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Sub-mm/mm astrophysics: How to probe molecular gas Yasuo Fukui Nagoya University Summer School

Sub-mm/mm astrophysics: How to probe molecular gas Yasuo Fukui Nagoya University Summer School The Gaseous Universe Oxford, 21-23 July 2010. Outline. Lecture 1 “Sub-mm and mm observations of molecules”

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Sub-mm/mm astrophysics: How to probe molecular gas Yasuo Fukui Nagoya University Summer School

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  1. Sub-mm/mm astrophysics: How to probe molecular gas Yasuo Fukui Nagoya University Summer School The Gaseous Universe Oxford, 21-23 July 2010

  2. Outline Lecture 1 “Sub-mm and mm observations of molecules” Molecular vs. atomic gas/ radiative and collional porcesses / rotational energy levels/ sub-mm transitions/ time scales/ cooling and heating/ chemical processes Lecture 2 “Sub-mm diagnostics; density and temperature”   LVG approximation and its application to three high temperature regions N159 and other GMCs in the LMC/ Westerlund 2 super star cluster/ Galactic centre loops Lecture 3 “Giant molecular clouds (GMCs)” GMCs/ star formation/ resolved GMCs in the LMC and M33/ three GMC types/ GMC lifetime/ GMC formation/ HI filaments/ shells or spiral density waves/ difference between disk and center of a galaxy

  3. Lecture 1Sub-mm and mm observations of molecules

  4. ISM between stars • We have interstellar medium ISM among stars • ISM consists of gas and dust Mgas/Mdust is 100, Dust grains include most of the heavy elements, abundance ratio; H:He:CNO = 1:10-1:10-4 • Gas consists of neutral and ionized components Here with an emphasis on neutral gas because neutral is dominant, related to star formation and ultimately galactic evolution, Ionized gas is minor in mass and probes UV radiation field, PDR • Neutral consists of molecular and atomic gas • 1951 discovery of 21cm HI • 1970 discovery of 2.6mm CO

  5. Molecular vs. atomic • HI gas is less dense, average is 1 cm-3 with a range of 0.01cm-3 to 100 cm-3, temperature average is 100K with a range of 20–3000 K • Molecular gas is dense, average is 1000 cm-3, up to 107 cm-3 or higher • Temperature is low, 10–20 K in the disk, can be higher in high-mass star forming regions • but is higher in the Galactic center, 30–300 K, due to not-well known heating

  6. Some chemistry • HI is converted into H2 on grain surface because gas phase reaction is very slow, exception the first stars form without dust grains • H2 is readily dissociated if Av is small, less than ~ 0.2 mag • but can survive if Av is more than 1 mag • Other molecules are often formed via ion neutral reactions • At very high densities more than 107cm-3 molecules freeze onto dust grain surface

  7. Radiative transitions The Einstein coefficients • (a) Spontaneous emission: A21n2 • (b) Photo absorption: B12Iνn1 • (c) Stimulated emission: B21Iνn2 (Electric dipole transition)

  8. Collisional Excitation • C coefficient : Excitation De-Excitation (N: density, σ: cross section, v: velocity)

  9. Excitation temperature • For non-LTE case (more realistic in molecular cloud), we can define the “Excitation temperature” as follows; (＊Especially, Tex of the spin excitation (e.g. HI 21cm line) is called “Spin temperature”, Ts) • Brightness temperature

  10. Detailed balancing • Ex. Simple two level system rate equation • Collision dominated • Radiation dominated

  11. Critical density • When Iν → 0 • Critical Density: • ncrit << n(H2) • ncrit ~ n(H2) • ncrit >> n(H2) : LTE : excited but subthermal : unexcited

  12. My recommendation • Keeep physical constants in mind • Ready to make order-of-magnitude estimate Planck const.：h = 6.63×10-27 erg s Boltzmann const.：k = 1.38×10-16 erg deg-1 1 eV = 1.60×10-12 erg（e.g., 1eV~kT => T〜104 K) electron mass：me = 0.911x10-27 g proton mass：mp = 1.67x10-24 g etc.

  13. Non-LTE case (Photon trapping) • Photon escape probability, β (0 ≤β ≤1) • Effective A coefficient: A21 → A21β • Effective critical density: ncrit = A21/C21 → A21β/C21 • Large Velocity Gradient (LVG) model Molecular cloud (Castor 1970; Goldreich & Kwan 1974) Velocity • Spherical • Slab Tk, n(H2)

  14. Heating processes • Based on the ionization of ISM components by an energetic radiations. Then, electrons quickly (~1Myr) interact with the ISM and thermalize. • Cosmic rays; heat gas to 10 K(Black 1987; Lequex 2002) • Photoelectric effect on small dust grains and PAH (Watson 1972; de Jong 1977; Draine 1978; Bakes & Tielens 1994) • Ionization of atoms and molecules (e.g., HCO+) froze-in condition is good approx. MHD • X-ray • Chemistry • Mechanical heating

  15. Cooling processes Cooling by line radiation processes is dominant. Proportional to n2. • Atomic gas • Forbidden lines. (< few 1000 K, e.g., CII) • Lyman α (> few 1000 K) • Molecular gas Cooling by the line radiation from molecules • CO, H2O and other molecules

  16. Thermal equilibrium curve WNM CNM Unstable Wolfire et al. 95 criterion for instability: (Field et al. 69, Wolfire et al. 95)

  17. Heating and Cooling processesfor the thermal equilibrium curve (NW~1019 cm-2) Atomic gas (solid lines: cooling, broken lines: heating) Wolfire et al. 1995

  18. Molecular cooling Tk = 40 K • CO is the dominant cooling line for low n and T • H2O and other molecules are dominant for n > 106 cm-3 and T > 200 K Goldsmith & Langer 1978

  19. Temperature and density balance of atomic gas (Goldsmith et al. 2007)

  20. Temperature • kinetic temperature (Maxwell distribution), Tk • excitation temperature, Tex • radiation temperature, Planck law, Trad • color temperature, Tc • dust temperature, Td These temperatures are generally not the same Collisional coupling between dust and molecules at density higher than 104 cm-3, Tkequal to Td

  21. Electronic state (1-104 eV) Vibration (10-2-10-1 eV) Rotation (10-3-10-2 eV) Spin (~10-6 eV) 104K ~ 1eV Excitation 1 Lower state Upper state

  22. Excitation 2 • Hydrogen molecules are not observable in radio. Too high energy levels. Only in absorption. • Carbon monoxide CO and others can be observed rotational energy levels, high excitation vibration. cf. electronic, spin-spin interaction • Sub-mm transitions generally higher excited states ratio between J and J’ gives density/tempearture.

  23. Molecular cloud Goldsmith 1987

  24. Time scale 1 • Crossing time scale • Velocity width (5-10 km/s): dv • Molecular cloud size (1-100 pc): r ＝ 105 – 107 yr

  25. Time scale 2 • Free fall time a：initial radius, ρ(0) : initial density n : initial number density, n = n(H) + 2n(H2)

  26. Time scale 3 • Cooling time shorter than its dynamical time isothermal is a good approximation

  27. Time scale 4 How frequently do molecules meet? • C(s-1) = n (cm-3) s (cm2) V(cm/s) • n(density) ~ 103 cm-3 • s(cross section) ~ πa2 ~ 10-16 cm2 • V(velocity) ~ 105 cm s-1 [mV2 ~ kT] • t ~ 1/C ~ 108 [s] ~ 1 [yr]

  28. Time scale 5 • Formation time scale of H2 (Hollenbach & Salpeter 1970; Jura 1974) γ：sticking probability for incident H atoms. <v2>: mean thermal velocity of H atoms. <σg>: average grain cross section. n1, n2 & ng: number density of HI, H2 and grains, respectively [yr]

  29. Time scale 6 Koyama & Inutsuka 2000

  30. Formation of H2 in gas phase • Permitted processes in warmer regions H+ + H → H2+ + hν H2+ + H → H2 + H+ e- + H → H- + hν H- + H → H2 + e- In very dense regions(> 108 cm-3), 3 body reaction 3H → H2 + H 2H + H2 → 2H2 This process is important in the early Universe. Very dense & hot HI cloud→ molecular cloud

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