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 (Lake): Introduction of dark matter streams in the local neighborhood and their signatures.

Week 2 (Saha): Dynamical interaction of dark matter streams in phase space. Assume we live in a one dimensional space and write a code to simulate the dark matter streams in two dimensional phase space. Discuss how they evolve in time and what determines the scale of clumpiness in phase space.

Week 3 (Saha): Assume that stars are practically the same as dark matter particles, but are of higher mass, and write a code to simulate how the dark matter streams and stellar particles evolve in two dimensional phase space.

Week 4 (Saha): Consider the internal structure of a massive particle, i.e., a star, by assuming some density profile, and throw this into the dark matter stream. What will happen? Write a code to simulate this and back up the arguments.

Week 5 (Saha): For next week's question, let's continue with the "8 MeV" theme.
Here's a figure -- which you have probably met in some course before -- with the information

Now suppose that all the hydrogen in the Universe gets converted to helium, and all the resultant energy hangs around as radiation. (For example, it may get absorbed and re-radiated by dust.) Call it the Olbers background.

How does the energy density of the Olbers background compare with the CMB? Hint: Googling Olbers is unlikely to help. You need astrophysical thinking.

Week 6 (Saha): As discussed at the end of the class last Thursday, the problem for this week continues the "8 MeV" theme.

Estimate the gravitational binding energy per unit mass of (a) the Sun, (b) a helium white dwarf, (c) a neutron star.
How do these compare with the nuclear binding energy per unit mass of helium and iron?

Week 10 (Yoo): Annihilating Dark Matter?
The AMS experiment on the international space station reported in late December that the positrons (also with anti-proton and protons) show excess above the usual astrophysical background at E~500 GeV. These excess features could be naturally produced by TeV dark matter particles annihilating.

The critical matter density is 10^-5 proton per cubic cm, and the local dark matter density is approximately 10,000 times larger. With some assumption about their self-annihilation interactions, work out the numbers and find what the averaged cross-section sigma x velocity is needed to explain the observations. Compare that to the constraints from the ground experiments (which is about 1 zeta barn for TeV mass particles).

Week 11 (Yoo): Tully-Fisher relation
For spiral galaxies, there exists a tight empirical correlation between the circular velocity vc and the luminosity (Tully-Fisher relation).

log L = (3.5~4) log vc + constant

After this relation was discovered, one can infer the intrinsic luminosity by measuring the circular velocities, and hence derive the distance to these galaxies.

Derive the Tully-Fisher relation and discuss the assumptions you made.

Week 12 (Yoo): Poisson statistics
Suppose you look at some region of our Galaxy with X-ray telescope and measure ~ 100 photon counts per pixel over some exposure t (~ksec). Because of the angular resolution, you have many sources within one pixel. While the photon counts are ~100 per pixel, the standard deviation is 20 counts per pixel. Assuming that the sources are the same, compute the luminosity of such X-ray sources in terms of photons per sec.

It is root N statistics! You can use this to estimate the distance as well!

Week 13 (Yoo): Finding Planet with Eclipsing Binary
Let's consider an eclipsing binary of period 0.1 day. For simplicity, we assume two equal mass components in a circular orbit (m1=m2=0.5Msun). Let's assume we make N (=1000) observations of the eclipse over one year period and the fractional measurement errors on the brightness is 1%. What is the measurement uncertainty in the eclipse timing?

Now assume a planet orbiting the binary system (not around an individual binary component) and the orbit is stable. Given the observational situation, what constraints can we derive in terms of the planet mass and the orbital separation? You can assume it is a Jovian planet.