The Conspiracy That the dark matter conspire to just make the rotation curves nearly flat Bottom line: M/L 40 M O /L O from these “flat rotation curves”.. Remember we got about 300 for clusters! And for GA !! => Larger scale, larger M/L Velocity of stars => elliptical gal M/L 10 M O /L O..

.. For Comparison: (  c  m) /  L = 450h M O /L O or = 290 M O /L O for h = 0.65, and  m = Where  L is based on adding up all the light from galaxies out to z = 0.25, MNRAS, VOL = 336, pp , (2002) Before Lambda was taken as fact, we needed “bias.” What? Why?

M/L from galaxies gives us  m of 0.3, then if  m = 1, there must have been a great deal of matter **not** associated with galaxies or clusters => Lots of mass were there is no light at all => CDM was thought to be more uniformly distributed than galaxies and clusters => We invented a “bais” parameter (b) to describe this! With  m now = 0.3 no general problem (b = or close to 1 now), but GA, weird as has M/L so high almost high enough to devive of  m =1, but we want  m = 0.3!!

For stars that make most of light (massive, young stars) M/L is less than 1 M O /L O => more evidence for dark matter and lots of it! For, we’re seeing M/L >> M O /L O...

Summary: Measure velocities and distances to infer masses and M/Ls. The keys are distance plus velocity plus modeling Results: GA (v = 4350 km/sec, M = 5 x M ) using T-F and J-F plus Fund Plane, M/L for GA = ?? Good guess is M O /L O local galaxy value is about M/L = 5 M O /L O O.

rotation curve for our galaxy => M/L = 20, and for external galaxies, M/L of about 40. => From direct measurements we infer the Universe contains a great deal of dark matter. Within factor of 2 consistent with indirect method of determining M/L

Before we leave this subject, though: Hard core M/L values all are scaled with h. What have I been assuming? Why doesn’t h matter for our galaxy? I’ve been assuming h = 0.5 ; or H 0 = 50

Epilogue: H 0 vs  m0  c = 3H 0 2 /8  G; Omega =  /  c, but  = M/Volume and we know M goes as h -1 and V does as D 3 means h -3 => M/V goes as h 2 and the h’s cancel out so  m0 is independent of H 0 (or h).

The Math The concept, mv 2 /r =GMm/r 2 =>M depends on r, but r depends on h -1, since we determine r from an angle and as calculated distance to the galaxy, smaller h for fixed angular extent, the larger the linear size = h -1 ; Remember D = v rec /H 0 and r =  D where  = the observed angular radius => r =  D =  v rec /H 0 L =F/4  D 2, and D depends on h -1 => M/L scales as h -1 /h -2 = h r =  D  D

Angular distance test Several key points: (1) the apparent size goes through a minimum. (2)We see evolution effects that we don’t know how to calculate because our long “bright rulers” are complicated

Angular distance test Lambda = 0 See that size goes through minimum

Angular distance test See that objects are complicated (but neat) Radio false color, red = brightest, blue next to faintest, black = faintest Galaxy, 100 kpc in diameter Blobs of radio emitting plasma, sep. about 1 Mpc

The Hubble Constant and Age Another classic test: Measure the age of the universe very carefully and compare with the model dependent predictions.

Details: suppose find t 0 = 15 billion years, and H 0 = 75 => 1/H 0 = 3x10 24 /(75 x10 5 x  x 10 7 ) = 12.7 billion => t 0 /H 0 -1 = 1.17 Look at t 0 /H 0 -1 versus  m => next slide

The Hubble Constant and Age  = _ 1.0_ 0.6_ 0 1  m 1.5 Flat,   +  m = 1 t 0 /H 0 -1 Too high for any  m,  =0

How do we measure age? Count tree rings :).. Only gives us very bad lower limit to the age “Radioactive dating” Gives another bound, age of the earth. (4.5 billion years) Look at star clusters + use theory => get age of our galaxy

Radio Active Dating Concept of 1/2 life. Every 1/2 life, one half of the total number of atoms in our sample decay. Uranium decays into lead. Assume a Uranium sample started out pure Uranium, Examine ore sample and judge its age. Oldest samples give us an age of about 4.5 x10 9 yrs

Math: N = N 0 x exp(-0.69t/t 1/2 ) ; where t 1/2 = 1/2 life; N 0 = the initial number of atoms

Little more math: Example: Uranium 1/2 life = 4.5 billion years, we find and ore that is 1/2 U and 1/2 Pb => = 4.5 billion year old. Now suppose we have 1/4 of the (pure) U we started with and therefore 3/4 of the sample must be Pb (lead), the how old would this sample be? Would we expect to find any samples like this?

Next Topic: Evolution of galaxies Questions: When did the first galaxies appear? What came first, the galaxies or the stars? Did all galaxies start from a black hole seed? Do ellipticals start out as spirals?

Old Philosophy: The study of shapes (Morphology) tells all! => Photograph galaxies, (1) look for common shapes and features. (2) classify (3) imply evolution (4) use redshift measurements to tell distance (5) look for changes in population versus redshift

Modern Version: Need to add spectral and color measurements to extend reach as when z gets high, features become difficult to distinguish, plus you need physics! First the naïve model by Hubble

So called “barred spirals”

Implied is that ellipticals evolve into spirals. And “from that day to this”, we’ve been stuck with calling ellipticals “early type” and spirals “late type.” But Hubble was WRONG!

Classification scheme: Ellipticals: “no” gas or dust and no “young” = million year old stars = no current star formation, and no disks Spirals: amounts of gas and dust such that there is active star formation and there are young stars SOs are galaxies with a disk similar to spirals, but no gas or dust in the disk

LMC SMC Andromeda and 2 dwarf (size of LMC/SMC) galaxies