The angular momentum of galaxies and their haloes: a tracer of - - PowerPoint PPT Presentation

The angular momentum of galaxies and their haloes: a tracer of galaxy evolution

The Role of Gas in Galaxy Dynamics, Valletta, 03/10/17

Lorenzo Posti (University of Groningen)

with G. Pezzulli (ETH), F . Fraternali (Bologna/Groningen), E. di Teodoro (ANU) MNRAS submitted.

Gaia DR1, Gaia Collaboration+2016

A tale of two galaxies

Mass ~ 2.6 x 1011 Msun Mass ~ 2.6 x 1011 Msun

A tale of two galaxies

Mass ~ 2.6 x 1011 Msun Mass ~ 2.6 x 1011 Msun J ~ 8 x 1014 Msun kpc km/s J ~ 2 x 1014 Msun kpc km/s

Fall (1983)

A tale of two galaxies, in their context

Romanowsky & Fall (2012) data from Fall & Efstathiou (1980) Fall (1983, 2002) Romanowsky & Fall (2012) Fall & Romanowsky (2013) …

Fall diagram:

The specific stellar angular momentum - stellar mass plane (j* - M*)

Fall relation:

1) j* - M* are correlated as , 2) spirals and ellipticals on parallel sequences, with 4-5x difference

j∗ ∝ M 2/3

∗

After Mike Fall’s major contributions:

Specific angular momentum - mass: the Fall relation

How do galaxies acquire angular momentum?

Tidal Torque Theory (TTT)

~

• ~

F ~ F

DM + gas

• Dark matter (and gas) spin due

to interactions w. neighbours

• λ~0.035 independent of mass

(Macciò+2007)

λ = J|E|1/2 GM 5/2 ' J/M RvirVvir

Peebles (1969)

How do galaxies acquire angular momentum?

Tidal Torque Theory (TTT)

~

• ~

F ~ F

DM + gas

• Dark matter (and gas) spin due

to interactions w. neighbours

• λ~0.035 independent of mass

(Macciò+2007)

λ = J|E|1/2 GM 5/2 ' J/M RvirVvir

• For NFW haloes:

Vvir ∝ M 2/3

h

, Rvir ∝ M 2/3

h

jh ≡ Jh/Mh ∝ λM 2/3

h

Peebles (1969)

f∗ ≡ M∗/Mh fj ≡ j∗/jh

jh ∝ λM 2/3

h

Galaxy - Halo spin

star formation efficiency retained fraction of angular momentum

jh ∝ λM 2/3

h

j∗ ∝ [λfjf −2/3

∗

]M 2/3

∗

f∗ ≡ M∗/Mh fj ≡ j∗/jh

star formation efficiency retained fraction of angular momentum

Galaxy - Halo spin

Fall & Efstathiou (1980) Dalcanton et al. (1997) Mo, Mao & White (1998)

jh ∝ λM 2/3

h

• λ ~ const.

f∗, fj = const < 1

• early semi-analytic models

with

j∗ ∝ [λfjf −2/3

∗

]M 2/3

∗

f∗ ≡ M∗/Mh fj ≡ j∗/jh

star formation efficiency retained fraction of angular momentum

Galaxy - Halo spin

f∗, fj = const < 1

∆λ

Can f*, fj = const explain the Fall relation?

• f* ~ fbaryon
• fj ~ 1
• Spirals in high-λ haloes and viceversa

. . .

Galaxy - Halo spin

∆λ

. . .

NO

Galaxy - Halo spin

Can f*, fj = const explain the Fall relation?

• f* ~ fbaryon
• fj ~ 1
• Spirals in high-λ haloes and viceversa

The stellar-to-halo mass relation (SHMR)

All galaxies Segregated by morphology

The stellar-to-halo mass relation (SHMR)

f* is not constant!

All galaxies Segregated by morphology

Does a fj = const model works?

fj=const is a standard assumption in semi-analytic models (after Mo, Mao & White 1998)

Does a fj = const model works?

f* from SHMR fj = const

fj=const is a standard assumption in semi-analytic models (after Mo, Mao & White 1998)

Does a fj = const model works?

f* from SHMR fj = const

fj=const is a standard assumption in semi-analytic models (after Mo, Mao & White 1998)

No constant fj reproduces the slope

• f the Fall relation

f* from SHMR fj = const spin-bias

high-λ halo low-λ halo spiral elliptical

Spin-bias

Can Δλ explain spirals/ellipticals?

f* from SHMR fj = const spin-bias

high-λ halo low-λ halo spiral elliptical

Spin-bias Δλ~0.3 dex is too small to explain ~0.6 dex shift in spirals/ellipticals

Can Δλ explain spirals/ellipticals?

Deriving fj = fj (M*) from observations

Empirical model: find fj = fj (M*) that is consistent with observations 1

Assume a SHMR M* = M* (Mh)

2

Compute jh ∝ λM 2/3

h

3

Find fj (M*) so that is as observed

j∗ ∝ [λfjf −2/3

∗

]M 2/3

∗

The stellar-to-halo angular momentum relation

• fj for spirals 3x-5x larger

than for ellipticals

• Strong dependence of fj
• n stellar (halo) mass!
• .

fj ∝ f 2/3

∗

SHMR from

Navarro & Steinmetz (2000)

The “retained” fraction of angular momentum depends

• n the star formation efficiency

A physical model for the relation

star formation cooling time angular momentum

• Star formation proceeds inside-out:

from low-j to high-j material Rout

• Cooling is efficient up to Rout (depends on f*):

j < jgas(< Rout)

• Baryonic collapse is biased: stars born with

fj ∝ f 2/3

∗

A physical model for the relation

star formation cooling time angular momentum

• Star formation proceeds inside-out:

from low-j to high-j material Rout

• Cooling is efficient up to Rout (depends on f*):

j < jgas(< Rout)

• Baryonic collapse is biased: stars born with
• If angular momentum is distributed as

j(< r) ∝ Mgas(< r)s

fj ∝ f 2/3

∗

e.g. Bullock et al. (2001)

A physical model for the relation

star formation cooling time angular momentum

• Star formation proceeds inside-out:

from low-j to high-j material Rout

• Cooling is efficient up to Rout (depends on f*):

j < jgas(< Rout)

• Baryonic collapse is biased: stars born with
• If angular momentum is distributed as

fj = (f∗/fbaryon)s

j(< r) ∝ Mgas(< r)s

⇒ fj ∝ f 2/3

∗

van den Bosch et al. (1999) Dutton & van den Bosch (2012)

e.g. Bullock et al. (2001)

star formation cooling time angular momentum

Rout Rout

• Best-fit slope: s = 2/3 ± 0.05
• Normalisation: fbaryon-s (spirals), fbaryon-s/3 (ellipticals)

A physical model for the relation

fj ∝ f 2/3

∗

star formation cooling time angular momentum

Rout Rout

• Best-fit slope: s = 2/3 ± 0.05
• Normalisation: fbaryon-s (spirals), fbaryon-s/3 (ellipticals)

mergers? dynamical friction?

A physical model for the relation

fj ∝ f 2/3

∗

Conclusions

• The stellar-to-halo angular momentum relation can be constrained

with current observations!

• fj = j*/jh can not be constant with mass
• Scatter in halo spin can not explain difference in j for spirals and

ellipticals alone

• The “retained fraction” of angular momentum scales as a power-law
• f the “star formation efficiency”
• The Fall relation is consistent with inside-out cooling model

(biased collapse)

SPARC galaxies

data from Lelli et al. (2016)