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Summary ISummary I

HH22 Shielding: -- Shielding: -- ββ((ττ) vs) vs full H2, full H2, correction for correction for

sphere/slab, Go/n sphere/slab, Go/n alone not whole story alone not whole story -- line overlap important -- line overlap important or not? or not? -- -- determine thin rates determine thin rates with with ∫I(∫I(λλ))σσ((λλ)d)dλλ (no fit) (no fit)

PDR Workshop

Summary IISummary II

Line Transfer: -- Optically thick, Line Transfer: -- Optically thick, effectively thin line has effectively thin line has

higher n_i higher n_i in sphere vs in sphere vs

slab (for same T) slab (for same T) -- In MC -- In MC vs ALI beware vs ALI beware convergence for convergence for ττ>>1 >>1 -- Check levels n_i not -- Check levels n_i not just T just TRR or total I or total I

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Photon Processes in Photon Processes in (Inhomogeneous) PDRs (Inhomogeneous) PDRs

Marco Spaans (Kapteyn) Marco Spaans (Kapteyn)

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ClumpinessClumpiness

Parameter k decreases in expression for Parameter k decreases in expression for RR

For given NFor given NHH columns of C+ and C not columns of C+ and C not strongly affected, but spatial extent isstrongly affected, but spatial extent is

Column density of CO is boosted in Column density of CO is boosted in dense clumpsdense clumps

Back scattering of UV photons causes Back scattering of UV photons causes complicated clump illumination: complicated clump illumination: <cos θ>(λ) and ω(λ)<cos θ>(λ) and ω(λ)

Influences C+ -> C -> CO transitionInfluences C+ -> C -> CO transition

PDR Workshop

S140, edge-on PDRS140, edge-on PDR n=Fn_c+(1-F)n_in=Fn_c+(1-F)n_i r=n_c/n_i, clump r=n_c/n_i, clump

size l_c=0.02 pc size l_c=0.02 pc Iuv=140, F=30%, Iuv=140, F=30%,

r=10, n=2(4) cm-3r=10, n=2(4) cm-3

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total total H density [CI] 609 H density [CI] 609 μμm & m & ¹³¹³CO 2-1CO 2-1

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HH22 emission emission

Fluorescence: Fluorescence: UV – Vis – IR UV – Vis – IR Diagnostic for Iuv/nDiagnostic for Iuv/nH H

No collisional de-excitation if density No collisional de-excitation if density less than 10^4 cm-3 less than 10^4 cm-3 (same for multiple pumping)(same for multiple pumping)

Scaling: IScaling: IFF/Iuv (Rn/Iuv (RnHH/Iuv,N/Iuv,NHH) and ) and N NHH(Rn(RnHH/Iuv,Av)/Iuv,Av)

Also pure rotational line emission Also pure rotational line emission

PDR Workshop

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26-ray 26-ray approximationapproximation

3-D3-D Isotropic Isotropic

illumination illumination IRAS G236+39: HI IRAS G236+39: HI

21 cm and 100 21 cm and 100 μμm m dustdust

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Photorates with depthPhotorates with depth

R=Ro e^(-k Av); Ro strong function of TeffR=Ro e^(-k Av); Ro strong function of Teff k is a fit and k~1-3k is a fit and k~1-3 CO (absorptions into pre-dissociated states) CO (absorptions into pre-dissociated states)

and Hand H22 (Lyman-Werner+cascade) self- (Lyman-Werner+cascade) self-shield; TH, de Jong et al.: shield; TH, de Jong et al.: ββH2H2(τ>10)={τ^-1[ln(τ/π^½)]^½+ (τ>10)={τ^-1[ln(τ/π^½)]^½+ (b/τ)^½}erfc(τb/πv^-2)^½ (b/τ)^½}erfc(τb/πv^-2)^½ R RCOCO * [1+ * [1+αβαβCOCO((ττ)]/(1+)]/(1+αα) or ) or shielding shielding functions van Dishoeck & functions van Dishoeck & Black (1988)Black (1988)

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Photorates with depthPhotorates with depth

Good if line overlap is ignored; edge effects Good if line overlap is ignored; edge effects still occur; Iuv/nstill occur; Iuv/nHH ratio crucial ratio crucial

HH22* (v=6/2.6 eV) versus H* (v=6/2.6 eV) versus H2 2 (J,v)(J,v) Line overlap: HLine overlap: H2 2 , H, CO, C, H, CO, C MC HMC H22: N=135, λ=1000 Å, f=3.5(-3), : N=135, λ=1000 Å, f=3.5(-3),

A=5.7(8) s-1, η=0.127 A=5.7(8) s-1, η=0.127 MC CO: N=33, λ=1002 Å, f=2.0(-2), MC CO: N=33, λ=1002 Å, f=2.0(-2),

A=3.0(11), η=1.0 A=3.0(11), η=1.0

PDR Workshop

Photorates with depthPhotorates with depth

Should integrate photo-ionization Should integrate photo-ionization and photo-dissociation cross and photo-dissociation cross sections: σ(λ)sections: σ(λ)

Note: CRs and X-rays can be Note: CRs and X-rays can be important; important; CRs no CRs no attenuation, X-rays attenuation, X-rays column of Ncolumn of NHH~10^22 cm-2~10^22 cm-2

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ReferencesReferences

Tielens & Hollenbach 1985Tielens & Hollenbach 1985 Kaufman et al. 1999; Spaans 1996; Kaufman et al. 1999; Spaans 1996;

Sternberg & Dalgarno 1995; Stőrzer et al. Sternberg & Dalgarno 1995; Stőrzer et al. 1995; Spaans et al. 1994; Wolfire et al. 1995; Spaans et al. 1994; Wolfire et al. 1993; le Bourlot et al. 1993; Tielens et al. 1993; le Bourlot et al. 1993; Tielens et al. 1993; Boisse’ 1990; van Dishoeck & Black 1993; Boisse’ 1990; van Dishoeck & Black 1988; Sternberg 1988; Black & van 1988; Sternberg 1988; Black & van Dishoeck 1987; de Jong et al. 1980; Black & Dishoeck 1987; de Jong et al. 1980; Black & Dalgarno 1976Dalgarno 1976

Maloney et al. 1996Maloney et al. 1996