ORBITAL DECAY OF HIGH VELOCITY CLOUDS

LUMA FOHTUNGUW-Madison Astrophysics REU 2004

What is the fate of the gas clouds orbiting the MilkyWay Galaxy?

HVC Overview

Definition : HI with velocities that cannot be due to Galactic rotation. Global Distribution: Covering over 40% of sky (depending on sensitivity). Distances: 1.5-4 kpc (Complex M) to 50 kpc (Magellanic Stream). Many at

unknown distance

Contours in above HI image at Column density ~2, 20, 40 x 1018 cm-2 (Wakker

et al 2003)

Note “stretched” appearance!

High Velocity Cloud “Streams”What determines

the orbit of a HVC?

• Gravity and random motions only?

50 kpc

How long does it take a HVC to merge with the Galaxy? What happens during the process?

• Drag forces due to gaseous halo

and disk of

Galaxy ?

Schematic diagram of Magellanic Stream

My ProjectGoal: Develop numerical models of orbital motion for high velocity clouds

Tools: Fortran code (for the models) and IDL (to view the output)

Method: Write programs, generate the output, use plots to check our results, and debugging… Lots of debugging…

Initial Conditions for Program

• Calculate the orbit of a “test cloud” of 10,000 points.

• Specify average position and velocity of test cloud. (x, y, z)average (vx, vy, vz)average

• Specify Gaussian scale length for cloud: R

• Specify Gaussian velocity dispersion for cloud: v

• Set up information on desired time step and stopping time.

• Choose model for gravitational field of Galaxy (Dehnen & Binney 1998 “Mass Models of the Milky Way”)

Numerical MethodsRandom number generator:

Needed to set up randomized position and velocity for test clouds.

Differential equation solver:

Needed to evolve equations of motion for test clouds. I used a Runge-Kutta method (Numerical Recipes).

€

dx

dt= vx

dvx

dt= gx

dy

dt= vy

dvy

dt= gy

dz

dt= vz

dvz

dt= gz

r g (x,y,z) = (gx,gy,gz)

Equations of motion:

Set of six coupled differential equations.

An example run

Before

After

Checking the calculations

1. I checked our differential equation solver with simple (not coupled) equations with known solution.

2. I used the Runge-Kutta method and gravitational field of a point source to calculate the orbit of the Sun.

3. Using a Galactic mass model, we calculated orbit for the current position and velocity of the Sun.

4. Checked total energy and orbital angular momentum. Both were conserved to within 0.01%.

Check: Energy vs. time

Kinetic Energy

PotentialTotal

So far…

• Development of the FORTRAN code to calculate orbits for clouds.

• Development of IDL routines to visualize output.

• Initializing using solar type orbits.

• Trace of resulting cloud and stretching of initial cloud.

Cases

Xi

(kpc)

Yi

(kpc)

Zi

(kpc)

VX,i

(km/s)

VY,i

(km/s)

VZ,i

(km/s)

R

(kpc)

V

(km/s)

Gravity Model

Time Step (Myr)

Run1 0 8.5 0 220 0 0 0.5 20 DB 0.2

Run2 0 8.5 0 220 0 0 0.5 40 DB 0.2

Run3 0 8.5 0 220 0 0 0.5 10 DB 0.2

Run4 0 8.5 0 220 0 0 1.0 20 DB 0.2

Run5 0 8.5 0 220 0 0 0.1 20 DB 0.2

Run6 0 0 8.5 220 0 0 0.5 20 DB 0.2

Run7 0 12 0 220 0 0 0.5 20 DB 0.2

Run8 0 20 8.5 220 0 0 0.5 20 DB 0.2

Run9 0 0 8.5 280 0 0 0.5 20 DB 0.2

Run10 0 0 8.5 160 0 0 0.5 20 DB 0.2

Run11 0 8.5 0 280 0 0 0.5 20 DB 0.2

Run12 0 8.5 0 160 0 0 0.5 20 DB 0.2

These cases are to “practice” with orbits similar to that of the Sun, and experiment with different parameters.

Polar orbit

Increase v dispersion

Comparison of Cases

Run 1: Standard Case

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

Effect of Increasing v

Run 2: Double velocity dispersion to 40 km/s

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

Polar orbit

Run 6: Orbit in XZ plane

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

What I have learnt….-A LOT of programming (IDL and Fortran)-a better insight about astronomy

A WHOLE LOT OF PATIENCE

Future work

Study the orbits of clouds much further away from the Galaxy, objects similar to the Magellanic Stream.

Add and test the effects of gaseous drag on our test particles. Experiment with different density distributions and include the effect of possible outflows from the center of the Galaxy.

Check on the importance of self-gravity for the cloud.

Consider how magnetic effects would alter drag on clouds.

Acknowledgements

• My advisor: Dr Bob Benjamin

• UW Madison REU program

• NASA

Any Questions?