How big and how opaque would the Helium exosphere have to be in order to match the Helium transit depth and duration?
We have two constraints from the HPF Helium data: how long the transit lasts and how deep the transit is. Assuming the exosphere has uniform opacity extending to a height h above the planet radius R. Leave the helium gas opacity as an unknown variable, 0<f<1. What values of h and f are consistent with the data?
A real exosphere doesn't have a sharp boundary as described above. Instead it resembles an exponential decay, ρ(z) = ρ_0 e^(-z/h), where h is the atmospheric scale height . Estimate the scale height for HAT-P-67b based on reported or derived values of its equilibrium temperature and surface gravity. What assumptions have to go into your calculation?
How big and how opaque would the Helium exosphere have to be in order to match the Helium transit depth and duration?
We have two constraints from the HPF Helium data: how long the transit lasts and how deep the transit is. Assuming the exosphere has uniform opacity extending to a height
habove the planet radiusR. Leave the helium gas opacity as an unknown variable,0<f<1. What values ofhandfare consistent with the data?A real exosphere doesn't have a sharp boundary as described above. Instead it resembles an exponential decay,
ρ(z) = ρ_0 e^(-z/h), wherehis the atmospheric scale height . Estimate the scale height for HAT-P-67b based on reported or derived values of its equilibrium temperature and surface gravity. What assumptions have to go into your calculation?