Limits on the cosmological abundance of supermassive compact objects from a search for multiple imaging in compact radio sources

4 Pages·0.14 MB·English

by  P. N. Wilkinson

Limits on the cosmological abundance of supermassive compact objects from a search
for multiple imaging in compact radio sources
P.N. Wilkinson,1 D.R. Henstock,1 I.W.A. Browne,1 A.G. Polatidis,1,2 P. Augusto,1,3
A.C.S. Readhead,4 T.J. Pearson,4 W. Xu,4 G.B. Taylor,4,5 and R.C. Vermeulen4,6
1University of Manchester, Jodrell Bank Observatory, Macclesfield, Cheshire SK11 9DL, UK
2Onsala Space Observatory, Chalmers Institute of Technology, S-43992 Onsala, Sweden
3Universidade da Madeira, Dep. Matem´atica, Caminho da Penteada, 9050 Funchal,Portugal
4California Institute of Technology, Pasadena, California, 91125
5National Radio Astronomy Observatory, Socorro New Mexico, 87801
6Netherlands Foundation for Radioastronomy, P.O. Box 2,
7990 AA Dwingeloo, The Netherlands Dwingeloo, The Netherlands
(Dated: February 1, 2008)
1 UsingVeryLongBaselineInterferometrywehavesearchedasampleof300compactradiosources
0 for examplesof multipleimaging producedby gravitational lensing; no multipleimages were found
0 withseparationsintheangularrange1.5–50milliarcsec. Thisnullresultallowsustoplacealimiton
2 thecosmological abundanceof intergalactic supermassive compact objects in themass range∼106
n to∼108M⊙;suchobjectscannotmakeupmorethan∼1%oftheclosuredensity(95%confidence).
a Auniformlydistributedpopulationofsupermassiveblackholesformingsoon aftertheBigBangdo
J not,therefore, contribute significantly to thedark matter content of the Universe.

8
1 PACSnumbers: 95.35+d 97.60.Lf 98.80.Es 98.90.+s

1
v I. INTRODUCTION pendent of the lens mass. However, the average image
8 separation measures MCO directly and is approximately
2 independentofΩ . Theseideaswerefurtherdeveloped
The possibility that a first generation of objects with CO
3 by Nemiroff [10] and by Nemiroff & Bistolas [11].
massescomparablewiththoseofglobularclustersformed
1
Sinceforalensatacosmologicallysignificantdistance
prior to galaxies has long been recognised [1, 2]. Such
10 Jeans–mass (∼ 106.5 M⊙ ) objects forming shortly after theimageseparationis∼2×10−6(MCO/M⊙)1/2 arcsec-
onds,searchingfor Jeans–massCO requiresthe milliarc-
0 the decoupling of matter and radiation in the early uni-
/ verse could have evolvedto black holes and it is possible sec (mas) resolution of Very Long Baseline Interferom-
h
etry (VLBI). Kassiola, Kovner & Blandford ([12]; here-
thatsomeofthedarkmattercouldbeinthis,difficultto
p
afterKKB),usedthelackof“millilensed”imagesinpub-
- detect,form[3,4]. BuildingontheseideasGnedin&Os-
o triker[5]andGnedin,Ostriker&Rees[6]exploredacos- lished VLBI maps of 48 compact radio sources, to place
str imsougponticomaondeolridnerwhoifchmtahgenbitaurdyoenhicigdheenrsittyha(nΩbt∼ha0t.1in5)- arannugpep1e0r7l–im10i9tΩMC⊙O.<In0a.4c(l9o9se.7ly%–rceolnatfieddensecae)rcihnNtheemmiraosffs
a
[13] used the lack of secondary “echoes” of gamma ray
: ferredfromprimordialnucleosynthesiswith the “excess”
v bursts, which would also arise from millilensing, to rule
baryons being lost in the collapse of such Jeans–mass
Xi objects. It has also been conjectured that relic massive out a closure density of supermassive CO. In this pa-
per we describe a millilens search based on high-quality
r black holes might provide the seeds for quasars [7].
a Press & Gunn [8] developed the idea of detecting su- VLBI maps of 300 sources which extends KKB’s lower
permassive compact objects (CO) by their gravitational mass range to ∼ 106 M⊙ and enables us to push their
limit on Ω for Jeans–mass objects down by a factor
lensing effects well before the actual discovery of gravi- CO
15. This is the most stringent limit to date on Ω for
tational lenses in 1979. They showed that in a universe CO
filled with a mass density Ω ∼ 1, the probability of a uniformly–distributedJeans–massobjectsandwediscuss
CO
some cosmologicalimplications of this result.
distantsourcebeingdetectablylensedbyasupermassive
CO is of order unity, while for Ω <1, the probability
CO
decreasesin directproportionto the mass density. From
II. SELECTION OF LENS CANDIDATES
thistheydrewtheimportantconclusionthatthefraction
ofdistantgalaxiesthatislensedbyCOdirectlymeasures
Ω and, ignoring angular resolutioneffects, is indepen- Theparentsamplewasdrawnfromcataloguesofcom-
CO
dent of the mass M ofthe lenses. The latter property pact radio sources which have been systematically ob-
CO
issimplyunderstood. AgivenvalueofΩ canbemade servedby the authors with intercontinentalVLBI arrays
CO
upofalargenumberoflow–massobjectsorasmallnum- at a frequency of 5 GHz and a resolution ∼ 1 mas; a
berofhigh–massones;hencethenumberdensitynofCO significant fraction of these sources was also observed
ofaparticularmassisproportionalto1/M . Forpoint at 1.6 GHz. The catalogues, radio images and full de-
CO
masses the gravitational lensing cross–section σ ∝ M scription of the observations can be found in the follow-
CO
[9] and hence the path length to lensing (1/nσ) is inde- ing papers: the Pearson& Readhead VLBI Survey (PR;
2
[14]); the first Caltech–Jodrell Bank VLBI Survey (CJ1;
[15,16,17]);thesecondCaltech–JodrellBankVLBISur-
vey (CJ2; [18, 19]). From these samples a large sub–set
of 300 sources was selected on the basis of a “flat” in-
tegrated radio spectrum between 1.4 GHz and 5 GHz.
In this context “flat” implies a source whose spectral in-
dex α ≥ −0.5, where the flux density at a frequency ν
is proportionalto να. The sample thus selectedcontains
nearlyallthestrongestflat–spectrumradiosourcesinthe
sky above declination 35◦.
Flat-spectrum radio sources are best–suited to a
millilens searchbecause they tend to be dominated by a
single compact (sub–mas) “core”, which originates close
to the massive central black hole in the nucleus of the
backgroundgalaxy. Thepresenceoftwocompactcompo-
nents(putativeimages)thenprovidesasimplediagnostic
ofgravitationallensingbyapoint–likemassandgenuine
images will have well understood, simply–related, prop-
erties[9]. Howevergreatcarehastobetakeninchoosing
lenscandidatessincecompactradiosourceshavearange
ofintrinsicstructureswhichcanconfusetheselectionpro-
cess. Guided by a series of simulations we decided only
tolookforcasesofmultipleimagingofthecompactcore. FIG.1: Upper) VLBImap ofamillilens candidate0740+768
It is much harder to be certain of recognising lensing ef- at 5 GHz and 1 milliarcsec resolution; the separation be-
fects on lower–brightness emission regions. We adopted tween the two components is 3.2 mas. Lower) VLBI map of
0740+768 at 22 GHz and 0.3 milliarcsec resolution; the two
the following quantitative selection criteria based on the
components, barely resolved at 5 GHz, have markedly dif-
Gaussian models listed in the original VLBI survey pa-
ferentsurfacebrightnesses. Ratherthanacharacteristiclens-
pers:
ingmorphology0740+768displaystheasymmetric“core–jet”
A candidate has to have two or more compact (< 1
structurecommonly found in flat–spectrum radio sources.
mas) components and the secondary component should
be smaller than the primary. Because of the surface–
brightnessconservingpropertyoflensing, weakerimages
observeata higher frequencyandhigher resolutionthan
aresmallerimages. However,conservativeallowancewas
the original 5 GHz survey maps. The candidates were
madeforGaussianmodel-fittinguncertaintiesbyaccept-
therefore all observed at 15 GHz using the Very Long
ing some candidates in which the secondary had an area
Baseline Array (VLBA). A minority of the candidates
up to twice, and in a few cases three times, that of the
were also observedat one or more of the frequencies 1.6,
primary. The separation of the primary and secondary
8.4 and 22 GHz. The observations and the radio maps
components, 1.5 ≤ ∆θ ≤ 50 mas. This is set by the
will be described elsewhere.
VLBI resolutionandfield–of–viewlimitations anddeter-
Many of the candidates turned out to be core–jet
mines the mass range to which the search is sensitive.
sources in which the jet is faint but contains a “hot–
The upper limit on the separation was set by the prac-
spot”. The VLBA 15– and 22–GHz maps reveal the
ticalities of map–making at the time the VLBI surveys
brightcoreandresolvethelower-brightnesshot-spot. An
were made. The ratio of the flux densities of the core of
example of such a candidate is shown in Figure 1. The
the primary component and the secondary component is
5 GHz mapof0740+768showsa simple unresolveddou-
≤ 40:1. At this level secondaries are detected with high
ble source but the higherresolution22–GHzmapclearly
signal–to–noise ratio.
showsthatthecompactcoreliesattheeastern(left)end
Fifty lens candidates were selected of which six could
withtheother“jet-like”emissionhavingmarkedlylower–
immediately be ruled out from other published VLBI
brightness. Other candidates turned out to be Com-
data. pactSymmetricObjects(CSOs)—anearly(<104 years)
high–luminosity phase of largedouble radio sources [20].
At high resolutionCSOs often show a single centralcore
III. SCRUTINY OF LENS CANDIDATES
straddledbyapairofouter“lobes”ofsignificantlylower
surface brightness; not only is there no detailed corre-
Since the brightness contrast between the core and spondence between sub–structures in the lobes but also
all other emission regions in a radio source increases their parities are incorrect for lensed images.
withincreasingfrequency,thesimplestwaytodetermine Component spectra can also be used to rule out can-
whether two or more of the components are compact, didates. For lensing on the present scales the time delay
and have properties appropriate for lensed images, is to between the light paths ranges from a few seconds to a
3
IV. LIMITS ON ΩCO
We used the detection volume method introduced by
Nemiroff[10]anddevelopedindetailforthespecificcase
of a VLBI search for point masses by KKB. We will,
therefore, only make a few points specific to our search.
The most important observational limit is the flux ra-
tio R(< 40 : 1) which sets the maximum source–lens
impact parameter and hence defines the basic detection
volume. Theusualdefinitionof“strong”lensing[9]refers
to images with a flux ratio of < 7 : 1; our < 40 : 1
flux ratio therefore corresponds to a configuration with
a larger lens–to–source “impact parameter” and hence
thecross-sectionforlensingisalmostfivetimesthatnor-
mally assumed for lensing calculations. Each source is
observedwith an approximatelyfixed angular resolution
andhence minimum imageseparationδ(=1.5)mas,and
limited field–of–view ∆(=50) mas, both of which act to
truncate the detection volume. In effect δ and ∆ define
the lower and upper limits of a mass range for which
the truncation is small. Our search is sensitive to the
FIG. 2: Limit on ΩCO at the 95% confidence level from the mass range ∼ 106 to ∼ 108 M⊙. For observations of a
failure to detect gravitational lensing amongst 300 compact
number of sources the individual detection volumes for
sources with image separations in the range 1.5–50 milliarc-
eachsourcecanbe summed togive atotaldetectionvol-
sec.
ume. In the calculation of these volumes one needs to
know the source redshifts and these are available for 270
out of the 300 sources in our sample; the mean redshift
is 1.30 and 20% of the sources have redshifts ≥ 2. For
few hours,whichis muchshorterthanthe timescalesbe-
theremaining30sourceswehaveassumedadistribution
tween sets of VLBI observations. Lensed images must,
in redshift similar to that exhibited by the other 270.
therefore,brightenandfade together. Astrongcorollary
For the calculation of the angular size distances we took
is that lensed images must have identical radio spectra H =65 km s−1 Mpc−1 and, for direct comparison with
0
or, equivalently, their flux ratio must not be frequency–
KKB’sresultweassumedanEinstein–deSitterUniverse
dependent. This argument should be used with care if
(Ω =1;Ω =0).
M Λ
one or both of the components is well resolved but we
ruled out candidates with compact components if the
Our null result allows an upper limit to be placed on
flux ratios at different frequencies were inconsistent by
> ΩCO and Figure 2 shows the limit atthe 95% confidence
∼30%.
level as a function of CO mass. The limit is approxi-
Component motion is also an excellent discriminant. mately constant from ∼ 106 to ∼ 108 M⊙ and in this
<
If the lens movesacrossthe line of sightthe relative sep- mass range ΩCO ∼0.013. If ΩCO was equal to 0.013 the
“expected” number of lenses in the total detection vol-
aration of the images will change. For example a lens at
z ∼0.5, moving transversely with v ∼1000 km s−1, will ume associatedwith our 300 sources would be three and
produce a relative image motion ∼ 1×10−5 mas yr−1. thefactthatnonearedetectedallowsustorejectthishy-
pothesiswith 95%confidence. IfΩ wasequalto 0.026
This is muchtoo small to be measurablewith VLBI and CO
then∼6lenseswouldbeexpectedandwecanrejectthis
thus,ifrelativemotionisdetected,the secondarycannot
higher mass density with 99.7% confidence.
be a lensed image. In a separate follow–up programme
forthePRandCJVLBIsurveysmostofthesourceshave
been observed more than twice over a period of several These limits are conservative because gravitational
years [21]. Currently over 30 of our 50 candidates are lensing increases the observed flux density of a back-
known to show component motions greater than ∼ 0.1 ground source and hence lensed sources are drawn from
mas yr−1 and hence can be ruled out by this means as a fainter source population than the unlensed sources;
well. a flux–limited survey will contain more lenses than ex-
pected. Ournullresultthereforecorrespondsformallyto
All 50 candidates were ruled out, often for a combina- astrongerlimit onΩ but the “magnificationbias”as-
CO
tion of the reasonscited above,and we now use this null sociated with flat spectrum radio sources, especially for
resultto setquantitativelimits onsupermassiveΩ for lens systems with high flux ratios, is of order unity [22]
CO
objects uniformly distributed throughout the universe. and we have therefore ignored this effect.
4
V. DISCUSSION about one third of Ω .
b
A large population of uniformly–distributed ∼ 106.5
KKB derived a limit on ΩCO (107–109 M⊙) < 0.4 M⊙ black holes is required by the cosmogonic model de-
(99.7% confidence); this corresponds to Ω <0.2 (95% veloped by Gnedin & Ostriker [5] and Gnedin, Ostriker
CO
confidence). The lower mass limit is larger than ours & Rees [6]. This model predicts that up to 5% of high
since they took δ ∼ 4 mas compared with our 1.5 mas. redshift sources should be detectably lensed by such a
The upper mass limit derived by KKB is high since it population i.e. there should be up to 15 lenses in our
is based on ∆ = 500 mas which is, in our view, opti- sample. They are notobservedandhence the model can
mistic; we used ∆ = 50 mas. Our null result implies be ruled out.
ΩCO <∼0.013 (95% confidence) in the mass range ∼ 106 Perhaps the next interesting limit is ΩCO <∼0.005
to∼108M⊙ whichisabout15timesmorestringentthan which would constrain the contribution of supermassive
KKB’s. The improvement arises from a combination of CO to be no more than the baryonic contribution of
moresources(300cf. 48),largerR(<40:1cf. <20:1) presently observable stars and galaxies. To reach this
andhencelargerlensingcross–sectionandahighermean limit about 1000 sources, with the same redshift distri-
redshift for the parentsample (1.30 cf. 0.89). Our result bution as the present sample, would have to be studied;
allows the following conclusions to be drawn. this would be a time–consuming, but relatively straight-
Uniformly distributed CO in the mass range ∼ 106 forward, task.
to ∼ 108 M⊙ do not make up more than ∼ 1% of the We thank Silke Britzen for providing results prior to
closure density Ω = 1 which is strongly supported publication. The VLBAisthe VeryLongBaselineArray
total
by the latest measurements of the angular spectrum of andisoperatedbytheNationalRadioAstronomyObser-
the Cosmic Microwave Background [23]. Similarly such vatorywhichisafacilityoftheNationalScienceFounda-
COdonotmakeupmorethan∼3%ofthe DarkMatter tionoperatedundercooperativeagreementbyAssociated
density Ω ∼ 0.3 favoured by current observations. Universities, Inc.
DM
ThefavouredvalueofthebaryondensityfromBig–Bang Note added in proof: Whenthis workwasalmostcom-
Nucleosynthesis is Ω h2 = 0.019±0.002 [24]. Taking a pleted we became aware of the millilensing results of
b
plausible value for h (0.65) implies Ω = 0.045±0.005 Nemiroff and collaborators (preceding PR Letter) using
b
thus our 95% confidence limit implies that uniformly– gamma ray bursts. Their work has produced limits on
distributed Jeans–mass CO do not make up more than the CO abundance which are similar to ours.
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