Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://hea.iki.rssi.ru/Z-90/arc/20/vikhlinin.pdf Äàòà èçìåíåíèÿ: Tue Dec 28 11:46:30 2004 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 23:45:13 2012 Êîäèðîâêà:

COSMOLOGY WITH BARYONS IN GALAXY CLUSTERS
z = 0.6

z = 1.2 z = 1.2


Cluster-based cosmological tests
· Composition of clusters and the Universe are the same


can constrain b /

M

· Mass function sensitive to P( k)


can constrain h M ,

8

· Growth of perturbations governs cluster evolution


can constrain M , [and , [and w], ...]

Need good data to do any of the above


Are clusters self-similar?
· Assumption: cluster dynamics governed mostly by gravity of CDM · Prediction: clusters look the same when appropriately scaled: /(1 + z)3 r r/ rvir r/ T T T/ T · Data: 12 "round" clusters at z < 0.2 with long Chandra exposures, T = 0.8 - 10 keV


Are clusters self-similar?


Temperature profiles from Chandra
6 r
2500

r

500

4 T , keV 2 0 0

500 r , kpc

1000


Temperature profiles from Chandra
1. 5

1. 0 T/ T 0. 5 0

5

10 15 r, arcmin

20


Temperature profiles from Chandra
1. 5

1. 0 T/ T 0. 5 0. 0

0. 2

0. 4 r/r180

0. 6
r

0. 8
1950 h-1 (T/10)
1/2

180

kpc


Temperature profiles from Chandra
1. 5

1. 0 T/ T 0. 5 0. 01

0. 1 r/r180

1

· Centers are different; outer regions are self-similar


A surface brightness profile
10 10
-5 -1

-2

r

2500

r

500

66

cm n2 d l , 10

10 10 10 10 10

-3

-4

-5

-6

-7

10

100 r , kpc

1000

· -model doesn't fit · Profile steepens gradually; r
-3

at r


Gas density profiles
10
-1

10
-3

-2

ng , c m

10

-3

10

-4

T > 4 ke V T < 2 ke V 10
-5

10

100 r , kpc

1000


Gas density profiles
10
-1

10
-3

-2

ng , c m

10

-3

10

-4

T > 4 ke V T < 2 ke V 10
-5

0 .0 1

0 .1 r/r180

1

· Centers are different; outer regions are self-similar


Are clusters self-similar?
· Accurate reliable measuremens T ( r) to r 0.6 - 0.7 rvir g ( r) to r rvir

· Clusters are self-similar

... but not in centers:

· Derive Mtot in relaxed clusters from hydrostatic equilibrium: GM r2
tot

Pg =- = -µ m p â T / r â g

d log n d log T + d log r d log r


Baryon fraction test
· Clusters are big so b /
M

= M b /M

tot

=f

b

· M b given by X-ray imaging ·M
tot

can be derived from dynamics or weak lensing

· Many works since White etal. 1993; latest results from Allen et al.: fgas at r
2500

from Chandra data


Baryon fraction test
within r
2500

0.25 r

vir

0 .2 5 0 .2 0
2500

0 .1 5 0 .1 0 0 .0 5 0 .0 0 10

f

g

at r

12

10

13

Mg , M

10

14

10

15


Baryon fraction test
within r
500

0.6 r

vir

0 .2 5 0 .2 0 0 .1 5 0 .1 0 0 .0 5 0 .0 0 10
500

f

g

at r

12

10

13

Mg , M

10

14

10

15


Baryon fraction test
within r
2500


500

0 .2 5 0 .2 0 0 .1 5 0 .1 0 0 .0 5 0 .0 0 10

f

g

within r

2500

-r

500

12

10

13

Mg , M

10

14

10

15


Baryon fraction test
within r
2500


500

, gas + 15% in stars

0 .2 5
500 2500

-r fg â 1.15 within r

0 .2 0 0 .1 5 0 .1 0 0 .0 5 0 .0 0 10

12

10

13

Mg , M

10

14

10

15


Baryon fraction test
within r
2500


500

, gas + 15% in stars + 7% b/o depletion

0 .2 5 -r fg â 1.15 â 1.07 within r
2500 500

0 .2 0 0 .1 5 0 .1 0 0 .0 5 0 .0 0 10

12

10

13

Mg , M

10

14

10

15


Baryon fraction test
within r
2500


500

, gas + 15% in stars + 7% b/o depletion

0 .2 5 -r
2500 500

0 .2 0 0 .1 5 0 .1 0 0 .0 5 0 .0 0 10 CMB: b /M = 0.166 ± 0.012

fg â 1.15 â 1.07 within r

12

10

13

Mg , M

10

14

10

15


Baryon fraction results

· Observed f b very close to b / M from CMB.

· Derived f b = 0.143 ± 0.008

=



M

= (0.30 ± 0.02) ( h/0.72)

-1/2

· ... correcting for 7% baryon depletion, f b = 0.153 ± 0.008 =
M

= (0.28 ± 0.02) ( h/0.72)

-1/2

·f

X-ray b

h

-1.5

;

f

X-ray b

=f

CMB b

implies h = 0.68 ± 0.04


f

gas

(z) test



f b (z) = const only if distances are for the "right" cosmology potential substitute for SN


Application to cluster abundance tests
· Rely on growth of structure instead of distances · Main problem -- estimate M ·M
tot tot

for many clusters

can be estimated from Mgas : M
tot

= 1.15 â

-1

âM

gas

M â , b

0.93

·M

gas

is measured easily from X-ray imaging.


Shape of Mass Function
older results published in Voevodkin & Vikhlinin 2004; see also poster A10

10 10 N (> M ), Mpc-3 10 10 10 10 10

-5 -6 -7 -8 -9

-10 -11

10

13

1014 Mb , M

10

15

· Sample: 111 clusters at z < 0.2 with T > 2 keV · Model: CDM power spectrum (Eisenstein & Hu); non-linear collapse (Jenkins et al.) ·M
tot

= M b â M / b â ;



0.93;

small trend in ( M) accounted for.


Shape of Mass Function
older results published in Voevodkin & Vikhlinin 2004; see also poster A10
10 10 10 P(k)
3

10
2

-5

10 10 N (> M ), Mpc-3 10 10 10 10 10 10

-5 -6 -7 -8 -9

clusters
-6 -7 -8 -9

10
1

N (> M ), Mpc-3

10 10 10

1 10 10 10
-1 -2



M

= 0.27

-10 -11



M

= 0.27

-3

10
-4

-10

10

10

-3

10-2 10-1 1 k, h Mpc-1 10-11

10

13

1014 Mb , M

10

15

10

13

1014 Mb , M

10

15

· Sample: 111 clusters at z < 0.2 with T > 2 keV · Model: CDM power spectrum (Eisenstein & Hu); non-linear collapse (Jenkins et al.) ·M
tot

= M b â M / b â ;



0.93;

small trend in ( M) accounted for.


Shape of Mass Function
older results published in Voevodkin & Vikhlinin 2004; see also poster A10
10 10 10 P(k)
3

10
2

-5

10 10 N (> M ), Mpc-3 10 10 10 10 10 10

-5 -6 -7 -8 -9

clusters
-6 -7 -8 -9

10
1

N (> M ), Mpc-3

10 10

1 10 10 10
-1 -2


-4

M M

= 0.27 10 =1

-10 -11


13

M M

= 0.27 =1 1014 Mb , M 10
15

-3

10
10
-3

-10

10

10-2 10-1 1 k, h Mpc-1 10-11

10

10

13

1014 Mb , M

10

15

· Sample: 111 clusters at z < 0.2 with T > 2 keV · Model: CDM power spectrum (Eisenstein & Hu); non-linear collapse (Jenkins et al.) ·M
tot

= M b â M / b â ;



0.93;

small trend in ( M) accounted for.


Shape of Mass Function
older results published in Voevodkin & Vikhlinin 2004; see also poster A10
10 10 10 P(k)
3

10
2

-5

10 10 N (> M ), Mpc-3 10 10 10 10 10 10

-5 -6 -7 -8 -9

clusters
-6 -7 -8 -9

10
1

N (> M ), Mpc-3

10 10

1 10 10 10
-1 -2


-4

M M

= 0.27 10 =1

-10 -11


13

M M

= 0.27 =1 1014 Mb , M 10
15

-3

10
10
-3

-10

10

10-2 10-1 1 k, h Mpc-1 10-11

10

10

13

· "Concordance" fits cluster data. · Cluster results:

1014 Mb , M

10

15



M

= 1 doesn't (big effect).

· Sample: 111 clusters at z < 0.2 with T >(many works since Henry & Arnaud 1991) 2 keV · Model: CDM power spectrum (Eisenstein & Hu); non-linear collapse (Jenkins et al.)

= 0.21 ± 0.05; 8 = 0.77 ± 0.03 · Mtot = M b â M / b â ; 0.93; small trend in ( M) accounted for. ± 0.015 for fixed
M

M


Data for distant clusters
· 50 clusters at z 0.5 from ROSAT surveys

· 160d -- 650 pointings, 160 square degrees, 201 clusters, 45 at z > 0.4, V similar to Local Universe (z < 0.1) (Vikhlinin et al. 1998, Mullis et al. 2003) · 400d -- 2.5 â 160d in volume and Ncl optical followup completed in 2004 Chandra followup underway check out poster A1


Data for distant clusters
A1651, z = 0.085, ROSAT CL 1221+4918, z = 0.70, Chandra

-1 s-1

keV

-1

10

-2

-- comparable to ROSAT and ASCA uncertainties for low-z clusters

f , cnt 10
-4

T/T 10%, M g /M g 20%

10

-3

1

E , keV

10


Cluster evolution test

10 N (> M ), Mpc-3 10 10 10 10

-6

z = 0 .0 5
-7

-8

z = 0 .5 5

-9

-10

10

13

1014 Mb , M

10


15


Cluster evolution test

10 N (> M ), Mpc-3 10 10 10 10

-6

z = 0 .0 5
-7

-8

z = 0 .5 5 = 0 .2 7

-9

M

-10

10

13

1014 Mb , M

10


15


Cluster evolution test

10 N (> M ), Mpc-3 10 10 10 10

-6

z = 0 .0 5
-7

-8

z = 0 .5 5 = 0 .2 7

-9

M

= 0
-10

10

13

1014 Mb , M

10


15


Cluster evolution test
0 .9 10 N (> M ), Mpc-3 G( z ) , z = 0 . 5 5
-6

z = 0 .0 5 10-8 .7
-8

10

z = 0 .5 5 = 0 .2 7

0 .7
-9 M

10

= 0
-10 100.6 13 10 0

G = 0.726 ± 0.027 for = 0.3 = 0.760 ± 0.045 for = 0.2

0.2 1014 0.4 MM b, M

1065 0. 1


Cluster evolution + shape of F( M)
0 .9 1 .0

SN Ia

D( z ) , z = 0 . 5 5

0 .8 WMAP 0 .5
cluster evolution

0 .7

0 .6 0 .2 0 .4
M

0



0 .6

0 .0 0 .0

0 .5

1 .0


Cluster evolution + shape of F( M) + flat space
0 .9

0 .0 - 0 .2
WMAP

D( z ) , z = 0 . 5 5

0 .8

SN Ia

- 0 .5 -1 w0 = -2

- 0 .4

w
0 .7

- 0 .6 - 0 .8
0 .6

0 .6 0 .0

0 .2



0 .4
M

- 1 .0 0 .0

0 .2

0 .4 M

0 .6

0 .8

For

M

= 0.3, w < -0.9 (68%), < -0.7 (90%), < -0.6 (95%)


Future
1 .1 0
CDM w0 = -0.6

1 .0 5 1 .0 0 0 .9 5 0 .0 160d 0 .5 1 .0 z 1 .5 400d (proj)

- 0.8

G( z ) / G( z )

-1 - 1.2 - 1.4

2 .0


CONCLUSIONS
· Chandra data: real-world clusters are self-similar (T ( r), g ( r)) · f b in clusters:
M

= 0.28 ± 0.02
M

· Mass function shape:

= 0.21 ± 0.05, 8 = 0.77

(and also from cluster P( k), Schuecker et al.) · Robust constraints from cluster evolution ( M 0.3): F( L x ) -- Borgani et al.; F(T ) -- Henry; F( M b ) -- Vikhlinin et al. · First constraints on dark energy ( 0.5 - 1, w < -0.7)