Stacy McGaugh

Dark Matter Laws of Galactic Dynamics: what every Physicist

should Know beyond Flat Rotation Curves

with collaboratorsFederico Lelli (CWRU/ESO)Jim Schombert (U. Oregon)

Marcel Pawlowski (CWRU/UC Irvine)

support fromNASA (Spitzer; ADAP)

The John Templeton Foundation

McGaugh, Lelli, & Schombert 2016, PRL, 117, 201101

Lelli

Schombert

PawlowskiLelli, McGaugh, Schombert, & Pawlowski 2016, ApJ, 836, 152

16 May 2017 CWRU

and input from the entire HI radio interferometry community

with collaboratorsFederico Lelli (CWRU/ESO)Jim Schombert (U. Oregon)

Marcel Pawlowski (CWRU/UC Irvine)

and support fromNASA (Spitzer; ADAP)

The John Templeton Foundation

McGaugh S. S., Lelli F., & Schombert J. M. 2016, PRL, 117, 201101

Lelli

Schombert

PawlowskiLelli F., McGaugh S. S., Schombert J. M., & Pawlowski 2016, ApJ, 836, 152

16 May 2017 CWRU

and the entire HI radio interferometry community

FL

SSM

Rubi

n, T

honn

ard,

& F

ord

1978

, ApJ

, 225

, L10

7Rotation curves become flat at large radii.

Rubi

n, T

honn

ard,

& F

ord

1978

, ApJ

, 225

, L10

7Rotation curves become flat at large radii.

There is ample evidence for mass discrepancies - not just rotation curves & clusters & CMB

Rubi

n, T

honn

ard,

& F

ord

(197

8)

Flat rotation curves

de Blok & McGaugh (1996, 1997)Lelli et al. (2011, 2013, 2016)Famaey & McGaugh (2012)

Tully-Fisher Relation

Tully

& F

isher

(197

7)

Pers

ic &

Sal

ucci

(199

1)

Surface brightness dependence

Sancisi (1995; 2004)

“When you see a feature in the light, you see a corresponding feature in the rotation curve, and vice-versa.”

Renzo’s Rule

Acceleration scale

Sanders (1990)

“Universal” Rotation Curve

Many regularities have been noted in rotation curves

SPARC is a sample of - 176 disk galaxies with - Spitzer 3.6 micron photometry tracing the stellar mass - high-quality HI/H! rotation curves tracing the gravitational potential

all have 21 cm cubes - all late morphological types (S0 to Irr - basically everything that rotates)

Federico Lelli | Stacy McGaugh | James Schombert

All data available on-line: http://astroweb.case.edu/SPARC/

Lelli, McGaugh, & Schombert 2016, ApJ, 827, 19

SPARC is a sample of - 176 disk galaxies with - Spitzer 3.6 micron photometry tracing the stellar mass - high-quality HI/H! rotation curves tracing the gravitational potential

all have 21 cm cubes - all late morphological types (S0 to Irr - basically everything that rotates)

Federico Lelli | Stacy McGaugh | James Schombert

All data available on-line: http://astroweb.case.edu/SPARC/

Lelli, McGaugh, & Schombert 2016, ApJ, 827, 19

SPARC provides a comprehensive view of disk galaxy properties

SPARC provides a comprehensive view of disk galaxy properties

F549-1Milky Way

NGC 6946 stars & gas

SPARC has well resolved data for both stars and gas for all galaxies

NGC 6946 velocity field

e.g., THINGS (Walter et al. 2008de Blok et al. 2008)

SPARC has rotation curves derived from 21 cm velocity fields

V sini = Vsys + Vc cosθ + Vr sinθ

F568-1

Surface photometry quantifies the variation of surface brightness with radius. These data are used to numerically solve the Poisson equation to obtain the gravitational potential of the stars.

bulge

stellar disk

Surf

ace

Bri

ghtn

ess

�@�⇤@R

= 2⇡G⌃⇤

M⇤ = ⌥⇤L

We observe the light distribution. We need to know the stellar mass distribution. This introduces an unavoidable conversion factor, the stellar mass-to-light ratio ⌥⇤

Expect the near-IR to be the best tracer of the mass. - least scatter - least dependent on color

Note: this is not necessary for the gas, as the conversion from flux to mass is well known from the physics of the 21 cm spin-flip transition of atomic hydrogen.

bulge

disk

⌥[3.6]⇤ = 0.7 M�/L�

⌥[3.6]⇤ = 0.5 M�/L�

Simple modelA single mass-to-light ratio for the bulge and disk of all galaxies

Only 31 SPARC galaxies have a significant bulge.

NGC 6946

Rotation curve data fromBoomsma et al (2008) [HI]Daigle et al (2006) [H!]Blais-Ouellette et al (2004) [H!]

VfMass model

bulge gas

stellar disk

baryons

Construct mass models for all SPARC galaxies Attempt to control for systematics: Reject

- 12 galaxies for being messed-up strong asymmetries in velocity field

indication of non-circular motions - 10 galaxies for being too face-on

i < 30o causes 1/sin(i) errors to blow up - 698 individual points with uncertainty > 10% in V

leaves 2693 points in 153 galaxies

baryons

Vf

Vbar

total

Vbar < Vf

The observed stars and gas cannot account for the total rotation (assuming Newtonian gravity).

Sancisi (1995; 2004)

“When you see a feature in the light, you see a corresponding feature in the rotation curve, and vice-versa.”

Renzo’s Rule

Sancisi (1995; 2004)

“When you see a feature in the light, you see a corresponding feature in the rotation curve, and vice-versa.”

Renzo’s Rule

Small bulge (4% of total light) causes sharp rise & fall of inner rotation curve

Sancisi (1995; 2004)

“When you see a feature in the light, you see a corresponding feature in the rotation curve, and vice-versa.”

Renzo’s Rule

Small bulge (4% of total light) causes sharp rise & fall of inner rotation curve

Asymmetry in gas distribution causes dip in rotation curve

Note that this occurs despite apparent dark matter domination

star

dom

inat

ed H

SB

gas dominated LSBs

Rotation curves are flat; amplitude of flat rotation correlates with mass

Stellar Mass Tully-Fisher relation

line-width outer (flat) velocityga

s dom

inated

star d

omina

tedX

McGaugh et al. (2000)

Gurovich et al. (2010)

Begum et al. (2008)Trachternach et al. (2009)

McGaugh (2005)Stark et al. (2009)Begum et al. (2008)Trachternach et al. (2009)

Stellar mass

M⇤ = ⌥⇤L

Baryonic Tully-Fisher relation

line-width outer (flat) velocityga

s dom

inated

star d

omina

tedX

McGaugh et al. (2000)

Gurovich et al. (2010)

Begum et al. (2008)Trachternach et al. (2009)

McGaugh (2005)Stark et al. (2009)

slope: x = 3.5 slope: x = 4

Begum et al. (2008)Trachternach et al. (2009)

Baryonic mass

Mb = M⇤ +Mg

outer (flat) velocityga

s dom

inated

star d

omina

tedX

McGaugh et al. (2000)

Gurovich et al. (2010)

Begum et al. (2008)Trachternach et al. (2009)

McGaugh (2005)Stark et al. (2009)

slope: x = 4

Begum et al. (2008)Trachternach et al. (2009)

Tully-Fisher is, fundamentally,

a relation between baryonic mass

(stars+gas) and the amplitude of the

flat rotation speed

Mb = AV 4f

A = 47± 6 M� km�4 s4

Negligible intrinsic scatter

Two galaxies with the same baryonic mass Mb, same Vf

- Indistinguishable on TF plane -

but have different baryonic mass distributions and different rotation curves

NGC 2403

UGC 128

Images as the same physical scale

HSB LSB

NGC 2403

UGC 128

mass

surf

ace

brig

htne

ss

radius in kpc

radius in scale lengths

Famaey & McGaugh (2012)

SPARC

optical data + popsynth M*/L

near-IR data with constant M*/L

The distribution of luminous mass is reflected in the shape

of the rotation curve.

High surface brightness galaxies have rapidly rising rotation curves

Low surface brightness galaxies have slowly rising rotation curves

Rb Re R2.2

Vb

Vf

[3.6] surface brightness profile

Rotation curve

HSB galaxy

High surface brightness galaxies have rapidly rising rotation curves

RbReR2.2

Vb

Vf

[3.6] surface brightness profile

Rotation curve

LSB galaxy

Low surface brightness galaxies have slowly rising rotation curves

⌃dyn(0) =1

2⇡G

Z 1

0

V 2(R)

r2dR

cent

ral d

ynam

ical

surf

ace

dens

ity

central surface brightness stellar mass

Light predicts mass. X & Y axes are independent.

Toomre (1963)

The central dynamical surface density measured by the inner rotation curve gradient correlates with the central surface brightness (more so than mass).

⌃dyn(0) =1

2⇡G

Z 1

0

V 2(R)

r2dR

cent

ral d

ynam

ical

surf

ace

dens

ity

central surface brightness stellar mass

Light predicts mass. X & Y axes are independent.

Light =

Mass

No dark m

atter

necessa

ry

Toomre (1963)

The central dynamical surface density measured by the inner rotation curve gradient correlates with the central surface brightness (more so than mass).

⌃dyn(0) =1

2⇡G

Z 1

0

V 2(R)

r2dR

cent

ral d

ynam

ical

surf

ace

dens

ity

central surface brightness stellar mass

Light predicts mass. X & Y axes are independent.

Light =

Mass

No dark m

atter

necessa

ry

Need dark matter

Toomre (1963)

The central dynamical surface density measured by the inner rotation curve gradient correlates with the central surface brightness (more so than mass).

Rb Re R2.2

Vb

Vf

[3.6] surface brightness profile

Rotation curve

The observed centripetal acceleration is linked to that predicted by the observed distribution of baryons.

gbar = |r�|r2� = 4⇡G⇢

gobs

=V 2

R

What about everything in between?

gobs

=V 2

Rgbar = |@�

@R|

determined from rotation curve determined from baryon distribution

independent quantities

Radial Acceleration

Relation

153 galaxies

rms = 0.13s = 0.11

Radial Acceleration

Relation

153 galaxies

gobs

=gbar

1� e�p

gbar/g†

well fit by

±0.02 (random)± 0.24 (systematic)

g† = 1.20⇥ 10�10 ms�2

rms = 0.13s = 0.11

Radial Acceleration

Relation

153 galaxies

gobs

=gbar

1� e�p

gbar/g†

well fit by

±0.02 (random)± 0.24 (systematic)

g† = 1.20⇥ 10�10 ms�2

observed rms scatter

scatter expected from observational errors

The data are consistent with zero intrinsic scatter

rms = 0.13s = 0.11

Residuals from the relation do not correlate with any physical property

radius

local gas fractionsurface brightness

residuals

±0.02 (random)± 0.24 (systematic)

g† = 1.20⇥ 10�10 ms�2

gobs

= F(gbar

) F =gbar

1� e�p

gbar/g†

gDM

= gobs

� gbar

gDM = F(gbar)� gbar

total

dark matter

The dark matter distribution is specified by the baryon distribution

The Radial Acceleration Relation can be used to infer the dark matter distribution just by looking at a galaxy.

One consequence for dark matter

That’s weirdThe baryonic tail wags the dark matter dog.

Sancisi (1995; 2004)

“When you see a feature in the light, you see a corresponding feature in the rotation curve, and vice-versa.”

Renzo’s Rule

Sancisi (1995; 2004)

“When you see a feature in the light, you see a corresponding feature in the rotation curve, and vice-versa.”

Renzo’s Rule

The Radial Acceleration Relation maps between what we see and what we get.

Laws of Galactic Rotation1. Rotation curves tend towards asymptotic flatness

2. Baryonic Tully-Fisher Relation

3. Central Density Relation

4. Radial Acceleration Relation

5. Renzo’s Rule

Vf ! constant

Mb / V 4f

g

bar

predictive of g

obs

⌃light predictive of ⌃mass

“When you see a feature in the light, you see a corresponding feature in the rotation curve, and vice-versa.”

gobs

=gbar

1� e�p

gbar/g†