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The Distribution of Thermal Pressures in the Diffuse Interstellar Medium of our Galaxy

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. Morphology of the ISM. Morphology of the ISM. Morphology of the ISM.

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The Distribution of Thermal Pressures in the Diffuse Interstellar Medium of our Galaxy

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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

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