The Birth of OB Stars in Spiral Galaxies

Frank H. ShuUCSD and ASIAA

KIAA-PKU17 November 2010

Outline

• Review of classical TASS picture• Expected color gradient from triggered OB SF• Spiral substructure

– Branches (ultraharminc resonances)– Feathers (role of B and self-gravity)– Flocculence (overlapping resonances & chaos?)

• GMAs and GMCs• Galactic cascade and interstellar turbulence

Spitzer Composite Image of M81

Spiral Shockwave in Visible/Blue Lightas Nonlinear Response of Gas

Roberts (1969)

Out-of-phase gaseous response damps stellar spiral density-wave (Kalnajs 1972). Presence of shockwave guarantees non-closure of streamlines (accretion inside CR) and saturates growth of stellar density wave (Roberts & Shu 1972).

Density wave supported by disk stars issmall amplitude, F ~ 5% (Lin & Shu 1964,Lin, Yuan, Shu 1969)

Color Gradients from Galactic Shock Triggering of OB SF

Martinez-Garcia, Gozalez-Lopezlira, Bruzual-A (2009)

10 out of 13 SA and SAB galaxies show predicted color gradients

Pop I Features Not Explained by Roberts (1969) Picture: Branches, Spurs, & Feathers

Branching at n = 2 Ultraharmonic

Model of M81 by Visser (1980) using WKBJ steady-flow code of

Shu, Milione, Roberts (1973) which ignores self-gravity of gas.

Ultraharmonic Resonances• Slightly nonlinear response (SMR):

Major branching at n = 2 (so-called 4:1 resonance if m = 2 because only mn = 4 enters if x = 0).

• Nonlinear forcing (CLS 2003): m → mj, j = 1, 2, 3, …• Observed infrared spirals are periodic but nonsinusoidal

(fractional surface-density amplitudes are not small). Nevertheless ratio of spiral field to axisymmetric field F may be small because rigid dark-matter halo helps to support axisymmetric field.

). (single forcinglinear and / where

,...3 ,2 ,1 ,1)(

222

2/1

2

mckx

nxn

m

g

p

κ

νκ

≡

=⎟⎠

⎞⎜⎝

⎛ +±=≡Ω−Ω

Lindblad (linear response)

Base flow is sonic at n = ∞.

Nonlinear response

Resonances & Chaos

Shu, Milione, & Roberts (1973)

• Nonlinear saturation by alignment or anti-alignment of response to forcing in case of one resonance (e.g., X1 and X2 orbits in case of bars).• Nonlinear resonances have finite width even in the absence of dissipation.• General impossibility of alignment in two or more different directions if there are overlapping resonances.• Result is chaos (“go crazy if have two bosses”).

Q=2.48, f=0.1, F=3.5%Chakrabarti, Laughlin, Shu (2003)

576 Myr 2870 Myr

ILR = 0.62, CR = 2.13, OLR = 3.63

Feathering Instability in Spiral Galaxies

Shetty & Ostriker (2006) include self-gravity and B; treat turbulence as isothermal EOS.

Relationship to K-S Law: Shu, Allen, Lizano, & Galli (2007)

Roberts & Yuan (1970); Mathewson, van der Kruit, & Brouw (1972); Braun et al. (2007)

Magnetically Mediated Feather Formation Behind Galactic Shocks

Kim & Ostriker (2002)

Spiral Substructure Involving Band Self-Gravity

• Turbulence treated by logatropic EOS, nondim characterized by xt0;

• B treated as if z-height were const, nondim characterized by xA0.

• Linear stability theory gives modification of dispersion relation as well as spacing for growing modes as function of

• Compare with simulations.• Compare with observations.

Nonlinear asymptotics

in (ξ,η) coordinates.

α ≡2πmGΣg /ϖκ 2 sin i,

ν ≡ m(Ωp − Ω) /κ ,

f = Ω /κ( )2mF /sin i.

ν, f ,α , xt0 , xA0 .Lee & Shu (in preparation)

W. K. Lee (PhD Thesis)

Feathers are bunched crests of nonlinear spiral density waves.

M51 CARMA (Koda et al. 2009)

Giant Molecular Associations (GMAs) are the bunched crests of nonlinear spiral density waves!

SummaryFeathers form by transient gravitational instability behind galactic shocks. In purely hydrodynamical simulations of long term, need either high Q or low F to prevent continued collapse of spiral arms. In reality, near free-fall collapse on large and small scales (i.e., rapid star formation) is prevented by interstellar magnetic field. Largest gaseous structures, GMAs, are bunched nonlinear spiraldensity waves. GMCs may result from parasitic instabilities and are probably more like material entities.Branches form by action of ultraharmonic resonances and are nonlinear SDWs.Flocculence probably arises from chaos created by overlapping ultraharmonic resonances, with some contribution from driven SDWs associated with lumpy dark matter halos.Galactic cascade may contribute to interstellar turbulence (vision of Prof. C. C. Lin).