Variability of Quasars
ErikZa krisson 1
,NilsBergvall 1
,andPhillipHelbig 2
1
DepartmentofAstronomyandSpa ePhysi s,Box515,SE-75120Uppsala,Sweden
2
Institut f urtheoretis hePhysik,JohannWolfgangGo ethe-Universitat
Postfa h111932,60054FrankfurtamMain,Germany
Abstra t. By omparing theresultsofnumeri almi rolensing simulations tothe
ob-servedlong-termvariabili tyofquasars,strongupp erlimitsonthe osmologi aldensity
of ompa tobje tsinthemassrange10 2
{10 4
M mayb eimp osed.Usingre ently
develop edmetho dstob etterapproximatetheampli atio n oflargesour es,we
inves-tigate inwhatwaythe onstraintsare a e tedby assumptions on erningthesize of
theopti al ontinuum-emitting region ofquasarsin the urrently favored(M=0:3,
=0:7) osmology.
1 Introdu tion
Although the opti alvariabilityof quasarson times ales of afew years ould
b e b othintrinsi innature(e.g. dueto a retiondiskinstabilitiesor sup ernova
explosions)and ausedbymi rolensingalongthelineofsight,addingthee e ts
ofb othme hanisms anonlyin reasetheprobabilityofvariations.Byassuming
that all variabilityis due to mi rolensingand omparingthe predi tions from
mi rolensings enariostotheobserved amplitudesofquasarlight urves,upp er
limitstothe osmologi aldensityof ompa tobje t maytherefore b eimp osed.
This te hniquewas rstimplementedin[1℄ to onstrain ompa t darkmatter
p opulations in the mass range 1{10 4
M
for an Einstein{de Sitter universe.
Here, we extendtheanalysistothe
M
=0:3,
=0:7 osmologyandthefull
rangeofquasarsizesallowed.
2 Analysis
Inourmo delofquasarmi rolensing,themultipli ativemagni ationassumption
outlined in [2℄ is assumed to adequately repro du e the statisti al probability
of variability.Theresults fromthenumeri al simulationsare ompared to the
observationalsampleof[3℄, ontaining117quasarsintheredshiftrangez=0:29{
3:23,monitoredfortenyears.Themetho dof omparingobservedandsyntheti
samples loselyfollowsthatof[1℄,whi hmayb e onsultedforfurtherdetails.
The onstraintsderivedassumethattheluminositiesoftheseobje tsare
in-dep endentoftheradiioftheiropti al ontinuum-emittingregions,R
QSO .Under
volume-3 UpperLimitson TheCosmologi al Densityof Compa t
Obje ts
The size of the opti al ontinuum-emitting region of quasars is not a
well-determinedquantity,buttypi allyassumedtoliesomewhereintherangeR
QSO = 10 12 {10 14
m.WhereasonlytheR
QSO =10
13
m asewas onsideredwhen
deriv-ingthe onstraintsin[1℄,wehereinvestigatetheimpa tthatsmallerandlarger
quasarsizesmayhave ontheupp er limitsinferred.
Figure 1 indi ates the onstraints on the osmologi al density of ompa t
obje ts,
ompa t
,fordi erentlensmasses,M
ompa t ,andR QSO inb oth Einstein-de Sitter and M =0.3,
=0.7 osmologies.Poisson probabilitiesof 10% (see
[1℄)haveb een hosentode ne theupp er limits.AHubble onstantofH
0 =65
km/s/Mp hasalsob eenassumed.
Eventhoughthetransitiontothe-dominateduniversesigni antly
strength-ens the onstraints,the limitson
ompa t
are seen to b e very sensitive to the
valueofR QSO used.
0
0.05
0.1
0.2
0.3
0.4
0.5
5
⋅
10
13
1
⋅
10
12
5
⋅
10
12
1
⋅
10
13
1
⋅
10
14
1
⋅
10
−4
1
1
⋅
10
−1
1
⋅
10
−2
1
⋅
10
−3
R
QSO
(m)
Ω
compact
Ω
M
=1.0,
Ω
Λ
=0.0
0
0.05
0.1
0.15
0.2
0.25
0.3
1
⋅
10
14
1
⋅
10
12
5
⋅
10
12
1
⋅
10
13
5
⋅
10
13
(solar masses)
1
1
⋅
10
−1
1
⋅
10
−2
1
⋅
10
−3
1
⋅
10
−4
M
compact
Ω
compact
R
QSO
(m)
Ω
M
=0.3,
Ω
Λ
=0.7
Fig.1. Allowed regions of the (M ompa t, RQSO, ompa t) parameter spa e in the
Einstein{de Sitter(Left)and
M
=0:3,
=0:7(Right) osmologies.Lowervalues
of ompa tindi atestronger onstraints
4 The Impa tof Large-Sour e Mi rolensing
In [4℄,the ampli ationformula derived in [1℄ was shown to underpredi t the
ampli ationoflargesour esandrepla edbyamo di edexpression.Aspredi ted
in[4℄,theimprovedampli ationformulashouldthereforeresultintighterlimits
on
ompa t
.InFig.2,however,weshowthattheimplementationofthe
large-sour eformalismmerelyhasamo deste e tontheupp erlimits,andonlyalters
the onstraintsatthelowestmass(10 4
0
0.05
0.1
0.15
0.2
0.25
0.3
1
⋅
10
−4
1
⋅
10
−3
1
⋅
10
−2
1
⋅
10
−1
1
M
compact
(solar masses)
Ω
compact
Ω
M
=0.3,
Ω
Λ
=0.7
Fig.2. Theallowedregion ofthe (M
ompa t ,
ompa t
) parameter spa e forasour e
sizeofRQSO=110 13
mintheM=0:3,=0:7 osmology, with(lightgray)and
without(darkgray)theuseoftheampli ation formulaforlargesour es([4℄)
5 Con lusions
By omparingtheresultsofnumeri almi rolensingsimulationstotheobserved
long-termvariabilityofquasars,strongupp erlimitsmayb epla edonthe
osmo-logi aldensityof darkmatterintheformof ompa t obje ts. In the urrently
favored -dominated universe (
M
= 0:3,
= 0:7), ompa t obje ts with
masses10 2 M and10 3 M
annot ontributemoretothe osmologi al
density than
ompa t
= 0:1 and
ompa t
= 0:05 resp e tively, provided that
the ontinuum-emittingregionofquasarsisnotsigni antlylarger than110 13
m. We do however note that the metho dused is sensitive to the assumptions
on erning the size of the ontinuum-emittingregion of quasars, and b e omes
e e tivelyuselessforR
QSO
510 13
m.
Thelargesour e ampli ationformuladevelop edin[4℄isshownnottohave
anysigni antimpa t inthe part of parameter spa e for whi h the long-term
variabilitymetho dprovidesthemostinteresting onstraints.
A more detailed analysis of the un ertainties present in this te hnique to
onstrain the osmologi al density of ompa t obje ts is urrently underway
([5℄).
Referen es
1. P.S hneider:A&A279,1(1993)
2. J.P.Ostriker, M.Vietri:ApJ267,488(1983)
3. M.R.S.Hawkins,P.Veron:MNRAS260,202(1993)
