10% of the entire quasar population. The Astrophysical Journal, 557:578-593, 2001 August 20
© 2001. The American Astronomical Society. All rights reserved. Printed in U.S.A.
WFPC2 Imaging of Quasar Environments: A Comparison of Large Bright Quasar Survey and Hubble Space Telescope Archive Quasars1
Rose A. Finn and Chris D. Impey
Steward Observatory, 933 North Cherry Avenue, Tucson, AZ 85721; rfinn@as.arizona.edu, cimpey@as.arizona.edu
and
Eric J. Hooper
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, MS 83, Cambridge, MA 02138; ehooper@cfa.harvard.edu
Received 2000 September 21; accepted 2001 April 4
ABSTRACT
We present Hubble Space Telescope (HST) Wide Field Planetary Camera 2 (WFPC2) data on the large-scale environments of 16 0.39 < z < 0.51 quasars from the Large Bright Quasar Survey (LBQS). The LBQS quasars are representative of the radio-quiet population, and this is one of the first looks at their large-scale environments. We compare the LBQS environments with the environments of 27 0.15 < z < 0.55 quasars selected from the HST archive. The majority of the Archive quasars are from the PG and PKS surveys, and these quasars are more luminous on average than the LBQS. By comparing the LBQS and Archive environments, we investigate whether previous quasar environment studies have been biased as a result of studying unusually radio or optically luminous quasars. We compare observed galaxy number counts with expected counts predicted from the CNOC2 field galaxy luminosity function in order to look for statistical excesses of galaxies around the quasars. We detect a significant excess around the Archive quasars but find no such excess around the LBQS quasars. We calculate the amplitude of the spatial correlation function and find that the LBQS environments are consistent with that of the typical galaxy while the Archive environments are slightly less rich than Abell 0 clusters. We find no difference between the environments of radio-loud and radio-quiet quasars in either sample. However, comparison with previously published work shows that the LBQS radio-loud quasars are in sparse environments when compared with other radio-loud quasars, and the Archive radio-quiet quasars are in dense environments compared to other radio-quiet quasars. The richer environments of the Archive radio-quiet quasars cannot be explained by their higher optical luminosities. We find a positive correlation (95%) between radio luminosity and environment for the radio-loud quasars. This may explain why the LBQS radio-loud quasars, which are less radio luminous, are in sparser environments.
Subject headings: galaxies: clusters: general; galaxies: interactions; quasars: general1 Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc.
1. INTRODUCTION
The conventional model explaining quasar activity consists of a supermassive black hole at the center of a galaxy. Accretion onto the black hole produces emission associated with the quasar, and interactions between the quasar host galaxy and its neighboring galaxies or intercluster gas help to keep the accretion disk and quasar fueled. The importance of interactions and mergers in triggering quasar activity is suggested by the high incidence of close companions (e.g., Weymann et al. 1978; Stockton 1982; French & Gunn 1983; Gehren et al. 1984; Malkan 1984; Yee & Green 1984; Yee 1987; Smith & Heckman 1990).
While the general quasar scenario is well accepted, the origin of the radio power from quasars is still mysterious. Blandford (1990) suggests that the angular momentum of a spinning black hole, extracted by a magnetic field, can provide the energy necessary to fuel radio jets. This may imply that radio-loud quasars have black holes that spin more than radio-quiet quasars, and Wilson & Colbert (1995) show that a merger event between two black holes of relatively equal mass will result in a spinning black hole. Such a situation might arise if two spiral galaxies merge and subsequently form an elliptical galaxy. If the spiral galaxies harbor black holes of comparable mass, then the elliptical could possess a black hole with sufficient spin to power a radio-loud quasar.
Recent studies of the radio properties of quasars indicate that quasars do not exhibit a bimodal distribution of radio power, as originally thought (Brinkman et al. 2000). Radio loudness is then more logically defined by radio luminosity, as opposed to the ratio of radio to optical luminosity. Various thresholds close to log L = 24 in units of W Hz-1 sr-1 (for H0 = 50 km s-1 Mpc-1) have been used to separate radio-loud and radio-quiet quasars (e.g., Hooper et al. 1996; Bischof & Becker 1997; Goldschmidt et al. 1999), and we adopt this definition. According to this criterion, radio-loud quasars account for 10% of the entire quasar population.
Significant progress in understanding the mechanism responsible for radio emission will be possible with X-ray satellites, such as XTXS. This telescope will be sensitive enough to detect signatures of the black hole rotation in iron K line emission, so astronomers will be able to look for a correlation between black hole spin and radio power. Until then, a less direct but more tenable approach for understanding the radio properties of quasars focuses on quasar host galaxies and the large-scale environments of quasars. The first quasar host galaxy studies concluded that radio-loud quasars reside in elliptical hosts and radio-quiet quasars reside in spiral galaxies (Malkan 1984; Smith et al. 1986). More recent work shows that while radio-loud quasars are found mostly in elliptical hosts, radio-quiet quasars form in both elliptical and spiral galaxies (e.g., Bahcall et al. 1997; Boyce et al. 1998; McLure et al. 1999; Schade, Boyle, & Letawsky 2000). Quasar host studies require very precise observations and analysis, and larger samples are needed in order to learn what differentiates radio-loud and radio-quiet quasars. The high contrast between nucleus and host and the small angular scale of the diffuse light make host studies very challenging.
Studies of the large-scale environments of quasars provide insight into the role of environment in triggering quasar activity and can be used to corroborate theories of radio power. The large-scale quasar environment can also be used as an indirect indicator of host morphology, according to the morphology-density relation that was first investigated by Dressler (1980). Dressler finds that local galaxy density is linked to galaxy type, namely, the fraction of elliptical and S0 galaxies increases with local galaxy density. From the beginning, quasar environment studies have searched for statistical excesses in galaxy counts around quasars, and we follow the same approach here. A more detailed understanding of the environments of individual quasars requires redshifts of faint galaxy companions.
This paper addresses two main questions. First, have previous quasar environment studies been biased by preferentially studying very strong radio sources or unusual optically selected quasars? Most studies from which the conventional picture of quasar environments was developed employ samples drawn mainly from the PG, PKS, 3C, and 4C surveys (e.g., Yee & Green 1987; Ellingson, Yee, & Green 1991). The radio surveys generally selected very luminous sources, which are quite rare in optical samples. Although the PG utilized selection techniques similar to other optically selected surveys, it is unusual in terms of its radio properties (e.g., La Franca et al. 1994; Hooper et al. 1996; Bischof & Becker 1997) and optical luminosity function (e.g., Wampler & Ponz 1985; Köhler et al. 1997; Goldschmidt & Miller 1998). Quasars from the Large Bright Quasar Survey (LBQS) are optically selected based on blue color, strong emission or absorption features, and a strong continuum break (Foltz et al. 1987). They are representative of the radio-quiet quasar population as a whole and are therefore more likely to reflect the incidence of clustering around quasars in general.
Second, are radio-loud quasars located in different environments than radio-quiet quasars? Yee and collaborators find that environment is linked to the radio properties of quasars. Radio-quiet quasars, while 6 times more likely to have a close companion than the average field galaxy (Yee 1987), are found in environments considerably less dense than those of radio-loud quasars (Yee & Green 1987; Ellingson et al. 1991). Other studies with smaller samples show no evidence of a correlation between radio properties and environment (e.g., Fisher et al. 1996; McLure & Dunlop 2001). In apparent contradiction, a recent study of 0.5 
z 0.8 radio-loud quasars finds a slight but significant positive correlation between strength of environment and radio power (Wold et al. 2000). Clearly, the connection between environment and radio properties of quasars requires further investigation.
In this study, we present HST WFPC2 data on the environments of 43 quasars spanning the redshift range 0.15 < z < 0.55, and we use this information to address the questions raised above. Although the field size of WFPC2 is relatively small, the superior resolution enables an accurate separation of stars from galaxies. This is a critical step in quantifying quasar environments. To investigate possible biases in quasar sample selection, we compare 16 LBQS quasars to a sample of quasars drawn from the Hubble Space Telescope (HST) Archive, consisting of mainly PG and PKS quasars. The LBQS and Archive samples contain six and 10 radio-loud quasars, respectively. We compare the environmental properties of the radio-loud and radio-quiet quasars within each sample and for the combined sample of LBQS and Archive quasars.
The layout of this paper is as follows. In § 2 we discuss the details of the quasar samples and observations. In § 3 we outline the procedure for photometry and source classification and compare the observed galaxy counts with expected counts derived from the CNOC2 luminosity function (Lin et al. 1999). We investigate the angular distribution of any observed excess counts (§ 3.3) and estimate the amplitude of the spatial correlation function for each quasar (§ 3.4). In § 4 we discuss the significance of our results in the context of previous work, and § 5 contains a summary. Cosmological parameters of H0 = 100 km s-1 Mpc-1, q0 = 0.5, and 
= 0 are assumed unless otherwise noted.
2. OBSERVATIONS AND DATA REDUCTION
Figure 1 shows MV versus z for the entire set of 43 quasars in this environment study. Radio-loud and radio-quiet quasars are depicted with filled and open symbols, respectively. The LBQS (Hewett, Foltz, & Chaffee 1995) sample, shown with triangles in Figure 1, contains 16 quasars in the redshift range 0.39 < z < 0.504, of which six are radio-loud. The remaining 10 quasars have 8.4 GHz luminosities less than 1024 W Hz-1 sr-1 (for H0 = 50 km s-1 Mpc-1). The 16 LBQS quasar fields were observed with HST in the F675W filter with WFPC2 during Cycle 4 with the quasar positioned on the PC, and an analysis of the quasar host properties is presented by Hooper, Impey, & Foltz (1997). For details on the observations, see Table 1 and Hooper et al. (1997).
 | Fig. 1 Absolute magnitude, MV, for the entire quasar sample vs. redshift. The LBQS absolute magnitudes are derived from published BJ magnitudes (Hewett et al. 1995), and MV was calculated using color and k-corrections from Cristiani & Vio (1990). For the Archive sample, MV was calculated using V magnitudes from Hewitt & Burbidge (1989) and k-corrections from Cristiani & Vio (1990). Radio-loud quasars are represented with filled symbols, and radio-quiet quasars are represented with open symbols. The LBQS quasars are represented by triangles, and the F606W and F702W quasars are represented by squares and pentagons, respectively. |
 | Table 1 LBQS Sample |
Details of the observations for a comparison sample of 27 quasars drawn from the HST Archive can be found in Table 2. The 19 quasars observed in F606W are shown with squares in Figure 1. These quasars have lower redshifts, with 0.15 < z < 0.29, and six of the 19 are radio-loud. All 19 F606W quasars were imaged on WF3. Studies of the host galaxies and large-scale environments of these quasars are presented by Bahcall et al. (1997) and Fisher et al. (1996), respectively. The remaining eight quasars of the Archive sample were observed in F702W; six of the quasars were positioned on the PC and the other two on WF3. The redshifts range from 0.223 z 0.514, and four out of eight are radio-loud. References for the F702W data are listed in Table 2.
 | Table 2 HST Archive Sample |
Figure 1 demonstrates that the combined quasar environment sample is free of the common correlation between absolute magnitude and z. A Spearman rank correlation test confirms this, yielding a rank correlation coefficient of 0.04, with an 80% probability of getting the same correlation from a random sample. Furthermore, a K-S test indicates with 84% significance that the absolute magnitudes for the radio-loud and radio-quiet quasars are drawn from the same parent population. However, a K-S test indicates only a 6% probability that the absolute magnitudes of the Archive and LBQS quasars are drawn from the same parent population, meaning that on average the Archive quasars are more luminous than the LBQS quasars.
For all quasar data, calibrated images are retrieved from the HST Archive, and cosmic-ray rejection is achieved with the STSDAS combine routine with the "crreject" option set. Magnitude zero points for the three HST filters are from Table 9 in Holtzman et al. (1995). The zero points are adjusted for differences in gain and are increased by 0.1 to convert to infinite aperture magnitudes.
3. ANALYSIS
3.1. Photometry and Geometry
SExtractor is used for photometry and source classification (Bertin & Arnouts 1996). For the wide-field cameras, a detection threshold of 1.5 
pixel-1 is used with a minimum object size of 32 pixels. The PC images are binned by 2 × 2 to improve signal-to-noise ratio, and a detection threshold of 1 pixel-1 with a minimum object size of 32 pixels is used. Total magnitudes are determined using the "mag-auto" algorithm. A top-hat 5 × 5 convolution kernel is used for both the PC and WF data.
SExtractor does a remarkably good job at classifying objects in HST data. Figure 2 shows the SExtractor classification index versus magnitude for all of the F675W LBQS fields, where a classification index of 1 indicates a star or unresolved source and 0 a galaxy. We achieve a clean star/galaxy separation down to mF675W = 22 for the LBQS data. In Figure 2, the bright (m < 20) objects in the LBQS PC fields with classifier indices between 0.5 and 0.95 correspond to the quasars, showing that a number of them are marginally resolved. The results of the star/galaxy separation are comparable for the Archive fields. We use a SExtractor classification index of 0.4 as our cutoff for galaxies. Note that the analysis is not sensitive to this value, since for mF675W < 22, the distribution of classification indices is bimodal, with very few objects having indices greater than 0.1 and less than 0.9.
 | Fig. 2 SExtractor classifier index (1 = unresolved) vs. magnitude for the entire LBQS F675W data set. Triangles represent WF data; open circles represent PC data. A classifier index of 1 represents a star and 0 a galaxy; objects with indices below 0.4 are considered galaxies. PC data with indices falling between 0.5 and 0.95 correspond to the quasars. |
We determine the completeness of the data by adding artificial galaxies to the final images using the IRAF "artdata" package. Parameters for the artificial galaxies are based on data from Griffiths et al. (1994a, 1994b) and include the following: 1
for the maximum half-light radius of an mF675W = 21 elliptical galaxy, a value of 1 for the ratio of elliptical to spiral half-light radii, and 0.3 for the fraction of ellipticals. For the F675W data, we place artificial galaxies with 20 mF675W 23 on the PC and WF images. We then estimate completeness based on how many of the artificial galaxies were recovered by SExtractor. In the 1200 s F675W data, 100% of 21.5 mF675W < 22 galaxies are recovered on the wide-field images. The results for the PC images are shown in Figure 3. The completeness drops to 
95% for 20.5 < m < 21.5 galaxies and falls below 80% for 21.5 < m < 22 galaxies. To assess the significance of this incompleteness, we compute the expected galaxy counts per field (as discussed in § 3.2). We find that the completeness-corrected counts do not differ significantly from the uncorrected counts down to mF675W = 22. We therefore use mF675W = 22 as the faint magnitude cut for the F675W data and do not apply a completeness correction. The Archive data suffer from a similar level of incompleteness, so again we limit our analysis to mF606W 22 and mF702W 22 galaxies for the Archive quasars and make no other adjustments for completeness.
 | Fig. 3 (a) Input (solid line) distribution of artificial galaxies with the distribution of galaxies recovered by SExtractor (dotted line) for a 1200 s F675W PC image. The data are binned 2 × 2. SExtractor detection parameters include a threshold of 1.0 |
Before proceeding, we need to comment on the geometry of the images. First, all the LBQS quasars are centrally positioned on the PC. Six of the Archive quasars are also positioned on the PC, but the remaining 21 are located on WF3. Our results could be affected by the asymmetric geometry of WFPC2. For example, if a quasar positioned on the PC is located at the edge of a cluster, as found in a recent study of 1.0 < z < 1.6 radio-loud quasars (Sanchez & Gonzalez-Serrano 1999), we might miss the cluster entirely. The inferred environmental density will then be underestimated. We will be better able to comment on the effect of WFPC2 geometry when we analyze our wider field, ground-based images of the LBQS quasars (see § 5). Another issue that complicates any measure of local density around the quasars is the relatively small field size of WFPC2. At a redshift of 0.3, the 2
5 field of WFPC2 corresponds to a projected size of 0.58 h
Mpc, whereas the expected diameter of a group is 1 Mpc (e.g., Zabludoff & Mulchaey 1998). Therefore, for the lower redshift quasars especially, we are sampling a limited volume around the quasar. Furthermore, since a group or cluster in which the quasar is located could fill the entire WFPC2 field, we cannot use the periphery of the images to estimate expected field galaxy counts. These issues are addressed in the next section, with a direct comparison with wide-field galaxy counts.
3.2. Comparison of Galaxy Number Counts with Surveys
Our first step in looking for excess galaxies around the quasars is to compare the observed galaxy number counts with published surveys. This allows us to make a reliable estimate of expected galaxy counts even though a group or cluster in which a quasar is located may fill the entire WFPC2 field. Unfortunately, we find no deep galaxy surveys conducted in the three HST filters of interest. (The Medium Deep Survey includes F606W data, but number counts have not been published yet.) Converting number counts from other filters requires detailed knowledge of the galaxy populations involved, which leads us to the CNOC2 data set. Lin et al. (1999) have calculated the galaxy luminosity function based on CNOC2 data, and they parameterize the evolution of the luminosity function with redshift for both the B and RC filters. Lin et al. (1999) classify galaxy spectral energy distributions (SEDs) using the Coleman, Wu, & Weedman (1980) templates, and knowing the percentage of different galaxy types allows one to transform the luminosity function parameters from RC to any band, in our case the HST F606W, F675W, and F702W filters. To recover the integrated luminosity function for the HST filters, we use equation (23) from Lin et al. (1999) and the RC luminosity function parameters. We obtain the absolute RC magnitudes from observed HST magnitudes by calculating the color and k-corrections from the Coleman et al. (1980) SEDs. The zero point of each filter is determined from the spectrum of Vega. We integrate the luminosity function between 0 < z < 1; integrating beyond z = 1 does not affect the counts below m = 22, but predicted counts at fainter magnitudes are affected.
As a test of the method, we calculate the integrated luminosity function for V, RC, and F555W filters. Figures 4a
4c show that the integrated luminosity function reproduces the CNOC2 V and RC counts (H. Lin 2001, private communication) as well as the Medium Deep Survey F555W counts (Casertano et al. 1995). The CNOC2 integrated luminosity function overpredicts the number of galaxies brighter than 19th magnitude. In terms of galaxies expected in a WFPC2 field with m
< 22, the integrated luminosity function predicts 32.6 galaxies per field while the CNOC2 counts give 31.5 galaxies per field. In the V band, an average of 16.2 galaxies are expected and 16.0 are observed. This means that in our F675W and F702W quasar fields, the expected field galaxy counts will be systematically high by approximately one galaxy per field. For the F606W data, which are closer to V, the expected field galaxy counts will be systematically high by less than 0.5 galaxies per field.
 | Fig. 4 Observed galaxy counts per square degree (triangles) with the integrated luminosity function (solid line) derived from CNOC2 galaxy survey (Lin et al. 1999). Panels (a), (b), and (c) show the results for the CNOC2 RC, V, and Medium Deep Survey F555W (Casertano et al. 1995) counts, and the integrated luminosity function matches survey data well. Panels (d), (e), and (f) show the galaxy counts derived from WFPC2 images of quasar fields. The integrated luminosity function matches the F675W galaxy counts, but the quasars imaged in the F606W and F702W filters show excess counts. Error bars are 1 |
Our next step in looking for excess galaxies is to use the CNOC2 integrated luminosity function to estimate the expected galaxy counts in the quasar fields. Implicit in this comparison is the assumption that the magnitudes derived from SExtractor are equivalent to the CNOC2 galaxy magnitudes. The CNOC2 galaxy magnitudes are determined using the PPP software (Yee 1991). To check the validity of this assumption, H. Lin ran SExtractor and PPP on the same data. A comparison of the SExtractor and PPP total magnitudes shows 0.2 mag of scatter but no systematic offset (H. Lin 2001, private communication). We therefore proceed in using the CNOC2 integrated luminosity function to predict the expected galaxy counts in the quasar fields.
The CNOC2 luminosity function is integrated for the HST F675W, F606W, and F702W filters, and the results are plotted with the galaxy counts from the quasar fields in Figures 4d4f. The integrated F675W luminosity function reproduces the observed galaxy counts from the LBQS fields within the errors down to m 23. The F606W Archive galaxy counts show a clear excess at magnitudes brighter than 21, but the integrated luminosity function matches the faint galaxy counts well. The F702W Archive galaxy counts show a slight excess above the predicted counts at almost all magnitudes.
To assess the significance of these findings, we translate from galaxies per square degree per magnitude into the average expected and observed counts per field. To determine the expected galaxy counts per field, we sum the integrated luminosity function between 14 < m < 22 and multiply by the area of WFPC2 in square degrees. This pushes slightly beyond the spectroscopic completeness level of RC = 21.5 for the CNOC2 survey. The observed, expected, and excess counts for the individual LBQS fields are listed in columns (5), (6), and (7) of Table 3. The same quantities are listed for the F606W and F702W Archive fields in Tables 4 and 5. We find that the LBQS quasars have an average of 16.1 galaxies per field, 1.8 ± 1.4 galaxies less than expected. The Archive F606W and F702W quasars have an average of 16.4 and 26.5 galaxies per field, 5.4 ± 1.0 and 7.0 ± 2.0 galaxies more than expected, respectively. The error in the excess counts is determined by propagating the error in expected counts. The error in expected counts is taken to be 1.3 times the Poisson error, where the extra factor of 1.3 accounts for variations associated with large-scale structure, as observed by Yee, Green, & Stockman (1986). We see no significant excess associated with the LBQS quasars. The Archive quasars, in comparison, have very significant excesses. The average excess of 5.4 galaxies per field associated with the F606W Archive quasars is a total that is slightly more than 5 above the noise associated with the expected galaxy counts. The average excess of 7.0 galaxies per field detected in the F702W Archive images is a 3 result overall.
 | Table 3 Galaxy Counts and Clustering for LBQS Sample |
 | Table 4 Galaxy Counts and Clustering for F606W Archive Sample |
 | Table 5 Galaxy Counts and Clustering for F702W Archive Sample |
Previous quasar environment studies have limited the analysis to galaxies with m < m* + 2.5 (Yee & Green 1987) or m* - 1 < m < m* + 2 (Fisher et al. 1996; McLure & Dunlop 2001), where m* is the apparent magnitude of the knee of the luminosity function at the redshift of each quasar. This acts to reduce the contamination from field galaxies. Since all of the F606W Archive fields are common to the Fisher et al. (1996) data set, we apply a magnitude slice of m* - 1 < m < m* + 2 to facilitate comparison. For consistency with the estimation of expected counts, we use the value of m* derived from CNOC2. Values of m* are listed in column (10) of Tables 3, 4, and 5 for the LBQS, F606W, and F702W Archive quasars, respectively. In addition, the observed, expected, and excess number of galaxies are listed in columns (11), (12), and (13). Applying this limited magnitude slice leaves the average observed excess for the LBQS fields unchanged: -1.8 ± 1.4 becomes -1.7 ± 1.4 galaxies. The negative sense of the average for the LBQS sample is not significant. The excess for the F606W Archive fields drops from 5.4 ± 1.0 to 3.7 ± 0.7 galaxies per field. The excess for the F702W Archive fields drops from 7.0 ± 2.0 to 5.8 ± 1.8 galaxies per field. This restricted magnitude slice does not change the significance of the observed excesses.
3.3. Radial Distribution of Galaxies
We detect an excess of galaxies above the CNOC2-derived field estimate in the Archive data. We observe no significant excess in counts in the LBQS fields. If we assume that the excess galaxies observed in the Archive fields are associated with the quasar and are located at the quasar redshift, then we might expect the excess counts to originate from regions close to the quasar, as seen in other studies (e.g., Yee & Green 1987; Ellingson et al. 1991; Smith, Boyle, & Maddox 1995; Fisher et al. 1996; Hall & Green 1998). Figure 5 shows the average excess number of galaxies per field versus angular distance from the quasar for the Archive and LBQS samples. The Archive fields show an excess with no obvious radial dependence, and the LBQS shows no excess. Since the Archive quasars span a large range in redshift, a given angular distance corresponds to a very different projected distance for the lowest and highest redshift Archive quasars. This could dilute an observed radial gradient of galaxies. Therefore, in Figure 6 we plot the spatial distribution of excess galaxies. Here we assume that all the galaxies in the field are at the quasar redshift and convert angular distance to projected physical distance. Counts are binned in equal-width annuli of 100 h kpc. This comparison shows a highly significant excess of galaxies out to 400 h kpc for the Archive quasars and no excess for the LBQS quasars. The difference between Figures 5 and 6 for the Archive data supports the assumption that the excess galaxies are associated with the quasar. The significance of the drop-off in excess counts at radii larger than 300 h kpc is difficult to assess because of the limited field size of WFPC2.
 | Fig. 5 Average number of excess galaxies per field vs. angular distance from the quasar for the (a) Archive and (b) LBQS samples. Error bars are 1 |
 | Fig. 6 Average number of excess galaxies per field vs. projected distance to quasar for the (a) Archive and (b) LBQS quasar samples. The Archive quasars show a centrally concentrated excess above background out to 300 h |
In looking for a radial gradient in galaxy counts around a given quasar, we are assuming that the quasar is at the center of the local mass concentration. A recent study of higher redshift quasars shows that this is not necessarily the case (Sanchez & Gonzalez-Serrano 1999). Unfortunately, the WFPC2 field is not big enough to explore this scenario. The possibility that quasars are not centered in their groups or clusters will be addressed with existing ground-based data for the LBQS sample, and these results will be presented in a future paper.
3.4. Amplitude of the Spatial Correlation Function
One common way to quantify the strength of clustering around quasars is to calculate the amplitudes of the angular and spatial correlation functions. For a given cluster around a quasar, the amplitude of the angular correlation function, Agq, will decrease with increasing quasar redshift. The amplitude of the spatial correlation function, Bgq, takes redshift into account by projecting angular distances into physical distances. Therefore, Bgq is a better way to compare our samples. However, Agq is the parameter that is measured observationally. Longair & Seldner (1979) derived the relation between Agq and Bgq, and a brief summary of their work is given below.
The angular correlation function, 
(
), is defined by
where n() and nexp are the surface densities of observed and expected galaxies, respectively, and d
is surface area. The spatial correlation function, 
(r), is defined as the excess number of galaxies at a distance r from an object in a volume element dV,
The quantities 
(r)dV and expdV are the number of galaxies observed and expected in volume element dV, respectively. Longair & Seldner (1979) show that (r) = Bgqr-
implies () = Agq-(-1). In deriving the relationship between Agq and Bgq, Longair & Seldner (1979) find
where 
(mo,z) is the luminosity function integrated at the quasar redshift down to limiting magnitude mo, D is the effective distance [making D/(1 + z) the angular diameter distance, DA], and I is the integration constant that arises from integrating the volume in a cone corresponding to surface area d.
In practice, in order to calculate Bgq, we must first calculate Agq. Substituting the functional form of () from Longair & Seldner (1979) into equation (1), integrating d over the image area, and solving for Agq, we find
The final expression for Bgq, obtained by substituting equation (4) into equation (3), is
If we consider only the Poisson error associated with Nexp and (mo,z)D
, the uncertainty in Bgq is
In calculating Bgq, we use = 1.77, the power-law index derived from local studies of the galaxy-galaxy covariance function (Seldner & Peebles 1978). Yee & Green (1987) demonstrate that = 1.77 is appropriate to use for z < 0.6 quasars. This makes the units of Bgq Mpc1.77. We evaluate
-
by summing in concentric, quasar-centered annuli from zero radius to the most distant point in the field. The field counts, Nexp, are derived from the CNOC2 luminosity function (Lin et al. 1999) as described in § 3.2. We also use the CNOC2 luminosity function for calculating (mo,z).
The results of the Bgq calculations are listed in Tables 3, 4, and 5 for the LBQS, F606W, and F702W Archive samples. The layouts of Tables 3, 4, and 5 are identical. Columns (1) and (2) give the quasar name and redshift. The angular distance from the quasar to the farthest corner of the WFPC2 field is listed in column (3), and the physical distance that this angle corresponds to at the quasar redshift, rmax, is listed in column (4). Columns (5)(9) correspond to all galaxies within the magnitude range 14 < m < 22. Columns (5) and (6) give the total number of observed and expected galaxies per WFPC2 field. The errors in the expected counts are 1.3 times the Poisson error, as described in § 3.2. Column (7) gives the excess number of galaxies per field, and column (8) expresses this excess in terms of 
, the ratio of the excess counts to the expected counts. Column (9) lists the calculated values of Bgq, with the errors derived according to equation (6). Columns (10)(15) refer to only those galaxies with m* - 1 < m < m* + 2. Column (10) gives the value of m* for each quasar, and columns (11)(15) are analogous to columns (5)(9), but for the narrower magnitude range.
The average Bgq for the LBQS sample is -16 ± 13 (h Mpc)1.77. As with the average number counts for the LBQS sample, the negative sense of the average Bgq value is not significant. The average values of Bgq for the F606W and F702W Archive samples are 59 ± 11 and 58 ± 18 (h Mpc)1.77. Considering m* - 1 < m < m* + 2 galaxies only leaves the average value of Bgq unchanged for the LBQS sample. The averages for the F675W and F702W Archive samples are 60 ± 10 and 49 ± 18 (h Mpc)1.77. For comparison, Davis & Peebles (1983) find that the average value for the amplitude of the galaxy-galaxy spatial correlation function, Bgg, is 20 (h Mpc)1.77, and Longair & Seldner (1979) find that clusters with Abell richness classes 0 and 1 have Bgg values of 90 and 250 (h Mpc)1.77, respectively. The LBQS quasar environments are consistent with that of a typical galaxy, while the average Archive quasar environment is slightly less rich than an Abell 0 cluster. We note that the relative values and significance levels of Bgq for the various samples match the simple estimates of galaxy excess with respect to published surveys, as expected.
Since our quasar sample spans a wide range of redshifts, measuring Bgq out to the edge of the field could introduce systematic differences in the results calculated for low- and high-redshift quasars. To make the measurements more uniform, we recalculate Bgq for galaxies within a projected distance of 200 h kpc from the quasar. This corresponds to the largest physical size imaged by WFPC2 for the lowest redshift quasar in the Archive sample. For 14 < m < 22 galaxies only, the average value of Bgq for the LBQS sample is 0 ± 11 (h Mpc)1.77. The average values for the F675W and F702W Archive samples are 53 ± 10 and 65 ± 16 (h Mpc)1.77. These values do not change significantly when considering only galaxies with m* - 1 < m < m* + 2. Thus, the distance at which Bgq is measured does not affect the average Bgq values significantly. Unless otherwise stated, we will refer to the Bgq values calculated for m* - 1 < m < m* + 2 galaxies using the entire WFPC2 field for the remainder of the paper.
Figure 7 shows a plot of Bgq versus redshift, and three interesting points emerge from this figure. First, we find no apparent radio dichotomy. A K-S test indicates that the radio-loud and radio-quiet samples are drawn from the same population with 58% confidence. Similar results are obtained for the three subsamples individually; for the LBQS, F606W, and F702W Archive fields, a K-S test indicates a 70%, 56%, and 53% probability that the radio-loud and radio-quiet subsamples are drawn from the same distribution of Bgq values. The similarity of radio-loud and radio-quiet environments is consistent with results of Fisher et al. (1996) and McLure & Dunlop (2001) but is not consistent with the findings of Ellingson et al. (1991). We will discuss this point in more detail in § 4.
 | Fig. 7 Bgq vs. redshift for the entire sample of quasars. Radio-loud quasars are represented with filled symbols, and radio-quiet quasars are represented with open symbols. The LBQS quasars are represented by triangles, and the F606W and F702W quasars are represented by squares and pentagons, respectively. There is no evidence for a radio dichotomy, and Bgq values for the LBQS sample lie systematically below the values of the Archive sample. |
The second point to draw from Figure 7 is that the values of Bgq for the LBQS sample lie systematically below those of the Archive quasars. The significance of this difference is 99%, as determined by the K-S test. This is consistent with the differences found between the LBQS and Archive samples based on number counts, described in § 3.2. Is something different about the LBQS environments, or is there some systematic error associated with the LBQS data or analysis? One possible systematic is the shorter exposure times of the LBQS data. Therefore, we might not be sampling far enough down the luminosity function to pick up companions. By applying a limiting magnitude cut of mF675W = 22, we sample to an average depth of m* + 1.4 in the LBQS data. To see how this shallower depth affects the inferred environmental density, we recalculate Bgq for the Archive fields using only m* - 1 < m < m* + 1.4 galaxies. The resulting Bgq values are plotted versus quasar redshift in Figure 8. A K-S test again indicates only a 0.6% probability that the Bgq values for LBQS and Archive quasars are drawn from the same parent distribution. We must then conclude that the LBQS quasars are located in environments less dense than the Archive quasars.
 | Fig. 8 Bgq vs. redshift, with Archive Bgq values recalculated using only m* - 1 < m < m* + 1.4 galaxies to mimic the completeness of the LBQS images. Radio-loud quasars are represented with filled symbols, and radio-quiet quasars are represented with open symbols. The LBQS quasars are represented by triangles, and the F606W and F702W quasars are represented by squares and pentagons, respectively. Again, the LBQS sample lies systematically below the values of the Archive sample. |
The final conclusion drawn from Figures 7 and 8 is that we do not see an increase in Bgq with increasing redshift out to z = 0.5. Hill & Lilly (1991) see a significant enhancement in the environments of radio galaxies with moderate to high radio power by z 0.5, and Yee & Green (1987) find evidence for a strong increase in the density of environments of radio-loud quasars at z > 0.6. A Spearman rank test performed on the data in Figure 8 indicates a negative correlation between Bgq and z at the 99% confidence level. However, this correlation disappears when considering the Archive data only, with a Spearman rank test indicating an 86% probability that no correlation exists. Therefore, the correlation of Bgq with z is due to the systematically lower Bgq values of the higher redshift LBQS quasars.
4. DISCUSSION
In this section we discuss our analysis and results in the context of previous work. We can compare our analysis of the F606W Archive data with that of Fisher et al. (1996) because we utilize the exact same data for 19 of the 20 quasars they imaged. Our radio-loud subsamples are identical, while Fisher et al. (1996) include one more quasar (HE 1029-1401 at z = 0.086) in their radio-quiet subsample. Fisher et al. (1996) do not list any individual statistics; we know only that the average value of Bgq for their entire sample, considering only m* - 1 < m < m* + 2 galaxies, is 75
(h Mpc)1.77. For the same magnitude slice, our value is 60 ± 10 (h Mpc)1.77. For the radio-loud and radio-quiet subsamples, their average values of Bgq are 84
and 72
(h Mpc)1.77, respectively. In comparison, our values are 66 ± 18 and 57 ± 12 (h Mpc)1.77. Although our results agree within the errors, our Bgq values are systematically lower than the Fisher et al. (1996) values. The discrepancies translate into a difference of approximately one galaxy in the calculated average excess. Differences in how the expected counts are estimated can probably account for the differences in Bgq values. For example, as mentioned in § 3.2, the background counts estimated from the CNOC2 luminosity function may be systematically high by less than 0.5 galaxies per field for the F606W filter. In addition, Fisher et al. (1996) do not use the PC data in their analysis, and they estimate the expected counts in WF3 using the observed counts in WF2 and WF4.
Another useful check of our analysis is to compare individual Bgq values with those published by other authors. McLure & Dunlop (2001) also analyze the F606W sample, and four of those quasars are common to Yee & Ellingson (1993). Table 6 compares Bgq for these four quasars plus one additional F702W quasar that is not in the McLure & Dunlop (2001) sample but is in the Yee & Ellingson (1993) sample. The agreement between our values and those of Yee & Ellingson (1993) is surprisingly good, considering the following differences: they use ground-based data covering a much wider field than WFPC2; they estimate field galaxy counts from control fields; and they use different parameters for calculating the luminosity function at the quasar redshift. McLure & Dunlop (2001) have analyzed the same HST data as we, so one might expect better agreement between our Bgq values. However, McLure & Dunlop (2001) consider only galaxies located on the same chip as the quasar (WF3) and estimate expected counts based on the number of galaxies on WF2 and WF4. Furthermore, they use different parameters when calculating the luminosity function at the quasar redshift. This comparison underscores how sensitive individual Bgq values are to the methodology and indicates that results should only be interpreted in a statistical sense.
 | Table 6 Comparison of Individual Bgq Valuesa |
Finding reasonable agreement among our analysis and those of Fisher et al. (1996), McLure & Dunlop (2001), and Yee & Ellingson (1993), we now discuss the significance of our findings in the context of previous research. Our two main results are that (1) the LBQS quasars lie in less dense environments than the more luminous Archive quasars and (2) radio-loud and radio-quiet quasars are found in similar environments. Table 7 compares our average values of Bgq to those of other studies. Note that the Archive F606W and Fisher et al. (1996) data and samples are identical except for one quasar, and McLure & Dunlop (2001) include all the F606W quasars in their sample. With this in mind, comparing Bgq values puts the findings of this study in a different light. First, the relatively sparse environments of the radio-quiet LBQS quasars are consistent with previous ground-based studies, but the radio-loud LBQS quasars are in unusually sparse environments when compared to other radio-loud quasars. Second, the richer environments of the Archive radio-loud quasars are consistent with previous ground-based studies, but the Archive radio-quiet quasars are in unusually dense environments compared with the radio-quiet quasars studied by Smith et al. (1995) and Ellingson et al. (1991). Furthermore, by comparing our values of Bgq to the Longair & Seldner (1979) value of 90 (h Mpc)1.77 for Abell 0 clusters, we find that the Archive quasars are located in galaxy environments slightly less rich than Abell 0 clusters. When compared with the galaxy-galaxy covariance amplitude of 20 (h Mpc)1.77 from Davis & Peebles (1983), the LBQS quasars are in environments comparable to the typical galaxy. This is not surprising for the radio-quiet LBQS subsample, but one might expect the radio-loud LBQS quasars to be in denser environments.
 | Table 7 Comparison of Average Radio-Loud and Radio-Quiet Bgq Valuesa |
How do we make sense of these results? Fisher et al. (1996) note that the F606W quasars are among the most luminous, and this might explain why the F606W radio-quiet quasars have denser environments than average. Furthermore, the LBQS quasars are less luminous on average than the Archive quasars, so maybe this explains why the LBQS quasars are in relatively sparse environments. Figure 9 compares Bgq with MV, showing clearly that environment is not correlated with optical luminosity. A Spearman rank test confirms this with a 60% probability that Bgq and MV are uncorrelated. Ellingson et al. (1991) look for a correlation between optical luminosity and environment with a sample of 96 quasars, and they also find no correlation. Therefore, it appears that optical luminosity cannot explain why the Archive radio-quiet quasars are in dense environments or why the LBQS radio-loud quasars are in sparse environments. Radio luminosity might help explain the sparse environments of the radio-loud LBQS quasars because the radio-loud LBQS quasars have lower radio luminosities than the Archive radio-loud quasars. To test this we compare radio power at 5 GHz with Bgq. Radio power is listed in Tables 1 and 2 for the LBQS and Archive quasars, respectively. The LBQS 8.4 GHz data from Hooper et al. (1997) are converted to 5 GHz using a spectral index of -0.32. Radio data for the F606W sample are from McLure & Dunlop (2001), and data for the F702W sample are from the NASA/IPAC Extragalactic Database.
 | Fig. 9 Bgq vs. MV for the entire sample of quasars. Radio-loud quasars are represented with filled symbols, and radio-quiet quasars are represented with open symbols. The LBQS quasars are represented by triangles, and the F606W and F702W quasars are represented by squares and pentagons, respectively. There is no correlation between density of environment and MV. |
Figure 10 shows Bgq versus radio power, and we find no correlation between radio power and environment when considering both radio-loud and radio-quiet quasars. We note that almost all the LBQS quasars are a factor of 10100 less powerful than the radio-loud Archive quasars, and it is not clear that the same emission mechanism holds across this large range in radio power. However, when considering the radio-loud quasars only, a Spearman rank test indicates a modest correlation (95% probability) between radio power and environment, which is dependent on the one point at extreme values of radio luminosity and Bgq (85% probability of a correlation if this point is removed). Wold et al. (2000) find a slight but significant correlation between radio power and environment, although they consider steep spectrum sources only. Most of the radio-loud quasars in our samples are flat spectrum, yet the correlation remains. Interestingly, McLure & Dunlop (2001) note that a weak trend between radio power and environment is suggested by their data, but the correlation is not statistically significant. The richest environments in the Yee & Green (1987) and Ellingson et al. (1991) samples are around very radio luminous, steep-spectrum sources. The addition of their data to Figure 10 might strengthen the correlation between environment and radio power, but we resist adding their numbers because of possible systematic differences in analysis. Since most of the radio data for the radio-quiet quasars are upper limits, we cannot test for an independent correlation between radio power and environment for radio-quiet quasars. The fact that the correlation in the radio-loud data does not apply to both radio-loud and radio-quiet quasars implies that two emission mechanisms may be at work (e.g., Stocke et al. 1992; Hooper et al. 1996), even though there appears to be a continuum of radio power among quasars.
 | Fig. 10 Radio power at 5 GHz vs. Bgq for quasars with available radio data. The LBQS quasars are represented by triangles and upper limits, and the F606W and F702W quasars are represented by squares and pentagons, respectively. We find no correlation between radio power and environment when considering both radio-loud and radio-quiet quasars. However, when considering the radio-loud quasars only, a Spearman rank test indicates a 95% probability that radio power is positively correlated with environment. |
Finally, what is the true incidence of clustering around quasars? As discussed in § 1, the LBQS is among the most representative surveys of the currently known radio-quiet quasar population, and the radio-quiet quasars make up 90% of the whole. Therefore, most quasars, like the LBQS sample presented here, lie in environments comparable to the typical galaxy. The Archive radio-quiet quasars have unusually dense environments and are thus not a representative sample of radio-quiet quasars. The clustering associated with radio-loud quasars correlates with radio power, and the environments of the radio-loud quasars presented here range from that of a typical galaxy to Abell 0 clusters. We present data for only 16 LBQS quasars, and a larger sample is needed to strengthen these results. In addition, spectroscopic studies provide more insight into the dynamics of quasar environments, enabling one to examine variations in environments as opposed to limiting analysis to the average properties of the sample. The fluctuations in field galaxy counts preclude the analysis of individual quasars using our current method.
The LBQS makes an excellent sample for extending quasar environment studies to higher redshift to look for evolution. This work has been started by Wold et al. (2001), who include 10 LBQS radio-quiet quasars in their study of 0.5 z 0.8 radio-quiet quasar environments. Wold et al. (2001) conclude that, on average, 0.5 z 0.8 radio-quiet quasars are found in environments that are 3 times more dense than the typical galaxy. However, the 10 LBQS quasars in their radio-quiet sample have environments comparable to the typical galaxy (for their star subtraction models 2 and 3). We have ground-based R- and H-band data for a larger sample of LBQS quasars, which includes the sample presented here as well as higher redshift quasars. The ground-based data are much deeper than the HST data, and their analysis will help elucidate the true incidence of clustering around quasars as a function of redshift.
5. SUMMARY
We present HST WFPC2 data on the large-scale environments of 16 0.39 < z < 0.51 quasars from the LBQS. This is one of the first looks at the large-scale environments of LBQS quasars, and this is significant because the LBQS quasars are representative of the radio-quiet quasar population. We compare the LBQS environments with the environments of 27 0.15 < z < 0.55 quasars selected from the HST Archive. The analysis of the Archive sample is useful for two reasons. First, the Archive sample provides a check of our methodology because most of these data have been published in previous environment studies. Second, the majority of the Archive quasars are from the PG and PKS surveys, and these quasars are more luminous on average than the LBQS quasars; by comparing the LBQS and Archive studies, we investigate whether previous quasar environment studies have been biased because of studying unusually radio or optically luminous quasars. To quantify the quasar environments, we compare observed galaxy number counts with expected counts predicted from the CNOC2 field galaxy luminosity function in order to look for statistical excesses of galaxies around the quasars. We detect a significant excess of galaxies around the Archive quasars but find no such excess around the LBQS quasars. We calculate the amplitude of the spatial correlation function, and we find that the LBQS environments are consistent with that of the typical galaxy while the Archive environments are slightly less rich than Abell 0 clusters. Contrary to previous ground-based studies, we find no difference between the environments of radio-loud and radio-quiet quasars of either sample. However, comparison of Bgq values with previously published values shows that the radio-loud LBQS quasars are in environments less dense than most other radio-loud quasars. In addition, the Archive radio-quiet quasars are in anomalously dense environments compared to other radio-quiet quasars. The richer environments of the Archive radio-quiet quasars cannot be explained by their higher optical luminosities because we find no correlation between optical luminosity and environment. We do find a positive correlation (95%) between radio luminosity and environment for the radio-loud quasars. The LBQS radio-loud quasars have lower radio powers than the radio-loud Archive quasars, and this might explain why the LBQS radio-loud quasars are in sparser environments.
The authors would like to thank H. Lin for kind assistance in utilizing CNOC2 results and for comparing PPP with SExtractor. This work was partially supported by NASA through GO program 5450 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. R. A. F. acknowledges support from the UA/NASA Spacegrant Fellowship, NSF grant AST-9623788, and NGT-5-50283, the latter a NASA Graduate Student Researchers Program Fellowship. E. J. H. acknowledges support from NASA grants NAGW-3134 and NGT-51152, the latter a NASA Graduate Student Researchers Program Fellowship at the University of Arizona.
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