Research School of Astronomy & Astrophysics, ANU Dark Matter in Galaxies Ken Freeman Research School of Astronomy & Astrophysics, ANU and UWA UWA: August 14, 2008

The Milky Way as seen from the sun NGC 4565: an edge-on spiral (see the flat rotating disk and the central bulge)

How do we know it is there ? There is a very important component that cannot be seen at all How do we know it is there ? Almost all galaxies have a dark halo .... we see its gravitational effect on their rotation curves ... the dark halo For example Rotation at large radii is much faster than can be understood from the gravitational field of the stars and gas alone.

For stars and gas moving around a circle of radius R with velocity V, the inwards acceleration is V2 / R Where does this acceleration come from in a galaxy ? it needs a force = mass x acceleration The force is the force of gravity, so measuring the rotation speed V and the radius R tells us directly how strong the gravitational force is at radius R

The ratio of dark mass to stellar mass is typically about 20: 1 We now know that the halos extend 5 to 10 times further out that the disks of these galaxies

The discovery of dark matter in galaxies in the 1970s led to the current ideas about how galaxies form from dark matter and gas in the early universe Early in the life of the universe, the distribution of matter was fairly smooth, with very small random fluctuations in density. These fluctuations grew under the influence of gravity: small objects merged to form larger objects in a hierarchy of merging The dark matter on galactic scales needs to be cold (moving slowly relative to the expansion of the universe) in order to condense into galaxy-sized dark halos It is called Cold Dark Matter or CDM

Dark Matter in Galaxies We believe that galaxies formed through a hierarchy of merging. The merging objects were a mixture of baryonic (ordinary matter) and dark matter. The dark matter settled into a roughly spherical halo while the baryons (in disk galaxies) settled into a flat rotating disk and central bulge • What can we learn about the properties of dark halos ? • Do the properties of dark halos predicted by simulations correspond to those inferred from observational studies ?

MOVIE Start by showing a numerical simulation of galaxy formation. The simulation summarizes our current view of how a disk galaxy like the Milky Way came together from dark matter and baryons, through the merging of smaller objects in the cosmological hierarchy.

Simulation of galaxy formation • cool gas • warm gas • hot gas

Reminder: in spiral galaxies ... halo The stars and the gas together do not provide enough gravity to explain the rotation: we need the extra gravity of the dark halo

Some problems ... The cusp-core problem CDM simulations consistently produce dark halos that are very dense (cusped) at the center Near the center, where the radius r is small, the density goes like so the density gets larger and larger as r gets smaller and smaller

If the halo density gets so high near the center of real galaxies, then it will have an effect on the shape of the rotation curves: the rotation curves would rise very steeply near the center Do we see such an effect ? No - most galaxies do not show such steeply rising densities near their centers. Here is an example: the nearby galaxy NGC 6822 - it is very close to us, so we can study its rotation curve in fine detail with the radio telescopes, using its neutral hydrogen (HI)

NGC 6822 Near infrared image of this Local Group galaxy

rotational velocity (km/s) 0 1 2 3 4 radius (kpc) High spatial resolution observations of the nearby galaxy NGC 6822 The rotation curve rises gently near the center. This is what we usually see (a kpc is about 3000 light years or 3.1016 km) Weldrake et al 2002

What is wrong ? Real galaxies don’t have central cusps like the simulations Does it matter ? Yes - the density distribution of the dark halos provides a potentially critical test of the CDM theory on galaxy scales

Maybe CDM is wrong. Alternatively ... There are ways to convert CDM cusps into flat central cores so that we do not see the cusps now ...

For example ... Bars are very common in disk galaxies - about 70% of disk galaxies (including our Galaxy) show some kind of central bar structure when we image the galaxies in the near-infrared.

The nearby spiral galaxy M83 in blue light (L) and at 2.2 (R) The blue image shows young star-forming regions and is affected by dust obscuration. The NIR image shows mainly the old stars and is unaffected by dust. Note how clearly the central bar can be seen in the NIR image

Weinberg & Katz (2000) proposed that the gravitational effect of a rotating bar in the inner halo can remove a central cusp in ~ 1.5 Gyr (the age of the universe is about 13.7 Gyr). This idea is controversial. density radius / (bar radius)

Current belief is that halos probably do form with cusps, but the cusp structure is flattened by the action of a bar or by gas being suddenly blown out of the inner galaxy by a burst of star formation. (This consensus keeps everyone happy but is still very uncertain)

Dark Halo Substructure problem In simulations of galaxy formation, the halos are quite lumpy, with a lot of substructure - simulations predict a lot more satellites and dwarf galaxies than observed. From simulations, we would expect a galaxy like the Milky Way to have ~ 500 satellites with masses > 108 M. These are not seen optically or in HI - we see about 40. What is wrong ? Could be a large number of baryon-depleted dark satellites, or some problem with details of CDM

CDM simulations of dark halos give too many small sub-halos relative to the numbers of observed small galaxies B. Moore

Moore et al 1999 showed the similarity of dark halos on different scales - clusters, large galaxies, small galaxies - note the substructure in the halos

More satellites of the Milky Way are being found gradually, with deeper wide-area imaging surveys. But it seems unlikely that another ~ 400 will turn up. A few years ago, we made a survey in neutral hydrogen of the southern sky, using the Parkes radio telescope. We expected to find many galaxies which had just dark matter and gas (no stars). They would be candidates for the "missing" satellites. But we did not find a single one - every galaxy that had hydrogen also had starlight. Not sure why these star-less galaxies don't exist, but they don't !

An alternative to dark matter is that Newton's inverse square law of gravity is not quite right. Why should that be - it is well tested in the solar system and seems to work ? Yes, but the acceleration in galaxies is very low: it is about 100,000 times lower than the acceleration that Pluto experiences as it goes around its orbit. Newton's law has not been tested at such low acceleration. Maybe it does not work so well. How would we have to change Newton’s law to make galaxies rotate like this without needing dark matter ? halo

The acceleration needed to go around a circle of radius R at velocity V is V2/R. From Newton's law, the gravitational acceleration due to a mass M is  M/R2, so V2/R  M/R2 and V  1/R like the (stars + gas) curve below Milgrom (1984) postulated that the force law changes at the very low accelerations which we see in galaxies. He proposed that the acceleration changes from  M/R2 to  M/R at low acceleration. Then V2/R  M/R and V would be approximately constant with radius (like the observed rotation below) halo His idea (MOND) now has a sound theoretical framework. This does not mean it is right, but so far it has been impossible to prove MOND wrong. Because of the problems with CDM, more people are starting to take MOND seriously

How large and massive are the dark halos of large spirals like the Milky Way ? Flat rotation curves mean that the mass of the galaxy increases linearly with radius: M(R)  R For the Milky Way, the mass out to a radius of R kpc is about 1010 x R M out to at least 50 kpc. This cannot go on for ever - the halo mass would be infinite. Halos must have a finite extent and mass - how large are they ?

Rotation of the Galaxy: Merrifield (1992)

Timing argument M31 (Andromeda) is now approaching the Galaxy at 118 km s-1. Its distance is about 750 kpc. Assuming their initial separation was small and the age of the universe is 13.7 Gyr, we can estimate a lower limit on the total mass of the Andromeda + Galaxy system. The Galaxy’s share of this mass is (13  2) x 1011 M A similar argument using the Leo I dwarf at a distance of about 230 kpc gives (12 2) x 1011 M.

M31 118 km s -1 Milky Way M31 and the Milky Way are now approaching at 118 km s -1. Their separation is about 750 kpc M31 To acquire this velocity of approach in the life of the universe means that the total mass of the Milky Way is at least 120 x 10 10 M. The stellar mass is about 6 x 1010 M, so the ratio of dark to stellar mass is ~ 20 118 km s -1 Milky Way The dark halo extends out to at least 120 kpc, far beyond the disk's radius of ~ 20 kpc (Kahn & Woltjer 1959)

This radius (120 kpc) is much larger than the extent of any directly measured rotation curves, so the “timing argument” gives a realistic lower limit on the total mass of the dark halo. For our Galaxy, the luminous mass (disk + bulge) is about 6 x 1010 M The dark halo mass is at least 120 x 1010 M The ratio of total dark mass to stellar mass is then at least 120/6 = 20

The dark halo of our near neighbour, the Andromeda galaxy M31, is similar to the halo of the Milky Way Its halo mass is also at least 120 x 1010 M, similar to the Galaxy

M31 has a flat rotation curve out to a radius of about 35 kpc Carignan et al 2006

Conclusion The total mass of the Milky Way is ~ 1.5 x 1012 M The MW and M31 are among the few galaxies for which we have an estimate of the total mass, rather than just the mass out to the end of a rotation curve. Their dark halos extends out to at least 120 kpc (compared to 20 kpc for the disk) The stellar mass is about 6 x 1010 M So the stellar baryons are only about 4% of the total mass Compare this with the universal fraction of baryons/matter = 16% Like most galaxies, our Galaxy has lost (or never acquired) a large fraction of its share of the baryons

Dwarf spheroidal galaxies Faint satellites of our Galaxy Very low surface brightness Some are almost invisible Total masses ~ 107 M These galaxies are not rotating, but we can measure their masses by using the velocities of their individual stars. These galaxies are almost pure dark matter: some of them have less than 1% of their mass in stars (compared to the cosmic fraction = 16%). They have lost almost all of their baryons.

The Density of Dark Halos • Use rotation curves for disk galaxies to measure the central densities of their dark halos The slope of the rotation curve for the dark halo gives its central density Kormendy & Freeman 2003

The central densities of dark halos The fainter galaxies bright The fainter galaxies have much denser halos. These galaxies formed very early in the life of the universe, when the universe was much denser. That is why their halos are so dense. The central densities of dark halos Kormendy & Freeman 2003

Summing up: where are all the baryons and dark matter ? (Baryons are ordinary matter, made of protons and neutrons) In the universe, most of the mass is in the form of dark energy. The total fraction of matter (dark + baryonic) is about 0.27 The fraction in baryons is 0.044 The fraction in dark matter is about 0.22 About half of the dark matter is in galactic dark halos (0.12) The rest is out in space, not condensed into halos The cosmic ratio of baryons to total matter is 0.044/0.27 = 0.16 In clusters of galaxies, the ratio has thisvalue, so clusters are a fair sample of the universe. In individual galaxies, the baryon/total matter ratio is only about 0.002 to 0.05, so galaxies have lost a lot of their baryons

Some recent developments in dark matter research

A cluster of galaxies: the ratio of baryonic to dark matter in clusters is similar to that in the universe as a whole (about 16%)

The dark matter ring Weak lensing of background galaxies is a new way to detect gravitational fields. Hubble telescope images were used to discover a vast ring of dark matter around the cluster of galaxies CL0024+17. The diameter of the ring is about 2 Mpc. It probably comes from a collision of two smaller clusters about 2 billion years ago

The Bullet Cluster Clusters of galaxies contain galaxies, dark matter and hot gas. Here, two clusters have collided: the two lots of galaxies and dark matter (blue) have passed through each other but the hot gas (pink) interacts and is left behind. Most of the baryon mass is in the gas ! The dark matter was measured by weak lensing (Hubble and groundbased telescopes: the dark matter lies with the galaxies) The hot gas gives off X-rays measured by the CHANDRA telescope Clowe et al 2006

Neutrinos are common, but do they have enough mass (~ 2 eV) ? This does not look good for MOND: most of the baryonic mass is in the (pink) gas, but most of the gravity is coming from the regions (blue) where the galaxies lie. Not a new problem ! MOND works well for individual galaxies, but not on these larger scales of clusters of galaxies. We need some kind of extra dark matter in clusters, as well as MOND: this could be hot dark matter (neutrinos) because clusters are large. Neutrinos are common, but do they have enough mass (~ 2 eV) ? (Remember: we needed the cold dark matter to make halos on the smaller scales of individual galaxies. Hot dark matter is OK for clusters which are much larger than galaxies)

And here is another example

What is dark matter ? The MACHO experiment, done at Stromlo during the 1990s, showed that dark matter in our Galaxy is not made up of compact objects (stars, planets) with masses between about 10-7 M (much smaller than the earth) and 30 M . This excludes most kinds of dead stars (neutron stars, white dwarfs) or failed stars like brown dwarfs

The most likely candidates for CDM are weakly interacting massive particles, many of which have not yet been seen in the laboratory: axions, neutralinos ... left over from the big bang. Neutrinos are candidates for hot dark matter. Many experiments are going on in physics laboratories to detect these particles: expect some news in the next few years. e.g the KATRIN spectrometer will measure the mass of the electron neutrino very accurately in the next few years: is it about 2eV ?

The KATRIN spectrometer vessel on the move in Leopoldshafen