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

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

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**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**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)**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**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.)**Audit & Hennebelle (2005: A&A, 473, 1)**Simulation Results Weak initial turbulence Strong initial turbulence**Simulation Results**Nakamura et al. (2007, ApJS, 164, 477)**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)**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**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**Observations**A study of interstellar absorption features that appear in the UV spectra of hot stars**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).**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)**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)**λ Cep**C I Column density per unit velocity [1013 cm-2 (km s-1)-1] C I* C I** Velocity (km s-1)**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**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**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**Tracks for Different Temperatures**T = 240 K T = 120 K n(H) = 100 cm-3 T = 60 K T = 30 K**Tracks for Different Temperatures**T = 240 K T = 120 K p/k = 104 cm-3 K T = 60 K T = 30 K**C I-weighted “Center of Mass” gives Composite f1,f2**A Theorem on how to deal with superpositions**Allowed Region for Composite Results**P/k ∞ Tracks shown are for different temperatures**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**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.)**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.)**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.**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**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)**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.**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).**Composite results for all sight lines**500K Observed composite f1, f2 80K**Log-normal Distribution of Mass vs. Density**Relative Mass Fraction n(H I) (cm-3)**H I**C I Log-normal distribution of H I mass fraction vs. p, with γeff = 5/3 Observed composite f1, f2**Observed composite f1, f2**H I C I Log-normal distribution of H I mass fraction vs. p, with γeff = 5/3**Observed composite f1, f2**H I C I Log-normal distribution of H I mass fraction vs. p, with γeff = 5/3**Observed composite f1, f2**H I C I Log-normal distribution of H I mass fraction vs. p, with γeff = 5/3**Observed composite f1, f2**H I C I Log-normal distribution of H I mass fraction vs. p, with γeff = 5/3**Observed composite f1, f2**H I C I Bimodal distribution of H I mass fraction vs. p, with γeff = 5/3 Model composite**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%**N(C I)/1012 cm-2**Log p/k**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**Total gas derived using an ionization correction with an**average Galactic radiation field N(C II)/1012 cm-2 Log p/k**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.**Distribution of radiation intensities**Assumed average field strength Log ( I / I0 )**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**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**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**Total gas derived using an ionization correction with an**explicit radiation field Log p/k