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Unformatted text preview: 1/15/12 Gala ie and he Uni e e - Da k Ma e D M I ,
gravitational le ns ing. N curve s , 10 ?T rotation
clus te rs of gala ie s ,
, ,... R (
, , ).
T -B ; M/L, .Y ; 10,
M/L , - Rotation curve s : A .
1/R, .T -- M/L 100
250 / ,
(1979, ARA&A 17, 135). .F
1.5 1014 H - IMF; ,
.T IR .S
' all IMF ,
- ; ( G 229B) .T K (J , ' ), .N
" - .O ",
- HI .C
.S , Ellipticals :
.O .a . . a.ed /keel/gala ie /da kma e .h ml M87
NGC 4472 . 270 (F G ,
1983 A J 267, 535). T ,
X- ,F ,
1986 (MNRAS 221, 1049)
1/8 1/15/12 Gala ie and he Uni e e - Da k Ma e 2,
A . shells
,H Q 200)
: P F . 3, , .T ,
1984, A J 279, 596). A
(1987, A J 312, 1)
.T ( ,
.T - . ,
.S (" ")
M/L 100- V
;R , , . D namics of s s te ms of gala ie s :
1937 (A J 86, 217)
t heorem U=-2 E. I
( , ) irial
U E, ( ,
' ). T
E .a 1987 A J 316, 36) T . a.ed /keel/gala ie /da kma e .h ml , ()
. 1979 (A J 228, 684): , .T
( 2/8 1/15/12 Gala ie and he Uni e e - Da k Ma e where v c is the cluster mean radial velocity (to be fully correct here one must either use the relativistic recession velocity
or correct for another factor (1+z) in the result) and rij is the projected separation between galaxies i and j . There are N
Claims are sometimes made that the M/L ratio is a systematic function of the size scale on which the measurement is
made, usually just before claiming that therefore &Omage;=1 for the Universe as a whole. Note, however, that different
techniques are used for various scales. The real point here is that a technique that applies to systems of a given scale is
sensitive only to mass that is clumped on that scale.
Smaller groups of galaxies might probe the mass on smaller scales, but there are uncertainties caused by (1) small- number
statistics, (2) the role of interlopers, at all distances, and (3) the possibility that these systems have yet to reach a virialized
state, which is hard to define for N<10 anyway. These get worse for binary galaxies; here the derived masses depend
critically on how one allows for contamination by nonbound apparent pairs. Karachentsev has made strong arguments for
halo masses not much larger than required by present rotation curves.
Gra itational le ns ing: at last, here is a probe which is unbiased by the luminosity of a target as long as it's transparent.
Dark matter is quite transparent; that's the problem. This phenomenon falls out of the principle of equivalence, with a
magnitude twice what you would get in a pseudo- Newtonian case assigning the photon a mass hν /c2 (Einstein 1935 , in
Science). Zwicky (1937 Phys. Rev. 51, 290 and 679) first suggested that lensing (in some languages more accurately
called the gravitational mirage) would be observable on the scale of galaxies, rather than for stars as originally treated by
Einstein. The basic equation gives the angular deflection α as a function of impact parameter of the asymptotic line of sight
b (note that one has to be very careful about linear measures when geodisics bend) as as a vector quantity traversing potential Φ ; for spherically symmetric masses (actually cylindrically symmetric is more
nearly appropriate) this becomes a scalar deflection and for a point mass α= 4GM/c2 ; for a spherically symmetric mass distribution, this is generalized by letting M be the
enclosed mass (within the deflected beam) M(b) (not the same as M(r)), following, for example, Refsdal 1964 (MNRAS
128, 295) and Young et al. 1980 (ApJ 241, 507). The obvious integration holds for extended masses, with the
approximation frequently possible that b is small compared to the line- of- sight distance. For a more galaxy- like potential
with a non- truncated (analytically approximated) King potential of core radius a and central density 0 . which has a maximum value at b ~ 1.8a of αma x = 45.2 G 0 a3 / c2 .
.a . a.ed /keel/gala ie /da kma e .h ml 3/8 1/15/12 Gala ie and he Uni e e - Da k Ma e Q .Q
.T .F D. O
. 1984 A J 284, 1),
. 1993 A J 409, 28),
Q SO (T
100 , ,
SDSS ID HST (M
- ; ) , c /4 (GMD)1 /2 r ( - : QSO 2 W ,C
381 7.1 3? W . 1982 A JL 255, L5 ... 1.72 0.31 0.42.3 4 W . 1980 N " 1634+267 1.96 ... 3.8 2 S 2016+112 3.27 0.24 3.4 3 L 2237+030 1.69 0.039 1.3 4 H . 1985, AJ 90, 691 0142- 100 2.72 0.49 2.5 2 S . 1987 N 1413+117 2.55 ... 4 M 0957+561 1.4 0.36 5.7 2345+007 2.15 ... 1115+118 10214+4724 2.3 1 0.7? 0.7 1120+019 1.47 ... 1422+231 ... ,W 1979 N &D 285, 641 1984, A JL 282, L1
. 1984, S " 223, 46 Q SO Q SO " Q SO
"E " UM 673 334, 325 "C . 1996 A J 461, 72 " ... ... 4 M 0.34 ... 4 I . 1996 A JL 462, L53 ... 1208+1011 3.8 ... 0.48 2 B . 1992 A JL 392, L1 ... B1359+154 3.2 . 1995A J 439, 599 1.0 2.0 6 I ,
- .A CASTLE ,
( A ,
( . .B 1981 A JL , , .T
1014 . 1995 A JL 453, L5).
.T . 1986 (N S , .A
T UM 425 ??? A .a " ... 329, 695 . 1988 N E 279, 321, 142) . a.ed /keel/gala ie /da kma e .h ml 1146+111,
4/8 1/15/12 Gala ie and he Uni e e - Da k Ma e be retracted (basically by the editor) when further data showed spectroscopic differences between the components.
Aside from global constraints on and A, detailed models are possible when the lens galaxy or cluster can be identified, a
redshift and velocity dispersion measured. and perhaps shear in the lens field measured (for example by VLBI mapping).
In the well- observed 0957+561 system, there is some evidence that not only does the cluster have huge unseen mass, but
that it is not quite concentric with the galaxy distribution. There are now several proceedings devoted to gravitational
lensing, where reviews may be found: the 1984 Liege meeting (Q a a and G a i a ional Len e ) and G a i a ional
Len e edited by Moran et al. (1989, Springer- Verlag) from a meeting at MIT. Also of interest is Da k Ma e in he
Uni e e, ed. J. Bahcall et al. (World Scientific, 1987).
A generalization of the gravitational lens technique uses large numbers of faint background galaxies to probe the cluster
potential. This was first tried for individual galaxies by Tyson et al. (1984 ApJLett 281, L59), and given new impetus by
the discovery of luminous arcs in galaxy clusters (Lynds and Petrosian 1986 BAAS 18, 1014; Soucail et al. 1987 A&A
172, L14; 1988 A&A 191, L19). The redshifts of the arcs (an impressive feat) are much higher than the clusters,
implicating gravitational lensing. Statistical models have been very successful in reproducing the occurrence and
appearance of the arcs (as in, for example, Grossman and Narayan 1989 (ApJ 344, 637). The arcs in Abell 2218 show
the effect quite intuitively (as discussed by Kneib et al 1996 ApJ 471, 643 and Smail et al 1996 ApJ 469, 508). This
image is from the HST SM3A OV phase (how's that for stacked acronyms?). Notice the divergence of arcs around the
bright galaxy to the lower left, showing that there is a significant concentration of total mass associated with it rather than
just the cluster as a whole. A remarkable extension was introduced by Tyson et al. (1990 ApJLett 349, L1) who analyzed the images of faint
galaxies around nearby clusters statistically and were able to derive not only masses but the mass distribution. Color
selection allowed discrimination between faint cluster members and the distant background galaxies that will show this
distortion. This approach, so- called weak lensing, can also be used statistically for individual galaxy masses. They find that
the matter is only slightly more extended than the galaxy distribution; the dark matter in these cases is associated more
with the cluster as a whole than with individual galaxies (see the work by Whitmore et al. on rotation curves in clusters for
more ramifications). The lensing mass distributions for two clusters are shown in their Fig. 4 (courtesy ofthe AAS):
.a . a.ed /keel/gala ie /da kma e .h ml 5/8 1/15/12 Gala ie and he Uni e e - Da k Ma e F (C 1981 N ,
296, 397, ( . . Q SO ) .T
). T ,
F T ' ,
MACHO, OGLE, EROS, AGAPE, MOA )
.T " "
M31 - 106- 107 , ,
G ' ( ) E , J LMC,
.H ' LMC , .I
( ' ),
, M ) W - .T , MACHO
AGAPE, .T ; MACHO WWW C . a.ed /keel/gala ie /da kma e .h ml 0.5
6/8 1/15/12 Gala ie and he Uni e e - Da k Ma e Gravitational lenses can also (again in principle) give the Hubble constant. This requires a measure of lens mass that has a
different dependence on distance than does itself, such as a cluster velocity dispersion. Rhee has done this for the
0957+561 lens cluster, claiming 0 = 42± 17 km/s from this single observation, while a recent compilation of available
time delays gives a value near 70. The best measure of mass scale in the lens is the differential time delay between the light
paths, measurable when the background QSO is appropriately variable. The QSO 0957+561 seems the best case so far,
with the delay pretty well constrained at 1.3 years; Schild has found that microlensing which must be from planetary- mass
objects in the main lens galaxy complicates the timing analysis but is at least as interesting from a mass standpoint.
Primordial nucle os nthe s is and 0 : the relative primordial abundances of H, D, He, Li, and Be are predicted by a
simple Big Bang model, since the universe from times 3- 11 minutes was almost perfactly flat and the rate of neutron
capture therefore depended on the baryon density. Observed abundances in old stars and pristine gas imply the the
baryonic mass density of the Universe is only 7- 10% of critical density - well below what is required for the total by
galaxy and cluster dynamics. This may be telling us that the remainder is non- baryonic (exotic particles), with matter
locked in black holes a wild card depending on whether they were formed before or after the epoch of nucleosynthesis.
There will be more on primordial nucleosynthesis later in the course.
Alte rnative e planations : it is puzzling that it took several years for anyone to seriously discuss the possibility that the
fault lay not in the stars but in ourselves - that perhaps our understanding of gravity is faulty on such large scales. Milgrom
(1983 ApJ 270, 365; 270, 371; 270, 384 and subsequent papers) took up the idea with vigor, proposing that there is a
.a . a.ed /keel/gala ie /da kma e .h ml 7/8 1/15/12 Gala ie and he Uni e e - Da k Ma e minimum gravitational acceleration somewhat by analogy with the quantum behavior of particles. Tests on galaxy rotation
curves look bad for the idea, but Milgrom claims they are still inconclusive. Still, someone needed to examine this
possibility, and the fact that it took about 5 years doesn't speak too well for the astronomical community.
A recent result which has attracted much attention, as possibly resolving the issue in favor of actual dark matter, is
illustrated below from HST/Chandra/Magellan data by Clowe et al. This galaxy cluster, 1E0657- 56 (the Bullet Cluster)
has long been seen to show evidence for being two dynamical systems in the throes of merging. Models indicate that the
hot X- ray gas should undergo strong dissipation, while dark matter and te relatively small galaxies would fly apart at least
temporarily after initial passage through each other. The X- ray gas (pink) indeed stayed put between the two galaxy
clouds. Gravitational lensing of deep background objects shows that the mass distribution (blue) stayed with the galaxies.
Since the hot gas dominates the baryonic mass in such rich clusters, this is strong evidence that the material in clusters is
indeed some kind of invisible material, weakly enough interacting to suffer no significant disruption when clusters pass
through each other.
How man kinds of dark matte r are the re ? Theory makes a convenient distinction between hot and cold dark matter,
where HDM is relativistic and therefore doesn't fall easily into galaxy- sized potential wells, and CDM ends up with the
dynamical properties of tracer particles just as stars do. Neutrinos would be hot unless their rest mass is higher than
experiment now indicates, and the often- hypothesized weakly interacting massive particles (WIMPs, as contrasted to
MACHOS = massive compact halo objects) and other baryonic forms would be cold. The implications for galaxy
formation are rather different, and some bold workers suggest that a mix is required. Baryonic dark matter would be cold,
as would massive enough neutrinos. While it seems to violate Occam's razor, there is compelling evidence for both
baryonic and nonbaryonic dark matter. There is a strong theoretical prejudice, driven by inflationary cosmologies, that
there be enough nonbaryonic material to give closure density ( 0 = 1/2), but regardless of the amount it is important in
galaxy formation. Nonbaryonic dark matter need not have been coupled to radiation before the epoch of recombination,
and could therefore have clumped gravitationally while ordinary matter was still as smooth as we see the microwave
background to be. In this scheme, the DM fluctuations seeded galaxy formation to occur much faster than might otherwise
have been the case. Locally, dim enough stellar remnants count as a form of dark matter (as for that matter did Sirius B
and Neptune before their visual identification), and in fact it is this component that the gravitational- lensing surveys see. As
we've seen, molecular gas, and for the intergalactic medium highly ionized gas, have enjoyed brief periods of vogue as
candidates for significant amounts of baryonic dark matter.
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This note was uploaded on 01/15/2012 for the course AY 620 taught by Professor Williamkeel during the Fall '09 term at Alabama.
- Fall '09