6: Observing Warm Phases: Dispersion ( n e dl ) & Emission ( n

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1 6: Observing Warm Phases: Dispersion ( n e dl ) & Emission ( n 2 e dl ) Measure James R. Graham University of California Berkeley

2 NGC 891 NGC 891 AY 216 2

3 Techniques & Components The Warm Ionized Medium (WIM) also known as DIG Pulsar dispersion measure + Cordes et al Nature Taylor & Cordes 1993 ApJ Optical emission lines: Hα, [SII], [NII] + WHAM: Reynolds 1985 ApJ , Haffner et al ApJSS COBE + N µm Radio recombination lines (ELDWIM) + Heiles Reach & Koo 1996 ApJ Models + McKee & Ostriker 1977 ApJ Kulkarni & Heiles 1988 Galactic & Extragalactic Radio Astronomy + Reynolds 1991 ApJL Slavin McKee & Hollenbach 2000 ApJ AY 216 3

4 Overview of the WIM Photoionized HII Warm (T ~ 10 4 K) Low-density (n e ~ 10-1 cm -3 ) Ionization requires about one O5 star per kpc 2 Thick & clumpy Occupies ~ 20% of the volume within a 2 kpc thick layer about the Galactic midplane + Near the midplane, n(hii)/n(hi) < N(HII)/N(HI) ~ 1/4 1/2 along high b (Galactic latitude) lines of sight + WIM may be the dominant state of the ISM above 1 kpc + Because of thickness WIM may contribute significantly to the midplane pressure & hence effect the expansion of hot (10 6 K) supernova created bubbles AY 216 4

5 Interstellar Refraction Dispersion Relation Treat the ISM as a cold plasma Wave equation in a dielectric medium is r 2 E = 1 2 D r c 2 t 2 Trial solutions E r ( r,t) = E r 0 e i( k r r ω t ) propagating with wave vector k r yield the dispersion relation k 2 = ε c 2 ω 2 where r D = ε r E = r E + 4π r P AY 216 5

6 The Interstellar Dielectric Constant The electric field polarizes the medium The solution to the equation of motion m e r = ee r ( r,t) = ee r 0 e i( k r r ω t ) for a free electron is r = The resultant polarization is So that ε r E = r E 4π n ee 2 m e ω 2 e m e ω 2 r E 0 e iω t r P = n e e r = n e e 2 r E or ε=1 4π n ee 2 Thus ε =1 (ω p /ω) 2 with plasma frequency m e ω 2 ω p 2 = 4π n e e 2 /m e numerically ν p 8.98 n e 1/ 2 khz r E m e ω 2 AY 216 6

7 Interstellar Refraction by Free Electrons The dispersion relation k 2 = εω 2 c 2 can now be written c 2 k 2 = ω 2 ω p 2 For ω > ω p the dielectric constant and wave vector are real Waves propagate without attenuation at group velocity v g = dω dk = c 2 k ω = c ε = c 1 ( ω p /ω) 2 Refractive index Group velocity increases with frequency AY 216 7

8 Interstellar Refraction by Free Electrons Delay time for a signal pulse observed at ω >> ω p t(ω) = d d dl = 1 ω p /ω 0 d 0 v g ω p /ω 0 [ ( ) 2 ] 1/ 2 dl [ ( ) ] dl d 1 = d /c + ω /ω 2 p = d /c c ( ) 2 dl /c c d 0 4πe 2 n e m e ω 2 dl /c Delay depends on the dispersion measure DM = d 0 n e dl AY 216 8

9 Interstellar Refraction by Free Electrons Radio signals from pulsars show progressive delay as ω decreases Measurement of dt/dω yields DM Differential delay ω >> ω p dt dω = 4πe2 m e cω 3 DM where DM = 0 d n e dl AY 216 9

10 Local DM DM from pulsars in globular clusters & the Magellanic Clouds (d=45 kpc) show that WIM extends ~ 1 kpc above the Galactic plane MC DM = n e z/sin b GC 24 cm -3 pc DM = n e z/sin b b z Solid line is for uniform n e = 0.03 cm -3 Dashed lines for n e (z) = 0.03 cm-3 cosh -2 (z/h) with h = 500 pc or 800 pc AY

11 Modeling the Galactic DM Distribution Taylor & Steinbring, 1986 AARA, 24, 285 Circles indicate the DM < 30, , & > 300 cm -3 pc for 398 pulsars AY

12 Modeling the Galactic DM Distribution Typical pulsar at 1 kpc has DM ~ 30 cm -3 pc <n e > ~ 0.03 cm -3 Combine DM with distance estimates to map n e Distances? + Association with SNR + 21 cm HI absorption + Parallax + Distance to binary companion Cordes et al 1991 Nature ; Taylor & Cordes 1993 ApJ AY

13 Axisymmetric Model Two component model for DM ( [ ] 2 ) + n e = n e1 exp( z /H 1 )exp R / A 1 ( [ ] 2 ) n e 2 exp( z /H 2 )exp (R 4) / A 2 Outer Galaxy (1) Inner Galaxy (2) ñ e cm cm -3 H 1 kpc 0.15 A > 20 kpc 2 kpc (Cordes et al Nature ) AY

14 Non-Axis Symmetric Distribution Abandon axisymmetry Sources of photoionization are hot young stars, which are correlated with spiral arms Explicity include location of spiral arms Famous Georgelin & Georgelin model of spiral structure based on radio recombination lines of HII regions and distances to exciting stars Georgelin & Georgelin 1976 AA 49 57: Spiral model from HII regions: 1 AY 216 Sagittarius-Carina; 2 Scutum; 1 Norma arm; 2 Perseus arm. Hatched areas are radio continuum and HI maxima 14

15 Spiral Arms Vallée 2002 ApJ Model of Galactic logarithmic spiral arms (p = 12, m = 4) Logarithmic spiral model fitted to the Galactic longitude values of the tangents to the observed spiral arms as seen from the Sun The Sun is at a Galactocentric distance of 7.2 kpc A central bar extends radially out to 3 kpc, inclined at 20 to the Sun-GC line Dots show Galactocentric radii of 1, 3, 5, 7, 9, 11, &, 13 kpc AY

16 Non-Axis Symmetric Distribution Parametric model for n e including spiral arms Near the sun n e ~ cm -3 Max n e ~ 0.25 cm -3 Radial Vertical AY

17 Non-Axisymmetric Distribution Grey scale representation of n e in the Galactic plane according to Taylor & Cordes Largest densities are ~ 0.18 cm -3 in the outer part of arm 2 Locally, in the Gum Nebula n e ~ 0.25 cm -3 Near the sun <n e > ~ cm -3 Inner ring is probably unresolved spiral arms #2 AY

18 WHAM The Wisconsin Hα Mapper surveys the distribution & kinematics (±100 km/s) of Galactic HII δ > -30 Angular resolution 1 Velocity resolution 12 km/s + First flux calibrated, kinematic maps of the WIM He, S +, N +, O 0, & O cm telescope Dual etalon Fabry- Perot AY

19 Interpretation of Data Assume that the observed surface brightness of Hα emission traces the column n e 2 dl di Hα = j Hα κ Hα I Hα dl j Hα = n e n H +α (2) f Hα hν 4π Assume n H + = n e and κ Hα = 0 ( ) 2 n e I Hα = hν 4π α Hα (2) dl where α (2) Hα = T cm 3 s 1 EM = 2 n e dl = 2.75 T (I Hα /rayleigh) cm -6 pc AY

20 WHAM Hα WHAM-NSS: total intensity. The integrated Hα intensity between v(lsr) = -80 and +80 km/s in Galactic coordinates. The scale runs from log 10 (I/R) =-0.5 to n e dl 2.75 T (I Hα /rayleigh) cm -6 pc AY

21 WHAM Hα Polar view of total integrated Hα intensity between v(lsr) = -80 and +80 km/s for the northern (b = +40 to +90 ) and southern (b = -40 to -90 ) Galactic poles AY

22 WHAM Hα Polar view of the total integrated Hα intensity between v(lsr) = - 80 and +80 km s -1 for the northern (b = +40 to +90 ) and southern (b = -40 to -90 ) Galactic poles AY

23 Scale Height of WIM Perseus arm 125 o < l < 152 o -100 < v/km s -1 < -25 Assume an exponential distribution n e (z) = n e 0 exp( z /H) n e 0 is the mid - plane density ln(i Hα ) Haffner et al ApJ f n e dl 2.75 T I Hα 0 I Hα = I Hα exp( 2 z /H) for constant filling factor f H = 1±0.1 kpc tan(b) AY

24 Ionizing Flux Total emission measure through the entire disk EM 4 cm -6 pc corresponds to an ionizing flux 2 n e α (2) dl = s -1 kpc -2 One O5 star per square kpc Mean free path at 912 Å λ = 1 n HI σ ν 1 = n HI cm 2 = n HI pc AY

25 Filling Factor & n e from EM/DM The WIM is lumpy The ratio EM/DM measures clumping along lines of sight to high latitude pulsars in globular clusters (M5, M13, M15 & M53) Adopt model with HII concentrated in clouds with volume filling fraction f z (Reynolds 1991 ApJL 372 L17) AY

26 Filling Factor & n e from EM/DM Adopt model with HII concentrated in clouds with volume filling fraction f Electron density ( ) n e = n e0 exp z /H n Filling factor f = f 0 exp( z /H ) f The dispersion measure for b = 90 0 DM= 0 n e0 exp( z /H n ) = n e0 f 0 H DM where f 0 exp( z /H ) f dz 1 H DM = 1 H n + 1 H f AY z

27 Joint EM/DM Constraints From observations of high latitude pulsars DM = 24sinb 1 cm -3 pc H DM = 960 pc (Reynolds 1991 ApJL ) From the definition of emission measure EM= 0 n 2 e0 exp( 2z /H n ) = n 2 e 0 f 0 H EM where f 0 exp( z /H ) f dz 1 H EM = 2 H n + 1 H f AY

28 The Reynolds Number Define R = H EM 2 so that EM = n e 0 H DM R = H nh f /2 H n /2 + H f = 1 H n + H f 2 H n /2 + H f H n + H f H n H f f 0 RH DM R =1/2 H f >> H n =1 H f << H n i.e. 1/2 R 1 Reynolds assumes that H f > 0 + Kulkarni & Heiles suggest that f increases with height AY

29 Density & Filling Factor We do not know H n and H f separately Expect n e to decrease with pressure as z increases Assume f decreases because there is less gas As an intermediate value assume Define R = 1 2 so that H n 2 e0 f DM cm-6 pc and n e 0 f 0 H DM 24 cm -3 pc n e0 2 / cm -3 and f H DM H DM 0.21 AY

30 Density & Filling Factor: II Observations in the plane give a higher EM EM 5-10 cm -6 pc (Reynolds 74 ApJL ) Path length set by dust absorption to 1 kpc Use lower range to exclude HII region contamination From EM n 2 e0 f pc = 5 cm -6 pc From DM n e 0 f n e /0.025 = 0.2 cm -3 and f 0 = 0.025/0.2 = AY

31 Physical Conditions Temperature Presence of [SII] 6716, 6730 & [NII] 6548, 6583 implies T e > 5500 K Line width of Hα, [SII] implies T < 10,000 K For collisional excitation Local arm WIM 6000 < T/K < 10,000 Haffner et al ApJ n << n CR I ~ n e n i I 6716 I T (S /H) (N /H) Ω ij g i e hν / kt dl (S + /S) (N + /N) e0.04t T 4 AY

32 Ionization State [OI] 6300 Å is weak WHAM: [OI] 6300/Hα 6563 ~ Charge exchange between O and H is almost resonant because ionization potential is so close + O ev + H ev IP = ev n(o+ ) n(o 0 ) n(h + ) n(h 0 ) e 220 /T n(h + ) n(h 0 ) for T >> 100 K For T e 8000 K low [OI]/Hα requires high ionization + n(h + ) /n(h 0 ) > 15 + If there is so much ionization, why is there any high latitude HI? + Weak [OIII] 5007Å means that ionization is lower than typical HII regions AY

33 Additional material & references AY

34 Ionization State Photoionization models O-star UV leaks from HII regions (Domgorgen & Mathis 1994 ApJ ) ~ 15% of the Galactic budget Low ionization parameter U of a typical HII region Two components + Ionized edges of HI clouds + diffuse component How does the UV get out of HII regions since HI covers the sky? + The HI must contain holes and tunnels (WORMS- Heiles Reach & Koo 1996 ApJ ) Faint HeI 5876Å + Few HeI ionizing photons AY

35 Radio Recombination Lines Envelopes of HII regions are traced by RRL n e ~ 1-10 cm -3 Scales ~ 100 pc Ionizing radiation escapes & produces an envelope of HII around an OB association Visible in its integrated effect in the Milky Way + Not detected as individual envelopes, except for regions like the Gum Nebula AY Heiles Reach & Koo 1996

36 The Worm Ionized Medium Combine pulsar DM and thermal radio observations to estimate the WIM density and filling factor for HII envelopes in spiral arms n e 5 cm -3 and f 0.01 (Heiles Reach & Koo 1996) This model accounts for arm and annulus component of Taylor & Cordes No ring in RRL data Heiles Reach & Koo 1996 AY

37 Ionization Source for the WIM The WIM is photoionzed Source O stars WR stars B PN + WD SNR QSO CR X-ray S (s -1 cm -2 )/ Reynolds 1984 ApJ AY

38 Ionization Source for the WIM Ionization requirement Requires ~ 10% of O stars UV photons to escape Revised O star contribution is 38 x 10 6 s -1 cm -2 S = α (2) n e 2 f L = α (2) EM = (at 8000 K) = cm -2 s -1 (McKee & Williams 1997) At high latitudes cooling hot gas in old supernova remnants may be important (Slavin McKee & Hollenbach 2000 ApJ AY

39 Models for the WIM McKee & Ostriker (1977 ApJ ) Properties of the WIM in the plane of the Galaxy are calculated based on ionization by B stars, WD & SNR n e0 2 f 0 = n e0 f 0 = Ionization of the WIM predicted to be low (x e 0.68) + HI absorbs the ionizing photons consistent with observations AY

40 WIM Models Miller & Cox 1993 ApJ Account for high latitude HII by O star radiation Stromgren spheres from OB associations break through the disk and ionize the halo Includes clouds but not photoevaporation Difficult to account for the low ionization (weak [OIII]) Local ionization EUVE showed that B star ε Canis Majoris dominates the local ionization ~ x 7 of all other stars and x 30 higher than predicted (Vallerga & Welsh 1995 ApJ ) AY