(dynamical) mass determinations and scaling relations of etgs … · 2014. 7. 23. · faber-jackson...

(Dynamical) Mass Determinations

and Scaling Relations of ETGs at Small Scale

Michele Cappellari

2014-07-21 M. Cappellari, IAU 311, Oxford 1

http://www.ox.ac.uk/

Why dynamical scaling relations?

Relate size, luminosity and kinematics

(Kinematics within 𝑅 ≲ 1𝑅e)

Originally proposed as distance estimators

Now ideal to compare galaxy formation models

Constrain evolution of

Mass, radius, density, M/L

Central dark matter

Stellar initial mass function


Faber-Jackson relation (𝐿, 𝜎)

𝐿 ∝ 𝜎4 (Luminosity versus velocity dispersion)

For elliptical galaxies

Implies M/L increase with luminosity

Faber-Jackson76 Bernardi+03 (9,000 SDSS)

log σ (km/s)

Mi (

mag)


Kormendy relation (𝐿, 𝑅𝑒)

Luminosity (or 𝜇e) versus half-light radius (𝑅𝑒)

For early-type galaxies

Popular at high-z as kinematics not needed

Kormendy77 Shen+03 (140,000 SDSS)

Mr (mag) Log Re (kpc)

μe (

ma

g/a

rcse

c2)

Re (

kp

c)


Fundamental Plane (𝐿, 𝜎, 𝑅𝑒)

Unifies luminosity, velocity dispersion and radius

For both elliptical and lenticular galaxies

Djorgovski-Davis87 Jorgensen+96

Dressler+87; Faber+87

E only E + S0


Fa

be

r+8

7 in

“N

ea

rly n

orm

al g

ala

xie

s”


Origin of Fundamental Plane

If galaxies were homologous systems in virial equilibrium with the same M/L

𝐿 ∝ 𝑀 ∝ 𝜎2𝑅

But observed slopes are different

𝐿 ∝ 𝜎1.25𝑅0.96

What produces ‘tilt’ in Fundamental Plane? Non-homology? (surface brightness/kinematics) Genuine M/L variation? (dark matter/population IMF)


Fundamental Plane Tilt Candidates

All candidates are possible: decades of debate (Renzini-Ciotti93; Prugniel-Simien94; Prugniel-Simien96; Ciotti+96; Busarello+97; Graham-Colless97; Prugniel-Simien97; Forbes+98; Bertin+02; Borriello+03; Trujillo+04)

Need to directly measure masses dynamics/lensing

Non-homology Stellar Population Dark Matter

Kormendy+09 Thomas+05 Moster+10


Orbit/particles-based modelling

images of model orbits (Cappellari+04) galaxy image (Schwarzschild codes: Richstone-Tremaine88; Rix+97; vanDerMarel+98;

Gebhardt+01; Valluri+04; Cappellari+06; Thomas+07; vanDenBosch+08)

V σ h3 h4 h5 h6

Syer-Tremaine96

Particle-based models

(de Lorenzi+09)

(also Dehnen+09; Long-Mao10;

Morganti-Gerhard12)

See review by Courteau+14 2014-07-21 M. Cappellari, IAU 311, Oxford 9

Jeans modelling Spherical models suffer from

mass-anisotropy degeneracy

(Binney-Mamon82)

Require high-order V moments

(vanDerMarel-Franx93; Gerhard93)

Axisymmetric models better constrained by 2-dim kinematics

Different PA show different components velocity ellipsoid

(e.g. Gerssen+97)

Mass and anisotropy act differently on kinematics

SAURON

𝑉2 + 𝜎2

𝛽𝑧 = 0

𝛽𝑧 = 0.1

𝛽𝑧 = 0.2

𝛽𝑧 = 0.3

Cappellari-08 JAM 2014-07-21 M. Cappellari, IAU 311, Oxford 10

The 𝑀 𝐿 − 𝜎 relation

Including non-homology of photometry/kinematics

Ever increasing data quality and sample size

M/L trend consistent with FP predictions

σ (not M or L) captures nearly all M/L variation

(Cappellari+06; Graves-Faber10)

Tilt is due to genuine M/L variation (DM/pop/IMF?)

log σ

log M

/L

log L

Magorrian+98 vanDerMarel-91 Cappellari+06 Cappellari+13a

log σ log σ

Long-slit + Jeans Iso. IFU + Schwarzschild IFU + Jeans Aniso.

36 gal. 37 gal. 25 gal. 260 gal.


Baryons dominate within 1Re

Flat rotation curves within ∼2Re (𝜌 ∝ 𝑟−2) (Gerhard+01)

Stars dominate within 1Re: 𝑓𝐷𝑀 𝑅𝑒 < 40% (Thomas+11)

Median 𝑓𝐷𝑀 𝑅𝑒 = 13% from 260 galaxies (Cappellari+13a)

Rotation curves from

spherical models

(Gerhard+01)

(Thomas+11)

Median(R)∼2Re

21 ETGs

16 ETGs


FP scatter due to population

Deviations from FP linked to population

Age, [Fe/H] and [Mg/Fe] increase with σ

“But no dependence on Re at fixed σ” (Graves+09)

(also Shankar-Bernardi09; vanDerWel+09; Valentinuzzi+10; Napolitano+10)

Graves+09b (SDSS) Springob+12 (6dF)

Magoulas+12

Population FP with population Fundamental Plane


FP = Virial equilibrium + M/L

MP has no intrinsic scatter FP scatter due to population

Follows virial prediction (as Cappellari+06, Bolton+08, Auger+10)

But technique used for Re does matter! (see Cappellari+13a)

Galaxy formation encoded in inclined views of MP

Mass Luminosity

(Cappellari+13a)

𝐿 ∝ 𝑅𝑒0.9𝜎𝑒

1.2 𝑀1/2 ∝ 𝑅𝑒1.0𝜎𝑒

2.0


Luminosity Mass

Replace LM in Faber-Jackson and Kormendy rel.

Both projection provide the same information

Linked by virial equation M ∝ 𝜎2𝑅𝑒

(see Cappellari+06; Bolton+08; Auger+10)

Both “relations” break at 3 × 1010𝑀⊙ (cfr. Kauffmann+03)

(Cappellari+13b: P20)

𝐌 ∝ 𝝈𝟐𝑹𝒆

𝑀 − 𝜎 𝜎4.7

𝜎2.3

𝑀 − 𝑅𝑒


Bulge drives galaxy properties

Bulge linked to quenching for 𝑀∗ ≲ 2 × 1011𝑀⊙ (also Cappellari-11; Bell+12; Saintonge+12; Cheung+12; Fang+13; Bluck+14)

Three characteristic galaxy stellar masses (cfr. Faber+97; Kauffmann+03; van der Wel+09; Bernardi+11; Geha+12)

(Cappella

ri+

13

b:

P20)


Stellar M/L ≠ Total M/L

Stellar and total M/L disagree

Excess depends on mass/luminosity/radius

Models cannot distinguish dark matter/IMF

Initially dark matter preferred to explain trend

(also Tortora+09; Graves-Faber10; Thomas+11)

Salpeter

Kroupa

Padmanabhan+04 Tortora+12 Cappellari+06

Axisymmetric fit IFU Spherical models fitting σ


Dark halo cannot explain M/L excess

Most general halo still requires IMF variation

IMF variation consistent with standard ΛCDM halos

(as Dutton+13; Tortora+13)

Salpeter IMF also consistent with lensing (Auger+10)

(Cappe

llari+

12,

Natu

re)


Summary 28 years of Fundamental Plane

Original insights confirmed FP = virial equilibrium + M/L

Dark matter unimportant within 1Re

M/L driven by bulge fraction (≈ 𝜎)

Stellar/Total M/L disagree

Dark matter cannot explain disagreement Is the IMF non-universal?

Can Dark Matter accurately follow stars?

Are all population models wrong with σ?

Future Synergy stellar population and dynamics

Good statistics: SAMI, MaNGA,…


(dynamical) mass determinations and scaling relations of etgs … · 2014. 7. 23. · faber-jackson...

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