17. Observational Cosmology
Textbook: 27.4
Co-moving coordinate as a function of redshift
Photon path has ds = 0. Hence,
t0
te
cdt
=
R(t)
0
1
arcsin( k)
k
d
=
1 k 2 1
arcsinh( |k|)
|k|
(k > 0)
(k = 0)
(17.1)
(k < 0)
Writing the integral over time in t
10. Main Sequence and Brown Dwarfs
Textbook: 10.6, 13.1 (p. 446451)
Zero-age main sequence
The zero-age main sequence (ZAMS) is dened as the beginning of the long, stable period of core
hydrogen burning during the stars lifetime. Stars burn up their (prim
5. Diusive energy transport, Ionisation/excitation, Opacity
Textbook: 9.2, 8.1, and parts of 9.3, 10.4
Radiative and conductive energy transport
Radiative ux
Frad =
4ac T 3 dT
1 c dUrad
=
.
3 dr
3 dr
(5.1)
Eddington equation
dT
3 Lr
=
,
dr
4ac T 3 4r 2
(
Mini-Problem Set IX: Dating stars using Lithium: Scalings
due 10 Feb 2014
We continue with the previous problem set, now estimating the rate at which Lithium depletes,
and how this rate scales with mass and time. In the next problem set, we will calculate
Mini-Problem Set X: Dating stars using Lithium: Burning
due 14 Feb 2014
We use the results from the previous two problem sets to calculate actual times at which Lithium
is depleted. We use numbers from, and compare with results of, Bildsten et al. (1997,
Mini-Problem Set XI: The First Stars
due 7 Mar 2014
We consider the dierences between the rst stars (X = 0.77, Y = 0.23, Z = 0), and current ones
(solar abundances: X = 0.708, Y = 0.273, and Z = 0.019).
1. Show that the equation of state is not inuenced m
Mini-Problem Set XIII: Neutrinos from Supernovae
due 14 Mar 2014
After the collapse of a stellar core, a proto-neutron star is formed, which is in hydrostatic equilibrium.
We will assume it has mass 1.4 M and radius 20 km, and use that models give a tempe
Mini-Problem Set I: Basics of a stars life
due 10 Jan 2014
Consider a star with a mass like that of the Sun, but starting with a larger radius and a temperature
too cool for nuclear fusion.
1. What happens to the total, potential, and kinetic energy of th
Mini-Problem Set XII: Properties of the First Stars
due 10 Mar 2014
Having considered the dierences between the rst stars and current ones, we continue by seeing
if we can understand the mass-radius relation shown in the Figure, which was found from detai
Mini-Problem Set III: Equation of state in the cores of stars
due 17 Jan 2014
What processes dominate the pressure in cores of stars? We use that due to the high temperature
sensitivity of nuclear fusion, stars on the main sequence all have rather similar
Mini-Problem Set II: Halting the collapse of a cloud
due 13 Jan 2014
Consider a cloud that has just started to collapse.
1. Use scaling arguments to show that for an isothermal gas, once collapse starts the gravitational
term in the equation of hydrostati
Mini-Problem Set VIII: Dating stars using Lithium: contraction
due 7 Feb 2014
As pre-main-sequence stars contract, at some point their internal temperature becomes suciently
hot that Lithium is destroyed. This will occur earlier for more massive stars, an
Mini-Problem Set IV: Basics of degenerate objects
due 20 Jan 2014
1. Write down the general scaling relations for central pressure and density as a function of mass
and radius. For all stars having the same polytropic equation of state, the constant terms
Mini-Problem Set VII: Fully ionised atmospheres
due 3 Feb 2014
Consider hydrostatic equilibrium in the atmosphere of a hot star.
1. Assume a B0 star. Look up its properties in Carroll & Ostlie, and calculate the gravity g and
escape velocity vesc , as wel
Mini-Problem Set V: Completely convective stars
due 27 Jan 2014
Stars with masses < 0.3 M are completely convective, and a polytropic model should work fairly
well. We will check this using the models shown in Fig. 3.3. Note: since we determine how well i
Mini-Problem Set VI: The luminosity of a star
due 31 Jan 2014
Consider a star in hydrostatic equilibrium in which energy transport is by radiation.
1. Use the equations of radiative energy transport and hydrostatic equilibrium to derive two scaling
relati