Dark matter and galaxy formation •  Galaxy rotation

–  The virial theorem –  Galaxy masses via K3 –  Mass-to-light ratios

•  Rotation curves –  Milky Way –  Nearby galaxies

•  Dark matter –  Baryonic or non-baryonic –  A problem with gravity?

•  Galaxy formation –  Hierarchical merging –  Monolithic collapse –  Secular evolution

Galaxy Rotation

•  Galaxies form via collapse due to gravity •  As they collapse the rotation increases (conservation of

angular momentum)

•  Eventually, equilibrium is reached:

2rGMmF =

rmvF

2

=GRAVITY  

=  CENTRIFUGAL  

The Virial Theorem •  The Virial theorem applies when the galaxy is in equilibrium

and we can equate these two Forces:

•  v = the velocity of rotation at radius r which depends only on

the mass interior to r

mv2

r=GMmr2

v = GMr

m v

r

The Mass of a Galaxy   A star at the edge of a distant galaxy has a velocity about the

galaxy’s centre of 200 km/s. Its distance from the centre of the galaxy is 15 kpc. What is the mass of the galaxy ?

kgsMGrvM

rGMv

41

11

164252

107.21067.6

103105.1)102(

!=!

!!!!!==

=

"

The Mass-to-light Ratio    For  the  same  galaxy  if  its  absolute  magnitude  is  -­‐20.5  mags  

what  is  its  mass-­‐to-­‐light  raHo  ?  

   So  the  mass-­‐to-­‐light  raHo        (within  the  stellar  disc)  is:  

47.510102.1

10102107.2

)48.55.20(4.011

)(4.030

41GAL

GAL

GAL

GAL

GAL

=

!!=

!

!=

=

=

""

"

#

#

#

#

#

XX

X

LLX

LX

L

MM

MM

MM

!

!

LM5.5

The Mass Distribution •  Stars and gas are centrally concentrated •  Hence if stars trace the mass then the mass must also be

centrally concentrated •  Stars at large radii should see almost all the mass, i.e.,

•  If stars trace mass:

A B

BABABA vvrrMM !"#$ so,

We need to measure v as a function of r => Rotation curve

Measuring Rotation Curves Take spectra at different locations in the galaxy

The two spectra are slightly offset and this difference gives a velocity difference between the centre and the edge of the galaxy

I

I

λ

crvBULGE!!"

=)(

Δλ

Rotation Curves •  As the stars and gas are

centrally concentrated we expect: v ∼ r -0.5

•  But by measuring rotation curves we observe: –  A flat rotation curve beyond

the stellar population

RADIUS

VELO

CITY

RADIUS

VELO

CITY

B A

B A

=> Additional Mass Component

MW rotation curve

A Universal Flat Rotation Curve

and a few more….

Implication •  At large radii:

•  Hence:

•  i.e., Mass is proportional to radius •  Or:

•  This is the equation for an isothermal sphere and implies a spherical halo of extra mass

BA vv =

B

B

A

A

rGM

rGM

=

rA !rB "MA !MB,"M #R

23

1RR

RVM

!!="

Conclusions •  Almost all spiral galaxies have flat rotation curves •  Those that don’t are usually interacting (not in equilibrium) •  Stars do not trace the mass •  Stars are a minor mass component, about 10% •  Some kind of DARK MATTER must exist •  It must be distributed in a large outer halo (isothermal sphere)

Our Working Galaxy Model

BULGE DARK MATTER HALO

STELLAR DISK

HI GAS DISK GLOBULAR CLUSTER

COMPANION

Dark Matter in Galaxy Clusters •  Original argument for Dark Matter originated in Clusters

–  Pre-dates rotation curve observations and analysis –  Discovered by Fritz Zwicky (1930s) –  Motions of galaxies within clusters suggests clusters should not be

bound: very large velocities observed –  The fact that clusters are bound indicates more mass than present in

luminous matter –  Dark matter required to keep cluster bound –  Can measure mass of cluster from dynamics, lensing and SZ effect all

imply a high mass-to-light ratio suggesting Dark Matter

•  Further evidence comes from Cosmology –  Big Bang Nucleosynthesis predicts the baryon density –  Large scale structure predicts the mass density –  Above are off by a factor of 6 implying Dark Matter in non-baryonic

Mass via Grav. Lensing

To  create  realisHc  simulaHons  of  Large  Scale  Structure  a  modest  to  high  mass  density  is  required  (25%  closure)    To  explain  the  element  abundances  in  low  metalicity  stars  a  low  baryonic  mass  density  is    required  (4%  closure)      The  baryonic  maSer  we    can  idenHfy  in  galaxies  adds  up  to  and  even  smaller  amount  (2%)    Results  imply  both  a  small    missing  baryonic  component    and  a  large  non-­‐baryonic  mass    component    But  what?  

Blue  =  data  Red  =  simulaHons  

DARK MATTER candidates •  Normal  (i.e.,  Baryonic)  

–  Ionised  gas  –  Cold  dust  –  Planets  –  White  dwarfs  –  Black  Holes  –  MACHOS  (Massive  Compact  Halo  Objects)  

•  ExoHc  (i.e.,  non-­‐Baryonic)  –  Cold  -­‐  WIMPs  (Weakly  InteracHng  Massive  ParHcles)  –  Warm  –  Sterile  Neutrinos,  GravaHnos  –  Hot  -­‐  Neutrinos  (A  wee  bit  of  nothing  that  spins)  

Many  studies  in  progress  

Many  DM  experiments  underway  

Alternatively… •  We do not have the correct theory of gravity

–  Enhanced GR •  In the same way that Newtonian gravity could not explain all

observations (e.g., Mercury’s orbit), General Relativity may not be the whole story…

•  We either need an observational breakthrough to “discover” the dark matter particle, or a more convincing theoretical model

•  Both avenues being heavily pursued: –  MOND – Modified Newtonian Gravity (non-relativistic) –  TeVeS – Tensor Vector Scalar theory (relativistic version of MOND) –  Weyl Gravity – Conformal Gravity (motivated by an attempt to unify

gravity and EM) •  See recent paper on this topic: http://arxiv.org/pdf/1110.5026

How did Galaxies Form? •  Hierarchical merging •  For

–  Mergers seen –  Ellipticals in high density

environments –  Irrs isolated

•  Against –  Ellipticals seen at early epochs –  Irregulars forming today

•  Initial Collapse •  For

–  Ellipticals are old –  Ellipticals seen at high z –  Spirals/Irrs rotating –  Irregulars forming today

•  Against –  Mergers seen

PROBABLY SOME OF EACH OCCURRING

How did Galaxies Form ?

•  Hierarchical Merging •  Initial Collapse TWO COMPETING SCENARIOES

TIME

The Antennae Galaxy: mid-merger

Formation of an Elliptical galaxy

Quiescent Period

Era of SF, Mergers and HTF formation

27  

Puang  it  together  ?  Dark  MaSer                                                        Baryonic  MaSer  0yrs      5Gyrs  

   

   13Gyrs  

Rapid  merging  

Slow  merging  

SMBHs  AGN  

BULG

ES  

DISKS  

P-­‐BU

LGES  

??  

??  ??  

??  

COLLAPSE  

INFALL  

SECULAR  

ACCE

LERA

TING                      DEC

ELER

ATING  

U  

Model  of  energy  output  of  Universe  v  data  

Orange  =  IniHal  collapse  &  mergers  Blue  =  Slow  gas  infall  Black  =  Total  energy  

UV  

OPTICAL  

NEAR-­‐IR  

Age  of  Universe  

Cluster Formation Simulation

John  Dubinski:  www.cita.utoronto.ca/~dubinski