Lecture 39:Lecture 39:

Dark MatterDark Matter

review from last time: review from last time: quasarsquasars

first discovered in radio, but not all first discovered in radio, but not all quasars are detected in the radioquasars are detected in the radio

appear ‘star-like’ (point-like) in ground-appear ‘star-like’ (point-like) in ground-based imagesbased images

huge luminositieshuge luminosities broad, flat spectra; strong emission linesbroad, flat spectra; strong emission lines emission comes from a very small regionemission comes from a very small region only at high redshiftonly at high redshift

related beastsrelated beasts

radio galaxiesradio galaxies normal looking galaxies with radio normal looking galaxies with radio

lobes/jets etclobes/jets etc found at all redshiftsfound at all redshifts

Seyfert galaxies/active galactic nucleiSeyfert galaxies/active galactic nuclei ‘‘mini-quasars’ buried inside of galaxiesmini-quasars’ buried inside of galaxies only found at low redshift (but too faint only found at low redshift (but too faint

to be seen at high redshift)to be seen at high redshift)

What do they have in What do they have in common?common?

very large energiesvery large energies fueled by accretion onto a fueled by accretion onto a

supermassive black holesupermassive black hole perhaps actually the same objectsperhaps actually the same objects

Example problem: Example problem: fueling a quasarfueling a quasar

How much mass, in solar masses per year, does a quasar with a luminosity of 1040 W need to accrete? Assume that the efficiency of the accretion process is ten percent.

Example 2: Weighing a Example 2: Weighing a super-massive black holesuper-massive black hole

The rotation curve of M31 peaks at about 100 km/s at a distance of 3.6 pc from the center. What is the mass enclosed within this radius?

The center of our GalaxyThe center of our Galaxy

visible

Infrared

Sagittarius A*Sagittarius A*

Radio

evidence for a evidence for a supermassive black hole supermassive black hole in our Galaxyin our Galaxy

dark matter: do we need dark matter: do we need it?it?

motions of stars/gas within galaxies motions of stars/gas within galaxies show that there is ‘dark matter’ show that there is ‘dark matter’ within galaxieswithin galaxies

motions of galaxies within groups motions of galaxies within groups and clusters show that there is dark and clusters show that there is dark matter matter betweenbetween galaxies as well galaxies as well

gravitational lensinggravitational lensing also provides a also provides a different sort of evidence for the different sort of evidence for the existence of dark matterexistence of dark matter

rotation curves: reviewrotation curves: review

draw a rotation curve for a ‘solid draw a rotation curve for a ‘solid body rotator’ (like a merry-go-body rotator’ (like a merry-go-round)round)

draw the rotation curve for our draw the rotation curve for our Solar SystemSolar System

draw the rotation curve for our draw the rotation curve for our GalaxyGalaxy

Evidence for dark matter Evidence for dark matter in galaxiesin galaxies

rotation curves of rotation curves of four typical spiral galaxiesfour typical spiral galaxies

elliptical galaxies: elliptical galaxies: absorption line broadeningabsorption line broadening

mass-to-light ratiomass-to-light ratio

the mass-to-light ratio is defined as the mass-to-light ratio is defined as the total mass in solar masses the total mass in solar masses divided by the luminosity in solar divided by the luminosity in solar luminositiesluminosities

for example: the mass of the Milky for example: the mass of the Milky Way within the Solar radius is about Way within the Solar radius is about 9x10 9x101010 M Msunsun, and the luminosity is , and the luminosity is 1.5x101.5x101010 L Lsunsun

the mass-to-light ratio is 6 Mthe mass-to-light ratio is 6 Msunsun/L/Lsunsun..

mass-to-light ratio mass-to-light ratio depends on radiusdepends on radius

the motions of satellite galaxies the motions of satellite galaxies around the Milky Way show that the around the Milky Way show that the mass within 100 kpc is about 10mass within 100 kpc is about 101212 M Msunsun..

the total luminosity within this radius the total luminosity within this radius is about 2x10is about 2x101010 L Lsunsun, so the mass-to-, so the mass-to-light ratio is about 50 Mlight ratio is about 50 Msunsun/L/Lsunsun!!

about 90% of the mass within 100 kpc about 90% of the mass within 100 kpc is dark matter.is dark matter.

dark matter in clustersdark matter in clusters

we can find the we can find the mass of a cluster mass of a cluster using the using the velocities of velocities of galaxies relative galaxies relative to the central to the central galaxygalaxy

Fritz ZwickyFritz Zwicky

clusters are full of hot gasclusters are full of hot gas

another way to weigh a another way to weigh a clustercluster

assuming that the hot gas in assuming that the hot gas in clusters is in gravitational clusters is in gravitational equilibrium, we can use the equilibrium, we can use the temperaturetemperature of the gas to estimate of the gas to estimate the mass of the clusterthe mass of the cluster

v = (0.1 km/s) x (T/Kelvin)v = (0.1 km/s) x (T/Kelvin)1/21/2

then use v in the usual formula then use v in the usual formula M = (vM = (v2 2 x r)/Gx r)/G

Example: the Coma Example: the Coma clustercluster

The galaxies in the Coma cluster have an average orbital velocity of 1200 km/s within a radius of 1.5 Mpc. The hot gas has an average temperature of 108 K. Find the mass of the Coma cluster using both methods. Do they agree?

a third way: a third way: gravitational lensinggravitational lensing

Abell 2218Abell 2218

cluster mass-to-light ratioscluster mass-to-light ratios

all three methods (galaxy all three methods (galaxy velocities, hot gas temperatures, velocities, hot gas temperatures, and gravitational lensing) show and gravitational lensing) show that clusters have mass-to-light that clusters have mass-to-light ratios of 100-500 Mratios of 100-500 Msunsun/L/Lsunsun!!

dark matter: what is it?dark matter: what is it?

there are two basic possibilities:there are two basic possibilities:1.1. baryonic dark matterbaryonic dark matter – ‘ordinary – ‘ordinary

matter’ (i.e. protons, neutrons, matter’ (i.e. protons, neutrons, electrons, etc.) perhaps faint stars, electrons, etc.) perhaps faint stars, brown dwarfs, planets, gas? brown dwarfs, planets, gas?

2.2. non-baryonicnon-baryonic dark matterdark matter – a new – a new kind of particle that we have never kind of particle that we have never seen directly!seen directly!

the search for MACHOsthe search for MACHOs

perhaps the dark “halo” of our perhaps the dark “halo” of our Galaxy is made up of normal Galaxy is made up of normal material (like faint stars or brown material (like faint stars or brown dwarfs)dwarfs)

these are called these are called MaMassive ssive CCompact ompact HHalo alo OObjects (MACHOs).bjects (MACHOs).

they might be detected by they might be detected by microlensingmicrolensing

exotic dark matter: WIMPsexotic dark matter: WIMPs

WIMPs stands for Weakly WIMPs stands for Weakly Interacting Massive ParticlesInteracting Massive Particles

the definition of a WIMP is a kind of the definition of a WIMP is a kind of particle that interacts with other particle that interacts with other matter matter onlyonly via gravity and the via gravity and the weak force (not the strong force weak force (not the strong force and electromagnetic force)and electromagnetic force)

hot and cold dark matterhot and cold dark matter

hothot dark matter is made of dark matter is made of particles that move very close to particles that move very close to the speed of light (such as the speed of light (such as neutrinos)neutrinos)

coldcold dark matter is made of dark matter is made of particles that move much slower particles that move much slower than the speed of lightthan the speed of light

we now think most of the dark we now think most of the dark matter must be coldmatter must be cold

the fate of the Universethe fate of the Universe

the total amount of dark matter in the total amount of dark matter in the Universe determines its fate…the Universe determines its fate…

will the Universe will the Universe expand foreverexpand forever expand forever but slow down until it expand forever but slow down until it

is expanding infinitely slowlyis expanding infinitely slowly turn around and start collapsing?turn around and start collapsing?

Tune in next time Tune in next time to find out!to find out!