Answer Happy

9 EXTRAGALACTIC ASTRONOMY [4.5 [2] This question deals with the gas content and structural properties of a Milky Way progenitor galaxy at 2-2. Near-IR imaging with the Hubble Space Telescope (HST) has revealed that the radial distribution of stellar mass in this galaxy follows the surface mass density profile of a classical disk galaxy with exponential scale radius hu = 2 kpc. The central surface mass density (of the stellar component) is 8x10M /kpc? (i) Calculate the total stellar mass M. of this z - 2 disk by integration of its mass profile. (ii) HST in its spectroscopic mode is used to determine the width of an emis- sion line from this galaxy which in turn is converted to an observed rota- tional velocity of 80 km/s. The disk is inclined by an angle i = 45° to a line of sight to the observer. Show that the intrinsic rotational velocity of the disk is Veire = 113 km/s. (ii) The disk galaxy we are considering lies exactly on the baryonic Tully-Fisher relation Mary = A Veles with a = 3.9 and A=63 M (km/s)-39. Calculate its gas fraction (gas = Mgas/Mary (iv) Calculate the average surface mass density of the gas in the disk assuming that all gas resides within 2h. of the galaxy centre. (v) Use the Schmidt-Kennicutt relation to estimate the total star formation rate (SFR) of our 2-2 galaxy. Begin by writing down the functional form of this star formation law. The normalisation constant has a value of 10-12 in the relevant units when, for all quantities involved, length scales are expressed in kpc. Write down the units of the normalization constant. Choose the other free parameter in accordance with the canonical form of the Schmidt- Kennicutt relation. (vi) Under normal circumstances, a star-forming galaxy with mass M. -10° M. at z-2 will grow into a Milky Way-sized galaxy (MMW ~6x10''M) by 2-0. Given its current baryon budget, could our example 2 -2 galaxy grow to be as massive as the Milky Way? If not, what would have to happen for the galaxy to acquire the necessary additional mass? Assuming a constant SFR, how long would it take the galaxy to double its stellar mass? Compare this time scale to the gas depletion time. : [2] [1] [2.5 [3]