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  1. The Distribution of Thermal Pressures in the Diffuse Interstellar Medium of our Galaxy Edward B. Jenkins Princeton University Observatory A research collaboration with Todd M. Tripp, U. Mass

  2. Morphology of the ISM

  3. Morphology of the ISM

  4. Morphology of the ISM Integrated 21-cm emission from the LMC (Elmegreen, Kim & Stavely-Smith 2001, ApJ, 548, 749) Hydrodynamical simulation of nonmagnetic turbulence with a Mach number of 1 (Porter, Woodward & Pouquet, 1998)

  5. Morphology of the ISM IRAS 100μm image A construction of a field containing random Gaussian amplitudes in k-space Images from Miville-Deschênes, Lagache, Boulanger & Puget 2007, A&A, 469, 595

  6. Cold phase 104 K Warm phase 1000 K 100 K 10 K Representative thermal pressure in the galactic disk Thermal Equilibrium Galactocentric radius = 8.5 kpc Thermally Unstable Teq = 2.3 × 104 yr Log p/k (K cm-3) Teq ~ 107 yr Heating rate = Cooling rate Log nH (cm-3) (Wolfire, McKee, Hollenbach &Tielens 2003: ApJ, 587, 278.)

  7. Audit & Hennebelle (2005: A&A, 473, 1) Simulation Results Weak initial turbulence Strong initial turbulence

  8. Simulation Results Nakamura et al. (2007, ApJS, 164, 477)

  9. Observational Diagnostics for Turbulence in the ISM • Statistical properties of structures seen in 2-D projections on the sky • Distribution of radial velocities • For ionized media: perturbations of radio wave propagation (scintillation decorrelation bandwidths, angular broadening of point sources, apparent changes in pulsar timing, fluctuations in pulsar dispersion measures and rotation measures of extragalactic sources). • Fluctuations in thermal pressures (nkT)

  10. Overall Average ISM Pressure in the Galactic Midplane • Total pressure p/k≈ 2.5 × 104 cm-3K • Arises from the weight of material in the Galactic plane’s gravitational potential (Boulares & Cox 1990: ApJ, 365, 544) • Many forms of pressure: • Thermal • Magnetic Fields • Dynamical (or Turbulent) • Cosmic Rays pressure p/k only of order 3 × 103 cm-3K

  11. Energy Sources that Could Drive Turbulence and Produce Pressure Fluctuations • Macroscopic • Supernova Explosions • Newly formed H II regions • Stellar Mass Loss • Infalling High-Velocity Gas from the Halo • Bipolar Jets from Star Forming Regions • Differential Galactic Rotation and Spiral Arm Shocks • Microscopic • Turbulent Downward Cascade from Macroscopic Motions • Dynamical Effects from the Thermal Instability

  12. Observations A study of interstellar absorption features that appear in the UV spectra of hot stars

  13. Observing Fundamentals … • Most of the free carbon atoms in the ISM are singly ionized, but a small fraction of the ions have recombined into the neutral form. • The ground electronic state of C I is split into three fine-structure levels with small energy separations. • Our objective is to study the relative populations of atoms in these three levels, which are influenced by local conditions (density & temperature).

  14. Fine-structure Levels in the Ground State of C I Upper Electronic Levels Optical Pumping (by Starlight) Spontaneous Radiative Decays E/k = 62.4 K C I** 3P2 (E = 43.4 cm-1, g = 5) Collisionally Induced Transitions E/k = 23.6 K C I* 3P1 (E = 16.4 cm-1, g = 3) C I 3P0 (E = 0 cm-1, g = 1)

  15. C I Absorption Features in the UV Spectrum of λ Cep Recorded at a Resolution of 1.5 km s-1 by STIS on HST From Jenkins & Tripp (2001: ApJS, 137, 297)

  16. λ Cep C I Column density per unit velocity [1013 cm-2 (km s-1)-1] C I* C I** Velocity (km s-1)

  17. Most Useful Way to Express Fine-structure Population Ratios • n(C I)total = n(C I) + n(C I*) + n(C I**) • f1  n(C I*)/n(C I)total • f2  n(C I**)/n(C I)total f2 Then consider the plot: Collision partners at a given density and temperature are expected to yield specific values of f1 and f2 f1

  18. Collisional Excitation by Neutral H T = 100 K n(H) = 105 cm-3 n(H) = 104 cm-3 n(H) = 1000 cm-3 n(H) = 100 cm-3 n(H) = 10 cm-3

  19. Collisional Excitation by Neutral H Plus Optical Pumping by the Average Galactic Starlight Field n(H) = 104 cm-3 n(H) = 1000 cm-3 n(H) = 100 cm-3 n(H) = 10 cm-3

  20. Tracks for Different Temperatures T = 240 K T = 120 K n(H) = 100 cm-3 T = 60 K T = 30 K

  21. Tracks for Different Temperatures T = 240 K T = 120 K p/k = 104 cm-3 K T = 60 K T = 30 K

  22. (Back to simple f1f2 diag.)

  23. C I-weighted “Center of Mass” gives Composite f1,f2 A Theorem on how to deal with superpositions

  24. Allowed Region for Composite Results P/k  ∞ Tracks shown are for different temperatures

  25. Ionization Equilibrium Photoionization Γn(C I) = [αrr ne+αgnH]n(C II) There are also charge exchange reactions, which have a very minor effect. Radiative recomb. Recomb. dust grains

  26. Cold phase 104 K Warm phase 1000 K 100 K 10 K Thermal Equilibrium Density of Ionizing radiation for C I equal to the average value in the galactic plane C I/Ctotal =0.001 Log p/k (K cm-3) C I/Ctotal = 0.0001 C I/Ctotal = 0.1 C I/Ctotal= 0.01 Log nH (cm-3) (Wolfire, McKee, Hollenbach &Tielens 2003: ApJ, 587, 278.)

  27. Cold phase 104 K Warm phase 1000 K 100 K 10 K Thermal Equilibrium Density of Ionizing radiation for C I equal to the average value in the galactic plane × 10 C I/Ctotal = 0.0001 Log p/k (K cm-3) C I/Ctotal =0.001 C I/Ctotal= 0.01 C I/Ctotal = 0.1 Log nH (cm-3) (Wolfire, McKee, Hollenbach &Tielens 2003: ApJ, 587, 278.)

  28. Relevant Time Scales for Physical Processes in Small Clouds in the CNM • Why are time scales important? • In a turbulent regime Δv rp where 0.4 <p< 0.6 • Hence the crossing time in a turbulent eddy Δt=r/Δv  r0.5 • Typical small clouds seen in H I have N(H I) ≈ 3×1018 cm-2; for n(H I) = 40 cm-3, this yields a characteristic dimension r= 7.5×1016 cm = 5000 AU. With a one-dimensional rms velocity dispersion of 1 km s-1, this makes Δt= 2.4×104 yr.

  29. Relevant Time Scales for the Cold Phase • Establishing the C I fine-structure level populations: {RnH+ A10 }-1=160 days (or less if f1 or f2 is large) • Ionization Equilibrium of C I and C II: {[αrr ne+αgnH]+Γ}-1=150 yr

  30. Relevant Time Scales for the Cold Phase • Cooling/heating time for reaching thermal equilibrium: 2.3×104[T80]1.2[(p/k)3000]-0.8 yr • Coupling time for the H2 J = 0 to 1 rotation temperature to the local thermal temperature: [Rn(H+)]-1 = 1.6×104 yr for n(H I) = 40 cm-3 and ζCR= 4×10-16s-1 based on the observations of H3+ by Mc Call et al. (2003: Nature 422, 500) and Indriolo et al. (2007: ApJ, 671, 1736)

  31. Relevant Time Scales for the Cold Phase • Conclusion: • Over scales larger than 5000 AU, the gas should respond to changes with γeff ≈ 0.7 (the slope of the thermal equilibrium line), while smaller structures should exhibit a trend closer to adiabatic (γeff≈ 5/3). But the r0.5behavior for Δtmakes this transition with scale size rather gentle. • H2 rotation temperatures could differ from kinetic temperatures over scales less than 5000 AU.

  32. Results • Original observations reported by Jenkins & Tripp (2001) included 21 stars. • We have now expanded this survey to 102 stars by downloading from the MAST archive all suitable STIS observations that used the highest resolution echelle spectrograph (E140H). • The archival results have somewhat lower velocity resolution because the standard entrance aperture was usually used (instead of the extremely narrow slit chosen for the earlier Jenkins & Tripp survey).

  33. Composite results for all sight lines 500K Observed composite f1, f2 80K

  34. Log-normal Distribution of Mass vs. Density Relative Mass Fraction n(H I) (cm-3)

  35. H I C I Log-normal distribution of H I mass fraction vs. p, with γeff = 5/3 Observed composite f1, f2

  36. Observed composite f1, f2 H I C I Log-normal distribution of H I mass fraction vs. p, with γeff = 5/3

  37. Observed composite f1, f2 H I C I Log-normal distribution of H I mass fraction vs. p, with γeff = 5/3

  38. Observed composite f1, f2 H I C I Log-normal distribution of H I mass fraction vs. p, with γeff = 5/3

  39. Observed composite f1, f2 H I C I Log-normal distribution of H I mass fraction vs. p, with γeff = 5/3

  40. Observed composite f1, f2 H I C I Bimodal distribution of H I mass fraction vs. p, with γeff = 5/3 Model composite

  41. Simplification: Measure T01 for H2 and then convert (f1,f2) readings those expected at a standard temperature of 80K. Generic high pressure contribution 90% Observed f1, f2; T01 = 240K 240K 80K reference temperature 10%

  42. N(C I)/1012 cm-2 Log p/k

  43. Next step: we need to correct for the density weighting arising from the shifts in the ionization equilibrium Suggests that compressions and expansions of the gas are roughly isothermal N(C I)/1012 cm-2 Log p/k T01(H2) < 75K T01(H2) > 85K

  44. Total gas derived using an ionization correction with an average Galactic radiation field N(C II)/1012 cm-2 Log p/k

  45. Ionization Corrections • Validation of the transformation from C I to C II: • The derivation of C II – a proxy for H I -- was based on our knowledge of the local n(H) and an application of the equation for ionization equilibrium with assumed parameters • We can also observe O I absorption and use it too as a proxy. Do the two agree? • They should -- to within the uncertainties of the interstellar C to O abundance ratio, various atomic parameters, and the assumed average radiation field strength. • But they do not, probably because the assumed level of ionizing radiation is wrong. Instead, we derive the level of radiation using the discrepancy between the two methods as a guide Thus we must reject the earlier derivation.

  46. Distribution of radiation intensities Assumed average field strength Log ( I / I0 )

  47. Collisional Excitation by Neutral H Plus Optical Pumping by the Average Galactic Starlight Field n(H) = 104 cm-3 n(H) = 1000 cm-3 n(H) = 100 cm-3 n(H) = 10 cm-3

  48. Collisional Excitation by Neutral H Plus Optical Pumping by 10X the Average Galactic Starlight Field n(H) = 104 cm-3 n(H) = 1000 cm-3 n(H) = 100 cm-3 n(H) = 10 cm-3

  49. Need to Iterate • Calculate, to first order, the strength of the ionizing field I • Recalculate p/k using a modified pumping rate based on the new I • Recalculate the strength of the ionizing field I, based on the new p/k • Recalculate p/k using a modified pumping rate based on the new I • Recalculate the strength of the ionizing field I, based on the new p/k • Recalculate p/k using a modified pumping rate based on the new I • Recalculate the strength of the ionizing field I, based on the new p/k • Recalculate p/k using a modified pumping rate based on the new I • Recalculate the strength of the ionizing field I, based on the new p/k • Recalculate p/k using a modified pumping rate based on the new I • Recalculate the strength of the ionizing field I, based on the new p/k • Recalculate p/k using a modified pumping rate based on the new I • Recalculate the strength of the ionizing field I, based on the new p/k • Recalculate p/k using a modified pumping rate based on the new I • Recalculate the strength of the ionizing field I, based on the new p/k • Recalculate p/k using a modified pumping rate based on the new I

  50. Total gas derived using an ionization correction with an explicit radiation field Log p/k