sigma_{V_{\rm HI}}$, respectively.

Of the 33 observed Virgo cluster objects, 12 (36%) were detected, of which 4 tentatively (see Table 1).

5 Discussion

The newly obtained H  I data were combined with those available from the literature for the $m_{\rm p}\leq 18.0$ late-type (Sa-Im-BCD) galaxies in the Virgo cluster, listed in Table 2. The sample comprises 355 galaxies, of which 296 were detected and 59 remain undetected.

The compilation of H  I data from the literature was carried out using a criterion of maximum reliability and homogeneity, i.e. recent Arecibo data were preferred to more ancient measurements. In most cases we were able to assess a quality flag to the quoted measurement by inspecting the individual HI profiles. It is known that the H  I distribution in normal late-type galaxies spatially exceeds the optical extent by a factor ranging from 1.2 (Hewitt et al. 1983) to 2 (Salpeter & Hoffman 1996) on average. Not accounting for such an effect makes the measurement of the total H  I flux significantly underestimated from single pointing observations of galaxies comparable in size to the beam (see Sullivan et al. 1981; Hewitt et al. 1983). Although this is not a big concern for galaxies observed in this work, because they are generally small compared to the Arecibo beam, it might be a problem for 107/355 galaxies with optical diameters >2 arcmin, whose H  I parameters have been taken from the literature. In order to minimize the missing flux problem we took the published HI parameters by selecting the references with the following priority: interferometer or mapping surveys were preferred to single beam pointings. Among the latter works we first selected those which include the flux correction for source to beam size. Only a small fraction of the large galaxies (14/107) were taken from references not including such a correction, that was not either applied by us. The reader should be aware that a possible overestimate of the H  I deficiency parameter among some of the largest (most luminous) galaxies might arise from this effect.

Distances were estimated as in Gavazzi et al. (1999b): individual objects were assigned to the various subclouds in the Virgo cluster according to a positional/velocity criterion: A = cluster A (M 87), B = cluster B (M 49), W = west cloud, M = M cloud, N = North cloud, E = East cloud, S = Southern extension. For each cloud a mean distance D is assumed: 17 Mpc for clouds A, E, S and N, 23 Mpc for cloud B, and 32 Mpc for clouds W and M. We estimate that the distances of individual objects are subject to $\sim$30% uncertainties.

The corrected H  I flux was transformed into H  I mass or mass limit, in solar units, adopting ${M}_{\rm HI}$ = $2.36 \times10^5 D^2$ $I_{\rm HI}$. For undetected galaxies we set $I_{\rm HI}$ =  $1.5 \times {rms}_{\rm HI} \times W_{\langle 20-50\rangle}$, where $rms_{\rm HI}$ is the rms of the spectra in mJy and the $W_{\langle 20-50\rangle}$ profile width is based on the following average line widths of the detected objects per Hubble type bin: 300 km s^-1 for Sa-Sbc, 190 km s^-1 for Sc-Scd, and 85 km s^-1 for Sm-BCD.

We also estimate the H  I deficiency parameter following Haynes & Giovanelli (1984) as the logarithmic difference between ${M}_{\rm HI}$ of a reference sample of isolated galaxies and ${M}_{\rm HI}$ actually observed in individual objects: ${Def}_{\rm HI}= \log M_{\rm HI~ref.} - \log M_{\rm HI~obs.}$. $\log M_{\rm HI~ref}$has been found linearly related to the galaxies linear diameter d as: $\log M_{\rm HI~ref}=a+b \log(d)$, where a and b are weak functions of the Hubble type, as listed in Table 3. The problem here is that Haynes & Giovanelli (1984) have included in their reference sample of isolated galaxies only relatively large (a>1 arcmin) UGC objects so that the $Def_{\rm HI}$ parameter is poorly calibrated for smaller objects, making determinations of the HI deficiency for the smallest objects uncertain, likely underestimated (Solanes 1996). Furthermore, as discussed in Solanes et al. (2001) galaxies in the latest Hubble types (Scd-Im-BCD), for which we have adopted a and b parameters consistent with those of Sc (Table 3), are more subject to observational biases than higher surface brightness galaxies. The reader should be aware that the determinations of the HI deficiency for these objects is highly uncertain.

Table 3: Adopted parameters of the ${M}_{\rm HI}$ vs. diameter relation.

5.1 Comparison with Leda

The H  I fluxes listed in Table 2 were compared to the H  I fluxes listed in the HyperLeda database (http://foehn.univ-lyon1.fr/hypercat/), found for 286 detected galaxies. The comparison of the two datasets is given in Fig. 3, showing excellent agreement: $I_{\rm HI}(T.W.) = I_{\rm HI}({\rm Leda})*1.04 \pm 0.25$. The most discrepant objects are VCC 66, 1987 and 2070 for which our flux is almost twice the flux in Leda, and VCC 1673 showing the reverse ratio. Assuming that the two data-sets are independent (which is not true because several measurements are in common) and assuming that the error is equally distributed among the two databases, we estimate that the flux uncertainty given in this work is $\sim$20%. Combining this error with the distance uncertainty ($\sim$30%) discussed in the previous section we conclude that the uncertainty on the ${M}_{\rm HI}$ estimates is $\sim$50%, or $\sim$0.2 on log( ${M}_{\rm HI}$).

	Figure 3: Comparison of the HI fluxes adopted in this work and those found in the Leda database.
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5.2 Comparison with HIJASS

It is worth comparing the H  I masses listed in Table 2 with those obtained by the HIJASS blind Virgo cluster H  I survey (Davies et al. 2004, hereafter D04) for the common galaxies in the area: $12^{\rm h}13^{\rm m}<{\rm RA (J2000)} <12^{\rm h}30^{\rm m}; +12^\circ00'<{\rm dec}<+20^\circ00'$. They are marked as "D04'' in the references to Table 2. Out of the 27 galaxies detected by HIJASS only 22 are included in our Table 2 because 3 are not in the VCC and 2 others, which were considered as spirals by HIJASS, are classified as S0 and "?'' in the VCC, and were thus not considered by us. The remaining 22 galaxies were detected also in the present survey. Moreover D04 narrowed their search velocity range to 500-2500 km s^-1 in order to avoid Galactic emission and background galaxies. Galaxies in common with D04, in the interval 500-2500 km s^-1, are marked with an asterisk in Table 2. With these restrictions, the HI mass measured by D04, re-scaled to the distance adopted by us (i.e. 17 Mpc for cluster A, and 32 Mpc for cloud M, instead of 16 Mpc adopted by D04) is plotted vs. our mass estimates in Fig. 4, including galaxies undetected by D04 that are plotted at $M_{\rm HI}=10^{7.7}~M_\odot$ (triangles). Two galaxies (VCC 119 = UGC 7249, VCC 483 = NGC 4298) are undetected by D04 in spite of their mass in excess of 10 $^{8.9}~ M_\odot$. However the first has a velocity (622 km s^-1) close to the HIJASS limit and NGC 4298 is confused with NGC 4302 (detected in HIJASS with $M_{\rm HI}=10^{9.2}~ M_\odot$). Altogether the two mass estimates appear consistent with eachother, with the exception of a few points at $M_{\rm HI}<10^{8}~ M_\odot$ that appear slightly underestimated by D04.

	Figure 4: Comparison of the HI masses as derived from this work with those derived in the blind HIJASS H  I survey (Davies et al. 2004) for galaxies in common in the radial velocity interval of 500-2500 km s-1. Open triangles are for undetected HIJASS galaxies.
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5.3 The Virgo H I mass function (HIMF)

Figure 5: The Virgo cluster H  I mass function (HIMF) as derived from this work using only the detected galaxies (histogram), together with the HIMF derived from the blind HIJASS survey (D04), normalized to our data as described in the text. Error bars represent purely statistical errors. For comparison, the dotted line gives the Field HIMF as derived by Zwaan et al. (2003), normalized arbitrarily in order to match our data at $M_{\rm HI}=10^{9.5}~ M_\odot$.

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The data of our optically selected Virgo cluster galaxy sample as listed in Table 2, disregarding the undetected galaxies, were binned in $\log(M_{\rm HI})=0.5$ intervals, i.e. $\sim$2.5 times the estimated uncertainty on log( ${M}_{\rm HI}$) and were used to construct the Virgo HIMF shown in Fig. 5 (solid histogram) and to compare it with the HIJASS HIMF of D04 (filled squares). The latter was normalized to our data by the ratio of the areas covered by the two surveys (a factor of 4.5) and by the ratio (a factor of 1.7) of the number of galaxies in the velocity interval -500<V<3000 km s^-1 surveyed by us and those in the interval 500<V<2500 km s^-1 surveyed by D04. Moreover the HIMF of D04 was shifted toward higher masses by $\log M_{\rm HI}=0.05$to account for the slightly larger distances assumed by us (see Sect. 5.2). In addition, Fig. 5 shows the Field HIMF of Zwaan et al. (2003) arbitrarily normalized to our data. In spite of the different construction methods the two Virgo HIMF are surprisingly consistent with eachother. Both HIMFs show a maximum at $M_{\rm HI}\sim 10^{8.5}~ M_\odot$ and a consistent negative slope for lower masses. Below $M_{\rm HI}\sim 10^{8.5}~ M_\odot$ the two are inconsistent with the field HIMF which follows the slope +1.3.

The consistency between the Virgo radio- and optically- selected HIMFs in Fig. 5 is not obvious. It implies that the contribution from isolated H  I clouds is negligible. Extrapolating from the 2 confirmed detections of D04 to the 7.5 times larger area covered in the present survey, only 15 such objects are expected in the whole cluster (that are missed by an optically selected H  I survey). It also implies that, besides the isolated H  I clouds, the bulk of the H  I emission is associated with the late-type galaxies, with a negligible contribution from the early-type objects that we did not survey in H  I. We show in Fig. 6 that also for the field the observed HIMF can be obtained purely from the contribution of the late-type population. Using the relation $\log~M_{\rm HI}=2.9{-}0.34\times M_{\rm p}$, which holds on average between the H  I mass and the optical luminosity in a population of isolated, unperturbed galaxies (taken from GOLDmine), we transform the optical luminosity function of field S+Im galaxies by Marzke et al. (1998) into an $\rm HILF_{S+Im}$, as shown by the dotted histogram of Fig. 6. The actual measured HILF obtained by Zwaan et al. (2003) is consistent with the $\rm HILF_{S+Im}$, at least for $M_{\rm HI}>10^{7.5}~ M_\odot$.

Similarly we transform the optical luminosity function of Virgo (Fig. 7) into the $\rm HILF_{S+Im}$ (dashed histogram in Fig. 6) and compare it to the measured HILF (continuum histogram). The two are in general agreement, with some noticeable differences: the $\rm HILF_{S+Im}$ is in excess over the measured HILF in the range $M_{\rm HI}>10^{9}~ M_\odot$, while it lies below the measured HILF for $M_{\rm HI}<10^{8}~ M_\odot$. Both discrepancies can be understood in terms of H  I deficiency. Massive spirals in Virgo have large $Def_{\rm HI}$ parameters that shift their measured ${M}_{\rm HI}$ one or two decades below the corresponding values for isolated spirals, producing the measured HILF excess over the $\rm HILF_{S+Im}$ at $M_{\rm HI}<10^{8}~ M_\odot$.

Figure 6: The dotted histogram is obtained from the late-type galaxies optical luminosity function, as determined in the field by Marzke et al. (1998), transformed into ${M}_{\rm HI}$using the relation $\log~M_{\rm HI}=2.9{-}0.34\times M_{\rm p}$ discussed in the text. It appears consistent with the field HILF of Zwaan et al. (2003) (long dashed line) indicating that most of the HI is contributed to by late-type galaxies. The dashed histogram is obtained from the late-type galaxies optical luminosity function of Virgo (see Fig. 7), transformed into ${M}_{\rm HI}$ using the same ${M}_{\rm HI}$ vs. $M_{\rm p}$ relation. The continuum histogram is the HIMF actually observed in Virgo (see Fig. 5). The filled dots represent the Montecarlo simulation described in the text aimed at modeling the effects of the H  I deficiency on the HIMF.

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	Figure 7: The optical luminosity distribution of the 355 late-type galaxies analyzed in this work, divided in Giants and Dwarfs, consistent with the one in Sandage et al. (1985) for $m_{\rm p}\leq 18.0$ mag, accounting for the different assumed distance.
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Solanes et al. (2001) found that the distribution of HI deficiency among galaxies of latest types in the Virgo cluster is skewed toward high values. This can be either due to a real higher than average gas depletion or to the poorly calibrated deficiency parameter for these systems, as mentioned earlier. However Hoffman et al. (1985) confirm that the HI (hybrid) surface brightness is monotonously decreasing toward later Hubble types and fainter optical luminosities. Disregarding these second order dependences of the HI deficiency parameter on the Hubble type at extreme low luminosities, we have simulated the first order effect of the HI deficiency on the HIMF by running a Montecarlo simulation with the simple assumption that the $Def_{\rm HI}$ parameter of galaxies in the Virgo cluster is Gaussian distributed with a mean of 0.4 and a FWHM of 0.8, independent of the galaxy luminosity. Starting from the optical luminosity function of S+Im of Fig. 7 and assuming the $\log~M_{\rm HI}=2.9{-}0.34~\times~ M_{\rm p}$ relationship we have been able to reproduce (filled dots) the observed HIMF (continuum histogram) of Fig. 6.

5.4 The HIMF adopting upper limits

So far we have shown that the HI mass function obtained from HI follow-up observations of an optically selected sample of late-type galaxies is in agreement with the HIMF derived from a blind HI survey. We have however not considered the relatively minor contribution from the upper limits, i.e. 59/355 galaxies that were surveyed but not detected.

Radio astronomers have developed a robust method to account for upper limits when deriving the continuum radio luminosity function (Avni et al. 1980; see a recent application to Virgo in Gavazzi & Boselli 1999) that we apply to the HI data. Figure 8 shows that the fractional HIMFs derived with (continuum histogram) and without (dashed histogram) taking into account the contribution from upper limits are identical above $\log~M_{\rm HI}=8~M_\odot$. Upper limits contribute for smaller masses, and make the faint-end slope of the HIMF less steep. This is a small difference that should however not be disregarded.

	Figure 8: The fractional HI mass function as derived from the detected objects alone (dashed histogram) and including undetected galaxies (continuum histogram).
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6 Conclusions

We have observed in the 21-cm H  I line, with the refurbished Arecibo telescope, 33 galaxies in the Virgo cluster. Given the high sensitivity of our observations (rms noise $\sim$0.5 mJy corresponding to $\log~M_{\rm HI}=6.6~ M_\odot$) 12 objects were detected and stringent upper limits were obtained for the remaining ones.

In the Virgo area covered by the VCC the new observations brought to 100% completeness the H  I survey of late-type galaxies with $m_{\rm p}\leq 18.0$ mag which are cluster members or bona-fide members.

Using the Virgo H  I data set, comprising 355 late-type galaxies (296 of which are positive detections) we construct the cluster H  I mass function (HIMF) as derived from an optically selected H  I survey. Considering or disregarding the contribution from HI non-detections, we find it in remarkable agreement with the radio selected HIMF available for this cluster from Davies et al. (2004).

The low-mass end of the Virgo HIMF is inconsistent with the field HIMF of Zwaan et al. (2003).

We show that both the Virgo and the field HIMFs can be obtained from the optical luminosity function of S+Im galaxies alone, under the assumption that ${M}_{\rm HI}$ scales with $M_{\rm p}$ according to the universal relation: $\log~M_{\rm HI}=2.9{-}0.34\times M_{\rm p}$.

The latter evidence allows us to conclude that neutral hydrogen in the local universe is primarily contributed by late-type galaxies, with marginal contributions from early-type galaxies and isolated H  I clouds.

The inconsistency between the cluster and the field HIMF derives primarily from the difference in the optical luminosity function of late-type galaxies in the two environments and from the HI deficiency occurring in spirals in rich clusters.

Acknowledgements

We thank Luca Cortese for running the Montecarlo simulations and for useful discussions. The Arecibo Observatory is part of the National Astronomy and Ionosphere Center, which is operated by Cornell University under a cooperative agreement with the National Science Foundation. This research also has made use of the Goldmine database, of the Lyon-Meudon Extragalactic Database (Leda), recently incorporated in HyperLeda and of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

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Online Material

Table 1: Parameters of the newly observed galaxies.

Table 2: Basic H  I properties of late-type Virgo galaxies.

Appendix A: Notes on individual galaxies

VCC 48: The possible line emission of this object, which has an optical redshift of $-52\pm60$ km s^-1, is masked by Galactic H  I emission. The object remains undetected in spite of the noise reduction from 1.1 mJy, as reported by Hoffman et al. (1987), to 0.64 mJy rms in the present work.

VCC 222: We did not detect this galaxy, with an rms noise level of 0.60 mJy. Its optical redshift, $2298\pm122$ km s^-1, is not well determined. An Effelsberg H  I detection was reported by Huchtmeier (1982) at 2410 km s^-1, with W₅₀=273 km s^-1 and $I_{\rm HI}=4.4\pm1.5$ Jy km s^-1, with an average line signal of 16 mJy. Although Magri (1994) reported a tentative detection at 2596 km s^-1, its low signal-to-noise ratio makes it appear spurious. Two published (Krumm & Salpeter 1979; Mirabel & Wilson 1984) estimated upper limits to its line flux are 2.4 and 3.4 Jy km s^-1, respectively. We conclude that the line signal reported by Huchtmeier is spurious and due to RFI.

VCC 227, 256: Marginal detections.

VCC 323: The object remains undetected in spite of the noise reduction from 6.0 mJy, as reported by Huchtmeier & Richter (1986), to 0.53 mJy rms in the present work.

VCC 341: We did not detect this galaxy, with an rms noise level of 0.76 mJy. Its optical redshift is $1827\pm60$ km s^-1. The Effelsberg H  I detection reported by Huchtmeier (1982) at 1846 km s^-1, with W₅₀=465 km s^-1 and $I_{\rm HI}=3.0\pm1.5$ Jy km s^-1, i.e. an average line strength of 6.5 mJy, appears spurious given its low signal-to-noise ratio.

VCC 358: Bad baselines due to the proximity of the 19 Jy continuum source NGC 4261 resulted in the very high rms noise level of 28 mJy, about 30 times that of similar observations made for this project. Our previous Nançay observations (van Driel et al. 2000) also had a high rms noise level of 11 mJy and a limit of 6 Jy km s^-1 was reported by Huchtmeier & Richter (1986) from Effelsberg data. An Arecibo detection at 2633 km s^-1 with $I_{\rm HI}$ = 9.0 Jy km s^-1 was reported by Magri (1994).

VCC 362: Given that its optical redshift is 156$\;\pm\;$44 km s^-1, our H  I detection ( $V_{\rm HI}=2350$ km s^-1, W₅₀=92 km s^-1 and $I_{\rm HI}=0.40$ Jy km s^-1) must be due to confusion. At $4'~\hspace{-1.7mm}.\hspace{.0mm}9$ lies VCC 367, a 17.4 mag object without published optical redshift, for which Hoffman et al. (1987) measured $V_{\rm HI}=2362$ km s^-1, W₅₀=98 km s^-1 and $I_{\rm HI}=0.59$ Jy km s^-1 at Arecibo. VCC 362 remains undetected in spite of the noise reduction from 3.5 mJy, as reported by Magri (1994), to 0.44 mJy rms in the present work.

VCC 524: Besides a detection of the target galaxy at 1035 km s^-1, our spectrum shows a detection near 5800 km s^-1with $I_{\rm HI}=0.45$ Jy km s^-1, which is due to confusion by VCC 526 (=NGC 4307A), a 15.7 mag Sc spiral  $3'~\hspace{-1.7mm}.\hspace{.0mm}2$ away, with $V_{\rm opt}=5989\pm46$ km s^-1, for which Magri (1994) measured $V_{\rm HI}$ = 5836 km s^-1, W₅₀=76 km s^-1 and $I_{\rm HI}=2.6$ Jy km s^-1 at Arecibo.

VCC 528: Is a background galaxy, at 7046 Jy km s^-1.

VCC 666: The possible detection at -250 km s^-1is doubtful. The object remains undetected in spite of the noise reduction from 1.3 mJy, as reported by Hoffman et al. (1987), to 0.51 mJy rms in the present work.

VCC 802: The object remains undetected in spite of the noise reduction from 1.5 mJy, as reported by Hoffman et al. (1987), to 0.58 mJy rms in the present work.

VCC 1086: Its optical redshift is $294\pm39$ km s^-1. Our H  I parameters ( $V_{\rm HI}=328\pm8$ km s^-1, W₅₀=240 km s^-1 and $I_{\rm HI}=0.93\pm0.09$ Jy km s^-1) are comparable to those ( $V_{\rm HI}=363$ km s^-1, W₅₀=224 km s^-1 and $I_{\rm HI}=0.96$ Jy km s^-1) measured by Hoffman et al. (1989a) at Arecibo. Profile contaminated by galactic absorption.

VCC 1189: Its optical redshift is $544\pm43$ km s^-1. Our H  I profile has $V_{\rm HI}=516\pm1$ km s^-1, W₅₀=112 km s^-1 and $I_{\rm HI}=4.2\pm0.1$ Jy km s^-1. The profile parameters measured by, respectively, Huchtmeier & Richter (1986) at Effelsberg, Hoffman et al. (1989a) at Arecibo & Schneider et al. (1992) with the NRAO 300ft are $V_{\rm HI}=530$, 537 and 543 km s^-1, W₅₀=98, 110 and 121 km s^-1 and $I_{\rm HI}=5.0$, 3.6 and 9.7 Jy km s^-1. Although the line fluxes vary considerably, they do not correlate with the size of the telescope beam, nor are there any candidates for confusion in the vicinity. The large line flux measured by Schneider et al. appears to be spurious.

VCC 1196: We did not detect this galaxy, with an rms noise level of 0.57 mJy. Its optical redshift is $908\pm36$ km s^-1. An Effelsberg H  I detection was reported by Huchtmeier & Richter (1986) at 2422 km s^-1, with W₅₀=446 km s^-1 and $I_{\rm HI}=6.5\pm1.5$ Jy km s^-1, i.e. an average line strength of 15 mJy, which we assume is spurious and due to RFI.

VCC 1287: The object remains undetected in spite of the noise reduction from 1.4 mJy, as reported by Hoffman et al. (1987), to 0.77 mJy rms in the present work.

VCC 1377: The object remains undetected in spite of the noise reduction from 1.1 mJy, as reported by Hoffman et al. (1987), to 0.51 mJy rms in the present work.

VCC 1435: The object remains undetected in spite of the noise reduction from 0.9 mJy, as reported by Hoffman et al. (1987), to 0.44 mJy rms in the present work.

VCC 1448: We did not detect this galaxy, which does not have a published optical redshift, with an rms noise level of 0.92 mJy. An Effelsberg H  I detection was reported by Huchtmeier & Richter (1986) at 2583 km s^-1, with W₅₀=66 km s^-1 and $I_{\rm HI}=1.5\pm0.26$ Jy km s^-1, i.e. with an average line signal of 23 mJy, which we assume is spurious and due to RFI.

VCC 1885: The object remains undetected in spite of the noise reduction from 0.7 mJy, as reported by Hoffman et al. (1987), to 0.38 mJy rms in the present work.

VCC 1970: Hoffman et al. (1987) reported undetection with 1.0 mJy rms. We detected it at a noise level of 0.37 mJy rms.