The impact of mergers on relaxed X-ray clusters - II. Effects on global X-ray and SZ properties and their scaling relations

0.71 MB·English

by  Gregory B. Poole

Mon.Not.R.Astron.Soc.000,1–24(2006) Printed5February2008 (MNLaTEXstylefilev2.2)
The impact of mergers on relaxed X-ray clusters
II. Effects on global X-ray and SZ properties and their
scaling relations
Gregory B. Poole1⋆, Arif Babul1, Ian G. McCarthy2, Mark A. Fardal3,
7
0 C. J. Bildfell1, Thomas Quinn4 and Andisheh Mahdavi1
0
2 1Dept. of Physics & Astronomy, University of Victoria, Elliott Building, 3800 Finnerty Rd., Victoria, BC, V8P 1A1, Canada
2Department of Physics, University of Durham, South Road, Durham DH13LE, UK
n 3Dept. of Astronomy, University of Massachusetts, Amherst, MA, 01003, USA
a 4Dept. of Astronomy, University of Washington, Seattle, WA 98195
J

0
2
draftversion5February2008

1
v
6 ABSTRACT
8 We use the suite of simulations presented in Poole et al. (2006) to examine global
5 X-ray and Sunyaev-Zel’dovich(SZ) observables for systems of merging relaxed X-ray
1 clusters. The time evolution of our merging systems’ X-ray luminosities, tempera-
0 tures, total mass measures, SZ central Compton parameters and integrated SZ fluxes
7 are presented and the resulting impact on their scaling relations examined. In all
0 cases, and for all parameters, we observe a common time evolution: two rapid tran-
/
h sient increases during first and second pericentric passage, with interceding values
p near or below their initial levels. This is in good qualitative agreement with previous
- idealized merger simulations (e.g. Ricker & Sarazin 2001), although we find several
o
important differences related to the inclusion of radiative cooling in our simulations.
r
t These trends translate into a generic evolution in the scaling-relation planes as well:
s
a rapid transient roughly along the mass scaling relations, a subsequent slow drift
a
: across the scatter until virialization, followed by a slow evolution along and up the
v
massscalingrelationsascoolingrecoversintheclustercores.However,thisdriftisnot
i
X sufficient to account for the observed scatter in the scaling relations. We also study
the effects of mergers on several theoretical temperature measures of the intracluster
r
a medium: emission weighted measures (T ), the spectroscopic-like measure proposed
ew
byMazzotta et al.(2004,T )andplasmamodelfitstotheintegratedspectrumofthe
sl
system (T ). We find that T tracks T for the entire duration of our mergers,
spec sl spec
illustrating that it remains a good tool for observational comparison even for highly
disturbedsystems.Furthermore,thetransienttemperatureincreasesproducedduring
first and second pericentric passage are 15−40% larger for T than for T or T .
ew sl spec
Thissuggeststhattheeffectsoftransienttemperatureincreasesonσ8 andΩM derived
by Randall et al. (2002) are over estimated. Lastly, we examine the X-ray SZ proxy
proposed by Kravtsov et al. (2006) and find that the tight mass scaling relation they
predict remains secure through the entire duration of a merger event, independent of
projection effects.
Key words: cosmology: theory – galaxies: clusters: general – intergalactic medium
– X-rays: general
1 INTRODUCTION perature, X-ray luminosity and mass). Due to their proven
utility in cosmological studies (see Voit 2005, for an excel-
It has been known for some time that clusters obey simple
lent review), their use as constraints on theoretical models
andrelativelywelldefinedpower-lawscalingsbetweenmany
ofgalaxyformation(Babul et. al. 2002)andthesignificant
oftheirgloballyintegratedoraveragedproperties(e.g. tem-
discrepancybetweenobservationsandsimpleearlytheoreti-
calexpectations(e.g. Kaiser1986;Markevitch1998),these
⋆ E-mail:[email protected]
2 Gregory B. Poole et. al.
relations have received a great deal of scrutiny in recent pact parameters and mass ratios of mergers between CCC
years. systems with a primary (most massive system) of 1015M⊙.
Significant progress has recently been made to- A detailed description of these simulations can be found in
wards reconciling theoretical expectations for the slope Poole06a.
and normalization of these relations with observations In Section 2 we will briefly summarize several aspects
(e.g. Borgani et al. 2004; Voit et al. 2002). As a result, of our method for constructing cluster mergers presented
attention is now turning towards accounting for their ob- in Poole06a which are relevant to this paper. In Section 3
served scatter. One significant early step towards this goal wepresentthetemporalevolutionandscalingrelationofour
was made by McCarthy et. al. (2004, M04 hereafter) who systems’X-rayluminosities(Lx)andtemperatures(Tx),ex-
illustrated thattheposition ofsystemsrelativetothemean amining theeffects of various temperature measures and of
observed L −T and M −L relations correlates with core excision on the behaviour of these quantities. In Sec-
x x t x
the system’s central entropy, and hence the morphology of tion4weexaminetheeffectivenessofhydrostaticestimates
a system’s core. Specifically, they found that systems with of total mass (Mt), its isothermal β-model implementation
compact cool cores (CCCs; classically identifiedas “cooling and the Mt − Tx and Mt − Lx scaling relations which
flow” systems) and low central entropies tend to lie on the are obtained from them. In Section 5 we study the evolu-
high-luminosity/low-temperaturesidesofobserveddistribu- tion of our systems’ SZ properties (both central Compton
tionswhilesystemslackingcompactcoolcores(NCCs;clas- parameters and integrated SZ fluxes), examining the effec-
sicallyidentifiedas“non-coolingflow”systems)andpossess- tiveness of the β-model approximation often implemented
ingelevatedcentralentropieslieonthelow-luminosity/low- by observers as well as the most relevant scaling relations
mass sides. Recently, O’Hara et al. (2006) have demon- which can be constructed from them. In Section 6 we ex-
strated that these two populations are indistinguishable in aminetheeffectsofmergersontheX-raySZproxyrecently
these planes when their cores are removed during analy- proposed byKravtsov et al. (2006). In Section 7 we discuss
sis. This suggests that variations in core properties are pri- several issues raised by our work and finally, we summarize
marily responsible for the scatter in observed scaling rela- themost notable results of our studyin Section 8.
tions, supporting previous findings of Fabian et al. (1994) In all cases our assumed cosmology will be
and Markevitch (1998). (ΩM,ΩΛ)=(0.3,0.7) with Ho=75km/s/Mpc.
These results are corroborated by Balogh et al. (2006)
who find that variations in dark matter structure and un-
certainties in cosmological models can not account for the 2 SIMULATIONS
scatterintheL −T orM −L scalingrelations.Theysug-
x x t x
gestthatvariationsintheminimumlevelofcoreentropydue We run our simulations with GASOLINE
to differences in heating and/or cooling efficiencies of core (Wadsley,Stadel, & Quinn 2004), a versatile parallel
material are responsible. Little speculation is made regard- SPH tree-code with multi-stepping. We include the effects
ingthephysicaloriginsofsuchefficiencyvariationsbutthey of radiative cooling in our simulations and feedback from
theorize that mergers are not likely the source, citing qual- star formation but the effects of jets from active galactic
itative observations made by authors of previous theoreti- nuclei(AGN) are omitted.
cal merger studies that mergers generally drive systems to The basis of our study is a set of 9 idealized 2-body
evolveparallel toobservedscaling relations (Rowley et. al. clustermergersimulations. Threemass ratiosareexamined
2004).ThisliesinstarkcontrasttotheworkofSmith et al. (1:1,3:1and10:1)withthemostmassivesystemsettohave
(2005) however, who use strong lensing measurements and amassof1015M⊙ ineverycase.Foreachmassratio,three
highresolutionChandra observationstoillustrateacorrela- impact parameters are examined (one head-on and two off-
tionbetweenthedegreetowhichlocal clustercoresaredis- axis cases). We express these impact parameters with the
turbedandtheirvariancefromthemeanMt−Lx,Mt−Tx, quantityvt/Vc,wherevt istherelativetangentialvelocityof
andL −T scaling relations.Hence,severalunresolvedis- theinteractingsystemswhenthecoreofthesmallersystem
x x
sues regarding the role of mergers in shaping the scatter in crosses the virial radius of the larger system and Vc is the
observed cluster scaling relations persist. larger system’s circular velocity at its virial radius.
In Poole06a we present a detailed account of how our
Scaling relations involving the Sunyuev-Zeldovich(SZ)
isolatedclustersandtheirorbitsareinitializedaswellasthe
properties of clusters, although previously considered
numericalmethodsandcodeparametersofoursimulations.
(McCarthy et al. 2003a,b; Cavaliere & Menci 2001), have
In this section we summarize key aspects of our approach
received significantly less attention than those involving
pertinentto ourpresent analysis and direct readers looking
mass,X-rayluminosityandtemperature.Withtheimpend-
for additional details to Poole06a.
ingavailability of large and statistically significant datasets
of SZ observations, a careful examination of the effects of
mergers on SZ scaling relations is warranted. In this paper
2.1 Initial conditions
we will use a set of nine idealized two-body cluster merger
simulations (first presented in Poole et al. 2006, Poole06a Wehavechosentofocus ourstudyonsystemsinitialized to
henceforth)toexaminetheeffectsofmergersonclusterscal- possescompactcores(r ∼50kpc).Wehavechosenthisini-
c
ing relations (refer to Poole06a for a review of pioneering tial configuration because it is thenatural convergent state
workinvolvingsuchsimulationsandRicker& Sarazin2001, for a relaxed cluster in the absence of feedback and rep-
RS01 hereafter, for a particularly good first examination of resentative of the structure of a large fraction of clusters
some of the issues revisited in this work). Our simulations (Peres et. al. 1998; Edge et al. 1992). In the context of hi-
havebeenconstructedtoprobearepresentativerangeofim- erarchicalclustering,suchsystemsarewellunderstood:they
The impact of mergers on relaxed X-ray clusters II 3
Table 1. Percentage difference of the global properties of our systems from the values required to preserve accepted mass scaling
relations at the end of our simulations and at trelax (in parenthesis). For X-ray observables, observed mass scaling relations are
used while for SZ observables (yo and Sν), mass scaling relations computed from our fiducial theoretical models are assumed (see
Section3.3).FortemperatureweusethemassscalingrelationofHorner (2001)andforluminosityweusethemassscalingrelationof
Reiprich&Bo¨hringer(2002)Correctedresultsareforanalysisconducted withthecentral0.1R200 excisedanduncorrected valuesare
performedwithoutexcisingthecentralregions.
Mp:Ms vt/vc Lx (uncorrected) Lx (corrected) Tx (uncorrected) Tx (corrected) yo Sν(R2500)
1:1 0.00 21.1 (-13.1) -13.0 (-2.0) 10.3 (5.5) 2.9 (-1.5) 28.8 (-3.3) 13.4 (14.7)
1:1 0.15 -25.6 (-38.3) -13.3 (-0.6) 8.2 (13.1) -1.3 (-0.4) -8.7 (-27.6) 10.0 (20.8)
1:1 0.40 -49.6 (-52.9) -27.6 (-26.1) 7.5 (9.2) -3.1 (-4.9) -24.2 (-39.3) 3.9 (6.7)
3:1 0.00 -13.3 (-27.1) 3.3 (14.6) 10.9 (14.7) 2.1 (2.2) -17.2 (-37.7) 12.9 (24.7)
3:1 0.15 -38.6 (-40.4) -3.2 (5.7) 14.6 (13.7) 0.9 (0.3) -29.8 (-47.6) 11.8 (18.2)
3:1 0.40 -31.7 (-35.2) -24.9 (-16.0) 5.3 (9.6) -1.7 (0.0) -15.0 (-33.6) -6.6 (1.6)
10:1 0.00 5.7 (12.3) -10.7 (19.1) 3.7 (13.1) -1.0 (4.4) -6.2 (-11.4) 2.4 (20.4)
10:1 0.15 -16.0 (-18.4) -13.5 (7.7) 6.5 (12.7) 0.6 (3.9) -18.0 (-23.8) -2.6 (12.0)
10:1 0.40 -17.5 (1.4) -23.3 (-7.7) 5.8 (11.8) -0.2 (4.4) -21.6 (-7.6) -7.2 (7.1)
are systems which have remained undisturbed long enough the more massive system the “primary” system (we arbi-
for vigorous radiative cooling to have produced a positive trarily choose one to be the primary in the 1:1 cases, with
centraltemperaturegradientandhighcentralgasdensities. no consequences for our results given their high degree of
To initialize the structure of our systems, we have fol- symmetry)andthelessmassivesystemasthe“secondary”.
lowed the analytic prescription of Babul et. al. (2002) and
McCarthy et. al. (2004)toproduceclusterswhichconform
2.2 Dynamical evolution
with recent theoretical and observational insights into clus-
ter structure. The dark matter density profiles of our sys-
InPoole06aweillustratedthegenericdynamicalprogression
tems follow an NFW-like form (Navarro, Frenk,& White which each of our simulations proceed through, identifying
1996; Moore et al. 1998) with the central asymptotic log-
fivedistinctstages:apre-interactionphase,firstcore-corein-
arithmic slope chosen to be β = 1.4 and the scale radius
teraction,apocentricpassage,secondarycoreaccretion,and
(rs) selected to yield a concentration c = R200/rs = 2.6 relaxation. These stages feature prominently in the discus-
(we will use R throughout to indicate the radius within
∆ sionwhichfollowssowewillbrieflyreviewtheirprogression
whichthemeandensityofthesystemis∆timesthecritical
here, for those who havenot read Poole06a.
density, ρc = 3H02/8πG; R200 = 1785kpc, R500 = 1166kpc As the cores accelerate towards each other during pre-
and R =180kpcinitially for ourprimary systems). The
cool interaction,apairofshockfrontsmaterializeandaredriven
initial gas density and temperature profiles of the clusters
towards each core, heating and compressing them briefly.
are set by requiringthat (1) thegas bein hydrostaticequi-
At t the cores of the two systems reach closest ap-
closest
librium within the halo, (2) the ratio of gas mass to dark
proach and these effects reach their maximum strength. In
matter mass within thevirial radiusbe Ω /(Ω −Ω ), and
b m b every case (including the head-on collisions), some part of
(3)theinitialgasentropy5scaleasS(r)∝r1.1 overthebulk
thesecondary’scoresurvivesitsfirstencounterwiththepri-
of the cluster body. We normalize the entropy profiles such
mary, tidally stripped into large cool streamers in off-axis
that the temperature of the ICM at R is half the virial
vir cases and strings of several clumps in the on-axis cases. At
temperature.
t the disturbed cores reach maximum separation. After
apo
Weconstructorbitsforoursystemswhichproducespec- subsequentlyreachingsecondpericentricpassageatt ,
accrete
ified radial and tangential velocities for the secondary sys- noobservabletraceof thesecondary coreremains. This pe-
tem(vr andvt respectively)whenitscentreofmassreaches riodmarksthebeginningofaprolongedperiodofaccretion
thevirialradiusoftheprimary(Rvir).Foreachofthethree when the plume of material generated from the disruption
mass ratios we study, we examine three orbits selected to of the secondary’s core accretes as a high velocity stream.
produce a typical value of vr(Rvir) and to cover a signif- Thisinstigates asecond episode ofcore heatingfollowed by
icant range of the transverse velocity vt(Rvir) giving rise a period of relaxation. At approximately t , the system
relax
to mergers found in cosmological dark matter simulations exhibits no obvious substructure in simulated 50ks Chan-
(Tormen 1997; Vitvitskaet al. 2002). dra imageswiththesystemplacedatz=0.1(seePoole06a
Throughout ouranalysis we shall refer to threecoordi- for details on how thisis done).
nateaxes;xandy will denotedirectionsintheplaneofthe This account of our systems’ dynamical evolution is
initial orbit (with the initial separation of the systems be- terse and we refer readers to Poole06a for a more detailed
ing along the x axis) and z the direction orthogonal to this and quantitativeaccount of thevarious processes involved.
plane. We shall also distinguish the two systems by calling
2.3 Some comments regarding the frequency of
mergers
5 We usethe standard proxyforentropy givenby S ≡kT/n2e/3
withneandT representingtheelectrondensityandtemperature In this paper, we seek to understand the role which merg-
ofthegas. ersare likely playingin shaping thestatistical propertiesof
4 Gregory B. Poole et. al.
clusters as studied through observed scaling relations. It is tions.Thiscantranslateintoaupwardbiasinσ ofasmuch
8
important to note however that our simulations certainly as 20% and a downward bias in Ω of comparable extent.
M
are not uniformly represented in thesestatistics. InFig.1wepresentinredthetemporalevolutionofthe
Incurrenttheoriesofhierarchicalclusterformation,the bolometric X-ray luminosities of our simulations integrated
likelihood of merger events is expected to have a strong within the varyingradius7 R (t). Although detailed com-
500
dependence on the mass ratio of the interacting systems. parisons to RS01 are complicated by the fact that we are
Equal mass mergers are expected to be rare while 10:1 not integrating over the entire simulation volume, we see
mergers are expected to be common. Recent studies exam- a similar double peaked evolution in luminosity to what is
ining merger statistics in cosmological N-body simulations notedintheirwork.Furthermore,wefindasimilartrendin
includeCohn & White(2005) and Wetzel et al. (2006).For thereductionofthefinalremnant’sluminosity with impact
the simulations presented by Wetzelet al. (2006), the frac- parameter.
tions of clusters which have experienced 2:1, 3:1 and 10:1 This plot illustrates an evolutionary progression with
mergers since z = 0.5 are 23%, 49% and 92% respectively featureswhichwewillshowarecommontoalloftheglobal
(private communication; from a sample of 37388 clusters X-ray and SZ observables we study in this paper. After a
with M > 1014M⊙ at z = 0 generated in a ΛCDM cos- short period with very little evolution, the system experi-
mology with Ω = 0.3, h = 0.7, n = 1 and σ = 0.9). encesadramatic“firsttransient”increasefollowingt which
M 8 o
These statistics are generated using a mas jump criteria reachesmaximumamplitudeatt .Thisisaproductof
closest
overconformaltimeintervalsofδτ =130h−1Mpc.However, theincreased densities andtemperaturesresultingfrom the
sincemultiplemergerswhichoccuroverthisintervalwillbe compressiveforcesandshocksformedduringthesecondary’s
countedassingleevents,thesenumbersarecertainlybiased approachtoitsfirstpericentricpassagethroughtheprimary.
high. These results are supported qualitatively by an ana- Followingt ,thesystemreturnstoastatesimilartoit’s
closest
lytic extended Press-Schechter analysis we have performed initial conditions. Dependingon theobservable,it can then
onasetofmergertreesgeneratedfollowing theapproachof experiencea“second transient”duetotherecollapse of the
Taylor & Babul (2004). system in head-on cases or the second pericentric passage
Thus, our 3:1 mergers should be representative of the of the surviving portion of the secondary core in off-axis
most massive merger events statistically important to the cases. This second transient is weak for the luminosity of
cluster population. Although there is evidence that equal our systems but as we will see, can be more significant for
mass mergers have occurred (e.g. the “Cloverleaf cluster” other observables (e.g. X-ray temperature). Following the
studied by Finoguenov et al. 2005), they are rare and we secondtransient,thesystemthenevolvesquiescentlyasthe
include them in this study primarily as theoretically inter- systemrelaxes.Thisprogressionisingoodqualitativeagree-
esting limiting cases. The vast majority of clusters should ment with the results of previous idealized merger studies
have experienced at least one merger similar to our 10:1 (e.g. RS01). Since all of the X-ray and SZ observables we
cases. study have direct dependencies on gas density and temper-
Forthesereasons,whenconsideringtheeffectsofmerg- ature, they all evolve with this same qualitative behaviour.
ersonscalingrelations,wewillprimarilybeconcernedabout This leads to a similarly generic qualitativeevolution (with
theeffects of 3:1 and 10:1 events. occasional important differences) inall thescaling relations
we will examine.
There is however one notable and generic feature in
the luminosity evolution of our simulations not present in
3 LUMINOSITY AND TEMPERATURE RS01: a persistent increase in luminosity after t . This
relax
increase follows the relation L (t) = L (t )exp(αt)
In this section we present the details of how we compute x x relax
where α = 0.08 − 0.14Gyr−1. We also plot, in blue on
global luminosities and temperatures for our simulations.
this figure, the evolution of each system’s luminosity with
Weshallfindthatthetemperaturesofourmergerremnants
the projected central 0.1R excised (a common measure
scale in accord with observed mass scaling relations, but 200
of the cooling radius of the system; R = 1785kpcand
thattheluminositydoesnot.Excisingthecoresofourclus- 200
R = 180kpc initially for our primary systems). These
ters improves this discrepancy. We will then illustrate the cool
consequences of this for the L −T scaling relation. curves (and an examination of the evolving surface bright-
x x ness profiles of our simulations) reveal that most of this
change is arising from increases in the surface brightness
of the system within this excised region. This is a result of
3.1 Luminosity
increasing central gas densities arising primarily from cool-
A cluster merger leads to transient increases in both X- ing and (to a lesser extent) the reaccretion of material to
ray luminosity (L ) and temperature (T ) which can pose thecenterof thesystem,dispersed tolarge radiiduringthe
x x
significant problemsforcosmological studies(Randall et al. interaction.
2002).Intheir study,RS01found that after an initial tran- Throughout this paper we will examine the degree by
sient increase at the time of first pericentric passage, the which our simulated mergers evolve to final states which
luminosity of the system drops to a fraction of its initial maintain observed scaling relations. We do not necessarily
value with a second smaller peak ∼ 2Gyrs later when the expect our simulations to preserve these scaling relations
secondarycorereturnsfromapocentricpassage.Thesesharp
transientincreasesinL cantranslateintoaskewingofthe
x
high-mass end of mass functions derived from observed X- 7 Throughout this paper, we adopt the peak of the projected
ray luminosity functions and mass-luminosity scaling rela- bolometricX-raysurfacebrightnessasthecenterofthesystem.
The impact of mergers on relaxed X-ray clusters II 5
Figure 1.BolometricX-rayluminosities (Lx) measuredwithin R500(t). The thin bluecurve traces the evolution of the system with
thecentral0.1R200 excisedfromconsideration(i.e. “corecorrected”luminosities)whilethethickredcurvetracestheevolutionwith
this region included (i.e. “uncorrected” luminosities). Thick horizontal dashes indicate the initial bolometric luminosities scaled by
the change intotal masswithin R500 frominitialto final states usingthe observed Mt−Lx scalingrelationofReiprich&Bo¨hringer
(2002). Vertical dotted lines indicate (from left to right) the times to (virial crossing), tclosest (first pericenter), taccrete (second
pericenter)andtrelax (themomentourremnantswouldappearrelaxedtoa50ks Chandra exposureatz=0.1).Blacktextaround
theboundaryindicates themassratioandvt/Vc depictedbyeachpanel.
but we use these measures as a means of estimating the 3.2 Temperature
degree by which we expect each event to contribute to the
Recently several authors have raised concerns that tradi-
observedrelation’s scatter.Forthisreason,wehaveplotted
tional methods of computing ICM temperatures in theo-
thickhorizontal dasheson Fig. 1to indicatethebolometric
retical studies may be introducing systematic biases dur-
luminositieswewouldexpectifourremnantsystemsevolved
to states which preserve the observed M −L scaling re- ingcomparisonstoobservations(Mathiesen & Evrard2001;
t x Gardini et al. 2004; Mazzotta et al. 2004; Vikhlinin 2006).
lation determined by Reiprich & B¨ohringer (2002). We use
This bias is introduced because the ICM of both theoreti-
the total mass integrated within R for this purpose. In
500 calandobservedsystemsisnotisothermalandthemethods
head-on cases we see that the total luminosity (in red) of
usedtocomputerepresentativetemperatureshavebeenfun-
our remnant systems generally manage to recover their ex-
damentally different.
pected values by the end of the simulation. However, the
Mosttheoreticalmeasuresoftemperaturearecomputed
luminosities of our off-axis merger remnants are systemati-
cally lower (by 16−50%; see table 1) than expected from throughoneofavarietyofpossibleweightedaverageswhile
observationaltemperaturesareobtainedfromfitsofplasma
the observed mass scaling relation. This discrepancy gener-
models to observed spectra. The most widely used theoret-
ally increases with impact parameter. It is consistant with
ical measure has been the emission-weighted temperature
the simulations of McCarthy et al. (2007a) who find that
computed from
off-axis mergers produce remnant cores with systematically
higherentropiesandhence,lowerdensitiesandluminosities.
Λ(T)n2TdV
T ≡ e (1)
ew R Λ(T)n2dV
e
R
where Λ(T) is the bolometric emissivity of the ICM and
n its electron density. More accurate but similarly conve-
e
Luminositiescomputedwiththecentral0.1R excised nient and computationally inexpensive “spectroscopic-like”
200
(inblue)aremoresuccessfulatpreservingtheobservedmass weightings have recently been proposed by Mazzotta et al.
scaling relation. The discrepancies of the final luminosities (2004) and Vikhlinin (2006). From comparisons to hydro-
from these scalings are only 3−28% (see table 1) in these dynamic simulations, Mazzotta et al. (2004) find that the
cases. weighting
6 Gregory B. Poole et. al.
Figure2.Temperatures(Tx)measuredwithinR500(t)usingseveraltechniquesdiscussedinthetext.Emission-weightedtemperatures
(Tew) are illustrated with red curves, spectrally fit temperatures (Tspec) with black curves, and “spectroscopic-like” (Tsl, computed
according to Mazzotta etal. 2004)temperatures withblue curves. Thethick magenta curves arespectrally fittemperatures withthe
cool cores (r <0.1R200) excised. Horizontal dashes indicate spectral temperatures scaled from their initial values using the observed
Mt−Tx scaling relation from the data of Horner (2001) and Reiprich&Bo¨hringer (2002). Vertical dotted lines indicate (from left
to right)the times to (virialcrossing), tclosest (first pericenter), taccrete (second pericenter) and trelax (the moment our remnants
would appear relaxedto a 50ks Chandra exposure at z =0.1). Black text around the boundary indicates the mass ratioand vt/Vc
depictedbyeachpanel.Notethechangeinverticalscale.
T may breakdown occasionally during the interaction. To
sl
n2T1−αdV check this we have also computed spectrally fit tempera-
Tsl ≡ R ne2T−αdV (2) tures (Tspec). To produce this measure we compute inte-
e gratedspectraovertheChandra bandpass(0.7-7keV with
R
withα=0.75givesresultsinmuchbetteragreementtotem- 20eV resolution) and fit isothermal plasmas to them (we
peraturesobtainedfromsimulatedChandra observations.In assume a metallicity Z = 0.3Z⊙ for all calculations in this
their analysis, they typically find Tsl to be lower than Tew paper). This is done via χ2 minimization weighted by the
by 20−30%. This relation is calibrated from mixtures of photonfluxofeachspectralbin.Theinstrumentalresponse
isothermal plasmas of two temperatures, with variations of of Chandra is included in this analysis as well as Galactic
Tsl from spectral fitsbeing less than 10%. absorption at a level of NH =2×1020cm−2.
The weighting of Vikhlinin (2006) is somewhat more
Intheanalysis ofRS01,theemission-weighted temper-
complicated but more accurately takes into account effects
atureofthesystemremainsrelativelyconstant,interrupted
onT introducedbyinstrumentalvariationsandmetallicity
x only by the pair of transients discussed above, during first
dependentlineemission.Theyfindaverysimilarpowerlaw
and second pericentric passages when the cluster cores are
scaling(α=0.79forChandra)asMazzotta et al.(2004)for
shock heated and compressed. As their systems relax, they
continuum contributions but significant spatial variations
recovertoslightlyhigheremission-weightedtemperaturesin
mayexist betweenthetwomeasures, particularly incluster
equal mass eventsand to approximately theinitial temper-
coreswhicharedominatedbylowtemperatureline-emitting
aturein 3:1 cases.
gas. However, we are only interested in globally averaged
InFig.2wepresentthetemporalevolutionofthethree
temperatures in this work, which are dominated by contin-
temperature measures discussed above, integrated within
uumemissionfromhotgas.Underthesecircumstances,very
R (t)foroursimulations.Inallcaseswewitnessthefamil-
little difference is expected between these measures and so 500
iar double peaked behaviour noted by RS01. We addition-
weshallpresentlyfocusourattentiononthesimplermethod
ally observethetrendnotedbyRS01that theamplitudeof
of Mazzotta et al. (2004).
the initial peak decreases with impact parameter while the
Oursystemsconstitutemixturesof gas coveringan ex-
relative strength of thetwo peaks becomes more similar.
tremelywiderangeofdensitiesandtemperatures,naturally
raising concernsthat thespecific weightings determined for It has been noted by Mazzotta et al. (2004) that the
The impact of mergers on relaxed X-ray clusters II 7
Figure3.X-raytemperatures(spectrallyfit)plottedagainstbolometricluminositiesforoursimulations(bothintegratedwithinR500)
andcomparedagainstobservations. Redfourandbluefivepointstarsindicatethestates ofthesystem atto andtrelax respectively.
The red vector indicates the evolution from to to tclosest while the blue vector illustrates 3Gyr of evolution following trelax. The
magenta line tracks the evolution from tclosest to trelax (generally 4-5Gyrs) during which the system is visibly disturbed. Green
crosses indicate the remnant state necessary to preserve the observed mass-scalingrelations. Black points are the observed catalogue
of Horner (2001). Dashedlines areour fiducial analytic entropy injectionmodels (So =10,100,300, and 500keVcm2,increasingfrom
righttoleft).Blacktextaroundtheboundaryindicatesthe massratioandvt/Vc depicted byeachpanel.
8 Gregory B. Poole et. al.
mismatch between T and T increases with the thermal interval of 4−5Gyrs, except for the 10:1 v /V = 0.4 case
ew sl t c
complexity of the system. This is reflected in our simula- which takes 7Gyrs toappear relaxed). This format will be
tionsbyanincreaseddiscrepancybetweenT andourother used for all the scaling relations we subsequentlypresent.
ew
temperature measures duringthe transient temperature in- It has been known for some time that variations in the
creasesatfirstandsecondpericentricpassage.Thisdiscrep- structureofthecentralregions ofclusterscontributesignif-
ancy, which is 15−40% larger than the difference between icantly to the scatter in both luminosity and temperature
TewandTslatallothertimes,suggeststhatthetransientin- mass scaling relations. For this reason, and out of a desire
creasesdeterminedbyRS01(whopresentemission-weighted toobtainthetightestrelationspossible(usuallyforthepur-
temperatures)aresignificantlyoverestimated.Consequently poses of obtaining mass functionsfor cosmological studies),
it suggests that the influence of transient temperature in- authors have typically presented “core-corrected” observa-
creases on measures of σ8 determined by Randall et al. tions for studying the Lx−Tx relation. It has been shown
(2002) are overestimated. by M04 however that there is very interesting structure in
Asexpected,TslandTspecaresystematicallylowerthan the Lx−Tx plane which correlates with themorphology of
Tew atalltimes.Initially,thisdifferenceissmall(∼3%)but the cores when the central regions are retained for analy-
at late times it can be as much as ∼ 10%. Given that Tsl sis.Toexploretheconsequences(andpossiblecontributions
producesresultsinverygoodagreementwithTspecthrough- of)mergers tothisstructure,weusethe“uncorrected”cat-
out our merger interactions (less than 5% difference in all alogue presented by Horner (2001) for comparison of our
casesandatalltimesexcept500Myrs duringfirstpericen- results to observations (presented in black on Fig. 3).
terinthe1:1near-axiscaseswhereweseea20%difference), On Fig. 3 (and most subsequent scaling relation plots)
we conclude that the methods of spectrally weighted tem- we havealso placed dashed lines depicting theoretical mass
perature averages developed by Mazzotta et al. (2004) and scaling relations for a set of fiducial analytic entropy injec-
Vikhlinin (2006) are indeed robust during the complicated tion models for systems with various minimum entropies.
evolution of a cluster merger. We shall use our spectrally These models are computed following the procedure of
fit temperatures for the remainder of our analysis however, McCarthy et. al. (2004) with the following exceptions: we
unless otherwise stated. use the mass-concentration relation from the Millennium
Given that there is such a persistent offset between Simulation,thebaselineentropyprofileofVoit et al.(2005),
Tew and Tspec, the normalization of theoretical tempera- and assume a bias Mg(< R200)/Mt(< R200) = 0.9Ωb/Ωm.
turescalingrelationsgeneratedwiththisapproacharelikely Fourlines are plotted for core entropies of 10, 100, 300 and
too high. This has important implications for cosmological 500 keVcm2 (increasingfromrighttoleft).InBabul et. al.
studiesutilizingemission-weightedtemperaturefunctionsas (2002)itwasfoundthatthe300keVcm2 modelbestfitsthe
well. median relation of the data. This model is thus indicated
In Fig. 2 we place thick horizontal dashes to indicate with a thicker line type and we shall consider it to repre-
the spectral temperature the final remnant would have if sentthemedianrelationofthedatainalldiscussionswhich
it were scaled from the initial temperature by the Mt−Tx follow.
relation derived from the temperatures of Horner (2001) In Section 3.1 we discussed the common temporal evo-
andmassesofReiprich & B¨ohringer(2002).Weseethatim- lution of the global X-ray and SZ observables we study in
mediately following trelax, thesystem is significantly cooler thispaper.Wealsonotedthatthisleadstoacommonqual-
than this scaled value. Late increases evolve according to itative evolution in their scaling relations as well. We see
Tx(t) = Tx(trelax)exp(αt) (with α = 0.01−0.03Gyr−1), the first illustration of this progression in Fig. 3. Initially,
takingthesystemtoroughlytheobservedmass-scaled tem- due to the shocks and compressive forces generated as the
perature by the ends of our simulations in all cases. Of the interactingsystemsreachfirstpericenter,thesystem’slumi-
three temperature measures, Tew produces results which nosityandtemperaturebothincreasesharply(illustratedby
most often and most significantly fail to yield the mass- red vectors). In all cases, these vectors run roughly parallel
scaled result, suggesting that previous theoretical studies to the mass scaling relations of our fiducial models in this
of theLx−Tx and Mt−Tx relations which haveemployed plane, supporting similar findings in previous merger stud-
Tew asatemperaturemeasurehaveexaggerated thescatter ies (e.g. Rowley et. al. 2004). This will be the general
in this relation introduced by mergers. In Table 1, we list case (with some important differences) in the other scaling
the discrepancies of our remnants’ temperatures from the relations we shall study as well.
observed mass-scaling relation. Following the first transient, the system returns to
nearly it’s initial state at t and subsequently evolves er-
o
3.3 L −T relation ratically until trelax (when the system appears relaxed in
x x oursimulatedChandra observationsandisvirializedwithin
In Fig. 3 we present the evolution of our systems in the R ).Themagentacurvetracesthesystem’sevolutiondur-
500
L −T plane. We illustrate the evolution from the initial ing this period, which lasts 4−5Gyrs. During this time it
x x
state(red4pointstar)tot (firstpericentricpassage) experiences a second transient (illustrated bya sharp jump
closest
with a red arrow and the evolution for 3 Gyrs following along the fiducial models in the magenta curve) when the
t (bluefivepointstar)withabluearrow.Ineachcase, systemrecollapsesinthehead-oncasesorthesurvivingpor-
relax
thefinalL andT ,scaledfromtheirinitialvaluesbytheob- tion of thesecondary’s corereturnsfor asecond pericentric
x x
servedmassscalingrelationsofReiprich & B¨ohringer(2002) passage in the off-axis cases. The magnitude of this second
andHorner (2001),areillustratedbyagreencross.Magenta transient increases with impact parameter due to the re-
curves track the evolution of the system from t to duced disturbance of the secondary core. It is during this
closest
t , while the system appears significantly disturbed (an period when most of the displacement across the scatter of
relax
The impact of mergers on relaxed X-ray clusters II 9
Figure 4. Total masses within R500(t) computed from our simulations. The actual total mass is plotted as a thick black curve, the
hydrostatic equilibrium mass (computed from Eqn.4) is plotted as a red curve and the isothermal β-model mass (computed from
Eqn.8)isplottedasadashedbluecurve.Verticaldottedlinesindicate(fromlefttoright)to (thetimeofvirialcrossing),tclosest (first
pericenter),taccrete (secondpericenter)andtrelax (themomentourremnantswouldappearrelaxedtoa50ks Chandra exposureat
z=0.1).Blacktextaroundtheboundaryindicatesthemassratioandvt/Vc depicted byeachpanel.
theobservationsoccurs.Althoughdifficulttoillustratewith cover the majority of the scatter in this plane. However, in
this plot, much this displacement occurs during the accre- themorecommonsituationsrepresentedbyour3:1mergers,
tion of streams following thesecondary’s second pericentric states represented by our fiducial entropy injection models
passageinseveralcases.Wewillexamineinmoredetailthe withentropieshigherthanS =300keVcm2 arenotreached,
complicated processes driving this evolution in Poole et al. noteven transiently.Our10:1 mergers fail toreach theme-
(2007a)wherewewillexaminetheeffectsofmergersonthe dian relation of thedata underany circumstance.
cores of our systems. Whenthisplotisgeneratedutilizingemission-weighted
Once second pericentric passage has passed and obvi- temperatures, the full dispersion of theobservations is cov-
oussubstructuredissolved,thebluevector(whichillustrates ered by both our 1:1 and 3:1 mergers. It is now well es-
3Gyrs of evolution following t ) shows that the system tablished that this temperature measure is not viable how-
relax
once again evolves parallel to the mass scaling relations of ever, so this does not represent a means by which to ac-
ourfiducialmodels.Thisoccursascoolingleadstoadenser, count for the observed scatter. Instead, it further empha-
more luminous core and material dispersed by the interac- sizes the importance of computing proper spectral temper-
tion reaccretes to the system centre, deepening its gravita- atureswhen comparingtheoretical modelsofX-rayclusters
tional potential and increasing its temperature. to observations. Furthermore, not only should the normal-
izationofpasttemperaturescalingrelationsgeneratedwith
Theinitialconditionswehavechosenplaceourprimary
the emission-weighted measure be viewed with some scep-
systems on the high luminosity side of the scatter in the
L −T plane, where systems with compact cool cores are ticism (as argued in Section 3.2), the scatter should be as
x x
well.
typicallyfound(M04).InSection3.2wefoundthatmergers
tend to evolve to states which preserve the observed mass-
temperature scaling relation but in Section 3.1 found that
theycreateremnantswhichareunderluminouswithrespect
4 MASS
to the observed mass-luminosity scaling relation. In Fig. 3
we see the consequences of these trends: off-axis mergers Todate,allcataloguesofclustermassesinvolvingsignificant
tendtopushtypicalcompactcoldcoresystemstowardsthe sample sizes have been compiled from X-ray observations.
low-luminosity side of theobserved Lx−Tx relation. Themethodsused are thusnot direct (suchas with lensing
Inouroff-axis1:1cases(whichwemustemphasize,are measures) but are inferred from temperature and surface
rarely observed and expected to be exceptionally uncom- brightnessprofiles using methods which may behighly sus-
mon) ourmergers are able todrive systems to states which ceptible to systematic biases, particularly during a merger.
10 Gregory B. Poole et. al.
These approaches generally assume that the system can be
described as being in a state of hydrostatic equilibrium; a ρ
ρ (r)= o (7)
condition given by g (1+(r/r )2)3β/2
c
Under these assumptions, fitting Eqn. 6 to the surface
dP GM (<r) brightness profile yields the logarithmic derivative of the
ρ−1 =− t (3)
g dr r2 densityprofile,producingthefollowingrelationforthetotal
mass within R
This yields a mass profile of thegeneral form 500
3βkT R (R /r )
M(r)=−kT(r)r dlogρg(r) + dlogT(r) (4) Mβ(R500)= Gµxm500 1+(R500 /cr )2 (8)
Gµm » dlogr dlogr – p 500 c
p
Temperature and β-model fits in the results presented by
where G and k are Newton’s and Boltzmann’s constants
Reiprich & B¨ohringer (2002) are fit to the flux which ex-
respectively, T(r) is the temperature profile of the system,
tendstotheobservedradiusofthesystem(withthecentral
µthemeanmolecularweight,m themassoftheprotonand
p
0.1R excised for the temperature fits). The observed ra-
ρ (r) the gas density profile. In Poole06a we examined the 200
g
diusis generally comparable to R which istheradius we
evolutionofahydrostaticdisequilibriumparametergivenby 500
use to generate the isothermal β-model masses (computed
from Eqn. 8) we present in Fig. 4 (in blue).
ρ−1dP Fromthisfigurewecanseethattheisothermalβ-model
H =1+ g dr (5) systematically underestimates the mass of our systems by
r−2GMt(<r) 25−40%. This result is in good agreement with the find-
and illustrated that clusters which appear relaxed can vi- ings of several other authors (e.g. Hallman et al. 2006;
olate the condition of hydrostatic equilibrium by H = Rasia et al. 2006; Kay et al. 2004). The general trends in
10−15% and occasionally even more. How does this affect the scaling relations should not be affected much by this
masses obtained from Eqn. 4? bias, but the normalization will be. This could have signif-
In Fig. 4 we present (in red) the evolution of the mass icant implications for cosmological studies conducted with
of our systems within R (t) computed directly from our isothermal β-model masses.
500
simulations using this relation. For comparison, the actual
totalmassispresentedaswell(thickblack).Wecanseefrom
thisplot that despitethelimited validity of thehydrostatic 4.1 M −T relation
t x
equilibrium condition, masses computed from Eqn. 4 after
In Fig. 5 we present the evolution of our isothermal β-
t (when the system appears as a single undisturbed
relax
remnant) generally reproduce the system mass to within ∼ model masses against temperature and compare them to
5−10%,withaslightsystematicbiastowardshighervalues. the observed temperature catalogue of Horner (2001) and
mass catalogue of Reiprich & B¨ohringer (2002). We follow
ToimplementEqn.4tomeasureclustermasseswithout
the same format here as for Fig. 3. Red four and blue five
additionalassumptions,accuratemeasurementsofρ (r)and
g
point stars indicate the system’s state initially and when
T(r)mustbemade.Theobservationalchallengesofdoingso
it appears relaxed at t . The red vector illustrates the
havebeenconsiderablebutwiththeincreasingavailabilityof relax
transient evolution from t tot (first pericentricpas-
high qualityChandra andXMM observations, significant o closest
sage) and the blue vector shows 3Gyrs of evolution fol-
progress hasrecentlybeen made.Vikhlinin et al. (2006) for
lowing t . The magenta line traces the evolution of the
instance have presented a method of gas density and tem- relax
system between t and t , when the system looks
perature deprojection which they have demonstrated to be closest relax
visiblydisturbed.Greencrossesindicatetheβ-modelmasses
accurate to a few percent for apparently relaxed systems
of our remnants scaled from their initial values by the ac-
(Nagai et al. 2006).
tual change of mass within R , and their temperatures
Presently however, statistically representative Chan- 500
similarly scaled by the observed M −T scaling relation.
dra and XMM catalogues of sufficient size to studymass t x
Dashed lines indicate our fiducial entropy injection models
scaling relations are not available. For this reason, we shall
(withtheentropyminimum increasingwith temperatureat
use for comparison the catalogue of Reiprich & B¨ohringer
aconstantmass).Forthisplot,wehavereducedthemasses
(2002) who report masses within R measured from
500
of these models by 30% to reflect the downward bias in
ROSAT and ASCA observations. These authors measure
isothermal β-model masses found in Section 4. When we
masses assuming that their observed systems are in hydro-
do so, we find a good agreement between our fiducial mod-
static equilibrium but make the further assumptions that
elsandtheobservedcatalogue.Sincetheobservedcatalogue
the gas is isothermal and that it’s density profile follows
and our simulation masses are compiled using the same β-
a parameterized form given by the β-model. For an X-ray
model techniques, they should be directly comparable and
surface brightness profilegiven by
donot requireany such adjustment.
First,weseethatthereisaconsiderablysmallerdegree
S ofscatter(inboththeobservationsandourfiducialmodels)
Sx(rp)= (1+(r /r )o2)(6β−1)/2 (6) inthisplanecomparedtowhatisseenintheLx−Tx plane.
p c Thisisnotasurprisegiventhestrongcorrelation weexpect
thegas density profile of an isothermal gas is given by between these quantities: it is the depth of the potential