Transcript From dark matter to MOND

From dark matter to MOND
or
Problems for dark matter on galaxy
scales
R.H. Sanders, Blois, 2008
MOND:
French: the world
German: the moon
Dutch: mouth
Astronomers: Modified Newtonian Dynamics.
(Milgrom 1983– alternative to dm.)
What is MOND?
(a minimalist definition)
MOND is an algorithm that permits calculation
of the radial distribution of force in an object from
the observable distribution of baryonic matter
with only one additional fixed parameter having
units of acceleration.
It works!
(at least for galaxies)
And this is problematic for dark matter.
Moreover, explains systematic aspects of
galaxy photometry and kinematics, and…..
makes predictions! (cdm gets it wrong)
The Algorithm: (acceleration based)
(Milgrom 1983)



g μ| g | / ao  = g N
g
gN
-- Newtonian acceleration
ao
-- fixed acceleration parameter
-- true gravitational acceleration
μ(x)= 1
x>>1
μ(x)= x
x <<1
Low accelerations:
g  GMa 0 / r
For point mass:
Flat rotation curves as
2
1/ 2
v  GMao 
 2 
r  r 
2
Asymptotically,
g  a0 g N
r 
or
4
v = GMao
, mass rotation vel. relationship
Predates most data.
An acceleration scale:
Newtonian M/L ( M  v2G / r ) for UMa spirals (Sanders & Verheijen 1998)
Discrepancy is larger not for larger galaxies but for galaxies with
lower centripetal acceleration!
There exist an acceleration scale:
8
10 cm / s  cH0
(cdm halos do not contain an acceleration scale.)
Asymptotically flat rotation curves:
(Begeman 1990)
But also reproduces structure in inner regions.
a0  1.2 108 cm / s2
4
v = GMao

Tully-Fisher Relation:
Lv
(MOND sets slope and intercept.)
log(L)  a log(v )  b
a4
 M 
ao

b  8.1  log

 8
2  
 L  10 cms  
 ao  108 cms2  cHo
Tully-Fisher relation for UMa
galaxies (Sanders & Verheijen 1998)
M  v
Mass-velocity relation
4
4
Baryonic TF relation (McGaugh):
Mass of stellar disk
Stellar disk including gas
Mb  50 v
4
The asymptotic rotation velocity ( dm determined by halo) is
tightly correlated with mass of baryons (including gas).
Mb  50 v
4
Prediction for cdm halos (Steinmetz & Navarro 1999):
All halos at a given time have similar densities:
M v
3
with large scatter
Baryon fraction must systematically decrease with halo mass—
(baryonic blowout?) and maintain tight correlation.
General trends:
(embodied by MOND)
1. There exists a critical surface density
Σc = ao / G
Σc  0.2 gm/cm  860 Mo / pc2
With M/L = 1-2 implies critical surface brightness.
μB  22 mag/ arcsec2
Σ > Σc then small discrepancy (HSB galaxies)
When
(Globular clusters, luminous ellipticals)
When
Σ < Σc
then large discrepancy (LSB galaxies)
(dwarf spheroidals, LSB spirals)
2. Newtonian discs are unstable. This implies an upper limit
to the mean surface density of discs Σ c
Freeman’s Law:
μB  22 mag/ arcsec2
3. Rotation curve shapes
Low surface
  c
brightness
Rotation curve rises to asymptotic value
High surface brightness
  c
Rotation curve falls to asymptotic value
LSB:
  c
(Broeils)
HSB:
  c
(Begeman)
4. Isothermal spheres
4. Isothermal spheres:
1 dp
 g
 dr
where g is given by the
MOND formula
\
is
Isothermal
spheres have finite mass; MOND regime:

 r d
GMao 

 dr
r
2
Thus…
1/ 2
or
 d ln  
 r  GMao 

 d ln r 
2
4
M





11
10 M o  100km / s 
Faber-Jackson relationship:
 r
L 
4
with
 4
4
Any object with
  100  200 km / s
  1000km/ s
  5  10 km/ s
-- galaxy mass.
-- cluster of galaxies
-- globular cluster
All pressure supported systems will lie on the same FJ
relation
Also– sphere is truncated beyond
reff
 GM

 a
o

1/ 2




This means that all isothermal pressure-supported objects have about
the same internal acceleration:
ao
Velocity dispersion vs. size for pressure supported systems
Points: molecular clouds
Stars: globular clusters
Triangles: dwarf Sph.
Crosses: E. galaxies
Dashes: compact dwarfs
Squares: clusters of galaxies
Solid line corresponds to
2
r
 ao
Within a factor of 5, all systems have same internal acceleration  ao
Rotation curve analysis
1. Assume– light traces mass (M/L = constant in a given galaxy)
But which band? Near IR is best.
2. Include HI with correction for He.
3. Calculate g N from Poisson eq. (stars and gas in thin disc).
4. Calculate g from MOND formula (ao fixed).
Compute rotation curve and adjust M/L until fit is optimal.
M/L is the single free parameter.
Warning: Not all rotation curves are perfect tracers of radial force
distribution (bars, warps, asymmetries)
Examples
Dotted: New. stellar disk
Dashed: New. Gas disc
Long dashed: bulge
Solid: MOND
ao  1.2 108 cms2
M/L is single
parameter
Are the fitted values of M/L reasonable?
Points are fitted M/L values
for UMa spirals (Sanders
& Verheijen 1998)
Curves are population
synthesis models
(Bell & de Jong 2001)
Can measure light and gas distribution, color,
take M/L from pop. synthesis, and…
Predict rotation curves!
(no free parameters).
Dark matter does not do this (can’t).
Fit rotation curves by adjusting parameters.
UGC 7524:
Dwarf, LSB galaxy.
Concentration of light
and gas 1.5<R<2 …
Corresponding feature
In Newtonian and
TOTAL rotation curves.
(largely from stars)
D = 2.5 Mpc, M/L = 1.6
a0  1.2 108 cm / s
2
(Swaters 1999)
UGC 6406:
LSB with cusp in
light distribution….
sharply rising rotation curve
Gas becomes dominant in
outer regions….
asymptotically rising
rotation curve
D = 26.4 Mpc, M/L = 2.5
a0  1.2 108
cm / s 2
(Zwaan, Bosma & van der Hulst)
Renzo’s law:
For every feature in the surface brightness distribution
(or gas surface density distribution) there is a corresponding
feature in the observed rotation curve (and vice versa).
Dark Matter?
Distribution of baryons determines the distribution of dark matter-Halo with structure.
Seems un-natural
But with MOND (or modification of gravity) this is expected.
What you see is all there is!
With MOND clusters still require undetected (dark) matter!
(The & White 1984, Gerbal et al. 1992, Sanders 1999, 2003)
Bullet cluster :
Clowe et al. 2006
No new problem for MOND– but DM is dissipationless!
Non-baryonic dark matter exists!
Neutrinos
Only question is how much.
When

T  2 MeV
  ?
neutrinos in thermal equilibrium with photons.
Number density of neutrinos comparable to that of photons.
3
n  n  112 cm
Three types of active neutrinos:
per type, at present.
 e ,  ,
Oscillation experiments measure difference in squares of masses.

m  0.05 eV for most massive type.
Absolute masses not known, but experimentally
m e  2.2
eV
(tritium beta decay)
If
m e  1 2 eV then m  1 2 eV for all types
   0.062m
Possible that
and
  0.12
 / b  1.4m
and
 / b  2.8
Phase space constraints– will collect in clusters, not in galaxies.
Successes of MOND
• Predicts observed form of galaxy rotation curves
from observable mass distribution. Reasonable
M/L.
• Presence of preferred surface density in spirals
(Freeman law). LSB– large discrepancy,
HSB– small discrepancy.
• Preferred internal acceleration in near-isothermal
pressure supported systems (molecular clouds to
clusters of galaxies).
• Existence of TF for spirals, FJ relation
for pressure-supported in general.
• All with ao  cHo
• But underpinned by new physics?
Or, is MOND a summary of how DM behaves?
Ubiquitous appearance of cH0
-- acceleration at which discrepancy appears in galaxies.
-- normalization of TF
-- normalization of FJ
-- internal acceleration of spheroidal systems (sub-gal.)
-- critical surface brightness
would seem difficult to understand in the context of DM.
Correlation of DM with baryons implied by MOND is curious
-- behave differently (dissipative vs. non-dissipative).
90% of baryons are missing from galaxies (weak lensing).
Baryonic blowout, halo collisions… haphazard processes.
Why is TF relation so good?
How do leftover baryons determine properties of DM halo?
Solar system tests
The holy grail of modified gravity theories.
Just as direct particle detection for dark matter theories.
(Sanders astro-ph/0602161, Bekenstein & Magueijo astro-ph/0602266)
Pioneer effect, MOND regions between earth and sun.
An alternative:
TeVeS as written:
,
L  q ,  V (q )
2
q is non dynamical scalar playing role of
2

.
An obvious extension is to make q dynamical.
then,
,
,
L  q, q  q ,  V (q )
2
2
Biscalar tensor vector theory
For reasonable V(q), oscillations develop early (pre-recombination)
Scalar field oscillations develop as q settles to bottom of V(q).
May have long de Broglie wavelength
NO CLUSTERING ON SCALE OF GALAXIES
but on scale of clusters and third-peak!

2 scalars:

q
matter coupling field
yields MOND
coupling strength
field– oscillations
provide cosmic CDM