Infrared emission from dust and gas in galaxies Manolis Xilouris Institute of Astronomy & Astrophysics National Observatory of Athens Nuclear activity in galaxies :: UOA 11 July 2016

Absorption coefficient and optical depth Consider radiation shining through a layer of material. The intensity of light is found experimentally to decrease by an amount dIλ where dIλ=-αλΙλds. Here, ds is a length and αλ is the absorption coefficient [cm-1]. The photon mean free path, , is inversely proportional to αλ. Ιλ Ιλ+dΙλ ds Two physical processes contribute to light attenuation: (i) absorption where the photons are destroyed and the energy gets thermalized and (ii) scattering where the photon is shifted in direction and removed from the solid angle under consideration. The radiation sees a combination of αλ and ds over some path length L, given by a dimensional quantity, the optical depth:

Importance of optical depth We can write the change in intensity over a path length as . This can be directly integrated and give the extinction law: An optical depth of corresponds to no reduction in intensity. An optical depth of corresponds to a reduction in intensity by a factor of e=2.7. This defines the “optically thin” – “optically thick” limit. For large optical depths negligible intensity reaches the observer.

Emission coefficient and source function We can also treat emission processes in the same way as absorption by defining an emission coefficient, ελ [erg/s/cm3/str/cm] : Physical processes that contribute to ελ are (i) real emission – the creation of photons and (ii) scattering of photons to the direction being considered. The ratio of emission to absorption is called the source function.

Radiative Transfer Equation We can now incorporate the effects of emission and absorption into a single equation giving the variation of the intensity along the line of sight. The combined expression is: or, in terms of the optical depth and the source function the equation becomes: Once αλ and ελ are known it is relatively easy to solve the radiative transfer equation. When scattering though is present, solution of the radiative transfer equation is more difficult.

Monte Carlo – The method Process with 3 outcomes: Outcome A with probability 0.2 Outcome B with probability 0.3 Outcome C with probability 0.5 We select a large number N of random numbers r uniformly distributed in the interval [0, 1). Approximately, 0.2N will fall in the interval [0, 0.2), 0.3N in the interval [0.2, 0.5) and 0.5N in the interval [0.5, 1). The value of a random number r uniquely determines one of the three outcomes. More generally: If E1, E2, …,En are n independent events with probabilities p1, p2, …, pn and p1+ p2+…+pn=1 then a random number r with p1+p2+…+pi-1 ≤ r < p1+p2+…+pi determines event Ei For continuous distributions: If is the probability for event to occur then determines event uniquely. 0.3N 0.2N [ ) 0.2 0.5 1

Monte Carlo – Procedure Step 1: Consider a photon that was emitted at position (x0, y0, z0). Step 2: To select a random direction (θ, φ), pick a random number r and set φ=2πr and another random number r and set cosθ=2r-1. Step 3: To find a step s that a photon makes before an event (scattering or absorption) occurs, pick a random number r and use the probability density where is the mean free path of the medium in equation Step 4: The position of the event in space is at (x, y, z), where: x= x0+ s sinθ cosφ y= y0+ s sinθ sinφ z= z0+ s cosθ Step 5: To determine the kind of event occurred, pick a random number r. If r<ω (the albedo) the event was a scattering (go to Step 6), else, it was an absorption (record the energy absorbed and go to Step1). (x,y,z) s θ (x0,y0,z0) φ

Monte Carlo – Procedure Step 6: Determine the new direction (Θ, Φ), where Θ is the angle between the old and the new direction (to be determined from the Henyey-Greenstein phase function *) and Φ=2πr. Step 7: Convert (Θ, Φ) into (θ, φ) and go to Step 3. Continue the loop described above until the photon is either absorbed or escapes from the absorbing medium. Θ * Henyey & Greenstein, 1941, ApJ, 93, 70 Φ s θ (x0,y0,z0) φ

Monte Carlo – Procedure Step 6: Determine the new direction (Θ, Φ), where Θ is the angle between the old and the new direction (to be determined from the Henyey-Greenstein phase function *) and Φ=2πr. Step 7: Convert (Θ, Φ) into (θ, φ) and go to Step 3. Continue the loop described above until the photon is either absorbed or escapes from the absorbing medium. Θ * Henyey & Greenstein, 1941, ApJ, 93, 70 Φ s θ (x0,y0,z0) φ

Scattered intensities - The method I=I0+I1+I2+…

Scattered intensities The method { Δs Henyey & Greenstein, 1941, ApJ, 93, 70 Weingartner & Draine, 2001, ApJ, 548, 296

Verification Scattered Intensities - Approximation Kylafis & Bahcall, 1987, ApJ, 317, 637 Verification 1. The scattering is essentially forward Henyey & Greenstein, 1941, ApJ, 93, 70

Approximation Verification 2. Computation of the I2 term Kylafis & Bahcall, 1987, ApJ, 317, 637 Verification 2. Computation of the I2 term

Approximation Verification 2. Computation of the I2 term Kylafis & Bahcall, 1987, ApJ, 317, 637 Verification 2. Computation of the I2 term

Model application in spiral galaxies Xilouris et al, 1999, A&A, 344, 868

M51 FUV 3.6 μm 8 μm 24 μm 160 μm model observation

DIRTY – M.C. SKIRT – M.C. TRADING –M.C. CRETE – S.I. Code Comparison in galactic environments DIRTY – M.C. SKIRT – M.C. TRADING –M.C. CRETE – S.I.

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http://dustpedia.com/

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CIGALE – Code Investigating GALaxy Emission - http://cigale.lam.fr MAGPHYS – Multi wavelength Analysis of Galaxy PHYSical properties http://www.iap.fr/magphys/magphys/MAGPHYS.html

Xiao-Qing Wen, et al. 2013, MNRAS, 433, 2946 Bell et al. 2003, 149, 289 Yu-Yen Chang, et al. 2015, ApJ, 219, 8 Bitsakis et al. 2011, A&A, 533, 142

Name log(M_star) log(SFR) NED_classification SDSS J094310. 11+604559 Name           log(M_star)   log(SFR)   NED_classification SDSS J094310.11+604559.1   9.7      -0.621    broad-line AGN MRK 1148                               10        1.401     Sy1-QSO MRK 0290                               10        0.99      Elliptical UGC 04438                             10.3   -0.679    Spiral KUG 0959+438                       10.5     0.66      Spiral 2MASX J08555426+0051110  10.6   -0.311    Sy1-QSO NGC 3188                               10.6      0.152    (R)SB(r)ab 2MASX J08413787+5455069  10.8   -0.931    broad-line AGN 2MASX J10074256+4252073  11      -0.634    AGN VV 487                                    11.1    1.095     Sc, Sy1 UGC 00488                             11.2     0.624    Sab, Sy1 IC 3078                                   11.3    1.199      Sb UGC 08782                             11.5     0.389    Spiral NGC 2484                               11.9   -2.109    S0 NGC 4151 10.1       0.057 Sy1