Line Emission from HD204598b

Blackbody luminosity

We have previously calculated the blackbody luminosity from the Intensity as

where

which gives

where

and has units of ergs/s/Hz

We also have from Bourrier et al, a theoretical line emission curve for Lyman Alpha

"Theoretical instrinsic stellar emission line profile scaled to the Earth distance"

with units of ergs/s/cm2/A

After multiplying by 4*pi*47.1 pc 2 to get Luminosity per angstrom, we need to convert to Luminostiy per Hz

To go from to

we need to multiply by

So after some conversions, I get the following which shows the previously used black body, along with the line emission profile.

Now if I assume that the atmosphere is optically thin, and integrate the emission profile (+ continuum) over the absorption cross section -

where

and

This cutoff frequency is much higher than the Lyman Alpha wings… Which is not terribly surprising… Lyman Alpha ( even thermally broadened) will not ionize any hydrogen… So, I don't need to change the Ionization Routines (except to adjust the temperature if necessary etc…)

And creating synthetic emission lines - is just a matter of multiplying the background brightness at each wavelength by the emission profile…

The first row shows from left to right the data extracted from the plot in Bourrier et al and the spline fit, the same plot with the x-axis in Angstroms instead of km/s, and the Luminosity per frequency from the line emission as well as the black body.

The second row shows the brightness as a function of time and frequency assuming the Line emission profile as well as lineouts at various times and frequencies. (Time is ordered correctly in all of these plots)

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