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Earth-like planet at the limits of the HZ, in terms of the stellar effective temperature.
To determine the locations of the inner and outer boundaries of the HZ of a main-
sequence star with an effective temperature of 2;600 K <T
Star
< 7;200K, we use
Eq. (
13.3
) (see Kopparapu et al.
2013a
)
"
#
1=2
L=L
Sun
1
C
Ǜ
x
.T
i
/l
xSun
l
xStar
D
l
xSun
(13.3)
In this equation, l
x
D
.l
in
;l
out
/ is in AU, T
i
.K/
D
T
Star
.K/
5;780,and
Ǜ
x
.T
i
/
D
a
x
T
i
C
b
x
T
i
C
c
x
T
i
C
d
x
T
i
;
(13.4)
where the values of coefficients a
x
;b
x
;c
x
, d
x
,andl
xSun
are given in Table
13.1
(see
Kopparapu et al.
2013b
). From Eq. (
13.3
), the flux received by the planet from its
host star at the limits of the habitable zone can be calculated using Eq. (
13.5
). The
results are given in Table
13.1
;
F
xStar
f;T
Star
D
F
xSun
.f;T
Star
/
1
C
Ǜ
x
.T
i
/l
xSun
:
(13.5)
From Eq. (
13.5
), the spectral weight factor W.f;T/can be written as
1
C
Ǜ
x
.T
i
/l
xSun
1
W
i
.f;T
i
/
D
:
(13.6)
Tab le
13.2
and Fig.
13.12
show W.f;T/ as a function of the effective temperature
of a main-sequence planet-hosting star for the narrow (left panel) and empirical
(right panel) boundaries of the HZ. As expected, hotter stars have weighting factors
smaller than 1, whereas the weighting factors of cooler stars are larger than 1.
Table 13.1
Values of the coefficients of equation (
13.4
). See Kopparapu et al. (
2013b
) for details.
Narrow HZ
Empirical HZ
Runaway
greenhouse
Maximum
greenhouse
Recent
Venus
Early
Mars
l
xSun
(AU)
0.97
1.67
0.75
1.77
Flux (Solar flux
@Earth)
1.06
0.36
1.78
0.32
10
4
10
5
10
4
10
5
a
1:2456
5:9578
1:4335
5:4471
10
8
10
9
10
9
10
9
b
1:4612
1:6707
3:3954
1:5275
7:6345 10
12
3:0058 10
12
7:6364 10
12
2:1709 10
12
c
1:7511 10
15
5:1925 10
16
1:1950 10
15
3:8282 10
16
d
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