Luminosity Function from dedicated SDSS-III and MMT data of quasars in 0.7

2.2 MB·English

by  N. Palanque-Delabrouille

Astronomy & Astrophysics manuscript no. LF (cid:13)c ESO 2012
September 19, 2012
New approach to measure the Quasar Luminosity Function
in 0.7 < z < 4.0 from dedicated SDSS-III and MMT data
N. Palanque-Delabrouille1, Ch. Magneville1, Ch. Y`eche1, S. Eftekharzadeh2, A. D. Myers2,3, P. Petitjean4,
I. Paˆris4,5, E. Aubourg6, I. McGreer7, X. Fan7, A. Dey8, D. Schlegel9, S. Bailey9, D. Bizayev10, A. Bolton11,
K. Dawson11, G. Ebelke10, J. Ge12, E. Malanushenko10, V. Malanushenko10, D. Oravetz10, K. Pan10, N. P.
Ross9, D.P. Schneider13, E. Sheldon14, A. Simmons10, J. Tinker15, M. White9, and Ch. Willmer7
1 CEA, Centrede Saclay, Irfu/SPP, F-91191 Gif-sur-Yvette,France
2 2 Department of Physics and Astronomy,University of Wyoming, Laramie, WY 82071, USA
1 3 Max-Planck-Institut fu¨rAstronomie, K¨onigstuhl 17, D-69117 Heidelberg, Germany
0 4 Universit´e Paris 6, Institut d’Astrophysiquede Paris, CNRS UMR7095, 98bis blvd Arago, F-75014 Paris, France
2 5 Departamento deAstronom´ıa, Universidad deChile, Casilla 36-D, Santiago, Chile
p 6 APC, 10 rueAlice Domon et L´eonie Duquet,F-75205 Paris Cedex 13, France
e 7 Steward Observatory,University of Arizona, Tucson, AZ 85721, USA
S 8 National Optical Astronomy Observatory,Tucson, AZ85726-6732,USA
9 Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA94720, USA
8 10 ApachePoint Observatory,P.O. Box 59, Sunspot,NM88349-0059, USA
1 11 University of Utah, Dept.of Physics & Astronomy,115 S 1400 E, Salt Lake City, UT84112, USA
12 Department of Astronomy, University of Florida, 211 Bryant Space Science Center, P.O. Box 112055, Gainesville,
]
O FL 32611, USA
13 Department of Astronomy and Astrophysics, The PennsylvaniaState University,UniversityPark, PA 16802
C Institutefor Gravitation and theCosmos, The PennsylvaniaState University,University Park, PA 16802
. 14 Brookhaven National Laboratory, Bldg 510, Upton, NY11973, USA
h 15 Center for Cosmology and Particle Physics, New York University,New York,NY 10003, USA
p
- Received xx;accepted xx
o
r
t ABSTRACT
s
a
We present a measurement of the quasar luminosity function in the range 0.68 < z < 4 down to extinction corrected
[
magnitude gdered = 22.5, using a simple and well understood target selection technique based on the time-variability
1 of quasars. The completeness of our sample was derived directly from a control sample of quasars, without requiring
v complex simulations of quasar light-curves or colors. A total of 1877 quasar spectra were obtained from dedicated
8 programs on the Sloan telescope (as part of the SDSS-III/BOSS survey) and on the Multiple Mirror Telescope. They
6 allowed ustoderivethequasarluminosity function.It agrees well with previously published results from Croom et al.
9 (2009)inthecommonredshiftrange0.68<z<2.6.Ourdeeperdataalsoallowustoextendthemeasurementtoz =4.
3 Wemeasuredquasardensitiestogdered <22.5,obtaining30QSOperdeg2 atz<1,99QSOperdeg2 for1<z<2.15,
. and 47 QSO per deg2 at z >2.15. Using pure luminosity evolution models, we fitted our LF measurements combined
9
with the data from Croom et al. (2009), and predicted quasar number counts as a function of redshift and observed
0
magnitude. These predictions are useful inputs for future cosmology surveys such as those relying on the observation
2
of quasars tomeasure baryon acoustic oscillations.
1
: Key words.Quasars: general, dark energy,surveys
v
i
X
r 1. Introduction Richards et al., 2002, 2004, 2009; Croom et al., 2009;
a
Bovy et al., 2011, 2012) present serious drawbacks for the
The measurement of the Baryon Acoustic Oscillation selection of quasars at redshifts near z∼2.7, which oc-
(BAO) scale (Eisenstein et al., 2005, 2007) relies on large cupy similar regions of ugriz color-space as the more
samples of objects selected with an unbiased method. To numerous white dwarfs and blue halo stars (Fan, 1999;
probethedistantUniverse,quasarsappeartobeoneofthe Richards et al., 2002; Worseck & Prochaska, 2010). To cir-
sources of choice, since they are both among the brightest cumvent this difficulty, Palanque-Delabrouille et al. (2011)
extragalactic objects, and expected to be present at suffi- developedaselectionalgorithmrelyingonthetimevariabil-
ciently high density. ity of quasar fluxes. This technique was tested in 2010 as
The selection of quasars to redshift z ∼ 4 and mag- part of the BOSS survey (Ross et al., 2012). It was shown
nitude g ∼ 23, which is the objective of current and to increase by 20 to 30% the density of identified quasars,
future cosmology projects dedicated to BAO studies in and, in particular, to effectively recover additional quasars
the distant Universe, is a major challenge. Traditional in the redshift range 2.5<z <3.5.
selections relying on quasar colors for several broad op- Here we use this variability-based selection to measure
tical bands (Schmidt & Green, 1983; Croom et al., 2001; thequasarluminosityfunctiontoextinction-correctedmag-
1
N. Palanque-Delabrouille et al.: Quasar Luminosity Function using dedicated data from BOSS and MMT
nitudeg =22.5andredshiftz =4fromtwosetsofded- single-epoch images.1 The completeness of the coadd cat-
dered
icatedobservations.Forthefirstsetofdata,wetookadvan- alog reaches 50% at a magnitude g = 24.6 for stars and
tage of the re-observation, as part of the SDSS-III/BOSS g =23.5forgalaxies.Theg magnitudementionedthrough-
survey (Eisenstein et al., 2011; Dawson et al., 2012), of a out the paper is computed on the coadd images, and effec-
14.5deg2 region in Stripe 82 (the SDSS Southern equa- tively represents the mean magnitude of a variable source.
torial stripe). The second set of data used the Hectospec The source morphology (point-like or extended) is also de-
multi-object spectrograph (Fabricant et al., 2005) on the termined from these coadds.
Multiple Mirror Telescope (MMT) and covered 4.7deg2. The lightcurves of our sources contained on average 52
Thequasarsamplesbeingselectedwithonlyminimalcolor individual epochs spread over 7 years. They were used to
constrains,theyareexpectedto behighlycomplete anddo computetwosetsofparametersthatcharacterizethesource
not suffer from the usual biases in their redshift distribu- variability:
tion induced by color selections. The selection algorithms
– the χ2s of the fit of the lightcurve by a single number
of both samples are well understood, and can be applied
(representing a non-varying lightcurve) in each of the
to large control samples of already identified quasars in
ugriz filters (yielding five parameters, one for each fil-
order to compute the completeness of the method. With
ter)
this strategy, all corrections can be derived from the data
– twoparameters,anamplitudeAandapowerγ asintro-
themselvesanddonotrequireanymodelingofquasarlight
duced by Schmidt et al. (2010), that characterized the
curves or colors.
variabilitystructure function V(∆t ), i.e. the changein
ij
The outline of the paper is as follows. In Sec. 2 we ex-
magnitude ∆m as a function of time lag ∆t for any
ij ij
plain the strategy for the selection of the targets and its
pair ij of observations, with
specific application to the BOSS and the MMT observa-
tions. In Sec. 3, we describe the different contributions to
V(∆t ) = |∆m |− σ2+σ2 (1)
theglobalcompletenesscorrectionforbothsetsofdataand ij i,j i j
q
presentthequasarcontrolsampleusedtoderivethem.The = A×(∆t )γ. (2)
ij
raw and the completeness-correctedquasar number counts
are given in Sec. 4, where we also present several cross- For each source, a neural network then combined the five
checksofthe resultsobtained.The quasarluminosityfunc- χ2, the powerγ (commonto allfilters) andthe amplitudes
tion in g derived from these data is given in Sec. 5. Ag,Ar andAiforthethreefiltersleastaffectedbynoiseand
observational limitations (gri), to produce an estimate of
quasar-likevariability.Anoutputy oftheneuralnetwork
NN
near0designatednon-varyingobjects,asisthecaseforthe
2. Target selection vast majority of stars, while an output near 1 indicated a
quasar (cf. Fig. 1).
Whilethebasisofthetargetselectionalgorithmisthesame This technique has been applied by BOSS for the se-
forthetwocomponentsofourprogram,itwasappliedwith
lection of z > 2.2 quasars in Stripe 82, down to g ∼
differentthresholdstoobtainthe targetsforthe BOSSand 22 (Palanque-Delabrouille et al., 2011). As was clearly il-
the MMT observations. The BOSS component was indeed lustrated by this study, this approach presents the ad-
designed to identify a large number of quasars to a magni- vantage of being highly complete (the selection reached
tude limit g ∼ 22.5 corresponding to the limit of BOSS the unprecedented quasar completeness of 90%), even for
spectroscopy at typical exposure times. The MMT data a sample purity of 92%, higher than for typical selec-
were primarily designed to complete the sample to fainter tions based on quasar colors. In addition, this variability-
magnitudes (g ∼ 23), since the telescope has a 6.5 m pri- based selection was shown to overcome the drawbacks of
mary mirror compared to the 2.5 m primary of the Sloan color-based methods and to recover quasars near redshift
telescope. In addition, the BOSS sample was restricted to z ∼3thataresystematicallymissedwithtraditionalselec-
point sources, while the MMT sample was also used to re- tions (Richards et al., 2002).
cover quasars lying in extended sources.
Here, we applied this technique to fainter magnitudes,
withtheaimofdetectingquasarstog ∼23.Themagnitude
dependence of the output of the variability neural network
2.1. Target selection algorithm
is illustrated in Fig. 1. Requiring an output y > 0.5
NN
selects 95% of the sample of known quasars with 18<g <
As a detailed descriptionof the variability selectioncan be
23(cf.thedescriptionofthiscontrolsampleinsection3.1).
found in Palanque-Delabrouille et al. (2011), we only sum-
Even when restricting to faint quasars with a magnitude
marize here the major steps of our algorithm.
g >22, 88% of them still pass this threshold.
For each source, lightcurves were computed from
In addition to the variability-based selection, a loose
the data collected by SDSS using the dedicated Sloan
color constraint was used to reject a region of color-space
Foundation 2.5 m telescope (Gunn et al., 2006). A
mostly populated by stars, in order to reduce the fraction
mosaic CCD camera (Gunn et al., 1998) imaged the
ofstellarcontaminantsin the targetlist.The cut consisted
sky in the ugriz bandpasses (Fukugita et al., 1996).
inrequiringc <a−c /3(cf.Fig.2),wherethelevelawas
The imaging data were processed through a series of 3 1
set to 1.0 or 0.6 depending on the target morphology (see
pipelines (Stoughton et al., 2002) which performed astro-
Sec. 2.2 and 2.3 for details), and c and c are defined as
metric calibration,photometric reductionand photometric 1 3
calibration.
1 We used the Catalog Archive Server (CAS) interface
The starting source list was built from images that re- (http://casjobs.sdss.org) to recover both the Stripe 82 coadd
sulted from the co-addition (Annis et al., 2012) of SDSS and the single epoch information.
2
N. Palanque-Delabrouille et al.: Quasar Luminosity Function using dedicated data from BOSS and MMT
The starting source list consisted of all point sources
in this area passing the usual BOSS quality cuts (on pho-
N
N
y 1 tometry,pixelsaturation,sourceblendingetc.)asdescribed
in the Appendix of Ross et al. (2012), as well as the loose
color cut (with a=1.0) mentioned in the previous section,
0.8
yielding about 5200 objects per deg2.
All objects passing y >0.5 were selected as targets.
0.6 NN
The resulting list contained ∼ 270 targets per deg2. We
removed from this list all targets that had already been
0.4 observedbyBOSS(Ahn et al.,2012).Thisreducedthelist
to ∼240 objects per deg2.
0.2 In case of fiber collisions during the tiling procedure,
priorities were set on the targets according to their mag-
0 nitude, giving higher priority to the brightestobjects since
18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 23
g these are more likely to obtain an accurate identification.
An identical maximal priority was attributed to all targets
Fig.1: Output of the variability Neural Network as a func- with g <22.7 (not corrected for extinction as the quantity
tionofgmagnitudeforasampleofknownstars(smallblack of interest here is the actual observed flux of the object),
dotsnearyNN =0)andforknownquasars(largerreddots and lesser priorities for fainter magnitudes.
at y ∼1).
NN SevenpartiallyoverlappingBOSShalf-plates were allo-
cated to the project (numbered 5141 to 5147 from low to
high α ), coveringa total of 14.5 deg2. The other plate
J2000
halveswereusedforthestandardBOSSsurveyandarenot
in Fan (1999) by:
included in this analysis. Plate 5141 was exposed for over
c = 0.95(u−g)+0.31(g−r)+0.11(r−i), 2 hours (ie. twice the normal time), without significant in-
1
crease in the number of quasars identified. The subsequent
c = −0.39(u−g)+0.79(g−r)+0.47(r−i). (3)
3
plates were thus exposed for 1 hour. All seven plates were
About 100% of z <2.2 and 98% of z >2.2 known quasars observed during July and September 2011.
(resp.95%and93%)passtheconditionwitha=1.0(resp.
a=0.6).
2.3. The MMT sample
Forthesakeofcompleteness,thestartinglistfortheMMT
sample was built from all SDSS sources in the area of the
c3 1.2 previousBOSSsample,whetherpoint-likeorextendedand
Stars
1 z<2.2 QSOs whetherornottheypassedthestandardBOSSqualitycuts,
0.8 z>2.2 QSOs Sanecd.2p.a1s.sTinhgisthineitlioaolsliestcocolonrsicsutetdwoifth∼a11=3010.0dedge−s2croibbjeedctisn,
0.6
60% of which were resolved (ie. “extended”, like galaxies),
0.4 and 40% of which were unresolved (ie. “point-like”, like
0.2 stars). As for the BOSS sample, all objects that have al-
0 readyobtainedspectrawithSDSS-III/BOSSwereremoved
from the target list. In addition, we rejected targets with
-0.2
g < 22 that were simultaneously selected for the BOSS
-0.4
sample,sincetheredshiftdeterminationefficiencyofBOSS
-0.6 is close to unity at least to that magnitude.
-0.8-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 Most quasars are expected to be significantly more lu-
c1 minous than their host galaxy,making them appear point-
like. We thus expect less quasars in the “extended” sub-
Fig.2: Locus of stars (upper thin blue contours), z < 2.2
sample. The fraction of random objects artificially drifting
quasars (lower left thick green contours) and z > 2.2
into the region of large y values being independent of
NN
quasars (lower right thick red contours) in the c vs. c
3 1 thesourcemorphology,however,theratioofthenumberof
color-color plane. The upper solid line corresponds to the
quasars to the total number of selected targets is therefore
color cut c < 1.0 − c /3 and the lower dashed line to
3 1 smaller for extended sources.We thus applied stricter cuts
c <0.6−c /3 (cf. Eq. 3).
3 1 to the extended sub-sample, which is affected by a higher
contamination, and we gave a higher priority to the MMT
point-like targets.
Thehighestpriority(priorityA)wasgiventopoint-like
targets with observed magnitude g <23.0, y >0.5 and
2.2. The BOSS sample c <1.0−0.33c , leading to ∼130deg−2 tarNgeNts.
3 1
The BOSSfields dedicated to this high density quasarsur- PriorityBwasgiventoextendedobjectswithg <23.0,
vey were part of Stripe 82 and located at 317◦ < α < y >0.8 and c <0.6−0.33×c . This led to 140 deg−2
J2000 NN 3 1
◦ ◦ ◦
330 and 0 <δ <1.25 . additional targets.
J2000
3
N. Palanque-Delabrouille et al.: Quasar Luminosity Function using dedicated data from BOSS and MMT
Priority C (respectively D) was given to objects with
23.0<g <23.2passingthe same conditionsasthe priority stars
A (resp. B) targets, leading to 40 deg−2 (resp. 30 deg−2) nt-like 1.1 32..04<<zz<<53..00 QQSSOO
additional targets. oi 1 2.0<z<2.4 QSO
diamAetteortawleorfe6obnsoenr-voevderwlaipthpinMgMciTrc/uHlaecrtfioespldescoinf 1thdeeglaisnt d as p0.9 11..50<<zz<<21..05 QQSSOO
pe0.8 0.8<z<1.0 QSO
tTrhimeefiseteldrsofw2e0r1e1l,owcaitthedexwpiotshuinretthime ecsovoefr1a5g0emofintuhteesBeOacShS. cts ty0.7 0.0<z<0.8 QSO
e
sample of Sec. 2.2, in the area farthest from the Galactic obj0.6
plane, which is least contaminated by Galactic stars. The of
hrMeiggMhioTenrfie3xe2lt6di.ns5c◦t(iA<onαo∼Jn200a0.v02er<faogr3e23(82A◦2g◦w∼a<s0.αa4v)otidheadn<bfoe3rc2at6hu.e5se◦otoahfnedar Fraction 00..45
g J2000 0.3
◦ ◦
A ∼ 0.3 for 328 < α < 330 ), where the extinctions
g J2000
0.2
come from the maps of Schlegel et al. (1998). 18 19 20 21 22 23 24
g
Becauseofweatherconditions,onlyfiveMMTfields(all
but the field with lowest Right Ascencion) produced us-
Fig.4:Fraction of knownquasars identified as point-like in
abledata.Thisresultedinatotalskycoverageof3.92deg2.
co-added images, as a function of magnitude, for several
bins in redshift (rising redshift from bottom to top). The
Figure3illustratesthelocationsoftheBOSSandMMT
asymptotic red histogram is the fraction of stars that are
fields dedicated to the present study.
identified as point-like.
s
e 1.2
e frame,pointingtowardsaphysicaleffectthatcannotbeex-
gr 1
e plained with the previous arguments. Even the curves for
d
0) 0.8 2.0<z <3.0 quasars are significantly lower than that ob-
00 0.6 tained for stars, our control sample of point-like objects.
2
ec (J 00..24 Tofhtehreeqisuaascalresa,resvteenpbartigahrte(dgsh<if2t0z)∼on0e.s8,,awphpeeraer6e0xtteond80ed%.
D
0 Theseresultsareconsistentwiththehostgalaxybecom-
318 320 322 324 326 328 330
R.A. (J2000) degrees ing detectable in the co-added images, making the quasar
appear extended. Fig. 4 thus indicates a statistical detec-
Fig.3: Footprint of the BOSS half-plates (black contours) tionofthehostgalaxyofquasars,evenatredshiftsaslarge
and of the MMT fields (filled red disks) dedicated to the as z ∼ 2. The brightest (g < 19) quasars, however, still
present study. BOSS plates were attributed the numbers sufficiently outshine their host galaxyto remain point-like,
5141 to 5147 from left to right. MMT fields were labeled 0 except in the lowest redshift bin where the host galaxy is
to 5 with increasing Right Ascension. resolved.
3. Completeness corrections
To estimate quasar densities and the luminosity function
2.4. Impact of source morphology
from raw quasar counts, the data have to be corrected for
While mostquasars,whatevertheir redshift, appear point- biases introduced by the cuts applied to select the targets
likeonsingle-epochSDSSimages,thisisnolongerthecase andforinstrument-relatedlosses.Theanalysis-relatedcom-
onco-addedframes,whichresultfromthesuperposition,at pletenesscorrectionsarecomputedfromcontrolsamplesof
the image level, of about 56 Stripe 82 scans, thus reaching knownquasars,while the instrument-relatedonesarecom-
a depth about 2 magnitudes fainter than individual scans. puted from the data.
In the BOSS sample, we thus rejected a large fraction of The different contributions to the completeness correc-
low-redshiftquasars by only considering point-like objects. tions aredetailed inthe followingsections,anda summary
Fig. 4 shows the fraction of quasars classified as point-like of the magnitude dependence of the corrections for BOSS
on the co-added images, for several bins in redshift. and the MMT is illustrated in Fig. 5.
Fig. 4 also displays the fraction of point-like objects
on a single-epoch image of excellent seeing (most of these
3.1. Control sample of known quasars
objects are indeed stars) that are classified as stars on the
co-addedframe.Whileallstarswithmagnitudesg <22ap- The analysis-related completeness corrections are deter-
pearpoint-likeinthedeepframe,upto16%ofthemappear mined using a list of 19215 spectroscopically confirmed
extendedatg =23,possiblydue tosmallmisalignmentsin quasars in Stripe 82 obtained from the 2dF quasar catalog
theco-additionprocedurethataffecttheobjectmorphology (2QZ; Croom et al.,2004),the2dF-SDSSLRGandQuasar
at faint magnitudes. High redshift (z > 3) quasars follow Survey 2SLAQ (Croom et al., 2009), the SDSS-DR7 spec-
the same trend as stars, therefore suffering from the same troscopicdatabase(Abazajian et al.,2009),theSDSS-DR7
technical drawbacks.In contrast, as the redshift decreases, quasar catalog (Schneider et al., 2010) and BOSS observa-
more and more quasars appear extended on the co-added tions up to July 2011(Ahn et al., 2012; Paˆris et al., 2012).
4
N. Palanque-Delabrouille et al.: Quasar Luminosity Function using dedicated data from BOSS and MMT
s s
s s
ne 1 ne 1
e e
et et
pl pl
m 0.8 m 0.8
o o
C C
0.6 0.6
0.4 0.4
BOSS new BOSS known
0.2 Quality 0.2
Quality x Selection Quality
Quality x Selection x Tiling Quality x Selection
018 18.5Quality x1 S9election1 x9 T.i5ling x Sp2ec0tro 20.5 21 21.5 22 22.5 018 18.5 19 19.5 20 20.5 21 21.5 22 22.5
Observed g magnitude Observed g magnitude
s s
s s
ne 1 ne 1
e e
et et
pl pl
m 0.8 m 0.8
o o
C C
0.6 0.6
0.4 0.4
MMT point-like MMT extended
0.2 0.2
Selection Selection
Selection x Tiling Selection x Tiling
Selection x Tiling x Spectro Selection x Tiling x Spectro
022 22.2 22.4 22.6 22.8 23 23.2 23.4 022 22.2 22.4 22.6 22.8 23 23.2 23.4
Observed g magnitude Observed g magnitude
Fig.5: Magnitude dependence of the contributions to the total completeness correction for the different samples. Upper
left: the new quasars identified in the BOSS sample. Upper right: the known quasars that were intentionally removed
from the target lists. Lower left (resp. right): the quasars identified in the MMT sample and that appeared point-like
(resp.extended)inthecoaddedSDSSframe.Thesecorrectionsarecomputedfromallquasarscontainedineithersample.
AsshowninFig6,thesequasarshaveredshiftsintherange and not to the intrinsic quasar magnitude). For the sake
0 ≤ z ≤ 5 and g magnitudes in the range 17 ≤ g ≤ 23 of clarity, the magnitude corrected for Galactic extinction
(Galactic extinction-corrected) with 212 quasars having a will henceforth be denoted g .
dered
magnitudefainterthang =22.5.Theirregularshapeofthe
distributions results from the use of several surveys with
different redshift goals and selection algorithms. At z > 2, Quality completeness ǫqual(g):
mostofthequasarscomefromcolor-selectionwiththestan-
dard BOSS survey (Y`eche et al., 2010; Kirkpatrick et al., This contribution is related to the quality cuts described
2011; Bovy et al., 2011; Ross et al., 2012). in the Appendix of Ross et al. (2012) that were applied to
obtaintheinitiallistofthesourcesfromwhichtheselection
Approximately 2%ofthe objects couldnot be matched
was made. It only affects BOSS data as no quality cut was
to any so-called primary target in the SDSS database, re-
applied to build the list of sources for the MMT sample
ducingthesampleto18910.Lightcurvesandvariabilitypa-
(seesections2.2and2.3).Themeanqualityfactoroverthe
rameterswere computed for these quasarsusing the proce-
BOSS data of the present study is 0.89, with a plateau at
dure described in Sec. 2.
0.90 for all bright sources with g <22, dropping to 0.70 at
g =23 (see blue curve in upper two plots of figure 5).
3.2. Analysis-related completeness corrections
The analysis-related corrections arise from two contribu- Target selection completeness
tions that affect the BOSS and the MMT samples differ- ǫ (g, z, sourcemorphology):
sel
ently:aqualityfactorǫ andaselectionfactorǫ .These
qual sel
correctionsdependonthesourcemorphology(point-likeor This contribution is related to the variability-based and
extended), the redshift z and the magnitude g uncorrected color-based selection algorithms, as described in Sec. 2. It
for extinction (since we are here sensitive to the observed dependsonthe telescopethatthetargetlistisdesignedfor
5
N. Palanque-Delabrouille et al.: Quasar Luminosity Function using dedicated data from BOSS and MMT

hift4.5
500 Reds 4 0.9
0.8
3.5
400 0.7
3
0.6
300 2.5
0.5
2
0.4
200
1.5
0.3
100 1 0.2
0.5 0.1
0 0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 18 19 20 21 22 23 24 25
redshift Observed g magnitude
Fig.7:Selectioncompletenessǫ (g, z)forthequasars
selBOSS
in the BOSS program.The significant drop at low redshift
600 is due to the fact that many quasars with z < 1 appear
as extended sources in coadded frames and were thus not
500
considered in the initial source list. We also observe the
expected efficiency drop at faint magnitudes. Bins are left
400
unfilled (white) are bereft of quasars.
300
200
fying the probability of obtaining a secure identification
andredshiftforagiventarget.Thesedependonthe source
100
morphology(point-likeorextended)throughthetargetpri-
ority, and on the observed magnitude g.
0
16 17 18 19 20 21 22 23 24
g
Tiling completeness ǫ (priority):
tiling
Fig.6: Distributions in redshift (top plot) and extinction-
corrected magnitude (bottom plot) for the sample of This contribution is related to the tiling proce-
quasars from previous quasar surveys covering Stripe 82. dure (Dawson et al., 2012), taking into account the den-
sity of allocated fibers and the target priorities in case of
fiber collisions. This correction just represents the fraction
of targets that were assigned fibers. It entirely depends on
onlybecauseofthedifferentthresholdsthatweresetonthe theinstrumentalconfigurationandthusmustbecomputed
selection variables. specificallyforBOSSandtheMMT.AsexplainedinSec.2,
BOSS targets were selected from an initial list limited thetargetpriorityvarieswithmagnitudeforBOSStargets,
topoint-sources.Totakeintoaccountthecompletenessloss and with both magnitude and source morphology (point-
due to the non-consideration of extended sources, ǫselBOSS like or extended) for MMT targets. In the case of BOSS,
was computed from the ratio, in the controlsample, of the however,the fractionofspectra thatcanbe correctlyiden-
point-likequasarsthatpassedtheselectioncutstothetotal tifieddropssignificantlybeyondg ∼22.5andonlythe first
numberofquasars.Thisyieldedthecorrectiontableshown prioritybin was usedfor the presentanalysis (cf. Sec. 4.3).
in Fig. 7 as a function of magnitude g and redshift z. The The mean tiling completeness correction is 0.95 for the
mean completeness correction for the selection step, over BOSS data and 0.84 for the MMT data. Corrections per
the BOSS sample, is 0.78. priority bin are given in table 1.
For the MMT data, the completeness correction for
the selection step was computed separately for point-like
Project MMT MMT MMT MMT
sources and for extended ones. For each source morphol- BOSS
(Priority) A B C D
ogy,ǫ (g, z)wasdeterminedfromthecontrolsample
selMMT ǫ 0.95 0.90 0.74 0.68 0.53
asthefractionofquasarsofagivenmorphologythatpassed tiling
the relevant selection criteria (cf. Sec. 2.3). The mean se-
lection completeness correction over the MMT sample of
Table 1: Tiling completeness correction for BOSS (unique
quasars is 0.76 (0.82 for the point-like sources and 0.57 for
priority level) and the MMT (priorities A through D).
the extended ones).
3.3. Instrument-related completeness corrections
Spectrograph completeness ǫ (g):
Thesecorrectionscomefromtwocontributions:atilingfac- spectro
tor ǫ quantifying whether a target could indeed have Somespectradidnotproduceareliableidentificationofthe
tiling
been observed, and a spectrograph factor ǫ quanti- source, either because the extraction procedure had failed
spectro
6
N. Palanque-Delabrouille et al.: Quasar Luminosity Function using dedicated data from BOSS and MMT
(hereafter“Bad”spectra)orbecausethespectrumhadtoo 4.1. Raw counts for the BOSS and MMT samples
lowasignal-to-noiseratioforadequateidentification(here-
We identified 1179 new quasars with BOSS (hereafter re-
after “?”). Fig. 8 illustrates the rate of the “bad” spectra
ferredto as“NewBOSS”orsimply “BOSS”)and262ones
as a function of magnitude g for the BOSS (filled black
with the MMT. To these, we add the 436 previously iden-
dots) and the MMT (open red circles) spectra. The over-
tified quasars in our area of interest that were explicitly
laiddashedcurvesarefitstothedata.Thefractionof“bad”
removed from the target lists and hereafter referred to as
spectrareaches15%atg =23.15fortheMMTandg =22.9
“Known”.
for BOSS. The upper blue dot-dashed curve illustrates the
Fig. 9 shows the distributions of the redshift and ob-
totalloss1−ǫ (g),similarforbothinstruments,when
spectro
servedmagnitudeinthegbandforoursampleofconfirmed
consideringboth the “bad”andthe “?” spectra.This total
quasars. While the redshift distributions of the BOSS and
fraction of inconclusive spectra is negligible for g < 22, it
MMT samples are similar in shape, the MMT sample
reaches 15% at g =22.8, and 30% at g =23.1.
reachesmorethanhalfamagnitudedeeperthanthe BOSS
sample. The averagemagnitude of eachof the two samples
is hgi = 22.2 and hgi = 21.5. The sample of pre-
MMT BOSS
viouslyknownquasarsthatwerenotincludedinthetarget
ectra 0.4 All "Bad" + "?" lists have a mean magnitude hgiKnown =21.0.
p
d" s0.35 BOSS "Bad"
Ba MMT "Bad"
Fraction of "00..0012..5523 2∆ g = 0.5) (O / deg 11226802
S
Q 14
0.00.51 Number of 1102
8
0
21 21.5 22 22.5 23 23.5 24 6
g 4
2
Fig.8: Fraction of inconclusive spectra (declared so after
017 18 19 20 21 22 23 24
visual inspection) as a function of observed g magnitude. Observed g magnitude
The curves are fits to the data. In our analysis, we use
the upper blue curve to correct for the total fraction of
inconclusive spectra. ∆ z = 0.25) 1146
2 (O / deg 12
QS 10
mber of 8
4. Results Nu 6
4
BOSS data were taken on the dedicated Sloan Foundation
2.5 m telescope (Gunn et al., 2006) using the BOSS spec- 2
trograph (Smee et al., 2012). The BOSS spectra were re- 00 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
duced with the standard BOSS pipeline (Bolton et al. Redshift
(2012); Dawson et al. (2012), see also Bolton & Schlegel
(2010)) which also provides an automated determination Fig.9:Quasarnumber counts per deg2 as a function of ob-
of the target classification and redshift. A manual inspec- servedg magnitude(top)andredshift(bottom).Theblack
tion was performed on all the spectra of this program, as (resp. red) line is for quasars measured by BOSS (resp.
forallquasartargetsofthemainBOSSsurvey(Paˆris et al., MMT). The BOSS histograms include the already identi-
2012). The MMT spectra were reduced with a customized fied quasarsin the area that were removedfrom the target
pipeline basedheavilyonthe E-SPECROADpackage2.All list.
the spectra were checked visually to produce final identifi-
cationsandredshifts.Thespectrawereclassifiedas“QSO”
for secure quasars with reliable redshift, “QSO?” for se-
As explained in Sec. 2.3, the MMT targets at g < 22
cure quasars but uncertain redshift, “Star”, “Galaxy” or
onlyconsistedintheselectedobjectsthatwerenotincluded
“Inconclusive”.Thelattercaseencompassesthe“bad”and
intheBOSSsample,i.e.,eitherthatdidnotpassthequality
the “?” spectra of the previous section. In our analysis, we
criteriaorthatappearedasextendedinthesourcecatalog.
use all spectra that were identified as “QSO” or “QSO?”.
Thisledto69quasarswithg <22intheMMTsample.For
g >22, the MMT sample included 116 quasars in common
2 http://iparrizar.mnstate.edu/juan/research/ESPECROAD/ with BOSS, and 77 additional ones.
7
N. Palanque-Delabrouille et al.: Quasar Luminosity Function using dedicated data from BOSS and MMT
Table2summarizestherawquasarcountsinthe BOSS From the set of targets with an identification in both
and MMT samples. samples (i.e., not considering those declared“unknown” in
either case),and assuming the true identification to be the
one from the MMT spectrum, we can estimate the iden-
Observed g magnitude
tification reliability with BOSS to be of order 237/251 =
Sample <22 22−22.5 22.5−23 >23 Total
94±2% at g > 22 and of order 59/61=97±2% over the
BOSS 692 231 165 91 1179
magnitude range 22<g <22.5.
MMT 69 88 73 32 262
Known 381 51 4 0 436
4.3. Corrected counts
Table 2: Raw number counts for the different samples in To study quasar number counts, we use the quasars iden-
several g magnitude bins.
tified in the BOSS sample to g < 22.5 and in the MMT
sample to g < 23.0. The depth of the observations is in-
sufficient to use identified quasars with g >23.0. All fields
suffer from relatively high Galactic extinction: hA i=0.27
g
4.2. Identification cross-checks (rms of 0.10) ranging from 0.15 to 0.60 in the BOSS fields
and hA i = 0.25 (rms of 0.04), ranging from 0.15 to 0.35,
g
We have intentionally observed some targets with both in- in the MMT fields. The previous limitations on observed
struments in the g > 22 magnitude regime where we ex- magnitude therefore result in the following effective limits
pecttheBOSSidentificationtobecomelesssecure.Table3 on the extinction-corrected magnitude: g < 22.35 for
dered
summarizesthecross-identificationofthe344commontar- BOSS and g <22.70 for the MMT.
dered
gets,amongwhich116quasarsidentifiedassuchfromboth
To compute completeness-corrected quasar counts, we
instruments. There are very few changes in identification.
defined three exclusive areas, based on observed g magni-
The most notable feature is that, as expected, more faint
tude and sky coverage:
quasarscouldbeidentifiedandgivenasecureredshiftfrom
MMTthanfromBOSS:19“QSO?”BOSStargetswerecon- – g < 22.0 : use of the BOSS sample over the entire
firmed as “QSO”with MMT, as well as 9 targets classified 14.5deg2 area(691BOSSand346known,foratotalof
as“Bad”inBOSS.Itisnoteworthythatevenatthesefaint
1037 quasars)
magnitudes, there were almost no false quasar detections – 22<g <22.5:useoftheMMTsampleoverits3.9deg2
in BOSS: only 1 “QSO?” BOSS target was identified as a
coverage (88 quasars) and of the BOSS sample for the
starfromthe MMT spectrum;allotherswere confirmedas remaining 10.6 deg2 area (169 quasars), completed by
quasars.
47 known quasars
– 22.5 < g < 23.0 use of the MMT sample over its
MMT\BOSS QSO QSO? Star Galaxy Unknown 3.9 deg2 coverage(105 MMT and 3 known quasars)
QSO 94 19 3 - 9
QSO? 2 1 3 - 2 This division ensures, for each magnitude range, the use
Star - 1 115 1 37 of the sample with best redshift reliability (cf. Sec. 4.2)
Galaxy - - 6 6 - andmaximalstatisticalsignificance.The data thatdidnot
Unknown 2 3 19 - 21 explicitly enter the computation of the correctedcounts or
quasar luminosity function were used for cross-checks (cf.
Table 3: Cross-identification between BOSS and MMT
Secs. 4.2 and 4.4).
spectra for the 344 targets with g >22 that were observed
The data from the BOSS sample were corrected for se-
by both telescopes.
lection(ǫ )andquality(ǫ )incompleteness.Inaddition,
sel qual
tiling (ǫ ) and spectrograph(ǫ ) completeness cor-
tiling spectro
rections were applied to the quasars that were identified
from this deep program. The previously identified quasars
At brighter magnitudes (22 < g < 22.5), table 4 sug-
in the area were only corrected by ǫ and ǫ since they
gests excellent consistency in the identification by either sel qual
were removed from the list prior to the tiling procedure.
telescope. Out of a total of 66 targets for which a secure
identification is available from the MMT spectra, 59 were The data from the MMT sample were corrected for
correctly identified by BOSS, 5 had too low S/N, and 2 spectrograph(ǫspectro)incompleteness,andfortherelevant
were misidentified. There are no false quasar detection. ǫtiling and ǫsel that, for the MMT sample, depended on the
target morphology.
The completeness-corrected number of quasars is thus
MMT\BOSS QSO QSO? Star Galaxy Unknown
computed from the following equation:
QSO 38 5 2 - 4
QSO? - - - - 1
1
Star - - 15 - - N =
QSO
GUnalkanxoywn -- -- 2- 1- -- NXBOSS ǫsel ǫqual ǫtiling ǫspectro
1
+
Table 4: Cross-identification between BOSS and MMT NKXnown ǫsel ǫqual
spectra for the 68 targets with 22 < g < 22.5 that were
1
observed by both telescopes. +
ǫpoint−like ǫ ǫ
NpoXint−like sel tiling spectro
MMT
8
N. Palanque-Delabrouille et al.: Quasar Luminosity Function using dedicated data from BOSS and MMT
1
4.4. Counting cross-checks
+ (4)
ǫextended ǫ ǫ
NeXxtended sel tiling spectro Because we had overlapping data in terms of magnitude
MMT
range or sky coverage from two different programs, sev-
where the completeness correctionsare2Dfunctions ofthe
eral counting cross-checks can be performed. Every single
quasar magnitude g and redshift z.
quasar observed was therefore used to compute the lumi-
Figure 10 illustrates the completeness-corrected quasar
nosity function or for cross-checks,and some for both.
number counts as a function of redshift for 3 magnitude
limits: g < 22 as in the BOSS survey (Schlegel et al.,
dered
2009), g < 22.5 as required for the eBOSS project3, Density comparison in 22<g <22.5
dered
and g < 23 as required for BigBOSS4. As explained
dered
The magnitude range 22<g <22.5 was accessible to both
above, however, the last set of histograms are only com-
the MMT and the BOSS samples. Because of the differ-
plete to g < 22.70 and thus represent lower limits for
dered
entconstraintsonsourcemorphologyandquality,however,
g < 23. On average over the quasars of this project,
dered
andsincetheMMTzoneonlycoversaportionoftheBOSS
total completeness corrections are at the level of 80% to
zone, the quasars observed in the two cases were not the
g <20,anddropsmoothlyto50%atg ∼22.5.Table5sum-
same. The completeness-corrected quasar number counts
marizes the total quasar number counts for various ranges
derived from either sample over 22<g <22.5 are given in
in corrected g magnitude and redshift.
table 6. The last column indicates the number of identified
quasars used to make the measurement. The quasar densi-
Redshift Extinction-corrected magnitude gdered ties derived from BOSS or the MMT over this magnitude
z <22 <22.25 <22.5 <22.75 <23 range are in excellent agreement.
<1 27(3) 29(3) 30(4) 30(4) 32(4)
[1−2.15] 75(3) 87(3) 99(4) 113(5) 119(6)
>2.15 34(2) 37(2) 47(3) 49(3) 53(3) QSO density Raw number
all z 136(5 ) 153(5) 175(6) 191(7) 205(8) Survey (deg−2) of quasars
BOSS overMMT zone 39.0 ± 5 72
BOSS complete sample 40.2 ± 3 276
Table 5: Number counts (quasars per deg2) for several MMT 39.1 ± 4 100
ranges in extinction-corrected magnitude g and red-
dered
shift z. The statistical uncertainty on the last significant Table 6: Efficiency-corrected number counts for the BOSS
digit is indicated in parentheses. Number counts are com- and MMT samples (including, in both cases, the BOSS
plete to g < 22.5, and only indicate lower limits at standardQSOsthatwereselectedbutnotre-observed)over
dered
fainter magnitudes. the magnituderange22<g <22.5accessibletobothsam-
ples.
2∆ z = 0.20) (O / deg2205 gc < 22 2205 gc < 22.5 2205 gc < 23 CTfrrohomesss-apcmhoeipncltke-loiokffeǫqqusuoaalusarucrsesinssgeilnMecMttheTde pfmooraingttnh-lieitkuMedtMearTrgaenotsgbesaetrggva<<tio22n22s
QS should allow recovery of the quasars that were not se-
Number of 15 15 15 lseocutrecdeiqnutahleityB.OTShSeytacragnetthliesrtebfoerceaubseeuosfetdhetocovnersitfryaitnhteseosn-
timated ǫ . This concerned N =22 MMT quasars, with
10 10 10 qual
ameantiling correction(correspondingtoprioritylevelA)
ǫ =0.903. Given a survey area S = 3.9 deg2, the den-
tiling
5 5 5 sity of point-like sources observed with MMT at g < 22 is
therefore N/ǫ /S =6.2±1.3 deg−2.
tiling
In the same magnitude range, the BOSS sample con-
0 0 0
0 1 2 3 4 05 1 2 3 4 50 1 2 3 4 5 sisted of N = 691 quasars, with a mean tiling correc-
Redshift
tion ǫ = 0.945 and a mean source quality complete-
tiling
Fig.10: Quasar number counts per deg2 as a function of ness correction ǫ = 0.897. Given a survey area S =
qual
redshift (∆z = 0.2). Blue is for the new sample of quasars 14.5 deg2, the estimated density of quasars not included
identified with our BOSS deep program,green for the pre- in the sample because of the quality constraint is thus
viously known BOSS sample, red is for the MMT sample N/ǫ /ǫ ×(1−ǫ )/S = 5.8±0.2 deg−2, in agree-
tiling qual qual
and black for the total. The blue, greenand red curves use ment within 1σ with what was estimated from the MMT
mutually exclusive samples and correspond to the zones sample.
defined in Sec. 4.3.
Cross-check of ǫ using MMT extended targets at g <22.5
sel
Finally, the quasars selected for the MMT observations
3 http://lamwws.oamp.fr/cosmowiki/Project eBoss from extended sources at g < 22.5 should allow recovery
4 http://bigboss.lbl.gov of the quasars that were not selected in BOSS because of
9
N. Palanque-Delabrouille et al.: Quasar Luminosity Function using dedicated data from BOSS and MMT
constraintson the sourcemorphology.This canbe checked 5.1. K-corrections
bycomparingthe densityofextendedquasarsinthe MMT
Selection for this survey was performed in the g-band, and
survey to the number of quasars that were not selected in
for the majority of the data this band provides the high-
BOSS for this same reason, estimated from the observed
est S/N. We define the K-correction in terms of the ob-
number of point-like quasars and the morphology-part of
served g magnitude and follow Croom et al. (2009) (here-
the selection completeness correction.
after C09) in applying the correction relative to z = 2,
whichisnearthemedianredshiftofourquasarsample(see
also Richards et al. (2009)). The absolute magnitude nor-
malized to z =2 is given by:
z 16
∆
4
2/0.g 14 Extended targets in MMT Mg(z =2)=gc−dM(z)−[K(z)−K(z =2)]. (5)
e
O/d 12 Morphology correction (BOSS) Hereafter we will use Mg as a shorthand for the redshift-
S corrected M (z = 2). The K-correction as a function of
Q 10 g
redshift is derived from model quasar spectra in a simi-
8 lar fashion to Richards et al. (2009). The quasar model in-
cludes a broken power law continuum with α = −0.5 at
ν
6 λ > 1100˚A and α = −1.5 at λ ≤ 1100˚A (Telfer et al.,
ν
4 2002). Strong quasar emission lines are included, where
the equivalent width is a function of luminosity according
2 to the well-known Baldwin Effect (Baldwin, 1977); thus,
the K-correction is a function not only of redshift but
0
0 0.5 1 1.5 2 2.5 3 3.5
also luminosity (or equivalently, observed g-magnitude).
z
The model also includes Fe emission using the template of
Fig.11: Comparison of the number of “extended” quasars Vestergaard and Wilkes(2001)andLyman-αforestabsorp-
estimated from BOSS data and completeness corrections tionusingtheprescriptionofWorseck & Prochaska(2010).
(blue curve) or observed in the MMT sample (purple Theforestmodelisparticularlyrelevanthere,asforz >∼2.5
points). the g-band K-correction necessarily includes a component
due to forestabsorption;ourK-correctionaccountsfor the
mean value but for high redshift objects the uncertainty in
individual K-corrections is increased by line-of-sight fluc-
Quantitatively, we compute the following two quanti- tuations in the amount of forest absorption within the g-
ties, in the g < 22.5 magnitude range. On the one hand, band. The models used to derive the K-corrections will be
the density of extended quasars identified in MMT: described in fuller detail in McGreer et al. 2012 (in prep).
In general, as shown in Fig. 12, the values are very sim-
1 1
ilar to those used by C09 (e.g., their Fig. 1), but are ex-
SMMT NeXxtended ǫesexltendedǫtiling ǫspectro tended to z = 4. At z ∼ 2−3, the luminosity-dependent
MMT K-correctionweuseintroducesadifferentialvalueof∼0.25
and on the other hand, the density of unselected extended mag across the luminosity range of quasars in our sample,
quasars in BOSS: as the Lyman-α and C IV lines are within the g-band and
contribute substantially to the flux within the bandpass.
1 1 1
× −1
SBOSS NXBOSS ǫtiling ǫspectro ǫqual (cid:18)ǫmorphology (cid:19) 5.2. Luminosity function model
1 1 1 We define eight redshift bins: the first five are
+ × −1
S ǫ (cid:18)ǫ (cid:19) the same redshift intervals as in C09, with limits
BOSS NKXnown qual morphology 0.68,1.06,1.44,1.82,2.2,2.6; the last three are specific to
where S and S are respectively the areas of the our analysis and have the limits 2.6,3.0,3.5,4.0.We calcu-
MMT BOSS
MMT and the BOSS programs,and ǫ is the frac- late the binned LF using the model-weighted estimator Φ
morphology
suggestedbyMiyaji et al(2001),whichpresentstheadvan-
tionofthetargetsthatarepoint-like(asafunctionofmag-
nitude andredshift).This correctionis the partofǫ that tage of not having to assume a uniform distribution across
sel
does not include the effect of the target selection based on eachbin, unlike 1/Vestimators.Instead, it models the un-
binned LF data and uses it to correct for the variation of
its color and time variability. These two densities are illus-
trated in Fig. 11. They are clearly in agreement. the LF and for the completeness within each bin, which is
here particularly critical at the faint end of the LF where
thelatterisincompletelysampled.Thisestimatorgivesthe
5. Luminosity function in g binned LF as
We compute the quasar luminosity function (LF) from the Φ(M ,z ) = Φmodel(M ,z ) Niobs , (6)
corrected number counts derived above, and considering gi i gi i Nmodel
i
our completenesslimit atg <22.5.The distance mod-
dered
ulus dM(z) is computed using the standard flat ΛCDM where Mgi and zi are, respectively, the absolute magni-
model with the cosmological parameters of Larson et al. tude and the redshift at the center of bin i, Φmodel is the
(2011): Ω =0.267,Ω =0.734 and h=0.71. model LF estimated at the center of the bin, Nmodel is
M Λ i
10