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): Consider a spacecraft in low-Earth orbit. During the day, the Sun's radiation pressure pushes it towards the Earth. This isn't much of a force compared to the Earth's gravity, and probably not even LISA Pathfinder can tell by this method whether the Sun is shining.

But suppose you scale down the Earth-spacecraft system, while keeping all densities fixed. For what sizes would radiation and gravity forces become comparable?

Week 2 (Yoo): As explained in the class, neutron stars are collapsed objects, supported by degenerate pressure of neutrons. However, unlike its interiors, the crusts are largely made of free electrons and irons.

Electrons are free, relativistic, and degenerate, while irons are non-relativistic forming a lattice. Such configuration of electrons and irons provides support for bulk and shear modulus, separately.

Find the expressions for the bulk and the shear moduli, and compute their ratio. Is the crust of neutron stars like rubbers?

Week 3: Swiss Astronomical Society Meeting

Week 5 (Yoo): Compute the total number of neutrinos produced over the lifetime of the Sun and the core-collapse type II supernova. What is the ratio?

The Sun produces neutrinos mainly through p-p chain, and it approximately burns 10% of its mass over the life time.

The iron core of massive stars collapses when the electron degenerate pressure is not enough to balance the gravity. The outcome is a neutron star, and most of its energy is carried away by neutrinos.

Week 6 (Saha): If we look at pictures of asteroids (link), the largest (Ceres) is very round, while small asteroids are invariably irregular in shape.

The problem is to estimate the threshold size beyond which rocky bodies become round. One way to do this is to consider mountains. The threshold radius is when the highest-mountain height equals the planetary radius.

Recall that mountains get much higher on Mars than on Earth: link. If Everest were much higher, it would collapse under its own weight. (Mauna Kea is helped by bouyancy.) Try to show that supportable mountain height is inversely proportional to planetary radius. See if you can get an order-of-magnitude estimate for the height of Everest from first principles.

Week 7 (Yoo): Over the lifetime of the Sun, what is the chance of getting a significant gravitational kick from other stars in our Galaxy?

What if we lived in a globular cluster? What about the Oort cloud in the Solar system?

Week 8 (Saha): The following program calculates the age of the universe at recombination, using tabulated values of the cosmological parameters. But the answer is not quite correct....

Some physics is missing, what is it?

Week 9 (Saha): Compare the brightness of the CMB sky and the Sun at the peak of CMB.

Week 10 (Saha): How long does it take to cook a Thanksgiving Turkey? Get a sensible answer from the first principle.

Week 11 (Yoo): To solve the hierarchy problem, n-number of extra dimension of size R is introduced, and it was postulated that the fundamental Planck scale is TeV, not "Planck scale" (eliminating the problem).

As explained, when scales are larger than R, the gravity becomes the usual, but it feels the existence of extra dimensions, when smaller than R. This implies gravity becomes strong faster in 4+n dimensions than in 4 dimensions.

Compute the size R of the extra dimensions as a function of n.

Since the fundamental Planck scale is lower, the emission of gravitons becomes important. The total rate of graviton emission is proportional to E^n/M_p^(n+2), where E is the energy available in a given system (apparently, this rate is totally negligible in the standard scenarios). The current constraint is that the rate is smaller than 1/F^2, where F=10^10 GeV. Consider what constraints can be put by using super nova explosions.

Week 12 (Yoo): As explained in the class, the Modified Newtonian Dynamics (MOND) attempts to explain the flat rotation curves by modifying the Newtonian dynamics in a way that the dynamical equations become scale invariant, i.e., (x,t) --- lambda (x,t), such that velocities remain unchanged. The modification takes places only in a regime, where the acceleration is lower than some threshold a < a0, so called, deep MOND regime.

So let's modify the dynamical equation as F=m a G(x), where x=a/a_o and some unknown function G must approach unity for x larger than unity, but it approaches something else in the opposite regime (deep MOND regime).

Find the asymptotic function of G in the deep MOND regime to make the rotation curves flat, and evaluate a0 that can match the observations. How is a0 also related to the value of a cosmological constant?

Discuss what are the theoretical problems in MOND and what are the ways to test MOND, compared to the standard cosmology.