ay202a galaxies & dynamics lecture 17: galaxy groups & clusters continued
TRANSCRIPT
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AY202a Galaxies & Dynamics
Lecture 17:Galaxy Groups & Clusters
continued
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And V = |V1 - V2| < Vlim(V1,V2,m1,m2)
with two choices, either fix V or scale it as D.
Then select
Dlim and
Vlim as needed
for the sample
you have.
RSA Sample
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2dF 2PIGS
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2MRS Sample (raw)
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2MRS Sample (filled)
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2MRS Selection Function
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2MRS Group Selection
Number of groups found f
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2MRS Groups
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3 largest 2MRS Groups Virgo, Fornax/Eridanus, Perseus-Pisces
/
=12
80
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2MRS Group Mass Function
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2MASS Galaxy Groups
δρ/ρ = 12 δρ/ρ = 80-------------------------------------------------------σP (km/s) 197 183RPV (Mpc) 1.71 0.97log MV/LK 1.70 1.53Log MP/LK 1.90 1.67ΩM,V 0.14+/-0.02 0.10+/-0.02ΩM,P 0.23+/-0.03 0.13+/-0.02-------------------------------------------------------- V=Virial Estimator P = Projected Mass
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# Density versus redshift for various group surveys:
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Cluster ClassificationJust like galaxies, clusters classified morphologically. Overall Compact Medium Compact Open LinearBautz Morgan classes I, I-II, II, II-III, III based on the
ratio between the brightness of 1st and rest I -- single central cD galaxy c.f. A2029 II -- intermediate III -- no dominant cluster galaxy c.f. Hercules
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Rood-Sastry cD -- like BM I
types B -- Binary c.f. Coma
L -- Linear
C -- Core Compact
F -- Flat
I -- Irregular
Tuning Forks
Rood-Sastry cD -- B
Struble & Rood I -- F B -- cD
L -- F
C -- I
L
C
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Sky Distribution of Abell Clusters 0.033 < z < 0.83
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Optical
Substructure
(Geller & Beers ’82)
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Cluster
MorphologyIrregular
A1367 A262
Regular
A2256 A85
(Jones & Forman ’84)
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A2029
A2142
Hydra
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Perrseus A. Fabian
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Physics of Galaxy ClustersTo 0th order, assume spherical,
decreasing density from the center. If n(r) is the 3-D number density,
the projected density, N(R), is
N(R) = n[(R2+z2)½ ] dz
= 2
where z is the coordinate along the l.o.s. and R is the projected radius
∞
-∞
r n(r) dr
(r2 – R2) ½
∞
R
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Hydrostatic Equilibrium
Good basic model for the hot gas is to assume Hydrostatic Equilibrium
dPg/dr = - g GM(r)/r2 P = where g means gas
= + differentiating the gas law
{ + } = - g GM(r)/r2
M(r) = { + }
kT
mp
dPg dg kT g k dT
dr dr mp mp dr k T dg g dT
mp dr dr
- rT d ln g d ln T
G mp d ln r d ln rdensity & temperature gradients
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You can also treat the galaxies this way, just as a “gas” of much more massive particles
= gal P gal = 1/3 <v2> gal
= n k Tgal
=
and we can compare the gas and galaxy distributions
since they are living in the same potential.
dPgal GM
dr r2
<v2> dPgal kTgas 1 dgas
3gal dr mp gas dr
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We can write for the relative density relations
( ) = ( ) β
where β = =
This is known as the Beta Model. If β = 1, gas and galaxies have the same distribution.
Generally β 1
IX (r) [ 1 + (b/rc)2 ]-3β + 1/2
gas gal
0,gas 0,gal mp <v2> mp 2los
3 k T kT
X-ray surface intensity and rc = optical galaxy core radius
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Other Dynamical Quantities
Crossing Time
tcross ~ R/ ~ 2 x 109 yr for R=RA and H=70
Dynamical relaxation (Virialization) takes places on timescales of the crossing time, so (1) clusters are generally relaxed, and the centers of the clusters relax first
Two-Body Relaxation time is long in clusters
trelax ~ tcross (N / ln N)
so cluster galaxies are not in “thermal” equilibrium
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X-ray Emission
Spectrum of x-ray gas is optically thin thermal bremhmmsstrahlung (free-free emission) plus emission lines
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X-ray emission from Coma. ROSAT (left) and XMM (right). Note structure in the images.
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Bremsstrahlung emissivity =
ευ = ( )½ e -hυ/kT gff(T,υ)
where ne and ni are the number density of electrons and ions, Z is the ion charge and gff is the Gaunt factor. Flat then exponentially decreasing. Typical x-ray temperatures are ~ 50 million degrees or kT = 5 kev
For a thermal pasma of solar abundance, bremsstrahlung alone gives
eff 3.0 x10-27 (T / 1K) ½ (ne / 1 cm-3)2 erg cm-3 s-1
32Z2e6neni 2
3 me c3 3kT me
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When line emission is included:
εtotal 6.2 x10-27 (T / 1K) ½ (ne / 1 cm-3)2 erg cm-3 s-1
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Use X-ray
features to study
Chemistry
(c.f. Mushotzsky)
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A Case Study - The Virgo ClusterAssume D = 16 Mpc (HST Key Project)
Zw-B(0) magnitudes
6o Core v = 716 km/s
rH ~ 0.8 Mpc
MP ~ 8 x 1014 M
M/LB ~ 750 (M/L)But (1) substructure exists, (2) there is at least one
background group contaminating at 2200 km/s (Virgo W), and (3) Spirals avoid the center and appear to be infalling.
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Virgo Cluster
Markarian’s Chain
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Bohringer et al.
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X-ray map
with contours
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First problem is to find where the cluster really is:
JH85 from CfA survey, luminosity weighted center of all galaxies with v < 3000 km/s, m 14.5
error ~ 3’ --- iterate on sample
Isopleths in the Zwicky catalog
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All known velocities in the 6 degree radius circle.
Virgo
Great Wall
Background Cl.
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Spirals and Ellipticals are not in the same place in the cluster --- Spirals avoid the center.
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Virgo Surface
Density
A hole around M87!
How much of this is just due to the Spirals?
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Velocity
Histogram by Type
E’s look Gaussian
S’s are flat
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Cluster Infall
JH ‘85
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