Problem set 4 for ASTR 323: The Local Universe

Due in class Wed March 29

This problem should be done as a group problem by undergrads, and as an individual problem by graduate students:

(1) Watch a dSph satellite disrupt in the Milky Way's halo: Here you will find 20 500 Myr time-steps following the disruption of a satellite in the Galaxy's potential. (This work was done by Paul Harding). The files contain 2000 test particles each, and each line contains the following quantities: x y z dist vel l b vx vy vz.
x,y and z are galactocentric coordinates of the particle in kpc, dist is distance from the Sun, vel is radial velocity viewed from the Sun, l and b are galactic longitude and latitude, vx, vy and vz are velocity components in the x, y and z coords in km/s. Make plots in x vs y or x vs z or something similar that illustrates the disruption.
Calculate the range of Jz (z component of angular momentum) and total energy for the satellite particles at the start of the simulation, assuming for simplicity that the Milky Way's potential can be approximated by a point source of mass 2x10**12 solar masses at the galactic center. Do all particles have the same Jz and energy? Why?
Then calculate the same quantities for the final time step. Has the energy and angular momentum of the particles changed as the satellite disrupts? Why?

(2) Here you will find files with the end-points of 10 Gyr of satellite disruption simulations for 23 different satellite orbits in a good approximation to the Milky Way's potential. (this work was done by Paul Harding as part of his dissertation at the University of Arizona). Plot x vs y and y vs z for each file, and use this information to classify the streams. You will find that some streams have dispersed much more than others. In each case the initial satellite properties were the same. What are the physical factors which lead to these differences?

(3) (attempt this for extra credit)
Reality: distance errors vs velocity information. In reality, while we can measure the position on the sky to huge precision, the distance estimates of the halo giants are only accurate to 25%. Take an illustrative subsample of streams including some that are much more messed up than others and calculate whether the streams will still be visible if we add 25% distance errors.
Now explore what additional information about velocity will do to our ability to see substructure. Unfortunately, it is only in the solar neighborhood that we can measure all 3 components of the velocity, and these streams are up to 100 kpc away. Plot up the observed distance from the Sun vs radial velocity of several streams with diverse orbital and disruption properties. How might we best detect such streams observationally?