Charging of Dust Grains in Photoionized Gas Marcos Hilsenrat

1. Charging of Dust Grains in Photoionized GasMarcos Hilsenrat

2. Outline • AGNs (Brief introduction) • Gas interaction with ionizing radiation • Scientific background • Evidence for dust in AGNs • Research goals • Calculations and results • Basic assumptions • Calculation steps • Results and discussion

3. Active Galactic Nuclei • Energetic phenomena in central regions of galaxies which cannot be attributed to stars. • Strongest persistent sources of ionizing radiation in the Universe. • The ionizing radiation is produced by gas accreting onto the central massive black hole. • The two largest subclasses of AGNs are: - Seyfert galaxies - LSeyfert ~ Lgalaxy - Quasars - Lquasar ≥ 100 Lgalaxy

4. Gas interaction with ionizing radiation • The temperature and ionization state of photoionized gas are set by interaction with the radiation field. • Low radiation intensity and energy  gas tend to becold and neutral. • Photon flux and energy rises  gas ionization state increases, but its temperature remains nearly constant at T ~ 104 K because the line cooling effect (Osterbrock 1989). • Above a critical ionization parameter, U ≡ nph/ ne  high ionization state  inefficient line cooling  runaway to Compton temperature, TC. • For AGNs, TC ~ 107 K (e.g. Krolik 1999).

5. Gas interaction with ionizing radiation (cont) • About 1 % of the gas mass in the Galactic ISM is in the form of small solid grains (e.g. Whittet 1992). • Inelastic scattering of electrons on the grains is an ionization independent cooling mechanism which increases with Te dominant at high enough U. • This cooling may stop the gas from reaching TC. • Grain surface provides a recombination site for incident ions  may lower the ionization state of the gas. • From X-ray absorption spectra  presence of highly, but not fully ionized plasma, not reaching TC (e.g. George et al. 1998). • Dust is rapidly spattered at Te > 106K (Draine & Salpeter 1979). • Only if Te < 106 K, dust may have a major effect on the temperature and ionization state of photoionized dusty gas in AGNs.

6. Gas equilibrium temperature • Simple analytic estimates suggest that Te may be kept below 106 K. • (Gas: Osterbrock 1989, Dust: Draine 1978) For typical values in a pure H region, the level of ionization is x ≡ nHII/nHI 3 x 103 U As U increases, x increases, therefore nH ~ nHII ‹gas› 2 x 10-18x-1cm2 ‹dust› 1.4 x 10-21 cm2/ (H atom) is independent of U For U > 3 x 10-3 dust > gas

7. Gas equilibrium temperature (cont.)

8. Gas equilibrium temperature (cont.)

9. Evidence for dust in AGNs

10. Research goals • Interactions of X-ray photons with grains • Grain photoelectric yield • Energy spectrum of ejected photoelectrons • Heating and cooling rates of gas by dust • Equilibrium grain charge as a function of grain size, composition, gas density and ionizing flux • Gas equilibrium temperature

11. Basic assumptions • Ionizing source (relevant to AGNs) • Luminosity: 1044 erg s-1 • Distance: 1 pc • Shape of the radiation field • Gas (normalizing parameters) • Composition : Hydrogen • Temperature: 104 K • Density: 1 cm-3 • Dust grains (observational data) • Composition: C (graphite) and (MgFe)SiO4 (olivine) (e.g. Laor & Draine 1993) • Mass fraction  mdust/ mgas 0.01 • Geometrical shape • Size distribution

12. Basic assumptions (cont.) • Shape of the radiation field • Power law spectrum (e.g. Peterson 1997) • dnph/dE [photons s-1 eV]  Eph- • 2 ≤ ≤ 3   =2.5, Eph ≤ 104 eV • Grains geometrical shape • Low polarization of extincted light (e.g. Draine & Lee 1984) nearlyspherical shape • Grains size distribution • Stellar light extinction  MRN grain size distribution (Mathis, Rumpl & Nordsieck 1977) • dn(a)/daa-3.5, 0.005 m ≤a ≤ 0.25 m • Optical geometry approach • Photons travel in straight lines, ignoring refraction and reflection inside the grain

13. Basic assumptions (cont.) Photoelectron current from grain (e.g. Evans 1991) Incoming current from ions and electrons impinging on grain from Draine & Sutin (1987) In electrostatic equilibrium:

14. Calculation steps • Grain composition and photon energy range: bound-free absorption cross section • Grain optical depth parameter and absorption efficiency • Pathlength distribution function • Energy of photoelectrons at their formation points, including Auger electrons • Electrons range • Energy distribution of photoelectrons at grain surface • Integration over the power law ionizing continuum and next, over the MRN size distribution • Current of impinging electrons and ions on grain • Grain potential to obtain a zero total current

15. Bound-free absorption cross section Calculated with the fit parameters given by Verner & Yakovlev (1995)

16. Grain absorption efficiency grain optical depth parameter:  = 2an

17. Absorption efficiency for extreme grain radius in the MRN grain size distribution

18. Absorption efficiencyaccurate vs. simplified calculations Accurate to ~ 20 % above 10 eV, and to better than 1 % above 100 eV.

19. Pathlength distribution functionDistribution of distances traveled by photoelectrons from their emission point to the grain surface (Voit 1991)Angular distribution of velocities (Agarwal 1991) 1. Distribution of dimensionless escape pathlengths 2. Probability of photoabsorption between η and η + d η for a given 

20. Pathlength distribution function (cont)

21. Pathlength distribution function (cont)

22. Electron energy deposition in matter Ee= Eph – Ebind R(Ee): Column density of the material necessary to stop an electron with initial energy Ee. Fittings from Ashley & Anderson (1981) and Ashley (1990)

23. Electron ranges(Comparison with Dwek & Smith (1996))

24. Electron energy distribution on grain surface for specific grain radius

25. Energy carried away by escaping electrons(Comparison with Dwek & Smith (1996))

26. Integration over the power law ionizing continuum

27. Integration over the MRNgrain size distribution

28. Incoming current (Draine & Sutin (1987))Maximal grain potential (Draine & Salpeter (1979))

29. Calculation of grain equilibrium charge

30. Equilibrium charge and equilibrium current as function of grain radius

31. Grain equilibrium potentialHeating and cooling rates Vg(graphite) = (993.84  11.13) V Vg(silicate) = (2274.27  41.03) V

32. Minimal surviving grain size as function of the distance to the continuum source

33. Summary • Flexible code • Build in parameter and assumption • Grain spherical shape • Optical geometry approach • Needed: Experimental data in the relevant energy regime for electron ranges in matter. • Inclusion of other physical effects • Sticking coefficient • Recombination rates on grain surface • Grain size time dependence: sputtering by ion impacts