You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


---
abstract: 'We investigate the extent to which the Palomar-Green (PG) Bright Quasar Survey (BQS) is complete and representative of the general quasar population by comparing with imaging and spectroscopy from the Sloan Digital Sky Survey. A comparison of SDSS and PG photometry of both stars and quasars reveals the need to apply a color and magnitude recalibration to the PG data. Using the SDSS photometric catalog, we define the PG’s parent sample of objects that are not main-sequence stars and simulate the selection of objects from this parent sample using the PG photometric criteria and errors. This simulation shows that the effective $\ub$ cut in the PG survey is $\ub<-0.71$, implying a color-related incompleteness. As the color distribution of bright quasars peaks near $\ub=-0.7$ and the 2-$\sigma$ error in $\ub$ is comparable to the full width of the color distribution of quasars, the color incompleteness of the BQS is approximately 50% and essentially random with respect to $\ub$ color for $z<0.5$. There is, however, a bias against bright quasars at $0.5 < z < 1$, which is induced by the color-redshift relation of quasars (although quasars at $z>0.5$ are inherently rare in bright surveys in any case). We find no evidence for any other systematic incompleteness when comparing the distributions in color, redshift, and FIRST radio properties of the BQS and a BQS-like subsample of the SDSS quasar sample. However, the application of a bright magnitude limit biases the BQS toward the inclusion of objects which are blue in $g-i$, in particular compared to the full range of $g-i$ colors found among the $i$-band limited SDSS quasars, and even at $i$-band magnitudes comparable to those of the BQS objects.'
author:
- 'Sebastian Jester, Donald P. Schneider, Gordon T. Richards, Richard F. Green, Maarten Schmidt, Patrick B. Hall, Michael A. Strauss, Daniel E. Vanden Berk, Chris Stoughton, James E. Gunn, Jon Brinkmann, Stephen M. Kent, J. Allyn Smith, Douglas L. Tucker, and Brian Yanny'
title: 'The SDSS View of the Palomar-Green Bright Quasar Survey'
---

Introduction {#s:intro}
============

The Palomar-Green Bright Quasar Survey {#s:intro.BQS}
--------------------------------------

The Bright Quasar Survey [BQS; @BQS hereafter referred to as ] is the set of quasars detected in the Palomar-Green (PG) survey of ultraviolet excess objects [@PG hereafter referred to as ]. The PG survey selects UV excess objects with $\ub<-0.46$ (corresponding to $\ub < -0.44$ for quasars with the mean color difference between stars and quasars assumed by ) brighter than an effective limiting magnitude of $B_\mathrm{lim}=16.16$. The BQS was the first large-area homogeneous quasar survey, and it remains the largest-area survey for bright quasars at $B<16$. Because of the UV excess criterion, it is primarily sensitive to quasars at redshifts up to $z=2.2$, where the Lyman-$\alpha$ line enters the $B$-band and gives quasars very red $\ub$ colors ($\ub > 0$).

inferred strong luminosity evolution of quasars from a combination of the BQS and fainter small-area quasar surveys. However, a number of authors find a substantially larger number of bright UV excess quasars, implying that the BQS is substantially incomplete. For example, @GMlFea92 reported that the bright quasar surface density from the Edinburgh Quasar Survey is three times that found by the BQS, leading to very different volume densities of low-redshift high-luminosity quasars and hence different results on the evolution of the quasar luminosity function [@GM98]. By contrast, @WCBea00 find that the BQS has a completeness of 68% compared to the Hamburg-ESO quasar survey (HEQS). Next to the BQS, the HEQS is the largest-area survey reaching similarly bright magnitudes as the BQS, but only overlaps part of the PG survey area as it surveyed the Southern hemisphere.

Some authors have raised concerns that the BQS incompleteness may be systematic with respect to optical color or radio properties. For example, @WP85 have suggested that the paucity of BQS quasars in the redshift interval $0.5 < z < 1.0$ may be caused by a BQS bias against redder quasars (or “quasars with yellow  colors”, as designated by @WP85) — in this redshift interval, the passage of the MgII line through the $B$ filter results in a $\ub$ color that is 0.2 mag redder than at lower and higher redshifts. However, @LFEea97 have argued that a cut of $\ub<-0.44$ is red enough to avoid this bias. Based on independent photometry of the luminous ($M_B<-24$) BQS objects, @WP85 also suggested that some of the PG limiting magnitudes (which varied from plate to plate) might have been “much fainter than stated”.

There are also concerns about a systematic incompleteness with respect to radio properties. @MRS93 found that 50% of $z<0.5$ BQS quasars are steep-spectrum radio-loud objects; they cautioned that this number might be spuriously high if the BQS selection favored the inclusion of radio-luminous objects. This cautionary note was interpreted by @GKMea99 and others as *suggesting* a radio-dependent incompleteness, casting doubts on the results obtained from statistical analyses of the radio properties of BQS objects.

In fact, PG quasars are often considered to be the archetype optically selected quasar sample, in particular when studying the properties of optically selected quasars at other wavelengths. Many other optically selected quasar surveys are now available which reach much fainter magnitudes and higher redshifts, use more general selection criteria, and generally have a much larger sample size (e.g., the Palomar Transit Grism Survey by [@SSG94] with 90 objects at $2.75 < z
< 4.75$ over an area of 61.5deg$^2$; the Large Bright Quasar Survey by [@HFC95], 1055 objects with $16 < B_J < 18.9$ at $0.2 < z <
3.4$ over 454deg$^2$; COMBO-17 by [@WWBea03], 192 objects with $17<R<24$ at $1.2 < z < 4.8$ over 0.78deg$^2$; the 2dF QSO redshift survey by [@CSBea04], 23 338 objects with $16 <
b_\mathrm{J} < 20.85$ at $z<3$ over 674deg$^2$); in particular, the SDSS quasar survey [@qso_ts] has cataloged nearly 50,000 quasars so far, including of order 500 at $z>4$ [@SFHea03; @SHGea05] and, in a separate search, 16 at $z>5.7$ [@FHRea04]. Each of these surveys will be more or less biased towards or against objects with a particular class of SEDs.

Because of the historical importance of the BQS in general, and its key role in anchoring the bright end of the local quasar luminosity function in particular, we investigate here whether the BQS suffers from any systematic incompleteness. By “incompleteness”, we refer both to lack of objects that in fact pass the survey’s magnitude and color limits, but also to the extent to which the survey is representative of quasars satisfying the broadest definition of the term (objects showing non-stellar continua and broad emission lines). We do so by comparing PG and Sloan Digital Sky Survey [SDSS; @Yorea00] photometry of PG sources (§\[s:SDSSphot\]), by considering the completeness of the PG UV excess sample relative to UV excess sources from SDSS (§\[s:simPG\]), and by comparing properties of BQS objects to those of “BQS-like” quasars from the SDSS (§\[s:compPGSDSS\]), with special attention to radio properties in §\[s:comp.radio.bias\]. We also consider which part of the quasar population found by the SDSS are selected by the BQS criteria. In our discussion section, we compare our findings to previous investigations of the BQS incompleteness (§\[s:disc.compBQS\]) and consider the biases induced by the selection criteria of the BQS and other quasar surveys. We summarize our findings in §\[s:sum\].

Selection of objects in the BQS {#s:intro.selBQS}
-------------------------------

For reference, we briefly review the construction of the BQS sample from and . The PG survey selects UV excess objects on double exposures of baked IIa-O photographic plates through filters $U$ (using Schott UG-2) and $B$ (GG-13) obtained using the Palomar 18inch (46cm) Schmidt telescope. The exposure times were adjusted to obtain equal image densities for objects with $\ub=-0.46$ (with the mean color difference between the spectral energy distribution \[SED\] of stars and quasars assumed by , this translates to $\ub = -0.44$ for quasars). The magnitudes were calibrated using photoelectric calibration exposures of local standards. The calibration was stabilized by fitting a model of star counts as function of galactic coordinates. The limiting $B$ magnitude varied from plate to plate; Figure \[f:intro.BQS.Blim\] shows the distribution of limiting magnitudes. give an effective limiting magnitude of $B<16.16$ and photometric errors of $\sigma_B=0.27$ and ${\ensuremath{\sigma_{U\!-\!B}}}=0.24$. These were later revised by to $\sigma_B=0.34$ and ${\ensuremath{\sigma_{U\!-\!B}}}=0.39$. The area covered by the complete PG survey was 10,668deg$^2$.

UV excess candidates passing the photometric selection criteria were observed spectroscopically to determine quasar redshifts and to remove main-sequence objects (i.e., all objects determined to have K lines) that had been scattered into the sample. Conversely, the spectroscopic observations were started before the photometric calibration had been finalized, therefore some objects that had been confirmed spectroscopically as objects that are not main-sequence stars (hereafter called “off-main sequence objects”) were retained in the PG sample even if the final photometric calibration formally caused them to fail the photometric selection criteria.

The BQS consists of 114 PG objects, which were required to have “dominant starlike appearance on blue prints of the 48 inch (1.2 m) Schmidt Sky Atlas” (the Palomar Sky Survey) and “broad emission lines with substantial redshift” [we use the most up-to-date version of the BQS object list from @KSSea94 see notes to Tab. \[t:BQSinSDSS\]]. Like all bright quasar surveys, the redshift distribution of BQS objects peaks at low redshift, with a median $z$ of 0.176, and 88 out of 114 objects (77%) at $z<0.5$.

The SDSS {#s:intro.sdss}
--------

The Sloan Digital Sky Survey [@Yorea00; @edr] is a photometric and spectroscopic survey of the extragalactic sky at high galactic latitude visible from the northern hemisphere. In this paper, we use the data set published as Data Release 3 [DR3; @DR3][^1]. The DR3 photometric catalog covers 5282deg$^2$, while the DR3 spectroscopic catalog covers 4188deg$^2$. The SDSS uses a wide-field camera [@Gunea98] to obtain ${\ensuremath{ugriz}}$ photometry [@ugriz; @LGS99; @Hogea01; @LIKea01; @ugrizstandards; @QA] with a photometric accuracy of 2–3%, a comparable precision of placing the photometry on the AB magnitude scale [@OG83; @dr2], and with an astrometric accuracy of better than 01 [@astrom]. The SDSS is also a spectroscopic survey of complete samples of galaxies [@lrg_ts; @gal_ts] and quasars. Quasar candidates are selected from SDSS photometry using an algorithm [@qso_ts] targeting objects with non-stellar colors or that are point-source optical counterparts of FIRST [@BWR95] radio sources. A tiling algorithm ensures uniformity and efficiency of the allocation of fibers to quasar candidates and other spectroscopic targets [@tiling]. A manually vetted quasar catalog based on DR3 data akin to that based on DR1 [@SFHea03] is given by @SHGea05 and contains over 46,000 quasars.

In this paper, we use $\Omega_{\mathrm{m}} = 0.3, \Omega_\Lambda =
0.7$, and $H_0 = 70$km/s/Mpc.

The photometric properties of PG sources in the SDSS {#s:SDSSphot}
====================================================

To evaluate the photometric completeness of the BQS, we perform separate comparisons of the PG and SDSS photometry for stars and quasars[^2]. The stellar photometry will be used to assess the photometric accuracy and precision of the PG survey using SDSS observations of PG objects. The quasar photometry transformations will be used to define a sample of SDSS quasars satisfying the BQS color selection criteria.

The SDSS photometric system is based on a set of standard stars which includes stars as blue as PG objects [@ugrizstandards]. The PG survey reports photometry transformed to the Johnson $U$ and $B$ system. Since a subset of the SDSS standard stars is taken from the Landolt standard fields with Johnson-Kron-Cousins  photometry [@Lan73; @Lan83; @Lan92], it is straightforward to establish color and magnitude transformations between the SDSS and the Landolt system. However, these transformations are not appropriate for quasars because of their different spectral shapes. Therefore, we determine separate color and magnitude transformations for quasars by performing synthetic photometry of composite quasar spectra in the SDSS and Landolt systems. We describe each process in turn.

Photometric transformation for stars {#s:phot.startrans}
------------------------------------

@ugriz and @ugrizstandards give color and magnitude transformations (synthetic and observed) between the Landolt system and the system of the United States Naval Observatory (USNO) 1.0m telescope (designated $u^\prime g^\prime r^\prime i^\prime
z^\prime$). We transform the USNO magnitudes of the SDSS standard stars to the system of the SDSS 2.5m telescope (i.e., the SDSS $ugriz$ system) using the equations given by @JEGphoteq. We use only those standard stars with $U-B < 0$ and perform linear least squares fits to determine the transformations from the SDSS system to $U$ and $B$. The resulting coefficients are given in Table \[t:phototrans\]. Ideally, separate transformations should be derived for stars of different spectral classes because of differences in the strength of the Balmer lines, in particular between white dwarfs and the remaining blue stars. Indeed, synthetic photometry suggests that DA white dwarfs have a $B-g$ that is greater by about 0.1 than that of the remaining white dwarfs and hot subdwarfs; however, we do not have enough stars with both accurate spectral classifications and Johnson photometry to confirm this using observed magnitudes (this is true both for the SDSS standards and for the subset of PG stars with photoelectric photometry). In any case, the standard stars that have been used include the full range of colors observed in the PG survey.

For reference in work with objects redder than $U-B=0$, we also give the coefficients obtained using all SDSS standard stars with ${\mbox{$R\!-\!I$}}<
1.15$ (stars with ${\mbox{$R\!-\!I$}}< 1.15$ have different color transformations than those with ${\mbox{$R\!-\!I$}}\ge 1.15$, but there is no Landolt photometry of a sufficient number of SDSS standards with ${\mbox{$R\!-\!I$}}\ge 1.15$ for us to derive reliable transformations), as well as coefficients for transformations between other filters.

[lrcll]{}\
Quasars at $z\leq 2.1$ (synthetic) & $\ub$ & = & $0.75 (u-g) -0.81$ & 0.03\
& $\bv$ & = & $0.62 (g-r) + 0.15 $ & 0.07\
& $\vr$ & = & $0.38 (r-i) + 0.27 $ & 0.09\
& ${\mbox{$R\!-\!I$}}$ & = & $0.72 (r-i) + 0.27 $ & 0.06\
& $B$ & = & $g + 0.17 (u-g) + 0.11$ & 0.03\
& $V$ & = & $g - 0.52 (g-r) -0.03 $ & 0.05\
Stars with ${\mbox{$R\!-\!I$}}< 1.15$ and $\ub < 0$ & $\ub$ & = & $0.77 (u-g) -
0.88$ & 0.04\
& $\bv$ & = & $0.90 (g-r) + 0.21 $ & 0.03\
& $\vr$ & = & $0.96 (r-i) + 0.21 $ & 0.02\
& ${\mbox{$R\!-\!I$}}$ & = & $1.02 (r-i) + 0.21 $ & 0.01\
& $B$ & = & $g + 0.33 (g-r) + 0.20$ & 0.02\
& $V$ & = & $g - 0.58 (g-r) -0.01 $ & 0.02\
All stars with ${\mbox{$R\!-\!I$}}< 1.15$ & $\ub$ & = & $0.78 (u-g) - 0.88$ & 0.05\
& $\bv$ & = & $0.98 (g-r) + 0.22 $ & 0.04\
& $\vr$ & = & $1.09 (r-i) + 0.22 $ & 0.03\
& ${\mbox{$R\!-\!I$}}$ & = & $1.00 (r-i) + 0.21 $ & 0.01\
& $B$ & = & $g + 0.39 (g-r) + 0.21 $ & 0.03\
& $V$ & = & $g - 0.59 (g-r) -0.01 $ & 0.01\
\
Quasars at $z\leq 2.1$ (synthetic) & $u-g$ & = & $1.25 (\ub) +
1.02$ & 0.03\
& $g-r$ & = & $0.93 (\bv) - 0.06 $ & 0.09\
& $r-i$ & = & $0.90 ({\mbox{$R\!-\!I$}}) - 0.20 $ & 0.07\
& $r-z$ & = & $1.20 ({\mbox{$R\!-\!I$}}) - 0.20 $ & 0.18\
& $g$ & = & $V + 0.74 (\bv) -0.07$ & 0.02\
& $r$ & = & $V - 0.19 (\bv) -0.02 $ & 0.08\
Stars with ${\mbox{$R\!-\!I$}}< 1.15$ and $\ub < 0$ & $u-g$ & = & $1.28 (\ub) +
1.14$ & 0.05\
& $g-r$ & = & $1.09 (\bv) - 0.23 $ & 0.04\
& $r-i$ & = & $0.98 ({\mbox{$R\!-\!I$}}) - 0.22 $ & 0.01\
& $r-z$ & = & $1.69 ({\mbox{$R\!-\!I$}}) - 0.42 $ & 0.03\
& $g$ & = & $V + 0.64 (\bv) -0.13$ & 0.01\
& $r$ & = & $V - 0.46 (\bv) +0.11 $ & 0.03\
All stars with ${\mbox{$R\!-\!I$}}< 1.15$ & $u-g$ & = & $1.28 (\ub) + 1.13$ & 0.06\
& $g-r$ & = & $1.02 (\bv) - 0.22 $ & 0.04\
& $r-i$ & = & $0.91 ({\mbox{$R\!-\!I$}}) - 0.20 $ & 0.03\
& $r-z$ & = & $1.72 ({\mbox{$R\!-\!I$}}) - 0.41 $ & 0.03\
& $g$ & = & $V + 0.60 (\bv) -0.12$ & 0.02\
& $r$ & = & $V - 0.42 (\bv) +0.11 $ & 0.03\

Photometric transformation for quasars {#s:phot.qsotrans}
--------------------------------------

To account for the different spectral shapes of stars and quasars, in particular the presence of strong emission lines, we derive separate transformation equations for quasars. Since all quasars are variable at optical wavelengths, it would be necessary to use contemporaneous SDSS and $U\!B$ photometry of a sample of quasars to derive adequate transformations from observations. As such observations are not available, we perform synthetic photometry of an updated version of the composite from @Berea01 using DR1 data ([@dr1]; changes in spectrophotometric calibration of SDSS data introduced in DR2 do not change the transformations appreciably) and the composite spectra from @Ricea03 for quasars with different intrinsic colors and reddening. We use the STSDAS Synphot package under the PyRAF scripting environment[^3] and the Landolt filter curves provided with that package as well as the SDSS transmission curves[^4] to determine color and magnitude differences for each composite. We compute a set of colors each at redshifts ranging from 0 to 2.1 in steps of 0.05 for the @Berea01 composite and 0.3 to 1.6 for the remaining composite spectra, which cover a smaller range of rest-frame wavelengths. For the comparison with BQS photometry, we fit  and $B-g$ as a function of both $u-g$ and $g-r$ for all composites simultaneously. As both  and $B-g$ are more tightly correlated with $u-g$ than with $g-r$, we use the fits as a function of $u-g$ to derive the transformations. The synthetic photometry results and best-fit lines are shown in Figure \[f:qsotrans\]. The resulting coefficients are also given in Table \[t:phototrans\], which again also contains transformations for the remaining SDSS and ${\mbox{$U\!BV\!R_\mathrm{C}I_\mathrm{C}$}}$ filters for reference.

The RMS scatter in the transformed quantities is 0.03, smaller than the plot suggests to the eye, although the $B-g$ residuals can be as large as 0.1 and show some systematic behavior with redshift. These systematics are caused by the presence of emission lines; the transformations as given have a precision of 0.06 or better in transforming pure power-law spectra. The  transformation is only slightly different from that for blue stars, but the $B-g$ transformation differs significantly — not only do we fit $B-g$ as a function of $u-g$ instead of $g-r$, but even if we had used $g-r$, the transformations would differ by between 0.06 to 0.2 magnitudes in the $g-r$ range of quasars ($-0.1$ to 0.5). With the transformations in hand, we now consider the SDSS photometry of PG sources.

SDSS observations of PG sources {#s:sdss.match}
-------------------------------

We are interested in the SDSS photometry of PG sources, both to determine whether there are any systematics in the photometric calibration of the PG survey, and to compare the PG quasars to those selected by the SDSS quasar survey with its much wider color selection criteria and magnitude cut in a much longer-wavelength band. To this end, we cross-match the PG catalog with the SDSS DR3 photometric catalog. The DR3 covers an area of 5282 square degrees; out of this area, roughly 3300 square degrees are contained within the PG area of 10,668 square degrees.

Because of the relatively large astrometric uncertainty of the PG survey and the different observing epochs, the closest SDSS object by position is not necessarily the correct match. We therefore use a generous positional matching radius of 2 arcminutes and employ cuts on the $B$ magnitude and  color transformed from SDSS photometry, accepting only objects within 1 magnitude of the PG photometry and with $\ub <
-0.2$. This procedure results in up to 3 SDSS matches per PG object; where multiple matches are present, the bluest object in  among them is always the correct match, the other matched objects being redder stars. Every PG object has a counterpart detected in the SDSS. In our analysis below, we do not use photometry of matches which are saturated in the SDSS or have otherwise unreliable photometry using the flag checking recommendations for point sources from the SDSS web site[^5]; this affected 9 objects.

We find 52 matches for BQS quasars in the DR3 photometric catalog which are shown in Table \[t:BQSinSDSS\]. All of these are either identified as quasar candidates by the SDSS target selection, have a cosmetic defect that excludes them from target selection (this affected 5 objects; the criteria for cosmetic defects are described in detail in [@qso_ts]; [@SOE] estimate that the fraction of quasars missed due to image defects and blends is approximately 4%), or are brighter than the SDSS spectroscopic bright limit of $i>15$ which has been introduced to avoid fiber cross-talk and saturation in the spectrograph. Thus, every BQS quasar is either targeted by the SDSS, or we understand why it was not targeted. However, even if target *selection* is complete, spectra of individual PG quasars may still be missing in the SDSS quasar survey if an object was not targeted by one of the pre-final versions of the target selection algorithm, or because of less reliable photometry in the TARGET version of photometry [see discussion of TARGET and BEST photometry in @dr2 §3]. This affects one PG object for which DR3 photometry is available: the final quasar target selection algorithm correctly identified PG 1012+00 as a quasar candidate, but the TARGET version of the photometry does not recognize it as a quasar, merely as a counterpart to a ROSAT source. The quasar resides in a host galaxy with complex morphology (perhaps a merging system), with a bright galactic nucleus approximately 2 away from the quasar. The galactic nucleus was targeted as a galaxy and obtained a fiber (Plate/MJD/Fiberid 270/51909/586), while the quasar itself did not, because galaxy targets obtain a fiber with higher priority than ROSAT matches [see @edr; @tiling].

The photometric calibration is most easily assessed by considering only non-variable stars, which are also much more numerous than the PG quasars. We obtain 466 SDSS matches of PG stars with clean SDSS photometry in the DR3 area. The SDSS-derived color-magnitude diagram of these stars shows that the White Dwarfs and hot subdwarfs of types sdO and sdB in the PG survey cover similar ranges in color and magnitude.

### SDSS observations of PG stars: the accuracy of the PG photographic magnitudes {#s:phot.sdss.accuracy}

Using the transformations established in §\[s:phot.startrans\], we derive the $U\!B$ photometry of non-variable PG stars from their matches in SDSS data. report a $B$-band magnitude (transformed to the standard Johnson system, which we assume to be identical to the Landolt system here) derived from the photographic photometry for every object in the survey, as well as a photoelectric $B$ magnitude (which we will designate [$B\!_p$]{}) and  color for a small subset of the stars. The photographic  colors were not reported by because they were deemed less reliable as indicator of each source’s spectral type than the spectroscopic information. However, one of the authors (RG) retrieved archival notes with the photometric  colors for most of the BQS objects (i.e., the quasars from the PG survey), we will compare those to SDSS photometry in §\[s:phot.sdss.colors\] below.

give an error of $\sigma_{{\ensuremath{B\!_p}}}=0.05$ for the photoelectric magnitudes, comparable to the accuracy of the SDSS CCD photometry ($\sigma_u=0.03,\sigma_g=0.02$). Both of these measures are much more accurate than the photographic-plate derived magnitudes with their quoted error of $\sigma_B=0.29$ .

We begin with a comparison of the PG and SDSS magnitudes of these stars in Figure \[f:phot.PGstars\_Bfit\] (left-hand panels). We first compare the PG photoelectric [$B\!_p$]{} and the SDSS $B$ magnitudes of the 104 stars in the overlap sample which also have photoelectric PG photometry. The mean difference of $-0.03$ is comparable to the photometric accuracy of the SDSS data. The observed RMS difference of 0.18 is much larger than the $\sigma_{{\ensuremath{B\!_p}}}=0.05$ given by . However, after iterative rejection of $3\sigma$ outliers, the RMS difference drops to 0.075, as expected when considering the difference of two quantities where each has an error of 3%-5%. The different RMS is thus caused by a non-Gaussian error distribution in the PG photoelectric photometry. A similar comparison of photoelectric and SDSS  shows a mean and median offset of 0.01 and a surprisingly small RMS difference of 6% (even without outlier rejection).

We next compare the photographic-plate derived $B$ magnitudes to SDSS-derived B magnitudes for all non-variable PG stars matched in the SDSS, as well as to the PG photoelectric [$B\!_p$]{}, where available (right-hand panels in Figure \[f:phot.PGstars\_Bfit\]). The comparison shows that there are systematic differences between the “low-accuracy” PG photographic magnitudes and both of the “high-accuracy” magnitudes, the SDSS $B$ and the photoelectric [$B\!_p$]{}magnitudes. The PG photographic magnitudes are too bright by about 0.2 magnitudes on average at $B\approx 17$, and similarly too bright at $B\approx 13$. At $B\approx15$, the photographic magnitudes agree with those from the SDSS, with a smooth transition from either extreme, although there is a much larger scatter at the bright end. The original photographic calibration approximated the photographic S-curve by a linear fit in the magnitude range $14 < B < 16$, consistent with the small calibration differences we find within this magnitude range and the larger differences outside it. There are no discernible systematic trends of this calibration difference with the  color. This calibration difference changes not only the magnitudes of the PG objects (and hence the limiting magnitudes), but also the inferred scatter between the PG and other photometry. We therefore wish to recalibrate the PG $B$ magnitudes using SDSS and/or PG [$B\!_p$]{} photometry.

This recalibration *cannot* be done simply by fitting the PG photographic $B$ magnitudes as function of the high-accuracy SDSS $B$ and PG [$B\!_p$]{} magnitudes because the machine used to digitize the photographic plates did not report measurements of any objects fainter than the plate limit (which varied from plate to plate). Therefore, the points shown in the right two panels in Figure \[f:phot.PGstars\_Bfit\] are restricted to lie below the line $B=B_\mathrm{lim}$ for each PG plate (the dotted line shows the average $B_\mathrm{lim}$ of 16.16). Hence, no PG data are available for those objects which have been scattered out of the PG sample, and the fit is biased towards artificially bright photographic $B$ values at the faint end.

To allow a correction of the limiting magnitudes of each PG field, we instead perform a fit of the inverse relation, i.e. the SDSS or [$B\!_p$]{}magnitude as function of PG photographic magnitude. In this case, the censoring is applied in the independent variable, resulting in a less biased fit, provided that errors in both coordinates are taken into account. We obtain the following fit: $$\begin{aligned}
B & = &  15.1364 + 0.9584\,(B_\mathrm{PG}-15) \nonumber \\
     &   & -0.1605\,(B_\mathrm{PG}-15)^2 -0.0160\,(B_\mathrm{PG}-15)^3
\label{eq:Bfit}\end{aligned}$$ where $B_\mathrm{PG}$ designates the photographic PG magnitude. This fit is shown as green dashed line in Figure \[f:phot.PGstars\_Bfit\]. This fit closely follows a non-parametric fit obtained by determining the median photographic magnitude as function of the high-precision magnitudes in bins of size $\Delta B= 0.1$.

We expect this calibration difference to be responsible for some of the scatter between photographic and other $B$ magnitudes, so that the error of $\sigma_B = 0.29$ should be an overestimate of the actual error. However, the residuals of the corrected photographic $B$ do not have a distribution that is appreciably narrower than the original residuals; in fact, both the original and the corrected residuals have an RMS of 0.34. Nevertheless, use of the fit clearly reduces the systematic calibration errors.

### SDSS observations of BQS quasars: the accuracy of the PG photographic colors and $B$-band variability {#s:phot.sdss.colors}

We now turn to the comparison of SDSS and PG  colors, where the latter are available. Figure \[f:phot.UBdiff\] shows the distribution of the difference between SDSS and PG-derived  for the 47 BQS objects for which clean SDSS photometry is available. The distribution of residuals is sharply peaked at $\Delta(\ub) =
(\ub)_\mathrm{PG}-(\ub)_\mathrm{SDSS} = 0.2$, with tails to $\pm0.5$. The RMS  difference is 0.21 and is dominated by photometric errors. (Since the PG magnitude measurements are based on double exposures of the same plate, the PG $U$ and $B$ measurements are effectively contemporaneous, as are the SDSS observations in $u$ and $g$.)

only performed photoelectric photometry of non-variable stars, but not of any BQS objects; however, any color variability over the epoch difference between PG and SDSS will be negligible compared to the PG photographic color error [@VBWKea04], so that the color comparison is not affected by variability. Thus, judging from the peak in the $\ub$ difference histogram, the PG-recorded photographic  colors are too red by about 0.2 magnitudes. As a consequence, we expect that the true color cutoff of the objects in the PG survey is in fact about 0.2 magnitudes *bluer* than assumed.

We compare SDSS and photographic $B$ magnitudes of the quasars in our overlap sample in Figure \[f:phot.Bdiff\]. On average, the quasars are fainter by 0.4 magnitudes at the SDSS epoch, with an RMS difference of 0.54 magnitudes. Given an RMS difference $\sigma$, the expected magnitude offset is $\sigma^2$ times the logarithmic slope of the number-magnitude counts, or about $2 \sigma^2$. Thus, the expected offset is about 0.5 magnitudes, consistent with the variability amplitude of 0.3 magnitudes expected over the approximately 30-year epoch difference between SDSS and PG observations [@HSWea01]. The variability amplitude found here also agrees roughly with the structure function for quasars presented by @dVBW03.

In conclusion, we have found two key differences between the PG photographic photometry on the one hand, on which the PG color and magnitude selection is based, and SDSS and PG photoelectric photometry on the other hand: there is an offset between the PG photographic and the true $B$-band magnitudes which varies systematically with magnitude, as well as an offset of 0.2 magnitudes between the photographic and true  color (objects appear redder in the PG survey than they are), for which no systematic variation with magnitude could be established. To double-check the validity of these conclusions, we now simulate the PG survey’s selection of objects from its parent sample as observed with the SDSS.

Completeness of the PG sample relative to UV excess sources from the SDSS {#s:simPG}
=========================================================================

We quantify the PG sample incompleteness by selecting SDSS object that pass the PG photometric selection criteria. Inclusion in the PG catalog of UV excess objects furthermore required that objects pass a spectroscopic confirmation as off-main sequence object or quasar. This process led to the exclusion of 1125 main-sequence objects that had been scattered into the photometric sample. SDSS spectroscopic target selection explicitly rejects objects with the colors of white dwarfs to improve the selection efficiency of quasar candidates [@qso_ts], so that a similar spectroscopic confirmation is not available for all objects passing the PG criteria in SDSS photometry. However, the photometric calibration of the SDSS is sufficiently accurate to allow a clean separation of main-sequence and PG-like UV excess objects in the $\ub$ against $B$ color-magnitude diagram. Essentially all objects with $\ub < -0.3$ that are not saturated in SDSS photometry are off the main sequence (the magnitude at which objects are saturated of course depends on the seeing; the brightest unsaturated object has a PSF magnitude $r=12.1$, and objects as faint as $r=14$ can contain saturated pixels).

From this parent sample, we can directly simulate the expected color and magnitude distribution of objects in the PG sample, in the following manner. Using the positions of the plate centers and limiting magnitudes from Table 1 in , we determine in which PG survey plates each SDSS object is contained, and hence the PG limiting magnitude for each object (for simplicity, we approximate the shape of PG survey plates as perfect circles of area 59.14 square degrees, i.e., with radius 433876). For objects covered by multiple plates with different PG limiting magnitudes, we use the faintest one. We transform SDSS magnitudes into the $U\!B$ system using the transformations derived above (we apply the quasar transformations from §\[s:phot.qsotrans\] to those objects with a quasar spectrum in the SDSS, and the stellar transformations §\[s:phot.startrans\] for all others). For every SDSS object, we also determine whether it has been included in the PG catalog. In this way, we can compare the completeness of the PG survey *relative* to the SDSS; i.e., we can determine whether there are any color or magnitude systematics to the incompleteness. We are not making any statements about the *absolute* surface density of UV excess objects in this section.

Figure \[f:simPG.UBB\] shows the color-magnitude diagram of our SDSS parent sample, defined as all objects with $\ub < -0.3$ and $B<17.6$ (3 $\sigma_B$ fainter than the faintest PG plate limit) found within 433876 of a PG survey plate center. This parent sample includes 546 objects which have been identified as quasars in the SDSS spectroscopic survey (green circles, Fig. \[f:simPG.UBB\]; the DR3 spectroscopic data set only covers a subset of the PG area, so that future SDSS data releases will contribute additional spectroscopic quasars in this area). We account for the calibration difference between PG and SDSS $B$ magnitudes by recalibrating the PG limiting magnitudes using the transformation from PG to SDSS magnitudes derived above (Equation \[eq:Bfit\]). We then calculate the PG detection probability for each object in our parent sample from the values of the limiting magnitude of each plate, the $\ub$ cut, and the respective PG photometric errors, assuming a Gaussian error distribution. By summing the detection probabilities for all objects in a given color or magnitude bin, we directly obtain the expected color and magnitude distributions for the PG survey.

Figure \[f:simPG.Lhood\] shows the predicted distributions for $B$ magnitude, $\ub$ color, and detection probability (dotted red histograms) and compares them to the distributions as observed in the PG (black histograms). The SDSS observations and the color cut and photographic errors as given by lead to an overprediction of the number of PG objects with colors close to the $\ub<-0.46$ cutoff and with magnitudes in the range $15 < B < 16.5$, i.e., within a magnitude or so of the average limiting B magnitude. These “missing” objects have PG detection probabilities near 50% based on SDSS photometry. With hindsight, Figure \[f:simPG.UBB\] already reveals that the PG is missing objects with $\ub$ colors close to the cutoff: for a Gaussian error distribution, the detection probability of an object close to the color cut is close to 50%, but PG detections nearly exclusively lie to the blue of the nominal color cut of $-0.46$. To reduce the number of red objects in the simulated PG and to match the slope of the $\ub$ histogram’s cutoff towards redder $\ub$ colors, it is necessary to adjust the color cut to $\ub=-0.71$ and the $\ub$ error to ${\ensuremath{\sigma_{U\!-\!B}}}=0.24$ , resulting in the cyan shaded histograms shown in Figure \[f:simPG.Lhood\]. The offset between the corrected $\ub$ cut and the value we find is comparable to the offset of about 0.2 magnitudes between SDSS and PG $\ub$ colors of quasars we determined above (§\[s:phot.sdss.colors\] and Figure \[f:phot.UBdiff\]).

There is a related test based on the number of main-sequence objects scattered into the photometric sample. At a given $B$ magnitude, the number of objects per unit $\ub$ color increases sharply into the main sequence, redwards of $\ub=-0.3$. Therefore, the number of main-sequence objects that are scattered into the PG photometric sample and subsequently need to be removed in the spectroscopic confirmation process is extremely sensitive to changes in the $\ub$ cut and error. We repeat the detection probability calculation for objects with $-0.3 < \ub < 0$ to obtain a lower limit on the average number of main-sequence objects we expect to be scattered into the photometric sample for a given combination of color and magnitude cuts and errors. We obtain a prediction of more than 17,000 main-sequence objects being scattered into the PG photometric sample for $\ub<-0.44$ and ${\ensuremath{\sigma_{U\!-\!B}}}=0.38$, while the prediction for the revised values $\ub<-0.71$ and ${\ensuremath{\sigma_{U\!-\!B}}}=0.24$ is roughly 500. These values are for the DR3-PG overlap area of roughly 3300 square degrees. The actual number of rejected main-sequence objects in the PG survey was 1125 over 10,668 square degrees, corresponding to roughly 300 over the overlap area considered here, and consistent with our revised color cut and photometric error. This finding is confirmed independently by a comparison of the sample of DA white dwarfs from the PG to samples selected in other wavebands, which shows color incompleteness beginning at $\ub=-1$ and increasing towards redder colors [@LBH04 and Liebert 2004, *priv. comm.*]. This color incompleteness is likely caused by the visual inspection process of the measurement-machine selected UV excess candidates, which cut down the number of candidates by a factor of 20 by removing objects that appeared to have a neutral $\ub$ color on the photographic plates.

In summary, we find that the PG survey had an effective color cut $\ub
< -0.71 \pm 0.24$. We now consider how different the BQS quasar sample is from the BQS-like part of the SDSS quasar sample.

Comparison of PG quasars to SDSS quasars {#s:compPGSDSS}
========================================

The SDSS quasar survey reaches both to much fainter magnitude limits and samples a larger portion of non-stellar color space than the BQS. Our comparison of these two quasar surveys has two aims:

1.  To consider whether the BQS has any systematic incompleteness. To address this question, we compare the BQS quasars to those DR3 quasars passing the nominal PG criteria $B<16.16$ and $\ub<-0.44$ (we discuss this choice in detail in §\[s:comp.opt\] below.)

2.  To consider the impact of the BQS selection criteria themselves, i.e., determine the selection effects present in the BQS. To address this question, we consider which part of the entire DR3 quasar catalog is selected by the BQS criteria.

In order to obtain a meaningful comparison, we need to apply some cuts to obtain comparable samples. First, SDSS quasar spectroscopic target selection has a bright limit of $i>15$ to avoid fiber cross-talk and saturation in the spectrograph. We therefore apply the same bright limit to SDSS matches of BQS quasars, leaving 39 BQS matches in the PG-DR3 overlap area of approximately 3300 square degrees. Furthermore, we restrict the SDSS spectroscopically identified quasars to $z<2.2$ quasars selected using the $ugri$ algorithm with faint limiting magnitude $i<19.1$, since the $griz$ algorithm is explicitly aimed at recovering quasars at $z>2.2$ to which the BQS UV excess cut is insensitive. The resulting sample consists of 30,975 quasars, drawn from a subset of the DR3 area totaling 4188 square degrees.

Comparison of optical properties {#s:comp.opt}
--------------------------------

### Selection of a BQS-like set of quasars from the SDSS quasar sample {#s:comp.opt.bqslike}

Even though we established above (§\[s:simPG\]) that the PG actually has an effective color cut $\ub<-0.71$, we select a “BQS-like” sample of SDSS quasars using the the intended limit $\ub<-0.44$ because this is the value assumed by all previous comparisons of other quasar surveys to the BQS. Of the 30,975 SDSS quasars remaining in the comparison sample, 26 satisfy the nominal BQS criteria $\ub<-0.44$ and $B<B_\mathrm{eff}=16.16$. We do not attempt to determine the surface density of bright quasars in the SDSS here since we have not yet completed the determination of the SDSS quasar survey’s selection function, which will appear elsewhere .

Furthermore, an object-by-object comparison between the BQS and BQS-like SDSS quasars is not particularly meaningful. First, the large photometric errors of the PG survey and the flux variability of quasars mean that a reobservation of the PG area using the same technology would not recover exactly the same set of objects. The BQS quasars in the range $15.4 < B < 17.2$ only have an average detection probability of 50%. Moreover, all quasars within $3\sigma$ of the intended PG cuts in color and magnitude (i.e., with photographic $B <
B_{\mathrm{lim}} + 3\, \sigma_B$ and $(\ub) < (\ub)_\mathrm{lim} + 3\,
{\ensuremath{\sigma_{U\!-\!B}}}$) have a non-negligible probability of being included in the sample, but their inclusion probability is only 10% on average. Therefore, it is very likely that an entirely different set of objects will be scattered into repeat observations of the entire BQS. Variability on average decreases the re-detection probability even more because quasars from a flux-limited sample on average become fainter. As a further consequence, the *number* of objects scattered into a BQS-like quasar sample will vary from reobservation to reobservation. Using the PG parent sample constructed in §\[s:simPG\], we simulated 1000 realizations of the BQS, by computing the detection probability of each of the 546 confirmed SDSS quasars in the parent sample from the corrected PG limiting magnitudes and the true limiting $\ub = -0.71$. The number of quasars included in the simulated BQS follows a Gaussian distribution with a mean of 27.9 and standard deviation of 4.4. In fact, 23 of the 546 SDSS quasars considered here have also been detected by the PG. Thus, the number of actual BQS quasars in the overlap area between the PG and the DR3 spectroscopic surveys is fully consistent with the range observed in the Monte-Carlo simulations of the BQS. This number is different from the number of BQS objects for which SDSS photometry is available (52 objects; §\[s:sdss.match\]), from the number of BQS objects with SDSS photometry and $i>15$ (39 objects) and from the number of “BQS-like” SDSS quasars with $i>15$, $B<16.16$ and $\ub <
-0.44$ (26 objects; see previous paragraph) because the comparison in this section is limited to objects which have both an SDSS spectrum and lie within 433876 of the PG plate centers listed in Table 2 of , i.e., to a smaller area of sky. Further differences between the number of SDSS and BQS quasars to the same flux limit arise because of Eddington bias [@Edd13; @Edd40]. However, the usual correction formulae [see also @Pet97 p. 162 ff., e.g.] only give an *average* correction, while the *true* bias depends on the details of the number counts at $B>B_{\mathrm{lim}}$ and the error distribution. In combination with the large errors of photographic surveys, this makes it impossible to determine the *actual* Eddington bias with any degree of accuracy [see @Jef38; @Lor04].

Secondly, the limiting magnitudes of the PG survey plates vary substantially (see Figure \[f:intro.BQS.Blim\]), and the surface density of bright quasars is very low (most PG fields contribute 0 or 1 quasars to the BQS). Therefore, a comparison of the full BQS to a survey with the same overall effective limiting magnitude, but a different distribution of limiting magnitudes on the sky, will be expected to result in many non-detections of BQS objects and detections of non-BQS objects.

Hence, we prefer to compare the two surveys in a statistical sense, by analyzing the distribution of BQS and BQS-like quasars in redshift, magnitude and color space. We consider each of the two-dimensional projections of this three-dimensional parameter space in turn. Using matches between the FIRST radio survey [@BWR95] and SDSS data, we also consider the radio properties.

### Magnitudes and colors as function of redshift {#s:comp.opt.magz}

It is instructive for the understanding of selection effects to compare the properties of BQS quasars as well as BQS-like SDSS quasars to the entire set of SDSS quasars. We begin with the Hubble diagram, the apparent magnitude plotted against redshift, in Figure \[f:SDSS\_Hubblediag\]. Note that the number of bright objects decreases with increasing redshift. As expected from the larger magnitude errors and the limiting magnitude varying from plate to plate, the BQS quasars show some scatter about the effective limiting magnitude $B_\mathrm{eff}$, while the BQS-like SDSS quasars have a sharp magnitude cutoff. Other than that, the BQS and the BQS-like quasars have a similar distribution in the Hubble diagram.

\

Next, we consider the distribution of quasar colors against redshift shown in Figure \[f:SDSS\_colz\]. As noted before by several authors [e.g. @WCBea00; @Ricea01 and references therein], there is a systematic variation of the  color of quasars as a function of redshift, caused by emission lines passing into and out of the two filters. As discussed in detail by @WP85, application of a UV excess criterion in conjunction with this variation may lead to an observed redshift distribution that is not representative of the true redshift distribution. But again, the distributions of both $u-g$ and $g-i$ against redshift are very similar between the BQS and BQS-like SDSS quasars.

In addition to the emission-line effect described here, quasar colors can be reddened by the presence of host galaxy starlight, especially at low luminosity (and therefore low redshift), where the host galaxy is apparent in SDSS imaging. Indeed, excluding extended quasars from the color-redshift distribution (right-hand panels in Figure \[f:SDSS\_colz\]) bluens the median $\ub$ color at $z=0.2$ by 0.2 magnitudes; the median $g-i$ colors are affected even more strongly. However, the BQS quasars are so luminous that the vast majority appear as point sources in SDSS imaging; thus it would be incorrect to compare colors of BQS quasars and the bulk of the SDSS quasars at the same redshift. Rather, we simply compare the *observed*  and $g-i$ colors of BQS and BQS-like SDSS quasars at each redshift.

A related concern is that the BQS criterion that quasar candidates should have a “dominant point-like appearance” biases the BQS against lower-luminosity quasars in higher-luminosity host galaxies. Because of the correlation between the host’s bulge mass and the black hole mass, this will bias against sources with lower Eddington ratios; together with correlations between luminosity or Eddington ratio and continuum spectral slope, this may introduce a systematic color bias . The importance of this effect can be assessed by performing a decomposition of the SDSS quasar spectra and colors into a galaxy and AGN component, which is, however, beyond the scope of the present work.

In conclusion, the colors and magnitudes of quasars as function of redshift are affected by the presence of emission lines and host galaxy starlight. These effects must be taken into account in the analysis of redshift, magnitude and color distributions of quasars, such as in the construction and interpretation of quasar luminosity functions.

### Color-magnitude diagrams {#s:comp.optt.cmd}

\

Figure \[f:SDSS\_CMDs\] shows the color-magnitude diagrams (CMDs) of the quasars at $z<2.2$ from the DR3 spectroscopic quasar sample and the BQS quasars reobserved with the SDSS. The SDSS sample is flux-limited in $i$-band, as can be seen in the right-hand panel. The skewed cutoff to the $B$ against  distribution is caused by a combination of two effects: one is that the H$\alpha$ line passes through the $i$-band at low redshifts, boosting quasars that are faint in $B$ above the $i$-band flux limit. The other effect is the increased importance of red host-galaxy starlight for lower-luminosity quasars we mentioned above. Hence, quasars which are faint in $B$ are also red in .

The CMD shows clearly that the multicolor-selected SDSS quasars which are sufficiently bright to pass the BQS limiting magnitude in the $B$-band have a similar  color distribution to the BQS quasars themselves. Moreover, in the limit of small photometric errors, the UV excess selection criterion does not remove any quasars from the BQS sample that are not already removed by the $B$-band brightness cut (we discuss the impact of the photometric errors below). In other words, the BQS is lacking red quasars not because of its UV excess criterion, but because *there are no red quasars which are bright in $B$*.

This can be understood by considering the shape of the distribution at fixed $B$. The quasar density peaks at a constant $\ub\approx -0.67$ at all $B$, and the dropoff in density towards both redder and bluer colors is also independent of $B$ (the contours in the flanks of the distribution are roughly parallel to each other down to $B\approx20$, where the cutoff becomes skewed as discussed above). Since the number counts of quasars fall rapidly with increasing brightness, nearly all BQS quasars are drawn from near the mode of the UV color distribution. To find significant numbers of both redder *and bluer* quasars than contained in the BQS, it is simply necessary to sample fainter magnitudes (or a larger volume of the Universe — in fact, a much larger volume than is actually available). Thus, the BQS criteria do not produce any color bias when considering only the UV colors of quasars that are bright in $B$-band. However, the $i$ against  and $i$ against $g-i$ CMDs shows that the BQS criteria do introduce a color bias against red quasars which are bright in $i$-band.

The SDSS selects such red quasars simply because it applies the brightness limit in the $i$-band. The faintest (in $i$) BQS-like SDSS quasar has $i=16.26$. There are only 26 DR3 quasars passing the BQS criteria, but there are 109 DR3 quasars with $i<16.26$ (even after rejecting extended sources, there are still 64 such quasars). Of the 109 sources, 96 have $\ub<-0.44$, while the remaining 13 redder quasars have colors extending to $\ub=-0.26$ (5 of these are point sources). A Kolmogorov-Smirnov (KS) test comparing the $g-i$ distributions of the BQS quasars and of all SDSS quasars at $i<16.26$ rejects the hypothesis that they are indistinguishable at $>99\%$ confidence level; the $\ub$ distributions are formally just indistinguishable (only 86% confidence level for a rejection), but the $\ub$ distribution of the $i<16.26$ SDSS quasars clearly extends to redder colors than that of the BQS and BQS-like quasars. Thus, the BQS selection criteria lead to the omission of quasars with red colors. This bias is not driven primarily by the UV excess criterion, but instead by application of the magnitude limit in the $B$-band.

\

We now return to the comparison of the of BQS-like SDSS quasars and actual BQS quasars. Figure \[f:SDSS\_KStest\] compares the redshift and color distributions of the 39 $i>15$ BQS objects inside the DR3 area to that of the 26 BQS-like SDSS quasars. The redshift distributions are indistinguishable by the KS test, which returns a very high probability for obtaining both observed distributions as realizations of the same underlying distribution. In fact, the redshift distribution of the BQS quasars is indistinguishable at 95% confidence level from that of DR3 quasars with $\ub<-0.44$ down to $B=17.0$. The distributions of  and $g-i$ are similarly indistinguishable between the BQS and the BQS-like SDSS quasars. Even though the BQS has relatively large color and magnitude errors and a number of quasars are scattered into and out of the sample, the optical properties of BQS quasars are not statistically distinguishable from BQS-like SDSS quasars. Thus, based on our comparison sample, the BQS is a representative survey of bright, blue quasars.

To summarize: Of the SDSS quasars above some limiting $i$, only the bluest ones are bright enough in $B$ to pass the BQS $B$-band cut. Therefore, the BQS flux cut excludes most SDSS quasars which have comparable $i$-band magnitudes as the $i$-faintest BQS objects. Only an additional 10% are redder than the BQS *color* cut. To recover the red end of the quasar color distribution, it would be necessary to extend the search to fainter $B$ magnitudes *in addition to* relaxing the UV color excess criterion.

Radio properties {#s:comp.radio}
----------------

### Continuum properties {#s:comp.radio.cont}

\

We next consider the radio properties of the quasars using matches to SDSS data from the FIRST survey. The FIRST survey itself has a flux limit (1 mJy at 1.4 GHz) which introduces selection effects in addition to those from the quasar surveys. Use of the FIRST data is preferable over the use of dedicated radio observations of the BQS because it provides a homogeneous data set for comparing the radio properties of the SDSS quasars to those of the BQS quasars. Since various claims of a radio-loud/radio-quiet bimodality have been made based on the radio flux [@KSSea89], radio/optical ratio [e.g., @SHPea80; @IMKea02] and the radio power $P$ [e.g., @PML86; @MPM90; @MRS93], we begin by considering these three quantities as a function of redshift. We use the integrated FIRST flux of all objects and [following @IMKea02] define a FIRST AB magnitude $$t = -2.5 \log \frac{f_\mathrm{FIRST}}{3631 \mathrm{Jy}}$$ and the logarithmic radio-optical ratio (without any $K$-correction) $$R = 0.4 (B-t).
\label{eq:R}$$ The FIRST limiting flux of 1mJy corresponds to $t=16.40$.

\

Figure \[f:radio\_z\] shows the distributions of radio flux, power, and radio-optical ratio for DR3 and BQS quasars. There are no obvious gaps in any of the distributions which would reveal a strong bimodality in the radio properties of optically selected quasars. Note, however, that the distributions are influenced by the selection limits in *both* the optical and radio surveys. For example, objects with small value of $R$ are concentrated at low redshift because the lowest $R$ is obtained for the objects which are brightest in $B$, which are concentrated at low redshift. Figure \[f:radioKS\] compares the distributions of $t$, $\log P$, and $R$ for the two sets of quasars. In all three cases, the distributions are again statistically indistinguishable, with KS probabilities of 0.83, 0.91, and 0.49 for obtaining the observed $t$, $\log P$, and $R$ distributions, respectively, from the same underlying distribution. Thus, we find no evidence for any radio dependence of the BQS incompleteness.

We noted above that the $g-i$ distribution of the 26 BQS-like SDSS quasars is different from that of all 109 SDSS quasars with $i<16.26$, the faintest $i$ magnitude of the BQS-like quasars. However, according to KS-tests, the radio properties of these two samples are entirely indistinguishable. We will return to this point in the next section, where we briefly consider the relation between emission-line properties and radio emission of objects in our BQS-like sample.

### Possible BQS biases with respect to radio properties {#s:comp.radio.bias}

As noted in the introduction, @MRS93 stressed “the rarely appreciated fact that, at $z\sim 0.3$, about 50 per cent of the brightest optically selected quasars …are steep-spectrum, radio-loud objects” (these authors use the \[OIII\] 5007 narrow-line luminosity to define “brightest”, i.e., in fact they appear to mean “most luminous”, and use an emission-line quantity rather than a continuum measure such as the continuum flux at a fixed rest-frame wavelength or the $B$-band magnitude). Their footnote cautioning that this number might be spuriously high if the BQS incompleteness favored the inclusion of radio-loud objects has been interpreted as *suggesting* such a radio-dependent incompleteness — however, these interpretations have not been supported by any additional evidence. In fact, we determined in the previous section that the BQS incompleteness appears to be random with respect to radio properties, given that BQS-like DR3 quasars have indistinguishable distributions of FIRST flux, luminosity, and radio-to-optical flux ratio. However, if the radio and optical properties of all or some quasars are correlated in some way, the BQS sample may not be a random sample of quasars with respect to radio properties.

As a rough check of their finding, we computed $L_{\mathrm{[OIII]
    5007}}$ from the $\mathrm{[OIII] 5007}$ flux determined by the SDSS pipeline and our custom spectral-line fitting routine for all SDSS quasars with $z<0.5$ and $B<17$, where we used a fainter flux limit to increase the sample size to 116 objects. All objects which @MRS93 classified as “classical double radio sources” (their category D), i.e., radio-loud objects, have $L_{\mathrm{[OIII] 5007}}>
5\times10^{35}$W.[^6] In our sample, there are 13 sources with $L_{\mathrm{[OIII] 5007}}>
5\times10^{35}$W. Of these, four have a detection of FIRST flux at the optical position. Inspection of FIRST and NVSS [@NVSS] images and a literature search reveal that three are “classical double” radio sources (4C +31.30, 4C +60.24 = 3C 351, and 4C +61.20); the fourth radio source has compact radio emission associated with the core, but no clear lobes. The remainder of the \[OIII\]-luminous sources have no radio emission detected in FIRST, NVSS, or the literature, but all have upper limits on the FIRST luminosity lying below the luminosity of the three double-lobed sources. The @MRS93 prediction was that 6.5 of the sources (50% of 13) should be double radio sources, but we found only 3. The Poisson probability to obtain 3 events where 6.5 are expected is 6.9%. Thus, our investigation of BQS-like objects does not allow us to rule out the @MRS93 result.

In order to obtain some clue as to what causes the large fraction of radio-loud objects at the high-\[OIII\] luminosity end of the BQS and our BQS-like sample, we have constructed a comparison sample of SDSS quasars using a bright $i$-band cut $i<16.34$, which contains a similar number of objects as the $B<17$ sample just employed. This $i$-band cut removes about 50% of the sources with $L_{\mathrm{[OIII]
5007}} > 10^{35}$W that were present in the $B$-band limited sample, including one of the three double-lobed sources mentioned above (4C +61.20). Of those objects in the $B$-band limited sample, the bluest (in $B-i$) are missing in the $i$-band limited one. Thus, there is some indication that quasars with a bluer continuum are more likely to be luminous in \[OIII\] 5007. If the link between radio and narrow-line luminosity identified by @MRS93 [also see @Wileta99] indeed holds for all quasars, the BQS is biased towards the inclusion of radio-loud objects because it preferentially includes objects which are luminous in \[OIII\] 5007. This would be consistent with the trend for more luminous quasars to have bluer optical/UV continua [@CGBea99 e.g.]. However, an apparently contradicting observation is that the radio-loud objects among the SDSS color-selected quasar sample (defined as having $R>1$, where $R$ is given by Equation \[eq:R\]) have *redder* $g-i$ colors than those with $R<1$ [see @Ricea01]. A more detailed investigation of these connections between \[OIII\] luminosity, radio morphology and continuum properties will require the analysis of a larger sample of bright quasars from the SDSS, and ideally complete radio imaging of an SDSS-defined bright quasar sample.

Summary of SDSS-PG comparison {#s:comp.summary}
-----------------------------

In summary, we find the following answers to the two questions posed at the beginning of §\[s:compPGSDSS\]:

1.  The distributions in redshift, , $g-i$, radio magnitude $t$, core radio power $P$, and radio-optical ratio $R$ of the 39 BQS quasars with $i<15$ inside the SDSS DR3 area are indistinguishable from those of the 26 SDSS DR3 quasars passing the BQS criteria. Thus, we find no evidence that the incompleteness of the BQS is biased with respect to radio or optical properties. We compare this finding to previous investigations of the BQS incompleteness in §\[s:disc.compBQS\] below.

2.  The BQS selection effects are predominantly caused by application of a flux limit in the $B$-band. All DR3 quasars passing the BQS flux limit also pass the color cut $\ub<-0.44$. However, the BQS limits introduce a bias against red objects relative to the SDSS sample when considering the colors (both and $g-i$) as a function of $i$-band magnitude (or equivalently, the BQS would sample the red part of the quasar population only if it was extended to fainter magnitudes). Thus, the application of optical flux limits at different wavelengths introduces a bias that is comparable to radio flux limits applied at different wavelengths: flat-spectrum (blue) sources are preferentially included in high-frequency ($B$-band) selected surveys, while the sample misses significant numbers of objects with comparable low-frequency ($i$-band) luminosities and steeper (redder) spectra.

Thus, the BQS is representative for quasars which are bright in the $B$-band, but it is clearly *not* representative even of quasars which are bright in $i$-band.

Discussion {#s:disc}
==========

Comparison to other determinations of BQS completeness {#s:disc.compBQS}
------------------------------------------------------

### Color and magnitude incompleteness {#s:disc.compBQS.colormag}

@WP85 presented one of the first investigations of the BQS completeness. Their main concerns were a possible color incompleteness biasing against the inclusion of redder objects, and that some of the PG limiting magnitudes might actually have been much fainter than stated by @BQS. Similarly, @WCBea00 noted a possible faint-end overcompleteness of the BQS relative to the stated flux limits. Our comparison of SDSS and PG photometry in §\[s:SDSSphot\] and our investigation of the PG completeness relative to an SDSS-selected sample of UV excess sources in §\[s:simPG\] confirm both of these suggestions: the recalibration of PG photographic magnitudes we found necessary (Figure \[f:phot.PGstars\_Bfit\]) agrees with that suggested by @WP85 and @WCBea00, with the PG overestimating the flux of faint objects. However, we can rule out a *constant* offset in the $B$ magnitude such as the one reported by @GMlFea92. We also found that the PG limiting $\ub$ color is in fact closer to $(\ub)_{\mathrm{lim}}=-0.71$ than to the intended $(\ub)_{\mathrm{lim}}=-0.44$ (Figure \[f:simPG.Lhood\]). This leads to an increased bias against quasars in the redshift range $0.5<z<1$, where their median $\ub$ colors make an excursion into the red (Figure \[f:SDSS\_colz\]) due to the presence of the MgII emission line in the $B$ filter [compare @WP85].

Since the $\ub$ distribution of bright quasars peaks at $\ub \approx
-0.7$ (Figure \[f:SDSS\_CMDs\]), applying the (revised) BQS color cut $(\ub)_{\mathrm{lim}}<-0.71$ removes about 50% of the quasars that should be in the sample. As long as the color distribution is roughly symmetric about the mode, this statement is true whatever the photometric error may be; since the 2-$\sigma$ PG photometric error actually encompasses the entire width of the $\ub$ distribution at bright $B$, the detection probability in the BQS will be approximately independent of $\ub$. Hence, the incompleteness of the BQS will be mostly random with respect to $\ub$ color, except for a bias against quasars with $0.5\la z \la 1.0$, where the median $\ub$ color reaches $-0.5$.

In this context, it is important to recall that the majority of bright quasars are found at $z<0.5$ in any case. This is true for the BQS, the HEQS [@WCBea00] and the SDSS quasar survey. Thus, while the color-redshift relation of quasars certainly introduces a bias against intermediate-redshift objects in the BQS, these objects are inherently rare in the BQS and fainter surveys are necessary for an accurate determination of the quasar space density at $z>0.5$.

### What is the surface density of bright quasars? {#s:disc.compBQS.surfacedensity}

Short of a determination of the surface density of bright quasars from the SDSS which requires a detailed analysis of the SDSS completeness to quasars ([@SOE]; Richards et al. 2005, in preparation), our best estimate of the incompleteness of the BQS is roughly 50% because the corrected $\ub$ cut of $-0.71$ approximately bisects the  distribution of bright quasars (Figure \[f:SDSS\_CMDs\]), in the sense that the BQS misses half of all quasars which are in fact brighter than its limiting magnitude. However, the incompleteness in terms of surface density can be different from this 50% number because of Eddington bias, i.e., the scattering of objects in and out of the sample due to photometric errors. As discussed in §\[s:comp.opt.bqslike\], the magnitude of the Eddington bias depends on the *actual* distribution of quasar magnitudes just fainter than the survey cutoff and the *actual* distribution of measurement errors, and cannot be determined exactly based on number counts exclusively from the bright side of the cutoff. In fact, our simulations in §\[s:comp.opt.bqslike\] indicate that the number of BQS objects in the area covered by our “PG parent sample” is consistent with the number expected from the distribution of $B$ magnitudes of the SDSS quasars, so that the surface density deficit introduced by the color error may have been compensated by “overcompleteness” due to Eddington bias.

@WCBea00 have presented the most comprehensive discussion to date of the BQS incompleteness in terms of surface density. They find 1.48 times as many quasars per square degree, i.e., an incompleteness of 32%, but cautioned that the true incompleteness may be as large as 50% if underestimated the Eddington bias; this is indeed the case if our $B$ recalibration is correct, since it makes the faint plate limits even fainter. A similar number (53%$\pm$10%) was obtained by @MGVea01 in their most recent analysis of the First Byurakan Survey, although these authors caution that their survey area was rather small and results should not be taken as definite. @KOKea97 find a similar surface density of UV excess objects in the Edinburgh-Cape survey as in the PG. Thus, the report by @GMlFea92 of a surface density of quasars exceeding that of the BQS by a factor of three seems to be an outlier. The most likely explanation again seems to be small-number statistics in combination with the revised  cut and the large photometric errors in the PG. We also note that the formal significance of the surface density difference between EQS and BQS shown in Figure 1 of @GMlFea92 is less than $2\sigma$.

In this context, let us reconsider what is meant by the term “effective magnitude limit”. Figure \[f:intro.BQS.Blim\] shows that the value $B_\mathrm{eff}=16.16$ is close to the area-weighted median limiting magnitude. However, this is not the same as the magnitude to which a uniform quasar survey yields the same number of objects as the entire BQS, with its magnitude limit that is varying from plate to plate. If number counts of quasars increase with limiting apparent magnitude $m$ as $10^{\beta m}$, the effective limiting magnitude of a survey with a set of limiting magnitudes $m_i$ and total area surveyed to that limiting magnitude $A_i$ is $$\frac{1}{\beta} \log\left(\frac{\sum_i{A_i 10^{\beta m_i}}}{\sum_i
  A_i}\right)$$ Using any value for $\beta$ from 0.77 [@WCBea00] to 0.9 [@BQS] with the areas and limiting magnitudes of the PG fields from @PG results in an effective limiting magnitude of $B_\mathrm{eff}=16.20$ (rounded to two decimal places), which would imply an increase in the expected surface density of the BQS of 7.4%–8.6%, and hence a corresponding decrease in all completeness estimates. But as with the determination of the Eddington bias in §\[s:comp.opt.bqslike\], this effective limiting magnitude is only an *average* value and does not necessarily provide an exact description of the particular survey under consideration.

In summary, most recent determinations of the surface density of $B$-bright quasars point to a surface density completeness of the BQS of 50% or more. This agrees with our expectation of an incompleteness of roughly 50% introduced by the revised BQS color cut $(\ub)_{\mathrm{lim}}=-0.71$, which bisects the color distribution of bright quasars, although the color incompleteness will have been compensated in part or fully by overcompleteness due to Eddington bias. In general, the magnitude of the Eddington bias is a random variable; it is determined by the particular realization of the probability density functions describing the quasar magnitudes and the photometric errors, so that techniques like Monte-Carlo simulations or maximum-likelihood parameter estimation are necessary to assess the significance of differences in the numbers of quasars found by different surveys. We found no strong differences between optical and radio properties of BQS and BQS-like SDSS quasars. Thus, we find no evidence for any systematic effects other than those caused by the color and magnitude cuts and errors.

Science impact of BQS selection effects {#s:disc.impact}
---------------------------------------

Having shown that bright $B$-band selected quasar surveys (and the PG survey in particular) are biased to the blue and fail to explore the reddest part of the quasar population that appears in surveys with fainter limits, it is important to take stock of the scientific impact of our reliance on such samples. This is important because follow-up studies that require high S/N data, long exposures, and/or good time sampling must necessarily concentrate on the brightest quasars.

The most obvious impact is on that of our understanding of the mean quasar spectral energy distribution [e.g. @SPNea89; @EWMea94]. The PG sample has a marked influence on these mean SEDs. Further exploration of how fainter, redder quasars fit into the mean SED picture is particularly important given that it is a nearly universal habit to assume that all quasars have exactly the mean SED (even though @EWMea94 clearly stress that there is a range of SEDs).

The computation of accretion rates ($\propto
L_\mathrm{Bol}/M_\mathrm{BH}$) generally assumes the mean SED in determining the bolometric correction rather than an SED tailored for each object. Similarly it is important that we reconsider the impact of the PG sample on the determination of black hole masses. The two largest samples of objects on which reverberation analysis has been applied [@WPM99; @KSMea00] are (necessarily) dominated by bright objects and the @KSMea00 sample exclusively consists of PG quasars. The issue here is whether the observed BELR size-luminosity relationship ($R\propto L^{\sim0.5}$) holds for redder quasars. If the optical/UV colors of quasars are an indication of the temperature of the accretion disk, it may not be unreasonable to expect some scatter in this relationship as a function of color.

The PG sample also impacts our understanding of the X-ray properties of quasars. For example, the @EWMea94 sample (19/47 PG quasars) was specifically chosen to have good S/N in both their [ *Einstein*]{} and [*IUE*]{} spectra and thus are unlikely to be representative of the typical optical to X-ray ratio, $\alpha_{ox}$. Furthermore, follow-up studies of quasars in the X-ray are heavily dominated by the sample of low-$z$ PG quasars defined by @LFEea97. In particular it has been recently suggested that [*XMM-Newton*]{} spectra of PG quasars reveals a near universality of the so-called “soft X-ray excess” below 2 keV [@PROea04; @PJGea05]. Again it is important to test if this feature is indeed universal or only characteristic of bright, blue quasars.

Finally, we emphasize the obvious influence of the PG sample on the so-called “eigenvector” analysis of quasars initiated by @BG92. This study is based on the analysis of the spectral properties of the 87 PG quasars with $z<0.5$. @BG92 demonstrate that a principal component analysis can be used to define two key eigenvectors that account for the majority of the variance in their sample. While it has been difficult to identify the underlying physical drivers behind these eigenvectors, one suggestion is that they might be accretion rate and black hole mass [@Bor02]. If red quasars lie [*along*]{} the principal component axes as they are currently defined, then existing eigenvector analysis is robust to their addition. If, however, red quasars lie preferentially off-axis, then their inclusion may cause a rotation of the axes that will have implications for the association of the dominant eigenvectors with underlying physical properties.

Summary {#s:sum}
=======

1.  We have presented separate transformations for stars and quasars between the SDSS survey system and Landolt photometry on the Johnson-Kron-Cousins system (§\[s:SDSSphot\]).

2.  A comparison of SDSS photometry and photographic plate-based magnitudes from the Palomar-Green (PG) survey of hot stars (which are not expected to be variable) reveals that the PG magnitudes require recalibration. PG photographic magnitudes are precise in the range $14\la B \la 16$, but too faint by up to 0.2 at $B\la14$ and $B\ga$ 16. PG photoelectric magnitudes of these objects agree with SDSS magnitudes to within the photometric errors (§\[s:phot.sdss.accuracy\]).

3.  The photographic-plate derived $\ub$ colors of the quasars from the PG survey are offset by about 0.2 magnitudes towards the red when compared to SDSS-derived $\ub$ colors. This difference is difficult to explain by variability, thus it is an indication the need to recalibrate the PG $\ub$ colors in addition to the $B$ magnitudes. The average and RMS difference in $B$-band magnitude between the recalibrated PG and SDSS measurements is consistent with the variability expected over a 30-year epoch difference (§\[s:phot.sdss.colors\]).

4.  We have simulated the color selection of objects in the PG survey from their parent sample as observed by the SDSS DR3 by computing each object’s detection probability from the appropriate PG limiting magnitude, color, and corresponding errors (§\[s:simPG\]). The parent sample was defined as all objects which are bluer than the main sequence ($\ub<-0.3$) and covers roughly 3,300 square degrees out of the PG’s total survey area of 10,668 square degrees. The distributions of $B$ magnitude, $\ub$ color, and detection probability of the simulated and actual PG survey can only be made to agree if we adjust the limiting color to $(\ub)_{\mathrm{lim}}=-0.71$ (in addition to recalibrating the limiting magnitudes as above), and the photographic color error to ${\ensuremath{\sigma_{U\!-\!B}}}=0.24$ (smaller than the value given by , but as given by ). The offset between our revised color cut and the cut $(\ub)_{\mathrm{lim}}=-0.44$ intended for quasars is similar to the offset in the $\ub$ color determined above. With the original color cut and error, we predict (*post facto*) that 17,000 main-sequence objects are scattered into the PG’s photometrically defined sample by photometric errors in color and magnitude. With our revised limits, the number is reduced to 500 objects, which compares well with the actual number of 1125 objects rejected over the full PG area.

5.  Comparing the properties of 39 BQS quasars inside the SDSS DR3 area to BQS-like quasars with $B<16.16$ and $\ub<-0.44$ selected from the SDSS quasar survey (26 objects), we find no statistically significant differences in the distributions in redshift, , $g-i$, radio magnitude $t$, core radio power $P$, or radio-optical ratio $R$ (§\[s:compPGSDSS\]). Moreover, as the $\ub$ distribution of $B$-bright SDSS quasars peaks at $\ub\approx -0.7$ and the 2-$\sigma$ $\ub$ color error is about as large as the width of the color distribution, inclusion or exclusion in the BQS will be essentially random with respect to $\ub$ color, except for a bias against objects in the redshift interval $0.5\la z \la 1.0$, where the median quasar $\ub$ is much redder than at other redshifts as the MgII line passes through the $B$-band. However, any bright quasar survey is limited to low-redshift objects, so that few objects from that redshift interval would be included even in the absence of color biases. Thus, we cannot identify any serious systematics to the BQS incompleteness.

6.  No SDSS quasar brighter than $B=16.16$ is *redder* than $\ub=-0.44$, so that the application of the UV excess criterion *with the high photometric accuracy of CCD photometry* does not remove any objects from the sample that have not already been excluded by the application of the $B$-band flux limit. In fact, the number of $B$-bright quasars is so small that the BQS only finds objects near the mode of the color distribution and it is necessary to reach much fainter $B$ magnitudes than the BQS to find quasars that are either much redder or much bluer than the BQS objects. However, the SDSS quasar survey does include objects which are redder in $\ub$ than the BQS quasars, but have $i$-band magnitudes similar to those of the BQS objects. Thus, while the BQS incompleteness with respect to its own selection criteria appears largely random, use of the BQS criteria does lead to selection effects compared to a sample defined by an $i$-band flux limit, such as the SDSS. These selection effects are predominantly caused by application of a flux limit in the $B$-band and not by the application of a UV color excess criterion. The $\ub$ color distribution of stars is much broader than that of quasars, so that the PG survey *is* progressively more biased against inclusion of redder stars.

7.  Our recalibration of PG $B$-band magnitudes and colors rules out a constant magnitude offset in the BQS magnitudes as reported by @GMlFea92, but agrees with the color and magnitude biases perceived by @WP85 and @WCBea00 (§\[s:disc.compBQS\]).

8.  Determination of the surface density of bright quasars from SDSS number counts requires detailed analysis of the SDSS quasar selection function which is beyond the scope of this paper. Given the coincidence of the revised color cut $(\ub)_{\mathrm{lim}}=-0.71$ with the mode of the quasar $\ub$ distribution down to at least $B = 19$, our best estimate of the BQS incompleteness is that the BQS misses roughly 50% of bright quasars due to color incompleteness; these losses are at least partially canceled by overcompleteness due to Eddington bias.

9.  @MRS93 reported that 50% of the BQS objects at $z<0.5$ with similarly high $L_{\mathrm{[OIII] 5007}}$ are steep-spectrum radio-loud objects. Of the SDSS quasars at $z<0.5$ and $B<17$, thirteen have an \[OIII\] 5007 narrow-line luminosity of above $5\times10^{36}\,$W; three of these are “classical double” radio sources (§\[s:comp.radio.bias\]). The Poisson probability for obtaining 3 sources where 6.5 are expected is 6.9%. It is necessary to investigate the radio and emission-line properties of a larger sample of SDSS-selected quasars in order to obtain a more significant rejection or confirmation of the @MRS93 result.

10. Results that have been obtained for PG quasars are commonly assumed to be representative for the entire quasar population in fundamental issues such as SED shapes, the determination of black hole masses via reverberation mapping and related scaling relations, quasar X-ray properties, and the physical drivers behind the @BG92 eigenvectors. Given that our work here shows that the BQS quasars are just the $B$-bright tip of the quasar iceberg, it appears prudent to reassess the impact of the BQS sample selection on these results, and to cross-check them for a wider range of spectral shapes than encountered among the BQS quasars.

We thank Huan Lin for useful conversations, Ari Laor for helpful comments, and the anonymous referee for constructive criticism. SJ is grateful for the hospitality of the Princeton University Observatory, where this paper was completed. SJ and CS were supported by the US Department of Energy under contract No. DE-AC02-76CH03000. DPS and DEVB were partially supported by National Science Foundation grant AST03-07582, and MAS was supported by grant AST03-07409. This research has made use of NASA’s Astrophysics Data System as well as STSDAS/synphot and PyRAF, products of the Space Telescope Science Institute, which is operated by AURA for NASA.

Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

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[lrrcccccccccrrrrrr]{} 0003+15 & 00 05 59.24 & 16 09 49.01 & 15.66 & 15.38 & 15.48 & 15.36 & 15.96 & 15.54 & $-$0.83 & $-$0.61 & 1000 & 0011& & & & &0.450\
0157+00 & 01 59 50.25 & 00 23 40.84 & 15.91 & 15.89 & 15.97 & 15.75 & 15.20 & 16.00 & $-$0.26 & $-$0.79 & 0000 & 0011& 403 & 51871 & 550 & 0.163 &0.164\
0844+34 & 08 47 42.47 & 34 45 04.40 & 14.80 & 14.65 & 14.57 & 14.18 & 14.00 & 14.79 & $-$0.75 & $-$0.70 & 1000 & 1001& & & & &0.064\
0921+52 & 09 25 12.85 & 52 17 10.50 & 16.72 & 16.35 & 16.19 & 15.97 & 15.62 & 16.53 & $-$0.35 & $-$0.54 & 0000 & 0011& 767 & 52252 & 418 & 0.035 &0.035\
0934+01 & 09 37 01.05 & 01 05 43.71 & 16.72 & 16.61 & 16.54 & 16.31 & 16.29 & 16.74 & & $-$0.73 & 0010 & 0001& 476 & 52314 & 523 & 0.051 &0.050\
0947+39 & 09 50 48.39 & 39 26 50.52 & 16.26 & 16.30 & 16.48 & 15.99 & 16.40 & 16.40 & $-$0.50 & $-$0.84 & 1000 & 0011& 1277 & 52765 & 332 & 0.206 &0.206\
0953+41 & 09 56 52.39 & 41 15 22.25 & 14.99 & 14.93 & 14.95 & 14.79 & 15.05 & 15.05 & $-$0.98 & $-$0.76 & 1000 & 1001& & & & &0.239\
1001+05 & 10 04 20.14 & 05 13 00.46 & 16.60 & 16.43 & 16.40 & 16.09 & 16.13 & 16.57 & $-$0.52 & $-$0.69 & 1000 & 0011& 995 & 52731 & 4 & 0.160 &0.161\
1012+00 & 10 14 54.90 & 00 33 37.41 & 16.36 & 16.27 & 16.11 & 15.86 & 15.89 & 16.40 & $-$0.44 & $-$0.75 & 1000 & 0111& & & & &0.185\
1022+51 & 10 25 31.28 & 51 40 34.88 & 16.27 & 16.11 & 16.04 & 15.89 & 16.12 & 16.25 & $-$0.37 & $-$0.69 & 0000 & 0011& 1008 & 52707 & 558 & 0.045 &0.045\
1049$-$00 & 10 51 51.44 & $-$00 51 17.66 & 16.00 & 15.80 & 15.70 & 15.82 & 15.95 & 15.95 & $-$0.49 & $-$0.66 & 1000 & 0011& 276 & 51909 & 251 & 0.359 &0.357\
1103$-$00 & 11 06 31.77 & $-$00 52 52.37 & 16.41 & 16.27 & 16.45 & 16.43 & 16.02 & 16.41 & $-$0.40 & $-$0.71 & 1000 & 0111& & & & &0.425\
1114+44 & 11 17 06.40 & 44 13 33.31 & 16.01 & 15.89 & 15.79 & 15.28 & 16.05 & 16.02 & $-$0.55 & $-$0.72 & 1000 & 0011& 1365 & 53062 & 378 & 0.144 &0.144\
1115+08 & 11 18 16.95 & 07 45 58.19 & 16.41 & 16.24 & 16.28 & 16.04 & 15.84 & 16.38 & $-$0.52 & $-$0.69 & 1000 & 0011& 1617 & 53112 & 467 & 1.734 &1.722\
1115+40 & 11 18 30.29 & 40 25 54.01 & 15.83 & 15.91 & 16.00 & 15.63 & 16.02 & 16.01 & $-$0.64 & $-$0.87 & 1000 & 0111& 1440 & 53084 & 204 & 0.155 &0.154\
1119+12 & 11 21 47.12 & 11 44 18.99 & 15.27 & 15.12 & 14.99 & 14.80 & 14.65 & 15.26 & $-$0.57 & $-$0.70 & 0000 & 1001& & & & &0.049\
1121+42 & 11 24 39.18 & 42 01 45.02 & 16.14 & 15.99 & 15.94 & 15.66 & 16.02 & 16.12 & $-$0.67 & $-$0.70 & 1000 & 0011& 1443 & 53055 & 358 & 0.225 &0.234\
1138+04 & 11 41 16.53 & 03 46 59.57 & 17.15 & 17.09 & 17.12 & 17.02 & 16.05 & 17.21 & & $-$0.77 & 1000 & 0011& 838 & 52378 & 47 & 1.877 &1.876\
1148+54 & 11 51 20.46 & 54 37 33.08 & 15.84 & 15.72 & 15.57 & 15.63 & 15.82 & 15.85 & $-$0.50 & $-$0.72 & 1000 & 0111& 1017 & 52706 & 187 & 0.975 &0.969\
1151+11 & 11 53 49.27 & 11 28 30.44 & 16.32 & 16.39 & 16.41 & 15.93 & 15.51 & 16.49 & $-$0.57 & $-$0.87 & 1000 & 0011& 1610 & 53144 & 249 & 0.176 &0.176\
1206+45 & 12 08 58.01 & 45 40 35.47 & 15.67 & 15.47 & 15.24 & 15.27 & 15.79 & 15.61 & $-$0.66 & $-$0.66 & 1000 & 0011& 1370 & 53090 & 360 & 1.164 &1.158\
1216+06 & 12 19 20.93 & 06 38 38.52 & 15.41 & 15.35 & 15.24 & 15.34 & 15.68 & 15.47 & $-$0.42 & $-$0.76 & 1110 & 0001& & & & &0.334\
1226+02 & 12 29 06.70 & 02 03 08.59 & 12.72 & 12.80 & 12.73 & 12.47 & 12.86 & 12.90 & $-$1.18 & $-$0.87 & 1110 & 0001& & & & &0.158\
1244+02 & 12 46 35.25 & 02 22 08.79 & 16.41 & 16.30 & 16.31 & 16.16 & 16.15 & 16.43 & $-$0.49 & $-$0.73 & 0000 & 0011& 522 & 52024 & 173 & 0.048 &0.048\
1254+04 & 12 56 59.93 & 04 27 34.39 & 16.47 & 16.24 & 16.06 & 16.07 & 15.84 & 16.39 & $-$0.40 & $-$0.64 & 1000 & 0011& 848 & 52669 & 154 & 1.025 &1.024\
1259+59 & 13 01 12.93 & 59 02 06.75 & 15.71 & 15.57 & 15.64 & 15.58 & 15.60 & 15.70 & $-$0.70 & $-$0.70 & 1000 & 0011& 957 & 52398 & 20 & 0.477 &0.472\
1307+08 & 13 09 47.00 & 08 19 48.24 & 15.56 & 15.64 & 15.62 & 15.14 & 15.28 & 15.74 & $-$0.82 & $-$0.87 & 1000 & 0011& & & & &0.155\
1322+65 & 13 23 49.52 & 65 41 48.17 & 16.18 & 16.16 & 16.12 & 15.77 & 15.86 & 16.27 & & $-$0.79 & 1000 & 0011& & & & &0.168\
1329+41 & 13 31 41.13 & 41 01 58.70 & 16.99 & 17.06 & 17.11 & 16.85 & 16.30 & 17.16 & $-$0.38 & $-$0.86 & 1000 & 0011& 1464 & 53091 & 433 & 1.938 &1.930\
1338+41 & 13 41 00.78 & 41 23 14.08 & 16.69 & 16.51 & 16.35 & 16.31 & 16.08 & 16.65 & & $-$0.67 & 1000 & 0011& 1377 & 53050 & 338 & 1.215 &1.219\
1351+64 & 13 53 15.83 & 63 45 45.65 & 14.66 & 14.54 & 14.54 & 14.24 & 15.42 & 14.67 & $-$0.53 & $-$0.72 & 1000 & 1001& & & & &0.087\
1352+01 & 13 54 58.68 & 00 52 10.89 & 16.23 & 16.07 & 15.92 & 15.94 & 16.03 & 16.21 & $-$0.47 & $-$0.69 & 1000 & 0011& & & & &1.117\
1411+44 & 14 13 48.33 & 44 00 13.96 & 14.53 & 14.47 & 14.55 & 13.91 & 14.99 & 14.59 & $-$0.81 & $-$0.76 & 1110 & 0001& & & & &0.089\
1415+45 & 14 17 00.82 & 44 56 06.36 & 16.67 & 16.53 & 16.32 & 15.81 & 15.74 & 16.66 & $-$0.79 & $-$0.70 & 0001 & 0001& 1287 & 52728 & 296 & 0.114 &0.114\
1426+01 & 14 29 06.57 & 01 17 06.09 & 14.36 & 14.45 & 14.61 & 14.05 & 15.05 & 14.54 & $-$1.32 & $-$0.88 & 1000 & 1001& & & & &0.086\
1427+48 & 14 29 43.07 & 47 47 26.20 & 16.95 & 17.02 & 16.92 & 16.54 & 16.33 & 17.12 & $-$0.43 & $-$0.86 & 1000 & 0011& & & & &0.221\
1440+35 & 14 42 07.47 & 35 26 22.97 & 15.10 & 15.00 & 14.97 & 14.54 & 15.00 & 15.13 & $-$0.53 & $-$0.73 & 1000 & 1001& & & & &0.077\
1444+40 & 14 46 45.94 & 40 35 05.76 & 15.85 & 15.88 & 15.85 & 16.07 & 15.95 & 15.99 & $-$0.58 & $-$0.83 & 1000 & 0011& 1397 & 53119 & 190 & 0.268 &0.267\
1501+10 & 15 04 01.20 & 10 26 15.76 & 14.27 & 14.24 & 14.22 & 14.09 & 15.09 & 14.36 & $-$1.16 & $-$0.79 & 1000 & 1001& & & & &0.036\
1512+37 & 15 14 43.07 & 36 50 50.41 & 16.75 & 16.67 & 16.75 & 16.83 & 15.97 & 16.79 & $-$0.46 & $-$0.74 & 1000 & 0111& 1353 & 53083 & 580 & 0.371 &0.371\
1522+10 & 15 24 24.53 & 09 58 29.12 & 15.97 & 15.93 & 15.74 & 15.70 & 15.74 & 16.04 & $-$0.50 & $-$0.78 & 1000 & 0011& & & & &1.321\
1534+58 & 15 35 52.41 & 57 54 09.55 & 15.34 & 15.29 & 15.12 & 15.04 & 15.54 & 15.41 & $-$0.54 & $-$0.77 & 0000 & 0011& 615 & 52347 & 108 & 0.030 &0.030\
1535+54 & 15 36 38.38 & 54 33 33.31 & 15.58 & 15.20 & 15.01 & 14.77 & 15.31 & 15.37 & $-$0.51 & $-$0.53 & 1000 & 1001& & & & &0.038\
1538+47 & 15 39 34.80 & 47 35 31.31 & 16.55 & 16.08 & 16.05 & 16.14 & 16.01 & 16.27 & & $-$0.46 & 1010 & 0001& & & & &0.770\
1543+48 & 15 45 30.24 & 48 46 09.07 & 16.56 & 16.44 & 16.44 & 16.46 & 16.05 & 16.57 & $-$0.54 & $-$0.72 & 1000 & 0111& 812 & 52352 & 355 & 0.400 &0.400\
1552+08 & 15 54 44.58 & 08 22 21.45 & 16.19 & 15.94 & 15.80 & 15.42 & 16.02 & 16.09 & $-$0.45 & $-$0.62 & 1000 & 0011& & & & &0.119\
1612+26 & 16 14 13.20 & 26 04 16.20 & 16.38 & 16.38 & 16.17 & 15.61 & 16.00 & 16.49 & $-$0.69 & $-$0.81 & 0000 & 0011& 1393 & 52824 & 35 & 0.131 &0.131\
1630+37 & 16 32 01.12 & 37 37 50.01 & 16.13 & 16.03 & 15.93 & 15.80 & 15.96 & 16.15 & $-$0.28 & $-$0.73 & 1000 & 0011& 1173 & 52790 & 198 & 1.476 &1.471\
1704+60 & 17 04 41.38 & 60 44 30.50 & 15.63 & 15.43 & 15.24 & 15.18 & 15.90 & 15.58 & $-$0.42 & $-$0.66 & 1000 & 0011& 353 & 51703 & 377 & 0.372 &0.371\
2130+09 & 21 32 27.82 & 10 08 19.16 & 14.73 & 14.70 & 14.80 & 14.28 & 14.62 & 14.81 & & $-$0.79 & 1000 & 1001& & & & &0.061\
2214+13 & 22 17 12.26 & 14 14 20.89 & 14.55 & 14.51 & 14.50 & 13.99 & 14.98 & 14.62 & & $-$0.78 & 1000 & 1001& & & & &0.067\
2233+13 & 22 36 07.68 & 13 43 55.32 & 16.30 & 16.28 & 16.28 & 16.41 & 16.04 & 16.39 & $-$0.62 & $-$0.80 & 1000 & 0011& 739 & 52520 & 388 & 0.326 &0.325\

[^1]: Available on-line at <http://www.sdss.org/dr3/>

[^2]: We use the term “quasar” here, but it should be understood as being synonymous with “QSO” without any implication about luminosity or presence of radio emission

[^3]: Obtained from <http://www.stsci.edu/resources/software_hardware/>

[^4]: Available at <http://www.sdss.org/dr2/instruments/imager/#filters>

[^5]: <http://www.sdss.org/dr3/products/catalogs/flags.html>

[^6]: @MRS93 used a cosmology with $H_0=50$km/s/Mpc, $\Omega_m = 0$, and $\Omega_\Lambda=0$, resulting in luminosities about a factor 2 greater than those in the current standard cosmology, which we employed ($\Omega_{\mathrm{m}}
      = 0.3, \Omega_\Lambda = 0.7$, and $H_0 = 70$km/s/Mpc).