# Basic model¶

## Cooling: Analytic models¶

Currently, we have 3 different simple cooling models (const-lambda, const-du and Compton). These are all based on analytic formulas and can be used to quickly understand how the cooling interacts with the rest of the code before moving to more complex models.

### Equations¶

The first table compares the different analytical cooling while the next ones are specific to a given cooling. The quantities are the internal energy ($$u$$), the density $$rho$$, the element mass fraction ($$X_i$$), the cooling function ($$\Lambda$$, the proton mass ($$m_H$$) and the time step condition ($$t_\text{step}$$). If not specified otherwise, all cooling contains a temperature floor avoiding negative temperature.

Analytical Cooling
Variable Const-Lambda Const-du
$$\frac{ \mathrm{d}u }{ \mathrm{d}t }$$ $$-\Lambda \frac{\rho^2 X_H^2}{\rho m_H^2}$$ const
$$\Delta t_\text{max}$$ $$t_\text{step} \frac{u}{\left|\frac{ \mathrm{d}u }{ \mathrm{d}t }\right|}$$ $$t_\text{step} \frac{u}{\ \left| \frac{ \mathrm{d}u }{ \mathrm{d}t }\right|}$$

TODO: Add description of the parameters and units.

### How to Implement a New Cooling¶

The developer should provide at least one function for:
• writing the cooling name in HDF5
• cooling a particle
• the maximal time step possible
• initializing a particle
• computing the total energy radiated by a particle
• initializing the cooling parameters
• printing the cooling type

For implementation details, see src/cooling/none/cooling.h

See General information for adding new schemes for the full list of changes required.