Transcript Dark Matter Mathematics

Dark Matter Mathematics
Janet Moore
NASA Educator Ambassador
Merry-Go-Round
Velocity (v)
Velocity vs. Radius
Distance (r)
Merry-Go-Round
Velocity (v)
Velocity vs. Radius
Distance (r)
Solar System
Velocity (v)
Velocity vs. Radius
Distance (r)
Solar System
Velocity (v)
Velocity vs. Radius
Distance (r)
Solar System
Mass (m)
Mass vs. Radius
Distance (r)
Solar System
Mass (m)
Mass vs. Radius
Distance (r)
In Summary - Solar System
 Orbital speed depends
on force of gravity
 Force of gravity
depends on mass within
the radius
 Therefore, orbital speed
depends on mass within
the radius
What About Galaxies?
 How would you
expect stars to move
around in a spiral
galaxy?
 What would you
expect the mass
distribution in a
spiral galaxy to be?
The Activity - NGC 2742
 You will be given:
 Rotation Curve
(velocity vs. radius)
 Luminosity Curve
(luminosity vs.
radius)
 Use the Data Chart
to analyze the mass
in the galaxy
 G = 4.31 x 10-6
Sample Data Chart
Radius
Grav.
Mass
1.5 e9
Lum.
1
Rot.
Vel.
80
3 e8
Lum.
Mass
6 e8
Lum/
Grav
0.4
3
100
6.9 e9
1 e9
2 e9
0.29
5
120
1.7 e10
2 e9
4 e9
0.24
8
140
3.6 e10 3.5 e9
7 e9
0.19
Evidence for Dark Matter
 Light (visible matter) drops off as you
go farther out in a galaxy
 BUT . . . Velocities do not drop off
 Result: Dark Matter mass is about 10x
Luminous Matter mass
What is Dark Matter?
 Baryonic (Normal) Matter:
Low mass stars, brown dwarfs (likely), large
planets, meteoroids, black holes, neutron stars,
white dwarfs, hydrogen snowballs, clouds in
halo.
 Non-Baryonic (Exotic) Matter:
Hot Dark Matter: fast-moving at time of galaxy
formation, eg massive neutrinos
Cold Dark Matter: slow-moving at times of
galaxy formation, eg WIMPs -- particle detector
experiments looking for them
NASA’s Fermi Mission
 Formerly known as the GLAST mission
 Launched June 11, 2008
 Studying gamma ray sources in the
universe
 Studying potential sources of dark
matter in the universe
Questions?
Janet Moore
[email protected]
epo.sonoma.edu
My Other Workshops:
NEWTON’S LAWS11:00 am - Room 207
PI IN THE SKY
3:30 pm - Room 262