External UV and infrared radiation field¶

There are three parameters to control how ProDiMo sets up the (isotropic) background radiation field.

1.0         ! CHI_ISM     [-]      : strength of external UV  ("Gknot")
2.7         ! Tback       [K]      : background temperature
.false.     ! IR_ISRF              : using Mathis interstellar radiation field?

The values listed above are the default values. Normally, ProDiMo sets up the background radiation field via

IISM(l) = CHI_ISM * 1.71 * 9.85357e-17 * MEAN_PL(20000.0,l) + MEAN_PL(Tback,l)

where MEAN_PL(T, lambda_index) is the Planck function integrated over the wavelength bin l. The value 9.85357e-17 is the dilution factor of the "distant O-stars". If CHI_ISM=1, that radiation field, integrated over 912 - 2050 A, matches a Draine field integrated over 912 - 2050 A. Tback is by default 2.7K (CMB).

You will find the bin center wavelengths [mic], frequencies [Hz], and background mean intensities [erg/cm2/Hz/s/sr] in output file BgSpectrum.out.

After the radiation field is setup this way, ProDiMo

1. normalises again to a Draine field, and then
2. calculates the radiative equilibrium temperatures of
   • a black body ("optically thick") and
   • the chosen dust ("optically thin"), just for information. The latter uses the dust absorption coefficient of the chosen dust.

If you stick to the default choices, the following results should be written to stdout:

INCIDENT INTENSITIES ...
 ... parameters CHI_ISM=1.000E+00,  Tback=  2.700E+00,  IR_ISRF=F
 before: chi=   1.09475360884345     
   norm: chi=   1.00000000000000     
 ... min dust temperature (opt.thick limit)=  2.97K
 ... min dust temperature (opt. thin limit)=  4.74K

The dust heating is dominated by the 2.7K CMB. But since there is also the external UV, a grey absorber has temperature 2.97K > 2.7K in that radiation field, and the chosen dust has 4.74K.

If you choose CHI_ISM=1000, the result is

INCIDENT INTENSITIES ...
 ... parameters CHI_ISM=1.000E+03,  Tback=  2.700E+00,  IR_ISRF=F
 before: chi=   1094.75360884345     
   norm: chi=  1000.000000000000     
 ... min dust temperature (opt.thick limit)= 12.55K
 ... min dust temperature (opt. thin limit)= 19.54K

so we would expect the dust in the disk to get no cooler than 12.55 K in this case, likely closer to 19.54 K. Thus, for CHI_ISM=1000, the 20000 K blackbody dominates the heating by the CMB already.

The easiest way to have additional far-IR in the model is to play with Tback:

INCIDENT INTENSITIES ...
 ... parameters CHI_ISM=1.000E+03,  Tback=  3.000E+01,  IR_ISRF=F
 before: chi=   1094.75360884345     
   norm: chi=  1000.000000000000     
 ... min dust temperature (opt.thick limit)= 30.23K
 ... min dust temperature (opt. thin limit)= 30.79K

But this is really adding only far-IR and mm/cm light in form of a Planck field(Tback) instead of the CMB Planck field(2.7K).

A physically more motivated way is to do the same thing by switching on IR_ISRF. In that case, we have

IISM(l) = CHI_ISM * 1.71 * 9.85357e-17 * MEAN_PL(20000.0,l) + MEAN_PL(2.7,l) + fac*MATHIS(l)

where MATHIS is the radiation field from Mathis et al.(1983), tables A3,B1. It accounts for the Cosmic Background background, Red Supergiants + IR cloud emission (HII regions). The ISRF is valid at 10 kpc from the Galactic center. The data is rescaled to $\lambda \times J_\lambda$ [W/m^2].

However, the MATHIS radiation field has no hard FUV, only from optical to 1 mm, so we have to patch it together. The idea in the formula above is to work out fac until Tback is reached:

 INCIDENT INTENSITIES ...
 ... parameters CHI_ISM=1.000E+03,  Tback=  3.000E+01,  IR_ISRF=T
 before: chi=   1094.75360884345     
 reading /home/pwoitke/ProDiMo/data//ISRF_ProDiMo_Mathis_highres.dat ...
 ... adding ISRF from Mathis et al.(1983)  Tback=  3.000E+01K  fac=  7.280E+03
  after: chi=   1097.28400902931     
   norm: chi=   1000.00000000000     
 ... min dust temperature (opt.thick limit)= 29.97K
 ... min dust temperature (opt. thin limit)= 38.48K

So ... we actually have two parameters (CHI_ISM and Tback) and one option (IR_ISRF). This is only consequent, as the sources for the UV and for the interstellar IR are not necessarily the same. If you only choose IR_ISRF=T, it will only have an effect if you also choose a value of Tback resulting in $\mathrm{fac}>0$. Otherwise, this option will be ignored.

In order to reduce the two parameters to one, one could argue that fac==CHI_ISM should hold. Here is a table showing the combination of values to achieve that

CHI_ISM  IR_ISRF  Tback   fac
     1      T      3.7K   1.01
    10      T      6.1K   10.0
   100      T     10.8K   102    
  1000      T     19.3K   1050
 10000      T     34.0K   10010

Peter Woitke, 07/2024