title: CO observations toward HI-rich Ultra Diffuse Galaxies
authors: Junzhi Wang Kai Yang Zhi-Yu Zhang Min Fang Yong Shi Shu Liu Juan Li Fei Li
text: 
  
  firstpage–lastpage
  Statistical inference for principal components of spiked covariance matrices
      Ke Wangt2[label=e2]kewang@ust.hk
      Aug. 2020
  ============================================================================
  
  
  
  
  
  We present CO observations toward a sample of six -rich Ultra-diffuse
  galaxies (UDGs)  as well as one UDG (VLSB-A) in the Virgo Cluster  with the IRAM 30-m telescope.  CO J=1-0 is marginally
  detected at 4 σ level in AGC122966, as the first detection of CO
  emission in UDGs. We estimate upper limits of molecular mass in other 
  galaxies from the non-detection of CO lines.  These upper limits and the 
  marginal  CO detection in AGC122966 indicate low mass ratios between molecular and 
  atomic gas masses. With the star formation efficiency derived from the molecular
  gas,  we suggest that  the inefficiency of star formation in such
  -rich UDGs is likely caused by the low efficiency in converting molecules from
  atomic gas, instead of low efficiency in forming stars from molecular gas.  
  
  
  
  
  
  galaxies: ISM; galaxies: star formation
  
  
  
  
  
  
  
  
  
  § INTRODUCTION
  
  
  Ultra-diffuse galaxies (UDGs) are extremely low surface brightness galaxies at
  the optical and near-IR wavelengths <cit.>. They have drawn much
  attention from both observers and theorists since the
  discovery of  47 UDGs in the Coma cluster  <cit.>.
  Observations of UDGs  mainly focused on optical and near-IR studies
  <cit.>, which
  show that the stellar components are much less than those in normal galaxies.
  A sub-set of  UDGs, which have high   to stellar mass ratio and  
  were normally found outside galaxy clusters, have been discovered in observations with large single dish radio telescopes, such as Arecibo,
  Effelsberg and GBT
  <cit.>. 
  High angular resolution observations with radio interferometers
  <cit.>
  showed that   emission are more extended than the stellar components traced
  by optical images. The line widths (FWHM) of  detected by single dishes
  <cit.>  and
  interferometers
  <cit.>  in such
  galaxies are only about or even less than 100 km s^-1. Such small
  linewidths led difficulties for determining dynamical mass of whole galaxy with
  large uncertainty of inclination angle. 
  
  With extremely high ratios of gas to stellar mass and with low stellar mass
  <cit.>, such -rich UDGs  should
  have inefficient star formation, low star formation rate (SFR), and low star
  formation efficiency (SFE) across cosmic time. -rich  UDGs with a size of
  the Milky Way may be “failed" L_⋆ galaxies or “failed" smaller
  galaxies, depending on the estimated halo mass  <cit.>.
  
  There are two major steps to form stars from    gas: atomic gas converts 
  to molecular gas, and molecular gas form stars. So, molecular to atomic gas
  fraction is a key parameter to understand the inefficient star formation in
  such galaxies. However, the lack of molecular gas information of such galaxies prohibits further distinction about 
  which step is more crucial for the 
  inefficient star formation in the history. Therefore, CO observations toward a sample of -rich
  local UDGs would help answer such questions:  
  The inefficient star formation in such UDGs is caused by   difficulties of forming
  molecular gas from atomic gas, or failed star formation from molecular gas?
  
  Although there have been several   CO observations with few detections   <cit.> 
    toward   rich Low Surface Brightness Galaxies (LSBGs), which have quite high gas to star mass ratios, there is still no report on CO observations toward UDGs in the literature, up to now.
  
  In this letter, we describe CO line observations and data reduction of a small
  sample of UDGs with the IRAM 30-m telescope in 2, present the main results
  and discussions in 3, and make the brief summary and future prospects in 4.
  
  
  
  
  
  
  
  
  § OBSERVATIONS AND DATA REDUCTION
  
  
   We select six -rich UDGs from the literature <cit.> to perform CO line
  observations,
  because they have enough gas materials to form stars.  The sample includes
  three Milky-Way-sized ones with   mass ≥10^9M_⊙, three dwarf
  galaxies with   mass < 2.5×10^8M_⊙ (see Table 1), and
  VLSB-A, which is one of the three UDGs in the Virgo Cluster with velocity
  measured through optical spectra toward the nucleus
  <cit.>. 
  
  
  The
  observations were carried out from July 31 to August 3, 2018  with  the IRAM 30-m
  millimeter telescope at Pico Veleta, Spain[Based on observations
  carried out with the IRAM 30m Telescope.  IRAM is supported by INSU/CNRS
  (France), MPG (Germany) and IGN (Spain).].  The Eight MIxer Receiver (EMIR)
  with dual polarizations, FTS backend, and  standard wobbler switching mode with
  ±120” offset at 0.5 Hz beam throw, were used. Focus calibrations were done at the
  beginning of the observations and during sunset or sunrise, toward planets or
  strong millimeter quasars. Pointing calibrations were done every 2 hours using nearby
  quasars.  CO 1-0 at E0 band and CO 2-1 at E2 band were covered simultaneously
  our observations. The observing frequency of CO 1-0 varies from ∼112.35 GHz with typical system temperature of 150K  in SECCO-dI-1 to ∼115.273 GHz with  typical system temperature of 300K  in VLSB-A.  The  system temperature also varies with different weather conditions and elevations of telescope. 
  One the other hand, CO 2-1 observations are from ∼ 224.7 GHz to 230.5 GHz, while the typical system temperature is about 500K and strongly depends on   weather conditions and elevations of telescope.
  
    The pointing center of each source is listed in Table
  1. The optical images of these sources  from the PTF (the Palomar
  Transient Factory) <cit.>  or
  the ZTF (the Zwicky Transient Facility) <cit.> are
  presented in Figure 1 and 2.
  
  The data were dumped every 1.7 minutes as one scan, and calibration was done
  every 6 scans. The beam sizes of the IRAM 30-m telescope are about 22” for
  CO 1-0 and 11” for CO 2-1, respectively.  The conversion from  T_
  A^*  to T_ mb is: T_ mb=T_ A^*F_ eff/B_ eff,
  where F_ eff=95% and B_ eff=81%  for CO 1-0, while  F_
  eff=92% and B_ eff=59%  for CO 2-1.
  
  
  
  
  
  
  The CLASS package of GILDAS[http://www.iram.fr/IRAMFR/GILDAS] was used
  for data reduction.  The effective on-source time and the noise level for each
  source are listed in Table 2. First order baseline fitting was done for each
  spectrum with 1.7 minutes integration time.  Then we smoothed and resampled
  each spectrum to ∼ 10 km s^-1, before averaging all spectra of
  each target (Fig. 1) with a weighting of 1/T_ sys^2.  For each target,
  we calculated the standard deviation of each channel across all spectra.  This
  gives a channel based noise, which is pretty flat for all sources and 
  is consistent with  the rms value  from the final spectrum  obtained with standard method using   class
  task `average' f in each source. Even though the rms noise increases with the increasing of the frequency at 3mm band due to the O_2 line in the earth's atmosphere, it is almost the same within ±500 km s^-1 for the observed CO 1-0 line.
  
   The noise level (σ) in T_ mb for each source
  is listed in Table 2 are obtained from the averaged spectrum at the original frequency
  resolution (0.195 MHz),  with line free channels using CLASS task `base' with first order polynomial. The upper limits of flux are calculated with
  3σ×√(δv×ΔV), where σ is the rms noise from
  the final spectrum for each source with 0.195 MHz resolution,  δv is
  the velocity resolution corresponding to 0.195 MHz (∼0.5 km s^-1), and
  ΔV is 50 km s^-1, as the assumed line width.  For most of the sources,
  since the observations were done in summer time, CO 1-0 data were much better
  than CO 2-1 due to weather conditions. Thus, CO 1-0, instead of CO 2-1 data,
  are used for estimation of the upper limits.  
  
  
  
  
  
  
  
  
  
  
  § RESULTS AND DISCUSSION
  
  
  
  CO 1-0 emission is marginally detected in AGC122966 at 4 σ level
  with velocity integrated flux of 0.23±0.057 K km s^-1 in T_mb (see
  Figure 1), while only upper limits at can be estimated in  other sources. The
  velocity range of CO 1-0 emission in AGC122966 is from about +50 to +150
  km s^-1, relative to the systematic velocity obtained from the  21-cm
  emission. 
  
  
  The CO 2-1 line of AGC122966, which was obtained simultaneously, was not
  detected at 3σ.  The non-detection of CO 2-1 may caused by the high
  system temperature at the 1.3 mm band. Further more, CO 2-1 has smaller beam
  size, which is only 25% of the CO 1-0 beam coverage. So, if the CO emission is
  clumpy and located off the pointing center of this observation, it is possible
  that CO clump is not fully covered by the CO 2-1 beam.  To present the
  difference of the beam sizes, we overlay the beams on the stacked R-band images
  of AGC122966, which are from the intermediate Palomar Transient Factor (PTF)
  survey, and show it in Figure 1.  
  
  
  The  velocity  integrated luminosity of CO 1-0 (L_CO) in AGC122966 is
  2.2±0.54 K km s^-1 pc^-2,  using the formula
  π/4ln2θ_mb^2 I × D_L^2×(1+z)^-3
  <cit.>,  where
  θ_mb=22” is the main beam size of the observation, I is the
  velocity integrated flux in  T_ mb, D_ L is the luminosity
  distance of the galaxy, and z is the redshift. The  CO 1-0 emission is
  out of   velocity range <cit.>
  within ±45 km s^-1. The marginal detection of CO 1-0 might not be real
   because of the different velocity ranges of   and CO 1-0.  However, even though no related   21-cm line emission at the same velocity range  as that of the  CO 1-0 peak are reported, weak   21-cm below the detection limit in the literature are still possible, which means that the CO 1-0 detection
  can still be real. Last, even if the 3σ upper limit of CO 1-0 is
  adopted to estimate molecular gas mass of AGC122966, instead of using the
  detection, the main result is still  similar to considering this feature
  as detection.  
   
  
  The metallicity in UDGs is difficult to be measured due to weak optical
  emission. Only SECCO-dI-2  and UGC 2162 have such measurements in the
  literature, which gave low metallicities of 8.2±0.2 of  12+log(O/H) for
  SECCO-dI-2 <cit.> and 8.22±0.07 of 12+log(O/H)  for
  UGC 2162 <cit.>, respectively.   SECCO-dI-2 and
  UGC 2162 do not follow the mass-metallicity relation in galaxies
  <cit.>, which gave the metallicity of ∼7.6 for
  12+log(O/H) for galaxies with similar mass to SECCO-dI-2 as
  M_∗=0.9×10^7M_⊙ <cit.> or  UGC 2162 as
  M_∗=2.0×10^7M_⊙  <cit.>. A tentative
  evidence that the gas-phase metallicities in  diffuse systems are high for
  their stellar mass had been found in two UDGs <cit.>.
  With limited information of metallicity  measurement toward these UDGs, we
  would like to assume similar metallicity to  that of SECCO-dI-2  in these UDGs
  in our discussion.
  
  For galaxies with a metallicity of 8.2±0.2,  the conversion factor
  (α_CO), which converts from CO luminosity to molecular mass, should be
  higher than that in the Milky Way, base on the relation of metallicity and
  α_CO <cit.>.  α_CO
  (8.6M_⊙/K km s^-1pc^2 ),  with twice of that in the Milly Way
   as a reasonable value for such metallicity, is adopted (see Table 2).
  The molecular gas mass in AGC122966 is then estimated to be
  1.9±0.46×10^8M_⊙,  if the emission feature is real. The
  H_2/   mass ratio is 0.19±0.05, while it ranges from ∼0.03 to 3
  in a large sample of galaxies <cit.>. 
  
   
   
   
   
  Using the same method as for AGC122966, the non-detection of CO emission in
  most of these -rich UDGs can give 3σ upper limits of
  molecular gas mass, assuming a line width of 50 km s^-1 in each
  galaxy.  Upper limits of H_2/  mass ratios for each galaxy can also be
  estimated (see Table 2), which are from 0.012  in UGC 2162 to 0.083 in
  SECCO-dI-1.  The upper limit of molecular gas mass is also estimated for AGC
  122966 if that emission feature is not real. The 3 σ upper limit of CO
  1-0 in AGC 122966 is about 1/4 of the flux of that feature, not only because
  that feature is only 4σ, but also because the line width of that feature
  is more than 50 km s^-1.  
  Note that the pointing centers of our observations are  with about 15” and 9”  offsets    from the optical centers in AGC 334315 and ComaP (see Figure 2.), respectively.
   The offset for AGC 334315 is about  70%  beamsize of  CO 1-0, while it is about 40% for  ComaP.  Most of the emission at optical band in ComaP can be covered with the beam of CO 1-0 observation. However, only 1/3 to 1/2 of the optical emission region in AGC 334315   can be covered by CO 1-0 beam. Such offset can cause underestimation of CO  upper limit in these two galaxies,  which  can further cause about a factor of 2 in ComaP    or  3 in AGC 334315  underestimation of H_2/HI ratio and overestimation of SFR/M_H_2.
  
  
   The ratio of molecular mass and stellar mass, M_H_2/M_∗, in each
  galaxy, is also derived and listed in Table 2. The upper limits of this ratio
  range from 0.12 to 10, while this ratio ranges from ∼0.01 in massive
  galaxies with M_∗∼10^11.5M_⊙ to  ∼1 in low mass end with
  M_∗∼10^8.5M_⊙, decreasing with  M_∗ at the massive end 
  and flatten at the low mass end with large scatter
  <cit.>. No clear difference of M_H_2/M_∗ between
  -rich UDGs to normal galaxies  can be justified with current results. On the
  other hand,  the ratios of M_ HI/M_∗ in these HI-rich UDGs, range
  from 8.3 to 120, are much higher than that in normal galaxies ranging from
  ∼0.01 at massive part to almost ten in the low mass end
  <cit.>. 
   
  
  
  
  The low H_2/  mass ratios, i.e., the lack of molecular gas,  in these
  -rich UDGs,  all of which are less than 0.1 (see Table 2), might be the main
  reason of inefficient star formation,  while such ratio in normal galaxies are from ∼0.03 to ∼3 with a median value of ∼0.3 <cit.>.  If only the molecular gas
  was used for calculating  SFE   (SFR/M_H_2), such value will not be
  significantly lower than that in nearby spirals as
  (5.25±2.5)×10^-10yr^-1  <cit.>. The SFR
  in AGC122966, the one with tentative CO 1-0 detection,  is 0.022 M_⊙ yr^-1
  <cit.>,  which gives an SFE of 
  1.3×10^-10yr^-1.  On the other hand, with an SFR of 0.045
  M_⊙ yr^-1 <cit.> and a non-detection of CO 1-0
  in AGC 334315, the derived SFE with molecular gas is greater than 12.1
  ×10^-10yr^-1, which is much higher than that in nearby spirals.
  Therefore, we suggest that the inefficient star formation in such galaxies
  is mainly due to the low efficiency of forming molecules from atomic gas, instead
  of forming stars from molecular clouds. 
  
   With limited information of metallicity in these UDGs,  the adopted
  α_CO may be lower than the real value, which would underestimate
  molecular gas mass. In this case, low SFE for molecular gas can not be the only
  explanation of inefficient star formation in such -rich UDGs.
  Deep CO observations toward UDGs with ALMA,  as well as  metallicity
  measurement with deep optical spectroscopic observations, will help us to
  derive molecular gas mass and determine the reason of inefficient star
  formation. 
  
  
  
  
  
  Since molecular gas and stellar masses are much less than the atomic mass in
  such galaxies, the baryonic mass can be estimated with only , to derive the
  dynamical-to-baryonic mass ratios.  As discussed in the literature
  <cit.>, the total masses estimated
  with dynamics are not massive enough, such -rich UDGs should not be failed
  L_⋆  spiral galaxies, even though some of them have  and optical
  sizes similar to those of L_⋆  spiral galaxies. 
  
  The properties of such galaxies, such as high halo spin parameters
  <cit.>, may bring down the efficiency of forming molecules
  from atomic gas.  AGC122966, with marginal detection of CO 1-0 emission, is the
  galaxy with lowest M_HI/M_* ratio (see Table 1) among the 6 -rich
  UDGs.  The relatively high H_2/ ratio in AGC122966 may cause higher star
  formation rate than other -rich UDGs in the past and nowadays, which can
  further explain the relatively low M_HI/M_* ratio in AGC122966. 
  Or, if that emission feature is not real, AGC122966 will be similar to
  other UDGs. Further confirmation of CO emission in AGC122966 with millimeter
  interferometers, such as ALMA or NOEMA, is necessary to make a conclusion.
  
  
  
  
  
  
  § SUMMARY AND FUTURE PROSPECTS
  
  
  As the first survey observations of CO 1-0 and 2-1 toward a sample of -rich
  UDGs with the IRAM 30-m telescope, we  marginally detected CO 1-0 in one
  galaxy (AGC122966) at 4σ level. The non-detection of CO lines in other
  sources provides good upper limits of molecular masses, which help 
  estimate upper limits of molecular gas mass. We find low ratios of molecular to
  atomic mass, which indicate that the inefficient star formation in such -rich
  UDGs should mainly be caused by the difficulty of forming molecules from atomic
  gas, while the star formation efficiency derived for molecular gas is not
  significantly lower than normal spirals. An alternative possibility is
  that CO lines are no longer good tracers of molecular gas in UDGs,  because the metallicity might be lower than assumed.
  
  Further large-sample high-sensitivity CO observations with ALMA can better
  derive molecular mass in such galaxies and can better provide the molecular to
  atomic mass ratios.  ALMA observations can also provide the spatial
  distribution of molecular gas, which can be used to compare with star formation
  informations using further optical emission line observations.  
  
  
  
  
  
  
  
  
  
  
  
  § ACKNOWLEDGEMENTS
  
  
  We thank the referee, Dr.  U. Lisenfeld,  for helpful suggestions to improve the manuscript.  
  This work is supported by  National Key Basic Research and Development Program
  of China (grant No. 2017YFA0402704) and the National Natural Science Foundation
  of China grant 11590783, and U1731237.  This study is based on observations
  carried out under project number 068-15 with the IRAM 30-m telescope. IRAM is
  supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). This work also
  benefited from the International Space Science Institute (ISSI/ISSI-BJ) in Bern
  and Beijing, thanks to the funding of the team “Chemical abundances in the
  ISM: the litmus test of stellar IMF variations in galaxies across cosmic time"
  (Principal Investigator D.R. and Z-Y.Z.). J.W. thanks Dr. Yu Lu for helpful
  discussion about UDGs.
  
  
  
  
  § DATA AVAILABILITY
  
  The original CO  data observed with IRAM 30 meter  can be accessed by IRAM archive system at https://www.iram-institute.org/EN/content-page-386-7-386-0-0-0.html, while optical images can be obtained from PTF and  ZTF archive system. If anyone is interested in the  reduced  data presented in this paper, please contact  Junzhi Wang at jzwang@shao.ac.cn. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
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