Properties of Early Type Galaxies in Rich Clusters

The Properties of EarlyThe Properties of Early
Type Galaxies in RichType Galaxies in Rich
ClustersClusters
Robert Berrington (U. of Wyoming)Robert Berrington (U. of Wyoming)
Charles D. Dermer (NRL)Charles D. Dermer (NRL)
Michael J. Pierce (U. of Wyoming)Michael J. Pierce (U. of Wyoming)
Andrew Monson (U. of Wyoming)Andrew Monson (U. of Wyoming)
Sehyun Hwang (U. of Texas)Sehyun Hwang (U. of Texas)

Physical Properties of GalaxyPhysical Properties of Galaxy
ClustersClusters
 Rich ClustersRich Clusters
 Contain thousands ofContain thousands of
Galaxies.Galaxies.
 Masses ~10Masses ~101515
MM..
 Poor ClustersPoor Clusters
 Contain hundreds ofContain hundreds of
Galaxies.Galaxies.
 Masses ~10Masses ~101414
MM..
Abell2218Abell2218
MKW4

The Physics of Cluster MergersThe Physics of Cluster Mergers
 Gravitational force drives collisionGravitational force drives collision
 Total gravitational energy availableTotal gravitational energy available
Thursday, November 20,
2008
Department of Physics and Astronomy
Colloquium
[ ]
3
2
merge3
1tot
)(2 







+
=
t
G
Mm
mM
E
π

The Merging Cluster ScenarioThe Merging Cluster Scenario
 Rich clusters from byRich clusters from by
accreting poor clusters.accreting poor clusters.
 Shocks form in ICM at boundary.Shocks form in ICM at boundary.
 if vif vss exceeds sound speed of ICMexceeds sound speed of ICM
 Thermal particles swept up in shockThermal particles swept up in shock
 Accelerated via first-order FermiAccelerated via first-order Fermi
 Sizes: ~1 Mpc are possible.Sizes: ~1 Mpc are possible.
 May also reaccelerate particles.May also reaccelerate particles.
 Head-tail radio galaxies nearby.Head-tail radio galaxies nearby.
 Total energy availableTotal energy available ~10~1063-6463-64
ergsergs..

Radio Halos and Cluster RadioRadio Halos and Cluster Radio
RelicsRelics
 Sources of extended radio emissionSources of extended radio emission
 No optical counterpartNo optical counterpart
 Typically with sizes ~1MpcTypically with sizes ~1Mpc
 Occur in only the most massive and X-ray luminousOccur in only the most massive and X-ray luminous
of Rich clustersof Rich clusters
 Radio HalosRadio Halos
 Mimic X-ray morphologyMimic X-ray morphology
 UnpolarizedUnpolarized
2008
Colloquium

RelicsRelics
 Cluster Radio RelicsCluster Radio Relics⇔⇔PeripheralPeripheral
HalosHalos
 Irregularly shapedIrregularly shaped
 Located on the cluster peripheryLocated on the cluster periphery
 Linearly polarized from shockLinearly polarized from shock
compressioncompression
 Found in clusters with evidence of a recent or ongoingFound in clusters with evidence of a recent or ongoing
mergermerger
2008
Colloquium

RelicsRelics
Radio (red) and optical (blue) image of Abell 3376 showing a collision
between two clusters. The large radio clouds on the right and left of the
image are shock fronts propagating through the ICM.

RelicsRelics
 Radio emission from relativistic electronsRadio emission from relativistic electrons
 EEee ≤≤ ~10~101717
eVeV
 Synchrotron radiationSynchrotron radiation
 Luminosity: ~10Luminosity: ~1043-4443-44
ergs sergs s-1-1
 Steep spectraSteep spectra
 Electrons also produce high energy photonsElectrons also produce high energy photons
 May be a dominant contributor to the diffuseMay be a dominant contributor to the diffuse γγ-ray-ray
backgroundbackground
 Observable by next generationObservable by next generation γγ-ray observatories-ray observatories
2008 8
Colloquium

Temporal Particle EvolutionTemporal Particle Evolution
 Fokker-Plank equationFokker-Plank equation
Coulomb diffusion term Energy loss rate Source term Catastrophic loss
from p-p, p-γ, and
diffusion out of
the system
[ ] [ ] ∑=
−+
∂
∂
−
∂
∂
=
∂
∂
dpppi i tE
tEN
tEQtENtEE
E
tENtED
Et
tEN
,,
2
2
),(
),(
),(),(),(),(),(
2
1),(
γ τ

2008 9
Colloquium

Shock DynamicsShock Dynamics
 Shocked fluid velocitiesShocked fluid velocities 2
infall
2
2
2
1
22
11
)(
)()(
)(31
)(31
)(
)(





 −
+
+
= −
−
tv
tvtv
tM
tM
tn
tn
µ
µ
2008 10
Colloquium

 Shock speedShock speed
 Forward and reverse mach numbers:Forward and reverse mach numbers:
 Compression ratio:Compression ratio:
 ΓΓ = 5/3 is the ratio of specific heats for an ideal= 5/3 is the ratio of specific heats for an ideal
gasgas
)(21
1
)( 2
2,1
2,1
t
tr −
Μ+−Γ
+Γ
=
and,
4
9
11
3
2
)( 2
2
1
1
1








++=
v
c
c
v
tM
( )
( ) 







−
++
−
= 2
infall
2
2
2
infall
2
)(4
9
11
3
)(2
)(
vtv
c
c
vtv
tM
2008 11
Colloquium

Particle InjectionParticle Injection
 Power law distribution with exponentialPower law distribution with exponential
cutoffcutoff
 NormalizationNormalization
 WhereWhere ηηe,pe,p is an efficiency factor, and is set to 5%.is an efficiency factor, and is set to 5%.
 Typical values are ETypical values are Etottot≈≈101063-6463-64
ergsergs






−





=
−
)(
exp
)(
),(
max
0
,,
tE
Epc
QtEQ pepe
β
α
( ) ( )sssp
e
pe
E
E
pepe vAvmndEtEQE 





=∫
2
HeICM,,,
2
1
,
max
min
ηη
2008 12
Colloquium

Particle InjectionParticle Injection
 Maximum particle energyMaximum particle energy
 Acceleration time constraintAcceleration time constraint
 Energy loss constraintEnergy loss constraint
 for electronsfor electrons
 for protonsfor protons
 Size scale limitationSize scale limitation
∫=⇒=
t
J
s
EdtE
fr
vB
E
0
1max,1max,
1-
2
ICM
1max, sMeV
100 
MeV
]μG[10)1(
]μG[]km[
108.2 2
ICM
14
ICM4
,2max,
Bz
B
fr
v
E
J
s
e −
++
×=
MeV
]μG[1.0
]km[
102
ICM
12
,2max,
Bfr
v
E
J
s
p ×=
MeV
MpcμG
10 max
14
3max, 











=
λB
f
E
2008 13
Colloquium

Physical Processes/Energy LossPhysical Processes/Energy Loss
RatesRates
ElectronsElectrons
 Synchrotron:Synchrotron:
 Bremsstrahlung:Bremsstrahlung:
 Compton:Compton:
 Coulomb:Coulomb:
ProtonsProtons
 Coulomb:Coulomb:
 Catastrophic Loss:Catastrophic Loss:






−=
π
βγσ
83
4
)(EE
2
ISM22
esynch
B
c eeT

)()36.0(ln
2
)(EE 2
42
HeISM
6
ebrem cmE
cm
ne
eee
e
n
++





−= γ
η


ph
22
eComp
3
4
)(EE Uc eeT βγσ−=
)](ψ(t)ψ[
(t)λ4
t),(EE HeISM
4
eCoul t
n
cm
πe
e
e
e
′−











−=
β
η
∫
−
=
x(t)
0
2/12
(t)ψ y
eydy
π
)(2
x(t)
2
tkT
vm
e
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=
)](/)ln[(24λ(t) eV2/1
ISMHe tTe
e
ηη−=

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
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

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)(4
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4
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e
β
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HeHISM
ppion
σσβ +
=
nc c

Particle SpectraParticle Spectra
2008 15
Colloquium

Nonthermal Photon SpectraNonthermal Photon Spectra

Nonthermal Particle LuminosityNonthermal Particle Luminosity
2008 17
Colloquium

Forward Shock Reverse Shock

Minimum Spectral IndexMinimum Spectral Index

Modeling the Coma ClusterModeling the Coma Cluster
 Likely a 3 body mergerLikely a 3 body merger
 NGC 4839NGC 4839
 Inbound orbitInbound orbit
 Mass ~ 0.6x10Mass ~ 0.6x101414
MM
 NGC 4889NGC 4889
 Near collision time withNear collision time with
main clustermain cluster
 Mass ~ 0.1x10Mass ~ 0.1x101515
MM
 Probable cause of radio haloProbable cause of radio halo
 NGC 4874NGC 4874
 Main Cluster with MassMain Cluster with Mass
~ 0.8x10~ 0.8x101515
MM
~0.8x1015
MM
~0.6x1014
MM
1253+275
~0.1x1015
MM
Coma C
NGC 4874
NGC 4839
NGC 4889
(Colless & Dunn 1996)

Parameters for Coma ClusterParameters for Coma Cluster
 Assuming HAssuming H00=70 km s=70 km s-1-1
MpcMpc-1-1
,,
((ΩΩ00,Ω,ΩRR,Ω,ΩΛΛ) = (0.3, 0.0, 0.7)) = (0.3, 0.0, 0.7)
 nn00 = 3.12 x 10= 3.12 x 10-3-3
cmcm-3-3
 ββ = 0.705= 0.705
 rrcc = 257 kpc= 257 kpc
 ηηe,pe,p = 1%= 1%
 ttageage = 9.7 x 10= 9.7 x 1088
yrs, tyrs, tcollcoll ≈≈ 1.0 x 101.0 x 1099
yrsyrs
 B = 0.22 µGB = 0.22 µG
 MM11 = 0.8 x 10= 0.8 x 101515
MM and Mand M22 = 0.1 x 10= 0.1 x 101515
MM
(Mohr, Mathiesen, & Evrard 1999)
2008 21
Colloquium

Coma ClusterComa Cluster
Radio X-ray

What is the Fundamental Plane (FP) ofWhat is the Fundamental Plane (FP) of
Elliptical Galaxies?Elliptical Galaxies?
 Galaxies occupy a plane in the 3-D spaceGalaxies occupy a plane in the 3-D space
defined by (Rdefined by (Ree,<,<μμ>>ee,, σσ))
 Can be used to calculate distancesCan be used to calculate distances
 Has been used to study evolution of galaxiesHas been used to study evolution of galaxies
 Virial Theorem predicts RVirial Theorem predicts Ree∝∝<I><I>ee
-1-1
σσ22
 Observed plane shows tiltObserved plane shows tilt
 Can also be used to study the dynamics ofCan also be used to study the dynamics of
galaxiesgalaxies
2008 24
Colloquium

Cluster Data SampleCluster Data Sample
 Cluster SampleCluster Sample
 33 Abell clusters33 Abell clusters
 average of ~60 galaxies/cluster.average of ~60 galaxies/cluster.
 Cluster SelectionCluster Selection
 Richness RRichness R≥≥11
 Redshift z<0.05Redshift z<0.05
 δδ ≥≥ -35-35°°
 Complete and homogeneous sample ofComplete and homogeneous sample of
Northern Abell clustersNorthern Abell clusters
2008 25
Colloquium

Spectral DataSpectral Data
 Spectral DataSpectral Data
 Calibration clusters (Leo, Virgo, Fornax)Calibration clusters (Leo, Virgo, Fornax)
 Obtained using IFU DensepakObtained using IFU Densepak
 Allows variable spatial sampling to match clusters at greater distancesAllows variable spatial sampling to match clusters at greater distances
using a fixed fiber aperetureusing a fixed fiber apereture
 Abell clustersAbell clusters
 Data obtained with the MOS Hydra at WIYNData obtained with the MOS Hydra at WIYN
 Spectral resolution 0.9Spectral resolution 0.9 ÅÅ (on WIYN/Hydra)(on WIYN/Hydra)
 S/N ~30-100S/N ~30-100
 Centered on redshifted Mgb absorption featureCentered on redshifted Mgb absorption feature
 Accurately measure logAccurately measure log1010((σσ)) ≥≥ 1.81.8
 All velocity dispersions corrected for (1+z) time dilationAll velocity dispersions corrected for (1+z) time dilation
2008 26
Colloquium

Example SpectraExample Spectra

Imaging DataImaging Data
 Photometric DataPhotometric Data
 I and V-band imagingI and V-band imaging
 Images obtained using both WIYN and WIROImages obtained using both WIYN and WIRO
 Surface photometry performed assuming circular aperturesSurface photometry performed assuming circular apertures
 Corrections appliedCorrections applied
 (1+z)(1+z)44
surface brightness dimmingsurface brightness dimming
 k-correctedk-corrected
 Galactic extinctionGalactic extinction
 Effective Radii (REffective Radii (Ree)--50% light radius--is used and)--50% light radius--is used and
determined empiricallydetermined empirically
2008 28
Colloquium

The Fundamental PlaneThe Fundamental Plane
 Various projections of the FPVarious projections of the FP
for the template clustersfor the template clusters
 Coma, Perseus, and A2199,Coma, Perseus, and A2199,
Fornax, Virgo, and LeoFornax, Virgo, and Leo
 Brightest ellipticals [logBrightest ellipticals [log1010((σσ) >) >
2.3] found in distinct region2.3] found in distinct region
of FPof FP
 Well known they come fromWell known they come from
old stellar populationsold stellar populations
 Show complex velocity fieldsShow complex velocity fields
2008 29
Colloquium

The Velocity Dispersion DistributionThe Velocity Dispersion Distribution
Function (VDDF)Function (VDDF)
 TheThe σσ distribution yields observed VDDFdistribution yields observed VDDF
 Cross-Correlation using IRAF package FXCORCross-Correlation using IRAF package FXCOR
 Corrected values for (1+z) time dilation factorCorrected values for (1+z) time dilation factor
 MotivationMotivation
 Tracer of galaxy gravitational potentialTracer of galaxy gravitational potential
 Minimal dependence on luminosity evolution.Minimal dependence on luminosity evolution.
 Directly comparable with N-body simulations.Directly comparable with N-body simulations.
 Quantitative measure of hierarchical merging?Quantitative measure of hierarchical merging?
2008 33
Colloquium

The Modified Schechter FunctionThe Modified Schechter Function
 Originates from Schechter Luminosity FunctionOriginates from Schechter Luminosity Function
 Transformed into velocity dispersion space (Transformed into velocity dispersion space (σσ) via) via
Faber-Jackson relation:Faber-Jackson relation:
 Takes the form:Takes the form:
 Under the assumption galaxy halos are isothermal, weUnder the assumption galaxy halos are isothermal, we
can convert the circular velocity (vcan convert the circular velocity (vcc) of spirals to) of spirals to σσ, and, and
compare to Ellipticals.compare to Ellipticals.
( ) dLe
L
L
L
dLLN
L
L 




−






= *
**
*
α
φ
β
σ∝L
( ) σ
σ
σ
σ
βφ
σσ
β
σ
σ
γ
dedN





−






= *
*
*

Individual ClustersIndividual Clusters
 Abell 1656 (Coma)Abell 1656 (Coma)
 Left: VDDF with best fitLeft: VDDF with best fit
(solid curve)(solid curve)
 Right: Error ellipses forRight: Error ellipses for
best fitbest fit
 Abell 548Abell 548
 Same as aboveSame as above
2008 35
Colloquium

Properties and PromiseProperties and Promise
 Steeper low-Steeper low-σσ-end power laws (-end power laws (αα))
have largerhave larger σσ**..
 Quantitative measure of hierarchicalQuantitative measure of hierarchical
merging?merging?
 Directly comparable with modelsDirectly comparable with models
 Weak correlation between clusterWeak correlation between cluster
velocity dispersion (velocity dispersion (σσclcl) and) and σσ**..
2008
Colloquium

Comparison with Other StudiesComparison with Other Studies
 Most Probable Velocity DispersionMost Probable Velocity Dispersion
 Average Velocity DispersionAverage Velocity Dispersion
 SDSS Data sample of Early-type galaxies (ShethSDSS Data sample of Early-type galaxies (Sheth et al.et al.
2003)2003)
 Our valuesOur values
( ) β
σ β
γ
σσ
σ
σ
1
*
ˆ
ˆ0 





=⇒=
∂
∂N
( )
( )
( )
( )



 +Γ



 +Γ
==
∫
∫
∞
∞
β
γ
β
γ
σ
σσ
σσσ
σ
1
2
*
0
0
Nd
Nd
95.0ˆseckm160 ==
σ
σσ
85.0ˆseckm4126 =±=
σ
σσ
2008 38
Colloquium

General Remarks Concerning theGeneral Remarks Concerning the
VDDFVDDF
 ProsPros
 Minimal dependence on Luminosity evolutionMinimal dependence on Luminosity evolution
 Galaxy merging is continuousGalaxy merging is continuous
 Should see evolution in the VDDF for clusters at z~0.5 (versus z~1.0Should see evolution in the VDDF for clusters at z~0.5 (versus z~1.0
for Luminosity evolution)for Luminosity evolution)
 ConsCons
 Cluster and galaxy evolution is stochasticCluster and galaxy evolution is stochastic
 Requires multiple moderate resolution (R ~ 6000) spectra ofRequires multiple moderate resolution (R ~ 6000) spectra of
galaxies—difficult at high zgalaxies—difficult at high z
 Requires sampling the low-log(Requires sampling the low-log(σσ) end to measure) end to measure αα
accuratelyaccurately
 Affected by cluster environmentAffected by cluster environment
2008 39
Colloquium

The Mass Function of Early TypeThe Mass Function of Early Type
GalaxiesGalaxies
 MassMass ∝∝ σσ22
RRee
 σσ22
RRee distribution yields mass functiondistribution yields mass function
 Reflects the true mass of a galaxyReflects the true mass of a galaxy
 Can be used to isolate environmental effects andCan be used to isolate environmental effects and
luminosity evolution from mass evolutionluminosity evolution from mass evolution
 Luminosity FunctionLuminosity Function ⇒⇒ Luminosity evolutionLuminosity evolution
 VDDFVDDF ⇒⇒ Mass and environmental effectsMass and environmental effects
 Mass FunctionMass Function ⇒⇒ Mass evolutionMass evolution
2008 40
Colloquium

Spectral Indices of Early Type GalaxiesSpectral Indices of Early Type Galaxies
 Spectral resolution 0.9Spectral resolution 0.9 ÅÅ (on WIYN/Hydra) with(on WIYN/Hydra) with
typical S/N ~30-100typical S/N ~30-100
 Flux calibrated using secondary standardsFlux calibrated using secondary standards
 Lick Indices HLick Indices Hββ, Fe5015, Mg, Fe5015, Mg11, Mg, Mg22, Mg, Mgbb, Fe5270,, Fe5270,
Fe5335, & Fe5470Fe5335, & Fe5470
 Corrected for velocity dispersionCorrected for velocity dispersion
 Calibrated to Lick StandardCalibrated to Lick Standard
 Spectral resolution of Lick Standard is 8Spectral resolution of Lick Standard is 8 ÅÅ
 Small index dependent shiftSmall index dependent shift
 Corrected for (1+z) redshift factorCorrected for (1+z) redshift factor
2008 41
Colloquium

Abundance trends with logAbundance trends with log1010((σσ))
 HHββ vs. logvs. log1010((σσ))
 Weak correlationWeak correlation
 Younger stellar population withYounger stellar population with
decreasing logdecreasing log1010((σσ).).
 Mgb vs. logMgb vs. log1010((σσ))
 Increases with logIncreases with log1010((σσ) (consistent with) (consistent with
literature)literature)
 Change in slope for logChange in slope for log1010((σσ) < 2.1) < 2.1
2008
Colloquium

Stellar PopulationsStellar Populations
 HHββ spread indicatesspread indicates
5 Gyr < age < 15 Gyr.5 Gyr < age < 15 Gyr.
 WeakWeak σσ dependencedependence
 Average age ~9 GyrAverage age ~9 Gyr
 [MgFe]’ spread indicates 0.0[MgFe]’ spread indicates 0.0
< [Fe/H] < 0.3< [Fe/H] < 0.3
 [Fe/H] increases with log[Fe/H] increases with log1010((σσ))
 All clusters show similarAll clusters show similar
CharacteristicsCharacteristics
SSP models from (Thomas, Maraston, & Korn, MNRAS, 351, L19)

Stellar PopulationsStellar Populations
 [[αα/Fe] increases with/Fe] increases with
loglog1010((σσ))
 αα elements come fromelements come from
Type II SNType II SN
 Fe produced in Type IaFe produced in Type Ia
SNSN
 Reflects length of starReflects length of star
formationformation
 All clusters exhibitAll clusters exhibit
similar characteristicssimilar characteristics
2008 46
Colloquium

Conclusions and the FutureConclusions and the Future
 Likely detection of the Coma Cluster by GLAST andLikely detection of the Coma Cluster by GLAST and
marginal detection by VERITAS.marginal detection by VERITAS.
 Radio halo and hard X-ray emission well fit by clusterRadio halo and hard X-ray emission well fit by cluster
merger modelmerger model
 Investigate mass and luminosity evolution and quantifyInvestigate mass and luminosity evolution and quantify
environmental effectsenvironmental effects
 Use the Fundamental Plane to decipher structuralUse the Fundamental Plane to decipher structural
properties and correlate with population modelsproperties and correlate with population models
 Stellar populations of elliptical galaxies have increasingStellar populations of elliptical galaxies have increasing
[Fe/H] and [[Fe/H] and [αα/Fe] with increasing log/Fe] with increasing log1010((σσ).).
 Further investigate star formation history of fainterFurther investigate star formation history of fainter
ellipticals.ellipticals.
2008 48
Colloquium

Properties of Early Type Galaxies in Rich Clusters

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