Studying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique
MMNRAS , 1–19 (2018) Preprint 29 August 2018 Compiled using MNRAS L A TEX style file v3.0
Studying Quasar Absorber Host Galaxy Properties UsingImage Stacking Technique
Bill Zhu, , (cid:63) Yinan Zhao, Jian Ge, Jingzhe Ma Department of Astronomy, University of Florida, 211 Bryant Space Science Center, Gainesville, FL 32611, USA Lynbrook High School, 1280 Johnson Ave, San Jose, CA 95129, USA Department of Physics & Astronomy, University of California, Irvine, 2156 Frederick Reines Hall, Irvine, CA 95129, USA
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Studying the stellar mass, age, luminosity, star-formation rate, and impact parameterof quasar absorber host galaxies can aid in the understanding of galaxy formationand evolution as well as in testing their models. We derive the Spectral Energy Dis-tribution (SED) and impact parameter limits of low redshift ( z abs = . − . ) MgII absorbers and of higher redshift ( z abs = . − . ) 2175 ˚A dust absorbers (2DAs).We use an imaging stacking technique to statistically boost the signal-to-noise ratio(SNR) to increase detection of the absorber host galaxies. The point spread functionof the background quasar is modeled with Principal Component Analysis (PCA). Thismethod efficiently reduces the uncertainty of traditional PSF modeling. Our SED forMg II absorbers indicates that low redshift Mg II absorber host galaxies are likelystar-forming galaxies transitioning into red quiescent galaxies, with a low star forma-tion rate of 2.2 M (cid:12) y r − . From the stacked images and simulations, we show that theaverage impact parameter of 2DAs is > < Key words: galaxies: photometry - galaxies: statistics - quasars: absorption lines -techniques: photometric
Galactic evolution is a cornerstone of astronomy that is be-ing widely and intensely studied all over the world. One ofthe most powerful ways to gain insight into the properties ofhigh-redshift galaxies is by tracking metal absorption linesin interstellar clouds. Quasars, powered by the accretion ofmaterials in supermassive black holes, are the brightest ob-jects in the early universe. They are able to probe metalabsorption lines in intervening galaxies between the quasarsand Earth, making quasar absorption line systems one of themost powerful tools in studying the gas content in the earlyuniverse to high levels of sensitivity that do not depend onredshift.Bahcall & Spitzer (1969) suggested that metal absorp-tion lines seen in quasar spectra are induced by large gashalos surrounding host galaxies. These gas halos can extendup to 100 kpc away. Thus, tracking quasar absorption linesto study these gas halos has been an active field for the pastfew decades. Previous studies that investigated host galax- (cid:63)
E-mail: [email protected] (BZ) ies of quasar absorbers have used deep imaging while thegas content has been extensively studied with spectroscopicfollow-ups. However, such studies are extremely restrictive,due to small sample sizes and high expenses in performingspectroscopic follow-ups of faint objects. Thus, most studiesin the late 1990s and early 2000s were limited to a few dozencase studies and focused on individual attributes of varyinghost galaxies. Furthermore, the wide distribution of redshiftsand magnitudes of the sample result in the inability to deter-mine strong statistical properties of the absorbers and theirhost galaxies. Overarching trends across different ranges ofredshifts and absorption strengths could not be found. Thesetrends are necessary for categorizing the major componentsfound in all absorbers, such as average luminosity-weightedimpact parameters for investigating location and geometryof absorbers, and average spectral energy distribution forstudying stellar population, mass, and star formation his-tory.On the other hand, ground-based telescope imaging iswidely available but significantly noisier, making detectionof absorber host galaxies in individual frames impossible.One method of boosting the signal-to-noise ratio (SNR), © a r X i v : . [ a s t r o - ph . GA ] A ug Bill Zhu, Yinan Zhao, Jian Ge, Jingzhe Ma and hence sensitivity, of ground-based imaging is by stackingmany frames of imaging data together, relying on statisticalproperties of large datasets to preserve the signals of eachindividual frame while decreasing the overall noise level. Bythe central limit theorem of statistics, the noise distributionin the mean image is tighter than the original images bya factor of √ N , where N is the number of frames stacked.Stacking images brings out signals that were previously un-detectable in individual frames since the background noiselevel is greatly reduced. This not only mitigates the chal-lenges associated with expensive, deep field, high contrastimaging follow-ups, but also offers a statistical method tostudy host galaxy properties as a galaxy population. Corre-lations between different attributes, such as surface bright-ness, galaxy age, mass and star formation history, can thenbe determined.Stacking approaches and studies have provided valuableresults in a number of areas. For example, Bartelmann &White (2003) demonstrated that stacking of ROSATA ll-SkySurvey X-ray images of high-redshift clusters detected in theSloan Digital Sky Survey (SDSS) can be used to derive theirmean X-ray properties. In the context of galaxies, Hogg etal. (1997) constrained the IR signal from faint galaxies usingstacked Keck data. Similarly, Brandt et al. (2001) measuredthe mean X-ray flux of Lyman break galaxies, Zibetti et al.(2004) characterized the very low surface brightness “diffuse”light in galaxy halos, and White et al. (2007) constrained theradio properties of SDSS quasars down to the nanojanskylevel. In spectroscopic studies, stacking techniques have beenextensively used to look for weak signals. Composite spectraof SDSS quasars were used to detect weak absorption lines,as well as dust reddening effects that are well below the noiselevel in individual spectra (Nestor et al. 2003; M´enard et al.2005; York et al. 2006). Clearly, the stacking approach isvery advantageous in investigating faint sources (Zibetti etal. 2007).Zibetti et al. (2005a, b, 2007) used such a stackingmethod for studying large samples of Mg II absorptionquasars. The Mg II absorption feature was chosen as theirinterest of study because of dominant ions in H gas. MgII possesses a resonance transition at the doublet (2796.35,2803.53˚A). Zibetti et al. (2007) extracted thousands of Mg IIabsorber quasar cutouts from the Sloan Digital Sky Survey’sData Release 4 (DR4). They binned the Mg II absorbersby the redshift of the absorbers and by the rest equivalentwidth (REW) of the 2796 ˚A absorption line. They then cen-tered the absorbers to their calculated centroids by way ofinterpolation in order to make the images super-imposable,subtracted the quasar’s point spread function (PSF) to di-minish the quasar’s light contributions, and finally rescaledthe intensity of the absorbers to achieve normality and con-sistency. Zibetti et al. (2007) corrected the images for galac-tic extinction and mean-stacked the images to reveal onefinal mean frame. Their results indicate that there is nosignificant redshift dependence for both impact parameterand rest-frame colors for redshifts up to z abs = . Theyalso showed that stronger absorption systems display thecolors of blue star-forming galaxies while weaker absorptionsystems mostly originate from red passive galaxies. Finally,Zibetti et al. (2007) demonstrated the stacking technique’susefulness in detecting the light of QSO hosts and their en-vironments. Since 2007, there have been numerous advances in cat-aloging quasar absorber host galaxies. Bouche et al. (2007)discovered that there may exist a correlation between starformation rate and the equivalent width of the Mg II ab-sorption doublet, indicating that gas content can possiblybe used as a predictor for starburst phenomena. Chen et al.(2010) used 70 low impact parameter Mg II absorbers fromthe Magellan Echellette spectrograph to determine that in-creased impact parameters of the absorbers result in de-creased absorber strength. Kacprzak et al. (2012) used 88spectroscopically confirmed Mg II absorbers from the Hub-ble Space Telescope and SDSS to demonstrate that thereexists an azimuthal bimodal distribution of absorbers, withblue star-forming galaxies driving the bimodality. They in-dicated that halo gas exists more commonly around theprojected galaxy’s major and minor axis. In addition, thebimodality is generated by the accretion of gas along thegalaxy’s major axis and outflowed along the galaxy’s minoraxis. This is consistent with galaxy evolution scenarios wherestar formation galaxies accrete gas. In these same scenar-ios, red galaxies typically have smaller star formation ratesdue to lower gas reservoirs. Nielsen et al. (2013) cataloged182 spectroscopically identified, high redshift ( . − . ) MgII absorbers, indicating that low stellar mass galaxies tendto be bluer and hence possess higher star formation rates.However, they also indicated that the Mg II absorption ispreferentially weaker in such systems. As shown, all of thesestudies required a lot of dedicated spectroscopic data ac-quired from telescopes and used a small sample size.A recently discovered type of absorber that is of greatinterest is the quasar 2175 ˚A dust absorbers (2DAs, Wanget al. 2004, Ma et al. 2017, 2018a). These dust absorbers,displaying strong broad 2175 ˚A absorption features anddust extinction (e.g., Wang et al. 2004; Zhou et al. 2010;Jiang et al. 2010a, b, Jiang et al. 2011; Wang et al. 2012;Zhang et al. 2015; Pan et al. 2017; Ma et al. 2015; 2017),closely resemble the Milky Way (MW). The similarity be-tween the extinction curve of these absorbers and that ofthe MW means that studying these systems might provideclues on the evolution of the MW. 2DAs are also a subgroupof Mg II absorbers, representing about 1 per cent of the to-tal Mg II absorber population detected (Zhao et al. 2018,in prep). While extensive studies on Mg II absorbers havebeen conducted, as shown above, very few studies on 2DAsand their host galaxies have been made. Ma et al. (2017,2018a) performed correlation analysis between metallicity,velocity width, redshift, depletion level, and other quan-tities to compare 2DAs with other absorption lines. Theyconcluded that the 2DA host galaxies contain high metallic-ity, high depletion, are generally massive, and are chemicallyenriched. 2DAs are also more massive than typical Damped-Lyman-alpha (DLA) and sub-DLA galaxies, showing greatermaturation and age. The median estimated stellar mass of2DA host galaxies is × M (cid:12) (Ma et al. 2018a).Thus, studying 2DAs will also give insight into the dustattenuation in high redshift galaxies, which is consequen-tial in the theory of galactic evolution. Early results (Ma etal. 2017, 2018a, b) show that 2DAs are likely matured andmassive. They also report that the impact parameter for one2DA system at z abs = . is only 5.5 kpc, or 0.65 arcsecaway from the quasar. However, this is only an isolated caseas acquiring HST time is extremely difficult and it is hard to MNRAS , 1–19 (2018) tudying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique study a large number of absorber host galaxies using HST.For a sample of 436 2DAs identified by us in the SDSS-IIIDR 12 imaging data (Zhao et al. 2018, in prep), HST imag-ing for each individual absorber system is cost inhibitive.Therefore, only stacking is a viable option that will result inthe sensitivity necessary for detection and for studying theoverarching statistical properties of all 2DA systems.Our research is to develop an automatic and fastimaging stacking and subtraction method using data fromground-based telescopes to study the statistical propertiesof host galaxies of Mg II absorbers and 2DAs i.e. their aver-age impact parameter and SEDs. The impact parameter willpossibly reveal the geometry of host galaxies and will alsohelp identify which components of host galaxies are observedthrough quasar absorption. In order to study the host galaxyproperties and impact parameter distributions of the newlydiscovered and extremely faint 2DAs, we create a stackingtechnique that is specialized in reducing noise levels as effec-tively as possible. We use better and more accurate stellarprofile approximation methods to decrease the noise leveland boost detection. We validate our technique by compar-ing our results with Zibetti et al.’s (2007). Because of thelarge datasets, we create an automated package for ease ofprocessing. This package can also be used to perform stack-ing analysis on other types of absorbers, such as Ca II, CIVor Fe II absorption systems. Our goal is to identify aspects ofgalaxy evolution, discover any new properties/correlations,and confirm previous studies’ results by probing the statis-tical properties of Mg II absorbers and 2DAs. Because the2DAs are largely precluded in the imaging data due to thehigh redshift range ( z abs = . − . ), our improvements tonoise-reduction in the stacking procedure will aid in reveal-ing properties of 2DAs. Hopefully, this will result in newfindings about the MW in the future.In Section 2 of this paper, we present our methodol-ogy of collecting imaging data and selecting both Mg IIabsorbers, 2DAs, and their corresponding reference QSOs.In Section 3 we present the image processing techniques interms of subtracting the sky background, masking unwantedsources, calibrating image intensities, etc. In Section 4 wecalculate surface brightness (SB) profiles and classify thederived SED of Mg II absorber host galaxies. We also per-form simulations of the 2DA host galaxies’ average impactparameter. In Section 5 we discuss our findings. In Section6 we compare our technique to previous studies. All data is retrieved from the Sloan Digital Sky Survey DataReleases 7 (DR7, Abazajian et al. 2009) and 12 (DR12,Alam et al. 2015). Both SDSS DR7 and DR12 provide large,detailed quasar catalogs (DR7QSO, Schneider et al. 2010;DR12QSO, Pˆaris et al. 2015) that contain the RA and DECvalues of the quasar, the run, rerun, frame, and camera num-bers, magnitudes in g , r , and i bands, redshift, etc. The se-lection criteria of quasars is detailed in Ross et al. (2012).We retrieved all the quasar field images from the SDSS DR7and DR12 databases in the five available color bands: u , g , r , i , z . We also retrieved the corresponding fpObj fits binarytable file that contains a detailed list of the physical coordi-nates in the field image, PSF counts, object type, flags, etc. The quasar’s ID number in the fpObj file is given in the DR7QSO catalog for the Mg II absorbers and in the DR12 QSOcatalog for 2DAs, so obtaining the physical coordinates ofthe quasar is accomplished efficiently.For the Mg II absorbers, We use DR7 “corrected” fpCimages, which are flat-field corrected but retain the origi-nal background signals. For the 2DA systems, we use DR12“frames”, which already have an accurate sky-backgroundsubtracted. Section 2.1 describes the selection of Mg II ab-sorbers. Section 2.2 describes the selection of 2DAs. Section2.3 details the selection of reference QSOs for both Mg IIabsorbers and 2DAs. In order to validate the effectiveness and accuracy of ourprocedure, we first emulate the Zibetti et al. (2007) study’sresults. We used the QSO-based Mg II absorber catalog inZhu et al. (2013) It contains >
880 Mg II absorbers in theredshift range of z abs = . − . , as shown in Figure 1. TheMg II absorbers were systematically found by comparingRight Ascension (RA) and Declination (DEC). All imagesused are the fpC imaging data files given by SDSS DR7,which are bias-corrected and flat-fielded but preserve theobserved background levels measured in counts. The 2DAs are characterized by dust extinction. A catalog of436 absorbers were selected from SDSS DR12 by Zhao et al.(2018, in prep). These absorbers have higher redshift thanthe Mg II absorbers and span a much greater redshift range( z abs = . − . ). The apparent magnitude distribution ofQSOs both with Mg II absorbers and 2DAs are approxi-mately normally distributed, with 2DA quasars being, onaverage, 0.5 magnitudes dimmer. Like any scientific study, a control sample is necessary toassert that our results are valid. Thus, a large sample ofquasars that lack the Mg II absorption lines is required toprove that any results gained from quasars with Mg II ab-sorption host galaxies are significant and unattainable fromnon-absorbing quasars. For each quasar with the Mg II ab-sorption spectrum, we selected four reference quasars. Thesequasars must match their absorption counterpart closely.The criterion for choosing reference quasars are as follows: • Difference in redshift must be less than 0.1 • Difference in magnitude must be less than 0.5 in u g riz bandsThese two boundaries ensure that the reference quasarsresemble the absorption quasars as much as possible so thatnew findings are strongly associated with the host galaxies.The quasars are then binned by the equivalent width of the2796 ˚A absorption line and by the redshift of the absorbers.The bins chosen were consistent with those of previous stud-ies: • Redshift z abs : . − . • Equivalent Width: W > . ˚A MNRAS000
880 Mg II absorbers in theredshift range of z abs = . − . , as shown in Figure 1. TheMg II absorbers were systematically found by comparingRight Ascension (RA) and Declination (DEC). All imagesused are the fpC imaging data files given by SDSS DR7,which are bias-corrected and flat-fielded but preserve theobserved background levels measured in counts. The 2DAs are characterized by dust extinction. A catalog of436 absorbers were selected from SDSS DR12 by Zhao et al.(2018, in prep). These absorbers have higher redshift thanthe Mg II absorbers and span a much greater redshift range( z abs = . − . ). The apparent magnitude distribution ofQSOs both with Mg II absorbers and 2DAs are approxi-mately normally distributed, with 2DA quasars being, onaverage, 0.5 magnitudes dimmer. Like any scientific study, a control sample is necessary toassert that our results are valid. Thus, a large sample ofquasars that lack the Mg II absorption lines is required toprove that any results gained from quasars with Mg II ab-sorption host galaxies are significant and unattainable fromnon-absorbing quasars. For each quasar with the Mg II ab-sorption spectrum, we selected four reference quasars. Thesequasars must match their absorption counterpart closely.The criterion for choosing reference quasars are as follows: • Difference in redshift must be less than 0.1 • Difference in magnitude must be less than 0.5 in u g riz bandsThese two boundaries ensure that the reference quasarsresemble the absorption quasars as much as possible so thatnew findings are strongly associated with the host galaxies.The quasars are then binned by the equivalent width of the2796 ˚A absorption line and by the redshift of the absorbers.The bins chosen were consistent with those of previous stud-ies: • Redshift z abs : . − . • Equivalent Width: W > . ˚A MNRAS000 , 1–19 (2018)
Bill Zhu, Yinan Zhao, Jian Ge, Jingzhe Ma
Figure 1.
Above are the distributions of the redshifts of the two classes of absorbers. We will only be focusing on z abs = . − . redshift Mg II absorbers, as indicated by the vertical dashed red lines marking the range. We will be using all the 2DAs at z abs = . − . . The reference quasars for both the Mg II absorbers and2DAs are selected using the above criteria, with the excep-tion that Mg II reference quasars are chosen from the DR7catalog; 2DAs are chosen from the DR12 catalog. The twoQSO Catalogs share many of the same attributes, some ofwhich are listed above. For now, we only report the stack-ing of all Mg II absorbers in the . − . redshift bin, inother words all Mg II absorbers as cataloged in Zhu et al.’s(2013) DR7 Mg II absorber catalog. In total, there are ap-proximately 880 Mg II absorber QSOs, 3500 Mg II referenceQSOs, 436 2DAs, and 1580 2DA reference QSOs. The ex-act number differs slightly among color bands, with slightlylower numbers in the z -band due to lower SNR and insuffi-cient numbers of PSF stars to choose from for training thePSF. The stacking approach capitalizes on the fact that the galax-ies linked to an absorbing system statistically produce an ex-cess of surface brightness (SB) around the absorbed QSOswith respect to unabsorbed ones. Such an SB excess can bemeasured to obtain both global photometric quantities forthe absorbing galaxies in different bands and the spatial dis-tribution of the light of the absorbing galaxies, from whichthe impact parameter distribution of absorbing gas cloudscan be derived. In this section we describe the techniquesthat allow us to optimally integrate and measure the fluxdistribution of exclusively all galaxies that cross-correlatewith the presence of an absorber. By “optimally” we meanthat any source of noise is minimized. There are three mainsources of noise: (1) the intrinsic photon noise, which is fixed by the number of stacked images, (2) the signal producedby field objects such as stars and galaxies which are notcorrelated with the absorbers, and (3) the light from theQSO itself. While the intrinsic photon noise appears to besufficiently low for a few hundred SDSS images, the signalfrom background sources and the brightness mismatch thatis allowed between absorbed and reference QSOs, althoughsmall, produce a noise that is orders of magnitude largerthan the signal to be detected. These two sources of noisemust be drastically reduced by applying accurate maskingand QSO PSF subtraction algorithms on each image. Thestacking and subsequent analysis is conducted simultane-ously in the four bands for which most of the flux is expected,i.e., g , r , i , and z . (Zibetti et al. 2007)Section 3.1 is devoted to the splicing of the field im-ages to retrieve the quasars. Section 3.2 details the mask-ing algorithm we employed. Section 3.3 explains our PSFsubtraction algorithm. Section 3.4 describes the backgroundsubtraction accuracy, photometric calibration, and stackingmethods used. The quasar’s location is first identified by extracting the re-quired object ID number located under the quasar’s indexin the catalog. For DR7, the specific ID of the QSO, as iden-tified in the fpObj binary table, is given directly in the DR7QSO Catalog. For DR12, a binary decomposition method isperformed to extract the ID number. After identifying thequasar, a × pixel region centered on the quasar iscut out. 2D interpolation is then performed to center thequasar at its centroid. The background is not subtracted inthis procedure, but rather when performing the PSF sub- MNRAS , 1–19 (2018) tudying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique traction. The same background is calculated for both thePSF fitting and the quasar from the 3 σ clipping medianvalue of the image data, ensuring consistency. For the DR12data, the background is already subtracted accurately. Zibetti et al. (2007) implemented a masking algorithm thatused flux-limited masks to mask all stars with apparentmagnitude < − . The actual masking radii is slightly enlarged toaccount for irregularities. However, as noted in DR12, thealgorithm used to calculate the isophotal semi-major radiusis inaccurate. In addition, circular radii are not effective inmasking highly irregularly shaped sources and may unnec-essarily alter pixels that do not have to be masked. Thus, weutilized a masking technique that used a flood-fill algorithmto mask non-circular objects. Once a source is identified inthe quasar cut out frame by way of calculating distancesbetween other sources and the quasar, the source is maskedout spreading from the centroid of the source, recursivelychecking every adjacent pixel to see if the counts are morethan 1 σ above the σ clipped mean background level of thewhole image. Extended sources such as oversaturated starsare more effectively and systematically suppressed this way.In order to better constrain the masking to ensure that thequasar itself isn’t accidentally masked, (due to close sourcesthat extend a 1 σ “band” to the QSO) the QSO’s light is firsttaken out by using SDSS’s “postage-stamp” images found inthe fpAtlas files. This postage-stamp image is meant to bedeblended from all other sources so the QSO is optimallycut out before masking takes place.The above masking scheme is used for all sources iden-tified as stars; for those identified as galaxies, an additionalstep is needed. In the redshift range that we are studying, . − . , some Mg II absorber host galaxies are visiblein the field images, and are subsequently cataloged in thefpObj files. In order to differentiate between galaxies thatcontain the Mg II absorption line and those that don’t, weadopt the galaxy fluxes derived for an unobscured, metal-poor stellar population produced in a 100 Myr long burst,observed right at the end of the burst itself, with rest frame g -band absolute magnitude M g , thresh = − . . This SED iscomputed from the Charlot & Bruzual (2007) SED modelswhich updated their 2003 models. Previous research has in-dicated that adopting a higher threshold of − . absolutemagnitudes for computing the SED results in no systematiceffect, although the number of bright interlopers significantlyincreases (Zibetti et al. 2007). Thus, the threshold computedwith M g , thresh = − . is satisfactory. To ensure the highestconsistency with Zibetti et al.’s (2007) study, we choose thesame flux-limited mask parameters. If a source is classifiedas a galaxy by SDSS, then its PSF counts in g riz bands areobtained and compared with the corresponding flux thresh-old PSF counts we calculated. If the galaxy’s PSF countsin the g , r , and i bands are lower than the correspondingthresholds, then the galaxy passes through the mask. Oth-erwise, the galaxy is masked in each of the four color bands.There is the chance that in the reference QSO imag- ing, faint galaxies documented by the object catalogs willpass under the flux-limited mask thresholds. Zibetti et al.(2007) used a σ clipping procedure to exclude these faintsources. However, in a large sample of images, the randomdistribution of these faint background galaxies in the refer-ence QSOs is also present in the absorber QSOs. Therefore,when the reference QSO stacking is subtracted from the ab-sorber QSO stacking, the excess residue contributed by thesefaint background galaxies is negated. As demonstrated bestby the r and i band QSO stackings, there is random residualat large impact parameters in the reference frame as well asthe absorber frame, but the net frame indicates significantresidue at lower impact parameters.After masking, the mean background value measuredbetween 400 and 500 kpc from the QSO’s centroid is sub-tracted from the image. This same background subtractionprocedure is used for every PSF star selected, as described inSection 3.4. In order to make sure that the background calcu-lation is not contaminated by significantly brighter sourcesthat pass under the masking algorithm, we employ a σ clip-ping procedure with a threshold of ± σ and 5 iterations toexclude bright pixels. Because a quasar’s light can spread to a few arcseconds andcontaminate the absorption host galaxies surface brightness,the quasar’s profile must be subtracted. Originally, like Zi-betti et al. (2007), we utilized single point source PSF sub-traction algorithm. However, upon closer analysis of individ-ual PSF subtracted frames, single source PSF subtraction isineffective, so we implemented a machine learning algorithm,Principal Component Analysis (PCA), to fit the QSO pro-files.At first, we chose one bright, unsaturated star as thePSF by comparing Full Width Half Maximum (FWHM),brightness, and color differences from the respective prop-erties of the quasar. The PSF stars are normalized to thequasar using the PSF magnitudes given in the QSO catalog,then subtracted from the absorption and reference quasars.Theoretically, subtracting the PSF source from the absorp-tion quasars should yield residues, which are the absorptionhost galaxies. Subtracting the PSF source from the referencequasars should yield mostly noise, as there are no absorbers.However, a substantial portion of the reference quasars leftbright residue after PSF subtraction. Previous studies indi-cate that this kind of “additive excess” (Zibetti et al. 2007)is caused by randomly distributed foreground galaxies in theline of sight towards the QSOs as well as by host galaxiesassociated with the QSOs themselves. Regardless, our singlesource PSF subtraction algorithm was insufficient for sub-traction especially since the availability of closely relatedstars in each frame was low.From a statistical standpoint, single source PSF sub-traction yields greater noise. Since the single source PSF andsurrounding background should closely match the quasar,the final σ is approximately 1.4 ( √ ) times the original σ .The SNR of individual images is already exceedingly low, soincreasing the noise by over 40 per cent is inhibitive. Thisis even more important with low sample sizes as with the2DAs.For those reasons, we employed Principal Component MNRAS000
Above are the distributions of the redshifts of the two classes of absorbers. We will only be focusing on z abs = . − . redshift Mg II absorbers, as indicated by the vertical dashed red lines marking the range. We will be using all the 2DAs at z abs = . − . . The reference quasars for both the Mg II absorbers and2DAs are selected using the above criteria, with the excep-tion that Mg II reference quasars are chosen from the DR7catalog; 2DAs are chosen from the DR12 catalog. The twoQSO Catalogs share many of the same attributes, some ofwhich are listed above. For now, we only report the stack-ing of all Mg II absorbers in the . − . redshift bin, inother words all Mg II absorbers as cataloged in Zhu et al.’s(2013) DR7 Mg II absorber catalog. In total, there are ap-proximately 880 Mg II absorber QSOs, 3500 Mg II referenceQSOs, 436 2DAs, and 1580 2DA reference QSOs. The ex-act number differs slightly among color bands, with slightlylower numbers in the z -band due to lower SNR and insuffi-cient numbers of PSF stars to choose from for training thePSF. The stacking approach capitalizes on the fact that the galax-ies linked to an absorbing system statistically produce an ex-cess of surface brightness (SB) around the absorbed QSOswith respect to unabsorbed ones. Such an SB excess can bemeasured to obtain both global photometric quantities forthe absorbing galaxies in different bands and the spatial dis-tribution of the light of the absorbing galaxies, from whichthe impact parameter distribution of absorbing gas cloudscan be derived. In this section we describe the techniquesthat allow us to optimally integrate and measure the fluxdistribution of exclusively all galaxies that cross-correlatewith the presence of an absorber. By “optimally” we meanthat any source of noise is minimized. There are three mainsources of noise: (1) the intrinsic photon noise, which is fixed by the number of stacked images, (2) the signal producedby field objects such as stars and galaxies which are notcorrelated with the absorbers, and (3) the light from theQSO itself. While the intrinsic photon noise appears to besufficiently low for a few hundred SDSS images, the signalfrom background sources and the brightness mismatch thatis allowed between absorbed and reference QSOs, althoughsmall, produce a noise that is orders of magnitude largerthan the signal to be detected. These two sources of noisemust be drastically reduced by applying accurate maskingand QSO PSF subtraction algorithms on each image. Thestacking and subsequent analysis is conducted simultane-ously in the four bands for which most of the flux is expected,i.e., g , r , i , and z . (Zibetti et al. 2007)Section 3.1 is devoted to the splicing of the field im-ages to retrieve the quasars. Section 3.2 details the mask-ing algorithm we employed. Section 3.3 explains our PSFsubtraction algorithm. Section 3.4 describes the backgroundsubtraction accuracy, photometric calibration, and stackingmethods used. The quasar’s location is first identified by extracting the re-quired object ID number located under the quasar’s indexin the catalog. For DR7, the specific ID of the QSO, as iden-tified in the fpObj binary table, is given directly in the DR7QSO Catalog. For DR12, a binary decomposition method isperformed to extract the ID number. After identifying thequasar, a × pixel region centered on the quasar iscut out. 2D interpolation is then performed to center thequasar at its centroid. The background is not subtracted inthis procedure, but rather when performing the PSF sub- MNRAS , 1–19 (2018) tudying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique traction. The same background is calculated for both thePSF fitting and the quasar from the 3 σ clipping medianvalue of the image data, ensuring consistency. For the DR12data, the background is already subtracted accurately. Zibetti et al. (2007) implemented a masking algorithm thatused flux-limited masks to mask all stars with apparentmagnitude < − . The actual masking radii is slightly enlarged toaccount for irregularities. However, as noted in DR12, thealgorithm used to calculate the isophotal semi-major radiusis inaccurate. In addition, circular radii are not effective inmasking highly irregularly shaped sources and may unnec-essarily alter pixels that do not have to be masked. Thus, weutilized a masking technique that used a flood-fill algorithmto mask non-circular objects. Once a source is identified inthe quasar cut out frame by way of calculating distancesbetween other sources and the quasar, the source is maskedout spreading from the centroid of the source, recursivelychecking every adjacent pixel to see if the counts are morethan 1 σ above the σ clipped mean background level of thewhole image. Extended sources such as oversaturated starsare more effectively and systematically suppressed this way.In order to better constrain the masking to ensure that thequasar itself isn’t accidentally masked, (due to close sourcesthat extend a 1 σ “band” to the QSO) the QSO’s light is firsttaken out by using SDSS’s “postage-stamp” images found inthe fpAtlas files. This postage-stamp image is meant to bedeblended from all other sources so the QSO is optimallycut out before masking takes place.The above masking scheme is used for all sources iden-tified as stars; for those identified as galaxies, an additionalstep is needed. In the redshift range that we are studying, . − . , some Mg II absorber host galaxies are visiblein the field images, and are subsequently cataloged in thefpObj files. In order to differentiate between galaxies thatcontain the Mg II absorption line and those that don’t, weadopt the galaxy fluxes derived for an unobscured, metal-poor stellar population produced in a 100 Myr long burst,observed right at the end of the burst itself, with rest frame g -band absolute magnitude M g , thresh = − . . This SED iscomputed from the Charlot & Bruzual (2007) SED modelswhich updated their 2003 models. Previous research has in-dicated that adopting a higher threshold of − . absolutemagnitudes for computing the SED results in no systematiceffect, although the number of bright interlopers significantlyincreases (Zibetti et al. 2007). Thus, the threshold computedwith M g , thresh = − . is satisfactory. To ensure the highestconsistency with Zibetti et al.’s (2007) study, we choose thesame flux-limited mask parameters. If a source is classifiedas a galaxy by SDSS, then its PSF counts in g riz bands areobtained and compared with the corresponding flux thresh-old PSF counts we calculated. If the galaxy’s PSF countsin the g , r , and i bands are lower than the correspondingthresholds, then the galaxy passes through the mask. Oth-erwise, the galaxy is masked in each of the four color bands.There is the chance that in the reference QSO imag- ing, faint galaxies documented by the object catalogs willpass under the flux-limited mask thresholds. Zibetti et al.(2007) used a σ clipping procedure to exclude these faintsources. However, in a large sample of images, the randomdistribution of these faint background galaxies in the refer-ence QSOs is also present in the absorber QSOs. Therefore,when the reference QSO stacking is subtracted from the ab-sorber QSO stacking, the excess residue contributed by thesefaint background galaxies is negated. As demonstrated bestby the r and i band QSO stackings, there is random residualat large impact parameters in the reference frame as well asthe absorber frame, but the net frame indicates significantresidue at lower impact parameters.After masking, the mean background value measuredbetween 400 and 500 kpc from the QSO’s centroid is sub-tracted from the image. This same background subtractionprocedure is used for every PSF star selected, as described inSection 3.4. In order to make sure that the background calcu-lation is not contaminated by significantly brighter sourcesthat pass under the masking algorithm, we employ a σ clip-ping procedure with a threshold of ± σ and 5 iterations toexclude bright pixels. Because a quasar’s light can spread to a few arcseconds andcontaminate the absorption host galaxies surface brightness,the quasar’s profile must be subtracted. Originally, like Zi-betti et al. (2007), we utilized single point source PSF sub-traction algorithm. However, upon closer analysis of individ-ual PSF subtracted frames, single source PSF subtraction isineffective, so we implemented a machine learning algorithm,Principal Component Analysis (PCA), to fit the QSO pro-files.At first, we chose one bright, unsaturated star as thePSF by comparing Full Width Half Maximum (FWHM),brightness, and color differences from the respective prop-erties of the quasar. The PSF stars are normalized to thequasar using the PSF magnitudes given in the QSO catalog,then subtracted from the absorption and reference quasars.Theoretically, subtracting the PSF source from the absorp-tion quasars should yield residues, which are the absorptionhost galaxies. Subtracting the PSF source from the referencequasars should yield mostly noise, as there are no absorbers.However, a substantial portion of the reference quasars leftbright residue after PSF subtraction. Previous studies indi-cate that this kind of “additive excess” (Zibetti et al. 2007)is caused by randomly distributed foreground galaxies in theline of sight towards the QSOs as well as by host galaxiesassociated with the QSOs themselves. Regardless, our singlesource PSF subtraction algorithm was insufficient for sub-traction especially since the availability of closely relatedstars in each frame was low.From a statistical standpoint, single source PSF sub-traction yields greater noise. Since the single source PSF andsurrounding background should closely match the quasar,the final σ is approximately 1.4 ( √ ) times the original σ .The SNR of individual images is already exceedingly low, soincreasing the noise by over 40 per cent is inhibitive. Thisis even more important with low sample sizes as with the2DAs.For those reasons, we employed Principal Component MNRAS000 , 1–19 (2018)
Bill Zhu, Yinan Zhao, Jian Ge, Jingzhe Ma
Figure 2.
The PCA PSF subtracted stars stacked frames in griz bands are shown here. As demonstrated, there is no significant residuein any of the bands, indicating that the PSF subtraction is good.
Analysis (PCA) as our means of PSF subtraction. The ideaof the PCA is to perform dimension reduction on the imagingdata of many PSF stars to simplify the large data sets. Thismethod is widely used in deriving quasar continuum in thequasar spectra analysis (Francis et al. 1992; Yip et al. 2004;Suzuki et al. 2005). Instead of 1D spectra, We used PCAto analyze 2D images. For each quasar target, we select allthe field stars that satisfy certain criteria to build the QSOPSF mask. Our criteria are that the PSF star must havea second moment within 10 per cent of the QSO’s secondmoment, the PSF star can not have interpolated or over-saturated pixels, cosmic rays, its apparent magnitude must be <
18, etc. Most QSO’s were matched with more than 20PSF stars. For each field star selected, a × pixels square cutout centered at and interpolated to the PSF star’scentroid is reshaped to a single row of 10201 pixels. Eachsource chosen is normalized by PSF counts (given by SDSS)to the quasar’s PSF counts, then put into a large array, witheach row holding one source. Normalization of each sourceis done before the actual fitting because PCA is very sen-sitive to the relative fluctuation of the original variables -inthis case, stars. The mean vector of the array for every pixelcolumn is calculated and subtracted from the large array.Here we used singular value decomposition (SVD) solver to MNRAS , 1–19 (2018) tudying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique Figure 3.
Top left the r band cutout of QSO J . + . . Right is the PCA generated PSF subtracted image of the samequasar. The two images are shown through the Z-scale setting in SAOImage DS9. (Version 7.5) The blotches of uniform gray are sourcesthat were effectively masked by suppressing the bright pixels to the σ clipped mean value. There is a clear bright patch near the centerof the PSF subtracted frame, which is likely the absorber host galaxy. Also note that the two frames appear almost geometricallyidentical: both bright and dark spots correspond almost identically in the two frames, demonstrating the low amount of noise addedduring PCA-generated PSF subtraction. Table 1.
Background Levels σ clipped mean background levels measured between − kpc in counts g . ± . r . ± . i . ± . z . ± . derive the “eigen-images” from the covariance matrix of fieldstars. We only used the central × eigenvectors to fit thecorresponding target. The coefficients are calculated by pro-jecting the “eigen-images” onto the target image. The QSOcutout and the generated PSF image, both × pixels ,are then subtracted to generate the final PSF-subtracted im-age. We used Incremental PCA (IPCA), a more memory-efficient solution than regular PCA. IPCA works similarlyto PCA with the notable exception that it does not storethe entire dataset in memory, making IPCA advantageousover regular PCA for large datasets, as in our case.One drawback of PCA is overfitting. If too many noisecomponents are included in the fitting calculation, then thefitting is too accurate. In addition, host galaxies close to theabsorption quasars may be fitted and subtracted, leaving novisible residue. The solution was to only perform PCA on thecentral portion of the quasar, roughly × pixels squareportion. The coefficients used in building the PCA mask arecomputed using only the central × pixel eigenvalues.The resulting PCA PSF mask is the same size as the QSO frame ( × pixel ). This greatly reduced overfittingwhile ensuring that a good profile fitting was produced.Again, from a statistical standpoint, using multiplesources yields a much smaller addition to the noise. Thecombined σ of multiple sources decreases by a factor of √ N which means the more sources used, the smaller the σ , andtherefore the smaller the noise added to the overall image. Asshown in Figure 3, the QSO’s profile is accurately subtractedfrom the frame, and the resulting images are geometricallysimilar because the noise level is significantly decreased by − times.In order to test the effectiveness of PCA PSF subtrac-tion, we first test model star profiles. We select a bright star >
18 mag that is similar to the Mg II absorber QSO in lightdistribution (second moment), contains no interpolated pix-els, is not over saturated, etc. We then apply the PCA PSFsubtraction procedure detailed above to build a PSF maskfor the chosen star, taking care to avoid including the star it-self in the PSF star sample used to build the PCA PSF. ThePSF subtracted frames are stacked (see Section 3.4 for moreinformation) and the resulting mean stack frame is plottedin gray scale. Some images are excluded because there was abright source nearby or insufficient PSF stars were found tobuild the PCA PSF mask. Apart from random backgroundphoton noise, there is no significant residue left over, thusdemonstrating the reliability of PCA PSF subtraction.
Due to the nature of PCA fitting and the size constraintsof the images, it is extremely difficult to perform a secondround background subtraction using the method detailed
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Bill Zhu, Yinan Zhao, Jian Ge, Jingzhe Ma
Figure 4.
The average σ clipped backgrounds of all the PSF stars used for creating the reference QSO PSF mask are plotted above(solid blue curve). A separate measurement is taken at each increasing arcsec annuli, and the mean is calculated for all PSF stars in thecolor band. For illustration, the red dashed line representing the average background at − kpc is also plotted, again calculatedas the mean of all PSF stars selected in the color band. The black curves represent the ± σ boundaries. The green bar represents therange that 400 kpc resides in given the redshift range of z abs = . − . , while the blue bar represents the range that 500 kpc residesin in the same redshift range. The red bar represents the range used to calculate the SED ( − kpc). above (taking the σ clipped mean background between 400and 500 kpc from the QSO centroid. In order to ensure thatthe initial background subtraction is accurate and the re-sulting “pedestal” left over is minimal, we measure the σ clipped mean background of each reference QSO PSF star(selected as described in Section 3.3) before PCA PSF sub-traction and background subtraction but after masking atincreasing arcsec annuli. No photometric calibration for in-dividual images (as described in the following paragraphs) isperformed in this procedure. We then take the mean countof all the background counts at each arcsec annuli for allfour color bands. In the individual frames, the σ clippedmean background varies < σ from ∼ arcsec and above,with slight random fluctuations. The background calculatedbetween 400 and 500 kpc is therefore very representative ofthe true background, as shown in Figure 4. The σ clippedmean background and σ counts are given in Table 1.For a more thorough analysis of the level of residue leftover in individual frames, we calculate the mean count be-tween 400 and 500 kpc after the σ clipped background levelis subtracted. The resulting histograms are plotted in Figure5. All four color bands show a Gaussian distribution of the residue with a center of 0. Thus, a second round backgroundsubtraction is highly unnecessary.Because the photometric calibration of each image isdifferent, i.e. different counts correspond to different magni-tudes, the images must be intensity rescaled to a uniform cal-ibration. Each quasar is then de-reddened using the Schlegel,Finkbeiner & Davis 1998 (SFD) extinction maps, as galacticextinction must be corrected for to ensure photometric accu-racy; the resulting images are slightly brighter. The formulaused is: I cal = I raw f , ref f . A λ . (1)Where I cal is the final calibrated intensity (Fukugita etal. 1996; Smith et al. 2002), I raw is the original intensity, f , ref is the counts that corresponds to 20 mag in the finalstacked frame, f is the pixel counts that corresponds to20 mag in the observed fpC frame, and A λ is the galacticextinction coefficient in the color band of the quasar, givenin the quasar catalogs.The images are then combined by taking the mean valueof each pixel value separately. Since the host galaxies are MNRAS , 1–19 (2018) tudying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique Figure 5.
The mean residue of all reference QSO PSF stars at − kpc after the σ clipped background is subtracted. As shown inall four histograms corresponding to the four color bands griz , the mean residue left over is roughly Gaussian with a mean of 0. clustered around the quasars, once all the PSF subtractedimages are stacked, a significant halo is observed. This halois the combined residue of all the absorption host galaxies,which were mostly undetectable in individual frames.Unlike in Zibetti et al.’s (2007) study, we do not phys-ically rescale the images to a common kpc pixel − scale.This is because the location dependent sky background isnot accurately subtracted from the entire image; only a σ clipped mean value is subtracted. Although the average skybackground has been greatly suppressed as demonstratedin Figure 4 and 5, localized sky level fluctuation still ex-ist. Thus, physical rescaling will result in flux deviations.The purpose of such rescaling was to ensure different hostgalaxies corresponding to different redshifts would have thesame kpc pixel − scale. Without rescaling, the final stackedimages would become slightly “blurred” as residues from dif-ferent physical impact parameters are combined. However,due to the low range of redshifts ( z abs = . − . ), thiswas deemed acceptable; ultimately, when calculating totalflux and SED, the “blurring” effect is minimized since thecumulative flux of the final stacked image is calculated. Forcalculating the SB profiles and fitting the SED, we use themean z abs ∼ . .All the processes performed are created from a pack- age developed by us, implementing standard libraries suchas Numpy, Scipy, Astropy, Photutils, sklearn, etc. The At-las.fits files that contain all the “poststamp” deblended im-ages of each individual object is processed through thesdsspy Python package which we modified and implemented.The flux-limited masks thresholds are calculated by imple-menting the EzGal Python package developed by Manconeet al. (2012), which utilizes the g riz band fluxes from SDSSand the stellar population SEDs calculated from Charlot &Bruzual (2007). A great majority of the processing code iswritten in Python 3. The data download from the SDSSData Archive Server is written in Batch programming. In this section we analyze the statistical properties of thestacked frames. In Section 4.1, we present the SB profile ofthe Mg II absorber host galaxies. In Section 4.2, we plot theSpectral Energy Distribution (SED) of the Mg II absorberhost galaxies. In Section 4.3, we simulate the upper limitthreshold of the average impact parameter of the 2DA hostgalaxies.
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Figure 6.
Above are the graphs of the four bands of PSF-subtracted images. The top row is the stacked Mg II frames, the middle rowis the stacked reference QSO frames, and the bottom row is the net frame resulting from subtracting the reference stacked image fromthe Mg II stacked image. All pixel intensities are converted to a common mag arcsec − scale. MNRAS , 1–19 (2018) tudying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique Figure 7.
The stacked frames of the 2DA systems in griz bands. There is little residue prevalent in each bandwidth, indicating that the2DA host galaxies are likely at extremely small impact parameters such that they are completely subtracted off during PSF subtraction.In all four bands, the Mg II absorbers clearly contain much more absorbed light than the 2DAs.
Despite our best fitting, there is still some residue left overfrom the PSF subtraction in the reference quasar framesas shown in Figure 6. This residue is demonstrated in theappendix section by Zibetti et al. (2007) as a systematiceffect of the redshift and magnitude of the QSO itself. Assuch, this is taken as the “additive excess” of the quasars.The stacked reference quasar residue is subtracted from thestacked absorber quasar reside to yield a net profile. Wecalculate the SB at annuli with geometrically increasing radiiin order to preserve a near-constant SNR. Figure 7 shows the residue left from the 2DA stacked frames. Figure 8 shows theradial distribution of SB profiles at g , r , i , and z bands forMg II absorber host galaxies, and Figure 9 shows the SBprofiles for 2DA host galaxies.It is worth noting that increasing redshifts lead to in-creasing physical scales of kpc pixel − . Because we did notphysically rescale the data to a constant kpc pixel − scale,our image stacking method results in slight blurring of ab-sorber host galaxies at different redshifts. In addition, dueto the normalization of the PSF to the QSO, the center iszeroed out to a high degree, indicative of the good quality of MNRAS000
Despite our best fitting, there is still some residue left overfrom the PSF subtraction in the reference quasar framesas shown in Figure 6. This residue is demonstrated in theappendix section by Zibetti et al. (2007) as a systematiceffect of the redshift and magnitude of the QSO itself. Assuch, this is taken as the “additive excess” of the quasars.The stacked reference quasar residue is subtracted from thestacked absorber quasar reside to yield a net profile. Wecalculate the SB at annuli with geometrically increasing radiiin order to preserve a near-constant SNR. Figure 7 shows the residue left from the 2DA stacked frames. Figure 8 shows theradial distribution of SB profiles at g , r , i , and z bands forMg II absorber host galaxies, and Figure 9 shows the SBprofiles for 2DA host galaxies.It is worth noting that increasing redshifts lead to in-creasing physical scales of kpc pixel − . Because we did notphysically rescale the data to a constant kpc pixel − scale,our image stacking method results in slight blurring of ab-sorber host galaxies at different redshifts. In addition, dueto the normalization of the PSF to the QSO, the center iszeroed out to a high degree, indicative of the good quality of MNRAS000 , 1–19 (2018) Bill Zhu, Yinan Zhao, Jian Ge, Jingzhe Ma
Figure 8.
Above are the SB profiles of the four bands: g , r , i , and z , where most of the flux originating from the absorbers lie in.The points represent the larger radius of each circular annuli, with the smaller radii being the next lower respective point. Error barsare calculated using SDSS photon count error calculations and intrinsic image noise values. The data points represent the average netresidual at each impact parameter. the PSF fitting. However, this also results in any low impactparameter host galaxy’s light being subtracted off. For MgII absorbers, this is not a problem since there are very few,if any, host galaxies associated with Mg II absorbers at animpact parameter of <
10 kpc, or roughly − pixels (Stei-del et al. 1994; Churchill et al. 2005a). Regardless, there issignificant residue left over in the net profile.The SB profiles for the 2DA host galaxies in the g riz bands are also given in Figure 9. From the plots, it is clearthat there is no significant residue left over in all four bands.As shown in Figure 7, there appears to be no significantresidue. Therefore, it is impossible to fit power laws or derivean SED. We then built an SED of the Mg II absorber host galaxies.The total flux of the absorbers from − kpc is inte-grated and converted to flux density units using the zero-point magnitudes given by SDSS. The magnitudes obtainedare consistent with Zibetti et al.’s (2007) results as illus-trated in Figure 10, further confirming the success of thePCA fitting algorithms. We then proceed to use the CIGALE Bayesian SEDfitting library developed by Burgarella et al. (2005). Thislibrary fits the SED in the observed frame; consequently noK-correction is necessary. Compared to the galaxy templatefitting used in Zibetti et al. (2007) that can only indicatethe general type of galaxy, CIGALE can derive the physi-cal parameters of Mg II absorber host galaxies. In order tofit the SED of Mg II photometry data we derived, we hadto decide many of the components used to fit the data. Weused the delayed τ model for the star formation history (Leeet al. 2009). We also used the models provided by Bruzual& Charlot (2003) to model the stellar population evolution.York et al. (2006) derived the mean extinction curve by geo-metrically combining Mg II absorber spectra and determinedthat there was an absence of the 2175 ˚A absorption bump.Therefore, we used the SMC extinction curve to model thedust attenuation of Mg II host galaxies. According to thewavelength coverage of SDSS, the imaging data does notextend to the infrared region. Thus, no dust emission com-ponent is included in the Mg II SED modeling. Here we usedthe z abs = . mean redshift of our Mg II absorber sampleas the redshift of the Mg II SED. Since the z -band data isvery close to the H α emission in the Mg II rest frame, we MNRAS , 1–19 (2018) tudying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique Figure 9.
Same arrangement as Figure 8, except for the g , r , i , and z bands for 2DAs. Note that no reference QSOs were subtractedfrom the stacked 2DA frame. Very little residue is detected in all four bands. add the nebular emission into the SED modeling. Becausethe average redshift of the Mg II absorbers is 0.48, the oldestage of stars in absorber galaxies is around 8.750 Gyr; thus,the highest age input for the oldest star parameter is 8.750Gyr. We carefully tuned the parameter ranges for each ofthe components, including metallicity and dust attenuationpower law, and the best fitting we obtained produced a χ of 0.67.Because of the uncertainty of the range of physical pa-rameters that would result in a best fit, we inputted a widerange for the parameters, including maximum star age, bestslope delta of the power law continuum, V-band attenuationof the young star population, etc. The Bayesian parametersand errors given are averaged over the posterior distributionsof the output parameters, while the best fit parameters arereported from the best χ fitting. We report both sets ofparameters in Table 2. Table 3 provides the apparent mag-nitudes derived from the integral flux between − kpc.Some of the best fit parameters diverge from theBayesian parameter i.e. stellar mass. This is most likely dueto the low wavelength range of our data which does not ex-tend into the UV range.The best fit (lowest χ ) star formation rate we derivedhere is 2.2 M (cid:12) y r − . The star formation rate of Mg II ab- sorbers are usually derived from the nebular emission linesin the spectra data. Noterdaeme et al. (2010) identified 46Mg II spectra in the redshift range < . with [OIII] emis-sion lines from SDSS DR7. The derived lower limits of SFRis in the range of . − M (cid:12) y r − , which is consistent withour result. Recently, Joshi et al. (2017) derived the star for-mation rate (SFR) of Mg II in the redshift range from 0.35to 1.1 by measuring [OII] luminosities from 198 spectra inSDSS DR7 and DR12. The SFR is in the range − M (cid:12) y r − , which is also consistent with our derived best fit SFRof 2.2 M (cid:12) y r − .No SED is produced for the 2DA stacked frame becausethe amount of residue left is insignificant; this implies thatthe average impact parameter of 2DA host galaxies is eithermuch smaller than that of Mg II absorber host galaxies orthe signal is still much too low for detection in the stackedframe. We will explore this in the next section. The over subtraction in the 2DA data points to an inherentweakness of the stacking method, and particularly of thePSF normalization section; if the impact parameter of theabsorber host galaxies is extremely low, then the stacking
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Figure 10.
The SED plots of the Mg II absorber Host Galaxies (Left) with error bars, calculated from intrinsic photon noise and skybackground noise. The magnitudes shown in the left plot are calculated by converting the integrated flux between 10 kpc and 100 kpcto magnitudes using SDSS zero point flux densities. Zibetti et al.’s (2007) SED for . ≤ z abs < . Mg II absorbers is also plotted.Note the remarkable consistency between our derived SED and Zibetti et al.’s (2007). The right plot is the best SED fitting generatedusing the CIGALE software described in Burgarella et al. (2005). The resulting χ fitting is 0.67. Table 2.
The best fitting produced by CIGALEAverage Mg II Absorber Host Galaxy Parameters z abs = . − . Best χ Star Formation Rate (SFR) . M (cid:12) yr − Best χ Stellar Mass . × M (cid:12) Best χ Av . Bayesian SFR . ± . M (cid:12) yr − Bayesian Stellar Mass ( . ± . ) × M (cid:12) Bayesian Av . ± . Table 3.
Integral Photometry MagnitudesIntegral flux from − kpc converted to apparent magnitudes g . + − r . + − i . + − z . + − method would likely only yield a upper limit for impact pa-rameter calculations and a lower limit for SED fitting. Thus,we perform simulations to test the upper limits of the aver-age 2DA host galaxy impact parameter. It should be noted that since 2DA systems possess largerest-EW of the 2796 ˚A absorption line, they are strong Mg IIabsorber systems. Previous studies have demonstrated thatthe larger the EW of W ( λ ) , the smaller the impact pa-rameter (Zibetti et al. 2007; Nielsen et al. 2013). Zibetti et al.(2007) showed that Mg II absorber systems with a W ≥ . have an average luminosity-weighted impact parameter of 43kpc, while weaker systems ( . ≤ W < . ) have an averageluminosity-weighted impact parameter of around 60 kpc. Inaddition, their redshift binning indicated that redshift doesnot significantly affect the impact parameter distribution.2DA systems possess an average W = . ± . (Zhao etal. 2018 in prep), which is on the strong side of the Mg II ab-sorber systems. Thus, it is expected that 2DAs have smallerimpact parameters.To test the upper limits of the 2DA’s luminosity-weighted impact parameters, we use the entire 2DA refer-ence quasar dataset (as selected in Section 2.3) of ∼ MNRAS , 1–19 (2018) tudying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique Figure 11.
This plot displays the net amount of residue present at different arcsec impact parameters of the simulated absorber hostgalaxy. The “seeing” FWHM is 1.4 arcsec. In order to keep noise introductions to a minimum, only unit pixel shifts of the galaxy from thecentered QSO are performed, which translates into impact parameter increments of ∼ − to clearly illustrate the differences in residue. Figure 12.
Same as Fig. 9 except with a seeing FWHM of 1.0 arcsec. Note that the residue becomes more pronounced at 0.8 arcsecwith this particular seeing than with a seeing FWHM of 1.4 arcsec.MNRAS000
Same as Fig. 9 except with a seeing FWHM of 1.0 arcsec. Note that the residue becomes more pronounced at 0.8 arcsecwith this particular seeing than with a seeing FWHM of 1.4 arcsec.MNRAS000 , 1–19 (2018) Bill Zhu, Yinan Zhao, Jian Ge, Jingzhe Ma
Figure 13.
Same as Fig. 9 except with a seeing FWHM of 0.6 arcsec. At 0.8 arcsec, the amount of residue is much more significant.Even at 0.4 arcsec there is a significant level of detection.
Figure 14.
The above graph plots the total flux of the residue present at each impact parameter as a percentage against the simulatedabsorber’s flux. Error bars calculated from the intrinsic photon noise and at 3 σ are also plotted in both directions. For clarity, horizontalred lines are plotted at the lower limit of the . − . impact parameters. MNRAS , 1–19 (2018) tudying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique proximations of both the QSOs and the PSF stars. SDSS“seeing” is standard at around 1.4 arcsec, with slightly vary-ing PSF FWHMs reported in the object catalogs, rangingfrom . − . arcsec. We choose the average of 1.4 arcsecin our simulation. For the absorbers, the profiles are scaledto the magnitudes of the reference QSOs for consistency,and a second Gaussian profile with a cumulative area = . magnitudes in the r -band is overlaid at different impact pa-rameters (0.4 arcsec, 0.8 arcsec, etc.) to simulate a 2DA hostgalaxy. This magnitude choice is derived from Zibetti et al.’s(2007) absolute magnitude converted to an apparent mag-nitude at a redshift z abs = . , and thus representative ofthe apparent magnitude of Mg II absorber host galaxies atthat redshift. We choose the redshift z abs = . becausethat is the average redshift of the 2DA absorbers. An al-most uniform sky-background measured from SDSS DR12field images is added to the resulting images, and photonnoise is applied for each pixel. This photon noise is drawnfrom a Poisson distribution. For each simulated absorber,10 PSF stars are created using the image-creation proce-dure with the exception that no host galaxy profile is addedand they are normalized to the QSO with the absorber. Forconsistency, the seeing for the QSO, host galaxy, and thePSF stars are held constant. For illustration, we limit thenumber of host galaxies per absorber to one. PCA is used tobuild a PSF mask from the PSF stars, and the constructedPSF is finally renormalized to the QSO’s total intensity asobserved within 1 FWHM from the centroid.As shown in Figures 11 and 14, at 0.4 and 0.8 arcsec im-pact parameters, the amount of residue present is insignifi-cant ( < σ ). Above 0.8 arcsec, significant residue is observed( > σ ). Thus, with SDSS field imaging data we can deter-mine that beyond 0.8 arcsec, which corresponds to ∼ z abs = . , we are theoreti-cally able to detect 2DA host galaxies in the stacked frameif they have the same magnitude as typical Mg II absorberhost galaxies at the same redshift. However, the lack of anysignificant residue in all four color bands ( g riz ) suggests thatthe 2DA host galaxies likely do not reside at such an impactparameter i.e. > σ .Hence, the minimum brightness threshold for determining asource is 25.5 magnitudes, which is lower than the predictedmagnitude of 23.7. Both Keck spectroscopy of 2DAs andHST imaging of the z abs = . J + show that host galaxies of 2DAs have stellar masses rangingfrom to × M (cid:12) y r − (Ma et al. 2018a), comparable tothat of z abs ∼ . Mg II absorber host galaxies (Table 2). Inaddition, Buat et al. (2012) showed that the global amountof dust attenuation increases with stellar mass. Since 2DAsystems are highly dust attenuated, this means that 2DAhost galaxies are likely much more massive than most of MgII absorber host galaxies which do not show strong dust at-tenuations. It is highly likely that the average host galaxymagnitude is around 23.7 mag or even brighter in the r -band.23.7 mag itself is well above the detection limit. Thus, wecan conclude that these host galaxies on average must resideat an impact parameter lower than 7 kpc since any higherimpact parameter should result in detection. This low im- pact parameter is also consistent with the HST deep imagingresults of the 2DA system at z abs = . (Ma et al. 2018b).In order to test if seeing-limited image quality affects thedetection limit of the impact parameter of the absorbers us-ing ground-based telescopes, we repeat the simulation usinga seeing limited image with FWHM of 1.0 and 0.6 arcsec. Asshown in Figures 12 and 13, the amount of residue detectedincreases as the seeing FWHM decreases; more residue is de-tected in the 1.0 arcsec seeing than compared to 1.4 arcsecseeing at all impact parameters, more residue is detected inthe 0.6 arcsec seeing than compared to 1.0 arcsec seeing atlow impact parameters. The absorber host galaxy becomesfully deconvolved from the quasar at 2.0 arcsec in the 1.0arcsec seeing simulation and at 1.6 arcsec in the 0.6 arcsecseeing simulation.It is clear that in the 0.6 arcsec seeing simulation, be-tween 0.4 and 0.8 arcsec, the amount of flux left over afterPSF subtraction jumps from ∼
35 per cent to ∼
92 per cent.The better (smaller) the seeing FWHM is, the steeper theslope is. For the best seeing of 0.6 arcsec, we can detect ahost galaxy of a dust absorber as close as 0.4 arcsec. Thismeans that studying host galaxies associated with 2DAs us-ing a stacking technique would likely require ground-basedimaging with much better seeing than 1.4 arcsec with theSDSS. On the other hand, the actual sample size of 2DAsystems is only a quarter of the sample size used in the sim-ulation (see reference quasar - 2DA system ratio as noted inSection 2.3). This means the error is actually twice as large.Thus, improving the sample size to reduce measurement er-rors would also allow detection of host galaxies with impactparameters < In this section we interpret our findings. The SED of Mg IIabsorbers follows that of intermediate spiral galaxies, con-sistent with Zibetti et al’s (2007) findings (with slightly dif-fering flux measurements). The stellar properties we derivedin Table 2 indicate that the majority of stellar populationsin these host galaxies are likely old. In the best fitting pro-duced, the stellar age was 8.750 Gyr. This is quite possiblesince bright and massive host galaxies at this redshift rangelikely dominate in their contributions to the final subtractedimage residuals (Figure 6).In addition, the average impact parameter of 2DAs isvery low as there is no apparent residue left over after PCAPSF subtraction. This agrees with Ma et al.’s (2018b) studyof one 2DA with redshift z abs = . where they found theimpact parameter to be 5.5 kpc (Ma et al. 2018b). Previousresearch has shown that within 10 kpc (i.e. ∼ z abs = . − . ), there are no Mg II ab-sorber host galaxies present (Steidel et al. 1994; Churchill etal. 2005a). However, because of the normalization of the PSFfitting to the QSO, the central portion is very nearly zeroedout. This is indicative of the high quality of PSF subtrac-tion, but is somewhat problematic for low-impact parametersystems like 2DAs.As demonstrated by our simulations, 2DA host galax-ies possess a luminosity weighted average impact parameterof < MNRAS000
92 per cent.The better (smaller) the seeing FWHM is, the steeper theslope is. For the best seeing of 0.6 arcsec, we can detect ahost galaxy of a dust absorber as close as 0.4 arcsec. Thismeans that studying host galaxies associated with 2DAs us-ing a stacking technique would likely require ground-basedimaging with much better seeing than 1.4 arcsec with theSDSS. On the other hand, the actual sample size of 2DAsystems is only a quarter of the sample size used in the sim-ulation (see reference quasar - 2DA system ratio as noted inSection 2.3). This means the error is actually twice as large.Thus, improving the sample size to reduce measurement er-rors would also allow detection of host galaxies with impactparameters < In this section we interpret our findings. The SED of Mg IIabsorbers follows that of intermediate spiral galaxies, con-sistent with Zibetti et al’s (2007) findings (with slightly dif-fering flux measurements). The stellar properties we derivedin Table 2 indicate that the majority of stellar populationsin these host galaxies are likely old. In the best fitting pro-duced, the stellar age was 8.750 Gyr. This is quite possiblesince bright and massive host galaxies at this redshift rangelikely dominate in their contributions to the final subtractedimage residuals (Figure 6).In addition, the average impact parameter of 2DAs isvery low as there is no apparent residue left over after PCAPSF subtraction. This agrees with Ma et al.’s (2018b) studyof one 2DA with redshift z abs = . where they found theimpact parameter to be 5.5 kpc (Ma et al. 2018b). Previousresearch has shown that within 10 kpc (i.e. ∼ z abs = . − . ), there are no Mg II ab-sorber host galaxies present (Steidel et al. 1994; Churchill etal. 2005a). However, because of the normalization of the PSFfitting to the QSO, the central portion is very nearly zeroedout. This is indicative of the high quality of PSF subtrac-tion, but is somewhat problematic for low-impact parametersystems like 2DAs.As demonstrated by our simulations, 2DA host galax-ies possess a luminosity weighted average impact parameterof < MNRAS000 , 1–19 (2018) Bill Zhu, Yinan Zhao, Jian Ge, Jingzhe Ma shift galaxies. This appears to be consistent with HubbleSpace Telescope imaging of high redshift main sequence star-forming galaxies (Kriek & Conroy 2013; Ma et al. 2018b).
In this study, we have shown that PCA is capable of repro-ducing quasar profiles to a high degree of accuracy. We nowexplore the differences in methodology.Zibetti et al. (2007) utilized a masking algorithm thatcovered up all sources deemed unlikely to be an absorbinggalaxy at the given redshift. They used SExtractor as theirbaseline masking, supplemented by a flux-limited mask de-rived from a metal-poor stellar population. We used thefpObj files released by DR7 and DR12, which contain de-tailed categorizations of the sources found in each field im-age, ensuring that our masking masks all stars, extendedsources (such as field galaxies, nebula), etc.Next, during the PCA fitting of the quasars, we choseto only take the components calculated in a × squarearound the centroid of the quasar. Although the fitting ishighly accurate in most cases, some reference quasars leavesignificant amounts of residue after masking and PSF sub-traction. The × was chosen to minimize overfittingbased on the average extension of a non-absorbing quasar’simmediate residues, which are calculated from their FWHM.Although the procedure was highly effective in retain-ing data ( >
425 out of 436 passed in all bands, with failedcases being where the QSO was unable to be cut due toboundaries or no suitable sources were found for PCA PSFfitting), the amount of residue left over is low; the surround-ing noise level is still very high. Two conclusions were madeafter comparison between the two absorber stackings:(i) The high redshift of the 2DAs ( z abs = − . ) meansthat the detection completion is very low. Assuming a stan-dard cosmological model, magnitudes in that range increaseby approximately − from the magnitudes recorded at z abs = . − . due to cosmological dimming. Thus, theSNR is already much weaker due to increased distance. Flux-limited masks that helped distinguish between Mg II ab-sorber host galaxies and non-absorbing galaxies were notnecessary for 2DAs.(ii) The impact parameters for most of the 2DA hostgalaxies are small: < < Using an independent image stacking procedure, we con-cluded that host galaxies of Mg II absorbers at z abs = . − . are, for the most part, evolved intermediate spiralgalaxies with lower SFR (2.2 M (cid:12) y r − ). Our SB profiles andintegrated fluxes for the Mg II absorber host galaxies closelyresemble Zibetti et al.’s (2007). This demonstrates that ourstacking technique is reliable. No SED or SB profile couldbe derived from the 2DAs due to the low impact parame-ter and low sample size. The average impact parameter of2DAs appears to be at least 5 times less than the average impact parameter of Mg II absorbers at around 7 kpc, ascompared to the Mg II average impact parameter of 48 kpc.This indicates that 2DAs are likely associated with the diskcomponents of high redshift galaxies. Our simulations showthat an imaging survey with better than 1.4 arcsec is neces-sary to possibly detect host galaxies of 2DAs.Due to the low amount of residue apparent, the stack-ing method may not prove to be effective for low impact pa-rameter host galaxy systems under seeing conditions of 1.4arcsec or worse. The normalization of the PSF most likelysubtracts off the host galaxy along with the QSO. However,we also demonstrated that at low impact parameters, thestacking technique is still capable of drawing upper limitsfor impact parameters.Our implementation of the Principal Component Anal-ysis machine learning algorithm for fitting astronomicalsource profiles was an improvement over single-source PSFapproximation, thereby reducing the noise level in the PSFframe by − times. To our best knowledge, this is the firsttime that the PCA method was used in PSF subtractionfor studying quasar host galaxies. PCA is extremely flexiblein terms of approximation power and noise level contain-ment, making it a strong method of fitting PSF profiles.In particular, despite the differences in methodology, ourSED (Figure 10) produced is very similar to Zibetti et al.’s(2007). This opens up new possibilities for approximatingstellar source profiles to much higher accuracies in futurestudies, while decreasing the overall noise level in the PSFframe during subtraction. In addition, our flood-fill maskingalgorithm was much more adaptive in effectively maskingnon-circular sources, thereby reducing the amount of databeing unnecessarily masked by up to 3 times depending onthe source’s geometry.For the 2DAs, hopefully the recent release of SDSS DataRelease 14 will yield more samples, allowing us to bin theabsorbers by redshift and REW of the 2175 ˚A absorptionline and perform more comprehensive studies in the future. ACKNOWLEDGEMENTS
MNRAS , 1–19 (2018) tudying Quasar Absorber Host Galaxy Properties Using Image Stacking Technique The SDSS is managed by the Astrophysical ResearchConsortium for the Participating Institutions. The Partic-ipating Institutions are the American Museum of Natu-ral History, Astrophysical Institute Potsdam, University ofBasel, University of Cambridge, Case Western Reserve Uni-versity, University of Chicago, Drexel University, Fermilab,the Institute for Advanced Study, the Japan ParticipationGroup, Johns Hopkins University, the Joint Institute forNuclear Astrophysics, the Kavli Institute for Particle As-trophysics and Cosmology, the Korean Scientist Group, theChinese Academy of Sciences (LAMOST), Los Alamos Na-tional Laboratory, the Max-Planck-Institute for Astronomy(MPIA), the Max-Planck-Institute for Astrophysics (MPA),New Mexico State University, Ohio State University, Uni-versity of Pittsburgh, University of Portsmouth, PrincetonUniversity, the United States Naval Observatory, and theUniversity of Washington.SDSS-III is managed by the Astrophysical ResearchConsortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, theBrazilian Participation Group, Brookhaven National Lab-oratory, Carnegie Mellon University, University of Florida,the French Participation Group, the German ParticipationGroup, Harvard University, the Instituto de Astrofisica deCanarias, the Michigan State/Notre Dame/JINA Partici-pation Group, Johns Hopkins University, Lawrence Berke-ley National Laboratory, Max Planck Institute for Astro-physics, Max Planck Institute for Extraterrestrial Physics,New Mexico State University, New York University, OhioState University, Pennsylvania State University, Universityof Portsmouth, Princeton University, the Spanish Partic-ipation Group, University of Tokyo, University of Utah,Vanderbilt University, University of Virginia, University ofWashington, and Yale University.This research has made use of the NASA/IPAC Extra-galactic Database (NED) that is operated by the Jet Propul-sion Laboratory, California Institute of Technology, undercontract with the National Aeronautics and Space Admin-istration.
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