Stars & galaxies, multiple-choice questions

[M_{⊙} = 1.989 × 10^{30} kg, m_{p} = 1.67 × 10^{−27} kg, k_{B} = 1.38 × 10^{−23} J K^{−1}, 1pc = 3.09 × 10^{16} m, G = 6.67 × 10^{−11} N m^{2} kg^{−2}] Problem 1.

The mass of the Andromeda galaxy is dominated by a dark halo with density profile ρ(r) ∝ 1/r^{2}, mass M = 2.0×10^{12}M_{⊙}, and extent r_{⋆} = 200kpc.

The circular velocity of a satellite galaxy at distance r = 300kpc is

(a) 170 km s^{−1}

(b) 207 km s^{−1}

(c) 220 km s^{−1} The circular velocity of a satellite galaxy at r = 100kpc is

(a) 170 km s^{−1}

(b) 207 km s^{−1}

(c) 293 km s^{−1} The galaxy in addition has a uniform density bulge with mass M_{b} =

2 × 10^{10}M_{⊙} and radius r_{b} = 4kpc. Combining dark halo and bulge, the circular velocity at r = 2kpc is

(a) 73 km s^{−1}

(b) 207 km s^{−1}

(c) 220 km s^{−1} Problem 2. Doppler motions show that the line-of-sight velocity dispersion of galaxies in a cluster of galaxies is σ_{z} = 800km s^{−1}. Assuming isotropic orbits, this means that the 3D velocity dispersion, σ, is

(a) 800 km s^{−1}

(b) 1386 km s^{−1}

(c) 2400 km s^{−1} The cluster’s radius R = 0.5 Mpc. The virial mass of the cluster is

(a) M = 7.4 × 10^{13}M_{⊙}.

(b) M = 2.2 × 10^{14}M_{⊙}.

(c) M = 6.7 × 10^{14}M_{⊙}. Another cluster has mass M = 1 × 10^{15}M_{⊙} and radius R = 1 Mpc

Compute its virial temperature T, assuming pure hydrogen gas. (The binding energey of the hydrogen atom is 13.6eV.)

(a) T = 1.7 × 10^{8} K and the gas is mostly ionised

(b) T = 3.5 × 10^{8} K and the gas is mostly ionised

(c) T = 1.7 × 10^{8} K and the gas is mostly neutral

(d) T = 3.5 × 10^{8} K and the gas is mostly neutral