Problem set 5 for ASTR 323/423: The Local Universe

Due 5pm Thursday April 24.

Individual problems (as always, you can talk about the problems as long as you hand in your own work)

(1) How can we use the fundamental plane to teach us about elliptical galaxy evolution?

(i) The equation for the z=0 fundamental plane is given by the work of Jorgensen et al (MNRAS 280, 167, 1996). Their main derivation is for the r band, so compare for the same passband in higher-redshift samples. (Why is it important to use the same passband in these comparisons? ) Using the units for surface brightness used in the field dataset below, the fundamental plane equation becomes log r_e = 1.24 log(sigma) + 0.328 mu_e,r + 9.12

(ii) Here is a dataset taken for a sample of field galaxies at z up to 1. NOTE: Because these galaxies are at significant redshift, cosmological surface brightness dimming will make their surface brightness lower. Also, the redshift affects the bands we observe. The data have been corrected so that the surface brightness at that filter is in the rest frame of the galaxy at that redshift, cosmological surface brightness dimming has been applied. The field galaxy data give both rest frame B and r: make sure you use r.
Plot up the positions of the galaxies in the higher-redshift sample on the fundamental plane, ie log re on x axis and 1.24 log(sigma) + 0.328 mu_e,r on the y axis. Compare them to the low-redshift (Jorgenson) relation given above.
Does this sample show differences from the z=0 fundamental plane? Do you see any trends with redshift in the field sample?

(iii) Show how one can use the fundamental plane to give an estimate of the galaxy's M/L ratio. Hint: you could look at the class notes..... We have assumed a constant M/L ratio in our derivations of the form of the fundamental plane from the virial theorem. How will a passively-evolving galaxy's M/L ratio change with time? Will a collisionless merger make any difference to this evolution? How will it affect the fundamental plane relation? Does this make sense with what you see?

(iv) Interpret your results -- what can you conclude about the formation and evolution of ellipticals in the field?