How Is Enclosed Mass Derived in the Hernquist Model?

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SUMMARY

The discussion centers on deriving the enclosed mass M(r) in the Hernquist model, which describes mass distribution in spheroids. The density function is given by ρ(r) = M(total)*a / 2πr(a+r)^3, where M(total) represents the total mass and 'a' is a constant with dimensions of length. The solution involves integrating the density function to find the relationship between mass density and enclosed mass. The integral approach is essential for solving this problem effectively.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with the Hernquist model of mass distribution
  • Knowledge of spherical coordinates
  • Basic concepts of mass density
NEXT STEPS
  • Study the process of integrating density functions to derive mass
  • Learn about spherical coordinates and their applications in physics
  • Explore the properties of the Hernquist model in astrophysics
  • Review examples of mass distribution models in cosmology
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Students in astrophysics, physicists studying mass distribution models, and anyone interested in understanding the mathematical foundations of the Hernquist model.

TheSpaceGuy
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Homework Statement


A popular model for the mass distribution in a spheroid (such as a bulge) is the
Hernquist model, with density

ρ(r) = M(total)*a / 2πr(a+r)^3


M(total) is the total mass. a is constant with dimensions of length. Derive the enclosed mass
M(r)

The Attempt at a Solution


I am completely unsure on how to go about doing this? Any help is appreciated!
 
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How are generally mass density and mass related ? (Hint: integral).
 

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