How Can We Estimate the Maximum Mass of a Satellite Merged with the Milky Way?

[kmoukiss]

Hi everyone, this is an interesting question i can't tackle as i don't really know where to start...


Spiral discs are found to be composed of both a thin and a thick disc population. One way that a thick disc can be created is through the merger of minor satellites. Consider the energy of a merger event and estimate the increase in the scale height of a disc through such an event. If the Milky Way's thick disc is approximately 3 times that of the thin disc, estimate the maximum mass of a satellite that has merged with the Milky Way. You should assume that the mass of the Milky Way disc is 10 Msun , a vertical velocity dispersion of
30 km s–1 and an encounter velocity of 200 km s–1.

Maye equation orbital energy with internal energy ??

THANK YOU VERY MUCH for any help :)

 

[lippyka]

The equation you are looking for is the equation of virial equilibrium, which states that the total potential energy of a system must equal twice its total kinetic energy. Using this equation, you can calculate the amount of energy needed to increase the scale height of a disc by a factor of 3. You can then use this result to calculate the maximum mass of a satellite that could have merged with the Milky Way to produce the observed thick disc. The equation is the following:E_total = 2*KE + PEWhere E_total is the total energy of the system, KE is the kinetic energy, and PE is the potential energy. The kinetic energy can be calculated using the following equation:KE = 1/2*m*v^2Where m is the mass of the system and v is the velocity of the system. The potential energy can be calculated using the following equation:PE = -G*M*m/(r^2)Where G is the gravitational constant, M is the mass of the Milky Way disc, m is the mass of the satellite, and r is the distance between them. Substituting these equations into the equation for virial equilibrium, you can solve for the maximum mass of the satellite that could have merged with the Milky Way to create the observed thick disc.