The Sloan Digital Sky Survey Reverberation Mapping Project: An Investigation of Biases in CIV Emission-Line Properties

1 MB·

by  K. D. Denney

Draftversion January25,2016
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
THE SLOAN DIGITAL SKY SURVEY REVERBERATION MAPPING PROJECT:AN INVESTIGATION OF
BIASES IN Civ EMISSION-LINE PROPERTIES
K. D. Denney1,2,3, Keith Horne4, W. N. Brandt5,6,7, Luis C. Ho8,9, B. M. Peterson1,2, Gordon T. Richards10, Yue
Shen11,12, J. R. Trump5,13, J. Ge14
(Received)
Draft version January 25, 2016
6
ABSTRACT
1
WeinvestigatethedependenceondataqualityofquasarpropertiesmeasuredfromtheCivemission
0
2 line region at high redshifts. Our measurements come from 32 epochs of Sloan Digital Sky Survey
(SDSS) Reverberation Mapping Project spectroscopic observations of 482 z > 1.46 quasars. We
n
compare the differences between measurements made from the single-epoch and coadded spectra,
a
focusing on the Civλ1549 emission line because of its importance for studies of high-redshift quasar
J
demographicsandphysicalproperties,includingblackholemasses. Inadditiontoincreasingstatistical
2
errors(byfactorsof∼2−4),wefindincreasingsystematicoffsetswithdecreasingS/N.Thesystematic
2
difference (measurement uncertainty) in our lowest S/N (<5) subsample between the single-epoch

and coadded spectrum (i) Civ equivalent width is 17˚A (31˚A), (ii) centroid wavelength is <1˚A (2˚A),
]
A and fractional velocity widths, ∆V/V, characterized by (iii) the line dispersion, σ , is 0.104 (0.12),
l
and (iv) the mean absolute deviation (MAD) is 0.072 (0.11). These remain smaller than the 1σ
G
measurement uncertainties for all subsamples considered. The MAD is found to be the most robust
h. line-width characterization. Offsets in the Civ full-width at half maximum (FWHM) velocity width
p andtheCivprofilecharacterizedbyFWHM/σlareonlysmallerthanthestatisticaluncertaintieswhen
- S/N>10,although offsets in lower S/N spectra exceed the statisticaluncertainties by only a factor of
o ∼1.5. Characterizing the Civ line profile by the kurtosis is the least robust property investigated, as
r
the median systematic coadded–single-epoch measurement differences are larger than the statistical
t
s uncertainties for all S/N subsamples.
a
Subject headings: galaxies: active — galaxies: nuclei — quasars: emission lines — quasars: general
[
— quasars: supermassive black holes — galaxies: distances and redshifts

2
v
5 1. INTRODUCTION derstood to be the visible growth phase of the su-
2 permassive black holes (BHs) that reside at the cen-
Since their discovery (Schmidt 1963), quasars (syn-
4 ter of massive galaxies. The strong correlations be-
onymously referred to in this work as active galac-
5 tween the properties of these BHs and their host galax-
tic nuclei or AGN) have evolved from a curiosity to
0 ies(Kormendy & Richstone1995;Magorrianet al.1998;
a powerful cosmological probe. They are now un-
1. Ferrarese & Merritt 2000; Gebhardt et al. 2000b,a,b;
0 1Department of Astronomy, The Ohio State Univer- Ferrarese et al.2001;Tremaine et al.2002;Wandel2002;
6 sity, 140 West 18th Avenue, Columbus, OH 43210, USA; Onken et al. 2004; Nelson et al. 2004; Graham 2007;
1 [e-mail] Physics, The Ohio Bentz et al. 2009b; McConnell & Ma 2013, see also the
v: State University, 191 West Woodruff Avenue, Columbus, OH review by Kormendy & Ho 2013 and references therein)
43210, USA strongly suggest that BHs may play an active role in
Xi 3NSFAstronomy&AstrophysicsPostdoctoral Fellow theevolutionofgalaxiesandtheirsurroundings,presum-
4SUPA Physics/Astronomy, Univ. of St. Andrews, St. An-
ably due to feedback produced from the energy released
r drewsKY169SS,Scotland, UK
a 5Department of Astronomy & Astrophysics, 525 Davey Lab, by the gravitational accretion of material onto the BH
The Pennsylvania State University, UniversityPark, PA 16802, (e.g., Hopkins & Elvis 2010; Debuhr et al. 2011; Fabian
USA 2012). Whether the growth and co-evolution of BHs
6InstituteforGravitationandtheCosmos,ThePennsylvania
and galaxies is mutually regulating and causal or not
State University,UniversityPark,PA16802, USA
7Department of Physics, 104 Davey Lab, The Pennsylvania (Jahnke & Macci`o2011;Sun et al.2015a),thesesystems
State University,UniversityPark,PA16802, USA remain important probes of the distant and nearby uni-
8KavliInstituteforAstronomyandAstrophysics,PekingUni- verse.
versity,Beijing100871, China
9Department of Astronomy, School of Physics, Peking Uni- Many physical properties of the accreting BHs, such
versity,Beijing100871, China as the mass and accretion rates, can be estimated
10Department of Physics, Drexel University, 3141 Chestnut from a single quasar spectrum (e.g., McLure & Jarvis
St.,Philadelphia,PA19104,USA 2002; Vestergaard 2002; Vestergaard& Peterson 2006;
11DepartmentofAstronomy,UniversityofIllinoisatUrbana-
Wang et al.2009;Rafiee & Hall2011b;Park et al.2013).
Champaign,Urbana,IL61801,USA
12National Center forSupercomputing Applications, Univer- This is possible through largely empirical scaling re-
sityofIllinoisatUrbana-Champaign,Urbana,IL61801,USA lationships calibrated using small samples of low-
13HubbleFellow redshift AGN. In particular, reverberation mapping
14Astronomy Department University of Florida 211 Bryant
(Blandford & McKee 1982; Peterson 1993, 2014) pro-
Space Science Center P.O. Box 112055 Gainesville, FL 32611-
2055, USA vides the calibration for estimating “single-epoch” (SE)
2
quasar masses, using only two observables measurable with spectral S/N<10 (per pixel) in the continuum.
from a single quasar spectrum: the broad line region Here, we investigate the effects of low S/N on Civ
(BLR) velocity — inferred from the velocity-width of a emission-lineproperties. Wefirstevaluatestatisticaland
broademissionline—andtheradiusofthevariableBLR systematicerrorsintheestimatesofthevelocitywidthof
gas — inferred from the quasar luminosity (Laor 1998; the broad Civλ1549 emission line. The broad emission
Wandel et al.1999;Kaspi et al.2000;Bentz et al.2009a, line velocity width is one of the two observables needed
2013). to estimate a virial BH mass, which allows subsequent
Using quasars for studying cosmology, galaxy evolu- studiesofcosmicstructuregrowth,seedblackholes,and
tion, and BH accretion physics requires an understand- the co-evolution of galaxies and BHs. We also look at
ing of their evolution in number and mass over cosmic other commonly-measuredCiv emission-line properties,
time. This requires measuring these properties for large including the Civ equivalent width, centroid, and line
samples across the universe. In the last several decades, shape, that may be useful in determining further details
photometric and spectroscopic quasar surveys operating of the accretion and feedback processes, structure, and
overawiderangeofwavelengthsandenergieshavevastly kinematics of the central engine and/or for evaluating
increased the number of known quasars and their red- otherbiasesinCiv-basedblackholemasses(e.g.,Denney
shifts. Inparticular,theSloanDigitalSkySurvey(SDSS; 2012).
York et al. 2000) has cataloged ∼300,000 spectroscopi- These measurable spectroscopic properties are impor-
cally confirmed quasars when combining the fifth edi- tantfordirectstudies ofquasarphysics anddemograph-
tion SDSS Quasar Catalog (Schneider et al. 2010) with ics, as well as the broader evolutionary studies based
theDataRelease10Quasarcatalog(DR10Q;Paˆris et al. thereon, as the Civ emission line is present in the opti-
2014) from the BaryonOscillation Spectroscopic Survey calwavelengthregimeinthe range1.4. z . 4.8,which
(BOSS; Dawson et al. 2013). coversthe quasar epoch and extends to a time when the
Largestatisticalsamplescanenabledetailedstudiesof universe was less than a tenth of its currentage. In Sec-
quasar demographics only if the systematic biases asso- tion 2 we present the data we use for this investigation,
ciated with survey limits and data quality are well un- while Section3 describesthe spectroscopicanalysisused
derstood. In this study we investigate possible biases in to fit and measure the properties of interest from our
severalspectroscopicproperties derivedforhigh-redshift quasar sample. We discuss trends and other results as
quasarsduetothelowsignal-to-noiseratio(S/N)oftyp- a function of the data quality and other quasar proper-
ical survey spectra. Since the goal of most surveys is tiesinSection4andmakeconcludingremarksaboutour
to measure redshifts with which to map the universe, results in Section 5.
this only requiresa highenoughS/Nto reliablydetect a
high-equivalent-widthemissionline. Despitetheintrinsic
high luminosity of quasars, the vast majority will have 2. CivSPECTRALDATA
observedfluxes closeto the flux limit of the survey(e.g., In 2014, the SDSS Reverberation Mapping Project
Paˆris et al.2014). Asaresult,thequasarcontinuumand (SDSS-RM) spectroscopically monitored 849 broad-line
lower equivalent width features (such as those used for quasars in the CFHT-LS W3 field (which is also the
BH masses and reliable redshifts) will be at significantly AEGIS field and a PanSTARRS medium-deep field)
lower S/N. Consequently, it is important to understand with the BOSS spectrograph (Smee et al. 2013) that is
thedata-qualitylimitatwhichthereliability(definedby mounted on the SDSS telescope (Gunn et al. 2006) as
bothprecisionandaccuracy)ofaninvestigationbecomes part of an ancillary program of the SDSS-III surveys
compromised. (Eisenstein et al. 2011). The SDSS-RM sample covers
Thedatausedfordirect,reverberation-mappingbased redshifts over the range 0.1 < z < 4.5 down to a flux
BH measurements are generally of very high quality. limit of i = 21.7 mag in a single 7 deg2 field. Each
psf
This is also true of the data used to calibrate SE of the 32 epochs of observations was a ∼2 hr exposure
virial BH mass scaling relations (e.g., Park et al. 2013). taken during dark/greytime with an averagecadence of
As such, our understanding of the general uncertainty ∼4daysoveraperiodof6months. Furtherdetailsofthe
in BH masses derived either directly through rever- SDSS-RM project, the technical overview, and program
beration mapping or indirectly through empirical scal- goals are provided by Shen et al. (2015).
ing relationships is based on high-quality data. Yet, Here, we only consider objects from the SDSS-RM
most of the higher-redshift quasar spectra to which samplewithz >1.46sothattheCivemissionlineanda
these scalingrelations areappliedare typicallylow-S/N, short ward continuum region are accessible. We further
“survey-quality”15 data. There canbe systematic differ- removed three objects for which low-EW emission lines,
ences between spectroscopic properties measured from althoughclearlyseenin the coaddedspectrum, were not
the high-quality calibration data and the survey-quality easily discernible in all or most of the single-epochspec-
data, leading to systematic errors in BH mass esti- tra, leading the fits (described below) to fail or provide
mates. Denney et al. (2009) examined this for Hβ line bogus results for most SE spectra. We also removed 12
width measurements for two low-redshift,relatively low- broad absorption line (BAL) quasars in which the BAL
luminosity AGN, and found statistical and systematic absorbedtoomuchoftheCivemissionlineforthewidth
effects that became a significant source of bias for data to be reliably characterized. On occasion, objects were
discovered to have “dropped spectra”, where the fiber
was not properly plugged into the plate. We visually
15 Here, we use “survey-quality” to refer to the typically lower
inspected all epochs for all 482 quasars, removing any
spectral S/N (.3−5 per pixel at the flux limit) data that is of-
tentheproductoflarge,moderate-resolution,flux-limited,redshift epoch in which the spectrum was completely absent due
surveys,suchastheSDSS. to this or other problems. We did not initially drop any
Biases Discovereddue to Low S/N Spectra 3
Fig. 1.— Distribution of redshifts and ipsf magnitudes for the
sample of 482 SDSS-RM quasars. The vertical dashed line in the
rightpanel showsthemagnitudelimitfortheSDSS-RMsample.
spectra based on their S/N.16 However, in a small num-
Fig.2.— Distribution of S/N of SE spectra (black) and coad-
ber of cases, the spectra were too noisy to even detect
ded spectra (red) for our sample of 482 SDSS-RM quasars. The
emission lines, and so these were omitted from subse- coadded S/N is measured per Angstrom in an emission-line-free
quentanalysis. ThisoccurredmostfrequentlyforEpoch continuum window near restframe 1700˚A of each coadded spec-
7,thelowestS/Nepochinthecampaign. Ourfinalsam- trum, and the SE S/N shown is the median of the distribution
ofS/NmeasurementsmadesimilarlyfromallgoodSEspectrafor
ple consists of 482 sources. Most (405) QSOs have all
eachobject. TheσSEerrorbarintheupperrightcornerrepresents
32 epochs of spectra included in our analysis, and only themedianofthedistributionofscattermeasurementsmadefrom
9 QSOs have more than 3 (10%) epochs discarded. Fig- theSES/Ndistributionsforallobjects. Fivecoaddedspectrahave
ure 1 shows the redshift and i magnitude distribution S/N>115.
psf
of our sample.
5−6 times higher than that of the SE spectra of each
3. SPECTROSCOPICANALYSIS object. Figure 2 shows the S/N distributions of the SE
and coadded spectra for our sample. The median SE
The SDSS-RM project provides a unique opportunity
(coadded) spectrum continuum S/N is 5.5 (25.7) with
tostudy data-qualitybiasesinthe measurementofspec-
a scatter, defined by the HIPR, of 4.9 (20.9). Figure 3
troscopicpropertiesofquasarsfromsurveyspectra. Each
shows examples of the Civ emission line region in two
epoch is representative of a typical survey-quality spec-
SEspectraofSDSS-RMsources,withS/Nnearthesam-
trum.17 We thus analyze all individual epochs to mea-
ple median (top panels), and the correspondingcoadded
sure a distribution of spectral properties expected for
spectra (bottom panels). The coadded spectrum S/N is
SE spectra of a single object. Throughout this work,
48 (46) for the object in the left (right) panel. In both
we use the median of these distributions for each ob-
cases, the median S/N of all SE spectra of these objects
jectasour“SEmeasurement”withthemeasurementun-
is∼8,but the SE spectrashowninFigure3 werechosen
certainty defined as half of the 16−84% inter-percentile
fromanepochwithaS/Ncloseto the medianofthe full
range (HIPR) of the distribution, which would corre-
sample (S/N∼5).
spond to 1-σ if the distribution were Gaussian. We
Biases in our coadded spectra due to intrinsic vari-
thencombine allthe spectra tomakea single,high-S/N,
ability are unlikely, given the relatively high luminos-
“coadded”spectrumusingthelatestBOSSspectroscopic
ity and high redshifts of our sample combined with the
pipeline idlspec2d (see Shen et al. 2015, and Schlegel et
short campaign period. Our 6-month campaign dura-
al., in prep.).
tion covers only ∼1−3 months in the rest frame of our
We define the S/N per Angstrom, determined by the
z > 1.46 quasars, and quasar (i) variability amplitudes
ratio of the mean flux to the dispersion in the flux in
and (ii) reverberation time-delays scale with luminosity
an emission-line-free continuum window near restframe
inverselyanddirectly,respectively. Suchvariability,even
1700˚A. We use the same red continuum window as for
if present on these timescales, would only change the
the fits described below. The coadded spectra have S/N
overall line flux, to first order. Gross profile change or
velocity-dependent flux changes occur on timescales not
16 Three out of the 32 epochs have relatively low S/N (S/N
probed by our campaign (see, e.g., Sergeev et al. 2007;
<0.7hS/Ni)duetopoorobservingconditionsand/ortheinability
toobtain the full2-hrexposure. Sunetal.(2015b)omitted these Shen et al. 2015).
epochsfromtheirinvestigation,astheywouldhavesystematically
biased the measured quasar structure function. We include these 3.1. CIV line profile fits
low-S/Nepochs,asourgoalistoanalyzespectraoverawiderange
ofS/N. Because we are only investigating properties of the
17 Note, the exposure time of our SE spectra is greater than a Civ emission line in this work, we only fit this local-
typical SDSS or BOSS quasar spectrum, with a 2-hr rather than
ized region of the spectra. Our general procedure for
the minimum 45-min exposure. However, these longer exposures
are offset by our deeper flux limit and so lead to a sample of SE fitting the Civ emission line follows that described by
spectra withsimilarS/N distributions to SDSSorBOSSquasars, Denney et al. (2013). We first fit a linear continuum
where the SDSS spectral S/N limits are set by the successive 15- beneath the line, anchored by the mean flux in a blue
minexposuresbeinghaltedwhentheS/Nperpixelexceeded4for
and a red continuum region on either side of Civ (see
fibermagnitudesofg=20.2andi=19.9andBOSSwassimilarly
limited by exposures stopping when the (S/N)2 exceeded 22 for Fig. 3). While the AGN continuum is best described by
i=21and10forg=22. a power law over longerwavelengthranges,there is very
4
Fig. 3.—Twoexamples(left: RM161andright: RM139)ofSDSS-RMSE(toppanels)andcoaddedspectra(bottom panels)areshown
in black. The best GH fits to the Civ emission lines are shown in red, and the best linear continuum fit is in green. The vertical black
dashedlinesshowtheexpected locationofthelabeledemissionlinesbasedontheSDSS-pipelineredshiftforeachobject. Theredvertical
solid lines show the boundaries of the two wavelength regions used to fit the continuum beneath the Civ emission, and the red vertical
dashedlinesboundthewavelengths overwhichtheCivlinepropertiesaremeasured. Shadedregionsweremaskedduringthefitting.
little difference locally (i.e., under a single emission-line tinuum noise level after subtracting each fit component.
region), between using a linear continuum and a power Spectra were fit interactively, but with an automated
law. Wethenmaskthewavelengthregionscoveringrest- pipeline to better reproduce typical literature practices
frame 1475−1495˚A and 1600−1680˚A to exclude possi- (e.g., Shen et al. 2008, 2011). The automated pipeline
ble contributions from blended Niv] λ1486 line emis- set the continuum regions at restframe wavelengths
sionandthe“redshelf”emissionoftenobservedbetween 1435−1465˚A and 1690−1710˚A, although adjustments
Civ and Heii λ1640 (see Fine et al. 2010; Assef et al. weremade for the lowestredshift objects where the blue
2011;Denney et al. 2013). We then fit the Civ emission regionfellatthenoisyedgeofthespectrum,forthepres-
line with 6th order Gauss-Hermite (GH) polynomials enceofsignificantabsorptionfrominspectionofthefirst-
thatadoptthe functionalformsof,e.g.,Cappellari et al. epochSEspectrumorthe coaddedspectrum,orforchip
(2002), andthe normalizationof van der Marel & Franx defectsinanyspectrum. Next,theregionoverwhichCiv
(1993). Iterative sigma-clipping was employed in fitting was fit was set to rest frame wavelengths 1466−1650˚A.
both the continuum and the Civ emission line to ex- This range was intentionally chosen to be broad enough
cludespuriousfluxcontributionstothefit,typicallyfrom toencompassallpossiblelinewidths. TheCivlineprop-
noise,poorly-subtractedskylineresiduals,ornarrow,un- erties are measured directly from the best-fit profile, so
masked absorption features. the usual blended emission that may fall within these
WeprefertheGHpolynomialfitsforCivbecausethey wavelengths, such as from Niv] or Heii, is masked dur-
model the typically non-symmetric and non-Gaussian ing fitting and does not contribute to the final fit.
profileofCivwithfewercomponentsthanrequiredwhen Manualinterventioninthefittingprocedurewasneces-
using(forexample)onlyGaussianfunctions. However,it saryfor severalreasons. First, fitting was interrupted to
is possible that in low S/N data, the freedom of the GH change or identify additional masking needs — most of-
polynomials may lead to fit profiles with more structure tenforabsorption. The identificationanddetails ofcon-
than is likely real, since a lower χ2 can be achieved by taminating features are more easily discerned in higher
matchingthefittowhatareultimatelyspuriousemission S/N spectra, so a more hands-onapproachto the fitting
signatures ascribable to noise. We do not ascribe phys- was allowed when the additional signal provided this in-
ical meaning to any of the fit components. We simply formation. As such,modificationstothe boundariesand
aim to reconstruct the best overall model of the intrin- maskswereoptimizedonanobject-to-objectbasis. This
sic, unblended, unabsorbed profile. We added fit com- wasoftenpossibleonlyforthecoaddedspectra,butwhen
ponents iteratively, only adding additional components applied to the SE spectra, any masking or boundary
whenresidualemissionlinefluxfromanypartoftheline changes were set by only the first-epoch spectrum and
— usually the peak — remained above the average con- then kept the same for all additional epochs. Common
Biases Discovereddue to Low S/N Spectra 5
modificationsweretowidentheredshelfmaskfurtherto cludedin the calculationofany line property.19 Individ-
the blueorthesize and/orlocationofthe Niv]andcon- ual spectra were not used when the measurement of any
tinuum masks to more optimal spectral regions. More of these quantities were bogus, e.g., when an undefined
detailed absorption line masks were also often needed EW measurement was returned because the mean con-
in higher S/N spectra because weak absorption features tinuum flux in the 1450˚A region was found to be ≤ 0,
were not always cleanly removed by the sigma-clipping evenif the fit found a weak line with a defined width, or
procedure. Manualinterventionwasalsousedtoconfirm when identification of the Civ emission line failed com-
whenmultiplecomponentswereneededtofittheprofile. pletelyduetolowS/N,resultinginanulllinewidthand
Thiswasdoneforboththecoaddedspectrumandforev- other properties. After dropping all such cases, the sub-
erySEspectrum. Finally,theinteractiveprocessalsoal- sequentanalysisisbasedonthe482coaddedspectraand
lowedus to flagand then removepreviouslyunidentified 15275 SE spectra from all “good epochs”.
“dropped” spectra from our analysis. These interactive SimilarlytotheSEspectraS/Nmeasurements,theSE
steps likely increase the robustness of our fits compared line property “measurement”for eachquasar is takento
to fully automated analyses of large survey samples for bethemedianofthedistributionofallthemeasurements
which it is infeasible to visually inspect the fits to every from all good epochs of that source, and the measure-
spectrum. ment uncertainty is taken as the HIPR of the distribu-
To prevent any unconscious bias in the way the SE tion. While all spectra nominally represent equivalent
spectra were fit or masked for contaminating features, and independent observations of each source,we use the
we fit the SE spectra before fitting the coadded spectra. median and HIPR as opposed to the mean and stan-
To do otherwise might bias our analysis because using dard deviation of these distributions to help account for
the information from the higher S/N coadded spectra possibleoutliersduetovariableobservingconditionsbe-
to inform treatment of the lower S/N SE spectra is a tweenepochs. The emissionline propertymeasurements
luxury not afforded in typical analyses of survey-quality for all objects based on the coadded spectra are made
data. ExamplesofGHfitsareshownwiththespectrain directly from the profile fit to the coadded spectrum for
Figure 3. thatsource. Theuncertaintiesinthesemeasurementsare
estimated by performing Monte Carlo simulations using
3.2. Measurements of Civ Emission Line Properties the fit to the coadded spectrum. We create 500 mock
spectra by resampling the flux in the GH polynomial fit
Wefocusourattentionononlythetwomostcommonly
based on Gaussian deviates derived from the coadded
employed emission-line width characterizations used to
error spectrum for each source. We assign the uncer-
derive BH masses: the FWHM and the line dispersion
tainty in the measured line properties of each coadded
(σ ), the square root of the second moment of the line
l spectrum to be the standard deviation about the mean
profile. However, we also consider the velocity width
of the distribution of 500 measurements of that prop-
characterized by the mean absolute deviation (MAD18)
erty made from the mock spectra. Figure 4 shows the
from the median velocity, defined following the notation
relative line width uncertainties, σ /V, for the FWHM
of Peterson et al. (2004) as V
and σ of the SE and coadded spectra with respect to
l
an approximated line S/N, for which we expect a linear
MAD= |λ−λ |P(λ)dλ P(λ)dλ, (1) relation. We find that line width uncertainties can be a
Z med Z
(cid:14) significantfractionofthemeasuredlinewidthinthelow-
where P(λ) is the continuum-subtracted emission-line est S/N spectra, and there is a factor of 2−3 increase in
profile,and λ is the flux-weightedmedian of the pro- the magnitude of the statistical line width measurement
med
file. uncertaintiesbetweenhigh-(S/N>10)andlow-(S/N<5)
Additional properties of the Civ emission line we in- quality data for all characterizationsof the Civ velocity
vestigate include (i) its peak wavelength, defined from width. Ontheotherhand,whiletherelativeuncertainty
thecentroidofthepixels≥95%ofthepeaklineflux,(ii) dropsto.5%forspectrawithS/N&10−20,wefindthe
the equivalent width (EW), defined here with respect to trendisshallowerthantheexpectedslopeof-1following
themonochromaticcontinuumfluxlevelmeasuredinthe σV/V ∝(S/N)−1(EW/WC)−1/2,giventhatthe linepho-
continuumwindowcoveringrestframe ∼1450˚A,andthe tons dominate the continuum photons and where WC is
line “shape”, characterized by (iii) the line kurtosis and the width of the continuum window over which the S/N
(iv)theratioFWHM/σ . Theamountbywhichthepeak was measured. This is likely because of the details of
l
ofCivisblueshiftedwithrespecttothesystemicisoften the FWHM and σl calculations. The FWHM does not
an additional line property of interest, but the determi- depend on the whole line, but rather only on a fraction
nation of the blueshift depends on the reliability of the of the pixels (i.e., those near the peak and the 50% flux
systemic redshift. Denney et al. (2016, in preparation) level). The shallowertrendwithσl is likelybecauseσl is
investigatesthepotentialforbiasesintheredshiftsdeter- relatively more weighted by the flux in the wings of the
minedforthissample,andwethereforedeferdiscussions line, where the line flux is lower. Table 1 lists the un-
of the Civ blueshift to that work.
Line properties are measured from the continuum- 19 These are zero-noise profile fits. Negative pixels are there-
subtracted best-fit GH polynomial fits. Any pixel with forenot due to noise characteristics, inwhich case they would be
negative flux after the continuum subtraction is not in- approximatelybalancedbypositivepixelsandtheirvaluesshould
remain in the calculation. Instead, the fit sometimes produces
negativepixelsinmaskedregions(e.g.,overabsorptionortheCiv
18WenotethatourdefinitionoftheMADisnotthesameasthe redshelf)wheretheprofileisunconstrained. Alternatively,itcould
standard definition of the MAD as the median absolute deviation occurincaseswhereabsorptionwasnotaccuratelymaskeddueto
fromthedistributionmedian. noise(see, e.g.,thetoprightpanelofFigure3).
6
tion of the left panel of Figure 6 demonstrates that this
asymmetryandthemagnitudeofthesystematicbiasare
anticorrelatedwith spectral S/N.
The right panel(s) in Figures 5 and 6 and the statis-
tics in Table 2 show the results for the line dispersion,
∆σ /σ. A small systematic bias also exists in the line
l l
dispersion measurements, but in the opposite sense —
the line dispersion tends to be underestimated in lower
S/N spectra. The magnitude of this bias also increases
with decreasing S/N. However, unlike the systematic
bias in the FWHM measurements,the measurementun-
certainties encompass the observed systematic shift in
the SE line dispersion measurements at all spectral S/N
levels. The ∆σ distributions are also more symmetric
l
than the ∆FWHM distributions, though the right panel
of Figure 6 and statistics in Table 2 demonstrate that
Fig.4.— Fractional FWHM (left) and σl (right) uncertainties
for the SE (black points) and coadded spectra (red points) as dataquality still contributesto both the systematicbias
a function of the signal-to-noise ratio of the line, estimated as and the broadening of the ∆σ distributions at lower
l
CwinS/NpEW/WC, where WC is width of the continuum win- S/N. We caution the reader, however, that these results
dow over which the S/N was measured, and Cwin is a normal- hold only when line dispersion measurements are made
ization factor related to the sizes of the continuum and line in-
self-consistently across a sample. Larger DC offsets in
tegration windows and the EW of the line. The S/N is measured
perAngstrominanemission-line-freecontinuumwindownearrest- line dispersion measurements, and thus BH mass esti-
frame1700˚A.Thesolidblacklineistheexpectedreferencerelation, mates, can arise between samples that are analyzedwith
σV/V ∝(S/NpEW/WC)−1. different spectral processing methods, i.e., continuum
and line boundary placements and emission deblending
certainty distribution properties for the full sample and
assumptions (e.g., Denney et al. 2009; Fine et al. 2010;
various sub-samples divided by S/N cuts.
Assef et al. 2011). Such offsets can be surmounted by
following the same spectral processing method used in
4. DISCUSSION
the calibration of the desired mass scaling relationship
We compare the line-property measurements between
(Vestergaard& Peterson 2006; Park et al. 2013).
the “highest-S/N” (coadded) spectra and the “lower-
S/N”(SE)spectrabylookingatthemeasurementdiffer- 4.2. Data-Quality Biases in Other Line Properties
ences, ∆(X) = X(coadded)−Median[X(SE)], in the line
Wealsoinvestigatethedata-qualitydependenceofthe
property, X, as a function of data quality. The S/N of a
other line properties we measuredabove — the Civ line
small percentage of the coadded spectra are also “low”,
MAD, EW, shape (kurtosis and width ratio), and cen-
compared to the median of the coadded spectrum S/N
troid (see Tables 1 and 2). The left panel of Figure 7
distribution (see Fig. 2), and fall within the lowestqual-
showsthattheMADbehavesmostsimilarlytoσ inthat
l
ity subsample we considerin ouranalysis(S/N<5). The
it increasingly underestimates the width with decreas-
coadded spectrum is, nonetheless, the highest-S/N ob-
ing S/N, although the relative magnitude of the bias is
servationofagivensourceandthereforealwayscontains
smaller than that observedfor both FWHM and σ , and
l
more information than a SE spectrum.
the systematic offset stays well within the measurement
uncertainties for all S/N subsamples. The MAD num-
4.1. Data-Quality Biases in Common Velocity-Width
ber distributions as a function of ∆MAD (right panel of
Characterizations
Fig. 7) are also relatively more symmetric with less ex-
We first investigate how data quality affects the tendedwingsineitherdirectioncomparedtotheFWHM
distributions of the fractional line width differences, and σ . This suggests it may be a more robust charac-
l
∆(X)/X(coadded), for both the FWHM and line dis- terization of the velocity width in low-quality data.
persion, σ . The left panel(s) in Figures 5 and 6 The trends with decreasing S/N differ between the
l
show the results for the fractional FWHM differences, otherthreepropertiesweinvestigated. TheCivlineEW
∆FWHM/FWHM. Table 2 gives the statistics of these issystematicallyunderestimatedinthelowS/Nspectra,
distributions. We find a systematic bias such that the butthedegreeofsystematicbiasiswithinthelargermea-
FWHM is overestimated in the SE spectra as compared surementuncertainties,whichisconsistentwiththefind-
to the coadded spectra. The magnitude of this bias, ingsofShen et al.(2011). Forthe Civcentroid,afactor
quantified by the median of the ∆FWHM/FWHM dis- of ∼2 increase in statistical uncertainty is seen between
tributions, is within the line width uncertainties only thehighestandlowestS/Nsubsamples,butasignificant
for the SE S/N>10 subsample, similar to other studies systematic bias is not detected for any S/N subsample,
(Denney et al. 2009; Shen et al. 2011). While the bias demonstrating it to be the most robust of all properties
is only marginally larger than the line-width uncertain- we investigated in this respect (see Shen et al. 2016, in
ties for the full sample and both subsamples with SE prep., for similar results using this sample). The kurto-
S/N<10, the distribution HIPR width, i.e., the scatter, sis of the Civ line, however, is the least robust, which
increasesbyafactoroftwofromhightolowS/Nandhas is not altogether surprising given its construction from
a significant asymmetry that suggests very large biases relatively higher moments of the line profile. The for-
are possible, much larger than the formal measurement mal measurement uncertainty only increases marginally
uncertainties, for some FWHM measurements. Inspec- with decreasing S/N, but there is a statistically signifi-
Biases Discovereddue to Low S/N Spectra 7
Fig.5.— Histograms of the fractional differences between coadded and SE Civ emission-line width measurements, FWHM (left) and
σl (right). The histograms are color-coded by data quality as shown inthe legend (note: the S/N<5 sub-sampleis contained within the
S/N<10 subsample). The similarly color-coded pairs of lines in the small top panels are centered on the median of each data quality
distribution,giveninTable2,andtherangecovered correspondstothedistributionmedian±themedianfractionaluncertainty givenin
Column 5 of Table 1. An increasing bias is seen for lower S/N subsamples that is encompassed within the statistical uncertainties at all
S/Nlevelsforσl butonlyforS/N>10fortheFWHM.
Fig.6.— Distribution of data-quality-related biases in the line width measurements. The left (right) panel shows the SE S/N as a
functionofthe fractionaldifference between thecoadded andSEFWHM (linedispersion,σl)of theCivemissionline. Thevertical lines
show the median velocity width difference of each histogram with the samecolor shown inFigure5 andshown inthe legend, and length
ofthelineswithinthelegendrepresentstheHIPRrangeofeachrespectivedistribution.
cant,>3σ,systematicbiasin∆KurtosisforallS/Nsub- S/N>10subsamplebutstillwithin∼1.5σ forlowerS/N,
samples we investigate. This bias improves somewhat demonstratingittobeamorerobustwaytocharacterize
when we characterize the Civ profile by the FWHM/σ the Civ profile than the kurtosis.
l
ratio. The measurement uncertainties increase by the Wealsoinvestigatethepossibledependenceoftheline-
same amount as the line width uncertainties — a factor widthdifferencesonotherlineproperties. Figure8shows
of ∼2−3 between the S/N>10 and S/N<5 subsamples the dependence of ∆FWHM (top panels) and ∆σ (bot-
l
—asexpectedbyconstruction,andtheshapeissystem- tom panels) on the Civ EW (left), kurtosis (middle),
atically overestimated in lower S/N spectra. This bias andthe FWHM/σ ratio(right). We performedaformal
l
is within the 1-σ measurement uncertainties of only the linear-regressionanalysisonthedependenciesusingLIN-
8
Fig.7.—Left: SameasFigure5butfortheMAD.Right: SameasFigure6butfortheMAD.
MIX ERR (Kelly 2007) and quantify the results with a population is dominated by the lowest S/N subsample,
Spearman rank order test. We evaluate the significance butstillincludessomeobjectswithreasonablyhighS/N.
of any correlations using the Spearman rank correlation Weseparatethesetwopopulationsinthemiddlepanel
coefficient, r , the probabilitythata correlationis found ofFigure9bycolor-codingthembytheir deviationfrom
s
bychance,P ,andtheformaluncertaintiesontheslope havingthesameshapemeasurements. Thebottompanel
ran
of the regression fit. of Figure 9 shows this same population division in the
The only statistically significant trend with ∆FWHM ∆σ –coadded Civ shape parameter space (same as the
l
is with the FWHM/σ ratio, but the correlation slope is bottom right panel of Figure 8). This division demon-
l
consistent with a slope of zero within the 3σ level. The stratesthattheobservedtrendisduetoobjectsforwhich
correlationappears primarily driven by the large scatter theCivprofileisnotaccuratelycharacterizableoncethe
seen only at small values of the FWHM/σ ratio. Di- S/N is degraded, even marginally, as we see deviations
l
rect inspection of the data (see, e.g., Figure 3) suggests of objects from all S/N subsamples, but this is a prob-
that the main driver for the systematic overestimation lem for only some quasars, which leads to the relatively
of the FWHM in lower S/N data is an underestimation larger scatter for smaller FWHM/σ ratios.
l
of the emission line peak due to noise. This is also con- Inspection of individual cases suggests that this bias
sistent with the findings of Denney et al. (2009) for Hβ (andthereforethepopulationseparationwithshape)oc-
FWHM measurements. With Civ, however, additional curswhenthewingsoftheemissionlinebecomemischar-
systematics contribute at low S/N in cases where ab- acterizedbecause ofcontaminationfromthe noiseof the
sorption cannot be accurately characterized. The peak continuum. The predominant effect is that the profile
and/or half-maximum flux width can thus be under- or defined by the GH polynomial fits becomes truncated at
over-estimated,onacase-dependentbasis,leadingtoad- artificiallylowervelocitiesthaninferredfromthehigher-
ditionaldispersioninthe∆FWHMdistributionthatmay S/N coadded spectrum. It is also possible that the con-
obscure other more subtle trends. tinuum level is more accurately characterized in higher
The trends in Figure 8 between ∆σ and the other S/N data, leading to lower overall accuracy of the pro-
l
Civ line properties are all statistically significant and file fit in the SE spectrum as compared to the coadded.
haveregressionfit slopesthatdeviate fromzeroby more This former effect can clearly be seen in the example
than 3σ. There does not appear to be any strong de- spectra shown in the left panels of Figure 3. Another
pendence on data quality — all data quality subsamples possible contributor to artificially truncated profile fits
followthesametrends. Wefocusadditionalattentionon is blending of the Civ wings with the red shelf of Civ.
the correlation with the FWHM/σ ratio because is has The profiles most affected by premature truncation due
l
thehighestsignificanceandthesmallestscatter. Wefirst to both noise and blending are those with small values
investigatepossiblesystematicdifferencesbetweenshape of the shape parameters, which corresponds to the pro-
measuredfromthecoaddedversusSEspectrum. Thetop files that are very ‘peaky’ with strong narrow velocity
panelofFigure9suggestsobjectscanberoughlydivided coresandverybroadwings. Thisbiasislikelythedriver
into (i) objects along the line of equal SE and coadded forthe trends between ∆σ and the other line properties
l
Civ shape, regardless of S/N, and (ii) a cloud of points shown in Figure 8, as well.
with significantly different SE and coadded shape mea-
surements, although there are points scattered between 5. SUMMARY
the two groups for low values of the coadded shape, and
We have investigated data-quality related statisti-
the two groups merge for large shape values. The latter
cal uncertainties and systematic biases in spectroscopic
Biases Discovereddue to Low S/N Spectra 9
Fig. 8.—Civlinewidthdifferencesasafunctionofother Civemissionlineproperties. Thetop(bottom) panelsshowresultsbasedon
the FWHM (linedispersion, σl). Theleft, middle, and rightpanels show the dependence of the difference on the Civ EW, kurtosis, and
shape(FWHM/σl),respectively. Thepointsarecolor-codedbythevaryingdataqualityofeachsubsample: S/N>10(orange),10<S/N<5
(blue),andS/N<5(green). Thesolidblacklinesshowthebestfitlinearregressionfit. TheSpearmanrankcorrelationcoefficient,rs,and
theprobabilitythatacorrelationisfoundbychance, Pran,aregivenineachpanel.
properties measured for high-redshift quasars. We have for a different sample suggest that the FWHM in low
been particularly interested in properties of the Civ S/N data may be systematically underestimated when
emission line, as this line is of interest for high-redshift the profiles are described by multi-Gaussian fits, so de-
BH-massestimates. Thisinvestigationwasonly possible tails of the bias may depend on the specific functional
because of the availability of spectroscopic monitoring form used to fit the data.
data taken by the SDSS-RM Project. Taken individu-
ally, these spectra are representative of typical survey- LineDispersion— Biasesinσl atlowS/Narelessthan
thoseinthe FWHM andscalewith the statisticaluncer-
quality data; however, coadding produces a higher S/N
tainty. When present, underestimation of σ is caused
spectrum,whichcanbeusedtomakedirectcomparisons l
mainlybytheinabilitytoaccuratelyfittheemissionline
of the measurements of spectral properties between low
wings in the presence of a noisy continuum. As a result
and high-S/N spectra.
Civ profiles with ‘peaky’ cores and extended wings are
Our analysis shows that the statistical measurement
likely to be biased more significantly than ‘stumpy’ or
uncertainties of all the Civ velocity width characteriza-
‘boxy’ profiles without extended wings (Figs. 8 and 9).
tions we consider (FWHM, σ , and MAD) increase sig-
l
nificantly, by a factor of 2−3, when going from high to
MAD— The systematic bias in the MAD measure-
low quality data (see Table 1, Columns 4 and 5, and
ments was relatively smaller than for the FWHM and
Fig. 4). The statistical uncertainty in the BH-mass es-
σ . The bias was also always well within the statistical
l
timates, which depend on the line width squared, are
uncertainties, and the distribution of ∆MAD measure-
therefore a factor of two larger than this. We also find
mentsremainsrelativelysymmetricandcentrallypeaked
the following systematic trends for the line-width char-
with decreasing S/N (see Fig. 7).
acterizations we consider:
These trends of FWHM and line dispersion measure-
FWHM— At low S/N, a systematic overestimation of ments with S/N are consistent with the results for Hβ
the Civ FWHM measurements is introduced, although fromsimilaranalysespresentedby Denney et al.(2009),
itisnotsignificantlylargerthanthemeasurementuncer- but that study did not investigate the MAD. We con-
tainties,onaverage. Theobservedbiascanbeattributed clude here that the MAD is the most reliable measure
to inaccuracies in characterizing the emission-line peak of the velocity width for low-quality data. Nonetheless,
fluxlevelinnoisydata(seeFig.6andTable2). Unchar- further analysis is needed to investigate how good of a
acterized absorption can exacerbate the FWHM biases proxythis characterizationis for the virialBLR velocity
(see also,Assef et al. 2011; Denney et al. 2013), and the (see Peterson et al. 2004), and SE BH mass scaling rela-
systematic bias can be severe in some cases. Interest- tionshipshavenotyetbeen developedandcalibratedfor
ingly, similar S/N investigations into potential biases in this characterization.
FWHM measurements described by Shen et al. (2011) Wealsostresstothereaderthatthe presentstudyhas
10
only been focused on biases due to data-quality consid-
erations. We make no preference for which line-width
characterization is a better proxy for the reverberating
BLRvelocitydispersionthattracesthegravitationalpo-
tential of the BH. The FWHM is often preferred be-
cause it is more simple to measure and less suscepti-
ble to the subjectiveness of deblending procedures. On
theotherhand,recentstudies(Assef et al.2011;Denney
2012; Denney et al. 2013) have demonstrated that σ is
l
less biased than FWHM for estimating Civ BH masses,
which is least partially attributable to the presence of
non-variable flux contributions to the Civ emission line
and/oracontinuumcolortermthatareyetunaccounted
for in Civ-based BH mass scaling relation calibrations
(see also Rafiee & Hall 2011a, for similar Mgii trends,
and Peterson 2014, for additional discussions).
We are grateful for the editorial contributions to this
work from C. S. Kochanek. KDD is supported by an
NSF AAPF fellowship awarded under NSF grant AST-
1302093. KH acknowledges support from STFC grant
ST/M001296/1. WNB acknowledges support from NSF
grant AST-1516784. LCH thanks Carnegie Observato-
ries for providing telescope access and acknowledges fi-
nancialsupportfromPekingUniversity,the KavliFoun-
dation, the Chinese Academy of Science through grant
No. XDB09030102 (Emergence of Cosmological Struc-
tures) from the Strategic Priority Research Program,
and from the National Natural Science Foundation of
China through grant No. 11473002. BPM is grate-
ful for support from NSF grant AST-10008882. Fund-
ing for SDSS-III has been provided by the Alfred P.
SloanFoundation,theParticipatingInstitutions,theNa-
tional Science Foundation, and the U.S. Department of
Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/. SDSS-III is managed by the
Astrophysical Research Consortium for the Participat-
ing Institutions of the SDSS-III Collaboration including
the University of Arizona, the Brazilian Participation
Group, Brookhaven National Laboratory, University of
Cambridge, Carnegie Mellon University, University of
Florida, the French Participation Group, the German
Participation Group, Harvard University, the Instituto
Fig.9.—TrendsbetweentheCivshapeparameter(FWHM/σl) de Astrofisica de Canarias, the Michigan State/Notre
andthecoadd−SElinedispersiondifferences. Thetoppanelcom-
Dame/JINA Participation Group, Johns Hopkins Uni-
parestheSECivlineshapemeasurementstothosemeasuredfrom
thecoaddedspectra;colorsrepresentdifferentS/Nsubsamplesand versity, Lawrence Berkeley National Laboratory, Max
arethe sameas inFigure8. Themiddlepanel isthe same as the Planck Institute for Astrophysics, Max Planck Insti-
top panel, except thecolor coding now reflects the divisionof ob-
tuteforExtraterrestrialPhysics,NewMexicoStateUni-
jectsintotwopopulations: theblack(red)pointsrepresentobjects
forwhichtheSEshapeis(isnot)roughlyconsistentwiththecoad- versity, New York University, Ohio State University,
dedshape. Theblack points aredefined by objects withinthe 1σ PennsylvaniaStateUniversity,UniversityofPortsmouth,
scatter of having the same shape (black solid line), where 1σ is Princeton University, the Spanish Participation Group,
definedfromonlypoints belowthisrelation. Allotherobjects are
UniversityofTokyo,UniversityofUtah,VanderbiltUni-
shown in red. The bottom panel is the same as the bottom right
panel of Figure 8 but uses the same color coding as the middle versity,UniversityofVirginia,UniversityofWashington,
panel. and Yale University.
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