Explore how TESS-to-K2 contrast maps to T_spot/T_ambient ratio

[gully]

The ratio that you derived in #25 is a single number between zero to one. For a given star the physics of what you are measuring is: the flux ratio of the spot in one color (TESS filter, "red") to some other color (Kepler filter, blue-green-orange ish? it is "white light").

That scalar number has a physical origin and physical interpretation: temperature.

The temperature of the spot is lower than the temperature of the ambient photosphere.

In this assignment, we are asking you to find a relationship between the contrast measured in #25 and the physical temperature of the spot. There are two main ways to obtain this relationship: A) through the ratio of black body radiation, or through the use of model photospheres (Figure 1 from the TESS Cycle 4 proposal text). I recommend we use the latter. You will have to install gollum to get the model atmospheres.

Pathological examples to check for understanding:

What contrast ratio would you measure if the spot were absolute zero Kelvin and the ambient photosphere were 5700 Kelvin?

What contrast ratio (approximately) would you measure if the spot were 5699.999 Kelvin and the ambient photosphere were 5700 Kelvin?

Subtasks for this goal:

1. Install gollum
2. Replicate Figure 1 from the proposal (ask for the Jupyter notebook that generated it), adapt it using gollum behind-the-scenes.