• Q: Describe a test for dark matter in the Solar System. Is there much (compared to the mass of the Sun)?
• A: To look for dark matter, we usually seek motions of objects that are not explainable by the gravity of visible objects. For example, we could accurately track the path of an asteroid and see if it follows the path predicted by gravity from Sun & known planets. If not, could be gravity of dark matter. There must not be much because motions in the solar system are explained to very high accuracy by known laws & objects.

• (go over the large-scale structure of the Universe, do theories match this pattern?)
• This week’s material is scattered throughout the textbook. See the syllabus. Much of it is not covered well or at all.
• Want to know how much stuff there is in the Universe (Omega?) What is that stuff?

• Census of luminous matter - omega in stars.
• Typical luminosity of a galaxy: M=-20 (h=75), 1e10 L_sun
• Density of galaxies; phi*=0.03 h³ Mpc^-3 = 0.0125 Mpc^-3 = 3.5x10^-4 (Mly)^-3 (typical distance 15 million light years apart (h=0.75))
• So light density is 3.5x10^-12 Lsun/ly³. If M per unit light is same as sun, then the mean density is 3.5x10^-12 Lsun/ly³ = 3.5x10^-12 x 2x10³⁰ kg / (9.5x10¹⁵ m)³ = 8.2x10^-30 kg/m³
• Remember that the closure density was 3H² / 8πG = 1.1x10^-26 kg/m³ (for H=75), which is what we'd get by spreading the sun out over a 600 ly cube.
• Thus if M/L=1, then Ω = 0.00075 ! WAY underdense. Would need to have M/L=1350 to have Ω =1.
• In other words: if every bit of mass in the Universe puts out light at about the same rate as a piece of the Sun, then omega<0.1% ! What forms of mass are less efficient that Sun at making light? Low-mass stars: higher M/L; "loose" gas in the MW (dust also); white dwarfs, n stars, black hole remnants.
• SLIDE: White dwarfs, Brown dwarfs
• If we do a census of nearby stars, we find that typical M/L is higher than Sun by about 5x; so still only about 0.4% of critical density is found in stars nearby. The dimmer stars are of course the hardest to find! So we don't have a great handle on the number of v. faint stars. Brown dwarfs: need to look into this more; now known to exist, but their numbers are uncertain (learning fast!). Limits from MICROLENSING, discuss later.

• The Big Bang Theory tells us how the light elements (H, He) were made; remember that the "nucleosynthesis" theory correctly predicted the amount of amount of H & He in the oldest stars, about 25% (by mass). Also created in the Big Bang: deuterium (1n, 1p); ³He (1n, 2p), ⁷Li (4n, 3p), in very small amounts. How much of these elements created depends upon the density of p’s & n’s in the 1^st 3 minutes! This makes sense because the rates of collision & fusion will depend upon how tightly the "baryons" are packed together.
• OVERHEAD: Wiley 100, light elements vs density.
• Looking for deuterium: best way now is to look at absorption lines of hydrogen from very distant clouds of gas in front of bright distant objects. D lines are slightly shifted from normal H – relative strengths gives D/H abundance.
• Attempt to measure the proportion of these light elements in very old stars. Must be very careful to avoid stars that have "polluted" their outer layers with fusion products.
• OVERHEAD: Li abundance vs. Fe abundance.
• Results: Ω =0.012--0.07 from p's, n's.

• Nucleosynthesis argument shows that there are more baryons than we can account for in stars, so there must be a lot of p's, n's that are NOT in stars like Sun. Where are they all?
• Stellar remnants (perhaps, more later this week on how to "look" for them)
• Neutral hydrogen? - no, would see 21 cm line or absorption lines.
• Beer cans? No, too much heavy elements. But if they were there we probably couldn't see them. 100g beer can, would take only 1 beer can every few million miles over the whole Universe to close the Universe!
• Hydrogen snow balls - would evaporate.
• Ionized hydrogen - perhaps, spread out between the galaxies? No absorption lines to give it away.

• How do you find matter that you can't see? Look for the effect of its gravity on other bodies that you can see. Remember that Neptune was the first dark matter example: its gravitational effect on Uranus was noted before it was actually seen. A simple example is to watch an object in a circular orbit. We know it should run off in a straight line if there were no gravity on it; gravity accelerates it in a circular motion. Object moving a speed v around orbit with radius R: being held in orbit by the M(R) mass enclosed within its orbit (the mass outside the orbit has no net effect).
• Review: a=v²/R, F=ma=m v²/R=GM(R)m/R² à M(R)=v²R/G. So if we can measure v & R, we can derive the total amount of gravitating mass, even if it’s invisible.
• If all the mass is in the middle (like Kepler’s solar system) than M is constant with radius, so v is proportional to R^-1/2. This is called a "Keplerian" rotation curve. Speed drops as we move away from the center.

• How about another spinning system: a spiral galaxy. Let's measure the rotation curve of a spiral galaxy, v(R) vs. R. How? Doppler shift, look at the spectral lines of H coming from stars or gas clouds. Better yet: use a radio telescope, look at H gas (not stars).
• Surprise #1: Gas goes out farther than we can see stars.
• SLIDE: 31 gas/stars, OVERHEAD: NGC3198
• Surprise #2: Look at the rotation curve. Outside where the stars end, what do we expect to happen? Keplerian rotation, v=1/sqrt(R). What do we see? Flat rotation curve.
• OVERHEADS: rotation curves
• Remember, GRAVITY must be pulling stars/gas towards center to keep them contained. Formula: M(R)=v(R)²R/G. Since v(R) is nearly constant, this means that as we go further out, we are collecting more and more mass. No dropoff seen in any spiral galaxy. Even though we are well outside the visible parts of the galaxy=> dark matter must be present.
• EXAMPLE: NGC3198 (vanAlbada ApJ 295 395 '85) (shown on overhead)
• Total light from this galaxy: 7e9 L_sun Rotation speed is 150 km/s at radius R=30 kpc=100,000 ly
• => M(<1e5ly) = v² R / G = 1.5e5² 1e5 * 9.5e15 / 6.67e11 = 3.2e41 kg = 1.6e11 Msun --->M/L>23!
• If M/L is like this everywhere, than Ω=0.02, close to BBN prediction. Thus the visible part of the galaxy is embedded in a dark halo (not to be confused with the stellar halo). Note that the gas that the radio telescope is seeing is way too little mass to make up the dark halo; its rate of motion merely indicates to us that there must be much more matter.
• Could this be where the missing p's & n's are? What form are they in? NOT in regular stars, in hydrogen gas, in hot, ionized H gas - we would see faint x-ray halos, do not.
• How about dead stars? Small black holes? Planets? Brown dwarfs? These would go under the collective name "MAssive Compact Halo Objects" (MACHOs). Maybe there, maybe not.
• We can't think of any good place to put all of those p's and n's, except between the galaxies. Now we have two problems: (1) Can't account for all of the p's, n's (2) Something ELSE must be making up the dark halo. Some kind of stuff that is dark, does not interact strongly with "regular" matter (p/n).
• Would call them "Weakly Interacting Massive Particles" WIMP's. The rotation curves of spiral galaxies show that there must be some unexpected form of matter in the Universe, present in large amounts (equal to the "normal" matter)? Either MACHOs or WIMPs (big lumps or little). Total amount found so far only a few percent of the amount needed to close the Universe.

• Before we continue looking for dark matter, describe another reason why galaxy rotation curves are very useful: turning spiral galaxies into "standard candles" so we can use them to measure distances. Remember problem with using galaxies as standard rulers or candles is that they come in a variety of sizes.
• SLIDE: dwarf spiral.
• But consider two spiral galaxies, one big & one small. Which has more mass? The larger. Its stars can then move more rapidly because more gravity to hold them in orbit. So the rotation speed of a galaxy should tell us roughly how large & bright a spiral galaxy is. This is observed to be the case! Called the Tully-Fisher Relation between rotation speed & abs. magnitude of a galaxy.
• OVERHEAD: TFR; distance scale.
• Now if we know the distance to a few galaxies using Cepheids (M31 + others with HST), we can use the TFR to measure distance to almost any spiral galaxy! Accurate to !15%.

• Would a neutrino be a WIMP or a MACHO?
• A: WIMP – weakly interacting particle describe neutrino very well. It is not a massive clump like a neutron star or black hole.

Dark Matter Scorecard
Method	Ω
Luminous Matter (M/L=5)	0.004
Big Bang Nucleosynthesis (Baryonic matter only)	0.012-0.07
Spiral Galaxy Rotation Curves	0.02
Galaxy Satellites	0.1-0.2
Galaxy Cluster Motions	0.25

• Found in spiral galaxies that there is about 0.02 of closure density lurking in dark halos of galaxies, NOT in any normal star or gas form. Either MACHOs (which could be burned-out p’s & n’s, & hence make up all the baryons in Universe) or WIMPs (some exotic particle, in which case p’s & n’s are spread between galaxies).
• In fact, the limit to our guess of spiral galaxy's mass was how far out we could measure rotation of H gas. Could be more dark matter even further out. What to use to test the gravity? Try other galaxies; in particular, small satellite galaxies:
• Zaritsky: 1.5x10¹² solar masses within 150 kpc (M/L~150-200, omega~0.1-0.2!)
• OVERHEAD: Zaritsky paper.
• "Mountain range" view of galaxies – the light is only the peak of snow atop large mountains of dark matter making up galaxies. Now note that we have found too much matter for it all to be made of baryons! There must be exotic forms of matter, e.g. WIMPs or black holes. And they greatly outweigh "normal" matter!

• Other places to look for dark matter: look at how galaxies pull on other galaxies. Look in a place where there are a lot of galaxies packed together, i.e. a galaxy cluster: velocity dispersion used to measure the mass & give M/L.
• Example: the Coma cluster of galaxies.
• SLIDE: Coma cluster
• Once again, we see how much gravity it takes to hold in the stuff flying around in it. In this case (as in an E galaxy) the orbits are not nice orderly circles - individual objects go on various shaped orbits, making it a little more complex. But we still find M(<R) ~ v^2 R / G, where v is the typical speed of the galaxy.
• OVERHEAD: Orbit shapes.
• In the Coma cluster of galaxies, we find v=1000 km/s. We also find that R>= 4 Mpc à M>10¹⁵ M_sun! Calculate M/L here: ~ 400!
• Thus there seems to be WAY more mass than accounted for by the stars and gas in clusters of galaxies. Enough to maybe make Ω=0.25! Still not 1 - maybe even darker between clusters?
• A possible trouble with this method is that we don’t get to watch the full orbits of the galaxies – just a snapshot in time, & don’t know if the orbits are really circles, etc. Takes a few hundred Myr for a galaxy to orbit its cluster, so they may not have settled down into normal orbits yet. A bit uncertain here.

• Another way to weigh a cluster of galaxies: see how fast the protons are going when they drop in. They will also be moving at ~1000 km/sec when they fall to the center of the cluster; in terms of temperature, this means that the H gas must be T=millions of degrees in the spaces between the galaxies of a big cluster. At this temperature, a gas will emit x-rays copiously.
• SLIDE of coma cluster in x-rays.
• Sure enough, the Coma cluster (& others) glow copiously in x-rays – easy to find clusters with an x-ray telescope! By measuring the strength & spectrum of the x-ray signal, we can determine the total mass in the cluster. Generally get the same answer as we did measuring the galaxy speeds – good!

• So far in our search for matter we have found surprising things: we require that something other than neutrons/protons to make up the vast majority of the Universe! We are not made of "normal matter" any more than we are the center of the Solar System. There must be a large amount of dark matter, non-baryonic.

• Different values of Ω give different geometries to the Universe. Example: open Universe has more space available at a given distance because C>2piR.
• OVERHEAD: Kaufmann 94, space in Universe.
• An observational consequence would be: see more numerous distant galaxies than in flat or closed Universe. If we count the faint galaxies, maybe we could tell? No – it didn’t work, because the galaxies are also brighter in the past (with younger stars) which confuses the issue a lot. Need to understand evolution of galaxies to get Ω, and that’s hard.
• Another approach: use a standard candle at very large distance: its brightness will depend on the geometry of the Universe! What standard candle could we see halfway across the Universe? Supernova! A type Ia SN is an excellent standard candle because they all form from same size star, 1.4 solar masses! Find Ia’s have same brightness to ~30%, measure their distance to 15% accuracy.
• High-z SN searches: hard to find, need to look at a LOT of distant galaxies. Use my camera (!) find 10-20 per night of looking, amazing.
• OVERHEADS: LBL SNe search results.
• Indicate an open Universe. In fact even indicate that the cosmological constant isn’t zero! Maybe Einstein was right when he was wrong!
• Exciting field, new developments each month.

• What could it be? A sign of some kind of particle that doesn't interact strongly with matter - "WIMP"...or maybe we don't quite understand gravity just right. Maybe MACHOs – black holes created in the Big Bang. Maybe neutrinos? More info on Friday.

• Q: Here are 3 methods to estimate the amt of dark matter in a cluster of galaxies. What equipment, operating in what part of the EM spectrum, is necessary for each method?
• dynamical method
• x-ray gas method
• grav. lensing method

• Gravitational lensing offers another way to "look" for dark matter: remember that GR predicted light beams should be deflected by the presence of nearby matter, in a manner inconsistent with Newton’s theory, because of the warping of spacetime. In Einstein's theory, the deflection is

• Possibility of Multiple Imaging?
• OVERHEAD: Explanation of multiple imaging geometry
• If the light ray is bent enough, one could be able to see the same source via two paths – so it would look like two copies of the same star. Einstein recognized the possibility but didn’t think it was possible since he was only thinking of stars as a possible lens. But an entire galaxy or cluster of galaxies could act as a huge cosmic lens, too.
• 1979 - 0957+561 double quasar discovered. Same general color. EXACT same redshift, spectrum! Take an extremely high-resolution radio telescope picture: see the SAME little bumps (with mirror flip as predicted).
• OVERHEADS: 0957+561
• Seems to be a gravitational lens. Where is the lens: find a fainter, red E galaxy in between!
• OVERHEAD: HST picture of lens.

• Gravitational lenses are real; what good is it? Known since 1960 that we can use lenses to measure H₀! How does this work? We observe a double image and measure the redshift velocity v. If we knew d to the source, we would know H₀ without using any of the distance ladder. But we don’t know d, we just know the angles of all the triangles involved – not the size.
• Note that the two paths are different lengths. So if the quasar blinks, it should be seen first in one image, then another. This is seen, time delay ~ 1 yr. (1 light-year difference in path length out of BILLIONS of light years!).
• OVERHEAD: 0957 light curves.
• Results of this study give H₀=50-75, just like old, more complicated measures. Maybe we are doing things correctly after all!

• Even better: if we are measuring the deflection of light, we are measuring the strength of gravity and hence determining the mass of the lens. It doesn’t have to be luminous mass – any matter, even dark matter, causes lensing. So lenses are dark matter detectors.
• More interesting cases: quadruple lens
• OVERHEAD: PG1115, Einstein Cross
• Case of perfect alignment: Einstein Ring
• OVERHEADS: Ring explanation; ring pictures.
• This lets us get the MASS of the galaxy, since we know the deflection angle and the radius. AGREES with other methods. Confirms presence of dark matter in individual galaxies.

• If alignment isn't quite right, we get pieces of Einstein rings: giant arcs. Galaxies stretched & distorted by the grav lens, allows us to make a map of where the DARK MATTER is!
• SLIDES: Arcs
• VIDEOTAPE.
• Giant Arcs - masses agree with the velocity & x-ray methods. Also get very large M/L ratios, Ω=0.2 roughly. Nice to get same answer 3 different ways!
• My project: measure the dark matter in random places, not just clusters!

• Still need to figure out what makes up the Dark Matter – MACHOs or some kind of WIMP? Another way in which lensing is very useful.
• DEMO: move the lens in front of the source. Note the brightening; the lens need not be visible nor need you observe the details of the image.
• A dark massive object comes between you & a star: does not block all the light; in fact can steer extra light toward you. Use this affect to search for MACHO's. It is called microlensing because it’s very small – we don’t see the details of the picture, but just see a star get brighter for no apparent reason then fade away.
• Look toward the LMC (just because there are a lot of stars there on the other side of MW dark halo). IF the dark halo is MACHO's, then once in a while a star will BLINK on for a short while as a MACHO passes in front (remember we're moving, they're moving, etc). Watch for this... Trouble is that we predict that at any given moment, only one per MILLION stars is being "microlensed" by a MACHO. 3 groups start searching for this. One looks at 40 million stars every night! Indeed, microlensing happens - find them!
• (OVERHEAD & slides).
• Note the good match of predicted shape to actual. Note the same in both filter (color of star did not change) Note that the star is otherwise stable (not a variable star).
• Dozens of ulenses now observed. New tool for astronomy to look for faint dark objects (i.e. brown dwarfs). What do they find?
• If we look down the disk of the MW, we see plenty of microlenses, just as we’d expect because of all the disk stars along the way. Confirms that the calculations are correct.
• Looking toward LMC: should see very few unless there are MACHOs in the halo. Current results suggest that there are not as many microlenses as there should be if the MW halo is made of MACHOs. This is still controversial – many claims that at least some of the halo must be MACHOs. But I think it’s clear that MACHOs can’t be most of the dark matter.
• OVERHEAD: binary microlens

• Still left with a big mystery: don’t know what makes up 90% of the Universe, and don’t know if the Universe is closed (current results point to NO, Ω~0.2).

• We need a WIMP – neutrinos are certainly weakly interacting particles. But are they massive? It does not seem that neutrinos have enough mass to do the job. We know they have very low mass, in fact maybe none at all (like photons). They move near the speed of light in any case. This means that they can’t be "trapped" by the gravity of the Milky Way. They would be moving too quickly to be able to be the dark matter that forms the structures in the Universe. Need something heavier than the neutrino.

• Leaves us with some as-yet-undiscovered particle. There are some theoretical candidates but nothing seen in a laboratory yet. A whole Universe of "shadow matter" is escaping our grasp!

• Prediction based upon general relativity/curved spacetime. Big triumphs:
• (1) expansion explained
• (2) cosmic blackbody radiation explained
• (3) primordial helium
• (4) age of Universe (roughly)
• (5) seeds of structure formation seen
• Problems:
• (1) age not in agreement exactly?
• (2) don't understand fully how structures formed.
• (3) Dark matter problem: have found 0.25 of closure density in galaxies and clusters. More could be hiding between galaxies but no real evidence for it yet.
• (4) Must be some non-baryonic dark matter (or we have gravity wrong). Does not seem to be made of MACHO's, at least around MW. Must be in some form of some other particle.
• (5) Einstein’s cosmological constant could be non-zero, and we don’t understand why.