Variability Selected Low-Luminosity Active Galactic Nuclei in the 4 Ms Chandra Deep Field-South

1.6 MB·English

by  M. Young

Draftversion January24,2012
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
VARIABILITY SELECTED LOW-LUMINOSITY ACTIVE GALACTIC NUCLEI IN THE 4 MS CHANDRA
DEEP FIELD-SOUTH
M. Young1,2, W. N. Brandt1,2, Y. Q. Xue1,2, M. Paolillo3, D. M. Alexander4, F. E. Bauer5,6, B. D. Lehmer7,8, B.
Luo9, O. Shemmer10, D. P. Schneider1,2, C. Vignali11
Draft version January 24, 2012
ABSTRACT
2 The 4 Ms Chandra Deep Field-South (CDF-S) and other deep X-ray surveys have been highly
1
effective at selecting active galactic nuclei (AGN). However, cosmologically distant low-luminosity
0
AGN (LLAGN) have remained a challenge to identify due to significant contribution from the host
2
galaxy. We identify long-term X-ray variability (∼month–years, observed frame) in 20 of 92 CDF-S

n galaxies spanning redshifts z ≈ 0.08 − 1.02 that do not meet other AGN selection criteria. We
a show thatthe observedvariability cannotbe explainedby X-raybinary populations orultraluminous
J X-ray sources, so the variability is most likely caused by accretion onto a supermassive black hole.

0 The variable galaxies are not heavily obscured in general, with a stacked effective power-law photon
2 index of Γ ≈ 1.93± 0.13, and are therefore likely LLAGN. The LLAGN tend to lie a factor
stack
of ≈6–80 below the extrapolated linear variability-luminosity relation measured for luminous AGN.

] This may be explained by their lower accretion rates. Variability-independent black-hole mass and
O
accretion-rate estimates for variable galaxies show that they sample a significantly different black-
C hole mass-accretion rate space, with masses a factor of 2.4 lower and accretion rates a factor of 22.5
. lower than variable luminous AGN at the same redshift. We find that an empirical model based on
h
a universal broken power-law PSD function, where the break frequency depends on SMBH mass and
p
accretionrate, roughly reproduces the shape, but not the normalization,of the variability-luminosity
-
o trends measured for variable galaxies and more luminous AGN.
r Subject headings: galaxies: active — X-rays: galaxies
t
s
a
[ 1. INTRODUCTION 2003;Goncalves et al. 2008) andthe lengths ofrelativis-

ticjetsandradiolobes(e.g.,Scheuer1995;Blundell et al.
1 Observations show that all nearby galaxies with a
1999) suggest that the episodic lifetime of luminous ac-
v massive bulge component host supermassive black holes
tivity is similar to the total lifetime, implying that a
1 (SMBHs) (e.g., Ferrarese & Ford 2005; Gu¨ltekin et al.
SMBH is triggeredto the luminous AGN phase no more
9 2009). SMBHs accreting near the Eddington limit
than a few times. SMBHs therefore spend significant
3 (L/L ∼ 0.1–1) are visible as luminous active galac-
4 tic nuEcdledi (AGN) that often outshine their host galaxies. amounts of time in quiescent or low-activity phases,
1. Models of AGN lifetime, constrained by observed Ed- which may contribute up to ∼20% of overall SMBH
growth (Hopkins & Hernquist 2009). A SMBH accret-
0 dington ratio distributions, suggest that SMBH growth
ing at lower rates (L/L ≪ 0.1) will appear as a
2 is dominated by this luminous phase, lasting ∼ a few × Edd
1 108 years (e.g., Marconi et al. 2004; Shankar et al. 2004; low-luminosity AGN (LLAGN). LLAGN share several
properties with more luminous AGN, including similar
: Hopkins & Hernquist 2009).
v X-rayspectralshapes(e.g.,Younes et al.2011)andsim-
Observations including constraints on the sizes of
i ilar radio-loud fractions and luminosity-dependent, in-
X ionized “bubbles” around quasars (e.g., Jakobsen et al.
trinsic X-ray to optical flux ratios (e.g., Maoz 2007). A
ar 1Department of Astronomy & Astrophysics, 525 Davey Lab, morecompletecensusofLLAGNisimportantforunder-
The Pennsylvania State University, UniversityPark, PA 16802, standingSMBHaccretionhistory,buttherelativesignif-
USA icance of the host galaxy in LLAGN makes a full census
2InstituteforGravitationandtheCosmos,ThePennsylvania
of accretion activity a challenge.
State University,UniversityPark,PA16802, USA
3Dipartimento di Scienze Fisiche, Universita‘ Federico II di Deep X-ray surveys have been effective at selecting a
Napoli,ViaCinthia,80126Napoli,Italy wide variety of AGN, including luminous, unobscured
4DepartmentofPhysics,UniversityofDurham,SouthRoad, AGN as well as faint and/or obscured AGN (e.g., see
Durham,DH13LE,UK
5Pontificia Universidad Cat´olica de Chile, Departamento de Brandt & Hasinger 2005, for a review). X-ray selection
Astronom´ıayAstrof´ısica,Casilla306,Santiago22,Chile criteria usually include cuts on X-ray luminosity and
6SpaceScienceInstitute,4750WalnutStreet,Suite205,Boul- X-rayspectralshape. Multi-wavelengthdata further aid
der,Colorado80301 X-rayselectionbyallowingselectionvia,forexample,ex-
7The Johns Hopkins University, Homewood Campus, Balti-
cess X-ray emission compared to what is expected from
more,MD21218,USA
8NASA Goddard Space Flight Centre, Code 662, Greenbelt, opticalflux (e.g.,Hornschemeier et al.2003) or radiolu-
MD20771, USA minosity (e.g., Alexander et al. 2005).
9Harvard-SmithsonianCenterforAstrophysics,60GardenSt. The above methods have been successful in select-
Cambridge,MA02138USA
10DepartmentofPhysics,UniversityofNorthTexas,Denton, ing a wide variety of AGN, but nevertheless miss cer-
TX76203,USA tain populations, such as very heavily obscured AGN
11Universita diBologna,ViaRanzani1,Bologna,Italy and LLAGN (e.g., Bauer et al. 2004; Alexander et al.
2
2005;Lehmer et al. 2008). While heavilyobscuredAGN 10−17 ergs cm−2 s−1, with multi-wavelength coveragein
can often be selected in the IR (e.g., Houck et al. 2005; more than 40 bands from the radio to the UV. Source
Martinez-Sansigre et al. 2005; Alexander et al. 2008), candidatesaredetected usinga10−5 false-positiveprob-
the spectral energy distributions (SEDs) of LLAGN are ability threshold in wavdetect (Freeman et al. 2002)
likelydominatedbythehostgalaxyinotherbands. Even and are then pruned using a binomial no-source prob-
in X-rays, X-ray binaries, ultraluminous X-ray sources, ability (see Appendix A2 of Weisskopf et al. 2007) P
and hot gas will provide significant contributions to the < 0.004 to obtain a more conservative list of 740 main-
overall power output. Simulated Chandra observations catalog sources, all of which are consistent with being
ofnearbylow-luminositySeyfertnucleiartificiallyshifted point sources. Source extraction and photometry were
to z ∼0.3 show that LLAGN would exhibit X-ray lumi- conducted with acis extract (AE; Broos et al. 2010).
nosities,spectralshapes,andX-ray-to-opticalfluxratios AE models Chandra’s High Resolution Mirror Assem-
consistentwiththoseofnormaloropticallybright/X-ray bly point spread function (PSF) using the MARX ray-
faint galaxies (Peterson et al. 2006). By relying on such tracingsimulator.12 ThePSFmodelisusedtogeneratea
criteria, deep X-ray surveys may be underestimating polygonalextractionregionfor eachsource that approx-
AGN fractions. imates the ≈90% encircled energy fraction (EEF) con-
Variability potentially provides a useful indicator of tour of a local PSF measured at 1.497 keV. For <6% of
whether an extragalactic X-ray source, classified as a the candidates, the sources are crowded (i.e., the polyg-
galaxy by other means, harbors an AGN. Variability is onal source regions overlap) and smaller extraction re-
a defining characteristicof AGN and has long been used gions that are as large as possible without overlapping
asanAGNselectiontechnique(e.g.,van den Bergh et al. (40 − 75% EEF) are used. The background is calcu-
1973). Numerous studies haveusedopticalvariabilityto lated from regions that subtract the contribution from
select AGN from deep surveys such as the 1 Ms CDF-S, the source of interest and its neighboring sources; the
the Subaru/XMM-Newton Deep Field, and the GOODS regionsaretypicallyafactor≈16largerthanthesource-
North and South Fields (e.g., Trevese et al. 2008; extractionregion. AEmergestheindividualobservations
Morokuma 2008; Villforth et al. 2010; Sarajedini et al. to estimate aperture-corrected, background-subtracted
2011, respectively). Spectroscopic observations of the 1 counts and the 1σ (asymmmetric) upper and lower sta-
Ms CDF-S (Boutsia et al. 2009) found that 17 of 27 op- tistical errors (Gehrels 1986). In this paper, we will use
tical variability-selected objects were broad-line AGN; 9 thestandardX-rayphotometricbands: 0.5–2keV(soft),
(5) AGN would have been missed if selected by color 2–8 keV (hard), and 0.5–8 keV (full).
(X-ray selection). Though most sources have a relatively small number
Similarly, UV variability has been used successfully of counts (median net counts ≈ 77), a roughestimate of
to identify LLAGN in galaxies with low-ionization nu- source spectral shape can be made by relating the band
clearemission-lineregions(LINERs). LINERshavebeen ratio (i.e., the ratio of the count rates in the 2–8 keV
found in the nuclei of a large fraction of nearby galax- and 0.5–2 keV bands) to an effective power-law photon
ies(e.g.,Ho et al.1997;Kauffman et al.2003),butthese index, Γ (F ∝ ν−α ≡ ν−Γ+1). For low-count sources
eff ν
regions could be ionized by either massive star clusters where Γ cannot be determined reliably, Γ is set to
eff eff
orlowaccretion-rateAGN.HST imaginghasfoundthat 1.4, the stacked (co-added) spectrum of all sources in
∼25% of LINERs are associated with compact (. few the CDF-S (Tozzi et al. 2001; Xue et al. 2011), which is
pc) UV sources (Maoz et al. 1995; Barth et al. 1998). A consistent with the unresolved spectrum of the cosmic
studyofLINERswithcompactnuclearUVsourcesfound X-ray background(Hickox & Markevitch 2006).
significantvariabilityin15of17,indicatingthe presence Of 740 X-ray sources, 716 (96.8%) contain matches
of an AGN (Maoz et al. 2005). in at least one of seven optical/near-infrared/radio
Deep X-ray surveys are able to detect variabil- (ONIR) catalogs: (1) the ESO 2.2 m WFI R-band cat-
ity in moderate-luminosity/high-redshift AGN (e.g., alog (Giavalisco et al. 2004), (2) the GOODS-S Hub-
Almaini et al.2000;Paolillo et al.2004;Papadakis et al. ble Space Telescope (HST) version r2.0z z-band catalog
2008b). The4MsChandra DeepField-South(Xue et al. (Giavalisco et al.2004),(3)theGEMSHSTz-bandcata-
2011),thedeepestX-raysurveytodate,allowsaprelim- log(Caldwell et al.2008),(4)theGOODS-SMUSICcat-
inary classification of AGN on the basis of several ob- alog (Grazian et al. 2006), (5) the MUSYC K-bandcat-
servedquantities (see §2 for details). This paper utilizes alog(Taylor et al.2009),(6)theSIMPLESpitzer/IRAC
X-ray variability techniques to search for AGN missed 3.6µmcatalog(Damen et al.2011),and(7)theVLA1.4
by these criteria. With 4 Ms of exposure time spanning GHz radio catalog (Miller et al. 2008).
10.8yearsfor466good-qualitysources(see §3),variabil- Of 716 X-ray sources with multi-wavelength iden-
ity can be detected in sources with time-averagedfluxes tifications, 419 (58.5%) have spectroscopic redshift
as faint as F0.5−8keV ≈ 5×10−17 ergs cm−2 s−1. We measurements, collected from Le F`evre et al. (2004),
use a cosmology with H0 = 70.4 km s−1 Mpc−1, ΩM = Szokoly et al. (2004), Zheng et al. (2004), Mignoli et al.
0.272, and ΩΛ = 0.728 (e.g., Komatsu et al. 2011). (2005), Ravikumar et al. (2007), Vanzella et al.
2. OVERVIEWOFTHE4MSCDF-SCATALOG (2008), Popesso et al. (2009), Treister et al. (2009),
Balestra et al. (2010), and Silverman et al. (2010). A
Thedetailsofthe4MsCDF-Ssourcecatalogareavail- total of 343 (81.9%) of the 419 spectroscopic redshift
able in Xue et al. (2011); we provide a brief summary measurements are “secure”, in that they are measured
here. The 4 Ms CDF-S, constructed from 54 Chan- at & 95% confidence levels with multiple secure spec-
dra observations over 10.8 years, covers an area of 464.5
arcmin2 and reaches highest sensitivities of F0.5−2keV ≈
9.1 × 10−18 ergs cm−2 s−1 and F2−8keV ≈ 5.5 × 12MARXisavailableathttp://space.mit.edu/CXC/MARX/index.html
Variability Selected LLAGN in the 4 Ms CDF-S 3
tral features. 668 (93.3%) sources have high-quality, throughout the various CDF-S pointings. To ensure ac-
accurate (|∆z|/(1 + z) ≈ 6.5%) photometric-redshift curate variability measurements, we also require that
measurements from at least one of three photometric- eachsourcehas atleast20net counts inthe 0.5–8.0keV
redshift catalogs: Cardamone et al. (2010), Luo et al. band(i.e., at least5 counts on averageper epoch, as de-
(2010), and Rafferty et al. (2011). The positions of fined below). These quality cuts result in a total sample
primary ONIR counterparts were cross-matched with of 466 CDF-S sources: 369 classified as AGN, 92 classi-
the photometric-redshift catalogs using a matching fiedasgalaxies,and5classifiedasstarsintheXue et al.
radius of 0.5′′, resulting in a false-match probability of (2011)catalog. AlloftheseAGNandgalaxieshavemea-
.1%. Subsequent spectroscopic observations published sured spectroscopic or photometric redshifts. The 92
in the Arizona CDF-S Environment Survey (ACES; sources classified as galaxies may nevertheless contain
Cooper et al. 2012) catalog show with a blind test that anAGN,aswouldbe indicatedby X-rayvariability,and
errors on the photometric redshifts are .1%. make up the sample investigated in this paper.
The4MsCDF-SX-raysourceswereclassifiedasAGN We divide the CDF-S observations into four epochs,
by the following criteria: each containing ∼1 Ms of integration: 2000 (943.1 ks),
• High luminosities: L0.5−8keV ≥ 3 ×1042 ergs s−1, 2007 (967.7 ks), 2010a (March–May; 1015.5 ks), and
where the rest-frame luminosity has been corrected for 2010b (May–July; 944.9 ks). As in Xue et al. (2011),
Galactic and intrinsic absorption. we merged observations within each epoch and, for a
• Hard spectra: A source with Γ < 1.0 is identified givensourcepositionfromthe CDF-Scatalog,measured
eff
as a heavily obscured AGN. the source and background counts and flux over three
•HighX-ray-to-opticalfluxratios: log(F /F )> −1, observed-frame energy bands: 0.5–8 keV, 0.5–2 keV,
X R
where FX = F0.5−8keV, F0.5−2keV, or F2−8keV and FR is and 2–8 keV. A source is considered variable if the
the R-band flux. variabilityobservedbetweenobservationsisgreaterthan
• Excess X-ray emission compared to that expected that expected from Poissonstatistics, with a probability
from star formation: L0.5−8keV > 3×(8.9 × 1017 LR) thresholdof5%thatthevariabilityisduetonoisealone.
(Alexander et al. 2005), where L is the 1.4 GHz (The choice of probability threshold is discussed further
R
monochromatic luminosity in W Hz−1. below.) To check whether a source can be considered
• An indication of broad emission lines in the optical variable, we calculate the quantity:
spectrum.
Stars were classified by cross-matching X-ray sources N (x −µ)2
(using the ONIR counterpart positions) with (1) the X2 = i , (1)
σ2
spectroscopicallyidentifiedstarsinSzokoly et al.(2004), i=1 i
X
Mignoli et al. (2005), and Silverman et al. (2010); (2)
where N = 4 is the number of epochs, x is the pho-
the likely stars with stellarity indices greater than 0.7 i
ton flux (background-subtracted counts with units of
in the GEMS HST catalog (Caldwell et al. 2008); and
cm−2 s−1) in a given epoch, µ is the mean photon flux
(3) the likely stars with best-fit stellar templates in the
over all epochs, and σ2 is the error squared on the pho-
MUSYCphotometric-redshiftcatalog(Cardamone et al. i
2010), using a matching radius of 0.5′′. ton flux for the ith epoch. The photon flux is calcu-
X-ray sources not identified as an AGN or a star were lated by dividing the full-band (0.5–8.0 keV) net counts
classified as galaxies. by the exposure time and the mean effective area across
Rest-frame 0.5–8 keV luminosities are calculated for the source aperture. The Gehrels (1986) approximation
all sources. For AGN, which make up the vast major- gives the error on the net counts, which is propagated
ity of CDF-S sources, the luminosity is corrected for to obtain the error on the photon flux. Since this error
Galactic and intrinsic absorption. AGN not detected is significantly asymmetric for low-count (. 15 counts)
in the full band have an upper limit on the X-ray lu- sources,weaveragetheupwardanddownwarderrorbars
minosity based on the 3σ Poisson error on the counts. for these objects to obtain the average error σi. (The
For galaxies, the intrinsic-absorption correction and K- same method is applied in the Monte Carlo simulations
correctionsmaynotbeappropriate. Of92CDF-Sgalax- below.)
ies with “good quality” observations (see §3), 78 are not For large photon fluxes, the X2 statistic follows a χ2
detected in the hard band and have poorly determined distribution, and any source with X2 > 7.82 (for 3 de-
photon indices. All galaxies are detected in the soft- greesoffreedom)hasaprobabilityPX2 <0.05(i.e.,95%
band. We perform a stacking analysis for galaxies with confidence level) that the variability is due to random
< 150 net counts (87 of 92) following the procedure de- noise. However, at low count rates, the error on the
scribedin§5.1. TheresultingaverageΓ =1.90±0.08 photon flux is not Gaussian. Since errors in the low-
stack
gives L0.5−8keV/L0.5−2keV = 2.35. We calculate the count regime are larger than expected from a Gaussian
rest-frame 0.5–8 keV luminosity for CDF-S galaxies as distribution,theresultingX2statisticissmallerthanex-
L0.5−8keV =4πd2L×2.35×f0.5−2keV(1+z)Γstack−2. Since pected and does not follow the χ2 distribution (see Fig.
galaxyX-rayemissionistypicallyunabsorbed,wedonot 2 of Paolillo et al. 2004).
apply any correction for intrinsic absorption. We therefore constructed a Monte Carlosimulation to
determine the distribution the X2 statistic should fol-
3. TESTINGFORX-RAYVARIABILITY low for eachsource,similar to the procedurefollowedby
We perform two quality cuts before conducting vari- Paolillo et al. (2004). We first scaled the total observed
ability analysis. First, we exclude the catalog sources source and background counts for each source, obtained
withoff-axisanglesgreaterthan8′toensurethatsources fromthefull4Msobservation,tothe exposuretime and
will have sufficient coverage (>50 of 54 observations) effective area for a given epoch. This procedure gener-
4
ates the source and backgroundcounts expected in each light curves (background-subtracted count rates in the
epoch if the source and background were constant over observed-frame0.5-8 keV band vs. MJD) representative
time, and it accounts for fluctuations in the background of the sample as a whole are shown in Figure 3.
that will affect low-count sources. To simulate the vari- TheX-rayluminositydistributionsofallCDF-Sgalax-
ance expected fromnoise, Poissondistributions werede- ies and those exhibiting significant variability are shown
fined using the expected source and background counts in Figure 4. A K-S test shows that the two samples
as the mean values. We then simulated 1,000 observa- are consistent with being drawn from the same parent
tions of each source by repeatedly drawing the expected population(P = 57%), and the variable fractiondoes
KS
counts from the Poisson distributions. For each simu- not show a significant dependence on X-ray luminosity
lated observation,we calculated the photon flux for four below L0.5−8keV ∼ 1043 ergs s−1. The possibility that
epochsandcalculatedX2 asdefinedabove. Asymmetric AGN-relatedvariabilitymaygoundetectedingalaxiesis
errorsonthesourceandbackgroundcountsareobtained discussed in §4.1.
from Gehrels (1986) and are propagated to get the er- WebrieflycompareAGNselectionbasedonvariability
ror on the photon flux. The observed X2 can then be to the following selectionmethods: (1) X-ray luminosity
comparedto the simulateddistributionto determine the cuts, (2) the X-ray-to-optical flux ratio, and (3) excess
probability PX2 that the observed variability is due to X-rayemissioncomparedtothatexpectedfromstarfor-
Poisson noise. Spurious sources of variability are negli- mation, based on the radio luminosity. Figure 5 shows
gible, since effective exposure maps are calculated sep- thefractionofvariablesourcesvs. X-rayluminosity. Be-
arately for each observation, taking into account issues low L0.5−8keV = 1042 ergs s−1, a luminosity cut often
such as vignetting, CCD gaps, bad pixels, bad columns, used for AGN selection in X-ray surveys, the variable
and Chandra’s spatial- andtime-dependent quantum ef- fraction remains significant at 20−30%. Of 64 CDF-S
ficiency degradation. galaxies with L0.5−8keV < 1042 ergs s−1, 17 (≈27%) are
While using a more conservative P = 1% on our variable.
crit
datasetwouldresultinfewerfalsepositives,itwouldalso AGN selection via the X-ray-to-optical flux ratio is
eliminate a similar number of truly varying sources. For demonstrated by the R-band magnitude vs. X-ray
example,in the sample of92galaxies,P = 5%results flux plane in Figure 6 (cf. Figure 16 in Xue et al.
crit
in 20variable sources(see §4), ofwhich 4.6are expected 2011). Sources classified as AGN, galaxies, and stars
to be false positives. Reducing P to 1% results in 13 in Xue et al. (2011) are marked as small red circles,
crit
variable sources, of which 0.9 is expected to be a false largerblack circles and blue stars,respectively. Variable
positive. So while the more conservative critical value sources are marked with filled symbols. The optically
eliminates ≈4 false positives, it also eliminates ≈ 3−4 bright, X-ray faint region, typically thought to exclude
truly varying sources. The PX2 values listed in Table 2 AGN(OBXF; FX/FR <−2;Hornschemeieretal. 2003)
can be used to screen the sources further as desired. contains27galaxies. Ofthese,6(22%)arevariable,with
4. GALAXIESWITH AGN-LIKEVARIABILITY X-AraGyNlummainyoaslistioesbespsaenlencitnegdlobgasLed0.5o−n8kaeVco≈mp3a9r.7is–o4n1.b4e.-
Ofthe369CDF-SsourcesclassifiedasAGNthatmeet tween X-ray and radio luminosities (Xue et al. 2011).
both the off-axis angle (θ < 8′) and count (total net TheradioluminositycanbeusedtopredicttheX-raylu-
counts>20)requirements,50.1%exhibitsignificantflux minosity in star-forming galaxies (e.g., Alexander et al.
variability(PX2 <0.05)on∼month–yeartimescales. For 2005, and references therein), so sources with excess
the 178 AGN with more than 100 counts, 74.2% exhibit X-ray emission may be classified as AGN. Of the 17
significant variability. The basic diagnostic plot in Fig- CDF-S galaxies with radio detections (none of which
ure 1 shows the rise in the AGN variable fraction with have excess X-ray emission), three (18%) are variable.
total net counts. The plot demonstrates that, given suf- These objects may have excess radio emission due to
ficientcountstodetectit,variabilityisanear-ubiquitous strong radio cores rather than star formation.
property of faint, X-ray selected AGN, even in the case
4.1. Measuring Variability Strength
of significant obscuration: ≈70% of the CDF-S sample
consists of obscured AGN (Xue et al. 2011), and 47.5% Due to the generally limited photon statistics of the
(51.5%) of obscured (unobscured) AGN are significantly CDF-S galaxy sample, most variable sources must be
variable. The variable fractions are consistent with the strongly variable to be detected. Significantly vari-
results from the 1 Ms CDF-S (Paolillo et al. 2004), al- able galaxies show maximum-to-minimum flux ratios
though obtained with different temporal sampling and R ≈ 1.5–9.3 (median = 4.1) over the observed
max/min
down to much fainter fluxes. 10.8-year time frame. The smallest max-to-min ra-
In sources classified as galaxies, the variable fraction tio (1.5) was measured for 033246.77−274212.7(XID =
is significant at low counts and equals that of AGN at 616), a source with &500 counts. For most galaxies, to-
higher counts (Figure 1). Table 1 describes the columns tal net counts are too low (. 100) to detect variability
of Table 2, which lists the attributes of the 20 variable below a factor of 2–3.
and 72 non-variable galaxies. (Variability properties of Toaddresswhetherthevariablegalaxymax-to-minra-
CDF-S AGN will be covered in the forthcoming Pao- tios sample the average AGN population or only the
lillo et al., in preparation.) The luminosity-redshift dis- highly variable “tip of the iceberg,” we ran a Monte
tribution of variable and non-variable galaxies is shown Carlo simulation. The procedure assumed that the en-
in Figure 2; almost all lie below z ∼ 1. Spectroscopic tire galaxy population is significantly variable andsimu-
redshifts are available for 18 of 20 variable galaxies and latedthe variability expected over10.8 yearsof observa-
for 61 of 72 non-variablegalaxies. Photometric redshifts tion. Following the procedure in Vaughan et al. (2003),
are available for the remaining sources. Six example we used the Timmer & Koenig (1995) algorithm to sim-
Variability Selected LLAGN in the 4 Ms CDF-S 5
ulate 5,000 light curves based on the mean and variance sistentwithnoiseratherthanduetointrinsicsourcevari-
of the flux for each of the 92 CDF-S galaxies. For non- ability;duetostatisticalfluctuations,theexcessvariance
variablegalaxies,the measuredvariancerepresentsnoise may also be negative in this case. The σ2 values are
nxs
inthemeasuredlightcurve,whichgivesanupperlimitto listed in Table 2. Note that the variability amplitude is
thevariabilitythatcouldbepresent. Thealgorithmpro- calculated for observed-frame energy bands. The vari-
duces a random, continuously sampled light curve from able galaxies cover a redshift range z = 0 − 1, so the
agivenpowerspectraldensity(PSD)function, whichwe excessvariancewillbe measuredover0.5−8keVatz =
assumed to be described by a broken power-law, where 0to1−16keVatz =1. Variabilitystrengthisknownto
the break frequency depends on SMBH mass and accre- depend on energy in some nearby Seyfert galaxies (e.g.,
tion rate (McHardy et al. 2006). Since the break fre- Ark120,MCG–6-30-15,andIZw1;Vaughanetal. 2004,
quency lies outside the range of timescales sampled for Vaughan & Fabian 2004, and Gallo et al. 2007, respec-
most variable galaxies (see §6.3), we simplify the model tively), while in others, variability remains nearly con-
to a power-law (P(f) ∝ fβ) with index β = −1, as is stant with energy (e.g., Ton S180 and NAB 0205+024;
typical for the low-frequency (long-timescale) PSDs for Vaughanetal. 2002andGalloetal. 2004,respectively).
nearby Seyferts (e.g., Vaughan et al. 2003). The time In the former cases, the change in variability strength is
units of the light curves are determined by the mini- small, with a < 10% difference from 0.5 to 10 keV, so
mumandmaximumtimescalesinputintothesimulation; thebandpasseffects atredshifts z =0−1shouldremain
the light curve durations are adjusted according to each small.
source’s redshift. We calculate the statistical error (i.e., measurement
We resampled/rebinned the light curve using the error) on the excess variance following Equation 11 of
CDF-S observing pattern and add Poisson noise to the Vaughan et al. (2003).
simulated light curve to account for measurement error.
Thefullsimulatedlightcurveswasmadefivetimeslonger 2 2
2 σ2 σ2 2σ
tthimanestchaelessammupclhedlorneggieorntihnanortdheorsteosparmopdluecdebvyartihateiodnatoan. err(σn2xs)=vuu rN · x¯er2r! +s Nerr · x¯nxs
This reproducesthe effectthat verylong-timescale(low- u
t  (3)
frequency) variations have on variability measured over
shorter timescales (i.e., “red noise leak”). The large errors on σn2xs (Table 2) are due to the small
Wecomparethesimulateddistributionofmedianmax- numbers of counts observed for most sources (e.g., 12 of
to-min ratios, where the median is calculated over 5,000 20 variable galaxies have . 100 net counts); four vari-
trials for each galaxy, to the observed distribution for able galaxies with net counts . 50 have excess variance
variablegalaxiesinFigure7. AK-Stestshowsthatthese measurements completely dominated by statistical un-
twopopulationshavea0.2%chanceofbeingdrawnfrom certainty [σn2xs . err(σn2xs)]. Nevertheless, most variable
the same parent population. Note that the simulated galaxieshaveexcessvariancemeasuredatthe &1σ level.
distribution (black histogram) illustrates an upper limit The excess variance contains additional sources of un-
to the variability that could be present in the CDF-S, certainty aside from statistical error: (1) random scat-
resulting in a lower limit on the detectable fraction of ter intrinsic to the stochastic nature of AGN variabil-
sources. The CDF-S detects at least ≈18% of sources ity (Vaughan et al. 2003) and (2) uncertainty and sys-
withmax-to-minratios>2andatleast≈57%ofsources tematic bias due to sparse sampling of the light curve.
with max-to-min ratios > 4. A significant fraction of The sparse pattern of CDF-S observations will lead to
non-variable galaxies may still host an AGN, but the large uncertainty in the mean flux measurement, and
variability may remain undetected due to low counts. since the measured mean will be closer to the sampled
For the galaxies exhibiting significant variability, datapointsratherthanthetruemean,thevariancemea-
we calculated the normalized excess variance (e.g., surementswilltendtobeunderestimated(Allevato et al.
Vaughan et al. 2003), which measures how strongly a in preparation). We again employ a Monte Carlo simu-
source varies in excess of the measurement error. The lation to model the uncertainty and systematic effects
excessvarianceisthe integralofasource’sPSDfunction produced by random scatter and sparse sampling.
over a given frequency range, which is defined by the We follow the same procedure described above to pro-
light curve’s duration (10.8 years, observed-frame) and duce 5,000 light curves for every variable source. The
minimum bin size (4.0 Ms,13 observed-frame). mean and variance are calculated after sampling each
simulatedlightcurvewiththeCDF-Sobservingpattern.
N N The sampling bias can be corrected by rescaling the ob-
1 1
σ2 = (x −µ)2− σ2 , (2) servedvariancebyafactorequaltotheratiobetweenthe
nxs (N −1)µ2 i Nµ2 err,i “true”inputvariance(i.e.,theobservedvarianceusedas
i=1 i=1
X X input in the simulations) and the median output vari-
where σ is the average of the asymmetric upward
err,i ance (i.e., the biased variance affected by sparse sam-
and downward measurement errors. Using the upward
pling): f =σ2 /median(σ2 ). Themedianoutput
(downward) error would overestimate (underestimate) scale meas sim
variance is calculated over all 5,000 light curves. The
the errors. Zero excess variance (σ2 = 0) would indi-
nxs amountofsystematicbiasdependsonthe frequencyand
cate that the observed count fluctuation is entirely con-
regularity of the sampling. If the sampling is regular,
the scaling factor will approach unity as the number of
13 While each CDF-S epoch totals ∼1 Ms in integration time,
samplesincreases;however,thescalingfactorwillremain
the timescale sampled is significantly longer due to the spread in
Chandra observations,ofwhichtheshortestis4.0Msforthe2007 above unity even at high sampling frequency if the sam-
epoch(Luoetal.2008). pling is irregular (Allevato et al. in preparation). The
6
slope of the PSD will also affect the sampling bias — populationoughttodominatethevariability. Inthevari-
a steeper PSD slope (i.e., β = −2 instead of β = −1) ablegalaxies,SFR rangesfrom0.04to 55M⊙ yr−1 with
will result in a larger bias for a given sampling pattern. a median of 2.2 M⊙ yr−1; M⋆ ranges from 2×107 to
Since the intrinsic PSD slopes are not known, we apply 6×1011M⊙ withamedianof1.2×1010M⊙. Wefindthat
uniform corrections assuming β = −1; however, source- all but six of 20 variable galaxies are expected to have a
to-source variations in PSD slope may be a significant larger HMXB contribution. L (SFR)/L (M )
HMXB LMXB ⋆
source of scatter in variability measurements. ranges from 0.01 to 75.8 with a median of 2.6 (Ta-
We find that the scaling factors range from f ≈ ble2). HMXBsaregenerallymorevariablethanLMXBs
scale
0.03 to 4.8, with a mean f ≈ 1.54 and a scat- (Gilfanov et al. 2004), so unless LMXBs dominate the
scale,mean
ter on f of σ ≈ 0.87. In ≈76% of the sources, X-ray output of a galaxy, we neglect their contribution.
scale,mean f
the scaling factor is greater than unity, indicating that To determine the variability expected from the
the varianceis underestimateddue to the sampling bias. HMXBs, we follow the relations in §4.2.3 of
Note that the Monte Carlo PSD is normalized by each Gilfanov et al. (2004), where the variability of the
source’s variance, which is calculated using the source’s HMXB population is roughly determined by the
light curve. Since the heavy binning could smear out galaxy’s SFR. The following relations were obtained
highfrequencyvariations,thismethodcouldresultinan from Monte Carlo simulations with a power-law HMXB
artificially smaller scaling factor. However, Allevato et luminosity function with slope α = −1.6 and a cut-off
al.,inpreparation,findasimilarlysmallbias(f <2) luminosity at L = 2×1040 ergs s−1:
scale cut
whensamplinghigherfrequenciesforawiderangeofS/N
σ
ratios, gap lengths and sampling patterns. More impor- σrms,tot ∼0.35+−00..3150 for SFR < 5 M⊙ yr−1 (4)
tantly,the scatter onthe f factorcalculatedforeach rms,0
scale
source is large (≈ 40%−190%), so individual measure- σ
ments,evenwhencorrectedforbias,arelikelytobepoor σrms,tot ∼0.30+−00..1005 for SFR = 5–10 M⊙ yr−1 (5)
rms,0
estimates ofthe intrinsic variance. Therefore,variability
properties of CDF-S galaxies are best considered in en- σ 0.93
seexmcebslsevraartihaenrctehsa(nσo2nanin)dairveidluisatledbaisnisT.aBbilaes-2coarnrdectaerde σrrmmss,t,o0t = SFR1/2 for SFR > 10 M⊙ yr−1 (6)
nxs,corr
used for all further analysis unless otherwise noted. Here,σrms,0 isthefractionalrms(i.e.,thesquarerootof
the excess variance) expected from an individual X-ray
4.2. Comparisons with XRB and ULX Variability binary, which can be as large as 20–30% on ∼year
timescales (e.g., Gilfanov 2010), and σ is the to-
The three most likely sources of X-ray variability are rms,tot
tal variability. We take σ = 0.3 and calculate the
X-ray binary (XRB) populations, ultraluminous X-ray rms,0
upper limit on σ . In the most extreme case, we
sources (ULXs), and accreting SMBHs. In this section, rms,tot
findthatthe upper limitonvariabilityexpectedfroman
we show that the first two possibilities are not likely to
HMXB population is σ2 <0.044.
dominate the measured galaxy variability. XRB
In six galaxies, LMXBs are expected to dominate the
To examine the potential contribution of X-ray bi-
X-ray luminosity. Four of the six have log M > 10.5
nary populations to variability, we must first deter- ⋆
mine the relative contributions of low-mass X-ray bi- M⊙, andtherefore have large enoughstellar mass to fol-
naries (LMXB) and high-mass X-ray binaries (HMXB) low a σσrrmmss,t,0ot ∝ Ms−te1l/la2r law (§4.4.2 of Gilfanov et al.
to the hard (2–10 keV), galaxy-wide X-ray luminosity 2004). For the remaining two galaxies, we follow the
(L ).14 Galaxystellarmass(M )scalesthe contribu- trend in Figure 12 of Gilfanov et al. (2004). The upper
XRB ⋆
tion of (older) LMXBs, and star formation rate (SFR) limit on variability expected from an LMXB population
scalesthecontributionof(younger)HMXBs(e.g.,Equa- is σ2 <0.02.
XRB
tion 3 of Lehmer et al. 2010). M and SFR are calcu- We find that XRB populations cannot explain the full
⋆
lated for each galaxy in Xue et al. (2010) using the op- extent of the X-rayvariability for variable galaxies. Fig-
tical colors and the UV and IR luminosities. Both the ure 8 plots the distribution of σ2 for CDF-S galax-
nxs,corr
Lehmer et al. (2010) relations and the Xue et al. (2010) ies, showing that all the variable galaxies exhibit vari-
calculations adopt the same initial stellar mass function ability in excess of that expected from XRBs. The vari-
(Kroupa2001). However,sinceLehmer et al.(2010)and able galaxies have a median σ2 /σ2 ≈ 42 (with-
nxs,corr XRB
Xue et al. (2010) use different formalisms for computing outthebiascorrection,σ2 /σ2 ≈14),indicatingthat
stellar masses (Bell et al. 2003 and Zibetti et al. 2009, nxs XRB
the contribution of an XRB population to the measured
respectively, which differ primarily due to their models
variability is small.
of star formation history), we apply a correction factor
We also consider whether one or more ultraluminous
of 2.6 to the stellar masses from Xue et al. (2010). The
X-ray sources (ULXs) may dominate a galaxy’s X-ray
SFRandM values foreachvariablegalaxyarelistedin
⋆ output. The nature of ULXs is still debated, but
Table 2.
most likely involves accretion onto massive stellar black
BycomparingtheexpectedLMXBandHMXBcontri-
holes (30–100 M⊙); a few cases may involve accretion
butions to the total luminosity, we can determine which
onto intermediate mass black holes (100–300 M⊙) or
beamed emission from 10–20 M⊙ black holes. Typical
the14cWomepmareiassounretovatrhieab2i–li1t0yikneVthelu0m.5i–n8oskietiVesb,awned,libmuittbthyelicmointtinrig- luminosities span L0.5−8keV ≈ 1039–1041 ergs s−1 (e.g.,
Lehmer et al. 2006; Swartz et al. 2011). In a survey of
bution of other sources of galaxy-wide X-ray emission (hot gas,
supernovae,supernovaremnants,andO-stars),whichfadesharply 1,441 X-ray point sources in 32 nearby galaxies in the
above2keVandcanbeconsiderednegligible. Chandra archive, Colbert et al. (2004) found ULXs in
Variability Selected LLAGN in the 4 Ms CDF-S 7
19 galaxies; the contribution of one or more ULXs to a Since 14 sources have poorly determined Γ , we per-
eff
galaxy’stotalX-raypointsourceluminosityrangedfrom form a stacking analysis on all variable galaxies with
7%–87%, with a median contribution of 43%. < 150 net counts to determine an average photon index
ULXs could potentially explain nine variable galaxies for the sample. The three highest count sources (with
with L0.5−8keV < 1041 ergs s−1. However, since ULXs 199.2,275.6,and608.9netcounts)areexcludedfromthe
tend to be associated with star-forming regions (e.g., stacking analysis since they could dominate the stacked
Swartz et al. 2004) and occur more frequently in late- signal, but the results remain the same within errors if
type/irregular galaxies than in early-type galaxies (e.g., these sources are included.
Walton et al. 2011), the five variable galaxies with both FollowingtheprocedureinLuo et al.(2011),wecalcu-
L0.5−8keV <1041 ergss−1 andlate-typemorphology(see latethesoftandhard-bandcountsina3′′diameteraper-
§5.2) are more likely to host ULXs. ture for each source. The background is calculated by
OnemethodoffindingULXsistosearchforoff-nuclear averaging the counts in 1,000 randomly placed, source-
sources. We plot postage-stamp images (8′′ × 8′′) of freeapertureswithina1′-radiuscirclearoundthesource
the GOODS-S/GEMS HST V606-band for the variable position. The individual source counts are summed and
galaxies in Figure 9. The circle overplotted on each im- background is subtracted. Aperture corrections are ap-
age has a radius 1.5 times the Chandra positional erro, plied, averagedoverall the observations weightedby ex-
which is calculated at the 90% significance level. As posure time (see Luo et al. 2011 for details), before cal-
in Lehmer et al. (2006), X-ray sources offset from the culating the band ratio.
galaxynucleus by more than 1.5 times the positionaler- The stacked effective photon index for the 17 relevant
ror are considered off-nuclear. variable galaxies is Γstack ≈ 1.93±0.13, which is consis-
We find one marginally off-nuclear source: tentwiththetypicalphotonindexforlocalSeyfertgalax-
033219.27−275406.7 (XID = 269). The primary ies (Γ ∼ 1.8; e.g., Dadina et al. 2008) at the 1σ level.
optical source appears to be an early-type galaxy with Including all 20 variable galaxies, Γstack ≈ 1.82±0.08.
blendingtowardthegalaxytothelowerright,suggesting While absorption may still be present in some individ-
amerger. Bothgalaxieshavesimilarredshifts(z =0.960 ualsources,the softspectrum implied by the stackedef-
and 0.956, respectively); the first redshift is spectro- fective photon index indicates that the average variable
scopic andsecure (see §2) and the secondis photometric galaxy is not heavily obscured. The X-ray luminosities
(Xue et al.2010). The highX-rayluminosity (L0.5−8keV are therefore intrinsically low and indicate that variable
≈ 2.2×1042 ergs s−1) suggests that a ULX is likely not galaxies are most likely LLAGN.
the dominant source of X-ray emission from this galaxy.
5.2. Galaxy Morphologies
Onevariablegalaxy,033230.00−274405.0(XID=418),
waspreviouslyidentifiedasbeingoff-nuclearinthe 1Ms Postage-stamp images (8′′ × 8′′) of the GOODS-
CDF-S (Lehmer et al. 2006). With the additional data S/GEMS HST V606-band for CDF-S variable and non-
from the 4 Ms CDF-S, the X-ray source position has variable galaxies are shown in Figures 9 and 10, respec-
been refined (with reduced uncertainty) to be consistent tively, with Chandra error circles overlaid. Galaxies are
with the galaxy’s nucleus. The off-nuclear source dis- classifiedbyeyeaslate-type,early-type,irregular,orun-
cussed in the previous paragraph (XID = 269) was not determined. Mergersarealsovisuallyclassifiedbasedon
detectedinthe 1 Ms CDF-S, soitwasnotconsideredby blendingand/ortidaltailsbetweentwoormoregalaxies.
Lehmer et al. (2006). Since visual classifications are subjective and are par-
We cannot rule out that a ULX may lie too close to a ticularly unreliable for distant, poorly resolved galax-
galaxy’s nucleus to be detected as an off-nuclear source. ies, we also apply the color-magnitude relation given in
However,the possibility ofULXs inmostvariablegalax- Bell et al. (2004), where galaxies are considered part of
ies is mitigated by highX-ray luminosities and/or early- the “red sequence” (i.e., early-type morphology) if they
typemorphology,sosincewefindnoplausibleoff-nuclear are redder than (MU – MV) = -0.31z – 0.08MV – 0.51.
ULXs, we conclude that ULXs are unlikely to dominate Galaxies with bluer colors are considered part of the
the emission from variable galaxies. Accretion onto a ”blue cloud” (i.e., late-type morphology). Although the
SMBHremainsthebestexplanationofvariablegalaxies. color-magnitude diagram leads to a more objective clas-
sification scheme, there are nevertheless significant un-
5. SUPPORTINGEVIDENCEFORLLAGN certainties, both in the rest-frame magnitudes and col-
We investigate the X-ray spectral shapes, the mor- ors, and in the definition of the Bell et al. (2004) rela-
phologies, and the optical spectral classifications of the tion. Moreover, the color classification is complicated
variablegalaxiesfortwopurposes: (1)characterizingthe by the fact that many of the galaxies lie in between the
variablegalaxypopulation,and(2)determiningwhether red sequence and blue cloud, in the so-called“greenval-
their properties are consistent with those of LLAGN. ley.” In cases where the color and the visually classi-
fiedmorphologydisagree,wechooseafinalclassification,
5.1. X-ray Spectral Shape
preferring the visually classified morphologies in nearby,
As discussed in §2, Xue et al. (2011) calculate the ef- well-resolvedgalaxies,and the color classificationin dis-
fective photon index for each source based on the ratio tant and/or poorly resolved galaxies. Considering only
of count rates in the 2–8 keV and 0.5–2 keV bands (Ta- galaxies classified as early or late-type, the visual and
ble 2). For10variablegalaxiesdetectedinthe softband color classifications agree ≈54% of the time. Table 2
butnotthehardband,lowerlimitsarelisted. For4low- lists each galaxy’s morphological type as determined by
count variable galaxies detected either in the full-band, visual classification, the rest-frame magnitude and color
soft-band,orboth,noreliableeffectivephotonindexcan (from Xue et al. 2011), the color classification according
be determined, so Γ is set to 1.40. to Bell et al. (2004), and the final classification.
eff
8
Based on the final classification from Table 2, we find errorsifcalculatedusingtheexcessvarianceuncorrected
that variability does not prefer one morphology type for sampling bias (σ2 ).
nxs
over the other. Variable galaxies have 40.0+11.3% early- Since both variability and luminosity may depend on
−9.5
type morphology and 50.0+10.6% late-type morphology, other parameters,such as black hole mass and/oraccre-
−10.6 tion rate, we fit the data using sixlin.pro, an IDL pro-
compared to 23.6+5.7% and 51.4+5.7%, respectively, in
−4.3 −5.8 gram adapted from Isobe et al. (1990). A least-squares
non-variable galaxies (the errors are 1σ binomial er- bisector fit to sources with L0.5−8 keV > 1041 ergs s−1,
rors). IfweinsteadapplyonlytheBell et al.(2004)color weighted by the uncertainties in σ2 , results in
classifications, then both the variable and non-variable nxs,corr
σ2 = (25.8±2.6) L−0.62±0.06. The slope and in-
galaxies prefer late-type morphologies (80.0+6.0 % and nxs,corr 0.5−8keV
−11.5 tercept are consistent within errors if the weights are
72.2+4.6%, respectively). The M andSFRdistributions
−5.8 ⋆ not included. Large blue squares in Figure 11 show the
forvariableandnon-variablegalaxiesshownosignificant
weighted means for each luminosity bin; as expected,
difference (P > 10%).
KS these are consistent with the weighted least-squares bi-
We find that the fraction of mergers among vari-
sector. Note thatsince weightedmeans willmostclosely
ableandnon-variablegalaxiesisconsistentwithinerrors
followdatawithsmallerrorbars,theyareweightedheav-
(9.1+−130.1.6% and 20.0+−53..59%, respectively). ily downward in this log-log plot. Limiting the sample
further tosourceswithL0.5−8keV >1042 ergss−1 results
5.3. Optical Spectroscopic Classification inσ2 =(31.9±2.7)L−0.76±0.06. Theslopesareboth
nxs,corr 0.5−8keV
Most (18/20) variable galaxies have optical spec- consistentwiththeresultsofNandra et al.(1997),where
tral observations (Szokoly et al. 2004; Zheng et al. a weighted least-squares bisector fit results in σ2 ∝
nxs
2004; Mignoli et al. 2005; Ravikumar et al. 2007; L−0.71±0.0.03(Nandraetal. 1997donotgivethenormal-
Popesso et al. 2009; Silverman et al. 2010), from which 2−10keV
ization of their relation). This result is notable because
spectroscopic redshifts were determined. In all cases,
the Nandra et al. (1997) data sampled shorter (hour–
the optical spectra are classified as galaxies, showing
day)timescalescomparedtothemonths–yearstimescales
only narrow emission lines or absorption lines.
sampled by the CDF-S.
Szokoly et al. (2004) classify objects in more detail.
The slope presented in this paper is significantly flat-
Of the eight variable galaxies listed in the Szokoly et al.
ter than that found in Paolillo et al. (2004; σ2
(2004) catalog, two have typical galaxy spectra showing nxs
∝ L−1.31±0.23), which included non-varying sources.
only absorption lines. The remaining six are classified 0.5−8keV
as having low-excitation emission lines consistent with We choose not to include upper limits for non-varying
H II region-type spectra. These objects would be classi- sources in our analysis because the assumptions under-
fied as normal galaxies based on the optical data alone lying survival analysis, which have been successfully ap-
asthe presenceofthe AGNcannotbeestablished. How- plied to deal with censored data in other astronomical
ever,oneofthese,033222.78−275224.2(XID=312),has situations, do not apply here because: (1) the excess
sufficient signal-to-noisein the optical spectrum to mea- variance measurements of most sources lie near the de-
sure line ratios. This object is classified as a LINER by tection limit, (2) a large percentage of sources do not
have detected variability (≈50% of AGN and ≈78% of
Szokoly et al. (2004) via the line ratio diagnostics given
galaxies), and (3) a significant percentage of sources
by Ho & Sargent (1993).
with no detected variability, especially those classified
6. GALAXYVS.AGNVARIABILITY as galaxies, may truly not be variable (i.e., σn2xs ∼ 0).
By not including censored data in this paper’s measure-
6.1. The Variability-Luminosity Anti-Correlation
ments, we likely bias the measured slopes and possibly
In this section, we investigate how galaxy variability thesignificanceofthe anti-correlation. Nevertheless,the
compares to AGN variability. We first confirm a signifi- variability-luminosityanti-correlationhas been observed
cant anti-correlation between excess variance and X-ray to follow a model based on SMBH mass and accretion
luminosity among AGN, as seen in previous work (e.g., rate (e.g., Papadakis et al. 2008b), suggesting that the
Barr & Mushotzky 1986; Lawrence & Papadakis 1993; anti-correlationis real, though probably not linear. The
Nandra et al. 1997; Hawkins 2000; Paolillo et al. 2004). model is discussed further in §6.3.
The anti-correlation is plotted in Figure 11 for signifi- Wecheckforotherpotentialbiasesthatmayaffectthe
cantly variable sources as σn2xs,corr vs. L0.5−8keV. The luminosity-variability anti-correlation. The log-log plot
excess variance includes the bias correction discussed in of Figure 11 has the disadvantage of “hiding” sources
§4.1. The rest-frame X-ray luminosities are calculated with negative σ2 values. Sources with low flux val-
nxs,corr
differentlyforAGNandgalaxies,asdescribedin§2. The ues, and hence higher scatter in σ2 will therefore
nxs,corr
Spearmanrankcorrelationcoefficient(ρs=−0.44)shows appear to have stronger variability, since the σ2
thecorrelationissignificantatP ≈10−9(5.9σ)forAGN nxs,corr
s values scattered to negative values will be hidden. To
only (red circles). The correlation increases in signifi-
check for this bias, we remove high scatter sources with
cance to Ps ≈ 8 × 10−12 (6.4σ) if all variable sources err(σ2 ) > 0.1, excluding all but 38 sources, and
ianbgovtehoLs0e.5c−la8ksesVifie=d1a0s4g1aelragxsiess−(1blaarcekccoinrscildeseraendd, isntcalrusd)-. findthnxast,ctohrreσn2xs,corr−L0.5−8keV correlationremainssig-
nificant at P ≈ 0.9% (2.6σ). The best-fit slope and
Nosignificantcorrelationisfoundifthesampleislimited s
intercept remain consistent at the 1σ level.
toonlythe variablegalaxies,whicharediscussedfurther
The flux-limited nature of the CDF-S survey presents
in §6.2. Note that the correlationcoefficient and best-fit
another potential bias. Since luminosity correlates with
line parameters (given below) remain consistent within
Variability Selected LLAGN in the 4 Ms CDF-S 9
redshift,andintrinsicvariabilitytimescalesdecreasewith CDF-S survey,which is more likely to detect the objects
redshift, the decrease in variability strength as luminos- atthebrightendofthegalaxyX-rayluminosityfunction,
ity increases could, in principle, simply reflect the fact and may result in a high percentage of “contamination”
that shorter timescales are studied at higher redshifts, by AGN.
andthereforeexhibitlessvariabilitydueto the red-noise The median X-ray excess for variable galaxies
nature of AGN light curves. To check for a possible red- (L2−10keV,tot/L2−10keV,XRB ≈ 9.2) suggests that XRBs
shift bias, we examine the σn2xs,corr-L0.5−8keV correlation contribute∼11%ofthe2–10keVluminosityfortheaver-
using a sub-sample within a narrow redshift range (0.55 agevariablegalaxy. Forsixvariablegalaxies,thetotalX-
< z < 0.75). This redshift range selects 10% of the to- ray emission is consistent with that expected from XRB
tal sample, covers luminosities from L0.5−8keV ∼ 1041.5 emission within the scatter of the Lehmer et al. (2010)
to 1044 ergs s−1, and results in minimal differences in relation (see Fig. 12), suggesting that dilution may be
rest-frame timescales. The Spearman rank correlation more significant in these sources. Three of these sources
coefficient for this sub-sample remains significant at P have variability consistent with the linear variability-
s
≈ 0.8% (2.6σ); the slope and intercept are consistent at luminosityrelation,whilethreehavesuppressedvariabil-
the 1σ level. ity (filled black stars in Fig. 11). Dilution by XRB vari-
The above test also addresses another potential bias abilitymaythereforeplayaroleinsuppressedvariability,
due to the redshift range of the sample. The σn2xs val- but cannot fully explain the extent to which σn2xs,corr is
ues listed in Table 2 measure the variability strength in suppressed at low luminosities.
the observed frame, so they will sample different energy An alternativepossible explanationfor the suppressed
bands depending on the source’s redshift (see §4.1 for variability at low luminosities is a change in accretion
discussion). This could introduce bias if the variablity structure. Ptak et al.(1998)foundasimilardropinvari-
amplitude changes with increasing energy: from 0.5−8 ability strength below L2−10keV ≈ 2×1041 ergs s−1 in a
keVatz =0to1−16keVatz =1. Theslopeandinter- sample of LLAGN and LINERs observedwith ASCA on
cept remain the same within the narrow redshift range variability timescales of less than a day. The authors
testedabove,suggestingthatanysuchbiasdoesnothave hypothesized that a radiatively inefficient accretion flow
a significant effect on the sample. (RIAF, e.g., Yuan & Narayan 2004) could be responsi-
ble for suppressed short-timescale variability at low lu-
minosities due to the larger extent of the X-ray source.
6.2. Suppressed Variability in LLAGN
This scenario would not obviously explain the reduced
Variable sources with luminosities less than L0.5−8keV variability on ∼month–year timescales seen here. RIAF
= 1041 ergs s−1 tend to fall significantly below the ex- models also predict a hard X-ray photon index due to
trapolated linear relation by factors of ≈6–80 (median the lack of an optically thick accretion disk, which pro-
factorof≈24),indicatingadropinvariabilityrelativeto vides the soft X-ray photons. The stackedX-ray photon
the linear relation on long timescales for LLAGN. This index for variable galaxies (Γ ≈ 1.93±0.13; §5.1) is
stack
“suppressed” variability can be shown to be intrinsic to inconsistent with this prediction.
propertiesofAGNvariabilityratherthanduetodilution Studies since Ptak et al. (1998) have found evi-
by unrelated XRB populations. dence both for “suppressed” variability in LLAGN
In §4.2, we showed that galaxy variability cannot be (e.g., Ptak et al. 2004; Markowitz & Uttley 2005;
attributed solely to XRB populations. We now check Papadakis et al.2008a)andagainstit(e.g.,Binder et al.
whether the XRB contribution could nevertheless dilute 2009; Pian et al. 2010). Similarly, objects such as
the observed variability by estimating how much XRBs narrow-line Seyfert 1 (NLS1) galaxies and the dwarf
are expected to contribute to the total hard (2–10 keV), Seyfert NGC 4395 (MBH ≈ 3.6 × 105M⊙) exhibit
galaxy-wide X-ray luminosity (L ; see §4.2; Lehmer
XRB “excess” vairability for their luminosity (Boller et al.
et al. 2010).
1996; Iwasawaet al. 2010). However, when plotting
We compare L to the measured, intrinsic X-ray
XRB variability against mass instead of luminosity (e.g.,
luminosity. First, L0.5−8keV is converted to L2−10keV, Papadakis et al. 2008a; Miniutti et al. 2009), such dis-
using the intrinsic photon index of Γ = 1.8 adopted by
crepancies disappear, with residual differences possibly
Xue et al. (2011) for AGN, and the stacked photon in-
due to varying accretion rates (e.g., McHardy et al.
dex Γ ≈ 1.9 for galaxies (see §2). Figure 12 plots
stack 2004; Markowitz & Uttley 2005).
themeasured2–10keVluminosityagainstthatexpected
To investigate the role of SMBH mass (M ) and ac-
BH
fromanXRBpopulationforvariablegalaxies(redstars)
cretion rate (normalized by the Eddington rate; m˙ =
andnon-variablegalaxies(greensquares). Forreference,
M˙ /M˙ ),wehaveobtainedroughestimatesforallvari-
we plot in the same figure 369 CDF-S AGN (open or- Edd
able sources. Masses and Eddington ratios for all galax-
ange circles), 32 localgalaxies(Colbert et al. 2004), and
ies, variable and non-variable,are listed in Table 2. The
20 local luminous infrared galaxies, which are likely to
SMBH masses are estimated via the scaling relation be-
be actively star-forming (Lehmer et al. 2010). The red
tween M and absolute K-band magnitude (Graham
solid line shows unity, while the dotted lines mark the BH
2007):
dispersion observed in Lehmer et al. (2010).
A K-S test shows no significantdifference between the M
relative XRB contribution in variable and non-variable log MBH =−0.37(±0.04)(MK+24)+8.29(±0.08) (7)
⊙
galaxies. The CDF-S galaxies on average tend to lie
above unity, with a median L2−10keV/LXRB ≈ 4.6. The The total absolute rest-frame K-band magnitudes
X-rayexcessinthenon-variablegalaxypopulationisper- are derived from SED fitting in Xue et al. (2010)
haps not surprising given the flux-limited nature of the with a random scatter of .0.3 mag. An X-ray
10
luminosity-dependent correction factor (Equation 1 of variability in variable galaxies.
Vasudevan et al.2009)correctsfornuclearemission. We
assume that the host galaxy is bulge-dominated, a valid 6.3. Comparing the Variability-Luminosity Relation
assumption for most AGN (e.g., Kauffman et al. 2003; with Empirical Models
Grogin et al. 2005). Several variable galaxies, how-
Anumberofrecentstudies(e.g.,McHardy et al.2004;
ever, are not bulge-dominated (nine are late-type; see
Papadakis 2004; O’Neill et al. 2005; Papadakis et al.
Table 2), so their black hole masses may be overes-
2008b) have shown that X-ray variability may be de-
timated. We apply a luminosity-dependent bolomet-
termined by a combination of M and m˙ , explain-
ric correction (κ2−10keV) to estimate the bolometric lu- BH
ing the observed variability-luminosity relation. AGN
minosity (Marconi et al. 2004) and calculate the Ed-
light curves appear to be universally described by a
dington ratio (Lbol/LEdd ≡ [κ2−10keV L2−10keV]/[1.25×
broken power-law PSD function, where the break fre-
1038 (MBH/M⊙)]). Note, that the Marconi et al. quency depends on mass and accretion rate: ν =
(12004024e)rgcosrsr−ec1t;iowneiesxctarlacpuolalatteedtehxipslirceiltaltyiofnordLo2w−n10tkoeVth>e 0.029ηm˙ (MBH/106M⊙)−1, where η is the accretiobnf ef-
ficiency, assumed to be η = 0.1 (McHardy et al. 2006).
lower luminosities of the variable galaxy sample.
The excess variance is equivalent to the integral of the
Both the M and L estimation techniques are
BH bol PSD between the minimum and maximum frequencies
known to have large dispersions. The M -M scaling
BH K sampled by the data, so as long as the break frequency
relationhasatotalscatterof0.33dex,andadditionalun-
falls within this range, the excess variance at a given lu-
certainty will come from the luminosity-dependent cor-
minositywilldecreasewithincreasingM andincrease
rection for nuclear emission, which is based on template BH
with increasing m˙ .
SEDs (Vasudevan et al. 2009). In addition, the assump-
We compare the M and m˙ values estimated in §6.2
tion that all the variable galaxies are bulge-dominated BH
will produce additional scatter.15 The bolometric cor- to the variability measured for the variable AGN and
galaxy populations. Assuming a universal PSD func-
rection, too, has large scatter due to the intrinsic dis-
tion, we derive the variability-luminosity relations ex-
persionin the SED. The uncertainty in L due to SED
bol pectedforthe CDF-Ssamplingpattern,givenarangeof
dispersionis∼20%forluminous AGN(Elvis et al.1994;
SMBHmassesandaccretionrates(e.g.,Papadakis et al.
Richards et al. 2006). There is some debate regarding
2008b, and references therein). The bolometric luminos-
the similarity between the SEDs of LLAGN and lumi-
ity,whichiscalculateddirectlyfromM andm˙ ,iscon-
nous AGN (e.g., §1; Ho 1999 and Ho 2002 vs. Maoz et BH
verted to X-ray luminosity via a bolometric correction
al. 2007); however, the luminous AGN SED dispersion
(Marconi et al. 2004). Where the break frequency lies
likely serves as a lower limit to dispersion in LLAGN
outside the timescales sampled by the data (depending
SEDs.
onthe combinationofm˙ andM ), the excessvariance
Variable galaxies tend to have lower accretion rates BH
(hm˙ i = 4 × 10−4) and masses (hMBHi = 2.6×107M⊙) wiTllhreemmaoindeclovnasrtiaanbti.lity-luminosity relations are plotted
than variable AGN (hm˙ i = 9 × 10−3; hM i = 6.2×
BH in Figure 14 for the average accretion rates for variable
107M⊙),wherewehavelimitedtheAGNsampletoz<1 (m˙ = 9 × 10−3; dashed line) and non-variable (m˙ =
for purposes of comparison. A K-S test shows that the 4 × 10−4; dash-dotted line) galaxies covering M =
differences in the m˙ and M distributions are signifi- BH
cant: P ≈ 1.7×10−5 andBPH ≈ 0.002, respectively. 105–1010 M⊙ (low to high L0.5−8keV). Both variable
KS KS populations are limited to z < 1 for comparison, and
The properties of variable AGN and galaxies are consis-
the relations are calculated at z = 0.5 and z = 0.7, the
tent with the range of estimates made by Babic et al.
median redshifts for variable galaxies and AGN, respec-
(2007) for X-ray selected, z < 1 AGN in the 1 Ms
tively; using model redshifts z = 0 or 1 resulted in neg-
CDF-S, whichspanm˙ ∼ 10−5−1(median ≈ 0.001)and
ligible changes. The shape of the observed variability-
MBH ∼106 − 1010M⊙ (median ≈ 108 M⊙). luminosity anti-correlation,including the plateau at low
Unlike previous studies (O’Neill et al. 2005;
luminosity, is roughly reproduced by the model. The
Papadakis et al. 2008a; Miniutti et al. 2009), we
plateau occurs when the break frequency lies outside
find no significant (anti-)correlation between σ2 and
nxs the range of timescales sampled by the data. Unfortu-
MBH, most likely due to the large scatter in σn2xs and nately,the longtimescales(especiallythelongminimum
MBH measurements, combined with the narrow range timescaleof4Ms;see§4.1)andthelargescatterprevent
of masses probed (since most sources lie between MBH the models from distinguishing between the significantly
∼ 107–109 M⊙). It is not surprising, therefore, that we different accretion rates estimated for variable galaxies
find a significant anti-correlation between σ2 and m˙ and AGN.
nxs
(P ≈1.6×10−11,6.3σ),plottedinFigure13,whichis Note that most sources are more variable than pre-
KS
likely an artefact of the σn2xs–L0.5−8keV anti-correlation. dicted by the model. We note some possible sources of
Nevertheless, it is interesting that in Figure 13 the vari- bias: (1) The normalization of the PSD function used
able galaxies (black circles) connect smoothly with the to calculate the models is based on a small sample of
more luminous AGN (red circles), with no discrepancy nearbyAGN(Papadakis2004)andmaythereforenotbe
in variability strength. This suggests that the factor representative of CDF-S AGN out to z ≈ 1. (2) Both
of 22.5 difference in m˙ may explain the “suppressed” the models and the bias correction applied to the mea-
sured excess variance (§4.1) depend on a universal bro-
15ThescalingrelationinKormendy&Gebhardt(2001),forex- ken power-law PSD function, but the slopes of the PSD
ample, has a much larger scatter of 0.56 dex largely because of may vary between individual sources, and some sources
poorbulge/discseparation(Graham2007). may even have a second break at shorter frequencies