HI (21cm) emissions from a nearby galaxy are detected at three locations: (C) – galaxy centre (E) – -10 arcmin to the east of the galaxy center (W) –-10 arcmin to the west of the galaxy center The emission peaks at 21.190 cm at (C), 21.204 cm at (W), and 21.176 cm at (E). (a) For a Hubble constant of 70 km/sec/Mpc, how far away is this galaxy (in Mpc)? Calculate redshift: z = (obs /emit) /emit z = (21.190 /21.106) /21.106 z = 0.0475 Calculate distance d ~ cz/H0 d ~ (c * 0.0475) /70 d ~ 203Mpc Distance is approx 203Mpc (b) How fast is the galaxy rotating? Assume that the galaxy is seen edge-on. f = c /w f(21.204cm) = 1.4138Ghz f(21.176cm) = 1.4157Ghz Width = 0.0019 v = (0.0019 /1.4138) * c v = 402.88985 km/s (c) Assuming the gas is on circular orbits, use Newton’s law of gravity to determine the amount of mass in the galaxy interior to 10 arcmin radius. M = (v^2 * r) /G r = d * angle * (Pi/180) r = 1.8221×10^19 km M = 402^2 * 1.8221×10^19 /G M = 4.412×10^34 kg M = 22,181 M_sun (d) The peak brightness temperature at location (C) is 12K -what is the peak column density of this galaxy at this location? ???