ake 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
mas/yr
Ro
kpc
= VLSR + v⊙
(1)
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
12.3
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:
v
2
esc
= 2|Φ| = 2 Z Gρ(rr) 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
2
