More NEQ stuff...

  1. Splitting DM into Hydrogen-Helium-Metal-Molecular processes
  2. Breaking up the metal cooling
    1. DM Curve
      1. Low Temperatures
      2. High Temperature
    2. Pat's Data
    3. Comparing the cooling curves
    4. Oxygen and Nitrogen cooling contributions
  3. About the attachments

Splitting DM into Hydrogen-Helium-Metal-Molecular processes

  • So I spent a fair amount of time breaking down the curve in DM into 12 various parts that we use in non-equilibrium cooling. Here is a plot showing all of the different processes:

Now defining:

  • x = HII/nH
  • xHe = HeII/nHe
  • yHe = HeIII/nHe
  • y = ne/nH

each process can be identified with proper weight factors (before being multiplied by nH2)

Process weight factors * f(Temp)
e Z excitation and bremsstrahlung y
e H excitation (1-x)*y
e He excitation (1-xHe-yHe)*y
e HeII excitation xHe*y
H ionization (1-x)*y
HII recombination x*y
He ionization (1-xHe-yHe)*y
HeII recombination xHe * y
HeII ionization xHe * y
HeIII recombination yHe * y
Molecular cooling 1
H Z excitation 1

And here is the reconstructed cooling function using equilibrium values from the code plotted alongside the total equilibrium curves extracted from the DM paper:

Other than the rise at 104 due to helium excitation, the majority of the cooling comes from metals excitation by electrons (especially Oxygen at 105). Of course the DM curve assumes some metal fractions (which are different from Pat's) so merging these two might be difficult. Though it would be possible to modify the DM curve to use Pat's metal fractions…

Breaking up the metal cooling

The form of the cooling function is dependent on the abundances of each element, and each of the sources used to construct the various tables use slightly different abundances:

CT DM PH GT RC
H 12.00 12.00 12.00 12.00 12.00
He 11.20 10.92 10.93
C 8.60 8.57 8.52 8.52
N 8.04 7.94 7.96 7.96
O 8.95 8.64 8.82 8.82
Ne 8.70 7.41 7.92
Mg 7.43 7.42 7.42
Si 7.50 7.51 7.52 7.52
S 7.30 7.15 7.20 7.20
Fe 7.51 7.60 7.60
Ar 6.80
Ca 6.30
Ni 6.30

DM Curve

Low Temperatures

The low temperature DM curve is dominated by carbon, silicon, and iron

The left plot shows the functional form for each of the lines considered from DM, while the right plot shows the total of all of the lines for each element along with data points extracted from a similar curve in the DM paper.

High Temperature

I also looked at how the abundance affects the cooling at high temperature. The DM curves are only for low temperature, although the completed curve uses cooling functions from Cox and Tucker. So, first I Combined the DM curves at low temperature, with the Cox and Tucker metal cooling curves (though using Gould and Thakur's hydrogen and helium excitation curves).

and then compared the resulting cooling function with total DM curve

The largest errors are around T=1e6 where the dm curve is weaker by a factor of ~2. Tucker and Koren give additional cooling functions for iron at high temperatures that I have not included…

Pat's Data

The data from Pat is a 3D-table while the DM metal curve is only a function of T

So I divided Pat's table by to get

so that since Helium is not ionized in the range of Pat's tables…

I then wanted to construct curves at constant nH so I took slices through the 3D data set at where nHi = [1e2,1e3,1e4]. I then took lineouts at xi = [.01, .1, and 1] to construct 9 curves which I then plotted against the DM metal curve.

They all agree fairly well at high temperatures and deviate at low temperatures when the ionization fraction is high (which is significantly out of equilibrium). But I took an average of these 9 curves to get a single metal cooling curve from Pat's table.

I also looked at the DM cooling function at low temperatures but using Pat's abundances.

The cooling strength from Pat's tables is still much less than the DM curve. But the DM curve appears to have several iron transitions - and if all of them are included, it does not agree with Pat's tables. If I play around with the various iron and carbon contributions I can get a curve that agrees at low temperatures with Pat's tables.

I then combined that curve, with Pat's 1D average curve, and the original DM curve to construct a new metal cooling curve that is more consistent with Pat's cooling tables.

Comparing the cooling curves

This plot shows the DM cooling curves built out of Pat's abundances, the DM abundances, as well as the total metal curve extracted from the DM graph. Also are shown metal cooling functions from Pat's tables at ionizations of .01, .1, and 1 and densities of 1e2, 1e3, and 1e4, along with their average value, and a complete cooling curve that blends the DM graph with Pat's data.

And here is a close up of the range covering Pat's tables

And here is a fun image showing the shape of Pat's metal cooling functions for each species.

As well as the total cooling function

and a breakdown of which species dominates the cooling

I also did a breakdown of Pat's tables where I averaged in X and ne to get functions of T for each species

As well as taking the maximum value in X and ne

Since the iron cooling seems to stick out - I looked in more detail at the DM iron cooling processes:

e+Fe+(a6D9/2) → e+Fe+(a6D7/2) Seaton 1955
e+Fe+(a6D9/2) → e+Fe+(a6D5/2) Seaton 1955
e+Fe+(a6D) → e+Fe+(a4F7/2) Pottasch 1968
e+Fe+(a6D) → e+Fe+(a4F9/2) Pottasch 1968

Oxygen and Nitrogen cooling contributions

Since Oxygen and Nitrogen ionization states are tied to hydrogen via charge exchange, I looked at dividing out 'xi' dependence to make all of the cooling graphs 2D instead of 3D.

Here is a comparison of the original cooling functions for OI and OII with the reconstructed version built from a 2D table.

Also talked with Pat about extending tables to higher temperatures and what new species would need to be tracked.

About the attachments

See the attachments for excitation cooling of hydrogen and helium as well as metals. The DMCooling spreadsheet has all of the calculations, while the DMTables has the various temperature dependent functions for the original DM. And the DMZ Blend has the modified metal cooling function that is more consistent with ZCooling (Pat's tables). And the PHCooling.bov/dat files can be loaded into visit to see the function PH'(ne, x, T)

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