Assume Earth has been wrenched out of the Sun's orbit and has become a rogue planet, with its surface equilibrium temperature falling to ~-240C.
At what depth will temperatures remain "comfortable" for human life (i.e. = current surface temperature of ~15C)?
In areas where today the average geothermal gradient is 3.5C/100m [red line].
In geothermally active areas, where the geothermal gradient is much flatter [green line].
In other words, how will a radical cooling of the planetary surface affect Earth's current geothermal gradients?
Will the gradient lines just be shifted 255C left? Or will it be a sort of gradual convergence like in the following diagram?
Thanks in advance for your input!
Optional, closely related question: I assume solid ground reach its equilibrium state much faster than the oceans due to the latter's vast latent heat capacity. But once the oceans do freeze over, after 100,000's of years, would the ice henceforth behave about the same as completely geothermally inert soil, and hence trend towards -240C as well (i.e. in areas of ice far from hydrothermal vents where liquid water may remain indefinitely)?