Astronomy 1143 – Spring 2014

Lecture 21:

The Evidence for Dark Matter

Key Ideas:Dark Matter - detected by its gravitational pullGravity appears stronger than can be accounted for by “normal” matter

• Expected: speeds lower if the star is very distant from the galaxy center

Mass-to-Light Ratios Evidence for Dark Matter

• Rotation curves of spiral galaxies• Hot gas halos around elliptical galaxie• Velocities of Galaxies in Cluster• Gravitational Lensing

Candidates for Dark Matter – stay tuned for evidence

Is that all there is?

We have measured many forms of normal matter from light

• Stars – absorption-line spectra• Low-density gas – emission-line spectra• Dust – blocks optical/emits in the far infraredIs that amount of matter enough to explain the

gravitational force pulling on stars in a galaxy or on galaxies in a cluster?

Matter produces gravity

Gravity depends on mass and distance

d M2M1

Planets in the Solar System

More distant planets move more slowly

From Solar System to GalaxyPlanets have smaller speeds the further they are

from the Sun• Sun has about 99.8% of the mass in the Solar

System• No substantial contribution from dark matter

When we look at the same idea in a galaxy it is a little more complicated because the mass isn’t essentially concentrated in the center.

• Clearest signal looking relatively far out from center

Inside the Galaxy

Gravity depends on mass and distance

rM2

M(r)

M(r) is the mass inside of radius (r)

Rotation of the DiskMeasure using the Doppler EffectStars:

• Doppler shifts of stellar absorption linesIonized Gas:

• Doppler shifts of emission lines from HII regionsAtomic Hydrogen (HI) Gas:

• Cold H clouds emit a radio emission line at a wavelength of 21-cm

• Can trace nearly the entire disk beyond where the stars have begun to thin out.

Measuring Masses of Galaxies

Star or Gas cloud is held in its orbit by the gravity of the mass interior to its orbit.

Newton’s Gravity:

M(R) = mass interior to radius R

Vrot = rotation speedSimilar to how we calculated the mass of the Sun in Lecture 8

Rotating Disk

Rotation Axis

Approaching SideBLUESHIFT

Receding SideREDSHIFT

Which galaxy is good for measuring rotation curves?

Example: Milky WaySun:

r=8 kpc, vcirc=220 km/secGives: M = 91010 Msun inside r=8 kpc

Gas Cloud in Outer Disk:r=16 kpc, Vcirc=275 km/secGives: M=2.81011 Msun inside r=16 kpc

Measuring the rotation curves gives us a good way to measure the masses of Spiral Galaxies.

How much mass can we find?

Gravity holding stars in their orbits tells us how much matter there needs to be

How much of that gravity is caused by the stars/gas/dust that we see?

Difference between mass needed and mass observed evidence for dark matter

Turns out that counting up the mass that we see is a little tricky, because what we see is light and what we want is mass

Mass-to-light Ratio

Some of the mass in a galaxy comes from “normal” matter – stars, gas, & dust

How do we find the amount of material?• Use the light we see from stars, gas and dust• Stars – optical/near infrared light• Gas – emission lines in radio• Dust – emission in far infrared

ExampleA spiral galaxy has a luminosity of 2.5x1010

LSun

If each star is like the Sun, the mass is 2.5x1010 Msun

But not every star has the same mass as the Sun – a 10 Msun main-sequence star radiates about 104 Lsun.

If each star is 10 MSun, the total mass of the Galaxy is

Example

A lot smaller!

The kind of stars in a galaxy makes a big difference in the amount of matter you infer

Mass in stars, gas, & dust

Measuring the amount of matter in stars, gas and dust is not easy

• Mass-to-light ratio of stars depends on age and composition

• Luminosity of starlight may be difficult to measure because of dust

• Radio and far-infrared maps need to measure gas and dust

Rotation Curve if no dark matter

Typical Spiral Galaxy Rotation Curve

0

0

25

200

100

5 10 15 20Radius from the Center (kpc)

Rot

atio

n S

peed

(k

m/s

ec)

Picture of rotation curve on galaxy

Dark matterDark matter = stuff that doesn’t emit, absorb, or otherwise interact with photons.

Other galaxies are found to have dark matterdark matter, too.

Andromeda Galaxy

Galaxies are surrounded by dark matter halos

Escape VelocityOne measure of the strength of the gravitational force is the escape velocityHow fast you need to be traveling to leave a gravitating mass and never come backEarth: 11 km/sJupiter: 59.5 km/s

Velocities < Escape VelocitiesFor long-lived systems:

• Planets in a solar system• Stars in a galaxy• Galaxies in a galaxy cluster

velocities should be less than the escape velocity, otherwise structures would disperse

• Measure a velocity• Calculate how much mass is needed for the

escape velocity to be larger than observed velocities

Velocity Dispersions in Ellipticals

Elliptical Galaxies have little to no organized rotation

But stars still bound to galaxy – cannot exceed escape velocity

Measure the velocity dispersion for ellipticalsShows that dark matter is neededBut it’s not just stars that have velocities –

gas particles do too!

Hot Gas in Ellipticals

We see hot X-ray emitting gas around ellipticals. The gas is gravitationally bound to the galaxy.

Velocities of gas particles must be smaller than escape velocity

Velocity from Temperature of Gas

ExampleThe T of X-ray gas in NGC 4636 is 11.6 million K. How

much mass is needed to hold onto that gas?T=11.6 million K velocity of proton = 437,740 m/s60 kpc from the center = 1.85 x 1021 m

Only about 1x1011MSun in stars, gas & dust. Need dark matter!

Velocities of Galaxies in Clusters

Additional evidence for the presence of dark matter comes from the high velocities of galaxies in clusters

Galaxies are moving at 800-1000 km/s compared to the cluster center

Amount of matter we measure from the light is not enough to prevent their escape!

90-99% of the matter in clusters is dark matter

Zwicky in actionWhere’s the matter?

Insight from Einstein: Gravitational Lensing

Gravitational LensingThe amount of

gravitational lensing depends on the curvature of spacetime

We see lots of bending – lots of matter

Conclusion: cluster masses are dominated by dark matter

Possible candidatesStellar remnants • Black holes• Neutron stars• White dwarfsBrown Dwarfs & PlanetsParticle• Neutrino• New Particle – Weakly Interacting Massive

Particles (WIMPs)

MACHOs --MAssive COmpact Halo Objects

Is “Dark Matter” the only possible explanation?It is not easy to believe that we are unaware of

the nature of something that has 5-6 times more mass than “normal” matter

However, many lines of evidence are pointing to the same conclusion!

Possible counter explanation: • Neither Newton nor Einstein got the law of gravity

quite right. • On galaxy-sized scales, gravity stronger than what

Law of Universal Gravity states