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 matterwith 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)

g

Ng

ao

1=μ(x) x >>1

x=μ(x) x <<1

-- true gravitational acceleration

-- Newtonian acceleration

-- fixed acceleration parameter

No g=agμg

/||(Milgrom 1983)

The Algorithm: (acceleration based)

Asymptotically, 2/1

2

2

r

GMa

r

v o or oGMa=v 4

Flat rotation curves as r

Low accelerations:Ngag 0

For point mass: 20 / rGMag

, mass rotation vel. relationship

Predates most data.

Newtonian M/L ( ) for UMa spirals (Sanders & Verheijen 1998)rGvM /2

Discrepancy is larger not for larger galaxies but for galaxies withlower centripetal acceleration!

There exist an acceleration scale: 08 /10 cHscm

(cdm halos do not contain an acceleration scale.)

An acceleration scale:

Asymptotically flat rotation curves:

But also reproduces structure in inner regions.

(Begeman 1990)

280 /102.1 scma

Tully-Fisher relation for UMagalaxies (Sanders & Verheijen 1998)

4 vM

bvaL )log()log(

4a

2810

log1.8cms

a

L

Mb o

oo cHcmsa 2810

oGMa=v 4 Mass-velocity relation

Tully-Fisher Relation: 4vL

(MOND sets slope and intercept.)

Baryonic TF relation (McGaugh):

The asymptotic rotation velocity ( dm determined by halo) istightly correlated with mass of baryons (including gas).

Mass of stellar disk Stellar disk including gas

450 vMb

450 vMb

Prediction for cdm halos (Steinmetz & Navarro 1999):

3vM

Baryon fraction must systematically decrease with halo mass— (baryonic blowout?) and maintain tight correlation.

All halos at a given time have similar densities:

with large scatter

Ga=Σ oc /

When then small discrepancy (HSB galaxies)cΣ>Σ

When then large discrepancy (LSB galaxies)cΣ<Σ

0.2cΣ gm/cm 2o pcM /860

With M/L = 1-2 implies critical surface brightness.2sec/22 arcmagμB

1. There exists a critical surface density

General trends:

(Globular clusters, luminous ellipticals)

(dwarf spheroidals, LSB spirals)

(embodied by MOND)

2. Newtonian discs are unstable. This implies an upper limit to the mean surface density of discs cΣ

Freeman’s Law: 2sec/22 arcmagμB

3. Rotation curve shapes

Low surface brightness

c

High surface brightness c

Rotation curve rises to asymptotic value

Rotation curve falls to asymptotic value

LSB:

HSB:

c

c

(Broeils)

(Begeman)

4. Isothermal spheres4.4. Isothermal spheres: g

dr

dp

1 where is given by the

MOND formulag

isIsothermal spheres have finite mass; MOND regime:

\

4

11 /10010

skmM

M

o

Faber-Jackson relationship: L with 4

r

GMa

dr

d or2/12

24

ln

ln

rd

dGMaor

or

Thus…

4 r

Also– sphere is truncated beyond

2/1

oeff a

GMr

This means that all isothermal pressure-supported objects have about the same internal acceleration: oa

skm /200100 Any object with

All pressure supported systems will lie on the same FJ relation

-- galaxy mass.

skm /1000skm /105

-- cluster of galaxies

-- globular cluster

Velocity dispersionvs. size for pressure supported systems

Points: molecular cloudsStars: globular clustersTriangles: dwarf Sph.Crosses: E. galaxiesDashes: compact dwarfsSquares: clusters of galaxies

Solid line corresponds to

oar

2

Within a factor of 5, all systems have same internal acceleration oa

Rotation curve analysis1. 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 from Poisson eq. (stars and gas in thin disc).

4. Calculate from MOND formula ( 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 forcedistribution (bars, warps, asymmetries)

Ng

goa

Examples

Dotted: New. stellar diskDashed: New. Gas discLong dashed: bulgeSolid: MOND

28102.1 cmsao

M/L is single parameter

Are the fitted values of M/L reasonable?

Points are fitted M/L valuesfor UMa spirals (Sanders& Verheijen 1998)

Curves are populationsynthesis 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:

D = 2.5 Mpc, M/L = 1.6

(Swaters 1999)8

0 102.1 a 2/ scm

Dwarf, LSB galaxy.

Concentration of light and gas 1.5<R<2 …

Corresponding featureIn Newtonian and TOTAL rotation curves.

(largely from stars)

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 = 2.58

0 102.1 a 2/ scm

(Zwaan, Bosma & van der Hulst)

Renzo’s law:

For every feature in the surface brightness distribution(or gas surface density distribution) there is a correspondingfeature in the observed rotation curve (and vice versa).

Dark Matter?

Seems un-natural

But with MOND (or modification of gravity) this is expected.

Distribution of baryons determines the distribution of dark matter-- Halo with structure.

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 :

No new problem for MOND– but DM is dissipationless!

Clowe et al. 2006

Non-baryonic dark matter exists!

Neutrinos

Only question is how much. ?

2TWhen MeV neutrinos in thermal equilibrium with photons.

112 nn 3cm

Number density of neutrinos comparable to that of photons.

per type, at present.

Three types of active neutrinos: ,,e

05.0m

Oscillation experiments measure difference in squares of masses.

eV for most massive type.

Absolute masses not known, but experimentally 2.2e

m eV

(tritium beta decay)

If eV then eV for all types

21e

m 21m

m062.0 and mb 4.1/

Possible that 12.0 8.2/ band

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 • But underpinned by new physics?

oo cHa

Or, is MOND a summary of how DM behaves?Ubiquitous appearance of -- acceleration at which discrepancy appears in galaxies. -- normalization of TF -- normalization of FJ -- internal acceleration of spheroidal systems (sub-gal.) -- critical surface brightnesswould seem difficult to understand in the context of DM.

0cH

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: )( 2,,

2 qVqL

q is non dynamical scalar playing role of

An obvious extension is to make q dynamical.then,

)( 2,,

2,, qVqqqL

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 GALAXIESbut on scale of clusters and third-peak!

2 scalars: matter coupling field yields MOND

coupling strength field– oscillations provide cosmic CDM

q