The Role of Gas in Galaxy Dynamics, Valletta, 03/10/17 The angular momentum of galaxies and their haloes: a tracer of galaxy evolution 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 10 11 M sun Mass ~ 2.6 x 10 11 M sun
A tale of two galaxies Mass ~ 2.6 x 10 11 M sun Mass ~ 2.6 x 10 11 M sun J ~ 8 x 10 14 M sun kpc km/s J ~ 2 x 10 14 M sun kpc km/s
A tale of two galaxies, in their context Fall (1983)
Specific angular momentum - mass: the Fall relation Fall diagram: The specific stellar angular momentum - stellar mass plane (j * - M * ) Fall relation: j ∗ ∝ M 2 / 3 1) j * - M * are correlated as , ∗ 2) spirals and ellipticals on parallel sequences, with 4-5x difference data from Romanowsky & Fall (2012) After Mike Fall’s major contributions: Fall & Efstathiou (1980) Fall (1983, 2002) Romanowsky & Fall (2012) Fall & Romanowsky (2013) …
How do galaxies acquire angular momentum? • Dark matter (and gas) spin due Tidal Torque Theory (TTT) to interactions w. neighbours ~ F ~ � λ = J | E | 1 / 2 J/M GM 5 / 2 ' R vir V vir Peebles (1969) ~ F λ ~0.035 independent of mass • DM + gas (Macciò+2007)
How do galaxies acquire angular momentum? • Dark matter (and gas) spin due Tidal Torque Theory (TTT) to interactions w. neighbours ~ F ~ � λ = J | E | 1 / 2 J/M GM 5 / 2 ' R vir V vir Peebles (1969) ~ F λ ~0.035 independent of mass • DM + gas (Macciò+2007) V vir ∝ M 2 / 3 , R vir ∝ M 2 / 3 • For NFW haloes: h h j h ≡ J h /M h ∝ λ M 2 / 3 h
Galaxy - Halo spin star formation f ∗ ≡ M ∗ /M h efficiency retained fraction of f j ≡ j ∗ /j h angular momentum j h ∝ λ M 2 / 3 h
Galaxy - Halo spin star formation f ∗ ≡ M ∗ /M h efficiency retained fraction of f j ≡ j ∗ /j h angular momentum j h ∝ λ M 2 / 3 h j ∗ ∝ [ λ f j f − 2 / 3 ] M 2 / 3 ∗ ∗
Galaxy - Halo spin star formation f ∗ ≡ M ∗ /M h efficiency retained fraction of f j ≡ j ∗ /j h angular momentum j h ∝ λ M 2 / 3 f ∗ , f j = const < 1 h j ∗ ∝ [ λ f j f − 2 / 3 ] M 2 / 3 ∗ ∗ Fall & Efstathiou (1980) • early semi-analytic models • λ ~ const. Dalcanton et al. (1997) with f ∗ , f j = const < 1 Mo, Mao & White (1998)
Galaxy - Halo spin Can f * , f j = const explain the Fall relation? - f * ~ f baryon - f j ~ 1 - Spirals in high- λ haloes and viceversa . . ∆ λ .
Galaxy - Halo spin Can f * , f j = const explain the Fall relation? - f * ~ f baryon - f j ~ 1 - Spirals in high- λ haloes and viceversa . . ∆ λ . NO
The stellar-to-halo mass relation (SHMR) All galaxies Segregated by morphology
The stellar-to-halo mass relation (SHMR) All galaxies Segregated by morphology f * is not constant!
Does a f j = const model works? f j =const is a standard assumption in semi-analytic models (after Mo, Mao & White 1998)
Does a f j = const model works? f j =const is a standard assumption in semi-analytic models (after Mo, Mao & White 1998) f * from SHMR f j = const
Does a f j = const model works? f j =const is a standard assumption in semi-analytic models (after Mo, Mao & White 1998) f * from SHMR f j = const No constant f j reproduces the slope of the Fall relation
Can Δλ explain spirals/ellipticals? Spin-bias high- λ spiral halo low- λ elliptical halo f * from SHMR f j = const spin-bias
Can Δλ explain spirals/ellipticals? Spin-bias high- λ spiral halo low- λ elliptical halo f * from SHMR f j = const spin-bias Δλ ~0.3 dex is too small to explain ~0.6 dex shift in spirals/ellipticals
Deriving f j = f j (M * ) from observations Empirical model : find f j = f j (M * ) that is consistent with observations 1 Assume a SHMR M * = M * (M h ) 2 Compute j h ∝ λ M 2 / 3 h 3 j ∗ ∝ [ λ f j f − 2 / 3 ] M 2 / 3 Find f j (M * ) so that is as observed ∗ ∗
The stellar-to-halo angular momentum relation • f j for spirals 3x-5x larger than for ellipticals • Strong dependence of f j on stellar (halo) mass! • . f j ∝ f 2 / 3 SHMR from ∗ Navarro & Steinmetz (2000) The “retained” fraction of angular momentum depends on the star formation efficiency
A physical model for the relation f j ∝ f 2 / 3 ∗ • Star formation proceeds inside-out: star formation from low- j to high- j material cooling time • Cooling is efficient up to R out (depends on f * ): • Baryonic collapse is biased: stars born with angular momentum j < j gas ( < R out ) R out
A physical model for the relation f j ∝ f 2 / 3 ∗ • Star formation proceeds inside-out: star formation from low- j to high- j material cooling time • Cooling is efficient up to R out (depends on f * ): • Baryonic collapse is biased: stars born with angular momentum j < j gas ( < R out ) R out • If angular momentum is distributed as j ( < r ) ∝ M gas ( < r ) s e.g. Bullock et al. (2001)
A physical model for the relation f j ∝ f 2 / 3 ∗ • Star formation proceeds inside-out: star formation from low- j to high- j material cooling time • Cooling is efficient up to R out (depends on f * ): • Baryonic collapse is biased: stars born with angular momentum j < j gas ( < R out ) R out • If angular momentum is distributed as j ( < r ) ∝ M gas ( < r ) s e.g. Bullock et al. (2001) f j = ( f ∗ /f baryon ) s ⇒ van den Bosch et al. (1999) Dutton & van den Bosch (2012)
A physical model for the relation f j ∝ f 2 / 3 ∗ star formation cooling time angular momentum R out • Best-fit slope: s = 2/3 ± 0.05 • Normalisation: f baryon-s (spirals), f baryon-s /3 (ellipticals) R out
A physical model for the relation f j ∝ f 2 / 3 ∗ star formation cooling time angular momentum R out mergers? • Best-fit slope: s = 2/3 ± 0.05 dynamical friction? • Normalisation: f baryon-s (spirals), f baryon-s /3 (ellipticals) R out
Conclusions • The stellar-to-halo angular momentum relation can be constrained with current observations! • f j = j * /j h 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 of the “star formation efficiency” • The Fall relation is consistent with inside-out cooling model (biased collapse)
SPARC galaxies data from Lelli et al. (2016)
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