### Deriving ionised electron densities within IllustrisTNG Charles Walker
• 2
• 19 Nov '19

Hello,

I've just completed the JupyterLab tutorials, and would like to calculate the ionised
electron density of cells in snapshots.

listing all the fields which may be loaded for snapshots, and come across
the field 'Electron Abundance, n_e', described as the fractional electron
number density with respect to the total hydrogen number density.

Does n_e refer to the fractional number density of specifically ionized
electrons? In which case, in the supplied equations:

n_e = ElectronAbundance x n_H
n_H = X_H x rho/m_p

do the values of X_H, rho, and m_p refer to the ratio between ionized and
total electrons, the 'density' field (i.e. the comoving mass density of the
cell) and the mass of a proton respectively?

Many thanks,

Charlie Dylan Nelson
• 19 Nov '19

Hi,

`X_H` is the hydrogen mass fraction, so always ~0.75, modulo small corrections.

`rho` is yes the comoving (total) mass density of the gas cell, and `m_p` the mass of the proton.

I'm not quite sure what you mean by "specifically ionized electrons"?

Please also note a complication: for star-forming gas (with `StarFormationRate > 0`), the snapshot values for `ElectronAbundance` will be modified due to the subgrid ISM model employed in the simulations. See e.g. this paper (page 4). Charles Walker
• 1
• 28 Nov '19

Dear Dylan,

Thanks very much for getting back to me so soon. I've taken the time to read the paper you recommended, and this associated paper it cites.

Regarding my original question, apologies for the confusion. By "specifically ionised electrons" I meant to refer to only the "free" or ionised electrons. In the Pakmor et al. paper you linked, they refer to the "thermal electron density" in Equation 1 when calculating rotation measures. The n_e in this equation is what I want to get out.

(My end goal is to generate dispersion measures along particular lines of sight in illustris -- the equation for which is exactly the same as Eq 1, but without the magnetic field component).

Regarding your note about the complication with star-forming gas, does this mean that in star forming regions in Illustris, the gas is split both into a hot phase and a cool phase, only the hot phase is considered ionised, and thus the ElectronAbundance only comes from the hot phase gas in the region?

Finally, as ElectronAbundance only refers to electrons with respect to the total hydrogen number density, does this mean I would need to calculate the thermal electron density associated with, e.g., helium, separately?

Many thanks,

Charlie Dylan Nelson
• 29 Nov '19

Hello,

Please also take a look at Katz+ 96, all the formulism here is essentially still true for Illustris and TNG. Namely, Section 3, Eqn 30, and surroundings. The `ElectronAbundance` refers to this 'single' `n_e` value. You could implement such a simple network to derive e.g. `n_{He+}` if needed.

The caution for star-forming gas is, that, the values of `ElectronAbundance` in this case are going to represent an effective mix (average) between the hot and the cold phases. The cold phase is essentially neutral, so for the DM I think you should consider only a line of sight contribution from intersecting the hot phase, in which case `n_e` value to use is perhaps not this average, but rather the hot-phase value. Charles Walker
• 4 Dec '19

Hi Dylan,

Thanks again for helping me out. If I understand correctly from your notes above, here and in the Katz+ 96 paper's Equation 31 then the `ElectronAbundance` returned by TNG is the same as:

`n_e = n_{H+} + n_{He+} + 2n_{He++}`

and accounts for all ionised electrons from ionised hydrogen and helium, and thus `ElectronAbundance` is all I need to integrate over to calculate DM for non star-forming regions in Illustris.

In regards to your caveat for star forming gas, if I understand correctly, then for all Illustris cells with a `StarFormationRate` > 0, I must multiply the `ElectronAbundance` by its mass fraction of warm-phase gas to total gas (Pakmor+ 18).

Pakmor+ refer to (Springel+ 02) for the calculation of this mass fraction. Springel+ 02 define the mass fraction of cold clouds as `x` (equations 17, 18). I would assume, therefore, that the mass fraction of warm-phase gas to total gas would be given by:

`1 - x = sqrt{ (1/y) + (1/(4y^2)) } - 1/(2y)`,

where `y` is Springel+ 02 Equation 16. I would then have to identify the appropriate constituents of `y` for Illustris. Am I on the right track here, or overcomplicating?

P.S., before I reinvent the wheel or overcomplicate things, I have also noticed that Illustris provides something called:

`profile_f_neutral_H_{proj}`, which seems to be related to the neutral gas density, and is described as the neutral Hydrogen fraction profile. Is this effectively the same as Springel+ 02's `x`, meaning I could use `ElectronAbundance*(1-profile_f_neutral_H_{proj})` instead?

Cheers,

Charlie Dylan Nelson
• 5 Dec '19

In that case I would agree, and to compute `1-x` you would follow the formalism in SH03. I think this should actually be quite easy, e.g. see also Marinacci+17 (Sec 3.1). Note that `x` is always basically between 0.9 and 1.

I wouldn't try to use this supplementary catalog of neutral hydrogen profiles unless you want to get in contact with the creator to clarify all of these details. Charles Walker
• 1
• 11 Dec '19

Hi Dylan,

Thanks for the useful paper. It simplifies things a lot. Marinacci+17 (Eq 2) defines the cold gas phase mass-fraction to be:

`x=(u_h - u)/(u_h - u_c)`.

Here `u` is the gas thermal energy per unit mass, which looks to be provided in Illustris by the `InternalEnergy` field. I can't find `u_c` and `u_h` (the gas thermal energies of the cold and hot ISM phases) in Illustris, however your FAQ provides a way to convert between thermal energy per unit mass and temperature.

The temperatures of both phases are discussed in M+17 (§3.1) and SH02 (§2). `T_c` is stated to be ~ 10^3 K, and `T_h` to be ~ 10^7K (M+17). SH02 also state `T_h` to be between 10^5 and 10^7 K, with the true value being dependent on metallicity (and therefore age, I suppose?).

Given this information, it seems I could potentually calculate `u_c` and `u_h` from their respective temperatures (10^3, 10^7 K), and thus calculate `x`. Would you say this is the way to go?

Cheers,

Charlie Andrés Arámburo
• 1
• 6 May '20

Hi Charlie and Dylan,
I'm trying to generate lines of sight of the electron density using the `TNG300-1 box` , but I'm getting weird results. So I was wondering if you could share some insight in my procedure:
First I'm masking the coordinates to use a specific region of the simulation box, in this case I'm having a region of `302.6 x 60 x 0.200 Mpc`. Later I calculate `n_e` as indicated in the data reference page as:

`n_e = ElectronAbundance × X_H × rho /m_p`

Where `X_H ~0.76`, `m_p = 1.6e-24`. And I'm calculating `rho` as `rho = Density × h² × Unitm_to_g × Kpc_to_cm⁻³`. Where `Unitm_to_g =1.989e43` and `Kpc_to_cm = 3.086e21`.

After this I use the function `QuickView` from `sph-viewer` which returns the surface density image of `ne`, so to get the volume density I divide each pixel value with the thickness of the region. Each pixel row/column of this image makes a LOS.

Now for redshift 0 I expect an average in the image around `ne~2e-7 [cm⁻³]` but I'm getting something around `1.3e-09`. Which suspiciously is about a factor of `100/h` so maybe there is some conversion factor that I'm missing. Also I thought about what you discussed about the star forming regions, but the amount of particles in my region that have a `StarFormationRate>0` is very low.

Any insight would be greatly appreciated,

Andrés. Dylan Nelson
• 6 May '20

Hi Andres,

The calculation seems fine to me (you would want to account for a factor of scalefactor `a^3` at redshifts other than zero).

Maybe you can check the density distribution itself (or the density-temperature phase diagram), without the complication of the sph projection.

Where are you imaging? The average `n_e` would depend strongly on environment (e.g. halo mass, if inside a halo). Andrés Arámburo
• 3
• 9 May '20

Hi Dylan,
This is the distribution that I get for the 100TNG-1 box, for a region of 100 x 20 x 0.1 Mpc.

The region that I'm trying to image is the large scale structure, the "cosmic web". One of the things that I find puzzling is the image that I get from sph-viewer when I give the density as a weight for the imaging. Here in the top figure I have the image with only the coordinates, and in the bottom is with coordinates + density as a weight. Should I expect this ?

Thank You

Andres Dylan Nelson
• 10 May '20

Hi Andres,

You could compare the distribution to just the global distribution of all n_e in the box, but otherwise I'm not sure there is any problem.

If you are computing N_e column densities, I wouldn't weight. I suppose the second image is reasonable if you weight by density, but this would be an unusual choice. Zijian Zhang
• 13 May '20

Hi Dylan,

Glad to see that there are several people who concern the ionization. I want to know what kind of reionization model is used by TNG simulation. I mean when the reionization begins and how it evolves?

Thank you!

Zijian Dylan Nelson
• 13 May '20

Hi Zijian,

All Illustris and TNG simulations have used the Faucher-Giguerre UVB (dec 2011 version), this is spatially uniform, but redshift dependent.

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