First Step
Make sure to have a cloned copy of your own repository on your computer (or nimoy if you are using nimoy for Jupyter). Create a directory Labs/Lab1.
From the command line git clone the class repository. If you have already done this, git pull to update the repository. There is a directory Labs/Lab1/ with a file Lab1.ipynb, which is the template for this exercise.
Copy this template to your own repository directory Labs/Lab1
2 Part A: Local Standard of Rest
The Proper motion of Sgr A* from Reid & Brunthaler 2004 μ = 6.379 mas/yr Peculiar motion of the sun, v⊙ = 12.24 km/s (Schonrich 2010)
vtan=4.74 μ Ro =VLSR+v⊙ (1) mas/yr kpc
2.1
Create a function called VLSR to compute the local standard of res (VLSR).
The function should take as input: the solar radius (Ro), the proper motion (mu) and
the peculiar motion of the sun in the v⊙ direction. Compute VLSR using three different values Ro:
1. Water Maser Distance for the Sun : Ro = 8.34 kpc (Reid 2014 ApJ 783)
2. GRAVITY Collaboration Distance for the Sun: Ro = 8.178 kpc (Abuter+2019 A&A
625)
3. Value for Distance to Sun listed in Sparke & Gallagher : Ro = 7.9 kpc
2.2
Compute the orbital period of the sun in Gyr using Ro from the GRAVITY Collaboration (assume circular orbit)
Note that 1 km/s ∼ 1kpc/Gyr
1
2.3
Compute the number of rotations the sun makes about the Galactic Center over the age of the universe (13.8 Gyr)
3 Dark Matter Profiles 3.1
Try out Fitting Rotation Curves: http://wittman.physics.ucdavis.edu/Animations/RotationCurve/GalacticRotation.html
3.2
In the Isothermal Sphere model, what is the mass enclosed within the solar radius in units of M⊙?
Where G = 4.4988e-6 kpc3/Gyr2/M⊙ What about at 260 kpc (in units of M⊙) ?
3.3
The Leo I satellite is one of the fastest moving Milky Way satellite galaxies we know. Vtot = 196 km/s at a distance of 260 kpc (Sohn 2013 ApJ 768)
If we assume that Leo I is moving at the escape speed:
2 ρ(r)
vesc=2|Φ|=2 G r dV (2)
and assuming the Milky Way is well modeled by a Hernquist Sphere with a scale radius of 30 kpc, what is the minimum mass of the Milky Way (in units M⊙) ?
How does this compare to estimates of the mass assuming the Isothermal Sphere model at 260 kpc (from your answer above)?
4 Last Step
Git push your Lab1.ipynb file to your repo. Recall steps: 1. git add filename
2. git commit -m ”COMMENTS”
3. git push
