Dark MatterASTR 333/433

Fall 2013MoTu 4:00-5:15pm

Sears 552

Prof. Stacy McGaughSears 573368-1808

stacy.mcgaugh@case.edu

Logistics:

• Abstracts for 433 talks due now• 433 talks 12/2 & 12/3 (next week)• Homework 4 due 12/3• Review 12/9 (11 AM)• Final 12/11 (9 AM)

Today: MOND

What gets us into trouble is not what we don’t know.

It’s what we know for sure that just aint so.

- Mark Twain

A few things we know for sure...

∇2Φ = 4πGρF = ma

which basically means

mV2/R = GMm/R2

i.e,

V2 = GM/R

The universe is filled with non-baryonic cold dark matter.

ergo...

Newton saysV2 = GM/R.Equivalently,Σ = M/R2

V4 = G2MΣ

ThereforeDifferent Σshould meandifferent TF

normalization.

μ = -2.5 logΣ +C

TF Relation

No residuals from TF with size or surface density for disks

V 2 =GM

R⇥ � log(V )

� log(R)= �1

2 expected slope (dotted line)

large range in size at a given mass or velocity

Note:

For disk galaxies

Newton says: V 2

R=

GM

R2= G(�b + �DM )

� =M

R2surface density

So we infer that �DM � �b

(i.e., that all disks are dark matter dominated)in order to explain the lack of TF residuals with luminous size Rp

But we also infer that the baryons do matter...

3. Gravitational force correlates with baryonic surface density

central baryonic surface density

acceleration at peak of baryonic rotation curvea � �1/2

b

(would be linear if just Newton with no dark matter)

Lack of TF residuals says baryon distribution does not matter.

V 2

R= G (�b + �DM )

Correlation of dynamical force with observed surface density says the baryon distribution does matter.

But wait - before we decided �b � �DM

Now is observed to correlate with gravitational force. Is this a contradiction?

⌃b

or maybe w

e’ve been using the wrong equation

74 galaxies> 1000 points

(all data)

60 galaxies> 600 points(errors < 5%)

radius

orbitalfrequency

acceleration

McGaugh (2004)

Not just any force law...

No unique size scale in the data. Can generically exclude any modification of gravity where a change in the force law appears at a specific length scale.

There is a characteristic acceleration scale in the data

a = gN for a ≫ a0

µ

(

a

a0

)

a = gN

µ(x) → 1 for x ≫ 1 µ(x) → x for x ≪ 1

a =√

gNa0 for a ≪ a0

MONDModified Newtonian Dynamics (Milgrom 1983)

a0

Instead of invoking dark matter, modify gravity (or inertia). Milgrom suggested a

modification at a particular acceleration scale

x =

a

a0

∇

[

µ

(

∇Φ

a0

)

∇Φ

]

= 4πGρ

Derived from aquadratic Lagrangian of Bekenstein & Milgrom (1984) to satisfy energy conservation.

(t,x) ! �(t,x)MOND regime invariant under transformations

Newtonian regime MOND regime

Regimes smoothly joined by

Modified Poisson equation

• The Tully-Fisher Relation

• Slope = 4

• Normalization = 1/(a0G)

• Fundamentally a relation between Disk Mass and Vflat

• No Dependence on Surface Brightness

• Dependence of conventional M/L on radius and surface brightness

• Rotation Curve Shapes

• Surface Density ~ Surface Brightness

• Detailed Rotation Curve Fits

• Stellar Population Mass-to-Light Ratios

MOND predictions

“Disk Galaxies with low surface brightness provide particularly strong tests”

None of the following data existed in 1983.At that time, LSB galaxies were widely

thought not to exist.

• The Tully-Fisher Relation

• Slope = 4

• Normalization = 1/(a0G)

• Fundamentally a relation between Disk Mass and Vflat

• No Dependence on Surface Brightness

• Dependence of conventional M/L on radius and surface brightness

• Rotation Curve Shapes

• Surface Density ~ Surface Brightness

• Detailed Rotation Curve Fits

• Stellar Population Mass-to-Light Ratios

MOND predictions

✔✔✔

✔ !

In MOND limit of low acceleration

a =

√

gNa0

V 2

R=

√

GM

R2a0

V4

= a0GM

observed TF!

• The Tully-Fisher Relation

• Slope = 4

• Normalization = 1/(a0G)

• Fundamentally a relation between Disk Mass and Vflat

• No Dependence on Surface Brightness

• Dependence of conventional M/L on radius and surface brightness

• Rotation Curve Shapes

• Surface Density ~ Surface Brightness

• Detailed Rotation Curve Fits

• Stellar Population Mass-to-Light Ratios

MOND predictions

✔✔✔

✔

✔

• The Tully-Fisher Relation

• Slope = 4

• Normalization = 1/(a0G)

• Fundamentally a relation between Disk Mass and Vflat

• No Dependence on Surface Brightness

• Dependence of conventional M/L on radius and surface brightness

• Rotation Curve Shapes

• Surface Density ~ Surface Brightness

• Detailed Rotation Curve Fits

• Stellar Population Mass-to-Light Ratios

MOND predictions

✔✔✔

✔

✔

✔

• The Tully-Fisher Relation

• Slope = 4

• Normalization = 1/(a0G)

• Fundamentally a relation between Disk Mass and Vflat

• No Dependence on Surface Brightness

• Dependence of conventional M/L on radius and surface brightness

• Rotation Curve Shapes

• Surface Density ~ Surface Brightness

• Detailed Rotation Curve Fits

• Stellar Population Mass-to-Light Ratios

MOND predictions

✔✔✔

✔

✔

✔

✔

surface brightness

mas

s su

rfac

e de

nsity

= V

2 /(G

h)

Not

a fit

MO

ND

D

In NGC 6946, a tiny bulge (just 4% of thetotal light) leaves a distinctive mark.

NGC 6946

D

In NGC 1560, a marked feature in the gas is reflected in the kinematics, even though dark matter should be totally dominant.

NGC 1560

Sand

ers &

McG

augh

200

2, A

RA&

A, 40,

263

Sand

ers &

McG

augh

200

2, A

RA&

A, 40,

263

Sand

ers &

McG

augh

200

2, A

RA&

A, 40,

263

Residuals of MOND fits

Famaey, B., & McGaugh, S.S. 2012, Living Reviews in Relativity, 15, 10

• The Tully-Fisher Relation

• Slope = 4

• Normalization = 1/(a0G)

• Fundamentally a relation between Disk Mass and Vflat

• No Dependence on Surface Brightness

• Dependence of conventional M/L on radius and surface brightness

• Rotation Curve Shapes

• Surface Density ~ Surface Brightness

• Detailed Rotation Curve Fits

• Stellar Population Mass-to-Light Ratios

MOND predictions

✔✔✔

✔

✔

✔

✔

✔

Line: stellar population model(mean expectation)

• The Tully-Fisher Relation

• Slope = 4

• Normalization = 1/(a0G)

• Fundamentally a relation between Disk Mass and Vflat

• No Dependence on Surface Brightness

• Dependence of conventional M/L on radius and surface brightness

• Rotation Curve Shapes

• Surface Density ~ Surface Brightness

• Detailed Rotation Curve Fits

• Stellar Population Mass-to-Light Ratios

MOND predictions

✔✔✔

✔

✔

✔

✔

✔

✔

Example utility: our own Galaxy

You are here

8 kp

c

Example utility: our own Galaxy

Put in mass distribution (Flynn et al 2006);Get out rotation curve (no fitting)

Luna et al. (2006: CO); McClure-Griffiths & Dickey (2007: HI); Xue et al. (2008: BHB)

You

are

here

McGaugh, S.S. 2008, ApJ, 683, 137

stel

lar d

isk

edge

Recovering surface density from rotation velocity:

Σ(R) =V 2

2πGR

Σ(R) =1

2πG

[

1

R

∫ R

0

dV 2c

drK

(

r

R

)

dr +

∫

∞

R

dV 2c

drK

(

R

r

)

dr

r

]

only works for spheres.

For disks, need

which has a proclivity to blow up.

Instead, do by trial and error

Can we do better?

McGaugh, S.S. 2008, ApJ, 683, 137

Can we do better fitting the details of the terminal velocity curve?

Luna et al. (2006: CO); McClure-Griffiths & Dickey (2007: HI); Xue et al. (2008: BHB)

Fitting the details of the terminal velocity curve

Fitting the details of the terminal velocity curve

Fitting the details of the terminal velocity curve

Fitting the details of the terminal velocity curve

Fitting the details of the terminal velocity curve

Milky Way structure

Surface density

total

gas

disk

bulge

Bovy & Rix (2013)

Bovy & Rix (2013)

Surface density from radial and vertical force in good agreement

I find your lack of faith disturbing.

• You don’t know the Power of the Dark Side

• Can MOND explain large scale structure?

• Can it provide a satisfactory cosmology?

• Can it be reconciled with General Relativity?

Review of relativistic theoriescontaining MOND in the appropriate limit

• You don’t know the Power of the Dark Side

• Can MOND explain large scale structure?

• Can it provide a satisfactory cosmology?

• Can it be reconciled with General Relativity?

7.1 Scalar-tensor k-essence 7.2 Stratified theory 7.3 Original Tensor-Vector-Scalar theory 7.4 Generalized Tensor-Vector-Scalar theory 7.5 Bi-Scalar-Tensor-Vector theory 7.6 Non-minimal scalar-tensor formalism 7.7 Generalized Einstein-Aether theories 7.8 Bimetric theories 7.9 Dipolar dark matter 7.10 Non-local theories and other ideas

{Famaey, B., & McGaugh, S.S. 2012, Living Reviews in Relativity, 15, 10

Bruneton - maximum acceleration inevitable in quantum gravity

I find your lack of faith disturbing.

• You don’t know the Power of the Dark Side

• Can MOND explain large scale structure?

• Can it provide a satisfactory cosmology?

• Can it be reconciled with General Relativity?

• Does it survive other tests?

Clusters problematic

Clusters of galaxies

(Sanders & McGaugh 2002)

dark matter shouldn’t needdark matter

1E 0657-56 - “bullet” cluster (Clowe et al. 2006)

direct proof of dark matter?

bullet cluster shows samebaryon discrepancy in MOND

as other galaxy clusters

MOND𝚲CDM

Famaey, B., & McGaugh, S.S. 2012, Living Reviews in Relativity, 15, 10

discrepancy in clusters appears real. LCDM not much better

observed shock velocity

CDM

bullet cluster collision velocity

Angus & McGaugh (2008) MNRAS, 383, 417

observed shock velocity

MOND

bullet cluster collision velocity

Angus & McGaugh (2008) MNRAS, 383, 417

Bullet cluster

• Mass discrepancy more naturally explained with dark matter.

• Collision velocity more naturally explained with MOND.

Bournaud et al. (2007) Science, 316, 1166

Tidal Debris Dwarfs - should be devoid of Dark Matter

Gentile et al. (2007)A&A, 472, L25

Tidal dwarfsdo show mass

discrepancies asexpected in MOND

A new test: the dwarf satellites of Andromeda

McGaugh & Milgrom 2013, ApJ, 766, 22; also ApJ, 775, 139

gin < gex < a0gin < a0 < gex

gin < a0gin > a0

Newtonian regime MOND regime

External Field dominantquasi-Newtonian regime

External Field dominantNewtonian regime

M =

RV 2

G

M =

RV 2

G

M =

a0

gex

RV 2

G

M =

V 4

a0G

e.g.,Eotvos-type

experiment on the surface of

the Earth

e.g.,remotedwarfLeo I

e.g.,nearbySgr

dwarf

e.g.,surfaceof theEarth

And XVII 2.60E+05 381 2.9 2.5

And XXVIII 2.10E+05 284 4.9 4.3

Name Luminosity Re �obs

�pred

isolated

EFE

• In some flavors of relativistic theories, e.g., TeVeS, what matters is the potential gradient.

‣ Predicts strong effects at saddle points between massive bodies (e.g., sun-planet)

• MOND violates the Strong Equivalence Principle, leading to the External Field Effect - the Galactic field might matter in the Solar System.

‣ Predicts modest precession of outer planets

There can be more subtle effects

Galianni et al. arXiv:1111.6681

EarthMoon

to Sun

⇥�� 0

near saddle point,so

|gN|a0

becomes small,and strong MONDeffects can occurin a small region (theory specific,e.g., TeVeS - Bekenstein & Magueijo 2006)

SP

contours of phantom dark matter

• Disk Stability • Freeman limit in surface brightness distribution• thin disks• velocity dispersions • LSB disks not over-stabilized

• Dwarf Spheroidals

• Giant Ellipticals

• Clusters of Galaxies

• Structure Formation

• Microwave background• 1st:2nd peak amplitude; BBN• early reionization• enhanced ISW effect• 3rd peak

Other MOND tests

✔✔✔

✔

✔

✔

?

✔✔

✔

X

XNo MetricDon’t know expansion history

XX