[SOLVED] ASTR400B lab 2

Description

 

1 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

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