The H i content of metal-poor blue compact dwarf galaxies

# The H i content of extremely metal-deficient blue compact dwarf galaxies

T. X. Thuan , K. M. Goehring, J. E. Hibbard, Y. I. Izotov and L. K. Hunt
Astronomy Department, University of Virginia, P.O. Box 400325, Charlottesville, VA 22904-4325, USA; txt@virginia.edu,
kmg4mx@virginia.edu
National Radio Astronomy Observatory, Charlottesville, VA 22903, USA; jhibbard@nrao.edu
Main Astronomical Observatory, National Academy of Sciences of Ukraine, 03680 Kyiv, Ukraine; izotov@mao.kiev.ua
INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy; hunt@arcetri.astro.it
19 January 2015
###### Abstract

We have obtained new H i observations with the 100 m Green Bank Telescope (GBT) for a sample of 29 extremely metal-deficient star-forming Blue Compact Dwarf (BCD) galaxies, selected from the Sloan Digital Sky Survey spectral data base to be extremely metal-deficient (12 + log O/H 7.6). Neutral hydrogen was detected in 28 galaxies, a 97% detection rate. Combining the H i data with SDSS optical spectra for the BCD sample and adding complementary galaxy samples from the literature to extend the metallicity and mass ranges, we have studied how the H i content of a galaxy varies with various global galaxian properties. There is a clear trend of increasing gas mass fraction with decreasing metallicity, mass and luminosity. We obtain the relation (H i)/ , in agreement with previous studies based on samples with a smaller luminosity range. The median gas mass fraction for the GBT sample is equal to 0.94 while the mean gas mass fraction is 0.900.15, with a lower limit of 0.65. The H i depletion time is independent of metallicity, with a large scatter around the median value of 3.4 Gyr. The ratio of the baryonic mass to the dynamical mass of the metal-deficient BCDs varies from 0.05 to 0.80, with a median value of 0.2. About 65% of the BCDs in our sample have an effective yield larger than the true yield, implying that the neutral gas envelope in BCDs is more metal-deficient by a factor of 1.5–20, as compared to the ionized gas.

###### keywords:
galaxies: dwarf – galaxies: fundamental parameters – galaxies: irregular – galaxies: ISM – galaxies: starburst

## 1 Introduction

The formation and evolution of the first galaxies in the universe remains a key issue in cosmology. It is now thought that large massive star-forming galaxies form in a hierarchical manner from the assembly of smaller dwarf systems, through accretion and merger processes. These galaxy interactions trigger the formation of stars which enrich the interstellar gas in metals by stellar winds and supernovae. In this scenario, the number of extremely metal-deficient (XMD) dwarf galaxies should be high in the early universe but considerably smaller at the present epoch (Mamon et al., 2012).

However, while much progress has been made in finding large populations of galaxies at high (3) redshifts (e.g. Steidel et al., 2003; Adelberger et al., 2005), truly chemically unevolved galaxies remain elusive in the high- universe. The spectra of distant galaxies generally indicate the presence of a substantial amount of heavy elements, implying previous star formation and metal enrichment. The discovery of XMD galaxies at high may have to wait until the advent of the JWST and 30 m-class ground-based telescopes.

We adopt here a different approach. Instead of searching for high- metal-deficient objects, we focus our attention on XMD star-forming dwarf galaxies in the local universe. They are the most promising local proxies of chemically unevolved galaxies in the early universe, and are usually found among a class of dwarf galaxies undergoing intense bursts of star formation called Blue Compact Dwarf (BCD) galaxies (Thuan & Martin, 1981). The optical spectra of the BCDs are characterized by a blue continuum on which are superimposed strong narrow emission lines. XMD BCDs are very rare (Izotov, Thuan & Guseva, 2012). For more than three decades, one of the first BCD discovered, I Zw 18 (Sargent & Searle, 1970), held the record as the most metal-deficient emission-line galaxy known, with an oxygen abundance [O/H]= 12 + log O/H = 7.170.01 in its northwestern component and 7.220.02 in its southeastern component (Thuan & Izotov, 2005) ( 3% solar, adopting the solar abundance 12+logO/H = 8.76 of Steffen et al., 2015). Only in 2005 has I Zw 18 been superceded in its rank by SBS 0335–052W with a metallicity [O/H] = 7.12 (Izotov, Thuan & Guseva, 2005).

Because of the scarcity of XMD emission-line galaxies, we stand a much better chance of discovering them in very large spectroscopic surveys such as the Sloan Digital Sky Survey (SDSS, York et al., 2000). We have carried out a systematic search for such objects with [O/H] in the SDSS spectroscopic data release 7 (DR 7) (Abazajian et al., 2009). Imposing cut-offs in metallicity and redshift results in a total sample of 29 XMD BCDs. Similar searches for XMD galaxies in the SDSS have been carried out by Morales-Luis et al. (2011) and Sánchez Almeida et al. (2016). We found a total of 10 galaxies in common between the present sample and that of Sánchez Almeida et al. (2016) so that the two samples are likely to have similar properties, and the H i characteristics discussed here probably apply to the Sánchez Almeida et al. (2016) objects as well.

The focus of this paper is the study of the neutral hydrogen content of these XMD objects. There have been previous H i studies of this type of extremely metal-poor galaxies. Thus, Filho et al. (2013) have carried out a single-dish H i study with the Effelsberg radio telescope of a subsample of 29 XMD galaxies selected from the Morales-Luis et al. (2011) list. We will use part of the data of those authors to supplement our own and will compare with our results with theirs when warranted. A handful of interferometric H i maps of other XMD galaxies have also been obtained by the Pune group with the Giant Metrewave radio telescope (see Ekta, Pustilnik & Chengalur, 2009; Ekta & Chengalur, 2010, and references therein). In Section 2, we define the XMD BCD sample and describe observations of their neutral hydrogen content with the Robert C. Byrd Green Bank Telescope (GBT) at the National Radio Astronomy Observatory 111The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.. This sample will be referred to hereafter as the GBT sample. Section 3 describes the H i data along with derived ancillary data such as metallicities, star formation rates, stellar masses needed to study trends of the neutral gas content with other properties of the BCDs. In Section 4, we discuss several comparison samples compiled from the literature, useful for studying the H i content of star-forming galaxies over a wider range of heavy element abundances and stellar masses. Our total galaxy sample, composed of the GBT and three comparison samples, includes 151 objects and covers the extensive metallicity range 7.20 [O/H] 8.76. We study in Section 5 the correlations of various quantities. In particular, we analyze the dependence of the neutral gas mass to light ratio on metal abundance, and that of the gas mass fraction on stellar mass. We also discuss the chemical evolution of XMD BCDs. We summarize our conclusions in Section 6. Throughout this paper, we adopt the cosmological model caracterized by a Hubble constant = 73 km s Mpc, a matter density parameter = 0.27 and a dark energy density parameter = 0.73 (Riess et al., 2011).

## 2 H i observations

### 2.1 The GBT sample

We have constructed our XMD BCD sample by applying the following selection criteria to the SDSS DR7 spectral database. As described in Izotov et al. (2012), we first select them on the basis of the relative fluxes of particular emission lines as measured on the SDSS spectra: [O iii]4959/H 1 and [N ii]6853/H 0.1. These spectral properties select out uniquely low-metallicity dwarfs since no other type of galaxy possesses them. Second, since one of the main scientific objectives here is to study how the H i properties of star-forming galaxies vary with metallicity, it is important to have accurate heavy element abundances for the XMD BCDs. Thus, we have included in our sample only those BCDs that have a well-detected [O iii]4363 line as this electron temperature-sensitive emission line allows a direct and precise abundance determination. Third, we have set a metallicity cut-off [O/H] 7.6 (8% solar) to choose only XMD galaxies. This metallicity threshold has been suggested by Izotov & Thuan (1999) to characterize very young galaxies, with most of their stellar populations formed not more than 1 Gyr ago. Lastly, we have chosen the BCDs to be not more distant than 85 Mpc, so we can measure their H i emission with a good signal-to-noise ratio within a reasonable integration time with the GBT. This distance upper limit corresponds to a recession velocity of 6200 km s. These selection criteria result in a total sample of 29 XMD BCDs. In contrast to many previous BCD samples that have been observed in H i (e.g. Thuan & Martin, 1981; Thuan et al., 1999b; Huchtmeier, Krishna & Petrosian, 2005; Filho et al., 2013), this BCD sample is unique in that : 1) it contains only very metal-deficient objects (7.35 [O/H] 7.60) as compared to previous samples which include many objects with [O/H] 7.7. This allows us to study very chemically unevolved galaxies; 2) it has O abundances determined precisely for each object, using the direct method based on the [O iii]4363 line. This is in contrast to the approximate abundances derived for many galaxies in previous samples, using the statistical strong-line method, because of the undetectability of the [O iii] line; 3) all objects possess accurate SDSS images and photometry with which we can derive optical luminosities and mass-to-light ratios.

### 2.2 Observations and Data reduction

The observations were obtained with the 100 m GBT during the periods September 2005 and January-February 2006. The GBT spectrometer backend was used with a total bandwidth of 12.5 MHz and 9-level sampling, resulting in a total of 16,384 spectral channels. We use two spectral windows centered at the same frequency (1420.4058 MHz) with two different linear polarizations (XX and YY). Each target was observed in total power mode with multiple (between 2 and 6) 10 minute on-source, 10 minute off-source pairs. The total on-source time for each galaxy was determined during the observing runs, depending on the strength of the spectral feature relative to the noise. Since the two polarizations were detected independently, they were averaged to improve sensitivity. The data were flagged for radio frequency interference (RFI) and all scans summed. The data were calibrated by observations of standard continuum calibrators from the list of NRAO VLA Sky Survey unconfused calibrator sources prepared by J. Condon and Q.F. Yin, using the same backend setup. We checked our calibration by observing standard spectral line calibrators from the list of Hogg et al. (2007) and found it to be good to 3%. All data reduction was done in GBTIDL. The data were boxcar-smoothed by 20 channels, for a final frequency resolution of 15.26 kHz, corresponding to a velocity resolution of 3.3 km/s. RMS noise levels were  3 mJy for a single 10 minute on/off scan. Spectral baselines were fit using line-free channels and subtracted out. Generally, a low-order fit, between 1 and 3, was used. Line fluxes and linewidth at 20% and 50% of peak intensity were measured in IDL. Distances were calculated from the measured redshifts, after correcting for Virgo infall, using the Virgocentric flow model of Mould et al. (2000).

Of the 29 XMD BCDs in our sample, 28 galaxies were detected. This corresponds to a 97% detection rate, considerably higher than those of previous BCD samples. For comparison, the detection rate of the Thuan & Martin (1981) sample is 80%, that of the Thuan et al. (1999b) sample 74%, and that of Filho et al. (2013) only 34%. The reason for the high detection rate of our GBT sample is probably the higher sensitivity of the present observations. Thus, the 5 uncertainties of our observations are 0.1 Jy km s while those of the Filho et al. (2013) observations are about 0.6 Jy km s.

### 2.3 H i data

H i profiles (after boxcar smoothing and baseline removal) of all galaxies in the sample are presented in Fig. 1. There is only one non-detection, the BCD J2238+1400 = HS 2236+1344. The profiles are arranged from left to right and from top to bottom in order of increasing right ascension. In addition, Fig. 2 shows the SDSS image of each galaxy, taken from Data Release 10 (DR10, Ahn et al., 2013). The images are useful for examining the morphology and colors of the sample objects and for evaluating potential H i contamination from neighboring galaxies. It is clear that our objects are generally very compact, the average half-light radius of the dwarf galaxies in our sample is about 10 (column 5 of Table 2), their linear diameters being generally less than 2 kpc. Adopting an average H i-to-optical size ratio of 3 (Thuan & Martin, 1981), the H i angular extent of all sample galaxies are considerably smaller than the 9 GBT beam at 21 cm, so we did not need to apply any beam correction to the flux densities. To check for potential contamination of the H i emission from neighboring galaxies, we have also examined the SDSS DR10 images in a square field of 12 on a side centered on each object. We have found no case of contamination. For J1214+0940 with = 1702 km s, there is a faint diffuse yellow galaxy at 45 of the BCD in the NW direction, but its velocity is 1245 km s.

Observed and derived H i parameters for all detected galaxies (28 objects) are given in Table 1. Column 1 lists the galaxies in order of increasing right ascension (given in Table 2). Column 2 gives the integrated H i flux densities and their errors. The errors are taken to be equal to (Thuan et al., 1999b)

 σ=2×√N×RMS×Δv, (1)

where is the number of channels over which the line is detected, is the root-mean-square deviation in mJy in the baseline fit to the 20-channel boxcar smoothed 21 cm spectrum, as given in column 3, and is the velocity resolution equal to 3.3 km s.

We can use the measured of 1.86 mJy of the spectrum of the non-detected galaxy J2238+1400, to derive an upper limit for its H i mass. This galaxy, at the distance of 86.4 Mpc, is the furthest object in our sample. We take its H i velocity width at zero intensity to be 192 km s, obtained by multiplying 155 km s, the largest in our sample (Table 1), by 1.2, assuming that the velocity width at zero intensity is 20% wider than . Assuming a rectangular profile, we obtain a 5 upper limit (H i) 3.1 10 M.

Columns 4 and 5 give respectively the velocity widths at 20% of maximum intensity and the mid-point velocities of the 20% profile widths, while columns 6 and 7 list the same quantities at 50% of maximum intensity. Column 8 lists H i masses calculated from the integrated line flux densities using the equation

 M(HI)=2.36×105∫SdvD2M\sun, (2)

where is the distance in Mpc given in column 3 of Table 2 and Sdv is the integrated H i flux density in Jy km s, given in column 2.

Column 9 gives the logarithm of the ratio of the H i mass to absolute g luminosity of each galaxy. The luminosity is given in column 4 of Table 2, and we adopt = 5.12 mag (Bessel, 2005).

### 2.4 Shapes of H i profiles and galaxy morphologies

Column 10 gives the classification of each H i profile. We have classified the H i profiles into two broad categories, depending on their shapes: the Gaussian (G) profiles characteristic of diskless dwarf galaxies without large rotational motions, and the steep-sided double-horn (DH) profiles characteristic of inclined disk galaxies with significant rotational motions. The reliabilty of the profile classification depends on the signal-to-noise ratio of the spectrum, decreasing with lower values of that ratio. Most of the H i profiles (20 out of 28, or 71%) have a Gaussian shape, indicating dominant random motions, while the remaining have double-horned profiles, reflecting dominant rotational motions.

We have examined the morphology of all galaxies in the sample using the SDSS images (Fig. 2). Using the classification terminology of Sánchez Almeida et al. (2016), we find 3 galaxies (J0133+1343, J1055+5111 and J1201+0211) or 10% of the sample to be symmetric, with a centrally concentrated emission, 3 galaxies (J1044+0353, J1202+5415 and J2238+1400) possessing 2 knots (10%), 5 galaxies (J0908+0517, J0944+0936, J1148+5400, J1150+5627 and J1335+4910) having multiple knots (17%) and the remaining 18 galaxies (63%) having a cometary structure. According to the BCD morphological classification scheme of Loose & Thuan (1985), the cometary BCDs are characterized by a high surface brightness star-forming region (the comet’s “head”) located near one end of an elongated lower surface brightness stellar body (the comet’s “tail”). The latter could be interpreted as a rotating thin stellar disk seen nearly edge-on, but with modest rotational velocities and significant random motions, as suggested by the predominance of the H i profiles with a Gaussian shape. It is interesting that the low-metallicity selection criterion has picked out a majority of cometary BCDs. How does the optical morphology classification of the GBT sample compare with that of other XMD samples such as the one assembled by Morales-Luis et al. (2011)? These authors also find in their XMD sample a predominance of cometary morphology (75%), the remaining 25% showing a single knot without any obvious underlying low-surface brightness component. Sánchez Almeida et al. (2016) found in their XMD sample that 57% of the galaxies are cometary, with 23% symmetric, 10% multi-knot and 4% 2-knot. The common feature of all these XMD samples is that they all show a large proportion (more than half) of cometary galaxies. Recently, Sánchez Almeida et al. (2015) have suggested that these metal-deficient cometary galaxies are the result of low-metallicity gas clouds falling onto low-surface-brightness galaxy disks, and triggering bursts of star formation. The star-forming regions tend to be at the ends of the low-surface-brightness disks because the impacting gas clouds have the largest effects on the outer parts of galaxies where the ambient pressure and column density are low.

### 2.5 Comparison with previous H i observations

A few galaxies in our sample have had previous H i observations. They are J0133+1342, J1121+0324, J1201+0211, J1215+5233 and J1202+5415 (Filho et al., 2013), J0944+0936 (Stierwalt et al., 2009), J0908+0517 and J1119+0935 (Popping & Braun, 2011), J1121+0324, J1201+0211 and J1215+5223 (Pustilnik & Martin, 2007), and J1214+0940 (Kent et al., 2008). Within the errors, our flux densities are in good general agreement with those of previous authors, except for two objects: J1215+5223 for which Filho et al. (2013) found 4.70.5 Jy km s and Pustilnik & Martin (2007) found 5.20.2 Jy km s as compared to our flux density of 7.1 Jy km s, and J1119+0935 for which Popping & Braun (2011) found a flux density of 1.40.1 Jy km s as compared to our value of 1.90.1 Jy km s. These measurements were made with telescopes having similar beam sizes so the cause of the discrepancies is not clear.

## 3 Supplemental data

Column 6 (upper line) gives for each galaxy the oxygen abundance [O/H]. As our galaxies were selected to possess a well-detected [O iii] 4363 emission line in their spectra, these abundances are well determined, using the direct method. The derived oxygen abundances are generally those of the brightest H ii region in the galaxy, typically the SDSS spectroscopic target. This however is a good indicator of the metallicity of the whole BCD as detailed spatial metallicity studies of a few of these objects show no evidence of large metallicity gradients (e. g. Thuan, Izotov & Foltz, 1999a; Noeske et al., 2000).

Column 6 (lower line) gives the the inclination angle in degrees of the plane of the galaxy to the plane of the sky ( = 0 for face-on and = 90 for edge-on). Following Thuan & Martin (1981), is calculated from

 cos2i=r225−r201−r20, (3)

where is the axial ratio as obtained from the SDSS DR10 and is the intrinsic axial ratio of the galaxy. Following Filho et al. (2013), we adopt =0.25, i.e. if a galaxy’s disk appears more than four times elongated than wide, then its inclination angle is set to 90. This relatively large value is motivated by the work of Sánchez-Janssen, Méndez-Abreu & Aguerri (2010) who identified a limiting stellar mass 2 10 M below which low-mass galaxies become systematically thicker because of the increasing importance of turbulent motions relative to rotational motions. The stellar masses of the GBT galaxies are all lower than this limiting mass, so this value is appropriate.

Column 7 gives the galaxy’s present star formation rate (SFR) as derived from the extinction-corrected H fluxes using Kennicutt (1998)’s relation:

 SFR(M⊙yr−1)=L(Hα)1.26×1041ergs−1. (4)

As the H fluxes have been derived from SDSS spectra obtained with fibers of 3″diameter, we need to correct these SFRs for aperture effects. We have multiplied each SFR by a correction factor equal to the ratio of the total flux to the flux within a 3″ aperture:

 fcor=10−0.4×[mr(tot)−mr(3\arcsec)], (5)

where and are respectively the magnitudes within the Petrosian 90% radius and 3″ fiber diameter, as given in the SDSS (we have used magnitudes because the Finding Chart site of the SDSS DR10 gives magnitudes within the 3″ fiber diameter only for the band). The logarithm of is given in the lower line of column 7. Except for four galaxies, all have log  1.0. The two galaxies J0944+0936 and J1148+5400 have a large difference between and (more than 4.5 mag), and hence large uncertain aperture corrections. We have thus decided not to include their SFRs in our statistical studies.

Column 8 gives the total stellar mass and the young (age 10 Myr) stellar mass in units of solar masses, derived by model-fitting the spectral energy distribution (SED) of each galaxy, as described in Izotov, Guseva & Thuan (2011) and more recently in Izotov et al. (2016). As all our objects show strong line emission, care was taken in deriving these stellar masses to subtract the ionized gas emission. Neglecting this correction would result in a significant overestimate of the galaxy stellar mass. As the are derived from spectra obtained with 3″ diameter fibers, we have also applied to each and the upwards correction factor defined by Eq. 5. Like the SFRs, the of the galaxies J0944+0936 and J1148+5400 are not included in our statistical studies because of their large uncertain aperture corrections.

To check the reliability of our derived SFRs and concerning the statistical studies in this paper, we have compared them with those obtained by the Max Planck Institute for Astrophysics – Johns Hopkins University (MPA-JHU) group (Kauffmann et al. (2003) and Brinchmann et al. (2004)). This constitutes a good check as the MPA-JHU group derives SFRs and from total photometric magnitudes and thus does not have to apply aperture corrections as done here. We have found a very good statistical relation between the MPA-JHU SFRs and and our aperture-corrected quantities. In a plot ot (MPA-JHU) vs. (our group), the points scatter nicely along the equality line, with a dispersion of 0.6 in log . The same holds for SFRs, with a dispersion of 0.2 in log SFR. We thus conclude that our aperture-corrected quantities are quite adequate for the statistical studies described here and do not introduce any systematic bias.

Column 9 (upper line) gives an estimate of the dynamical mass of each galaxy. We emphasize that these dynamical masses are only approximate. However they may help to reveal potentially interesting trends. is calculated in the following way. For galaxies with rotation, characterized by a double-horned H i profile, the dynamical mass is estimated according to the following equation, derived by assuming an object in dynamical virial equilibrium where the gravitational force is balanced by the centrifugal force due to rotation:

 Mdyn(M⊙)=F×2.3×105v2c(kms−1)R(HI)(kpc). (6)

Here is a multiplicative factor that takes into account the degree of flattening of the galaxy. Lequeux (1983) has shown that varies between 0.6 for a flat disk system and 1 for a spherical system. We adopt here = 0.7 which corresponds to a flat disk with a flat rotation curve. (H i) is the radius of the H i gas component. It is generally larger than the optical radius of the stellar component in the case of dwarf galaxies. From interferometric H i maps of several BCDs, Thuan & Martin (1981) have derived the approximate relation

 R(HI)=3×Rg, (7)

which we adopt. Here, is the Petrosian g-band 90% linear radius (column 5). is the galaxy’s rotational velocity corrected for inclination (column 6):

 vc=vsini=Δv50/2sini, (8)

where is the galaxy’s observed rotational velocity, set to be equal to half of the velocity width at 50% of maximum intensity (column 6 of Table 1).

For galaxies with weak rotation, in virial equilibrium, supported against gravitational collapse by random motions, and characterized by a Gaussian H i profile, we estimate the dynamical mass by:

 Mdyn(M⊙)=2.3×105σ2(kms−1)R(HI)(kpc). (9)

Here is the gas velocity dispersion where

 σ=√3×Δv50/2.36. (10)

The factor converts the 1-dimensional velocity dispersion based on the H i velocity width to a 3-dimensional velocity dispersion, and the factor 1/2.36 converts the Full Width at Half Maximum (FWHM) of the Gaussian profile to a velocity dispersion. Column 9 (lower line) gives the ratio of the H i mass to the dynamical mass.

Finally, column 10 (upper line) gives the gas depletion timescale = (H i)/SFR in units of log (yr). Column 10 (lower line) gives the gas mass fraction defined as

 fgas=MgasMbaryon, (11)

where

 Mgas=1.4×M(HI). (12)

The multiplicative factor 1.4 takes into account the masses of helium and metals. We do not include a correction for molecular hydrogen (H) as we have no H observational constraints in these galaxies, and they are almost certainly H i-dominated.

M is the baryonic mass, defined as the sum of the gaseous and stellar masses:

 Mbaryon=Mgas+M∗. (13)

## 4 Comparison samples

One of the main aims of this paper is to study how the H i content of a galaxy varies statistically with various global galaxian properties such as metallicity, SFR or stellar mass. To this end, the 28 galaxies in our GBT sample are not sufficient. As mentioned before, this sample spans only a very narrow range of oxygen abundances: 7.35 [O/H] 7.60. We need to supplement our data on the GBT sample with data on other galaxy samples that span a larger metallicity range. Because of the mass-metallicity relation of galaxies, this means that the galaxian mass range will also be extended. We have thus searched the literature for other galaxy samples that possess data of the same nature as the GBT sample, but which span a larger range in metallicity and stellar mass, so that statistical trends can be studied. We have chosen three additional samples for comparison with the GBT sample.

The first sample consists of a subsample of the extremely metal-poor (XMP) galaxy sample of Filho et al. (2013) and Morales-Luis et al. (2011). Out of the 140 objects studied by these authors, there are 39 galaxies with the necessary ancillary data (oxygen abundances, derived using either the direct or strong-line methods, and H i fluxes), forming what will be called hereafter the ‘XMP sample’. This sample extends the metallicity range at the low-end (to [O/H] = 7.07) and augments the number of very low-metallicity galaxies, leading to better statistics in the low-metallicity range. The relevant data for the XMP sample is given in Table 3.

The second galaxy sample is that of Engelbracht et al. (2008). This sample was assembled to study metallicity effects on dust properties in starbursting galaxies so it is useful for our purposes as it spans a large metallicity range. We have added 31 objects from their study (those with oxygen abundances and H i measurements, and which are not already present in the XMP sample). They form what will be called hereafter the Engelbracht sample. The relevant data for that sample are given in Table 4. It spans the metallicity range 7.20[O/H]8.76.

Finally, we have added a third galaxy sample, assembled from the SIRTF Nearby Galaxy Sample (SINGS) of Kennicutt et al. (2003), hereafter called the SINGS sample. This sample is useful for increasing the number of galaxies and hence the statistics in the high mass and metallicity ranges. Selecting the galaxies with available oxygen abundances and H i fluxes results in a sample of 53 galaxies. The relevant data for the SINGS galaxies is given in Table 5.

The majority of the galaxies in the Engelbracht and SINGS samples do not possess but . To convert into , we have used the following transformation equation from Jester et al. (2005):

 g=V+0.74(B−V)−0.07. (14)

For galaxies that do not have a known , we have adopted the mean given by Buta et al. (1994) corresponding to the morphological type of the galaxy as listed by Kennicutt et al. (2003).

To compare the four samples with one another, we have attempted to minimize as much as possible systematic effects by using quantities that are derived in the same manner in the different samples. For example, the inclinations for the dwarf galaxies are derived using the same intrinsic ratio in both the GBT and XMP samples. The metallicities of many objects in the XMP sample came from publications from our group, ensuring that they are derived in the same way as the metallicities of the GBT sample. In any case, we expect small systematic differences in quantities such as stellar masses and metallicities to be overcome by the wide range of parameter space covered by these samples. Combining the GBT, XMP, Engelbracht and SINGS samples, we end up with a final sample of 151 objects. All data are scaled, when necessary, to a distance based on = 73.0 km s Mpc.

Fig. 3 shows the metallicity histogram of the four samples. Examination of the figure shows that including the comparison samples extend the oxygen abundance range from 7.1 (1/40 solar) to 8.7 (solar), with the XMP and GBT low-mass low-luminosity galaxies covering the low-metallicity range, while the Engelbracht and SINGS higher-mass higher-luminosity galaxies span the high-metallicity range. Extending the metallicity range of the total sample extends the ranges of (from 9 to 23 mag, Fig. 6), and of SFRs (Fig. 9) and sSFRs (Fig. 10).

## 5 Analysis

We now combine the four galaxy samples to explore possible correlations between various quantities.

### 5.1 H i mass-to-optical light ratio as a function of metallicity and absolute magnitude

We study here how the H i gas content depends on the galaxy’s metallicity and luminosity. We first plot in Fig. 4 the (H i)/ ratio against oxygen abundance for the galaxies in the four samples. The figure shows a clear trend of increasing ratios for lower metallicity galaxies. A linear least-square fit to the data, where [O/H] = 12+log O/H, gives:

 log[M(HI)/Lg]=(−0.83±0.08)×[O/H]+(6.47±0.66). (15)

Staveley-Smith, Davies & Kinman (1992) found the (H i)/ ratio to increase with decreasing galaxy luminosity. A linear least-square fit to our data gives (Fig. 5):

 log[M(HI)/Lg]=(−0.30±0.03)×logLg+(2.53±0.29). (16)

The slope -0.30 of this relation is the same as the one obtained by Staveley-Smith et al. (1992), based on a smaller sample of 36 BCDs and low-surface-brightness dwarf galaxies, and spanning only 10 magnitudes in (from 11 to 19 mag) instead of our luminosity range of 14 magnitudes in (from 9 to 23 mag). Our slope is however steeper than the one of 0.2 obtained by Lee et al. (2002). The difference probably arises because of the more restricted luminosity range of the sample of Lee et al. (2002) , spanning only 4 mag in , from 14 to 18 mag.

### 5.2 Metallicity-luminosity and Mass-metallicity relations

Fig.6 shows the well-known metallicity-luminosity relation for galaxies. Our fit (solid line)

 [O/H]=(−0.12±0.01)×Mg+(5.82±0.12) (17)

is in good agreement, within the errors, with the ones obtained for a local dwarf irregular galaxy sample by Skillman et al. (1989) (dot-dashed line), and for a local emission-line galaxy sample by Guseva et al. (2009) (dashed line). We note that four of the lowest-metallicity objects in our total sample, SBS 0335052E, J0113+0052 = UGC 772, I Zw 18 and SBS 0335052W (labeled in Fig. 6) deviate strongly from the above relation, being several magnitudes too bright for their oxygen abundance. These four galaxies are all undergoing strong bursts of star formation which increase significantly their luminosities. Izotov et al. (2011) have shown that all galaxies undergoing strong starbursts also define their own luminosity-metallicity relation. This relation would have about the same slope, but would be shifted by several magnitudes towards higher luminosities. Similarly, Filho et al. (2013) found the metallicity-luminosity relation for their XMP galaxy sample to be shifted towards higher luminosities.

Fig. 7 shows the relation between stellar mass and metallicity. The best fit (solid line) is given by the equation:

 [O/H]=(6.00±0.11)+(0.23±0.01)×logM∗. (18)

where represents the stellar mass in units of solar masses.

For comparison, we have also shown the relations derived by Tremonti et al. (2004) (dashed line) and Lee et al. (2006) (dotted line). It is seen that, in the region of stellar mass overlap (8.6log /M11), the Tremonti et al. (2004) curve is offset towards higher metallicities relative to ours by 0.2-0.7 dex. In this stellar mass range, our fit is mainly defined by the SINGS data points. The oxygen abundances of the SINGS galaxies are determined by Moustakas et al. (2010), using both a theoretical (Kobulnicky & Kewley, 2004) and an empirical (Pilyugin & Thuan, 2005) strong-line abundance calibration. We have adopted here the abundances resulting from the empirical calibration. The shift of the Tremonti et al. (2004) curve is probably due to systematically too high oxygen abundances derived for their SDSS objects. Our fit is slightly flatter than the linear least-square fit [O/H] = (5.650.23) + (0.300.03) obtained by Lee et al. (2006). They are however consistent within 2.

### 5.3 The gas mass fraction as a function of metallicity

In Fig. 8 (left), we plot the distance-independent gas mass fraction (Eq. 11) as a function of the oxygen abundance. It is seen that while the high-metallicity ([O/H] 8.0) SINGS galaxies span the range 00.95, the lower-metallicity GBT objects (with the exception of one galaxy, the BCD J1214+0940 with = 0.27) span the more restricted range 0.650.99, i.e. the vast majority of low-metallicity ([O/H] 7.8) have more than 65% of their baryonic mass in gaseous form. This is consistent with the range 0.3–0.99 found by Bradford et al. (2015) for their sample of 148 isolated low-mass galaxies. As noted by those authors, the lower limit of 0.3 for puts constraints on the internal feedback processes in low-mass and low-metallicity galaxies as they should not remove all of the galaxy’s atomic gas. We note also that in the low-metallicity regime, the GBT sample spans a larger range of gas mass fractions than the XMP sample of Filho et al. (2013): the vast majority of XMP galaxies have 0.85. We have examined J1214+0940 to see if it possesses any particular characteristic that would make it relatively gas-poor, but found none. The median for the GBT sample is 0.94, while the mean is equal to 0.900.15. Our median value is higher than the value = 0.820.13 obtained by Bradford et al. (2015) for their larger SDSS dwarf galaxy sample. Evidently, the low-metallicity selection criterion selects out more gas-rich dwarf galaxies.

In Fig. 8 (right), we have plotted the atomic gas mass against the stellar mass. While our data for the GBT and the 3 comparison samples can be fitted by a single linear least-square fit (solid line), Bradford et al. (2015) obtained for their considerably larger sample of SDSS dwarf and non-dwarf galaxies a fit with a similar slope for non-dwarf galaxies (10 M) and a steeper slope for dwarf galaxies (10 M), with a break in the fit at about 10 M (dashed line). We are not able to see the slope break in our data because of the smaller number of galaxies with 10 M in our sample.

### 5.4 Star formation rate

Fig. 9 (left) and Fig. 9 (right) show respectively the trends of SFR with oxygen abundance and H i mass. It is seen that there is a general correlation of increasing SFR for galaxies with higher metallicities (and hence higher stellar masses) and higher H i masses. However, when the SFR is normalized to the galaxy’s stellar mass, i.e. if we plot the specific sSFR = SFR/ against metallicities (Fig. 10, left) and stellar masses (Fig. 10, right), then the trend is reversed. The galaxies with the lowest metallicities and stellar masses have the highest sSFRs. Similar trends were found by Filho et al. (2013) for their XMP galaxy sample and by Hunt et al. (2015) for a sample of metal-poor BCDs together with other galaxy samples from the literature.

### 5.5 Depletion time scales

We consider here the H i depletion time scale as defined by (yr) = (H i)/SFR. This quantity measures the time left for a galaxy to form stars at the present rate before exhausting its gas supply. Galaxies with less than the Hubble time cannot make stars at the present rate without running out of fuel.

Fig. 11 (left) and Fig. 11 (right) show that there is no dependence of log on either oxygen abundance or M, with a large scatter. This is in agreement with the conclusion of Schiminovich et al. (2010) who find a relatively constant mean = 3.4 Gyr across their GALEX Arecibo SDSS galaxy sample. Hunt et al. (2015) also find a similar mean constant value, also with a large scatter (see also Filho et al., 2016). This mean value is shown by a dashed horizontal line in both panels of Fig. 11. While this line bissects well our data, the scatter about the mean is 1.5 dex on either side of the line. Using interferometric maps of a sample of spiral and dwarf irregular galaxies, Roychowdhury et al. (2015) have also found that the H i depletion time scale shows no strong dependence on metallicity within individual galaxies.

Why does sSFR= SFR/ decrease steeply with increasing (Fig. 10, right) while or, equivalently, the inverse ratio which represents the H i-based star formation efficiency SFE = SFR/(H i) remains relatively constant with (Fig. 11, right)? Schiminovich et al. (2010) interpret this approximate constancy as indicating that external processes or feedback mechanisms controlling the gas supply are important for regulating star formation in massive galaxies. Our results show that these regulation mechanisms operate also in low-mass galaxies. Sánchez Almeida et al. (2014, 2015) have argued, based on observations of metallicity drops shown by localized starburts in XMD galaxies, that accretion flows of external metal-poor gas may be a dominant regulation mechanism.

The majority of the GBT galaxies (77%) have shorter than the Hubble time. This is consistent with the idea that their star formation histories are composed of short bursts lasting 10 yr, interspersed with quiescent periods of 10 yr (Thuan, 2008). This appears also to be the case for the Engelbracht galaxies classified as BCDs. As for the XMP and SINGS galaxies, slightly more than half have shorter than the Hubble time.

### 5.6 Baryonic mass fraction

Fig. 12 shows the plot of the baryonic mass fraction versus the dynamical mass for the GBT and XMP samples. The Engelbracht and SINGS samples do not have readily available dynamical mass data. No correlation is evident in the dynamical mass range beween 10 and 10 M. The baryonic fraction of the GBT and XMP objects varies from 0.05 to 0.80, with a median value of 0.2. This is similar to the results of Bradford et al. (2015) who found for their large dwarf and non-dwarf SDSS galaxy sample a median baryon to dynamical mass ratio of 0.150.18, although this agreement may be somewhat fortuitous as these authors calculate differently from us: they use the H i velocity width at 20% instead of 50% of maximum intensity, and the radius of the H ı component is derived from a statistical relation between H i mass and H i radius. Our value is slightly smaller than the median baryon to dynamical mass ratio (within 3 optical scale lengths) of 0.3 obtained by Lelli, Verheijen & Fraternali (2014), using H i rotation curves derived from interferometric maps. These baryonic mass fractions derived from H i rotation curves are likely more reliable. However, given that our dynamical masses are only approximate estimates from the H i velocity widths, the relatively good agreement implies that our dynamical mass estimates are not too far off.

### 5.7 Chemical Evolution

Knowledge of both the gas mass and the (ionized) gas metallicity allows us to test chemical evolution models of galaxies. In particular, for galaxies that evolve without gas infall or wind outflow, i.e. that can be described by closed box chemical evolution models, it is predicted that the effective stellar yield is a simple function of the metallicity (in units of mass fraction) and the gas mass fraction .

 yeff=Zgasln(1/fgas), (19)

where = 12 (O/H).

Here, we use the oxygen abundance as a proxy for the gas metallicity, and the factor 12 is the conversion from the number ratio O/H to oxygen mass fraction (Garnett, 2002). If the galaxy truly evolves as a closed box, then the effective yield should be equal to the true yield calculated from stellar evolution models. These models give log -2.4 (Dalcanton, 2007).

In Fig. 13 (left), we plot the histograms of for the four samples. The value is shown by the solid vertical line. It is seen that while the line bissects the data, there are many galaxies with inferior to or superior to . Edmunds (1990) has shown that would be lower than if metals have been lost from the galaxy through supernova-driven outflows, or if the current gas in the galaxy has been diluted with inflows of metal-poor gas. But how do we understand objects with effective yields greater than the theoretical yield? As discussed by Filho et al. (2013), this can be accounted for by either an underestimate of the true yield, or an overestimate of the effective yield, or both. For example, the true yield can be underestimated if the stellar Initial Mass Function (IMF) depends on metallicity, for example if the IMF slope flattens with decreasing metallicity (e.g. Bromm & Larson, 2004). A top-heavy IMF would give a higher true yield. However, the spectral energy distributions of low-metallicity star-forming dwarf galaxies are well fitted with an IMF with a Salpeter slope, and do not show evidence for a top-heavy IMF (e.g. Izotov et al., 2011). It is more likely that the effective yields have been overestimated. In calculating it, we have assumed that the metallicity of the neutral gas is equal to that of the ionized gas, an assumption not likely to be true. In fact, we can estimate the ratio of the ionized gas metallicity to that of the neutral gas metallicity as it is roughly equal to the ratio of the effective yield to the true yield (Filho et al., 2013). Fig. 13 (right) shows that, for the majority of the GBT sample, this ratio ranges from about 1 to 20. This is very similar to the range of values found by Thuan, Lecavelier des Etangs & Izotov (2005) in their UV absorption line studies of BCDs. They show that the metallicity of their neutral gas is systematically smaller than that of their ionized gas, by a factor varying between 20 for the higher-metallicity BCDs, and 1.5-2 for the lowest-metallicity BCDs, such as I Zw 18 or SBS 0335052E. This metallicity difference is likely due to the fact that metals produced in the H ii regions have not had time to diffuse out and mix with the H i gas in the outer regions. Thus the H i gas in the envelope of BCDs is relatively metal-free. This is in agreement with the results of Filho et al. (2013) who found the ratio of the metallicity of the ionized to that of the neutral gas to range between 1 and 10 for their XMP objects.

In summary, the distribution of the effective yields on either side of the true yield in Fig. 13 (left) can be understood as gas outflow and/or inflow of unenriched gas in the case of objects with , and a relatively metal-free H i envelope for objects with .

Fig. 13 (right) shows as a function of the baryonic mass of the galaxy. Both dwarf and non-dwarf galaxies display a large scatter on either side of the true yield line (Dalcanton, 2007). There is no evident variation of the effective yield with the baryonic mass of the galaxy. This result appears to be at odds with those obtained Garnett (2002) and Tremonti et al. (2004). Analyzing a sample of 40 nearby spiral and irregular galaxies, Garnett (2002) found to be constant for galaxies with rotational velocities larger than 100 km s, but to decrease by a factor of 10-20 below that threshold. Tremonti et al. (2004), using the spectroscopic data base of 53,000 SDSS star-forming galaxies at 0.1, and using indirect estimates of the gas mass based on the H luminosity, also found that decreases with decreasing baryonic galaxy mass. Both sets of authors attribute the decrease of the effective yield at low galaxy masses to galactic winds removing metals more efficiently from the shallower potential wells of dwarf galaxies (see also Silich & Tenorio-Tagle, 2001). However, Sánchez Almeida et al. (2014, 2015) have argued that the low metallicities of the XMD galaxies are an indicator of infall of pristine gas. This process would increase the effective yield of low-mass galaxies as compared to more massive galaxies. The real situation is likely described by both gas outflow and infall, so that the effective yields of the GBT dwarf galaxies do not decrease significantly as compared to the effective yields of more massive galaxies (like the SINGS galaxies).

## 6 Summary and Conclusions

New H i observations with the Green Bank Telescope (GBT) are presented for a sample of 29 extremely metal-deficient star-forming Blue Compact Dwarf (BCD) galaxies. The BCDs were selected from the spectal database of Data Release 7 of the Sloan Digital Sky Survey (SDSS) to have a well detected [Oiii]4363 line (for direct abundance determination) and an oxygen abundance 12 + log O/H 7.6. Neutral hydrogen was detected in 28 galaxies, a 97% detection rate. For each galaxy, we have derived ancillary data from the SDSS optical spectrum such as oxygen abundance, star formation rate, and stellar mass.

Because of the narrow metallicity range of the GBT sample (the lower limit of 12 + log O/H is 7.35), we have also added published H i and optical data for three complementary galaxy samples to extend the metallicity and mass range and study statistically how the H i content of a galaxy varies with various global galaxian properties. We have found the following:

1) The lowest-luminosity lowest-metallicity galaxies have the largest neutral hydrogen mass to light ratios, following the relation (H i)/ , in good agreement with the dependence found in previous studies of galaxy samples with a smaller luminosity range. Our derived mass-metallicity relation is also in good agreement with those derived by other authors.

2) Metal-deficient low-mass dwarf galaxies are gas-rich. The median gas mass fraction of the GBT sample is 0.94, while its mean gas mass fraction is 0.900.15. The vast majority of the GBT galaxies have more than 65% of their baryonic mass in gaseous form. The existence of a lower limit, also found for larger dwarf samples, puts stringent constraints on feedback mechanisms in low-mass galaxies as they should not remove all of the galaxy’s atomic gas.

3) The H i depletion time is independent of metallicity or stellar mass. Although there is a large scatter about the median value of 3.4 Gyr, the relative constancy of the gas depletion time implies that external processes or feedback mechanisms that control the gas supply are important for regulating star formation in both low- and high-mass galaxies.

4) The ratio of the baryonic mass to the dynamical mass varies over a wide range, from 0.05 to 0.80, with a median value of 0.2 and no dependence on the dynamical mass.

5) About 35% of the GBT galaxies have an effective yield less than the true yield, which can be understood as the result of the loss of metals due to supernova-driven outflows, and/or the consequence of dilution by inflows of metal-poor gas. However, the remaining 65% show an effective yield larger than the true yield. This can be understood if the metallicity of the neutral gas is lower than the metallicity of the ionized gas by a factor 1.5–20, as UV absorption studies of BCDs also show.

## 7 Acknowledgements

T.X.T. thanks the support of NASA grant GO4-15084X. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. This research made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA.

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