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Halpha or Lyman alpha intensity greater than total cooling

Huanian Zhang
 

I run a grid of model with different gas temperatures. And the model is as follows:

print last

table star kurucz 36000 K

ionization parameter -2.5

stop temperature off

constant temperature 4.25 vary

grid 3.0 5.0 0.05

stop AV 100

stop column density 20.0

hden -3.0

metals -0.5

iterate to convergence

save grid "gridrun.grd" last no hash

## save intensities of selected lines

save line, intensity absolute emergent list "gridrun.lin" "LineList_BLR.dat" last no hash

save cooling "cooling.txt" last

save heating "heating.txt" last

save overview "overview.txt" last


I found out that at low temperature, we have Halpha/Lyman alpha intensity greater than total cooling (data appended below), how do we interpret this result? 

T  =  [3.   3.05 3.1  3.15 3.2  3.25 3.3  3.35 3.4  3.45 3.5  3.55 3.6  3.65

 3.7  3.75 3.8  3.85 3.9  3.95 4.   4.05 4.1  4.15 4.2  4.25 4.3  4.35

 4.4  4.45 4.5  4.55 4.6  4.65 4.7  4.75 4.8  4.85 4.9  4.95 5.  ]

cooling  =  [4.70808845e-08 5.08890269e-08 5.48699245e-08 5.90120545e-08

 6.33621504e-08 6.79581750e-08 7.15983981e-08 7.06824777e-08

 6.89389002e-08 6.76588312e-08 6.66669276e-08 6.62600646e-08

 6.64069230e-08 6.78506513e-08 7.04548735e-08 7.52190440e-08

 8.32802779e-08 9.50928910e-08 1.12521907e-07 1.37714691e-07

 1.72722651e-07 2.21207322e-07 2.85634093e-07 3.75135652e-07

 4.96409693e-07 6.60659831e-07 8.85894220e-07 1.19189151e-06

 1.59858459e-06 2.11723081e-06 2.73334100e-06 3.45391967e-06

 4.31136547e-06 5.28754774e-06 6.59862078e-06 8.68979211e-06

 1.18150171e-05 1.53894939e-05 1.78585505e-05 1.87594433e-05

 

 1.89065184e-05]                 ### in unit of erg/cm2/s

Ha intensity  =   [1.4261e-07 1.4174e-07 1.4083e-07 1.3978e-07 1.3866e-07 1.3734e-07

 1.3481e-07 1.2567e-07 1.1546e-07 1.0575e-07 9.6711e-08 8.8356e-08

 8.0657e-08 7.3561e-08 6.7068e-08 6.1109e-08 5.5653e-08 5.0670e-08

 4.6132e-08 4.1987e-08 3.8217e-08 3.4800e-08 3.1719e-08 2.9004e-08

 2.6708e-08 2.4891e-08 2.3779e-08 2.3626e-08 2.4523e-08 2.6202e-08

 2.7863e-08 2.9028e-08 3.0395e-08 3.0248e-08 2.7383e-08 2.3519e-08

 

 1.9676e-08 1.6591e-08 1.4157e-08 1.1734e-08 9.5351e-09]   ### in unit of erg/cm2/s

The lyman alpha intensity is roughly 10 times higher than the Ha intensity.


Gary Ferland
 

Hi there,
This question has been asked and answered a few times.  The answer is that the heating / cooling is not related to the radiative losses.  Heating / cooling is the rate that thermal energy is given to free electrons.  The ionization / recombination energy does not count since the zero point of energy is the ionization limit, as set up by Menzel+ in the 1930s.  See the texts by Spitzer or Osterbrock for a discussion.  The total radiative losses do include ionization / recombination energy so is much greater.
hope that helps,
Gary

On Tue, Jul 7, 2020 at 5:33 PM Huanian Zhang <fantasyzhn@...> wrote:
I run a grid of model with different gas temperatures. And the model is as follows:

print last

table star kurucz 36000 K

ionization parameter -2.5

stop temperature off

constant temperature 4.25 vary

grid 3.0 5.0 0.05

stop AV 100

stop column density 20.0

hden -3.0

metals -0.5

iterate to convergence

save grid "gridrun.grd" last no hash

## save intensities of selected lines

save line, intensity absolute emergent list "gridrun.lin" "LineList_BLR.dat" last no hash

save cooling "cooling.txt" last

save heating "heating.txt" last

save overview "overview.txt" last


I found out that at low temperature, we have Halpha/Lyman alpha intensity greater than total cooling (data appended below), how do we interpret this result? 

T  =  [3.   3.05 3.1  3.15 3.2  3.25 3.3  3.35 3.4  3.45 3.5  3.55 3.6  3.65

 3.7  3.75 3.8  3.85 3.9  3.95 4.   4.05 4.1  4.15 4.2  4.25 4.3  4.35

 4.4  4.45 4.5  4.55 4.6  4.65 4.7  4.75 4.8  4.85 4.9  4.95 5.  ]

cooling  =  [4.70808845e-08 5.08890269e-08 5.48699245e-08 5.90120545e-08

 6.33621504e-08 6.79581750e-08 7.15983981e-08 7.06824777e-08

 6.89389002e-08 6.76588312e-08 6.66669276e-08 6.62600646e-08

 6.64069230e-08 6.78506513e-08 7.04548735e-08 7.52190440e-08

 8.32802779e-08 9.50928910e-08 1.12521907e-07 1.37714691e-07

 1.72722651e-07 2.21207322e-07 2.85634093e-07 3.75135652e-07

 4.96409693e-07 6.60659831e-07 8.85894220e-07 1.19189151e-06

 1.59858459e-06 2.11723081e-06 2.73334100e-06 3.45391967e-06

 4.31136547e-06 5.28754774e-06 6.59862078e-06 8.68979211e-06

 1.18150171e-05 1.53894939e-05 1.78585505e-05 1.87594433e-05

 

 1.89065184e-05]                 ### in unit of erg/cm2/s

Ha intensity  =   [1.4261e-07 1.4174e-07 1.4083e-07 1.3978e-07 1.3866e-07 1.3734e-07

 1.3481e-07 1.2567e-07 1.1546e-07 1.0575e-07 9.6711e-08 8.8356e-08

 8.0657e-08 7.3561e-08 6.7068e-08 6.1109e-08 5.5653e-08 5.0670e-08

 4.6132e-08 4.1987e-08 3.8217e-08 3.4800e-08 3.1719e-08 2.9004e-08

 2.6708e-08 2.4891e-08 2.3779e-08 2.3626e-08 2.4523e-08 2.6202e-08

 2.7863e-08 2.9028e-08 3.0395e-08 3.0248e-08 2.7383e-08 2.3519e-08

 

 1.9676e-08 1.6591e-08 1.4157e-08 1.1734e-08 9.5351e-09]   ### in unit of erg/cm2/s

The lyman alpha intensity is roughly 10 times higher than the Ha intensity.




--
Gary J. Ferland
Physics, Univ of Kentucky
Lexington KY 40506 USA
Tel: 859 257-8795
https://pa.as.uky.edu/users/gary

Huanian Zhang
 

Hi Gary,

Thank you very much for the explanation. I wonder how can we account for those recombination/ionization energy for the cooling/heating? I checked the hazy documentation, but I could not find such content, neither the total radiative losses. 

Would you shed a light on me? 

Thanks,
Huanian

Gary Ferland
 

heating / cooling is described in the Osterbrock book in Chapter 3.  It is also extensively discussed in the Spitzer 1978 and 1962 books, and his 1948, 1948 ApJ papers.

On Mon, Jul 27, 2020 at 4:46 PM Huanian Zhang <fantasyzhn@...> wrote:
Hi Gary,

Thank you very much for the explanation. I wonder how can we account for those recombination/ionization energy for the cooling/heating? I checked the hazy documentation, but I could not find such content, neither the total radiative losses. 

Would you shed a light on me? 

Thanks,
Huanian



--
Gary J. Ferland
Physics, Univ of Kentucky
Lexington KY 40506 USA
Tel: 859 257-8795
https://pa.as.uky.edu/users/gary

Huanian Zhang
 

I checked the Osterbrock Chapter 3. The equilibrium condition is G = L_R + L_C + L_FF. However, I set constant temperature for the gas, which means it is non equilibrium. I suspect the "G" is the total heating in Cloudy. The total cooling explanation in Cloudy is "Cooling is the total energy in collisionally excited lines and part of the recombination energy, but does not include
recombination lines (AGN3 Chapter 3)", so I suspect the total cooling is L_C + L_FF. Then I would need L_R to account for the truly total cooling for the gas. It looks I found it in the output file, one example from my output file is as follows:

 ENERGY BUDGET:  Heat:  -6.775  Coolg:  -6.761  Error:  3.1%  Rec Lin:  -6.755  F-F  H  0.000    P(rad/tot)max     8.93E-03    R(F Con):1.737e+05


There is still one place that I do not understand. Since for low temperature (T < 10^4 K), the Rec Line (Cloudy explanation is "The next numbers give “Rec Lin”, the log of the total luminosity in
recombination lines") is still less than the Lyman alpha or Halpha intensity. I am quite confused since Lyman alpha or Halpha is from recombination for those low density gas. WHy the Lyman/Balmer series is not included for recombination lines? 

Thanks,
Huanian