2) (10 points) The dark matter halo of a galaxy can be described by...

  1. Home
  2. Homework Library
  3. Physics
  4. Astrophysics
  5. 2) (10 points) The dark matter halo of a galaxy can be described by...

QuestionQuestion

Transcribed TextTranscribed Text

2) (10 points) The dark matter halo of a galaxy can be described by the equation: ATGA(+)== r2 + 2 where p(r) is the density of the halo at distance r from the galactic centre, V is the velocity of an object in the halo, and a is the "length scale" for the halo. Consider an object of mass M orbiting through the dark matter halo of the Milky Way which has a density as described by the equation above and a = 30 kpc. a) (4 points) Using equations derived in our notes, prove that the force opposing the motion of object M through the MW's dark matter halo is: 22 GM² A where: A-Tmas b) (4 points) If the dynamic frictional torque acting on object M (i.e. T = r Fill ) is equal to the rate of change of its momentum (i.e. dL/dt = MV dr/dt), show that the time (ts) it would take for the object to spiral in from a maximum galactocentric distance (Imax at t = 0) to a minimum galactocentric distance (Imin at t = ts) is given by: = 2GM V In A - c) (2 points) The LMC has a mass of M = 2x1010 Mo, a velocity of V = 200 km/s, and is currently at a distance of Imax = 50 kpc. A globular cluster in the MW's halo has M = 106 Mo, a velocity of V = 200 km/s, and a distance of Tmax = 30 kpc. Calculate how long (in yrs) it will take the LMC and the globular cluster to spiral in to a distance of Tmin = 4 kpc.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution1.pdf and Solution2.m.

    $28.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Astrophysics Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats