Accretion Onto Compact Objects

Question 1

What is gravitational potential energy released when a proton falls into a star of mass Mx and radius Rx?

Answer 1

Change in E grav = GMxmp/Rx

Question 2

How do you estimate temperature of a material heated by accretion onto a compact object?

Answer 2

Equate gravitational energy to thermal energy.

3/2 kT ~ GMxmp/Rx —> T = 2/3 GMxmp/kRx

Question 3

Express accretion-heated temperature in solar units.

Answer 3

T ~ 10^7 K times Mx/Msolar / Rx/Rsolar

Question 4

What is physical meaning of compactness parameter in accretion physics?

Answer 4

The ratio Mx/Rx ; higher compactness—> higher temperature and luminosity

Question 5

How is X-ray luminosity from accretion calculated for a mass accretion rate M dot?

Answer 5

Lx ~ GMxMdot/ Rx

Question 6

How does the X-ray luminosity scale with compactness of object?

Answer 6

Lx ~ Mx/Rx; more compact objects produce higher luminosity for same M dot.

Question 7

Give a typical X-ray luminosity for Galactic X-ray binaries using Mx ~ M solar Rx ~ 10^6 cm, M dot~ 10^17 g/s

Answer 7

Lx ~ 10^37 erg/s consistent with observed X-ray sources.

Question 8

Why do neutron starts and black holes produce X-rays while normal stars generally do not?

Answer 8

Their high compactness leads to high temperatures and high luminosity sufficient for X-ray emission.