Solve Astrophysics Problems: Quasar Time Scale and Density Models

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SUMMARY

The discussion focuses on solving astrophysics problems related to quasars and density models. Specifically, it addresses the maximum size of the emitting region of a quasar that varies on a time scale of 4 months in relation to the Schwarzschild radius of a 10^4 Msun black hole. Additionally, it involves calculating the density function omega(r) and the velocity function v(r) for two specific density models: one where all mass M is concentrated at the center of the Milky Way galaxy and another with a constant density up to a mass M(Rnought) at the Sun's orbit, with no mass beyond that point.

PREREQUISITES
  • Understanding of Schwarzschild radius and its implications in black hole physics.
  • Familiarity with quasar variability and its significance in astrophysics.
  • Knowledge of density models in galactic dynamics.
  • Ability to perform calculations involving gravitational dynamics and astrophysical equations.
NEXT STEPS
  • Research the relationship between quasar variability and black hole mass using Schwarzschild radius calculations.
  • Study the derivation and implications of density models in astrophysics, particularly in galactic contexts.
  • Learn how to calculate gravitational potential and velocity profiles for different mass distributions in galaxies.
  • Explore advanced topics in astrophysics, such as the dynamics of quasars and their role in galaxy formation.
USEFUL FOR

Astronomy students, astrophysicists, and researchers interested in black hole dynamics and galactic density models will benefit from this discussion.

jdw_
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Hi. If anyone could help me start or solve these problems it'd be greatly appreciated.

Homework Statement


If a quasar varies on a time scale of 4 months, how does the maximum size of the emitting region compare with the Schwarzschild radius for a 10^4 Msun black hole?

2.Calculate omega(r) and v(r) for the following density models: all of the mass M is at the center of the galaxy (milky way) b) a constant density adding up to a mass M(Rnought) at the suns orbit and no mass beyond
 
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