A survey of low-z weak absorbers

COS-Weak: Probing the CGM using analogs of weak Mg ii absorbers at

Abstract

We present a sample of 34 weak metal line absorbers at complied via the simultaneous detections () of the Si ii and C ii absorption lines, with  Å and  Å, in archival Hubble Space Telescope Cosmic Origins Spectrograph (COS) spectra. Our sample increases the number of known low- “weak absorbers” by a factor of . The column densities of H i and low-ionization metal lines obtained from Voigt profile fitting are used to build simple photoionization models using cloudy. The inferred densities and total hydrogen column densities are in the ranges of and , respectively. The line of sight thicknesses of the absorbers have a wide range of 1 pc – 50 kpc with a median value of  500 pc. The high-ionization O vi absorption, detected in 12/18 cases, always stems from a different gas-phase. Most importantly, 85% (50%) of these absorbers show a metallicity of . The fraction of systems showing high metallicity (i.e., ) in our sample is significantly higher than the H i-selected sample (i.e., Wotta et al., 2016) and the galaxy-selected sample (i.e., Prochaska et al., 2017) of absorbers probing the circum-galactic medium (CGM) at similar redshift. A search for galaxies has revealed a significant galaxy-overdensity around these weak absorbers compared to random places with a median impact parameter of 166 kpc to the nearest galaxy. Moreover, we find the presence of multiple galaxies in % of the cases, suggesting group environments. The observed of indicates that such metal-enriched, compact, dense structures are ubiquitous in the halos of low- galaxies that are in groups. We suggest that these are transient structures that are related to outflows and/or stripping of metal-rich gas from galaxies.

keywords:
galaxies: formation – galaxies: haloes – quasar: absorption line
12

1 Introduction

Metal absorption lines detected in quasar spectra are thought to arise from the circum-galactic medium (CGM) of intervening galaxies close to the lines of sight (e.g., Bergeron, 1986; Bergeron & Boissé, 1991; Steidel & Sargent, 1992; Adelberger et al., 2005; Kacprzak et al., 2008, 2015; Chen & Mulchaey, 2009; Steidel et al., 2010; Stocke et al., 2013; Werk et al., 2013; Bordoloi et al., 2014; Turner et al., 2014; Johnson et al., 2015; Keeney et al., 2017). The absorption strength of a metal line depends primarily on the metallicity and on the ionization parameter of the absorbing gas. The metallicity of an absorber is an important diagnostic of the physical processes at play. For example, high metallicity gas is likely to observe in galactic outflows (Tripp et al., 2011; Muzahid, 2014; Muzahid et al., 2015b), whereas the gas infalling from the inter-galactic medium (IGM) on to a galaxy halo is expected to be metal-poor (Ribaudo et al., 2011; Churchill et al., 2012; Kacprzak et al., 2012a). The ionization parameter, usually determined from the ratio of two consecutive ionic states of the same element, provides the density of the absorbing gas, provided the intensity of the incident radiation is known. It is generally assumed that the extra-galactic ultraviolet (UV) background radiation (UVB; Haardt & Madau, 1996, 2012; Khaire & Srianand, 2015a) prevails in the CGM of a galaxy at impact parameters greater than several tens of kpc (Werk et al., 2014; Narayanan et al., 2010). The relative abundances of heavy elements in an absorption system provide important clues regarding the star formation history and the initial mass function of the host-galaxy Pettini et al. (1999, 2002); Becker et al. (2012); Zahedy et al. (2017). Metal lines are, thus, essential for determining the physical conditions of the otherwise invisible, diffuse gas in the CGM and for inferring the physical processes that determine the evolution of a galaxy.

The rest-frame wavelengths of the Mg ii 2796,2803 doublet transitions are such that it is easily observable using ground based optical telescopes for a wide redshift range (). Consequently, Mg ii absorbers have been studied for the last couple of decades by a significant number of authors (e.g., Lanzetta et al., 1987; Petitjean & Bergeron, 1990; Steidel & Sargent, 1992; Charlton & Churchill, 1998; Churchill et al., 1999, 2003; Rigby et al., 2002; Nestor et al., 2005; Kacprzak et al., 2008; Chen et al., 2010; Zhu & Ménard, 2013; Nielsen et al., 2013a, b; Joshi et al., 2017; Dutta et al., 2017, and references therein). In addition, recent infrared surveys have identified Mg ii absorbers all the way up to (Matejek & Simcoe, 2012; Chen et al., 2016; Bosman et al., 2017; Codoreanu et al., 2017). In all these studies, Mg ii absorbers are found to probe a wide variety of astrophysical environments. Based on the rest-frame equivalent width of the 2796 transition () Mg ii absorbers are historically classified into weak (0.3 Å) and strong (0.3 Å) groups. The strong absorbers are sometimes categorized into very strong (1 Å) and ultrastrong (3 Å) systems (Nestor et al., 2005; Nestor et al., 2007). The very strong/ultrastrong Mg ii absorbers are generally found to be associated with luminous galaxies (). They often show velocities spread over several hundreds of km s and hence are thought to be related to galactic superwind driven by supernova and/or starburst (e.g., Bond et al., 2001; Prochter et al., 2006; Zibetti et al., 2007, but see Gauthier (2013) for an alternate scenario).

In a detailed study of the Mg ii absorbing CGM, Nielsen et al. (2013b) have found a covering fraction () of 60–100% (15–40%) for systems with 0.1 Å (1.0 Å) out to 100 kpc. The does not change significantly with the host-galaxy’s color and/or luminosity (see also Werk et al., 2013). However, a bimodality in the azimuthal angle distribution of Mg ii absorbing galaxies has been reported in the literature, such that the gas is preferentially detected near the projected major and minor axes of star-forming galaxies (Kacprzak et al., 2012b; Bouché et al., 2012). Galaxies with little star-formation do not show any such preference. The observed bimodality is thought to be driven by gas accreted along the major axis and outflowing along the minor axis.

The weak absorbers with  Å, that are distinct from the strong population in several aspects (e.g. Rigby et al., 2002), are of particular interest in this paper. The first systematic survey of weak Mg ii absorbers was conducted by Churchill et al. (1999) in the redshift range using HIRES/Keck spectra. They found that the number of weak absorbers per unit redshift of is 4 times higher than that of the Lyman Limit Systems (LLSs) which have neutral hydrogen column density  cm. Therefore it is suggested that a vast majority of the weak Mg ii absorbers must arise in sub-LLS environments. The evolution of the for the weak absorbers shows a peak at (Narayanan et al., 2005, 2007) which was thought to be connected with the evolution of the cosmic star-formation rate density of dwarf galaxies (see also Fig. 9 of Mathes et al., 2017). However, in a recent survey, Codoreanu et al. (2017) have found that the of for the weak absorbers with  Å at , increases to by (see also Bosman et al., 2017). The number of weak absorbers exceeds the number expected from an exponential fit to strong systems with  Å. The at these high redshifts, however, is consistent with cosmological evolution of the population, suggesting that the processes responsible for weak absorbers are already in place within the first 1 Gyr of cosmic history. One of the most intriguing properties of the weak absorbers is that, in most cases, they exhibit near-solar to super-solar metallicities (Rigby et al., 2002; Lynch & Charlton, 2007; Misawa et al., 2008; Narayanan et al., 2008) in spite of the fact that luminous galaxies are rarely found within a 50 kpc impact parameter (Churchill et al., 2005; Milutinović et al., 2006). Studying weak absorbers at low- () is advantageous since it is relatively easy to search for the host-galaxies.

Because of the atmospheric cutoff of optical light, a direct search for the Mg ii doublet at is not viable. Instead, Narayanan et al. (2005), for the first time, used weak Si ii 1260 ( Å) and C ii  ( Å) lines as proxies for the weak Mg ii absorbers. Both and are -process elements. The creation and destruction ionization potentials of Si ii (i.e., 8.1 and 16.3 eV, respectively) are very similar to Mg ii (i.e., 7.6 and 15.0 eV, respectively). The abundance of Si in the solar neighborhood (i.e., ) is also very similar to that of Mg, i.e., (Asplund et al., 2009). All these facts indicate that Si ii and Mg ii arise from the same gas phase and Si ii is a good proxy for Mg ii (see also Narayanan et al., 2005; Herenz et al., 2013).

Narayanan et al. (2005) searched for weak Si ii 1260 and C ii  absorbers in high resolution STIS Echelle spectra of 25 quasars. They found only six weak Mg ii analog absorbers over a redshift pathlength of . Their estimated of is consistent with cosmological evolution of the population. By considering the effect of the change in the UVB on an otherwise static absorbing gas, their photoionization models suggested that the low- weak Mg ii population is likely composed of both kiloparsec-scale, low density structures that only gave rise to C iv absorption at and parsec-scale, higher density structures that produced weak Mg ii absorption at . This was the only known systematic search for weak absorbers at low- that exists in the literature.

In this paper we have studied weak Mg ii absorber analogs detected in COS spectra via the Si ii 1260 and C ii  transitions. With 34 absorbers in total, here we present the first-ever statistically significant sample of weak absorbers at low-. The paper is organized as follows: In Section 2 we provide the details of the observations, data reduction, absorber search techniques, and absorption line measurements. In Section 3 we present our analysis which includes estimating , measuring H i and ionic column densities, and building photoionization models. The main results based on the ionization models are presented in Section 4. In Section 5 we discuss our main results, followed by a summary in Section 6. Throughout this study we adopt a flat CDM cosmology with  km s , , , and . Abundances of heavy elements are given in the notation with solar relative abundances taken from Asplund et al. (2009). All the distances given are in physical units.

2 Data

2.1 Observations and data reduction

We have searched for weak Mg ii analogs in 363 medium resolution, far-UV (FUV) spectra of active galactic nuclei (AGN)/quasars (QSOs) observed with the Hubble Space TelescopeCosmic Origins Spectrograph (COS). These spectra were available in the public archive before February, 2016. Note that all these spectra were obtained under programs prior to the Cycle-22. The properties of COS and its in-flight operations are discussed in Osterman et al. (2011) and Green et al. (2012). We have used only spectra that were obtained with the medium resolution () FUV COS gratings (i.e. G130M and/or G160M). The data were retrieved from the archive and reduced using calcos pipeline software. The pipeline reduced data (’’ files) were flux calibrated. The individual exposures were aligned and co-added using the idl code (’’), developed by Danforth et al. (2010) and subsequently improved by Keeney et al. (2012) and Danforth et al. (2016), in order to increase the spectral signal-to-noise ratio (). The final co-added spectra typically have spectral coverage of  1150–1450 Å for the G130M grating and  1450–1800 Å for the G160M grating. Since these archival spectra come from various different observing programs, they show a wide range in (i.e., 2–60 per resolution element). In our analysis, we do not include 67 spectra that show per resolution element over most of it spectral coverage. The details of the remaining 296 spectra used in this study are given in Table 1. There are 174 spectra with data from both the G130M and G160M gratings, 114 spectra with only G130M grating data, and 8 spectra with only G160M grating data. The median of the 288 G130M grating spectra is 9 per resolution element. The median of the 182 G160M grating spectra is 7 per resolution element. In Table 2 we list the 67 spectra that are available in the archive but are not used in this study due to poor (i.e. per resolution element). The COS FUV spectra are highly oversampled with 6 raw pixels per resolution element. We, thus, binned the spectra by three pixels. All our measurements and analyses are performed on the binned data. We note that while the binning improves per pixel by a factor of , it does not affect the absorption line measurements (i.e. and ). For each spectrum continuum normalization was done by fitting the line-free regions with smooth low-order polynomials.

[t]

Table 1: List of 34 weak Mg ii analogs.
QSO RA Dec Gratings (mÅ) Flag PID
(J2000) (J2000) (G130M) (G160M) Ly C ii Si ii
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
PG0003+158 1.49683 16.16361 0.451 0.16512 3 15 9 6963 55 5 22 4 1 12038
Q0107-025A 17.55475 -2.33136 0.960 0.22722 3 10 12 69619 8720 11113 1 11585
HE0153-4520 28.80500 -45.10333 0.451 0.22597 3 20 13 6284 1527 735 1 11541
3C57 30.48817 -11.54253 0.670 0.32338 3 17 10 6365 18316 7812 1 12038
SDSSJ0212-0737 33.07633 -7.62217 0.174 0.01603 3 7 4 101626 24417 16122 0 12248
SDSSJ0212-0737 33.07633 -7.62217 0.174 0.13422 3 7 4 44914 8916 675 0 12248
UKS-0242-724 40.79000 -72.28011 0.102 0.06376 3 11 8 8868 1129 1135 1 12263
Q0349-146 57.86900 -14.48556 0.616 0.07256 3 10 6 11558 10815 13611 0 13398
PKS0405-123 61.95180 -12.19344 0.573 0.16710 3 50 22 9042 2334 1553 1 11508/11541
IRAS-F04250-5718 66.50321 -57.20031 0.104 0.00369 3 40 22 4882 461 252 1 11686/11692
FBQS-0751+2919 117.80129 29.32733 0.916 0.20399 3 23 23 7025 1989 1044 1 11741
VV2006J0808+0514 122.16187 5.24444 0.360 0.02930 1 5 74117 20618 17719 0 12603
PG0832+251 128.89917 24.99472 0.329 0.02811 3 7 8 3449 467 7210 1 12025
SDSSJ0929+4644 142.29080 46.74000 0.240 0.06498 3 11 6 2428 438 408 0 12248
PMNJ1103-2329 165.90667 -23.49167 0.186 0.08352 3 9 6 91712 1108 679 1 12025
PG1116+215 169.78583 21.32167 0.176 0.13850 3 25 18 5124 824 611 1 12038
SDSSJ1122+5755 170.68704 57.92861 0.906 0.05319 3 5 4 34628 6120 6115 0 12248
PG1121+422 171.16324 42.02917 0.225 0.19238 3 11 7 70522 13613 1055 1 12024
3C263 174.98746 65.79700 0.646 0.06350 3 23 17 9855 596 273 1 11541
PG1202+281 181.17599 27.90331 0.165 0.13988 3 4 6 75715 7615 5610 0 12248
PG-1206+459 182.24171 45.67653 1.163 0.21439 3 16 17 5972 16012 1195 1 11741
SDSSJ1210+3157 182.65650 31.95167 0.389 0.05974 3 5 5 56724 12810 14526 0 12248
SDSSJ1210+3157 182.65650 31.95167 0.389 0.14964 3 5 5 67420 21324 10815 0 12248
SDSSJ1214+0825 183.62729 8.41892 0.585 0.07407 1 5 62821 14319 10713 1 11698
RXJ1230.8+0115 187.70834 1.25597 0.117 0.00575 3 30 19 5992 852 552 1 11686
PKS1302-102 196.38750 -10.55528 0.278 0.09495 3 18 11 7035 706 546 1 12038
SDSSJ1322+4645 200.59450 46.75978 0.374 0.21451 3 5 4 105220 27371 19232 0 11598
SDSSJ1357+1704 209.30254 17.07892 0.150 0.09784 3 10 7 91114 11610 767 0 12248
SDSSJ1419+4207 214.79250 42.12969 0.873 0.17885 3 5 4 85443 14729 11922 0 11598
PG1424+240 216.75163 23.80000 0.12126 3 14 12 6726 244 265 1 12612
PG1424+240 216.75163 23.80000 0.14683 3 14 12 8344 908 716 1 12612
PG-1630+377 248.00466 37.63055 1.479 0.17388 3 26 11 7143 1937 1316 1 11741
PHL1811 328.75623 -9.37361 0.190 0.07774 3 25 14 4265 312 323 1 12038
PHL1811 328.75623 -9.37361 0.190 0.08091 3 25 14 9335 1353 1672 1 12038
    Notes– (1) QSO name; (2) Right-ascension (J2000); (3) Declination (J2000); (4) QSO redshift from NED except for QSO PG1424+240, which is from Furniss et al. (2013); (5) Absorption redshift; (6) COS gratings used for observations, 1: G130M, 2: G160M, 3: G130M+160M; (7) SN of the G130M data estimated near 1400 Å; (8) SN of the G160M data estimated near 1600 Å (blank when data are not avilable); (9) Rest-frame equivalent width of Lyin mÅ (10) Rest-frame equivalent width of C ii1334 in mÅ (11) Rest-frame equivalent width of Si ii1260 in mÅ (12) Spectrum flag, 1: part of the statistical sample, 0: not part of the statistical sample; (13) proposal ID. Besides these systems we found two tentative systems that are not part of this study. These are: (a) towards QSO-B2356-309 in which Si iiis noisy and barely detected at level. In addition, what would be the C iiof this system has been identified as Lyof by Fang et al. (2014). (b) towards Q2251+155 in which the profiles of C iiand are not consistent with each other and with the Si iilines. These systems are not used for photoionization model due to the lack of Si iiicoverage (see text).
Figure 1: The rest-frame equivalent widths of the low-ionization metal lines (C ii and Si ii) against (Ly). All the “weak” absorbers have  mÅ and  mÅ by design. A mild correlation between and (Ly) is present. An upper envelope with an apparent lack of data points in the upper-left corner (i.e. the region with (Ly mÅ and  mÅ) is evident.
Figure 2: Velocity plot of a weak absorber at   0.08091 detected towards PHL1811. The smooth solid red curves over-plotted on top of data (black histogram) are the best fitting model profiles. Unrelated absorption lines are shown in cyan. Since the Si iii line is blended with the Galactic Si ii line, we have generated a synthetic profile corresponding to the maximum allowed column density. Single component C ii and Si ii lines are detected at  km s. The C iv absorption shows another component at  km s. Both the C iv and Ly lines are fitted with two Voigt profile components. The line centroids of the individual components are marked by the vertical ticks in each panel. Velocity plots, Voigt profile fits, and comments about each absorbers can be found in Appendix B as online material.

2.2 Search techniques and the sample

Our search for the weak absorbers relies on the simultaneous presence of the Si ii and C ii lines. Note that the presence of C ii restricts our survey to a maximum redshift of . First, we assume every detected absorption in a spectrum above  Å is due to the Si ii line from redshift  , where is the rest-frame wavelength of the Si ii transition 3. Next we check for the presence of the corresponding C ii line using the . We build a “primary” list of absorbers using each of the identified coincidence. We then check for the presence of other common transitions ( e.g., Ly, Si ii, C ii, Si iii). Since some amount of neutral hydrogen is expected to be associated with these weak low-ionization absorbers, we have excluded any “primary” system that does not exhibit any detectable Ly absorption. The presence of other metal lines would depend on the phase structure, ionization parameter, and metallicity of the absorber. We, therefore, do not impose the detection of any other metal line as a necessary criterion to confirm a weak absorber. Next, we investigate if the identified Si ii andor C ii lines can have any other identity (i.e. other lines from other redshifts). We include a system in our “secondary” list when both the lines are free from significant contamination.

For each absorber in the “secondary” list we measure rest-frame equivalent widths () of Si ii and C ii lines. We consider only systems in which both the lines are detected with significance. Next we impose the threshold criteria so that each system in our final sample, listed in Table 1, has mÅ and mÅ. The equivalent widths of the C ii and Si ii lines of our final sample are plotted against the (Ly) in Fig. 1. A mild correlation between the equivalent widths of low-ionization metal lines and Ly is apparent. A Spearman rank correlation test suggests a correlation coefficient, , of with a significance. We notice an upper envelope in the figure which is likely due to a metallicity effect. In particular, the systems with (Ly mÅ would require unreasonably high metallicities in order to produce Si ii and/or C ii absorption with  100 mÅ. The systems with (Ly mÅ, on the other hand, show a wide range in Si ii and C ii equivalent widths. This could be because of poor small scale metal mixing so that the observed H i need not entirely be associated with the low-ionization metal line (e.g., Schaye et al., 2007). This is certainly the case for systems for which the H i is not centered in velocity around the low ionization absorption (see e.g., Fig. 2).

The Si ii/C ii systems that show higher than our thresholds, i.e. the strong absorbers, are listed in Table 3 for completeness. The systems with  within 5000 km s of the emission redshift () of the background AGNQSOs, as listed in Table 4, are excluded for this study since they might have different origins (see e.g., Muzahid et al., 2013) than the intervening absorbers we are interested in. Additionally, the systems with  km s are not considered here, since they are likely to be related to our own Galaxy andor local group galaxies. We refer the reader to Richter et al. (2016a) for a detailed analysis of such absorbers. There are a total of 34 weak Mg ii absorber analogs in our sample satisfying all of the above requirements.

Figure 3: The absorption redshifts plotted against the values estimated for individual systems. The median values of  and are indicated by the horizontal and vertical arrows, respectively. Symbol sizes are scaled by the corresponding quality factors (). The distribution is shown in the top panel. In total there are 16 systems with for which estimates are reliable.

2.3 Absorption Line Measurements

Besides measuring equivalent widths, we used vpfit 4 to obtain column densities of H i, Si ii, and C ii. The column densities of Si iii, C iv, and O vi are also measured whenever available. Since the line spread function (LSF) of the COS spectrograph is not a Gaussian, we use the LSF given by Kriss (2011). The LSF was obtained by interpolating the LSF tables at the observed central wavelength for each absorption line and was convolved with the model Voigt profile while fitting absorption lines or generating synthetic profiles. For fitting an absorption line, we have used the minimum number of components required to achieve a reduced . However, owing to the limited resolution of the COS spectrograph, we may be missing the “true” component structure. As a consequence, the Doppler parameters generally turn out to be larger compared to the high- weak absorbers detected in high-resolution UVES spectra (e.g., Narayanan et al., 2008). For a strong line this would lead to an underestimation of the corresponding column density. Nevertheless, the column density can be accurately measured for a weak line that falls on the linear part of the curve-of-growth (COG). COS wavelength calibration is known to have uncertainties at the level of  km s (Savage et al., 2011; Muzahid et al., 2015a). We do see velocity misalignments of the same order between different absorption lines from the same system. An example of a weak absorber with the model profiles is shown in Fig. 2. System plots with Voigt profiles fits of the full sample are available in Appendix B.

3 Analysis

Figure 4: versus (bottom) and versus (top) for each absorber. Note that is more tightly correlated with as compared to in our sample. The (dotted) line is shown just for comparing the relative strengths of the low-ionization metal lines. The tight correlation between and indicates that they trace the same phase of the absorbing gas. The somewhat larger scatter in the top panel possibly suggests that Si iii might have an additional contribution from the high-ionization gas phase for a fraction of the absorbers.

3.1 Absorber’s Frequency,

We have read through the titles and the abstracts of all the relevant program IDs, under which the 296 COS spectra were obtained, in order to inspect whether the spectra were taken to probe the CGM of known foreground galaxies. The spectra obtained from dedicated CGM programs (e.g. PID: 11598, 12248) were assigned to “flag = 0”, meaning that they are not part of our statistical sample. The remaining spectra with “flag = 1” constitute our statistical sample. There are 178 (118) “flag = 1” (“flag = 0”) spectra in our sample. The redshift path-length covered for simultaneously detecting Si ii (0.2 Å) and C ii  (0.3 Å) in the 178 spectra in our statistical sample is . There are 22 bona fide weak absorbers identified in these spectra (see Table 1). This yields the number density of weak absorbers, at . This is consistent with the value () obtained by Narayanan et al. (2005) using a much smaller sample size. We note that the of H i absorbers (Danforth et al., 2016) with  cm at (the median redshift of our sample) matches with that of the weak absorbers. Interestingly, the median in our sample is  cm, as we describe in the next section. This re-confirms the finding of Churchill et al. (1999) that the majority of the weak absorbers arise in a sub-LLS environment.

Recently Richter et al. (2016b) have presented a sample of Si iii absorbers at similar redshift using archival COS spectra. They have found of for Si iii down to a of  cm. Comparing this to the frequency of weak absorbers, we suggest that roughly half of the Si iii population should show associated weak Si ii absorption. From the middle panel of Fig. 6 of Richter et al. (2016b), there are 24 Si ii absorbers with  mÅ. This leads to a of (using for their sample) which is consistent with our estimate.

In Table 1, there are 12 absorbers that are detected in the “flag = 0” spectra. We did not use them for the calculation in order to avoid any possible observational bias. However, those systems are considered in all other analyses related to the chemical/physical conditions of the absorbing gas.

3.2 Neutral Hydrogen Column Density,

Owing to the low redshifts of the weak absorbers (), higher order Lyman series lines are not covered by the COS spectra for most cases. 17/34 systems have only Ly and 7/34 systems have both Ly and Ly coverages. The remaining 10 systems have Ly, Ly, and Ly (or higher order lines) coverages. Estimating reliable values in the absence of unsaturated higher order Lyman series lines is challenging. We, thus, assign a quality factor “” for each of our measurements based on the absorption strength (level of saturation) and the presence (or absence) of the higher order lines. The quality factor can take values from 1–5, with 5 being the best/secure measurements. values with and are not well constrained. For each absorber listed in Table 1, we checked the literature to see if a measurement is available from fuse data. For 7 systems we have adopted values from the literature that were well constrained from higher-order Lyman series lines covered by the fuse spectra. These systems are   towards HE0153-4520 (Savage et al., 2011),   towards PKS0405-123 (Prochaska et al., 2004),   towards PG1116+215 (Sembach et al., 2004),   towards 3C263 (Savage et al., 2012),   towards PKS1302-102 (Cooksey et al., 2008),   towards PHL1811 (Lacki & Charlton, 2010), and   towards PHL1811 (Jenkins et al., 2005). There are 3 additional systems for which we have adopted values from the literature. These systems are   towards Q0107–025A (Muzahid, 2014),   towards SDSSJ1322+4645, and   towards SDSSJ1419+4207. The estimates for the latter two systems are obtained from the Lyman limit breaks seen in the G140L, G130/1222 grating observations using COS (see Prochaska et al., 2017). For all of these 10 systems we assign . The absorption redshifts and estimates are shown in Fig. 3. The median is  cm for the full sample. The median value becomes  cm for the systems with . The median value of redshifts changes from to when we consider the systems with as opposed to the full sample. This follows from the fact that the most of the lower redshift systems do not have higher order Lyman series lines covered.

Figure 5: Bottom: cloudy predicted Si iii to Si ii ratios against the gas density for two different metallicities as indicated by the two different line styles. For each metallicity, four different models are run corresponding to four different values as shown by different colors. Clearly, the ratio is degenerate with respect to the assumed model metallicity. The distribution of observed ratio is shown in the right panel. Top: The density distribution corresponding to the observed ratio distribution for the two different model metallicities. The solid black histogram indicates the final density distribution after correcting for the metallicity degeneracies (see text).
Figure 6: The C ii (left), Si ii (middle), and Si iii (right) column densities against , as measured in different systems. The filled squares represent systems with . The PI model curves corresponding to two different metallicities are shown in two different line-styles. For each model, we show three curves in three different colors corresponding to three representative densities (i.e., ).

3.3 Metal Column Densities

Besides H i, we have measured the column densities of C ii, Si ii, Si iii, C iv and O vi when available. All the measured total column densities (i.e. the sum of the component column densities) are listed in Table 2. The systems in our sample are weak by design and therefore it is expected that the C ii and Si ii lines are not saturated in most cases. In fact, for 29/34 cases we could measure the adequately. The minimum and maximum values of for these systems are 13.22 and 14.40, respectively, with a median value of 13.9. The median value increases only by dex for the full sample. For all 34 systems we could measure reliably. The minimum and maximum values of are 12.23 and 14.14, respectively, with a median value of 12.9. The median value of is an order of magnitude lower than that of .

Owing to the large value (i.e. 2027) of the Si iii transition, the Si iii absorption lines in our sample are saturated for nearly half (15/32) of the systems. We note that for two systems (i.e.   towards UKS-0242-724 and   towards SDSSJ1214+0825) Si iii lines fall in the spectral gap and hence no information is available. The minimum and maximum values of are, respectively, 12.43 and 13.47 for the 18 systems in which we could measure adequately. The median value of the distribution is  cm, which is close to that of the distribution but a factor of smaller than the distribution. The median value of increases to for the full sample.

In the bottom panel of Fig. 4, the C ii column densities are plotted against . Note that when multiple components are present, we have summed the component column densities. The values are tightly correlated with . A Spearman rank correlation test gives with a significance. If we consider only systems in which both and are measured adequately (i.e. excluding the limits) we obtain with a significance. The strong correlation coefficient ensures that the C ii and Si ii arise from the same phase of the absorbing gas.

In the top panel of Fig. 4, the Si iii column densities are plotted against . A statistically significant correlation between and , with (), is apparent from the figure. Nevertheless, there is more scatter in this plot compared to the bottom panel ( vs ). It is likely due to the fact that some amount of Si iii might be contributed by the high-ionization gas phase giving rise to C iv/O vi absorption for at least some fraction of the systems. We will discuss this issue in more detail in the following section.

3.4 Ionization Modeling

We use the photoionization (PI) simulation code cloudy (v13.03, last described by Ferland et al., 2013) to infer the overall physical and chemical properties of the weak absorbers in our sample. In our constant density PI models, we have assumed that (a) the absorbing gas has a plane parallel geometry, (b) the gas is subject to the extragalactic UV background (UVB) radiation at as computed by Khaire & Srianand (2015a, KS15 hereafter)5, (c) the relative abundances of heavy elements in the absorbing gas are similar to the solar values as measured by Asplund et al. (2009), and (d) the gas is dust free. Models are run for two different gas-phase metallicities, i.e., and . The KS15 UVB calculations make use of an updated QSO emissivity and star-formation rate density (see Khaire & Srianand, 2015b, for details). Their models with escape fraction (of H i ionizing photons from galaxies, ) of provide H i photoionization rates () at that are consistent with the measurements of Shull et al. (2015) and Gaikwad et al. (2016). We therefore use their model corresponding to .

PI models for all the absorbers are done in a uniform fashion. First, we assume that the Si ii and Si iii absorption lines originate in the same phase of the absorbing gas and hence the ratio of uniquely fixes the (or ) of the absorber. We, however, note that the Si iii need not entirely stem from the low-ionization gas phase that produces Si ii. If some amount of Si iii arise from high-ionization gas phase, the Si iii to Si ii ratio would provide an upper limit on the ionization parameter (a lower limit on density). Next, we use the ionization corrections of H i and Si ii ( and , respectively) at the derived and calculate the Si abundance, [Si/H] , of the absorber using the observed and . The ratio shows a relatively flat peak for a large range in density of , and falls off rapidly at both below and above this density range. Thus, even if the measured has some contribution from a high ionization gas phase, our inferred metallicity will essentially be unaltered (see also Section 5.3).

4 Results based on the PI models

4.1 The density (ionization parameter) distribution

In the bottom panel of Fig. 5 we show the variation of the model predicted ratio with density for two different model metallicities, i.e., solar and 1/10th of solar values. We note that the ratio depends on the metallicity assumed in the cloudy model. This is likely due to the increased electron density in high metallicity gas increasing the recombination/cooling rate for a fixed density and temperature. For each model metallicity we have used four different values (i.e., 15, 16, 17, and 18) as the stopping conditions for the simulations. Note that, for a given metallicity, the ratio is independent of the values as long as the gas is optically thin to the hydrogen ionizing photons (i.e.,  cm). We, however, used the observed values as stopping conditions for cloudy for each of the absorbers in order to derive individual constraints.

[t]

Table 2: Summary of column density measurements and photoionization model parameters.
QSO
(kpc) (observed) (model) (observed) (model)
PG0003+158 0.16512 18.16 0.03 13.60 0.05 12.23 0.09 12.60 3 2.9 (3.1) 2.5 19.9 2.02E+01 NC 12.2 13.82 0.12 9.7
Q0107-025A 0.22722 15.92 0.08 13.85 0.07 13.04 0.06 12.90 0.05 5 2.6 (3.4) 0.2 17.7 6.91E-02 14.24 0.12 12.4 14.57 0.23 9.2
HE0153-4520 0.22597 16.83 0.07 14.09 0.03 12.78 0.04 13.73 4 3.1 (2.9) 0.7 19.2 6.34E+00 NC 13.9 14.24 0.02 11.9
3C57 0.32338 16.14 0.02 14.05 0.02 12.83 0.11 13.61 5 3.3 (2.7) 0.0 18.6 2.47E+00 NC 14.2 13.4 12.6
SDSSJ0212-0737 0.01603 18.27 0.17 15.50 14.14 0.14 14.65 3 3.1 (2.9) 0.7 20.2 5.33E+01 15.03 0.25 14.5 NC 12.3
SDSSJ0212-0737 0.13422 14.95 0.08 13.91 0.10 12.81 0.04 12.43 0.15 3 2.5 (3.5) 0.9 16.6 3.59E-03 13.4 11.8 13.7 8.1
UKS-0242-724 0.06376 15.270.27 13.73 0.09 12.90 0.05 NC 1 13.3 NC
Q0349-146 0.07256 16.24 0.53 13.91 0.09 13.18 0.05 13.01 0.09 1 2.6 (3.4) 0.0 18.0 1.34E-01 13.5 12.5 NC 9.3
PKS0405-123 0.16710 16.45 0.05 14.40 13.33 0.03 13.40 5 2.8 (3.2) 0.1 18.4 4.56E-01 14.16 0.05 13.1 14.73 0.13 10.3
IRAS-F04250-5718 0.00369 15.85 0.08 13.49 0.04 12.25 0.17 12.78 0.06 1 3.1 (2.9) 0.4 18.1 4.92E-01 13.21 0.15 13.0 NC 10.9
FBQS-0751+2919 0.20399 17.77 0.05 14.23 0.06 12.97 0.07 13.55 2 2.8 (3.2) 1.5 19.8 1.40E+01 NC 13.1 14.35 0.07 10.5
VV2006J0808+0514 0.02930 17.56 0.43 14.17 13.46 0.09 14.11 1 2.8 (3.2) 0.8 19.7 9.66E+00 NC 13.7 NC 11.1
PG0832+251 0.02811 14.28 0.14 13.56 0.08 12.79 0.10 12.51 0.11 2 2.5 (3.5) 1.6 16.0 1.01E-03 13.3 11.9 NC 8.5
SDSSJ0929+4644 0.06498 14.67 0.71 13.50 0.11 12.68 0.06 12.50 0.09 2 2.6 (3.4) 1.1 16.4 3.35E-03 13.1 12.0 NC 8.7
PMNJ1103-2329 0.08352 17.74 0.44 14.03 0.10 12.82 0.13 13.37 1 2.8 (3.2) 1.6 19.7 1.15E+01 14.43 0.06 12.9 NC 10.2
PG1116+215 0.13850 16.20 0.05 13.84 0.02 12.86 0.06 12.87 0.03 5 2.7 (3.3) 0.3 18.1 2.07E-01 13.19 0.08 12.5 13.84 0.02 9.6
SDSSJ1122+5755 0.05319 15.16 1.43 13.56 0.13 12.80 0.08 12.85 0.11 1 2.7 (3.3) 0.7 17.1 2.03E-02 13.71 0.15 12.5 NC 9.6
PG1121+422 0.19238 15.64 0.05 14.12 0.02 13.07 0.02 13.34 0.06 2 2.9 (3.1) 0.5 17.7 1.26E-01 NC 13.2 13.4 10.8
3C263 0.06350 15.40 0.12 13.55 0.06 12.35 0.05 13.09 0.02 4 3.2 (2.8) 0.3 17.8 3.66E-01 14.13 0.15 13.6 NC 11.9
PG1202+281 0.13988 15.73 0.10 14.04 0.17 12.79 0.09 13.41 0.24 1 3.1 (2.9) 0.3 18.1 5.15E-01 13.9 13.8 13.6 11.8
PG-1206+459 0.21439 15.71 0.06 14.24 0.05 13.13 0.05 13.65 3 3.1 (2.9) 0.6 18.0 3.44E-01 NC 13.9 NC 11.8
SDSSJ1210+3157 0.05974 14.83 0.27 14.06 0.05 13.10 0.08 13.23 0.11 1 2.8 (3.2) 1.3 16.8 1.23E-02 14.50 0.10 13.0 NC 10.2
SDSSJ1210+3157 0.14964 17.28 0.12 14.23 0.11 12.98 0.12 13.69 1 2.8 (3.2) 1.0 19.4 5.95E+00 14.35 0.13 13.4 14.72 0.11 10.8
SDSSJ1214+0825 0.07407 15.00 0.40 14.13 0.07 13.05 0.06 NC 1 NC NC
RXJ1230.8+0115 0.00575 15.42 0.43 13.79 0.01 12.64 0.02 13.47 0.07 1 3.3 (2.7) 0.6 17.9 5.48E-01 13.32 0.19 14.2 NC 12.6
PKS1302-102 0.09495 16.88 0.03 13.65 0.09 12.58 0.11 13.02 0.06 4 2.6 (3.4) 1.1 18.8 7.78E-01 13.0 12.3 13.9 9.2
SDSSJ1322+4645 0.21451 17.14 0.05 14.40 0.05 13.27 0.09 13.71 4 2.6 (3.4) 0.6 19.0 1.46E+00 NC 13.0 14.55 0.08 9.9
SDSSJ1357+1704 0.09784 15.79 0.52 13.97 0.04 12.76 0.05 13.64 1 3.3 (2.7) 0.4 18.3 1.60E+00 13.92 0.12 14.4 14.1 13.0
SDSSJ1419+4207 0.17885 16.63 0.30 14.32 0.14 13.37 0.09 14.18 4 3.3 (2.7) 0.1 19.2 9.34E+00 NC 14.9 14.43 0.05 13.2
PG1424+240 0.12126 14.96 0.08 13.22 0.08 12.36 0.09 12.46 0.10 3 2.8 (3.2) 0.4 16.9 1.50E-02 13.70 0.06 12.2 14.44 0.05 9.4
PG1424+240 0.14683 16.56 0.96 13.71 0.06 12.59 0.07 13.04 0.05 1 2.6 (3.4) 0.7 18.5 3.84E-01 14.18 0.06 12.4 14.04 0.13 9.3
PG-1630+377 0.17388 15.83 0.08 14.20 0.03 13.07 0.02 13.14 0.02 1 2.8 (3.2) 0.3 17.7 1.03E-01 NC 12.8 13.86 0.03 10.0
PHL1811 0.07774 16.00 0.05 13.26 0.03 12.35 0.05 12.48 0.04 5 2.4 (3.6) 0.4 17.6 3.24E-02 13.0 11.4 NC 6.6
PHL1811 0.08091 17.94 0.07 14.55 13.79 0.04 13.80 4 2.5 (3.5) 0.8 19.4 2.42E+00 14.04 0.04 12.8 NC 8.9
    From Muzahid (2014), From Savage et al. (2010)

The red (135) hashed histogram in the top panel of Fig. 5 represents the distribution corresponding to the observed ratios, shown in the bottom-right panel, for an assumed metallicity of . The blue (45) hashed histogram, on the other hand, represents the same for an assumed metallicity of . Clearly, an assumption of any particular model metallicity for all the absorbers in a sample leads to an incorrect density distribution6. In order to overcome this problem we have performed our PI modelling in an iterative way. First, we used the density solution corresponding to the model and calculate the Si abundances for each absorber. We then select the systems with (i.e. half solar) and redo the density calculation using the model. The distribution of our final density solutions is shown by the black histogram in the top panel of Fig. 5. The distribution has a median value of with minimum and maximum values of and , respectively. For the adopted UVB, this leads to a range in ionization parameter, , of to with a median value of .

4.2 The column density trends

In the different panels of Fig. 6, column densities of low-ionization metal lines are plotted against the corresponding . A mild trend of increasing low-ionization metal line column densities with increasing is noticeable. A similar trend has also been reported for the COS-Halos sample (i.e., Werk et al., 2013; Prochaska et al., 2017). A Spearman rank correlation analysis, assuming limits are detections, also confirms the trends with a when the full sample is considered (see Table 3). It is important to note that when we consider the sub-sample with  cm (median value), the correlation coefficients remain high (i.e. ). The sub-sample with  cm, on the contrary, show consistent with 0.0. Though the sample size is small, it seems that the mild trends seen in the full sample are mainly driven by the systems with  cm.

In each panel in Fig. 6, six different PI model curves, corresponding to two different metallicities and three different densities, are overplotted. Note that the three representative densities span the density range we obtained from the ratios as discussed above. It is apparent from the three panels that the majority of the systems with are not reproduced by the models with th of solar metallicity. Moreover, even the solar-metallicity-models fail to reproduce the systems with . It is, therefore, clear that the vast majority of the weak absorbers studied here have very high metallicities.

4.3 Trends in the model parameters

The PI model predicted densities (), Si-abundances (), total hydrogen column densities (), and line of sight thicknesses () are listed in columns 8, 9, 10, and 11 of Table 2, respectively. As mentioned before, the densities of the absorbers show a range of with a median value of  . The density range and the median value do not change when only systems are considered. The inferred values show a range of to with a median value of (i.e. solar abundance). However, when we considered only systems the maximum value drops to (i.e. times solar) and the median value becomes . The total hydrogen column densities for the weak absorbers show a range of 4 orders of magnitude, i.e.,  cm, with a median value of  cm. The line of sight thicknesses, , also exhibit a wide range of 1 pc – 53 kpc with a median value of  pc. The median value changes to  pc for the systems with .

The PI model parameters are plotted against the observed column densities of H i (top row), C ii (middle row), and Si ii (bottom row) in Fig. 7. The inferred densities do not show any trend with the neutral hydrogen and/or low-ionization metal line column densities. No significant correlation is seen between and or . A strong anti-correlation (, ) between and , however, is apparent from the figure. The trend remains statistically significant (, ) when only systems with are considered. A similar trend has been recently reported by Prochaska et al. (2017) in the COS-Halos sample. Such a trend is generally expected in a metal line selected sample of absorbers, because, in practice, there are many low- systems without any detectable low-ionization metal lines that are not considered in our study. In order to investigate the dependence of the correlation on , we have performed the Spearman rank correlation analysis for two different sub-samples, one with  cm and the other with  cm, separately. We obtain and ( and ) for the upper- (lower-) sub-samples, suggesting a statistically significant anti-correlation between and for the systems with  cm. Note that, 80% of the low- H i absorbers with  cm exhibit low-ionization metal lines (see Fig. 8 in Danforth et al., 2016). Thus, the strong anti-correlation seen in the full sample cannot be fully attributed to sample selection bias (see also the discussion of Misawa et al., 2008). However, we do point out that our survey is limited to weak absorbers only. Inclusion of strong absorbers would introduce more scatter in the relation, particularly at the higher end.

The strong anti-correlation between and is not surprising since the expected variation in over the inferred narrow density range of  cm is small and () is directly proportional to . The correlation between and follows from the fact that is strongly correlated with whereas is not. The also show a significant (mild) correlation with (). If the column density of the (i+1)-th ionization state of an element , with ionization fraction of , is , then

(1)
(2)

Thus, a correlation between (and/or ) and metal line column density is generally anticipated. Any anti-correlation between the metallicity () and the ionic column density, as seen for C ii, would further strengthen the correlation. The apparent lack of any correlation between and has been manifested by the mild correlation seen between and in contrast to the strong correlation seen between and .

Figure 7: Scatter plots of PI model parameters (, 1st column; , 2nd column, , 3rd column; , 4th column) and the observed column densities (, top row; , middle row; , bottom row). The filled squares represent the systems with . The results of the Spearman rank correlation analysis are mentioned on the top of each panel. Possible origins of the observed correlations are discussed in the text. In particular, we argue that the anti-correlation seen between and cannot be entirely attributed to selection bias.

[b]

Table 3: The details of Spearman rank correlation analysis
Sample Data1 Data2
Full 0.48 2.8
Full 0.28 1.6
 cm 0.30 1.2
 cm 0.20 0.8
 cm 0.10 0.4
 cm

4.4 High-ionization metal lines

Although the main focus of this paper is the weak absorbers detected via the low-ionization metal lines, in all but a few cases high-ionization metal lines (e.g. C iv and/or O vi) are also covered. For example, information is available for a total of 23 systems (15 measurements and 8 upper limits, see Table 2). All the upper limits on are consistent with our PI model predictions. For the 15 systems with positive detection of C iv, the column densities are found to be in the range  cm with a median value of  cm. Our measurements are at least 0.5 dex higher than the model predicted values for 12/15 systems, suggesting a separate gas phase for C iv absorption in those absorbers. For the   system towards IRAS-F04250-5718, the difference is only 0.2 dex, which is well within our PI model uncertainties. For the two other systems (  towards RXJ1230.8+0115 and   towards SDSSJ1357+1704) the model predicted C iv column densities are higher than the observed ones. In both these systems the Si iv line is detected. It is likely that the majority of the Si iii absorption in these systems arises from the gas phase giving rise to Si iv (and C iv) absorption. In that situation the ionization parameter of the low-ionization phase can be a lot lower which, in turn, will reduce the predicted . In the   system towards SDSSJ1357+1704, the stronger Si iii component at  km s, which dominates the total , is not seen in the low-ionization lines but is seen in the Si iv line (see Appendix B). We further note that the majority of systems for which the predicted values are considerable (i.e.  cm) show strong Si iv absorption. These facts demonstrate the need for component-by-component, multi-phase photoionization models (see e.g., Charlton et al., 2003; Milutinović et al., 2006; Misawa et al., 2008), which is beyond the scope of this paper.

The O vi doublet is covered for 18/34 of the weak absorbers, of which 12 show detectable absorption. The O vi column densities in these absorbers vary between  cm with a median value of  cm. The maximum predicted by our PI models (i.e.,  cm) is 0.6 dex lower than the lowest measured value. It clearly indicates that in all these systems O vi must originate from a separate gas phase. In 10/34 of the weak absorbers both the C iv and the O vi doublets are covered. In 6/10 cases both C iv and O vi are detected, and it is likely that they arise in the same gas phase. In one case (  0.09784 towards SDSSJ1357+1704 discussed in the paragraph above) only C iv is detected. Finally, in 3/10 cases neither C iv or O vi are detected. We conclude that about two thirds of the weak absorbers have a separate, higher ionization or hotter phase.

5 Discussion

5.1 Redshift Evolution

Our sample of 34 weak Mg ii absorber analogs at represents a substantial increase over the sample of 6 absorbers found by Narayanan et al. (2005) at low redshift. However, the value of that we have derived is consistent with that earlier study, and a factor of a few smaller than what would be expected if static populations of weak Mg ii and C iv absorbers were simply evolved to the present era subject to the decreasing UVB. Narayanan et al. (2005) noted that both pc-scale structures that produce weak Mg ii absorption at and kpc-scale structures that are detected in C iv absorption, but not in low ionization transitions, would evolve from to produce weak low ionization absorption at . To some extent, both populations must be less abundant at low redshift than they were at . The present sample of 34 absorbers is large enough that we can attempt to determine how the low redshift population compares to the population, however Narayanan et al. (2005) warned that “hidden phases” would in some cases make it impossible to extract accurate physical properties (see their Figs. 10–12).

We begin by noting that 7/34 of our weak absorbers are very small ( pc) structures with solar or super-solar metallicity and with derived densities in the upper half of our sample. Although these overlap with the densities derived by Narayanan et al. (2008) for weak Mg ii absorbers (using coverage of Fe ii to constrain density), they are at the low end of the range. All but one of these seven small absorbers has only one low ionization component, and C iv is either not detected at all (in 4/7) or it could be in the same phase with, and centered on the low ionization absorption. Even these absorbers, for which the metallicity is inferred to be quite high, could have two phases that contribute roughly equally to the Si ii/C ii absorption, as in the simulated system in Fig. 11 of Narayanan et al. (2005). However, it is still clear that there is a smaller, higher density phase which has a surprisingly high metallicity.

Furthermore, many of the remaining 27/34 absorbers, though they have larger derived line of sight thicknesses based on our conservative estimates, are likely to have a hidden phase. The inferred density of that phase would be higher than we estimate if some of the Si iii is in fact in a lower density phase that produced C iv absorption. The inferred metallicity of that phase would be higher if some of the H i is associated with the higher ionization transitions, C iv and/or O vi.

Thus, despite our larger sample, the situation remains unclear. We can, however, affirm that there are fewer weak, low ionization absorbers at present than we would expect if we took the absorber population at and simply evolved the same structures to the present day subject to a lower UVB. However, as we discuss below, it seems more likely that the weak absorbers are transient, and that the processes that create these small, high metallicity structures faraway from galaxies are less active at present than they were in the past.

5.2 Cosmological Importance

If the comoving number density of the weak absorbers at is and the proper cross-section is typically then can be expressed as:

(3)

If we assume a spherical geometry for the weak absorbers with a characteristic radius of , where  pc is the median line of sight thickness we obtained from PI model, then the comoving number density becomes Mpc for the observed of . Integrating the -band luminosity function of galaxies in SDSS (Blanton et al., 2003b), the number density of galaxies down to is Mpc. Therefore, the population of weak absorber clouds must have been huge, and outnumbered bright galaxies by tens of thousands to one. Similar conclusions have been drawn for the weak absorber population at high- (Rigby et al., 2002), for metal-rich C iv absorbers at (Schaye et al., 2007), and for Ne viii absorbers at (Meiring et al., 2013).

Under the assumption of spherical geometry, the cloud mass can be expressed as:

(4)

where, is the mean atomic weight. Using the median and values we derived from the PI models, we obtain  . The cosmic mass density of the weak absorbers at is then , where  Mpc is the critical density of the universe. Clearly, the weak absorbers at carry a negligible fraction of cosmic baryons ().

If the weak absorber clouds are associated with the CGM of a galaxy population with comoving number density at , then the derived can, alternatively, be used to estimate the characteristic radius of the halo using the following relation:

(5)

Here is the covering fraction of the weak absorbers. Note that the halo radius can be much larger if the covering fraction of the weak absorbers is significantly lower than unity. Following the prescription detailed in Section 5 of Richter et al. (2016b), Eqn. 5 can inversely be used to obtain . Assuming that the absorber’s population extends out to the virial radii of galaxies with , they have derived a relation: . The observed for weak absorbers, thus, corresponds to a covering fraction of . This is roughly half of the covering fraction derived for the Si iii population studied in Richter et al. (2016b). This is expected since they have noted that about half of the Si iii absorber population with is associated with Si ii absorption.

Figure 8: The line of sight thickness versus gas density as obtained from the PI models. Each data point is color-coded by the corresponding metallicity. The dashed line marks the relationship under local hydrostatic equilibrium (Schaye, 2001). High metallicity systems are too small to be self-gravitating. The dotted lines indicate the lines of constant masses. The majority of the systems contain gas masses of .
Figure 9: Bottom: Metallicity distribution of the weak absorbers in our sample (black histogram with orange shade). The red histogram in the bottom panel shows the bimodal metallicity distribution of H i-selected low- Lyman limit systems studied by Wotta et al. (2016). The blue histogram in the middle panel shows the metallicity distribution of the COS-Halos (galaxy-selected) sample from Prochaska et al. (2017). The top panel shows the cumulative distributions of all three sample with respective colors. Both the galaxy-selected and H i-selected absorbers show very different metallicity distributions when compared to the weak absorbers. Our sample shows the highest fraction (%) of solar/super-solar metallicity absorbers.

Following Stocke et al. (2013), the number of metal-rich clouds inside the characteristic radius is , assuming the “shadowing factor” () and to be of order unity. The volume filling factor of these clouds is then (i.e. only %). The total gas mass () associated with these absorbers is  . This mass estimate is significantly lower compared to the COS-Halos sample (i.e.,  ; Werk et al., 2014) but roughly matches with the calculation of Stocke et al. (2013) for their sample of dwarf galaxies. The mass in Silicon () is  . It corresponds to an Oxygen mass of  , assuming solar relative abundance. This Oxygen mass estimate is orders of magnitude lower than the estimate of Tumlinson et al. (2011) for the O vi absorbing gas in the COS-Halos sample. Here we note that, all our mass estimates are lower limits in the sense that we do not take the possible contribution from the high-ionization gas phase into account.

From the discussion above, it is clear that the weak absorbers may stem from extended gaseous halos that are filled with large numbers of pc–kpc-scale clouds. Given the high metallicities of the majority of the weak absorbers, it is most natural to think that they arise in large scale galactic outflows. An important question in this context is the stability of the absorbing clouds. Self-gravity and external pressure due to an ambient medium are generally thought to be the two main channels that can confine the small, metal-rich clouds (see e.g. Schaye et al., 2007). The typical size for an optically thin, self-gravitating, purely gaseous cloud with density is 10–30 kpc (see Eqn. 7 in Schaye et al., 2007), whereas, the median line of sight thickness of our sample is  pc. As demonstrated in Fig. 8, a vast majority of the weak absorbers in our sample are too tiny to be supported by self-gravity unless they are significantly dark matter dominated structures.

The presence of another gas phase, giving rise to the high-ionization metal lines, particularly the O vi, is almost certain (see Section 4.4). This phase, presumably with lower density and higher temperature, can, in principle, confine the low-ionization gas phase. However, in cases where detailed ionization modelling has been done the two phases are not found to be in pressure equilibrium (e.g. Meiring et al., 2013; Muzahid, 2014; Muzahid et al., 2015b; Hussain et al., 2015). But the high-ionization gas phase traced by O vi could arise from the mixing layers of cool and an ambient medium too hot for UV line diagnostics. This hotter unobserved gas, e.g., hot halo created via accretion shocks and/or shocks due to large-scale galactic outflows, might well be the confining medium (e.g., Mulchaey & Chen, 2009; Narayanan et al., 2011). Indeed, X-ray observations have revealed the presence of such a medium with  K in the halo of Milky Way (Gupta et al., 2012). In the absence of any confining agent, the clouds will expand freely until they reach pressure equilibrium or will eventually be evaporated. For a  K gas cloud with  pc, the free expansion time scale is  yr, much shorter than the Hubble time. This suggests that the high metallicity weak absorbers could be transient in nature.

Figure 10: Left: The distribution of impact parameters of nearest known galaxies (top) for 22 of the weak absorbers. The impact parameter ranges from 31–850 kpc with a median value of 166 kpc. Only 3/22 absorbers show host-galaxy impact parameters  kpc. In 17/22 cases at least 2 galaxies are found within 1 Mpc from the QSO sightline and within a velocity window of 500 km s around the absorption redshift. In the bottom panel, the Si ii column densities are plotted against the impact parameters of the nearest galaxies (blue star) and the second nearest galaxies (grey star) connected by the dotted (magenta) line. The (red) filled circles represent the galaxies that do not have a known companion. No significant correlation is seen between and . Right: The H i absorption profiles of 6 weak absorbers around which different number of galaxies ( 0–23) have been identified. No galaxy information is available for the system towards 3C57. The C ii absorption profiles are shown in grey. Note that all of them show additional H i absorption within 500 km s of the absorption redshift (0 km s) indicated by the arrows. The presence of additional absorption clouds further indicates that they arise from a group environment (see text).

5.3 Metal Abundance

The most interesting physical properties of the weak absorbers is their unusual high metallicities. The median value of the distribution of indicates that 50% of the weak absorbers in our sample show a solar/super solar abundance. Moreover, 27/32 absorbers (%) show . If we consider only systems, then the fraction of absorbers showing () is % (%). Here we note that the fraction of weak absorbers showing high metallicity is significantly higher compared to the H i-selected sample of Wotta et al. (2016) and the galaxy-selected sample of Prochaska et al. (2017). In Fig. 9 we compare the metallicity distributions of these three samples. The cumulative metallicity distribution, shown in the top panel, of our low- sample is significantly different compared to that of Wotta et al. (2016). A two-sided KS-test gives and confirming that the difference has a 99.99% significance. The significance is somewhat lower (%) with a when compared with the COS-Halos sample (Prochaska et al., 2017). The median metallicities of Wotta et al. (2016) and Prochaska et al. (2017) samples, i.e., and dex respectively, are much lower than our sample. Only 3/58 (5%) of the absorbers in Wotta et al. (2016) and 7/31 (22%) of the absorbers in Prochaska et al. (2017) have solar/super-solar metallicities. Clearly, the weak absorbers are significantly more metal-rich when compared to the galaxy-selected and H i-selected samples of absorbers probing the CGM at, by and large, similar redshifts.

Here we point out that both Wotta et al. (2016) and Prochaska et al. (2017) have used an UVB calculated by Haardt & Madau (2012, HM12 hereafter). The intensity of the HM12 UVB is somewhat lower than that of the KS15 UVB used in this study, for energies Ryd (see e.g., Fig. 1 of Hussain et al., 2017). In order to assess the effect of the UVB on our metallicity estimates, we model an imaginary cloud at with column densities of H i, Si ii, and Si iii equal to the corresponding median values we obtained for our sample (i.e. , , and  cm, respectively). Grids of constant density cloudy models were run with a solar metallicity and with a stopping of  cm. The density derived for the HM12 UVB (i.e.,