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Ye Wang
�
-2
-1.5
-1
-0.5
0
100 105 1010 1015 1020
log 1
0(n(
HII)
/n(H
)
Density (cm-3)
T = 12600 K
Simulation Result2-level SystemSaha Equation
Ionization Shift due to Density
�
0.01
0.03
0.05
5 10 15 20 25 30
n HII/
n H
Metallicity (Zsun)
T = 12600 K
All ElementsAll Elements Except Mg
Only H&Mg
Ionization Shift due to Metallicity
� Primordial Case
10^{-35}
10^{-30}
10^{-25}
10^{-20}
10^{-15}
10^{-10}
10^{-5}
10^{0}
10^{1} 10^{2} 10^{3} 10^{4}
Coo
lling
Rat
e (e
rg s
^{-1
} cm
^{-3
})
Temperature (K)
primordial
n_{H}=1cm^{-3}n_{H}=10^{2}cm^{-3}n_{H}=10^{4}cm^{-3}n_{H}=10^{6}cm^{-3}n_{H}=10^{8}cm^{-3}
n_{H}=10^{10}cm^{-3}
�
1e-35
1e-30
1e-25
1e-20
1e-15
1e-10
1e-05
1
10 100 1000 10000
Coo
lling
Rat
e
Temperature (K)
primordial_crb-4
n_{H}=1cm^{-3}n_{H}=10^{2}cm^{-3}n_{H}=10^{4}cm^{-3}n_{H}=10^{6}cm^{-3}n_{H}=10^{8}cm^{-3}
n_{H}=10^{10}cm^{-3}
Primordial Case with low CRB
�
1e-35
1e-30
1e-25
1e-20
1e-15
1e-10
1e-05
1
10 100 1000 10000
Coo
lling
Rat
e
Temperature (K)
primordial
n_{H}=1cm^{-3}n_{H}=10^{2}cm^{-3}n_{H}=10^{4}cm^{-3}n_{H}=10^{6}cm^{-3}n_{H}=10^{8}cm^{-3}
n_{H}=10^{10}cm^{-3}
Primordial Case with Low CRB and High CMB
�
10^{-40}
10^{-35}
10^{-30}
10^{-25}
10^{-20}
10^{-15}
10 100 1000 10000
H2C
oollin
g R
ate
Temperature (K)
primordial_crb-4_cmb20
n_{H}=1cm^{-3}n_{H}=10^{2}cm^{-3}n_{H}=10^{4}cm^{-3}n_{H}=10^{6}cm^{-3}n_{H}=10^{8}cm^{-3}
n_{H}=10^{10}cm^{-3}
H2 Cooling at high CMB
�
10^{-40}
10^{-35}
10^{-30}
10^{-25}
10^{-20}
10^{-15}
10 100 1000 10000
H2
Coo
lling
Rat
e
Temperature (K)
primordial_crb-4
n_{H}=1cm^{-3}n_{H}=10^{2}cm^{-3}n_{H}=10^{4}cm^{-3}n_{H}=10^{6}cm^{-3}n_{H}=10^{8}cm^{-3}
n_{H}=10^{10}cm^{-3}
H2 Cooling at low CMB
� H2 Cooling problem at 4000K
1.00E-23
1.00E-22
1.00E-21
1.00E-20
1.00E-19
1.00E-18
1.00E-17 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08 1.00E+09 1.00E+10
W
W
�
1e-12
1e-10
1e-08
1e-06
0.0001
0.01
1
10 100 1000 10000
H2
Temperature (K)
primordial_crb-4
n_{H}=1cm^{-3}n_{H}=10^{2}cm^{-3}n_{H}=10^{4}cm^{-3}n_{H}=10^{6}cm^{-3}n_{H}=10^{8}cm^{-3}
n_{H}=10^{10}cm^{-3}
H2 fraction at low CMB
�
1e-12
1e-10
1e-08
1e-06
0.0001
0.01
1
10 100 1000 10000
H2
Temperature (K)
primordial_crb-4_cmb20
n_{H}=1cm^{-3}n_{H}=10^{2}cm^{-3}n_{H}=10^{4}cm^{-3}n_{H}=10^{6}cm^{-3}n_{H}=10^{8}cm^{-3}
n_{H}=10^{10}cm^{-3}
H2 fraction at High CMB
�
10^{-40}
10^{-35}
10^{-30}
10^{-25}
10^{-20}
10 100 1000 10000
HD
Coo
lling
Rat
e
Temperature (K)
primordial_crb-4_cmb20
n_{H}=1cm^{-3}n_{H}=10^{2}cm^{-3}n_{H}=10^{4}cm^{-3}n_{H}=10^{6}cm^{-3}n_{H}=10^{8}cm^{-3}
n_{H}=10^{10}cm^{-3}
HD Cooling at high CMB
�
10^{-40}
10^{-35}
10^{-30}
10^{-25}
10^{-20}
10 100 1000 10000
HD
Coo
lling
Rat
e
Temperature (K)
primordial_crb-4
n_{H}=1cm^{-3}n_{H}=10^{2}cm^{-3}n_{H}=10^{4}cm^{-3}n_{H}=10^{6}cm^{-3}n_{H}=10^{8}cm^{-3}
n_{H}=10^{10}cm^{-3}
HD Cooling at low CMB
�
10^{-30}
10^{-25}
10^{-20}
10^{-15}
10^{-10}
10^{-5}
10^{0}
10^{1} 10^{2} 10^{3} 10^{4}
Coo
lling
Rat
e (e
rg s
^{-1
} cm
^{-3
})
Temperature (K)
z1-cooling
n_{H}=1cm^{-3}n_{H}=10^{2}cm^{-3}n_{H}=10^{4}cm^{-3}n_{H}=10^{6}cm^{-3}n_{H}=10^{8}cm^{-3}
n_{H}=10^{10}cm^{-3}
Solar Abundance Cases
� z=1z_{sun}
10^{1}10^{2}
10^{3}10^{4}
Temperature (K) 10^{0}10^{2}
10^{4}10^{6}
10^{8}10^{10}
Density (cm^{-3})
-9-8-7-6-5-4-3-2-1 0
-9-8-7-6-5-4-3-2-1 0
Molecular Cooling at Z=1
� z=-4z_{sun}
10^{1}10^{2}
10^{3}10^{4}
Temperature (K) 10^{0}10^{2}
10^{4}10^{6}
10^{8}10^{10}
Density (cm^{-3})
-12-10-8-6-4-2 0
-12
-10
-8
-6
-4
-2
0
Molecular Cooling at Z=-4
� z=10z_{sun}
10^{1}10^{2}
10^{3}10^{4}
Temperature (K) 10^{0}10^{2}
10^{4}10^{6}
10^{8}10^{10}
Density (cm^{-3})
-9-8-7-6-5-4-3-2-1 0
-9-8-7-6-5-4-3-2-1 0
Molecular Cooling at Z=10
�
10-29
10-28
10-27
10-26
10-25
10-24
101 102 103 104
Coo
lling
Rat
e (e
rg s
-1 c
m-3
)
Temperature (K)
n = 1 cm-3
z=1z=10z=-2z=-4z=3z=5
Normalized Cooling n=1
� Normalized Cooling n=4
10-22
10-21
10-20
10-19
10-18
10-17
10-16
101 102 103 104
Coo
lling
Rat
e (e
rg s
-1 c
m-3
)
Temperature (K)
n = 104 cm-3
z=1z=10z=-2z=-4z=3z=5
�
10-12
10-11
10-10
10-9
10-8
10-7
10-6
101 102 103 104
Coo
lling
Rat
e (e
rg s
-1 c
m-3
)
Temperature (K)
n = 1010 cm-3
z=1z=10z=-2z=-4z=5
Normalized Cooling n=10
�
0.0e+00
1.0e-09
2.0e-09
3.0e-09
4.0e-09
5.0e-09
60 80 100 120 140 160 180 200
Coo
lling
Rat
e (e
rg s
-1 c
m-3
)
Temperature (K)
z=1zsun
Cooling Rate/HI densitynH=1010cm-3
Bump around 140K
�
10-29
10-28
10-27
10-26
10-25
10-24
10-23
10-22
101 102 103 104
Coo
lling
Rat
e (e
rg s
-1 c
m-3
)
Temperature (K)
z=1zsun
crb0crb-2crb-4crb-6crb-8
CRB’s effects on Cooling