Final exam - due noon, Friday May 16

1) Choose one of the cosmological models in figure 5.23 with a non-zero cosmological constant. Describe the evolution of that model in detail. Be sure to relate it to the relative contributions of matter and "dark energy" over time. Hint - refer to figure 5.30

2) Refer to figure 1.32. Note the scale is 0.2" = 0.008 pc. Estimate the semimajor axis of the star's orbit around SgrA*. Use this data to estimate the mass of the Milky Way's central black hole.

3) Refer to figure 2.17. Pick any galaxy and any distance beyond 15 kpc and calculate the mass of your galaxy interior to that distance.

4) A Cepheid variable is seen at magnitude 17.3 in a distant galaxy and has a period of 40 d. Use figure 2.25 to estimate the absolute magnitude and find the distance.

5) The Lyman forest of a quasar's spectrum has absorption lines seen at 325 nm, 472 nm, and 526 nm. The Lyman emission line itself appears at 654 nm. Explain this spectrum, and calculate the various redshifts and distances involved.

6) Refer to figure 6.6. What if the energy density of the cosmological constant is NOT constant? Can we make any reasonable assumptions about how it may change as a function of time given the fact that it has only recently (past few billion years) dominated the universe? How might any time dependence affect the future evolution of the universe?

7) Are the following combinations of quarks possible (at least in terms of electric charges)? In other words, could there exist detectable particles made of these combinations?

uddc

uuu

ddd

cdd

8) Suppose that the primordial abundances shown in figure 6.13 for a hypothetical universe are 10^-9  < Li < 10^-8 and 10^-7 < D < 10^-6 . What is the range of possible values for Ω_b,0 for this universe?

9) A distant quasar has a redshift of 0.8. Assuming H_o = 72 km/sec/Mpc and q_o = -0.3, calculate its distance. Suppose this quasar is "lensed" by an invisible intervening cloud of dark matter. The einstein angle is 5". Find a relationship between the mass and the unknown distances. Although we cannot calculate the mass, what constraints can you place on the mass based on reasonable assumptions for the distances?

10) Look at the three Friedmann eqn of motion for a nonzero cosmological constant. Assume a model where "rho-dot" =0 and "R double dot" = 0.

a) what do these assumptions mean physically?

b) From F#3, find a relationship between the density and pressure. What does this mean physically?

c) Substitute this into F#2 and solve for Λ.

d) Substitute this into F#1 and solve for "R dot".

e) Solve the differential equation to find R(t). Sketch and explain the evolution of this universe. Does it match up to any of the cases in figure 5.23?