Systematic or Signal? How dark matter misalignments can bias strong lensing models of galaxy clusters

2.3 MB·

by  David Harvey

Mon.Not.R.Astron.Soc.000,1–7(2013) Printed27January2016 (MNLATEXstylefilev2.2)
Systematic or Signal? How dark matter misalignments can
bias strong lensing models of galaxy clusters
D. Harvey1(cid:63), J. P. Kneib1,2 and M. Jauzac3,4,5
1Laboratoire d’Astrophysique, Ecole Polytechnique Fe´de´rale de Lausanne (EPFL), Observatoire de Sauverny, CH-1290 Versoix, Switzerland
2Aix Marseille Universit, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388, Marseille, France
3Centre for Extragalactic Astronomy, Department of Physics, Durham University, Durham DH1 3LE, U.K.
4Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, U.K.
5Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041, South Africa
6
1 Accepted—.Received—;inoriginalform27January2016.
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2
ABSTRACT
n
Weexplorehowassumingthatmasstraceslightinstronggravitationallensingmodels
a
can lead to systematic errors in the predicted position of multiple images. Using a
J
model based on the galaxy cluster MACSJ0416 (z =0.397) from the Hubble Frontier
5
Fields, we split each galactic halo into a baryonic and dark matter component. We
2
then shift the dark matter halo such that it no longer aligns with the baryonic halo

] and investigate how this affects the resulting position of multiple images. We find for
O physically motivated misalignments in dark halo position, ellipticity, position angle
C anddensityprofile,thatmultipleimagescanmoveonaveragebymorethan0.2(cid:48)(cid:48) with
individual images moving greater than 1(cid:48)(cid:48). We finally estimate the full error induced
.
h byassumingthatlighttracesmassandfindthatthisassumptionleadstoanexpected
p RMS error of 0.5(cid:48)(cid:48), almost the entire error budget observed in the Frontier Fields.
-
o Given the large potential contribution from the assumption that light traces mass
r to the error budget in mass reconstructions, we predict that it should be possible
st to make a first significant detection and characterisation of dark halo misalignments
a in the Hubble Frontier Fields with strong lensing. Finally, we find that it may be
[ possible to detect ∼1kpc offsets between dark matter and baryons, the smoking gun

for self-interacting dark matter, should the correct alignment of multiple images be
1
v observed.
3
Key words: cosmology: dark matter — galaxies: clusters — gravitational lensing
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7
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0
1. 1 INTRODUCTION Liesenborgsetal.2006;Mertenetal.2009).Underthelight
0 tracesmassesassumptionitisassumedthatwhereverthere
Mapping the distribution of total matter in galaxy clusters
6 is a galaxy there also exists a dark matter halo, the mass
hasbecomecommonplacewiththeadventofhighresolution
1 of which far out exceeds that of the baryonic component
optical imaging from space (e.g. Merten et al. 2011; Jauzac
: (e.g. Limousin et al. 2007). Specifically, the assumption is
v etal.2012,2015).Deepimagesofgalaxyclustersrevealthe
thatthepeakofthedarkmatterhaloliesexactlycoincident
i apparent distortion of distant background galaxies whose
X withthegalaxy,withanequalellipticityandequalposition
lighthasbeensplitintomanygeodesicsproducingmultiple
r angle, the only difference in being the scale at which the
a images of the same galaxy. Strong gravitational lensing has light and dark halos extend to. The main advantage of as-
becomeavitaltoolinmappingoutthedistributionofmat-
sumingthatmasstraceslightisthatbyscalingtheDMhalo
ter in galaxy clusters as well as its behaviour during highly
directly to the light distribution of the galaxy it is possible
energetic collisions (e.g. Bradaˇc et al. 2006; Merten et al.
to significantly reduce the number of free parameters in a
2011). For a review see Bartelmann (2010).
stronglensingmodelofagalaxyclusterthatmaycontainup
Methods to reproduce the distribution of matter in
toafewhundredindividualgalaxies.Thisreducesthecom-
galaxy clusters can be split into two categories: those that
putationaltimeforasinglereconstructionandincreasesthe
assume that light traces mass (e.g. Zitrin et al. 2013; Jullo
constrainingpowerofthemodelbyplacingheavypriorson
et al. 2007) and those that do not (e.g. Bradaˇc et al. 2005;
eachgalactichalo.However,converselysuchanassumption
may lead to inaccuracies whereas free-form reconstructions
that do not assume this may not impose a bias but will
(cid:63) e-mail:[email protected]
©2013RAS
2 D. Harvey, J. P. Kneib & M. Jauzac
blethatdarkmattercouldindeedseparatefromitsbaryonic
1.00 counterpart.
24.06 Aside from the peak position of the dark matter halo,
1.25 it isn’t clear whether the dark matter halo should mimic
the geometrical properties of the baryonic component. A
1.50
recent study using the MassiveBlack II cosmological hydro-
dynamicalsimulationsfoundthatthiswasnottrue(Tenneti
degrees) 24.07 21..0705log( ebtearol.u2n0d1e5r),.bTyhuepytfoofuancdtotrhsaotfdtwarok,amndatttherathtahloesmtaenjodreadxteos
c ( ) could become severely misaligned with offsets of θ = 90◦
e
D
2.25 notuncommon.Theyfoundthattheoffsetsweremostcom-
mon at galaxy scale masses, with larger, cluster size halos
24.08
2.50 better aligned. These findings are consistent with others in
thefield(e.g.Bailinetal.2005;Deasonetal.2011;Velliscig
2.75 et al. 2015). Additionally, assuming that light traces mass
often assumes an empirical relation between the size of the
3.00
dark matter halo and the luminosity (e.g. Limousin et al.
24.09
64.05 64.04 64.03 64.02
2007). Although well constrained, these relations can ex-
RA (degrees)
hibitavarianceofupto50%(Fritzetal.2005;Wuytsetal.
100
2004).Giventhatsimulationspredictthatdarkmatterand
10-1 baryonichalosshouldnotnecessarilytraceeachotherweare

/ρ010-2 Total Density motivatedtotesthowthisassumptioncanaffectthestrong
ρ
10-3 Baryons lensing models.
Dark Matter Previousworkstudyingthealignmentofdarkwithlight
10-4
100 101 102 matter using strong lensing is limited. Minor & Kapling-
r [ kpc ] hat(2008)firststudiedhowmultipleimageseparationscan
be altered by misalignments between the dark matter and
Figure 1. The cluster model we used. The top panel shows the
galaxy cluster with the convergence map in grey scale and the galactic halo. They showed how the statistics of image sep-
resultingcriticallinesinwhite.Thewhitestarsrepresentthetrue aration can avoid the need to model each lens and hence
positionofmultipleimages.Thebottompanelshowsanexample can be useful for large scale surveys. More recently Brud-
ofhowwesplitagalaxywithatotalPIEMDprofileofrcore=5 erer et al. (2016) carried out a study of 11 lensing galaxies
kpcandrcut=100kpc,into2PIEMDsofrcBore=5kpc(vertical examining their alignment with their baryonic component.
dotted line) , rcBut = 25 kpc and rcDoMre = 25 kpc (vertical dot- Similar to simulations they found that halos are rounder
dashedline),rDM=100kpc(verticalsolidline).
cut thantheirgalacticcounterpartandthosegalaxieswithlarge
amountsofsheararehighlymisaligned.Althoughveryinter-
esting,thisislimitedtosmallnumberofgalaxiesingroups.
suffer in precision. It is in this paper that we explicitly ex- In this work we will look at carrying out a similar study
amine these underlying assumptions. We ask whether these exceptoverlargenumbersofgalaxiesthatresidewithinthe
assumptionsaresuitableandintheeventthattheyarenot, high density cluster environment.
howdotheyaffectthesmall-scalepropertiesofstronglens-
ing models used. Similarly, we also determine whether the
misalignment of dark matter could be detected for the first
2 METHOD
time with current data.
To study the effect that assuming light traces mass has we
useamodelofaclusterbasedonrealdatathatcontains174
1.1 Does light trace mass? small scale galaxy-scale halos (spectroscopically identified
by Grillo et al. 2015) embedded in two large, cluster-scale
Inordertomotivatethestudyofhowassumingmasstraces
dark matter halos Jauzac et al. (2014); Grillo et al. (2015).
light affects strong lensing models, we must first question
In this study we act only to study the effect of changes to
whether we would expect the profile of dark matter halo to
the galaxy scale halos on the positions of multiple images.
mimic that of the baryonic component. In a ΛCDM Uni-
WeusethepositionofmultipleimagesintheHubbleFron-
verse, cosmological simulations predict that dark matter
tier Field galaxy cluster, MACSJ0416 and the best fitting
should lie coincident with the baryonic component, with
cluster model that fits these multiple images as derived by
no physical offset of δr > 3kpc being observed (Schaller
the parametric strong lensing algorithm Lenstool (Jauzac
et al. 2015). However, extensions to the collisionless cold
et al. 2014; Jullo et al. 2007). This equates to 140 multiple
dark matter model have been proposed that could lead to
images, and 174 cluster members. Each potential was orig-
offsets between baryonic and dark component (Kahlhoefer
inally fitted with a pseudo isothermal elliptical mass dis-
et al. 2014; Harvey et al. 2014). For example, Williams &
tribution (PIEMD) (Kneib et al. 1996; Natarajan & Kneib
Saha(2011)andsubsequentlyMasseyetal.(2015)observed
1997;El´ıasd´ottiretal.2007;Julloetal.2007),whichfollows
a 1.5kpc offset between the two components in an elliptical
the analytical density profile,
galaxy in the cluster Abell 3827, at the 3σ level. This off-
setwasattributedtopotentialdarkmatterself-interactions ρ(r) 1 1
= √ − , (1)
causing a lag on the dark matter halo. It is therefore possi- ρ0 r2+rc2ore (cid:112)r2+rc2ut
©2013RAS,MNRAS000,1–7
Dark matter misalignments in HFF 3
1.0
0.8
)
s
c
e 0.6
s
c
r
a 0.4
(

t
e
s 0.2
f
f
o
e 0.0
g 0.2 0.6 1.0 1.4 1.8 40 20 0 20 40 72 36 0 36 72 40 20 0 20 40
a
m 1.0
i
e
pl 0.8
ti
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m

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0.4
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0.2
0.0
0.2 0.6 1.0 1.4 1.8 5 15 25 35 45 9 27 45 63 81 5 15 25 35 45
Position (arcsecs) Ellipticity (%) Position angle ( degrees ) Cut radius (%)
Figure2.ResultsfromMACSJ0416simulation.Eachcasethefaintlinesshowthetrackofindividualimages,andtheblacklinerepresents
the RMS of all of the images with respect to the original catalogue. In each case in the top row the dark matter component in all the
galaxieshavebeensystematicallychanged(suchthatallgalaxieshavethesameoffset),andthebottomrowgivesthestandarddeviation
ofthenormaldistributionfromwhichtheoffsethasbeenrandomlyselected(suchthateachgalaxyinthemodelhasadifferentoffset).In
thecaseofthepositionoffset(firstcolumnandtoprow)eachgalaxyhashadtheirdarkmatterhalopushedawayfromthecentreofmass
ofthecluster.
where r is the radial distance from the centre of the halo, the two PIEMD component model of the galaxy. The solid
andtheprofileisparameterisedbythecoreradius,r ,and blacklineisagalaxywithar =5kpcandr =100kpc,
core core cut
the cut radius, r . The cluster itself has a measured mass and the resulting baryonic (dotted) and dark matter (dot-
cut
within a 200kpc aperture of (1.6±0.01)×1014M (Jauzac dashed)componentswhenthegalaxyissplitintotwo.The
(cid:12)
et al. 2014), and the mass of each galaxy has a lognormal dotted,dot-dashedandsolidverticallinesgivethescalesof
distribution centred around log(M/M ) = 10.1±0.6. The thebaryoniccoreradius,thedarkmattercoreandbaryonic
(cid:12)
distribution of ellipticities peaks at 0.1 and decreases to- cut radius and finally the dark matter cut radius respec-
wardslargerellipiticites.Thegalaxiesspantheentirerange tively.
between 0 and 0.9. We split each galaxy halo potential into To test the validity of assuming that light traces mass
two components: a baryonic core and a dark matter halo. we shift the dark matter component of the lensing model
We separate the halo into two PIEMDs with the baryonic howeverkeepthebaryoniccomponentconstant.Weproject
rcBore =rcore. For the baryonic cut radius, we conservatively the sources back through to the image plane with the new
cutittoaquarteroftheoriginalcutradiusrcBut =rcut/4(Ve- darkmattermodelandcalculatetheshiftinpositionofeach
lander et al. 2014), although this could be smaller. We also multipleimage.Wetestfourshiftsinthedarkmattercom-
forcethedarkmattercoreradiustothebaryoniccutradius, ponent:
rDM = rB and the dark matter cut radius as the original
core cut
cut radius rDM = r . Separating the halo like this means
cut cut (i) Position:offsettingthepeakpositionofthedarkmat-
that the mass of each halo is conserved with respect to the
ter halo from the baryonic;
pre-split halo. Given this two component galaxy model we
(ii) Ellipticity: stretching or squashing the dark matter
project the images back to the source plane to create a list
halo with respect to the baryonic component;
ofbackgroundsourcesforthecluster.Todothisweusethe
(iii) Position angle: rotating the halo such that the dark
same redshift information for the sources as that in Jauzac
matter and baryonic component are misaligned;
et al. (2014).
(iv) Cut radius: we vary the cut radius and velocity dis-
persion of the dark matter halo to change the profile of the
Figure1showsthemakeupofthemodel.Thetoppanel
galaxy however conserve the total mass of the dark matter
showstheclustermodelwiththepositionofthemultipleim-
halo.
ages as white stars, log of the normalised projected surface
density(convergence)mapingreyscaleandthecriticallines
in the white solid line. The bottom panel of Figure 1 gives Additionally, for each case we will either shift the halo sys-
©2013RAS,MNRAS000,1–7
4 D. Harvey, J. P. Kneib & M. Jauzac
Figure 3.Histogramsofthedistributionofmultipleimagesw.r.ttheRMSofalltheimages.Ineachcasethesystematicoffset(toprow
ofFigure2)isshownwiththedistributionofmultipleimagesoffsetwiththesolidlineshowingtheRMSofthemultipleimages.Itcanbe
clearlyseenthattheRMSisbiasedhighbyoneortwoindividualspuriouslyoffsethalos.
tematicallyinthesamedirection,orrandomlywithamean the cut radius but conserving mass has a symmetric effect,
of zero and a standard deviation of the given value. whetherwedecreasethecutradiusandincreasethevelocity
dispersionorviceversa.Wefindthatashiftintheposition
angleorcutradiusresultinsimilarmagnitudeoffsets,both
3 RESULTS insystematicallyandrandomly,withmeanoffsetsofroughly
∼0.2(cid:48)(cid:48).
We first test each assumption individually, beginning with
peakpositionoffset.Westartbysystematicallyshiftingthe
dark matter halos position away from the peak of the light 3.1 Sensitivity of the model RMS to individual
distribution.Weshiftthehaloinadirectionanti-parallelto images
the centre of mass of cluster, to imitate a shift in the dark
ThebottomrowinFigure2showsthatinallfourtestscar-
matter halo due to self-interactions (see Kahlhoefer et al.
riedoutwefindthatthepositionofindividualimagescanbe
2014). The first panel on the top row of Figure 2 shows the
very sensitive to misalignment of dark matter and baryons.
meanmultipleimageoffsetasafunctionofdarkmatterhalo
This can be important since in a strong lensing reconstruc-
offset. In each case the solid black line gives the root mean
tion individual images can significantly bias the RMS value
square (RMS) of all the multiple images for a given offset,
of predicted image position to actual image position. Not
and the fainter coloured lines, the offset of each individual
onlythis,butitmaybiastherestofthereconstructionand
image.Wefindthatforagivenoffsetδp,themeanmultiple
anyderiveddeflectionmaps.Weillustratethispointfurther
image offset, δr ≈0.2δp.
im
by binning the shift in multiple image position into a his-
Following this, we then shift the position of the dark
togram and overlaying the RMS. Figure 3 shows the result
matter halo by a random amount, sampled from a normal
foreachtestinthesystematicoffsetmode(sameastoprow
distributionwithameanofzeroandanincreasingstandard
of Figure 2). We see that in all cases except ellipticity, the
deviation.ThefirstpanelofthebottomrowofFigure2gives
thick solid line which represents the RMS is significantly
themultipleimageoffsetasafunctionoftheinputstandard
above the majority of the actual image offsets. Particularly
deviation. We find that for random offsets with a standard
the offset due to position angle, whereby the majority are
deviation of δp, the mean multiple image offset is slightly
<0.1(cid:48)(cid:48) howeversomeimagesat0.8(cid:48)(cid:48) canbiastheRMSvery
less sensitive at, δr ≈0.1δp.
im
high. However, interestingly, the RMS statistic well repre-
Thefollowingthreetestsstudythesensitivityofmulti-
sents the error imposed by a an ellipticity offset.
pleimagepositiontoascalarquantity,andthereforeunlike
theposition,donotrequireareferencepointinwhichtobe
systematically offset. We therefore show in the top row of
3.2 Sensitivity of image position to individual
Figure 2 how a common offset in ellipticity, position angle
cluster members
and mass can alter the position of multiple images (second,
third and fourth column respectively) and the bottom row In order to better understand the origin of the RMS for
how a random offset, selected from a normal distribution each offset, we take a multiple image that is particularly
with a mean of zero and an incrementally larger standard sensitivetoashiftandwestudyitsenvironmentandhowit
deviation can alter the mean position of multiple images. changes with respect to the change in its dark matter halo.
Ourtestsrevealthathighlyellipticaldarkmatterhalos The top panel of Figure 4 (20(cid:48)(cid:48)×20(cid:48)(cid:48)) shows how the posi-
resultinverylargeshiftsinthepositionofmultipleimages, tion of one multiple image is sensitive to the position angle
with shifts of greater than one arc-second not uncommon. ofnearbygalaxies.Wecarryoutastudywherebywerotate
More circular halos, also gave an offset, except less signifi- the nearby dark matter halos by incremental amounts, as
cant. We also find that the changing position angle of the represented by each coloured ellipse. For each incremental
darkmatterhalohassinusoidalrelation,withsomemultiple rotation we calculate the resulting position of the image,
imagesexperiencinghighlysensitiveangles.Finallyvarying which we represent as a star whose colour matches that of
©2013RAS,MNRAS000,1–7
Dark matter misalignments in HFF 5
thedarkmatterpositionanglethatcausedit.Inthebottom
panel, the stars correspond to the stars of the same colour
in the top panel except shown as a magnitude offset from
the original position. The coloured diamonds shows the off-
set when just the closest lens is altered (as shown by the
lens with the arrow). It can be seen that when the major
axis of the rotated dark matter halo aligns radially (points
towards) with the image the resulting error in the image is
largest, however when the galaxy lies tangentially then the C
errorisverysmall.This,alsoexplainsthesmoothsinusoidal E
D
function observed in Figure 2. Furthermore, we find when -90.0
wealterjustasinglegalaxy(diamonds),thiscancontribute -60.0
themajorityoftheerrorinthepositionofamultipleimage,
-30.0
showingthatthisperturbativeeffectisalocaloneconcern-
0.0
ingonlyverynearmassivehalos.Weconfirmthisbytesting
thecorrelationbetweentheobservedoffsetofanimageand 30.0
distance to the closest lens weighted by its mass. We find a 60.0
positive correlation for all offsets except the cut radius, for 90.0
which we find no such dependence.
Wefinallytestthethreeremainingshifts(ellipticity,po- ) RA
c
sition angle and cut radius) and how perturbing the closest e
lens affects the position of the image. The inset in Figure 4 s 1.2
c
(2(cid:48)(cid:48)×2(cid:48)(cid:48))showstheresultsfromthesetests,withthearrow r 1.0
a
indicating the direction in which we shift the dark matter ( 0.8

t
peak position. We find that when the ellipticity, position e 0.6
s
angle and dark matter peak position of the nearest lens is f 0.4
f
altered, the effect is a tangential movement on the image o 0.2
e
and completely degenerate. However, when we change the
g 0.0
cut radius of the galaxy, this results in a radial movement a
m 100 50 0 50 100
ofthemultipleimage.Thisorthogonalmovementwillallow
I
future models to constrain which effect is causing the RMS Position angle offset (degrees)
offset.
Figure 4. Top : Dependency of a given multiple image on the
Given that the positional test is only for a shift in one
positionangleofclustermemberpositionangles.Themainimage
directionwetestallotherpossibledirections.Figure5(same
(20(cid:48)(cid:48)×20(cid:48)(cid:48))givesthepositionofonemultipleimageasafunction
dimensions as Figure 4) shows the behaviour of the multi-
ofclustermemberpositionangle.Thecoloursrelatetheposition
ple image when shifting the lens in every possible way. The
angleofthedarkmattertothepositionofamultipleimage,and
coloured arrows define the offset direction of the potential howthiscorrespondstoaradialoffsetfromtheoriginalposition
and the corresponding coloured lines in the inset show the in the bottom panel. The stars in this panel correspond to the
movement of the multiple image from the original position star positions in the top, the diamonds give the image offset in
given by the star. We find that the movement of the im- theeventthatonlythelensneartheimageisrotated.Toppanel
ageisalwaystangentialwithsomesmallrangeofangle.We Inset (2(cid:48)(cid:48)×2(cid:48)(cid:48)) shows how the same multiple image moves w.r.t
confirmthisbystudyingotherclustermembersandfindthe differentchangesinthedarkmatterhaloofonlythelensnearest
image.Orangetrackshowstheeffectofchangingthecutradius,
same effect.
green shows the movement due to changing the ellipticity, blue
thepositionangleandpurplethepeakpositionofthedarkmatter
3.3 Combined all the offsets: testing the halo.
assumption
Inpracticeallfourassumptionswillaffectthepredictability
ofastronglensingmodel.Hereweestimatehowtheseoffsets imagesthatareapparentlyclosertolensesontheskywillbe
combine and what the expected RMS would be. To do this themostsensitivetoamisaligneddarkmatterhalo.Figure6
weproducemanyrealisationsofthesameclusterusingfixed givesthemeanandonesigmastandarderrorintheposition
offset parameters for the galaxy-scale halos and continuing offset for each multiple image as a function of the distance
to keep the large scale cluster halo fixed. We select at ran- theimageisfromtheclosestlens.Thesolidblacklineshows
dom, offsets in position, ellipticity, position angle and cut the mean RMS over all realisations. The bars in each case
radius for each galaxy within the cluster with standard de- give the approximate contribution from each effect to the
viations of σ =0.1(cid:48)(cid:48), σ =20%, σ =20◦ and σ =10%. total offset. We find that assuming that light traces mass
p e a cut
These values are physically motivated and based on the re- results in an estimated ∼0.5(cid:48)(cid:48) RMS error in the position of
sultsofTennetietal.(2015)andtheoffsetobservedinA3827 multipleimages.Themajorityoftheoffsetiscontributedby
(Massey et al. 2015). We simulate the positions of the mul- a shift in the cut radius and angle position, however these
tiple images 20 times and find the mean positional offset appearnottodependondistancefromthenearestlens.We
of each image and the expected RMS given the assumption dofindthoughthatthepositionandellipticityhaveaslight
that light traces mass. We also test the hypothesis that the tendency to have a larger effect as the lens is closer to the
©2013RAS,MNRAS000,1–7
6 D. Harvey, J. P. Kneib & M. Jauzac
Distance from closest lens (kpc)
10.8 21.6 32.4 43.2 54.0
1.0
Peak Position
)
s
d Ellipticity
n
o Angle position
c0.8
se Cut radius
c-
r
a
(
C hift 0.6
E e s
D g
a
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e i0.4
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0.2
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Distance from closest lens (arc-seconds)
RA
Figure6.Weincludevariationsinallparametersassociatedwith
Figure 5. The same as Figure 4 (with the same dimensions)
assuming that mass traces light and randomly offset the dark
exceptthisshowshowshiftingthedarkmatterhalopeakposition
matterhalosinfourwaysinordertomeasuretheexpectedRMS
in any direction results only in a tangential movement of the in the multiple image position. Using σp = 0.1(cid:48)(cid:48), σe = 20%,
multipleimage. σa=20◦andσcut=10%allwithmeansofzero,anditeratedover
20realisations.Wemeasurethemeanandvarianceintheposition
of each multiple image and the expected RMS as a function of
image.GiventheaccuracyofcurrentHFF,the0.5(cid:48)(cid:48) hereac- distance from the closest lens in angular and proper distances.
WeshowthemeanRMSoveralltheimageswiththesolidblack
counts for the majority of this error, and any future survey
line. We also determine the approximate contribution for each
attemptingtogobelowthislimitwillnotbeabletoassume
parametertothemeanimageshift
that mass traces light.
mological gravitational lensing (see Joachimi et al. (2015)
3.4 Prospects of detecting misaligned halos in the
for review).
Hubble Frontier Fields
ModelsintheHubbleFrontierFieldscurrentlyreportaRMS
error of 0.6(cid:48)(cid:48) for a single cluster (Jauzac et al. 2014), of
4 CONCLUSION
which most could be accounted for by assuming that light
tracesmass.TheseparationobservedinA3827wasoforder The assumption that light traces mass is often used when
∼2kpc,whichis≈0.4(cid:48)(cid:48) ataredshiftofz∼0.397.Wefound modelingthedistributionofmassingalaxyclusters.Strong
that should all galaxies have their dark matter component gravitational lensing models, which assume this report root
coherently offset by this amount we would observe a mean meansquareerrorsbetweenthepredictedpositionofmulti-
shiftof∼0.05−0.1(cid:48)(cid:48),whichiscurrentlybeyondtheaccuracy ple images and actual positions of ∼0.6(cid:48)(cid:48). In this study we
of strong lensing models. However, given that this is based testthevalidityofthisassumptionbyalteringthedarkmat-
on one cluster and individual images very close to a lens terhaloofgalaxiesinamodelbasedontheHubbleFrontier
can be shifted significantly, it is highly likely that future FieldclusterMACSJ0416whilstkeepingthelarge-scaleclus-
Frontier Fields should observe a configuration of multiple ter component and stellar component fixed. Assuming that
images that are sensitive to the offset between dark matter light traces mass often requires the peak dark matter halo
and baryons in particular lenses. Apart from this, cosmo- and baryonic halo to be exactly coincident, the ellipticity
logical simulations predict that the position angle of halos andthepositionangleofthehalotobealignedandthecut
can be misaligned by large amounts and dark matter halos radiustohavesomekindofrelationwiththeluminosity.In
can be rounder than their baryonic counterparts by factors thisstudywetestallfourassumptionsindividually.Wefind
of two. The predicted shift inmultipleimages forthese two whether we commonly shift dark matter halos or individu-
properties means that it is it is possible to make a first de- ally randomly offset them, each individual case produces a
tection of misalignment in the Frontier Fields. Having said meanoffsetof∼0.2(cid:48)(cid:48) inthepositionofmultipleimages.We
this, the movement of multiple images with respect to each findthatalthoughthemeanoffsetforeachimageisoforder
offset is highly degenerate, and hence in order to charac- ∼0.2(cid:48)(cid:48), some images can be very sensitive to perturbations
terise the statistical properties of the misalignments it will in the galactic dark matter halo with some misalignments
requireahighdensityofmultipleimagesaroundthelenses. resulting in a multiple image shift of ∼1(cid:48)(cid:48).
Such a discovery would have far-reaching implications for Followingthiswestudyhowindividualmassivelensesin
galaxy formation models and also intrinsic alignments that closeproximitytoimagescansignificantlyperturbtheimage
have become a vital systematic in the measurement of cos- position finding that some individual galaxy misalignments
©2013RAS,MNRAS000,1–7
Dark matter misalignments in HFF 7
caninduceimageshiftsof>1(cid:48)(cid:48).Additional,wealsofindthat Limousin M. et al., 2007, ApJ , 668, 643
thepeakposition,positionangleandellipticityoffsetresult Massey R. et al., 2015, MNRAS , 449, 3393
inatangentialmovementofimageswhereasachangeinthe Merten J., Cacciato M., Meneghetti M., Mignone C.,
cutradiusresultsinaradialmovement,meaningthatfuture Bartelmann M., 2009, A&A , 500, 681
studies should be able to discern between misalignments in Merten J. et al., 2011, MNRAS , 417, 333
the halo and departures from mass - luminosity relations. Minor Q. E., Kaplinghat M., 2008, MNRAS , 391, 653
We finally combine all four effects and find that the Natarajan P., Kneib J.-P., 1997, MNRAS , 287, 833
mass to light assumption can result in ∼ 0.5(cid:48)(cid:48) root mean Schaller M., Robertson A., Massey R., Bower R. G., Eke
square error in the position of multiple images, almost the V. R., 2015, MNRAS , 453, L58
entire error budget of the Frontier Field lensing models. Tenneti A., Mandelbaum R., Di Matteo T., Kiessling A.,
Given that misalignments are of physical interest to Khandai N., 2015, MNRAS , 453, 469
galaxyformationmodelsandasasystematicerrorformea- Velander M. et al., 2014, MNRAS , 437, 2111
surements of cosmic shear, we find that given the current Velliscig M. et al., 2015, MNRAS , 453, 721
sensitivity and depth of the HFF, it should be possible to Williams L. L. R., Saha P., 2011, MNRAS , 415, 448
detectandcharacterisemisalignmentsbetweendarkmatter Wuyts S., van Dokkum P. G., Kelson D. D., Franx M.,
andbaryonichalosintheHubbleFrontierFieldgalaxyclus- Illingworth G. D., 2004, ApJ , 605, 677
ters. We also find that given an expected offset of ∼ 2kpc Zitrin A. et al., 2013, ApJ , 762, L30
betweendarkmatterandbaryons,thesmokinggunforself-
interacting dark matter, it maybe possible to detect some
ThispaperhasbeentypesetfromaTEX/LATEXfileprepared
offset in the Hubble Frontier Fields, given the correct mul-
by the author.
tiple image configuration.
ACKNOWLEDGEMENTS
TheauthorswouldliketothankDavidMartinandMatthew
NicholsforvaluableadviceinconstructingtheMNHfigure.
DH is supported by the Swiss National Science Foundation
(SNSF).JPKacknowledgessupportfromtheERCadvanced
grant LIDA and from CNRS. MJ acknowledge support by
theScienceandTechnologyFacilitiesCouncil[grantnumber
ST/L00075X/1 & ST/F001166/1]
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