Monte Carlo Photoionization Simulations of Diffuse Ionized Gas Kenneth Wood University of St Andrews In collaboration with John Mathis, Barbara Ercolano, Ron Reynolds, Torsten Elwert, Matt Haffner, Greg Madsen

Milky Way’s DIG: Recap Wisconsin H  Mapper: DIG everywhere n(z) ~ 0.2 exp(-|z|/H) cm -3, ff ~ 0.2 H ~ 1 kpc, if isothermal T ~ 8000 K Reynolds, Tufte, Haffner, Madsen,…

Line Ratios: Physical Conditions [N II]/H  increases with height => T increases Problem for spherically averaged models Extra heating (Reynolds et al. 1999) Haffner et al. (1999) HH [N II]/H  [S II]/H  [S II]/[N II]

Scatter Plots [N II]/H  large where H  faint Note tightness of correlation Haffner et al. (1999) [N II]/H  H  (R) [S II]/H  [N II]/H 

Need 3D Photoionization Codes

Monte Carlo Photoionization Wood, Mathis, & Ercolano (2004) 3D density structure and radiation transfer Ions: H, He, C, N, O, Ne, S Stellar and diffuse photons in Cartesian grid Input: ionizing spectrum from source(s) Output: 3D temperature & ionization structure Emissivities, emission line maps, line ratios See also:Och, Lucy, Rosa (1998) Ercolano et al. (2003)

Lexington H II Benchmarks T * =40000K, Q(H)=4.26E49 s -1, n(H)=100 cm -3 + Monte Carlo ( CLOUDY

2D Ionization & Temperature Point source, Q = s -1, n(z) ~ exp(-|z|/H) Slices through grid in x-z plane Temperature rises away from source Wood & Mathis (2004) z (kpc)

2D Models: Line Ratios [N II]/H , [S II]/H  increase with height Highest energy photons penetrate to high z Harder radiation field at large distances from source Wood & Mathis (2004) z (kpc)

Scatter Plots 1D models predict tight correlation: each sightline samples same temperature and ionization structure Elwert & Dettmar (2004) [N II]/H  H  (R)

2D models show scatter: sightlines probe different temperatures and ionization Slope change in [S II]/H  – [N II]/H  : interfaces, not seen in Milky Way’s DIG Wood & Mathis (2004)

Scatter Plots: 3D Structure? Multiple sources with different spectra 3D Density structure Strategy:Planar emission at z = 0 Repeating boundariesin x, y Smooth and two-phase densities Vary Q, n(z) to fit H  (z) What is [N II]/H , extra heating?

Two Phase Density Dense grid cells with filling factor 0.01 < ff < 1 Minimum “clump” size set by grid resolution

Smooth Model n(z) = 0.1 exp(-|z|/1.3) Large Q to ionize grid: high ionization parameter N mostly N ++ at low z: [N II]/H  too low at large H 

Clumpy Models Decrease ff => lower U => less N ++ => higher [N II]/H  ff =80% ff =40% ff =10%ff =5%

Summary Photoionization heating explains most line ratios Extra heating ~ n e erg cm -3 s -1 for largest line ratios, [N II]/H  Smooth models: too low [N II]/H  at large H  Clumpy models with ff ~ 0.2 look good Caution: 3D Toy Model!

Future Work More 3D models: lots of parameter space Apply this to WHAM B star H II regions Constrain models with additional WHAM data: [S II], [O I], [O II], [O III], He I Need S dielectronic recombination rates Merge 3D photoionization with MHD…

Future Work Take 3D density from MHD simulation 3D ionization simulation Density from De Avillez & Berry (2001) log n