A Robust Determination of the size of quasar accretion disks using gravitational microlensing

0.19 MB·English

by  J. Jimenez-Vicente

Draftversion January17,2012
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
A ROBUST DETERMINATION OF THE SIZE OF QUASAR ACCRETION DISKS
USING GRAVITATIONAL MICROLENSING
J. Jim´enez-Vicente
DepartamentodeF´ısicaTeo´ricaydelCosmos. UniversidaddeGranada,CampusdeFuentenueva, 18071, Granada,Spain
Instituto CarlosIdeF´ısicaTeo´ricayComputacional. UniversidaddeGranada,18071, Granada,Spain
E. Mediavilla
2
InstitutodeAstrof´ısicadeCanarias,V´ıaL´actea S/N,LaLaguna38200,Tenerife,Spain
1
DepartamentodeAstrof´ısica,UniversidaddelaLaguna,LaLaguna38200,Tenerife,Spain
0
2
J. A. Mun˜oz
n
Departamento deAstronom´ıayAstrof´ısica,UniversidaddeValencia,46100Burjassot,Valencia,Spain
a
J

6 C. S. Kochanek
1 DepartmentofAstronomy,TheOhioState University,140West18thAvenue,Columbus,OH43210,USA
CenterforCosmologyandAstroparticlePhysics,TheOhioStateUniversity,191WestWoodruffAvenue, Columbus,OH43210, USA

] Draft version January 17, 2012
O
C ABSTRACT
. Usingmicrolensingmeasurementsfromasampleof27image-pairsof19lensedquasarswedetermine
h a maximum likelihood estimate for the accretion disk size of an average quasar of r = 4.0+2.4 light
p s −3.1
- days at rest frame hλi = 1736˚A for microlenses with a mean mass of hMi = 0.3M⊙. This value, in
o good agreement with previous results from smaller samples, is roughly a factor of 5 greater than the
r predictions of the standard thin disk model. The individual size estimates for the 19 quasars in our
t
s sample are also in excellent agreement with the results of the joint maximum likelihood analysis.
a
Subject headings: accretion, accretion disks — gravitationallensing: micro — quasars: general
[

1
v 1. INTRODUCTION objects based in microlensing chromaticity (Eigenbrod
7 The thin disk (Shakura & Sunyaev 1973) is the stan- et al. 2008, Poindexter et al. 2008, Mosquera et al.
8 dardmodeltodescribetheinnerregionsofquasars. This 2011, Mediavilla et al. 2011a, Mun˜oz et al. 2011) also
1 found that the size estimated from microlensing is sub-
model predicts typical sizes for the accretion disks of
3 luminous quasars of ∼1015cm (∼0.4 light days) in the stantially larger than the values predicted by the thin
. disk theory (by factors of about 10 in HE0435−1223, 5
1 (observer frame) optical bands. However, recent mea-
in SBS0909+532, and 4 in HE1104−1805). Upper lim-
0 surements based on quasar microlensing are challenging
its on the sizes of MG0414+0534 and SDSSJ0924+0219
2 this prediction. Based on a combined optical and X-ray
1 study of microlensing in 10 quadruply lensed quasars, havealso been set by Bate et al. (2008)and Floydet al.
: Pooley et al. (2007) found that the source of optical (2009), respectively.
v Here, we will generalize these results by extending the
light is larger than expected from basic thin accretion
i
X disk models by factors of3 to 30. Studying microlensing studytothesampleof20lensedquasarsofMediavillaet
al. (2009, hereafter MED09). Our data consists of mi-
r variabilityobservedfor11gravitationallylensedquasars
a Morganetal. (2010)alsofoundthatthemicrolensinges- crolensing amplitude measurements for 29 image-pairs
from 20 lensed quasars based on a comparison between
timates of the disk size are larger (by a factor ∼4) than
the flux ratios in the continuum and an adjacent emis-
would be expected from thin disk theory. Other mon-
sion line. The emission line flux ratio provides an un-
itoring based studies focused on individual objects like
microlensed baseline that also removes the effects of ex-
QSO2237+0305 (Kochanek 2004, Anguita et al. 2008,
tinction (see e.g. Falco et al. 1999, Mun˜oz et al. 2004)
Eigenbrod et al. 2008, Mosquera et al. 2009, Agol et
and lens models in the determination of the magnifica-
al. 2009, Poindexter & Kochanek 2010), PG1115+080
tion anomalies. As noted in previous works (Kochanek
(Morgan et al. 2008), RXJ1131−1231(Dai et al. 2010),
2004, Eigenbrod et al. 2008, Blackburne et al. 2011a),
HE1104−1805(Poindexteretal. 2008)orHE0435−1223
studies favouringthe selectionofobjects withnoticeable
(Blackburne et al. 2011b) generally support these con-
magnificationanomalies (or epochs with highmicrolens-
clussions.
ing activity) may lead to a bias towards smaller quasar
From single-epoch optical/IR and X-Ray measure-
size determinations. The fact that one object does not
ments, Blackburne et al. (2011a) used the wavelength
show microlensing magnification anomalies may be due
dependence of microlensing (chromaticity) to study the
to the fact that it is either too big or that it lies in
structureofaccretiondisksin124-imagelensedquasars,
a region without significant magnification fluctuations.
finding disk sizes larger than predicted by nearly an or-
Thus,non-detectionofmicrolensingalsoputsconstraints
der of magnitude. More detailed studies of individual
2
on the size of the sources and should be taken into ac- In order to describe the structure of the source, we
count. TheMED09sampleisalsounaffectedbythisbias model the accretiondisk with a Gaussianprofile I(R)∝
(indeed the histogram of estimated microlensing magni- exp(−R2/2r2),wherethecharacteristicsizer isawave-
s s
fications in this sample peaks at ∆m = 0). However, lengthdependentparameter(relatedtothehalf-lightra-
the data from MED09 do not include, for most image- dius as R = 1.18r ). The wavelength dependence of
1/2 s
pairs, enough measurements at different wavelengths to the disk size is parametrized by a power law with expo-
address chromaticity. For this reason we will start dis- nent p such that r (λ) ∝ λp. We smooth the magnifica-
s
cussing the impact of chromaticityonthe determination tion maps with Gaussians scaled to two wavelengths λ
B
of microlensing based sizes (§2) to show that size esti- and λ representing characteristic blue and red wave-
R
mates are dominated by microlensingamplitude andare lengths. We chooseλ /λ =2.3,the ratiobetweenLyα
R B
relatively independent of chromaticity. In §3 we will use andMgII,whichisroughlythewavelengthrangecovered
the microlensing data from MED09 to calculate a maxi- by observations in the optical band.
mum likelihood estimate of the accretion disk size. The We calculate the probabilityof observingmicrolensing
estimate will be for the typical size of the accretion disk magnifications ∆m =µ −µ (where µ and µ are the
2 1 1 2
of an average quasar rather than that of any particular magnifications at the positions of image 1 and 2 respec-
source. Wealsomakeindividualsizeestimatesforthe19 tively) at wavelengths λ and λ , namely, ∆m and
B R B
objects using a complementary Bayesianapproach,find- ∆m , for a grid in the size at λ , r (λ ), and the ex-
R B s B
ingexcellentagreementwiththelikelihoodanalysis. The ponent p. We use a logarithmic grid in r such that
s
main conclusions are presented in §4. logri = 0.3×i for i = 0···11 (ri in light days) and a
s s
linear grid in p such that pj = 0.25×j for j = 0···13.
2. SIZEDETERMINATIONFROMSINGLE WAVELENGTH We restrict ourselvesto the case |∆m |>|∆m |, as we
MICROLENSINGMEASUREMENTS B R
assume that the size of the source increases with wave-
We will base our analysis on the microlensing mea- length, and therefore the largest magnifications are ex-
surements inferredby MED09 fromopticalspectroscopy pected for the smallest (i.e. bluest) sources1.
available in the literature (29 quasar image pairs seen The probability of observing ∆mobs and ∆mobs in a
through 20 lens galaxies). The microlensing magnifi- B R
model with parameters ri and pj is given by
cation between two images 1 and 2 is calculated as s
∆m=(m −m ) =(m −m ) −(m −m ) ,
where (m22−m11)lminicerois the fl2ux ra1tioconint an em2issio1nlliinnee prsi,pj(∆moBbs,∆moRbs)∝Z d∆mBZ d∆mRNije−21χ2,
and (m − m ) is the flux ratio of the continuum
2 1 cont (1)
adjacent to the emission line. With this method the mi-
where
crolensing magnification is isolated from extinction and
from the mean lensing magnification, as these effects af- (∆m −∆mobs)2 (∆m −∆mobs)2
fect the line and the adjacent continuum equally. The χ2 = B B + R R (2)
σ2 σ2
consistency of this procedure has been confirmed with ∆mobs ∆mobs
B R
mid-IR data (MED09).
Here, N is the number of trials with ∆m and ∆m
Thehistogramofobservedmicrolensingmagnifications ij B R
for the case with parameters ri and pj, and σ and
in MED09 showed that 93% of the quasar image pairs s ∆mobs
B
have microlensing |∆m| ≤ 0.8mag. In this section, we σ∆mobs aretheuncertaintiesintheobservedmicrolensing
R
are going to use this statistical constraint to estimate magnifications, for which we have taken a typical value
quasar accretion disk sizes from single wavelength mi- of σ =σ =0.05 mags.
∆mobs ∆mobs
crolensing measurements. B R
The calculations are performed for a grid of pairs
We will apply a statistical approach similar to that
∆m ,∆m with ∆m = 0.2×k for k = −4···4 and
B R B
usedbyMediavilla et al.(2011a)toarepresentativelens
∆m = 0.2×m for m = 0···k (so we always have
R
system. Therefore, we take for the lens a standard SIS
|m|<|k|and|∆m |>|∆m |)forα=0.05andα=0.1.
B R
with values κ = γ = 0.45 and κ = γ = 0.55 for the
1 1 2 2 This range of values for the strength of microlensing
convergenceandshearatthepositionsofthetwoimages.
covers the vast majority of observed cases as shown in
These values are typical of the lenses in the MED09 (cf.
the histogram of observed microlensing strengths in the
their Table 4). For the redshifts of lens and source we
sample of MED09 (their Fig. 1). Thus, the probabi-
havetaken the values z =0.57and z =1.76,which are
l s lity distribution p (∆mobs,∆mobs) is calculated for
the average values for the sample. rsi,pj B R
14×12×29×2 = 9744 cases. For each one of those cases
Using these parameters for the macro lens, we ge-
(i.e. for every quadruplet (p,r ,∆mobs,∆mobs)), the
nerate microlensing magnifications maps at the posi- s B R
probability is calculated using 108 trials.
tions of images 1 and 2 using the inverse polygon
The results for the case α = 0.05 are shown in Figure
mapping algorithm described in Mediavilla et al. (2006)
1 for ∆m > 0. We have shown only the right side
and Mediavilla et al. (2011b). The calculated maps are B
of the full figure, as the cases with ∆m < 0 are very
2000×2000 pixels in size, with a pixel size of 0.5 light B
days,or equivalently1.295×1015cm. In the imageplane, similartothosewiththesamevalueof|∆mB|sothatthe
scenario is fairly symmetric with respect to ∆m = 0.
thecoveredareaisthesourceplaneareaincreasedbyfac- B
tors 1.5(1−κ±γ)−1. For the fractionof projectedmass For the case α = 0.1 the results are very similar but
the peaks in the probability distributions are displaced
density in stars, α, we use current estimates (Pooley et
towards slightly higher values of r .
al. 2009, MED09, Mosquera et al. 2011) and consider s
only the cases with α = 0.05 and α = 0.1. We used
microlenses of 1M⊙. 1 Inversionsarepossiblebutrare(seePoindexter etal. 2008)
3
Fig.1.—Gridof two dimensional probability distributions prsi,pj(∆moBbs,∆moRbs)for the 15 cases with ∆mB >0and α=0.05. Each
column corresponds to the distribution for a given value of ∆mB indicated at the top of the column. Each row corresponds to the
distribution for a given value of ∆mR indicated at the right. For each distribution the abcissae represent p from 0.0 to 3.25 and the
ordinatesrepresentlogrs from0.0to3.3(rs inlightdays). Thecontourlevelsaredrawnatintervalsof0.25σ(thecontouratnσisdrawn
atexp(−n2σ2/2)fromthepeakofthedistribution). Thecontour at1σ isthicker thantherest.
With the exception of the cases in which ∆m = remain roughly constant along each column in Figure
B
∆m , the distributions show a clear covariance in the 1 as we move through the different rows. That means
R
sense that larger sizes imply lower values of the expo- that even if we lack information on chromaticity, we
nent p. We also see that larger values of ∆m favour can still obtain valuable information on the size of the
B
smaller values for the source size r . sources from measurements of microlensing at a single
s
The most important result from this figure is that the wavelength. Another interesting and robust result from
probability distribution with respect to the size r is Figure 1 is that, with the exception of the case with no
s
dominated by the strength of microlensing (∆m ) with detectedmicrolensing(∆m =0),the maximums ofthe
B B
very little dependence on the amount of chromaticity. distributionsarealllocatedinafairlyrestrictedrangein
Conversely,thevalueofthechromaticity(∆m −∆m ) r . Therefore, microlensing magnifications in the range
B R s
is the main factor in determining the exponent p. In- 0<|∆m |≤0.8 will provide sizes in a rather restricted
B
deed, the most probable values of rs (values within 1σ rangebetween∼1 M/M⊙ and∼16 M/M⊙ lightdays
around the maximum of the distributions in Figure 1) irrespective of chrpomaticity, with laprger magnifications
4
favouring smaller sizes.
3. DISCUSSION
Based on the results of the previous section, it is pos-
sible to constrain the size of the sources from measure-
ments of the microlensing strength at a single wave-
length, even if we have no informationon the amount of
chromaticitypresent. Asnotedabove(seealsoKochanek
2004, Eigenbrod et al. 2008, Blackburne et al. 2011a),
each single microlensing measurement is affected by a
degeneracybetween the range of possible magnifications
and source size effects. Statistics of large samples of
lensed quasars (like MED09) can be used to minimize
this uncertainty. In particular, we are going to use a
maximum likelihood method to estimate an averagesize
from the product of the individual likelihood functions
foreachimagepair. Thismethodincludesthecaseswith
little or no microlensing that by themselves would give
rise only to lower limits on the size on an equal footing
with those showing significant microlensing.
The microlensing magnifications in this sample have
been calculated using the continuum to line flux ratios
of different lines for different objects. As size is related Fig.2.— Likelihood functions for the size of the accretion disk
towavelength,weshouldideallyuseobjectswithmagni- logrs for α=0.05 (continuous line) and α=0.1 (dashed line) in
fications obtained from lines at similar wavelengths. On thefullsampleofquasarsbyMED09.
the other hand, to have good statistics, we should also
The results of this procedure for α=0.05 and α=0.1
try to keep the sample as large as possible. With these
are shown in Figure 2. The maximum likelihood occurs
restrictions in mind, we have chosen a compromise in
which we used all objects with magnifications measured forlogrs =2.0+−00..48 andlogrs =2.3+−00..48 (rs inlightdays)
in the wavelength range between Lyα (1216˚A) to Mg II for α = 0.05 and α = 0.1 respectively. Taking into ac-
(2798˚A).Withthischoice,theaveragerestwavelengthis count that rs ∝ hMi1/2 where hMi is the mean mass
intherelativelynarrowrangeofhλi=1736±373˚A,while of the microlenses, our results for the mean size of the
we stillkeep27 imagepairsfrom19 lensedquasars. The accretion disk of quasars are rs = 7.4+−34..61(hMi/M⊙)1/2
dispersion introduced by the effect of wavelength in the light days for α = 0.05 and rs = 10+−55..05(hMi/M⊙)1/2
size estimate will be taken into account later. We then for α = 0.1. When scaled for a mean microlens mass
use the measured microlensing magnifications in these of hMi = 0.3M⊙, representative of the stellar popula-
27 pairs as observed ∆m (where B stands now for the tions in galaxies,the sizes of the accretion disks become
B
averagewavelength hλi=1736˚A). We computed magni- rs = 4.0+−22..02 light days and rs = 5.5+−23..61 light days for
ficationmapsforeachoneoftheimagesofthe27pairsin- α=0.05 and α=0.1, respectively, at our averagewave-
dividuallytakingtheκandγvaluesfromMED09(except length hλi=1736˚A. The intrinsic dispersion in λ in be-
for SBS0909+532 for which we take the values in Medi- tween the sources implies an additional dispersion in r
s
avillaetal. 2011a). Weagainconsideronlyα=0.05and ofabout20%. Whentakingthiseffectintoaccountinthe
α = 0.1. The calculated maps are 2000×2000 pixels in error bars, we finally have r =4.0+2.4 and r =5.5+3.1
s −3.1 s −3.7
size,withapixelsizeof0.5light-days. Wehaveusedthe light days for α=0.05 and α=0.1, respectively.
same logarithmic grid in rs from §2, as well as a linear Usingequation(3)andaBayesianapproachwithalo-
grid ri = 1.0+2.0×i light days for i = 0···24. Using garithmic prior on r (see e.g. Mediavilla et al. 2011a),
s s
the magnification maps, the probability of observing a we also made individual estimates of r for each one of
s
microlensing magnification ∆mobs in image pair j for a the19quasarsinoursample. Forthoseobjectsforwhich
j
model with parameter ri is given by: there are several image pairs, the probability distribu-
s
tions for the different pairs were combined into a single
prsi(∆mojbs)∝Z Nie−12χ2d∆m (3) pforrobhMabiili=ty0fu.3nMct⊙ionanfodrαtha=to0b.0j5ecatr.eTphreesreensuteltdinignvTaalubeles
1 and in Figure 3. It is worth noting that the average
where
valueofthese individual estimates(hr i=4.2±4.4light
χ2 = (∆m−∆mojbs)2. (4) days) is very close to the one obtainsed with the joint
σ2 likelihood analysis (although the use of a linear prior
∆mojbs would increase the individual size estimates by 80%).
Notethatthe averagesize shrinksnoticeably(by ∼30%)
We can calculate a likelihood function for r as
s
if the pairs with |∆m | < 0.1 are excluded from the
B
L(ri)∝ p (∆mobs), (5) sample. Thus we confirm that favouring the selection of
s Y rsi j quasars with noticeable microlensing introduces a clear
j
biastowardssmallersizes(Kochanek2004,Eigenbrodet
where j runs over the 27 image-pairs considered. al. 2008, Blackburne et al. 2011a). In Figure 3 we com-
5
TABLE 1
Sizes forindividualobjects at1736˚A
Object rs(1736)˚A MBH(109M⊙) Line
HE0047−1756 4.0+8.5 1.38 (CIV)
−2.7
HE0435−1223 4.4+5.6 0.50 (CIV)
−2.4
HE0512-3329 2.6+3.2 ....
−1.4
SDSS0806+2006 1.4+1.9 ....
−0.8
SBS0909+532 1.8+1.9 1.95 (Hβ)
−1.0
SDSSJ0924+0219 10.1−4.6a 0.11 (MgII)
FBQ0951+2635 1.8+2.9 0.89 (MgII)
−1.2
QSO0957+561 3.5+7.3 2.01 (CIV)
−2.3
SDSSJ1001+5027 4.6+10.5 ....
−3.2
SDSSJ1004+4112 2.2+2.2 2.02 (CIV)
−1.1
QSO1017−207 3.2+6.02 1.68 (CIV)
−2.12
HE1104−1805 1.0+0.9 2.37 (CIV)
−0.5
PG1115+080 2.3+2.6 0.92 (CIV)
−1.2
SDSSJ1206+432 1.2+1.4 ....
−0.6
SDSSJ1353+1138 7.5−4.4a ....
HE1413+117 2.7+2.7 0.26 (CIV)
−1.3
BJ1422+231 20.017.3 4.79 (CIV)
−9.2
SBS1520+530 2.4+3.5 0.88 (CIV)
−1.5
WFIJ0233−4723 3.6+5.3 ....
−2.2 Fig.3.— Size of the accretion disk at 1736 ˚A as a function of
themassoftheblackhole(fromMosquera&Kochanek 2011) for
Note. — Sizes in light days for individual objects at 1736 ˚A hMi=0.3M⊙ . Resultsfromourjointanalysisarethesolidtrian-
obtained from microlensing magnifications of image pairs. Black gleand square for α=0.05 and α=0.1 respectively. Our estimates
holemassesaretakenfromthesummaryinMosquera&Kochanek for individual objets are shown as filled diamonds (or upward ar-
(2011). Emission line used for the mass estimate is indicated in rows for lower limits). Open triangles are from Blackburne et al.
fourthcolumn. (2011a) for objects with available black hole masses in Mosquera
a These values have been calculated for ∆mB = 0 and are lower &Kochanek(2011). TheasteriskistheestimateforSBS0909from
limitsratherthantrueestimates Mediavillaet al. (2011a). Estimates for HE1104 by Mun˜oz et al.
(2011) and Poindexter et al. (2008) are shown as an open square
pareourestimateswithpreviousresults. Estimatesfrom and an X respectively. The estimate for HE0435 by Mosquera et
the present work are indicated with filled symbols, and al. (2011) isshownasanopencircle. Upperhalfcircle,lowerhalf
circleand star show the estimates forQSO2337 byAnguita et al.
estimates from previous works with open symbols. We
(2008),Kochanek(2004)andEigenbrodetal. (2008)respectively.
have taken black-hole masses from Table 1 in Mosquera The estimate for Q0957 by Hainline et al. (2012) is shown as a
& Kochanek (2011), which they take from Peng et al. bow tie. Downward arrows indicate the upper limits for MG0414
by Bate et al. 2008 (right) and for SDSSJ0924 by Floyd et al.
(2006), Greene et al. (2010) and Assef et al. (2011).
2009 (left). Thin line is the prediction from the thin disk model
The thin line corresponds to the theoretical prediction
(with L/LE = 1 and η=0.1). The thick solid line is the fit from
for the thin disk model at 1736 ˚A (with L/L = 1 and Morgan et al. (2010) with their measurements shown as pluses.
E
η = 0.1). The thick line corresponds to the empirical Thedashedlines showingthelimitsduetothe uncertainty inthe
y-intercept.
fit by Morgan et al. (2010) scaled to hλi=1736 ˚A using
p=4/3 rest wavelength of hλi=1736˚A. For a typical mean mass
Our estimates are in good agreement with previous
inthestellarpopulationofthelensofhMi=0.3M⊙,and
results (Blackburne et al. 2011a,Mediavilla et al 2011a,
taking into account the intrinsic dispersion in λ, we find
Mosquera et al. 2011, Mun˜oz et al. 2011, Morgan et al.
r =4.0+2.4 andr =5.5+3.1 lightdaysforα=0.05and
2010,Floyd et al. 2009,Anguita et al. 2008, Poindexter s −3.1 s −3.7
α = 0.1 respectively. These estimates are in agreement
et al. 2008,Eigenbrodet al. 2008,Bate et al. 2008,and
with other studies (Blackburne et al. 2011a, Mediavilla
Kochanek 2004)and show a discrepancy with respect to
et al 2011a, Mosquera et al. 2011, Mun˜oz et al. 2011,
the predictions of the thin disk model of approximately
Morgan et al. 2010, Floyd et al. 2009, Anguita et al.
a factor of 5.
2008, Poindexter et al. 2008, Eigenbrod et al. 2008,
4. CONCLUSIONS Bate et al. 2008, and Kochanek 2004) and again find
thatdisksarelargerthanpredictedbythe thindiskthe-
Weperformedastatisticalanalysistoestimatetheav-
ory. Wehavealsoestimatedthesizesofthe19individual
erage size of the accretion disks of lensed quasars from
objects in the sample to find that they are in very good
thelargesample(MED09)ofmicrolensingmagnification
statistical agreement with the result from the maximum
measurements. We find that most information on the
likelihood analysis.
size of the accretion disk is contained in the amplitude
ofthe microlensingmagnificationandfairlyindependent
of the amount of chromaticity. This research was supported by the Spanish Mi-
From a statistical analysis using measured microlens- nisterio de Educaci´on y Ciencia with the grants
ing magnificationstrengths from 27 image pairs from 19 C-CONSOLIDER AYA2007-67625-C02-02, AYA2007-
lensedquasarsinthesampleofMED09wemeasuredthe 67342-C03-01/03,AYA2010-21741-C03/02. J.J.V.isalso
average size of the accretion disk of lensed quasars at a supportedbythe JuntadeAndaluc´ıathroughthe FQM-
6
108 project. J.A.M. is also supported by the General- C.S.K. is supported by NSF grant AST-1009756.
itat Valenciana with the grant PROMETEO/2009/64.
REFERENCES
Agol,E.,Gogarten, S.M.,Gorjian,V.,&Kimball,A.2009, ApJ, Mediavilla,E.,Mediavilla,T.,Mun˜oz,J.A.etal.2011b,ApJ,
697,1010 741,42
Anguita,T.,Schmidt,R.W.,Turner,E.L.etal.2008, A&A, Morgan,C.W.,Kochanek, C.S.,Dai,X.,Morgan,N.D.,&
480,327 Falco,E.E.2008,ApJ,689,755
Assef,R.J.,Denney, K.D.,Kochanek, C.S.etal.2011,ApJ, Morgan,C.W.,Kochanek, C.W.,MorganN.D.&FalcoE.E.
742:93 2010,ApJ,712,1129
Bate,N.F.,Floyd,D.J.E.,Webster, R.L.&Wyithe, J.S.B. Mosquera,A.M.,Mun˜oz,J.A.,&Mediavilla,E.2009, ApJ,691,
2008, MNRAS,391,1955 1292
Blackburne,J.A.,Pooley,D,Rappaport,S.&Schechter, P.L. Mosquera,A.M.&KochanekC.S.2011,ApJ,738,96
2011, ApJ,729,34 Mosquera,A.M.,Mun˜oz,J.A.,Mediavilla,E.,Kochanek, C.S.
Blackburne,J.A.,Kochanek, C.S.,Chen,B.,Dai,X.,Chartas, 2011,ApJ,728,145
G.2011,arXiv:1112.0027v1 Mun˜oz,J.A.,Falco,E.E.,Kochanek, C.S.,McLeod,B.A.,&
Dai,X.,Kochanek, C.S.,Chartas,G.etal.2010,ApJ,709,278 Mediavilla,E.2004,ApJ,605,614
Eigenbrod,A.,Courbin,F.,Meylan,G.etal.2008, A&A,490, Mun˜oz,J.A.,Mediavilla,E.,Kochanek, C.S.,Falco,E.E.&
933 Mosquera,A.M.2011, ApJ,742,67
Falco,E.E.,Impey, C.D.,Kochanek, C.S.etal.1999,ApJ,523, Peng,C.Y.,Impey, C.D.,Rix,H.W.etal.2006,ApJ,649,616
617 Poindexter,S.,Morgan,N.&Kochanek,C.S.2008,ApJ,673,34
Floyd,D.J.E.,Bate, N.F.,&Webster,R.L.2009, MNRAS, Poindexter,S.&Kochanek, C.S.2010,ApJ,712,668
398,233 Pooley,D.,Blackburne,J.A.,Rappaport, S.,&Schechter, P.L.
Greene,J.E.,Peng,C.Y.,&Ludwig,R.R.2010,ApJ,709,937 2007,ApJ,661,19
HainlineL.J.,MorganC.W.,BeachJ.N.etal.2010,ApJ,744, Pooley,D.,Rappaport, S.,Blackburne,J.etal.2009, ApJ,697,
104 1892
Kochanek, C.S.2004,ApJ,605,58 Shakura,N.I.&Sunyaev, R.A.1973,A&A,24,337
Mediavilla,E.,Mun˜oz,J.A.,Lopez,P.,etal.2006,ApJ,653,942
Mediavilla,E.,Mun˜oz,J.A.,Falco,E.,etal.2009,ApJ,706,1451
Mediavilla,E.,Mun˜oz,J.A.,Kochanek, C.S.,etal.2011a, ApJ,
730,16