PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

Photo-cross sections

Photo-cross sections

1) H₂

Itis not simple, I use what I found but it could probably be improved

Ionization of H₂ : 15.4 eV (807 Å). The link between λ (Å) and E (eV) is given by

With, h : Plank’s constant, c : light velocity and q electron charge (all in International Unit System).

I distinguish several wavelength domains

0 < λ < 50 Å (Compton should dominate but σ~ 1.d-24 cm2 = negligible)

- 50Å < λ < 750 Å (Ionization only can produce H+ (dissociative) or H₂⁺) (double ionization H⁺ + H⁺ negligible)

- 750 Å < λ < 804 Å (Ionization : H₂⁺ and excitative dissociation)

- 804 Å < λ < 1116 Å (No Ionization, only dissociation and excitation)

Above 1116 Å cross sections are negligible (Fox et al. 2008)

1.1) Photoionization cross section

I use the results from Yan et al. (1998). According to these authors, the ionization cross section of H₂ can be represented under the form

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

The resulting ionization cross section is displayed below versus to the wavelength (Å). The results from Samson et al. (1994) are represented by squares.

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

1.2) Probability H⁺/ H₂⁺

The ionization of H₂ can produce H₂⁺ or H⁺ (dissociative ionization), the branching ratio of these two channels are derived from Chung et al. 1996. The results are represented below

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

I plot, the ionization cross sections for the two channels and compare with the cross section found on the amop website.

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

Until 400 Å all cross sections are in good agreement, below 400 Å, the total ionization cross sections are in good agreement but not the ratio between the two channels !!

As indicated, I choose the Chung results, because it is more recent. But I can’t pretend that’s it is the better choice.

1.3) Dissociation and absorption cross section

I use the results from Zhong et al. for λ < 900 Å and McCandliss H2ools to describe the excitation region between 900 – 1200 Å ( ~ 10.5 – 13.7 eV). I have resampled the McCandliss results to the wavelength grids.

I only use the v’’ = 0 level (probably not very good for Jupiter, but I don’t know the distribution, possibility to check this assumption using Cravens 1987 model ??).

McCandliss provide : – τ(J’’) for a column density N(J’’) = 1.d21 cm².

I derive the cross section σ(J’’) = τ(J’’)/1.d21 in cm-2

I compute the total cross section:

Where p(J’’) is the relative population of J’’ rotational state (see introduction). I compute them assuming a temperature of 500 K.

Zhong et al. 1999 provide the oscillator strength density df/dE (eV-1)

The link between the cross section and the oscillator strength density is given by (e.g., Gerhart 1974)

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

First a comparison with a resolution of 5Å resolution for McCandliss data (Use the average cross section over 5Å step, I’m not sure that, theoretically, the average is good but as seen it give good agreement with other data, so I maintain this choice). I also represent the values given on AMOP website. I also add the not-resampled McCandliss cross section.

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

Great!, we have a global agreement between AMOP values, Zhong et al. 1999, and McCandliss resampled cross sections, there’s no “discontinuity” in the red line near the boundary 900 Å. So I can resample McCandliss as I want. It’s working.

Note that AMOP values decrease more quickly above 1000 Å (probably because they do not include non dissociative excitation which I expect dominate at large wavelengths). I’m confident on the process. Now I compute the McCandliss on a more refined grid (0.1 Å), and still use Zhong et al. 1999 to describe cross section below 900 Å.

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

A zoom near 900 Å

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

I don’t choose 900 Å arbitrarily but only because McCandliss H2ools does not describe lower wavelengths.

Note : In the excitation region ( > 900 Å), the excited electronic states (Lyman ; Werner) are discrete and absorption can be describe by oscillator strength. This discretization leads to a highly structured cross section. Near the ionization threshold the states become nearest each other leading to the possibility to describe them as continuous (explaining the notion of oscillator strength density). The cross section become less structured, these high energy levels (B’, D) often leads to dissociation of the molecule (e.g : Glass-Maujean 1986 ; Fox et al. 2008). Cross sections in this region are difficult to measure.

On the two next figures, the ionization and absorption cross section s are displayed function of wavelength and energy of the photon. The total absorption cross section is the sum. I don’t sum between 750 and 804 Å, because ionization is already included in Zhong et al. 1999. I use Zhong et al. 1999 between 750 – 900 Å, and Yan et al. 1998 only below 750 Å.

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

Triangles : Photoionization cross section

Points : Photoabsorption above 700 Å

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

2) H

I assume that the absorption cross section is equal to ionization cross section everywhere (neglect absorption for atoms as done by Solomon et al. for O).

I use the analytic formulation from Bethe and Salpeter (1967)

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

 : Fine structure constant

a₀ : Bohr radius

R_e : Rydberg constant (13.6 eV)

The Hydrogen cross section of photoionization is represented below

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

3) He

I assume that the absorption cross section is equal to ionization cross section everywhere (neglect absorption for atoms as done by Solomon et al. for O)

I use the results from Yan et al. 1998. These authors give two different analytical fit, I use the first one given by

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

The cross section is represented below (solid line). The cross section derived from the second analytical fit is also represented (squares). Comparison with Samson et al. 1994 and Bizau and Wuilleumier (1995) can be found in Yan et al. (1998).

PHOTOCROSS SECTIONS 1) H2 ITIS NOT SIMPLE I USE

I finally build three ASCII .dat files as used in the GLOW model of S. Solomon

Auger effect:

The Auger ionization is consisting of ejecting a core electron (not valence) from an atom by an energetic photon or electron. The void is therefore filled by a valence electron producing an X-ray emission.

H : no core electron but just one valence  no Auger effect

H₂ : As H : no Auger effect

He : 2 electron in the same electronic state : no Auger effect

 On Jupiter, only CH₄ could produce Auger effect, so I will describe it only if I include CH₄.

Because I use a new wavelength grid, I need to recomputed the solar flux on this new grid.

The solar UV flux given in euvac.dat (reference spectrum) is the total flux for different bin. It is not a flux per wavelength unit, therefore I assume a uniform distribution of the flux for each feach bin of the reference spectrum.

Next figure represent the refence spectrum/Δλ compared to spectrum on the newgrid /δλ.

The total flux between 0 -1400 Å is of course the same.

Tags: photocross, simple, sections