Extragalactic Astronomy (ASTRO 504)Spring 2020

Problem Set 6

Due 6 March 2020

Solving problem sets is one of the most efficient ways of learning the subject. You are encouraged tocollaborate with fellow students and/or to consult senior students, local postdocs and me. But, pleasewrite the solution by yourself.No homework will be accepted after I post the solution on the course webpage.

1. (30 pts) The Coma cluster.(Note: this problem is originaly from Chris Mihos at Case Western) Everything you ever wantedto know about the Coma cluster! First, go to ADS, and find/download a data table (“Catalog ofComa Cluster Galaxies”) associated with Doi et al., 1995, ApJS, 97, 77.(a) Make an x-y plot of the galaxy distribution by placing NGC 4886 at the center (x , y) =(0,0). Use TAN projection defined in following document: “AIPS Memo 27, Non-linear coordinatesystems in AIPS reissue of November 1983 version” by Eric W. Greisen (NRAO).(b) Make a histogram of the radial velocity of all the galaxies with measured redshifts. How wouldthis help you decide which galaxies actually were part of the Coma cluster?(c) Looking only at galaxies with 4000 < cz < 10000 (why?), calculate the mean velocity andvelocity dispersion of the galaxy sample.(d) From your data, how far away is Coma? Use ⌦⇤ = 0.7, ⌦M = 0.3, h= 0.7.(e) Calculate the total blue luminosity (in solar luminosities) for the Coma cluster. Ignore galaxieswith cz < 4000 and cz > 10000, but include galaxies with unmeasured redshifts. For reference,the absolute blue magnitude of the Sun is MB = 5.5.(f) Figure out the radius (in arcminutes) which contains roughly half the total blue luminosity.What is the half-light radius of Coma in Mpc?(g) Now calculate the virial mass of Coma.(h) If the stars in the Coma cluster galaxies have a mass-to-light ratio of (M/L) = 3M�/L�, whatis the total mass of stars in the Coma cluster?(i) If the galaxies in the Coma cluster have a mass-to-light ratio of (M/L) = 20M�/L�, what isthe total galaxy mass of Coma (this will consist of stellar mass and the mass of any dark matterand gas which is contained inside galaxies).(j) X-ray measurements indicate that Coma has a hot gas mass of 3 ⇥ 1014M�. What fractionof Coma is dark matter unassociated with galaxies (i.e., distributed smoothly throughout thecluster)?

2. (20 pts) X-ray and Sunyaev-Zel’dovich effect.Explain how one can measure the angular diameter distances to the regular galaxy clusters by com-bining the measurements of thermal Sunyaev-Zel’dovich effect and the X-ray intensity of galaxycluster. What are possible systematics?

1

°6 °4 °2 0 2 4 6L (degree)

°8

°6

°4

°2

0

2

4

6M

(deg

ree)

tan projectionangular separation

1.

Ca)

0 2000 4000 6000 8000 10000 12000 14000 16000cz (km/s)

0

5

10

15

20

25

30

35nu

mbe

rofg

alax

ies

1.

( b ) & (c)

(cz7 = 692T Kmb{ga = loots Kmt

1.

(d) Zama = 0.023

→

amongdistance = 98.3T Mpa

(e) F a 10-0 '4Bt

L KTLDLCZana)-

Ft

4 To- hataopdyooaxs. } (to)=fYgt÷nYTonxkioo*y.

. 1.03×1013

(f) Re a 3.6 ° a 216'→ Re - 6Mpc

(g) M ~ 1.1×10'Mo (E.) (Fan,D ~ 6.7×10'tMo

l4 the ~ 3 (Moon) L ~ 3.1×1013 Mo

C i) Mq ~ 2. (Meo) L ~ 2.1×1014140

(j) Mph = ( 67 - 2.1 - 3) ×lo4 Mo = 6.19×10*140

a 92% of total mass ! !

2- SZ Measures I = theft fnetedl a fnetedl ~ the> Lte

{X-ray measures Sx a fnenepdl ~ CME > L Aep

⇒ ¥ . :::÷h÷Hi÷H÷if the > = Cnet ( that is

, clump.mess inside of cluster -- o)

⇒ 4¥ a L → measure the site of the cluster.

⇒Da-- YooTs observed angular she of the cluster.

'

- - Da - ÷o(¥f

possible systematics f A dump-mess② non- trivial temperature structure .