Table Of ContentMNRAS000,1–14(2016) Preprint12January2017 CompiledusingMNRASLATEXstylefilev3.0
A counter-image to the gravitational arc in Abell 1201:
Evidence for IMF variations, or a 1010 M black hole?⋆†
⊙
Russell J. Smith‡, John R. Lucey and Alastair C. Edge
Centre forExtragalactic Astronomy, Universityof Durham, Durham DH13LE
7
1
0 12January2017
2
n
a ABSTRACT
J Abell 1201 is a massive galaxy cluster at z=0.169 with a brightest cluster galaxy
0 (BCG)thatactsasagravitationallenstoabackgroundsourceatz=0.451.Thelensing
1 configuration is unusual, with a single bright arc formed at small radius (∼2arcsec),
wherestarsanddarkmatterarebothexpectedtocontributesubstantiallytothetotal
] lensingmass.Here,wepresentdeepspectroscopicobservationsoftheAbell1201BCG
A
with MUSE, which reveal emission lines from a faint counter-image, opposite to the
G main arc, at a radius of 0.6arcsec. We explore models in which the lensing mass is
. described by a combination of stellar mass and a standard dark-matter halo. The
h
counter-image is not predicted in such models, unless the dark-matter component is
p
negligible, which would imply an extremely heavy stellar initial mass function (IMF)
-
o in this galaxy. We consider two modifications to the model which can produce the
r observedconfigurationwithoutresortingtoextremeIMFs.Imposingaradialgradient
t
s inthestellarmass-to-lightratio,Υ,cangenerateacounter-imageclosetotheobserved
a positionifΥincreasesby >60percentwithintheinner∼1arcsec(e.g.variationfrom
[ ∼
a Milky-Way-like to a Salpeter-like IMF). Alternatively, the counter-image can be
1 produced by introducing a central super-massive black hole. The required mass is
v MBH=(1.3±0.6)×1010M⊙, which is comparable to the largest black holes known to
5
date, several of which are also hosted by BCGs. We comment on future observations
4
which promise to distinguish between these alternatives.
7
2 Key words: gravitational lensing: strong – galaxies: elliptical and lenticular, cD –
0 galaxies:clusters: individual: Abell 1201
.
1
0
7
1
1 INTRODUCTION (1995) (NFW) functional form (e.g. Kneib et al. 2003;
:
v Schmidt& Allen 2007). The slope of the DM profile to-
Xi Richgalaxy clustersareextremelocations: theyoccupythe wards the cluster centre is sensitive to the micro-physics
largest dark-matterhaloes intheuniverse,and harbourthe
of the DM particle (Spergel& Steinhardt 2000), as well as
r most massive galaxies at their centres. In turn, the central
a tointeractionsbetweenbaryonicanddarkcomponents(e.g.
galaxies of massive clusters host some of the most extreme
Blumenthalet al. 1986). Determining the inner halo profile
black holes known to date.
slopeis,however,hamperedbythepresenceofthebrightest
Clustersaredominatedbydarkmatter(DM)atallbut
cluster galaxy (BCG), located at or near the halo centre.
thesmallest radii,sotheyprovideimportantconstraintson
Withinaradiusofafewkpc,thestellarmassdensityofthe
the structures of DM haloes. At large radii, weak-lensing
BCG is comparable to, or exceeds, the DM density. Hence
andX-raydatalargelysupporttheNavarro, Frenk& White
theobservationalchallengeofstudyingthecentralstructure
oftheDMhaloiscoupledtothatofunderstandingthestel-
⋆ BasedonobservationscollectedattheEuropeanSouthernOb- lar component (Sandet al. 2004).
servatory,Chile(ESOProgramme077.A-0806(A)). The BCG stellar mass contribution is also a matter
† Based on observations made with the NASA/ESA Hubble
of interest in its own right, since massive elliptical galax-
Space Telescope, obtained from the Data Archive at the Space
ies are widely suspected to harbour stars formed accord-
TelescopeScienceInstitute,whichisoperatedbytheAssociation
ing to an initial mass function (IMF) different from that
ofUniversitiesforResearchinAstronomy,Inc.,underNASAcon-
pertaining to the Milky Way (MW) (e.g. Treu et al. 2010;
tract NAS 5-26555. These observations are associated with pro-
gram08719. Conroy & vanDokkum 2012b; Cappellari et al. 2012). If
‡ E-mail:[email protected] the IMF variations are associated with the physical con-
(cid:13)c 2016TheAuthors
2 Russell J. Smith et al.
ditions in violent starburst events at early epochs (e.g. matic measurements and dynamical modelling will be pre-
Chabrier, Hennebelle& Charlot 2014), then the centres of sentedinaforthcomingpaper.Here,wefocusonthestrong-
BCGs are a likely site to habour the affected populations. lensing constraints, showing that the unusual configuration
In a recent study using a combination of stellar dynam- ofAbell1201allowsustoinferthepresenceofanadditional
ics and gravitational lensing constraints on the mass pro- centrally-concentrated mass, of order 1010M⊙, with no de-
file of BCGs, Newman et al. (2013b) found a preference for tectableluminous counterpart.
both shallower-than-NFW DM profiles and heavier-than- Theremainderofthepaperisstructuredasfollows:Sec-
MW IMFs, on average. tion 2 describes the observations and data reduction steps,
Finally, the most massive galaxies, in the most mas- and presents the general lensing configuration, including
sive haloes, are also likely hosts for the largest central identification of a faint counter-image close to the centreof
black holes (BH) in the universe (McConnell et al. 2011; the BCG. Section 3 presents a lensing analysis constrained
Hlavacek-Larrondoet al. 2012). In distant lensing clusters, only by the main arc, using models with a constant stel-
kinematicdatadonotresolvethedynamicaleffectsofBHs, lar mass-to-light ratio combined with a parametrized dark-
and therelative contribution of theBH tothe lensing mass matter halo. Section 4 then discusses the interpretation of
is usually negligible. However, for clusters at lower red- thecounter-image,proposingthreealternativescenarios:(a)
shift, sufficiently massive BHs may have measurable ef- a very heavy IMF throughout the BCG, (b) a steep radial
fects on the stellar kinematics at small radius. For cer- variation in the stellar initial mass function, and (c) a very
tain configurations, massive BHs can also affect the lensing massivecentralblackhole.InSection5wediscussthemerits
caustic structure, altering the numberof images observable and implications of these solutions, with reference to exter-
(Mao, Witt & Koopmans 2001). nal evidence, and Section 6 considers future observations
In this paper, we present the first results from new which might help discriminate between them. Brief conclu-
wide-field integral-field spectroscopic observations of the sions are summarized in Section 7.
z=0.169 cluster Abell 1201. Edge et al. (2003) (hereafter For computing physical scales we adopt the relevant
E03) identified a bright tangential arc around the BCG us- cosmological parameters from Planck Collaboration et al.
ing shallow Hubble Space Telescope imaging with WFPC2 (2016): h=0.678, ΩM=0.308 and ΩΛ=0.692. In this cos-
(Wide Field and Planetary Camera 2), obtained as part of mology, the spatial scale at the redshift of Abell 1201 is
a systematic search for lensing clusters (Sand et al. 2004). 2.96kpcarcsec−1.
The lensing configuration of Abell 1201 is unusual, in that
the arc is located at a radius of only ∼2arcsec (∼6kpc),
well within the effective radius of the BCG, rather than
2 MUSE OBSERVATIONS
at the ∼10arcsec scales typical for cluster lenses. E03
also presented Keck spectroscopy from which they mea- We observed Abell 1201 with the Multi-Unit Spectroscopic
sured a redshift of z=0.451 for the arc. X-ray observa- Explorer (MUSE) (Bacon et al. 2010) on the 8.2m Yepun
tions of Abell 1201 (Owers et al. 2009; Ma et al. 2012) in- (Unit Telescope 4) of European Southern Observatory’s
dicate a post-merger morphology for Abell 1201, with the VeryLargeTelescope. Thedatausedinthispaperwereob-
merger direction aligned with the BCG major axis, and tained on the nights of March 31 and April 2, 2016, under
the BCG itself offset from the X-ray peak by ∼11kpc good seeing conditions.
along the same axis. From the radial velocities of 165 A total of twelve 940-second exposures were obtained,
member galaxies, Rineset al. (2013) measure a cluster ve- using the standard spectral configuration, covering 4750–
locity dispersion σcl=683+−6583kms−1, and derive a virial 9350˚A, sampled at 1.25˚A per pixel, with resolution 2.6˚A
mass M200=(3.9±0.1)×1014M⊙ (for h=0.678) from the FWHM(atλ=7000˚A).Each exposurespansa ∼1arcmin2
infall caustic fitting method. Based on Sloan Digital Sky field-of-view,with0.2arcsecspatialpixels.Tohelpsuppress
Survey (SDSS) photometry, the BCG has a luminosity of the effects of instrumental artifacts, the observations were
Lr≈4×1011L⊙,r, while the Two Micron All Sky Survey arrangedinfourgroupsofthreeexposureseach.Eachgroup
(Jarrett et al. 2000) yields LK≈1.6×1012L⊙,K. The BCG was observed at a different position angle (0, 90, 180, 270
has a half-light radius of reff≈15kpc. Sand et al. (2004) degrees), and thefield centres for thegroups were arranged
measuredavelocitydispersion ofσ=230–250kms−1 inthe in a 2×2 grid, with separation of 15arcsec. Hence the total
inner 1.5arcsec; SDSS reports σ=277±14kms−1. The lu- fieldobservedis75×75arcsec2,whilethefullexposuretime
minosity, radius and velocity dispersion for the Abell 1201 of 3.1hourswas obtained only in thecentral 45×45arcsec2.
BCGareconsistentwiththeearly-typegalaxyFundamental Furthersmallditheroffsets(∼0.5arcsec)weremadebetween
Plane. theexposuresin each group.
Our new integral-field observations were motivated by The initial data reduction steps were accomplished us-
the unusually small separation of the bright arc in Abell ing the standard MUSE pipeline. Each of the twelve expo-
1201, which makes it feasible to combine stellar kinematics sures was reconstructed to generate a separate datacube,
and strong-lensing information across an overlapping range using an initial “global” sky spectrum obtained from the
in radius, which is not possible in most lensing clusters. darkest parts from the complete field of view. This leaves
The velocity dispersion measurements from the Sand et al. awavelength-dependentbackground“striping”effect,appar-
(2004) long-slit spectra do not reach the radius of the entlyduetoresidualbias-levelvariationswhichdifferamong
arc in Abell 1201, while previous integral-field observa- the 24 separate spectrograph“channels”of the instrument.
tions (Swinbank 2003) covered a much narrower field-of- Toreducetheimpactofthesevariations,wederivedandsub-
view and sampled a limited spectral range, not including tractedaseparate“residualsky”spectrumfrom thedarkest
thebright[Oiii]emissionlinefromthearc.Ourstellarkine- spatial pixels in each channel, prior to combining the sepa-
MNRAS000,1–14(2016)
Abell 1201 counter-image 3
(a) 10" (b) 2"
50kpc 10kpc
Figure1.CollapsedimageoftheAbell1201field,fromthefinalcombinedMUSEdatacube,overthewavelengthinterval6600–7600˚A.
Panel(a)showsthefullfield-of-viewwiththegrey-scaleoptimisedtoshowfaintgalaxiesandtheouterpartsoftheBCG.Theredsquare
indicates the region expanded in Panel (b), in which the grey-scale is scaled to show the continuum light from the main arc. In both
panels,thegreensquareindicatesthe6×6arcsec2 areadepicted inFigures3,4,5,7and9.
rate observations into a single final data-cube. During this subtracting a model for the BCG spectrum) show that the
final combination, integer-pixel astrometric offsets were ap- excess flux is clearly centred on the expected wavelengths
plied,andpixelsattheedgeofeachchannelweremaskedto of the [Oiii] and [Oii] lines (Fig. 2e,f). The weaker [Oiii]
improvetheflatness of thebackground. 4959˚AandHβ linesarenotclearly detectedfrom theinner
A broad-band image generated from the combined image, but given thespatial coincidence of HST continuum
MUSEdata-cubeisshowninFig.1.Thepoint-spreadfunc- emission with the significant emission in two lines, both of
tion, measured at ∼7000˚A from stars in the combined ob- whicharewell-matchedtotheexpectedwavelengths,wecon-
servation, has a FWHM of 0.6arcsec (2.9pixels). The tan- sider it beyond reasonable doubt that the faint source is a
gentialarcisclearlyseeninthecontinuumimage,aswellas lensed counter-image to themain arc.
numerousotherclusterandbackgroundgalaxies1.TheBCG
light can be traced to ∼20arcsec (∼60kpc).
Fig.2presentsthediscoveryofafaintcounter-imageto
the main arc. Extracting the MUSE spectrum of the main
arc, we find that the [Oiii] 5007˚A is the brightest emis- ThespatialresolutionoftheMUSEdataismuchlower
sion line in the MUSE spectral range. Integrating over this than that of the HST image, so in the lens modelling re-
line,andsubtractingacontinuumderivedfromneighbouring ported in Sections 3 and 4 we primarily use HST-derived
wavelengths, we obtain the net emission-line image shown positional constraints. However, the emission-line data can
inFig.2a,b.InadditiontothemainarcreportedbyE03,a provide additional information to help verify the solutions
significant excess emission is observed 0.6arcsec SSEof the obtained. Although matching the overall form of the arc as
BCG centre, with a flux ratio ∼1:200, relative to the inte- seen by HST, there are notable differences which cannot
grated value for the main arc. A faint peak is seen at the be attributed to the difference in resolution. Strikingly, the
same location in a similarly-constructed net [Oii] 3727˚A bright image pair at ∼(0.0,+2.3)arcsec, denoted A1b/c by
image (Fig.2c).Infact, aresidualfeature isalready clearly E03,andusedbythemtolocatethecriticalcurve,doesnot
visibleatthislocationintheE03HSTWFPC2image,after correspondtoanypeakintheemission-linemap.Conversely,
subtracting a model for theBCG light (Fig. 2d).Note that theregionofweakercontinuumat∼(–2.2,+1.2)arcsecisco-
thebrightobject at∼(–4,+0.5)arcsecisanunrelatedback- incidentwith themaximuminthe[Oiii]image.Otherlocal
ground galaxy at z=0.273, which is not multiply-imaged.) peaks are located at the extremities of the arc (A1a, A1f
Spectra extracted at the location of the faint peak (after in the E03 nomenclature), roughly coincident with contin-
uum maxima, and at ∼(–0.5,+0.2)arcsec, which does not
have a continuum counterpart. Fig. 3 shows the velocity
1 Wehaveconductedacarefulsearchforadditionallensedgalax- mapderivedfromthe[Oiii]line.Thetotalvelocityrangeis
iesbehindAbell1201,whichcouldprovideimprovedconstraints ±25kms−1. A reversal in the velocity trend along the arc,
onthelensingmodel.Althoughmanyfaintemission-lineobjects due to the lens folding, is clearly seen at ∼(0,+2.2)arcsec,
werefound,noneofthemcanbeidentifiedasmultiplyimaged. as reported previously by Swinbank(2003).
MNRAS000,1–14(2016)
4 Russell J. Smith et al.
(a) MUSE [OIII] 5007A (b) MUSE [OIII] 5007A (c) MUSE [OII] 3727A
4 4 4
main arc main arc
c]2 c]2 c]2
e e e
s s s
c c c
ar ar ar
c [ c [ c [
e e e
D D D
0 0 0
D D D
counter−image
2 2 2
− − −
2 0 −2 −4 2 0 −2 −4 2 0 −2 −4
D RA [arcsec] D RA [arcsec] D RA [arcsec]
2 2
(d) HST/WFPC2 resid 0. (e) MUSE [OIII] 5007A 0. (f) MUSE [OII] 3727A
44
e] e]1
Dec [arcsec]22 arbitrary scal0.1 arbitrary scal0. counter−image
D 00 flux [ counter−image flux [0.0
0
0.
22 main arc
−− main arc
1
0.
2 0 −2 −4 7240 7260 7280 7300 − 5380 5400 5420 5440
D RA [arcsec] observed wavelength [angstrom] observed wavelength [angstrom]
Figure 2. Discovery and confirmation of a faint counter-image to the bright arc in Abell 1201. Panel (a) shows the net [Oiii] 5007A˚
emission-line image derived from our MUSE observations, scaled to show structure within the main arc. The green cross indicates
the position of the BCG centre. Panels (b) and (c) show net emission-line images for [Oiii] 5007A˚ and [Oii] 3727A˚, with grey-scale
emphasizing the faint peak seen close to the lens centre, which we identify as a lensed counter-image. Panel (d) demonstrates that a
peak is also visible in the HST continuum image (WFPC2/F606W), after careful subtraction of the foreground lens galaxy using an
ellipse-fittingmethod.Finally,panels(e)and(f)showtheextractedspectraofthemainarcandcounter-imagecentredontheemission
lines,confirmingtheircommonorigininaz=0.451source.
3 MODELS CONSTRAINED BY THE MAIN 0.025arcsec in each coordinate, i.e. a quarter of the HST
ARC pixel.
All lensing calculations here are made using the
E03 showed that the main arc could be reproduced by a gravlens/lensmodel software (Keeton 2001).
“cusp” configuration, where the unlensed position of the
source crosses one of the points of the tangential caustic.
In this case, each point in the source maps to three neigh- 3.1 Constant M/L models
bouring images close to the tangential critical line; for an
The first models we attempt to fit are those in which the
extended source, the images merge to form a single large
mass distribution is fully determined by the observed lumi-
arc.
nosity of theBCG.
In this section, we develop models for the lens, con- The luminosity profile of the Abell 1201 BCG exhibits
strained by three positions on the main arc proposed by aclearflatteningnearthecentre,wellbeyondtheradiusaf-
E03 to be sister images of one another: the A1b/c im- fectedbytheHSTPSF.Withintheradiusofthetangential
age pair bracketing the critical curve, and A1f at the far arcbutoutsidethePSFdisk,theprofileiswelldescribedby
end of the arc. The location of the velocity fold in Fig. 3 anelliptical“Nuker”law(Laueret al.1995),withouterand
strongly supportsthecritical curvepassing throughA1b/c, inner logarithmic slopes of β≈1.2 and γ≈0.4 respectively,
though we note that the velocity near A1f appears dis- and break radius rb≈1kpc, or “cusp radius” rγ≈0.5kpc.
crepant with the measurements near A1b/c. The coordi- Cores of this size are typical for BCGs of comparable lu-
nates for the constraints, in arcsec relative to the BCG minosity: at MV ≈–23.7, Laueret al. (2007) derive a mean
centre, are: A1b=(−0.24,−2.34), A1c=(+0.24,−2.24), rγ=0.45kpcwith a factor-of-two galaxy-to-galaxy scatter.
A1f=(+3.13,−0.26), determined by computing centroids Forthelensmodelling,wechoosetorepresentthestellar
within a 2-pixel window around each flux peak in the HST mass using a pixelized convergence map, to account for the
image. The estimated positional error on all constraints is detailed profile and angular structure in the BCG. Specifi-
MNRAS000,1–14(2016)
Abell 1201 counter-image 5
4 image and source positions, for the best-fitting model with
A1a A1b D v [km/s] constantM/Landshear.Themodelmatchestheinputposi-
−20 −10 0 +10 +20 tionconstraintsessentiallyperfectly;thereisonlyoneresid-
3 ualdegreeoffreedomin thefit.Moreover,themodelrepro-
duces the overall morphology of the main arc: pixels in the
arc map to one another successfully, despite not being used
asconstraintsin themodelfitting.Thearcpointsalso map
2
toacrediblemorphologyinthesourceplane,lyingacrossthe
c]
e cuspofthetangentialcaustic.Theemission-linestructureof
s
arc 1 A1c thearcprovidesadditionalsupportforthisgeneralscenario:
c [ the critical curve passes directly through the continuum-
De faint but line-bright region at ∼(–2.2,+1.2)arcsec. This is
D suggestiveofanemission-linepeaklocatednearthecaustic,
0
at the northern tip of the unlensed source, and mapping to
an image pair that is unresolved at the MUSE resolution.
The third image corresponding to this pair would be close
1 A1f
− to A1a, the peak at the north-eastern extremity of the arc,
which is also bright in theemission map (see Fig 2a).
Thederivedshearislargeinamplitude (γ=0.22),and
2
− directed 31deg West of North, in a convention where the
2 1 0 −1 −2 −3 −4
angleindicates thedirection of anexternalmass concentra-
D RA [arcsec]
tion generating the shear. This direction is consistent with
Figure3.Velocityfieldinthearc,derivedfromagaussianfitto the overall cluster axis along which the BCG and merging
the[Oiii]line,afterapplyinga3×3pixelspatialsmoothing.Con- substructureare aligned. We derive a total mass-to-light of
toursshowtheHSTresidualimage.Thethinandthicklinesare M/L=10.6±0.3inr,wheretheerrorsareestimatedbysim-
thecausticandcriticalcurvesfromthelensingmodelinFig.7d. ple Monte Carlo simulation, perturbing the positional con-
The labels A1a, etc, show nomenclature for local maxima intro- straintsbyerrors of0.025arcsec ineach coordinate,and re-
ducedbyE03andreferredtointhetext.
fitting the model. This result is consistent with the value
of M/L=9.4+2.4 in V, estimated by E03 from their two-
−2.1
component parametric model. The total mass-to-light ra-
cally, we construct an ellipse-fit representation of the HST tio is much larger than the expected value of ∼4 for an
image,derivedaftermaskingpixelsaffectedbythemainarc oldstellarpopulationwithMW-likeIMF2,indicatingeither
and by the z=0.273 source. We calibrate to the r-band by a heavier IMF, or significant dark-matter contributions, or
matching the large-aperture flux of the BCG as measured both. The projected mass inside a 1.6arcsec (4.75kpc) ra-
from Data Release 8 of SDSS (Aihara et al. 2011), and use diusapertureis Map=(37±1)×1010M⊙.
the source and lens redshifts to compute a lensing conver-
gencemapunderanassumedmass-to-lightratioofM/L=1
3.2 Models with a dark-matter halo
(in solar units). A scaling parameter applied to this con-
vergence then yields the lensing estimate for M/L. For the Wenowconsidermodelswithanexplicitdescriptionforthe
mass-follows-light models, M/L is formally identical to the darkhaloasaseparatemasscomponent,assumed tofollow
stellar mass-to-light ratio Υ, but in practice of course we a Navarro,Frenk & White(1996) (NFW)density profile.
expect themass toincludecontributionsfrom dark matter. In the cases shown in Fig. 4, we impose a 25 or 50 per
Without additional freedom, the constant M/L model centdark-matterfraction withinanapertureof4.75kpcra-
is unable to fit the three positional constraints or produce dius. Panels (b) and (c) show the models with a spherical
the observed arc morphology. This is a generic result, al- halo, while in panel (d) the halo is flattened with elliptic-
ready noted by E03: any model matched to the orientation ity e=0.4. In each case, the NFW break radius is fixed at
and ellipticity of the BCG light, in which the critical curve rs=300kpc(∼100arcsec).Forthevirialradiusof 1.47Mpc
bisects A1b/c, will produce a third image that does not lie (for our cosmology) measured by Rineset al. (2013), this
on the arc. The simplest solution is to include greater free- corresponds to a halo concentration c= 4.9, which is typi-
dom in the model, by introducing an external linear shear cal in simulations for clusters with mass similar to that of
term, with amplitude γ and direction θ. The shear is in- Abell12013
tended as a first-orderapproximation to theeffect of struc- After optimising the stellar mass-to-light ratio and the
ture beyond the modelled region. (E03 achieved a similar
effect by adding a highly-elliptical mass component to rep-
resenttheclusterpotential.)Theinclusionoftheshearterm 2 For example, a single-burst population formed at z≈4, has
is motivated by the complex and asymmetric mass struc- age ∼10Gyr at z=0.169. In the Maraston (2005) models, with
Kroupa (2001) IMF, this population has Υ=3.5 for [Z/H]=0.0
ture surrounding the lens: X-ray observations and optical
or Υ=4.4 for [Z/H]=+0.35. This value is for observed SDSS
spectroscopy (Owers et al. 2009; Ma et al. 2012) indicate a
r-band,aftercorrectingfora18percentbandshiftingeffect.
post-mergermorphologyforAbell1201,withthemergerdi- 3 Netoetal.(2007)reportameanc=4.8,witha2σrangeof3.0–
rectionalignedwiththeBCGmajoraxis,andtheBCGitself 7.4,atM200=3.5×1014M⊙,forourcosmology.Wehaveverified
isoffsetfromtheX-raypeakby∼11kpcalongthesameaxis. that even adopting rs=150kpc, corresponding to c≈10 makes
Fig. 4a shows the lensing caustics, critical lines, and nosubstantivedifferencetotheresultsinthispaper.
MNRAS000,1–14(2016)
6 Russell J. Smith et al.
4 4
(a) M = 37.0· 1010 M (b) M = 35.8· 1010 M
ap sun ap sun
Stars=37.0, DM=0.0, BH=0.0 Stars=26.8, DM=8.9, BH=0.0
3 3
No DM Sph DM
2 2
c] c]
e e
s s
c c
ar 1 ar 1
c [ c [
e e
D D
D D
0 0
1 1
− −
¡ = 10.6 g = 0.22 q = −31 ¡ = 7.7 g = 0.18 q = −31
2 2
− −
2 1 0 −1 −2 −3 −4 2 1 0 −1 −2 −3 −4
D RA [arcsec] D RA [arcsec]
4 4
(c) M = 34.6· 1010 M (d) M = 34.7· 1010 M
ap sun ap sun
Stars=17.3, DM=17.3, BH=0.0 Stars=17.4, DM=17.4, BH=0.0
3 3
Sph NFW Ellip NFW
2 2
c] c]
e e
s s
c c
ar 1 ar 1
c [ c [
e e
D D
D D
0 0
1 1
− −
¡ = 4.9 g = 0.15 q = −31 ¡ = 5.0 g = 0.09 q = −30
2 2
− −
2 1 0 −1 −2 −3 −4 2 1 0 −1 −2 −3 −4
D RA [arcsec] D RA [arcsec]
Figure4.Lensingmodelsforthemainarc.Ineachpanel,thebluelinesshowcriticalcurvesintheimageplane,andtheredcurvesare
thecorrespondingsource-planecaustics.Heavyblackcirclesaretheinputimagepositionsusedasconstraintsforthemodeloptimization.
Black crosses are the output predictions for these images, and the square marks the corresponding position in the source plane. The
orange crosses show all observed pixels in the main arc, identified above a threshold in the HST image. These points are not used as
constraints inthefitting, butprovideindependent validationofthemodels:thepredicted sisterimagestothearcpoints areplotted as
cyan circles, and their source-plane counterparts are shown in green. The grey contours show the net [Oiii] emission from MUSE. For
eachmodelweindicatethetotalmassprojectedwithinacircularapertureof4.75kpc(1.6arcsec),andthecontributionsfromstarsand
darkmatterwithinthisaperture.Wealsonotethestellarmass-to-lightratio,Υ,andtheexternalshearamplitude,γ,andangle,θ.Panel
(a) shows the minimal model, in which all mass follows the observed light, with an external linear term. Panels (b) and (c) include a
sphericalNFWdark-matterhalocomponent,contributingrespectively25or50percentoftheprojectedmasswithin4.75kpc.InPanel
(d),theDMisassignedanellipticitysimilartothatoftheBCG.
externalshear,themodelswithdarkmatteryieldfitstothe reducesthe derived stellar mass-to-light ratio, to Υ≈5. In-
main arc that are virtually identical to those of the mass- creasing the halo ellipticity reduces the required external
follows-light models.Thisisconsistentwiththeexpectation shear amplitude,to γ=0.12. Regardless of theform of the
that only the total projected mass within the arc would be adoptedhalo,thetotalprojectedmasswithina4.75kpcra-
wellconstrained.Adding∼50percentdarkmatternaturally
MNRAS000,1–14(2016)
Abell 1201 counter-image 7
dius aperture is slightly reduced from the no-dark-matter slope f0 between the galaxy centre and some threshold ra-
case, with Map=(35±1)×1010M⊙. dius,r0.Themass-to-lightratioisunchangedbeyondr0.To
have the desired effect, r0 must be smaller than the radius
probed by the main arc. We limit our exploration to cases
4 INTERPRETATION OF THE with r0=1.5arcsec or r0=0.75arcsec, and tune the dark-
mattercontent in each model toretain Υ=4.0 in theouter
COUNTER-IMAGE
(unaffected)region, compatiblewith a MW-like IMF.
In this section, we turn to considering models which can Fig. 5 illustrates several representative models with Υ
adequately predict the presence of the inner counter-image gradients.Foreachvalueofr0,weshowthecasecorrespond-
shown in Fig. 2. ing to the minimum gradient necessary to produce a radial
arc(Panelsa,c),andforalargervalueillustratingtheeffect
ofincreasingf0,with Υandr0 heldfixed(Panelsb,d).The
4.1 A uniformly very heavy IMF?
main result of these tests is that a radial arc counter-image
In the models with dark-matter haloes (Fig. 4b,c,d), the is formed if Υ increases by a factor of 1.5–1.7 towards the
sourceliesinsideaso-called“nakedcusp”,wherethetangen- galaxycentre,dependingonlyslightlyonr0.Thesecasesef-
tialcausticcurveextendsbeyondtheellipticalcaustic.This fectively add (1–4)×1010M⊙ at small radius, relative to an
unusualconfiguration leads toexactly threeimages, of sim- assumptionofconstantΥ=4.0.Atthisthreshold,theradial
ilar magnification, close to the tangential critical line. The arcissimilartothatinthecaseoftheuniformlyheavyIMF
naked cusp arises from the combination of high ellipticity model, forming compact pair of images close to the critical
andstrongshearinAbell1201(whichdeterminesthesizeof line, and somewhat offset from the observed counter-image
thetangentialcaustic),togetherwiththeshallowtotalmass location,withafluxratiocomparabletothe1:200observed.
profile(which sets thelocation of theradial caustic). For steeper Υ gradients, a larger part of thesource falls in-
In the case where all of the gravitating mass is dis- sidethequadruply-imagedregion,andtheradialarcbright-
tributed identically to the stellar light (Fig. 4a), the total ensandbecomesmoreextended,toalengthof0.5arcsecor
massprofileissteeper,sothatsomepointsinthesourcefall more,incontrasttothecompactobservedHSTmorphology.
inside both caustics, and generate additional images, form- The >∼60percentvariationrequiredinΥislargerthan
ing a radial arc4. The new images will be faint compared the∼10percentattributabletotypicalage andmetallicity
to the main arc (both because they are relatively demag- gradientsinmassiveellipticalsandBCGs(Kuntschneret al.
nified by the lens, and because they map to outer parts of 2010; Oliva-Altamirano et al. 2015). Hence this model ap-
the source). Simple elliptical source models can adequately pears to require radial gradients in the IMF; for example
match the observed 1:200 flux ratio. The predicted posi- a factor of 1.55 in Υ corresponds to the difference between
tion of the radial arc is close to, but not exactly coincident a Kroupa(2001) and an extrapolated Salpeter (1955) IMF.
withtheobservedlocationofthecounter-image,beingoffset In summary, a model with spatial variation in the IMF di-
∼0.15arcsec towards thelens centre. rectly alters the slope of the lensing potential, and conse-
If we interpretthis model as apure“stellar-mass”lens, quently produces radial-arc counter-image without requir-
thenthemass-to-lightratioofΥ=10.6impliesanextremely ing such extreme variation away from the MW IMF as in
heavyIMF,withamassexcessfactorof2.4–3.0 (relativeto thespatially uniform scenario.
Kroupa),dependingonthemetallicity,ifthestellarpopula-
tionisold.Thisislargerthanthetypicalmass-excessfactors
4.3 A very massive central black hole?
of 1.5–2.0 reported for giant ellipticals (see Section 5), and
ofcoursetheDMcontributionisunlikelytobenegligibleat An alternative route to steepening the inner mass profile,
the centre of a massive cluster. We therefore consider this without invoking a non-standard IMF at all, is to include
uniformlyheavyIMFinterpretationimplausibleonbalance, contributionsfrom a central super-massiveblack hole.
and explore alternativescenarios in thefollowing sections. The presence of a central point mass can qualitatively
alter the structure of caustics and critical lines in a lensing
system, as described in detail by Mao et al. (2001). For the
4.2 Stellar M/L gradients? purposes of this paper, the relevant aspect is that above a
critical black hole mass (a few per cent of the total mass
Generically, the presence of the counter-image implies that
insidethecriticalcurve),theusualradialcausticcanbede-
the mass profile is at least as steep as the luminosity pro-
stroyed,and all source-plane positions inside thetangential
file,onsmallscales.Thiscannotbeachievedbyalteringthe
caustic become quadruply imaged. Hence the observability
distributionofdarkmatter,aslongasthiscomponentisflat-
and location of a counter-image, for a source located in an
terthanthestellarprofile,asexpected.However,variations
“otherwise-naked cusp”, can become sensitive to the pres-
in the stellar mass-to-light ratio Υ, as a function of radius,
enceandmassofacentralblackhole.Weillustratethissit-
could provide a way to steepen the mass profile sufficiently
uation,asitappliesspecificallytoAbell1201,inFig.6(see
to produce the radial arc without requiring an excessively
fig. 3 of Mao et al. for a more general description). Here,
heavyIMF throughout thegalaxy.
as before, the model is constrained using only the three
We test this scenario by modulating the lensing con-
sister-images identified on the main arc (A1b, A1c, A1f),
vergence generated by the stars, with a linear function of
and the stellar mass-to-light ratio (Υ) and shear (γ,θ) are
re-fitin eachpanel,assumingafixedblackholemasswhich
4 We use the term“radial arc”specifically to refer to an image increases from panel to panel. For relatively small valuesof
generatedbyanextendedsourcewhichcrossestheradialcaustic. theblack-holemass,MBH.0.3×1010M⊙,thecausticstruc-
MNRAS000,1–14(2016)
8 Russell J. Smith et al.
4 4
(a) M = 34.6· 1010 M ((bc)) M = 35.0· 1010 M
ap sun ap sun
Stars=15.2, DM=19.4, BH=0.0 Stars=16.8, DM=18.2, BH=0.0
3 3
r =0.75, f =1.5 r =0.75, f =2.0
0 0 0 0
2 2
c] c]
e e
s s
c c
ar 1 ar 1
c [ c [
e e
D D
D D
0 0
1 1
− −
¡ = 4.0 g = 0.09 q = −30 ¡ = 4.0 g = 0.11 q = −31
2 2
− −
2 1 0 −1 −2 −3 −4 2 1 0 −1 −2 −3 −4
D RA [arcsec] D RA [arcsec]
4 4
(c) M = 35.3· 1010 M (d) M = 37.0· 1010 M
ap sun ap sun
Stars=18.4, DM=17.0, BH=0.0 Stars=25.9, DM=11.1, BH=0.0
3 3
r =1.5, f =1.7 r =1.5, f =2.9
0 0 0 0
2 2
c] c]
e e
s s
c c
ar 1 ar 1
c [ c [
e e
D D
D D
0 0
1 1
− −
¡ = 4.0 g = 0.13 q = −31 ¡ = 4.0 g = 0.24 q = −32
2 2
− −
2 1 0 −1 −2 −3 −4 2 1 0 −1 −2 −3 −4
D RA [arcsec] D RA [arcsec]
Figure 5. Examples of lensing models with radially-variable stellar mass-to-light ratio Υ in the central part of the BCG. A linear Υ
gradient isappliedwithinaradiusof r0 (0.75or 1.5arcsec, inthe cases shown), andcauses afactor of f0 increasebetween r0 andthe
BCGcentre.ThevalueofΥquotedineachpanelisthe(constant) valueatradiusgreater thanr0.
tureiscomplex,andahighlydemagnifiedimageisproduced counter-image consistently into our modelling, we add it as
at extremely small separation (.0.1arcsec) from the lens a fourth positional constraint, C=(−0.26,−0.50), and re-
centre.Formoremassiveblackholes(MBH≈0.5×1010M⊙), fitforfourmodelparameters,includingtheblack-holemass
thereisonlyasinglecaustic,andthefourthimagebeginsto (Υ,γ,θ,MBH). As before, the fit does not distinguish be-
extendawayfromthelenscentre.AsMBH increasesfurther, tween dark matter and stellar mass, so we test the results
thecounter-imagebecomesbrighterandmorecompact,and usingdifferentfixedassumptionsforthehaloshapeandmass
moves to larger separation, reaching the observed position contribution.FourillustrativecasesareshowninFig.7.For
forMBH≈(1–2)×1010M⊙.Forthesamemass,thefluxratio each form assumed for the halo, we find that the presence
between main arc and counter-image is ∼1:100. andposition ofthecounter-imagearereproducedforblack-
In the black hole model (unlike the Υ-gradient case), hole masses of (1.2–1.3)×1010M⊙. Adopting the flattened-
all multiply-imaged parts of the source are quadruply im- halo case with ∼50 per cent halo contribution (Fig. 7d) as
aged, so the unresolved inner image can be assumed to our default solution, and using Monte Carlo simulations as
be a sister image to points A1b/c/f. To incorporate the before to propagate positional errors, we obtain a mass of
MNRAS000,1–14(2016)
Abell 1201 counter-image 9
2 2 2
M = 0.1· 1010 M M = 0.2· 1010 M M = 0.5· 1010 M
BH sun BH sun BH sun
c]1 c]1 c]1
e e e
s s s
c c c
ar ar ar
c [ c [ c [
e e e
D D D
D0 D0 D0
1 1 1
−1 0 −1 −2 −1 0 −1 −2 −1 0 −1 −2
D RA [arcsec] D RA [arcsec] D RA [arcsec]
2 2 2
M = 1.0· 1010 M M = 2.0· 1010 M M = 4.0· 1010 M
BH sun BH sun BH sun
c]1 c]1 c]1
e e e
s s s
c c c
ar ar ar
c [ c [ c [
e e e
D D D
D0 D0 D0
1 1 1
−1 0 −1 −2 −1 0 −1 −2 −1 0 −1 −2
D RA [arcsec] D RA [arcsec] D RA [arcsec]
Figure6.TheeffectofaddingacentralblackholetothemodelshowninFig.4d.Forthisfigure,wezoomintothe3×3arcsec2regionto
showmoreclearlythebehaviouroftheinnercounterimage.Thelensingmodelisconstrainedonlyusingthethreesisterimagesidentified
on the main arc, and the stellar mass to light ratio (Υ) and shear (γ,θ) are re-fit in panel, assuming a fixed black hole mass which
increasesfrompaneltopanel.Inthisfigure,thegreycontoursarefromtheHSTresidualimage.Allofthemodelsshownreproducethe
positional constraints for the main arc, but make different predictions for the location and flux of the inner counter-image. Black hole
massesof∼2×1010M⊙ providethebestmatchtotheobservedposition,andalsoyieldafluxratiocomparabletotheobserved1:200.
MBH=(1.3+−00..65)×1010M⊙. In this model, the stellar mass- Scenarios(a)and(b)bothrequirevariationsinthestel-
to-light ratio is Υ=4.5±0.3, consistent with a Milky-Way- lar IMF away from the form pertaining apparently almost
likeIMF.Reducingthedark-matterfractionleadstoslightly universallywithintheMilkyWay(Bastian, Covey & Meyer
more stellar mass in thegalaxy centre, and henceless mass 2010). The evidence for heavier5 IMFs in massive galaxies
is allocated to the black hole. This is a small effect, how- has been discussed widely in recent years. From dynami-
ever: halving the dark-matter content reduces the derived calmodellingofnearbyearly-typegalaxies,Cappellari et al.
MBH by only ∼10 per cent (Fig. 7b). Finally, we note that (2013) found a trend of increasing IMF mass factor, from
in these models the total mass projected within 4.75kpc MW-like(α≈1)atσ=100kms−1 toSalpeter-like(α≈1.6)
is Map=(33±2)×1010M⊙,including contribution from the at σ=300kms−1. Treu et al. (2010) combined stellar dy-
black hole itself (∼4 per cent of the total). The aperture namics with strong lensing for the SLACS (Sloan Lens-
mass is consistent with that derived for the models with ing Advanced Camera for Surveys) lens sample, and de-
stars and DM only. rived larger mass excesses, α≈2, for the most massive
galaxies (σ >∼ 300kms−1), under the assumption of univer-
sal NFW haloes. Conversely, for a sample of three very
nearby strong-lensing ellipticals with σ >∼ 300kms−1 (sub-
5 DISCUSSION ject to smaller corrections for dark matter), Smith et al.
(2015) found α≈1, from a pure lensing analysis, i.e. with
We have proposed three possible interpretations for the nodynamicalinputs.Independently,thestrengthofgravity-
newly-discovered counter-image to the Abell 1201 arc: (a) sensitivefeaturesinthespectraofmassivegalaxiessuggests
averyheavyIMFthroughouttheBCG,(b)asteepincrease they harbour an excess of dwarf stars compared to a MW-
in the stellar mass-to-light ratio towards the galaxy cen-
tre,or(c)averymassivecentralblackhole.Inthissection,
we assess the plausibility of each scenario with reference to 5 Eitherbottom-heavywithanexcessofdwarfstars,ortop-heavy
evidence from other studies, and discuss possible routes to withanexcessofremnants,relativetotheMilkyWaycase.Both
distinguishing observationally between thepossibilities. leadtolargerstellarmass-to-lightratios.
MNRAS000,1–14(2016)
10 Russell J. Smith et al.
4 4
(a) M = 33.9· 1010 M (b) M = 33.9· 1010 M
ap sun ap sun
Stars=24.6, DM=8.2, BH=1.2 Stars=24.5, DM=8.2, BH=1.2
3 3
Sph NFW Ellip NFW
2 2
c] c]
e e
s s
c c
ar 1 ar 1
c [ c [
e e
D D
D D
0 0
1 1
− −
¡ = 7.0 g = 0.22 q = −31 ¡ = 7.0 g = 0.19 q = −31
2 2
− −
2 1 0 −1 −2 −3 −4 2 1 0 −1 −2 −3 −4
D RA [arcsec] D RA [arcsec]
4 4
(c) M = 32.6· 1010 M (d) M = 32.7· 1010 M
ap sun ap sun
Stars=15.7, DM=15.7, BH=1.3 Stars=15.7, DM=15.7, BH=1.3
3 3
Sph NFW Ellip NFW
2 2
c] c]
e e
s s
c c
ar 1 ar 1
c [ c [
e e
D D
D D
0 0
1 1
− −
¡ = 4.5 g = 0.19 q = −32 ¡ = 4.5 g = 0.14 q = −31
2 2
− −
2 1 0 −1 −2 −3 −4 2 1 0 −1 −2 −3 −4
D RA [arcsec] D RA [arcsec]
Figure 7. Lensing models incorporating a central black hole to account for the observed counter image, which is included as a fourth
positionalconstraint.Eachpanelshowstheresultforadifferentassumptionregardingthedark-matterfractionandellipticity.Panels(a)
and (b) have stellar mass-to-light ratios corresponding to heavy (Salpeter-like) IMFs, while panels (c) and (d) correspond to MW-like
IMFs.Inallcases,ablackholemassof(1.2–1.3)×1010M⊙ isrequiredtoreproducethecounter-image.
likeIMF,leadingtohighermass-to-lightratios,e.g.α=1.5– profiles of massive galaxies (M∗>1011M⊙, σ>250kms−1)
2.0 from Conroy & van Dokkum (2012b). However, direct fromtheEAGLE6 simulation(Schayeet al.2015),wefinda
comparisonsoftheseresultstoM/Lmeasurementsareham- typicaldark-mattermassof∼10×1010M⊙ projectedwithin
peredbytheunknowndetailedshapeoftheIMFatverylow 4.75kpc,i.e.about athirdof thetotallensingmass. Inrich
mass (Lyubenovaet al. 2016). clusters (which are not well represented in the simulation
The mass excess factor of α=2.4–3.0 (relative to the dataset)theDMfractionmaywellbelarger. Alternatively,
KroupaIMF),requiredbyourspatially-uniformIMFmodel integrating an NFW halo with c=5, M200=3.9×1014M⊙
fortheAbell1201counter-image,issubstantiallylargerthan and R200=1.5Mpc (Netoet al. 2007; Rineset al. 2013),
thefactorsdiscussedintherecentliterature.Moreover,this yields ∼20×1010M⊙ projected within 4.75kpc (two thirds
scenario would imply that dark matter contributes negligi-
bly within the aperture probed by the main arc, contrary
to theoretical expectation. For example, extracting average 6 EvolutionandAssemblyofGaLaxies andtheirEnvironments.
MNRAS000,1–14(2016)
