Answer Happy

(a) Show that reasonable assumptions about spiral galaxies together with the relationship between luminosity and absolute magnitude lead to expressions of the form M = -10.0 log Vmax + C where M is the absolute magnitude of the galaxy, Vmar is the maximum observed rotational velocity of the galaxy, and C is a constant. [5 marks] (b) The following empirical relationship has been found for Sa galaxies: MB = -9.95 log Vmax +3.15 where Vmar is the maximum rotational velocity in km/s. NGC 2639 is an Sa galaxy with Vmar = 324 km/s and an apparent extinction-corrected B magnitude of 12.22 mag. Estimate the distance to NGC 2639 and the galaxy's B luminosity. If the radius of NGC 2639 is R = 28 kpc, estimate the mass of this galaxy in solar masses and its mass-to-light ratio. [4 marks) (c) The shortest wavelength at which VLBI can be carried out routinely is 7.0 mm. How long a time interval in years would you need between "global” VLBI observations in order to just resolve the rotational motion of a galaxy such as NGC 2639 that is oriented with its disk perpendicular to the plane of the sky? Assume that the effective telescope diameter in the resolution relation is the maximum distance between the telescopes in the array. How long a time interval would you require if it were possible to do VLBI at optical wavelengths? [6 marks