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(Dynamical) Mass Determinations
and Scaling Relations of ETGs at Small Scale
Michele Cappellari
2014-07-21 M. Cappellari, IAU 311, Oxford 1
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
2014-07-21 M. Cappellari, IAU 311, Oxford 2
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)
2014-07-21 M. Cappellari, IAU 311, Oxford 3
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)
2014-07-21 M. Cappellari, IAU 311, Oxford 4
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
2014-07-21 M. Cappellari, IAU 311, Oxford 5
Fa
be
r+8
7 in
“N
ea
rly n
orm
al g
ala
xie
s”
2014-07-21 M. Cappellari, IAU 311, Oxford 6
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)
2014-07-21 M. Cappellari, IAU 311, Oxford 7
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
2014-07-21 M. Cappellari, IAU 311, Oxford 8
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.
2014-07-21 M. Cappellari, IAU 311, Oxford 11
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
2014-07-21 M. Cappellari, IAU 311, Oxford 12
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
2014-07-21 M. Cappellari, IAU 311, Oxford 13
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
2014-07-21 M. Cappellari, IAU 311, Oxford 14
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
2014-07-21 M. Cappellari, IAU 311, Oxford 15
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)
2014-07-21 M. Cappellari, IAU 311, Oxford 16
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
2014-07-21 M. Cappellari, IAU 311, Oxford 17
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)
2014-07-21 M. Cappellari, IAU 311, Oxford 18
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,…
2014-07-21 M. Cappellari, IAU 311, Oxford 19
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