Dark Matter MathematicsDark Matter Mathematics

Janet MooreNASA Educator Ambassador

Janet MooreNASA Educator Ambassador

Merry-Go-RoundMerry-Go-Round

Velocity vs. Radius

Distance (r)

Velo

cit

y (

v)

Velocity vs. Radius

Distance (r)

Velo

cit

y (

v)

Merry-Go-RoundMerry-Go-Round

Velocity vs. Radius

Distance (r)

Velo

cit

y (

v)

Velocity vs. Radius

Distance (r)

Velo

cit

y (

v)

Solar SystemSolar System

Velocity vs. Radius

Distance (r)

Velo

cit

y (

v)

Velocity vs. Radius

Distance (r)

Velo

cit

y (

v)

Solar SystemSolar System

Velocity vs. Radius

Distance (r)

Velo

cit

y (

v)

Velocity vs. Radius

Distance (r)

Velo

cit

y (

v)

Solar SystemSolar System

Mass vs. Radius

Distance (r)

Mass (

m)

Mass vs. Radius

Distance (r)

Mass (

m)

Solar SystemSolar System

Mass vs. Radius

Distance (r)

Mass (

m)

Mass vs. Radius

Distance (r)

Mass (

m)

In Summary - Solar System

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

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?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?

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

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

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 ChartSample Data Chart

Radius

Rot. Vel.

Grav. Mass

Lum. Lum. Mass

Lum/Grav

1 80 1.5 e9

3 e8 6 e8 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

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

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?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

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 MissionNASA’s Fermi Mission

Formerly known as the GLAST mission

Launched June 11, 2008Studying gamma ray sources in the universe

Studying potential sources of dark matter in the universe

Formerly known as the GLAST mission

Launched June 11, 2008Studying gamma ray sources in the universe

Studying potential sources of dark matter in the universe

Questions?Questions?

Janet MooreJanetMoore@gmail.com

epo.sonoma.edu

My Other Workshops:NEWTON’S LAWS 11:00 am - Room 207PI IN THE SKY 3:30 pm - Room

262

Janet MooreJanetMoore@gmail.com

epo.sonoma.edu

My Other Workshops:NEWTON’S LAWS 11:00 am - Room 207PI IN THE SKY 3:30 pm - Room

262