Class description: In this "shotgun seminar", students will calculate order of magnitude estimates of astrophysical interest, such as the size of an active galactic nucleus, the height of tides on the earth, the lifetime of radiatively supportive star. The goal is to acquire broad knowledge of astrophysical phenomena and the ability to estimate quantities so that astrophysical scales become intutive.

Prerequisites: Good understanding of astrophysics.

Grades: Pass or fail.

References: to be listed

Problem sets:
Week 1 (Saha): The paper 2014, ApJ, 783L, 11S claims a constraint on the equation of state of dark matter from observations of galaxy clusters: pressure/(c^2 x density ) = 0 ± 0.2

You don't need to read the paper. Instead, we ask you to think about something [remember the name of this course!] that the authors and referee of the paper obviously overlooked...

Consider a ball with a typical mass and size of a cluster of galaxies. It is self-gravitating. If it had too much pressure, it would explode. What is the maximum pressure such that it doesn't explode. What does that give you for P/(c^2 rho) ?

You should be able to do better than the above paper. Quite a bit better.

Week 2 (Saha): Estimate the solar neutrino flux (neutrinos per square metre per second) using general principles with minimal special information. The only numbers needed, apart from physical constants, are the following.

-- Sunlight is close to a black body spectrum with peak at 0.5 microns.

-- The Sun has apparent diameter of half a degree on the sky.

-- Tables of atomic weights give 1.0078 for H and 4.0026 He.

Week 3 (Saha): Diamonds can form at depths of 2 percent of the Earth's radius, where the pressure is high enough. Does the Moon have enough pressure to form diamonds?

The Moon has about 1/4 the radius and 1/6 the surface gravity of the Earth. No more numbers should be necessary to find the answer.

Week 4 (Saha): How old was the universe when Helium was first formed? [As came up two weeks ago, He has a mass defect of 0.7 percent.]

As usual in this course, try to use general principles and minimal special information.

Week 6 (Saha): Massive black holes tidally disrupt stars, but the most massive ones accrete stars without disruption. Estimate the threshold black-hole mass needed to swallow the Sun whole.

Week 7 (Saha): Consider a spherical isotropic distribution of stellar orbits in a potential V = V_0 ln(r). What is the ratio r_apo/r_peri for a typical stellar orbit in this system? Choose a reasonable definition of 'typical' here.

Week 8 (Saha): As Joe Silk reminded us today, in the far-enough future, Lambda will push every other large galaxy out of the observable universe.

Estimate the mass-equivalent of dark energy within the solar radius (8 kpc). How does this compare with the actual mass? Recall that the local circular velocity is about 200 km/s.

Week 10 (Yoo): How many type Ia supernovae at z=0.5 are needed to distinguish different cosmological models from a LCDM with Omega_m=0.3 ? say, 1) Omega_m=0.3, w=-0.9, 2) Omega_m=1

We would like to have a 3-sigma detection, assuming that the intrinsic scatter in peak luminosity of SNIa is ~ 0.1 magnitude.

Week 11 (Yoo): The bolometric surface brightness from all AGNs is estimated to be ~ 10^{-6} erg/s/cm^2/Sr What would be the black hole mass density today? Ignore the cosmological expansion and simply the situation. Compare to the local black hole mass density.

Week 12 (Yoo): Look at the attached figure for the cosmic ray spectrum and compute how many cosmic ray particles interact in your head and how much energy is deposited in terms of our daily experience. Also estimate the mean free path in your head for proton collisions.

Repeat the calculations with your favorite dark matter model. Are We in Trouble?

Week 13 (Yoo): A metal free star of 100 Msun forms at z ~ 20 in a halo of 10^6 Msun. Assume half the energy of hydrogen fusion is converted to ionizing photons of ~ 30eV. Can this lone star in a halo ionize the halo and send ionizing photons to IGM?

What is the impact on the reionization of the Universe?

Week 14 (Yoo): The minimum mass solar nebula has a surface density profile Sigma ~ 30 g/cm^2 * (a/AU)^{-3/2}, where a is the separation. What is the growth time scale for a planetary embryo of M ~ 10^25 g and rho ~ 1 g/cm^3 at a=1 AU and 5AU?