4 ms·
Looking closer: >"Given the high stellar luminosity and close orbit, the planet receives a large stellar insolation flux (Table 1). As a result, it has an extr
by nonbel 9y ago
Looking closer:
>"Given the high stellar luminosity and close orbit, the planet receives a large stellar insolation flux (Table 1). As a result, it has an extremely high equilibrium temperature: calculations, assuming zero albedo and perfect heat redistribution, give a value of approximately 4,050 K."[1]
That 4,050 K value is reported as the equilibrium temperature, which I understand to be the output of the Stefan-Boltzmann law:
T = (I*(1-alpha)/(epsilon*sigma))^.25
where,
I = Incident Flux
alpha = albedo
epsilon = emissivity
sigma = SB constant = 5.670373e-8
According to the paper the planet receives 61.1 x10^9 erg/s/cm^2.[1] The solar constant is ~1360 W/m^2.[2] In the same units the planet gets 6.11 x 10^7 W/m^2, which is about 45 thousand times greater than what the earth receives. Anyway, plugging into the SB law I get:
(6.11e7*(1-0)/(1*5.670373e-8))^.25 = 5729.377 K
So I am certain it is I rather than them with the error. Where did I go wrong?
[1] http://www.nature.com/nature/journal/vaop/ncurrent/full/nature22392.html http://www.nature.com/nature/journal/vaop/ncurrent/full/natu...
[2] https://en.wikipedia.org/wiki/Solar_constant https://en.wikipedia.org/wiki/Solar_constant
- nonbel 9y agoI see now, I was calculating the temperature at the subsolar point, they are averaging over a uniformly illuminated sphere. Since the illuminated side is a disc with area pi x R^2 and the sphere has surface area 4 x pi x R^2 we need to include a factor of 1/4: (6.11e7*(1-0)/(4*1*5.670373e-8))^.25 = 4051.281 K