1. ISM Lecture 7 H I Regions I: Observational probes

2. H I versus H II regions  T and n H are different in H I regions   Different processes play a role  Different observational techniques  H II regions  Mostly emission lines at optical wavelengths  H I regions  H I radio line at 21 cm  Optical absorption lines Ref: Kulkarni & Heiles 1987, in Interstellar Processes, p.87 Burton 1992, in Galactic ISM

3. 7.1 Review of radiation transport  Radiative transfer equation or with the optical depth  General solution of radiative transport equation with  r = total opacity from s=0 to s=r Source function

4. Special case: Thermodynamic Equilibrium  In thermodynamic equilibrium, Kirchhoff’s Law applies:  I =B ν (T) is the Planck function  The radiative transfer equation then becomes

5. General ISM case (non-TE)  Suppose line has Gaussian profile    V  one-dimensional velocity dispersion   V 2 =kT/M for thermal velocities

6. Absorption and emission coefficients    

7. Excitation temperature T ex   with excitation temperature

8. General radiation transport  =>  Rayleigh-Jeans limit: h <<kT

9. Antenna temperature  The antenna temperature T A is defined by  Advantage  T A is a linear function of I  For h /kT<<1, B (T A )=I => Rayleigh-Jeans limit, which is a good approximation at radio wavelengths  Disadvantage  For h /kT  1, B (T A )<I => e.g. at sub-mm wavelengths T A does not correspond to a physical temperature, even if emission is thermal

10. 7.2 H I 21 cm line emission  H atom consists of 1 proton + 1 electron  Electron: spin S=1/2  Proton: nuclear spin I=1/2  Total spin: F = S + I = 0, 1  Hyperfine interaction leads to splitting of ground level:  F = 1 g u = 2F+1 = 3 E = 5.87  10 –6 eV  F = 0 g l = 2F+1 = 1 E = 0 eV

11. H I 21 cm line emission  Transition between F = 0 and F = 1:  ν = 1420 MHz, λ = 21.11 cm  ΔE / k = 0.0682 K  A ul = 2.869  10 –15 s –1 = 1/(1.1  10 7 yr) (very small!)  f lu =5.75  10 -12  For all practical purposes kT ex >> hν  T ex for H I is called “spin temperature” T S

12. Spin temperature and kinetic temperature  Often excitation is dominated by collisions  T S = T kin (e.g., in cold clouds with n  0.05 cm –3 )  In warm, tenuous clouds (T  300 K): T S < T kin  In some regions: upper level pumped by Lyα radiation  T S > T kin

13. Optical depth of H I line  Consider uniform cloud of length L and Gaussian line with FWHM Δν = ν/c ΔV (see eq. 7.1, with  V=2  2  V )   N(HI) = 4 n l L is the total HI column density   V=FWHM in km s -1

14. Example of optical depth H I line  T S = 100 K, Δ V = 3 km/s  τ << 1 for N(HI) << 5.5  10 20 cm –2  For τ << 1 or N(H I)  1.818  10 18 T A  V => T A proportional to N(H I), independent of T S  In most cases N(H I) << 5.5  10 20 cm –2 => 21 cm emission usually gives information on column density of H I, but not on temperature

15. 7.3 H I emission-absorption studies  Study extended cloud in front of extragalactic radio source  Observe two positions (on-source and off-source = blank)  Assume that cloud is uniform  properties of H I are the same in source and blank positions

16. H I emission-absorption studies (cont’d)  Measure on-line and off-line at each position 

17. H I emission-absorption studies (cont’d)  Both τ and T S can be measured  both N(H I) and T S can be determined!  Holds only over small regions  need small beam size (3 for Arecibo 330 m,  30  for VLA and Westerbork interferometers)  Recall  τ very small if T S large  warm H I regions cannot be measured in absorption

18. Two clouds along the line of sight: apparent T S  Assume T bg definition of “naïvely-derived” spin temperature at velocity V  If cloud homogeneous, T S = T N  Often, there are two H I clouds along the line of sight with overlapping V. Assume cloud 1 closer than cloud 2 => T N depends on V and lies between T 1 and T 2

19. Consider 3 examples  Optically thick foreground:   >>1 => T N (V)=T S,1 no information on cloud 2  Optically thick background, thin foreground: T N (V)=T S,1  1 (V)+T S,2 => T N is larger than T S,2  Both clouds optically thin (usual case): T N is weighted harmonic mean of T 1 and T 2

20. Effect of foreground cloud on observed T S  Example: T 1 = 8,000 K, T 2 = 80 K, N 2 /N 1 = 0.1  Small cold cloud can reduce “naïvely derived” spin temperature of warm background cloud from 8,000 K to 800 K

21. 7.4 Evidence for two-phase ISM  Good agreement between narrow absorption lines and narrow peak emission lines:  V  3 km/s  There is emission outside region over which absorption occurs (dashed lines):  V  9 km/s

22. H I emission and absorption spectrum  Note that the absorption features are sharper than the corresponding emission spectrum => Observations indicate that H I consists of 2 components

23. 1. Cold Neutral Medium  Cold diffuse clouds with T  80 K => narrow absorption + emission components  Every velocity component corresponds to an individual cloud  CNM occurs in clumps throughout the disk of the Milky Way with z  100 pc  Typically in disk: N(HI) full thickness  6  10 20 cm -2  Locally: N(HI)  4  10 20 cm -2 => We live in a “H I hole”

24. 2. Warm Neutral Medium  Broad emission component => temperature difficult to estimate   V  9 km s -1 => T<10000 K  Limits on  => T>3000 K  WNM is distributed throughout Milky Way with substantial filling factor  “raisin- pudding” model of ISM  Large scale height (Gaussian z  250 pc or exponential z  500 pc >> z of CNM) => warm H I halo? => T  8000 K

25. T –  relation?  Clouds with higher optical depth tend to have lower temperatures

26. ‘Luke-warm’ H I in Milky Way?  In general, absorption lines narrower than corresponding emission features => do cold clouds have a warm (T  500 K) envelope?  T lower if  larger  Maps indicate  Clumps are responsible for H I absorption  T  30-80 K, n  20-50 cm -3  Filaments/sheets have T  500 K and are responsible for 80% of the H I emission not seen in absorption

27. 7.5 Optical absorption lines: Voigt profiles and equivalent widths  Traditional way of studying H I clouds: mostly Na I and Ca II lines  Optical lines => ΔE >> kT for T  80 K  neglect (stimulated) emission where  =N l  with N l =column density in level l

28. Line broadening mechanisms  Upper level has finite radiative lifetime  Lorentzian profile with damping width α L  Thermal and random / turbulent broadening  Gaussian profile with HWHM α D

29. Gaussian vs. Lorentzian profiles

30. Measures of Doppler width  α D is HWHM by definition; units are Hz  FWHM in velocity units is  Frequently the width of the Gaussian is given in terms of the “Doppler parameter”

31. Voigt profile  Convolution of Lorentzian and Gaussian profiles  Define  Voigt profile: with Here

32. Equivalent width of spectral lines  In practice, resolution at optical wavelengths often insufficient to resolve line  measure only line strength or equivalent width  Definition of equivalent width of line:  W ν is the width of a rectangular profile from 0 to I ν (0) that has the same area as actual line  W ν measures line strength, but units are Hz  In wavelength units

33. Schematic drawing of equivalent width of line

34. Curve of growth analysis  Goal: relate equivalent width W ν or W to column density N l  Relation is monotonic, but non-linear  Classical theory developed in context of stellar atmospheres, but equally applicable to ISM  Three regimes, depending on τ at line center:  τ 0 << 1, linear regime  τ 0 large, flat regime  τ 0 very large, square-root (damping) regime

35. Curve of growth (schematic) DD DD LL LL

36. Universal curve of growth

37. Curve of growth: linear regime  Weak lines, τ 0 << 1  Linear regime: W  N l  If W λ and λ in Å,

38. Curve of growth: flat regime  Large τ 0 : all background light near line center o is absorbed, line is “saturated”  Far from line center there is partial absorption because σ is smaller => W ν grows very slowly with N l : flat part of the curve of growth  Onset if deviation from linear >10%, depends on Doppler parameter:

39. Curve of growth: square root regime  Very large τ 0 : Lorentzian wings of profile dominate the absorption  Asymptotic form  Square-root or damping regime: W  N l 1/2

40. Examples of interstellar Na absorption lines  Linear and flat regimes  Flat regime  Square-root regime Hobbs 1969

41. UV absorption lines in ISM towards ζ Oph

42. 7.6 Optical absorption line observations  Technique limited to bright background sources  Mostly local (< 1 kpc), mostly A V < 1 corresponding to N(H) < 5  10 20 cm –2  Strong Na I lines in every direction, same clouds as seen in H I emission and absorption, also seen in IRAS 100 μm cirrus  CNM  H I column densities from Lyα observations in UV at 1215 Å  Information about T, n H from excitation C II, C I lines (see later): T  80 K, n H  100 cm -3

43. Depletions  Absorption line studies of various atoms  abundances w.r.t. H  information on depletions  In diffuse clouds many abundances are much smaller than solar  depletion onto grains  log D = log abundance meas – log abundance cosmic  Ca: log D  –4  10,000 times less than solar  Plot log D as a function of condensation temperature T c  strong correlation  elements with large T c condensed onto grains when formed in circumstellar envelopes

44. Depletions log D versus condensation temperature Jenkins 1987, in Interstellar Processes