atmosentry

atmosentry is a numerical integrator that simulates the atmospheric entry of comets. For full description of the numerical model see this article. Key details are described below, focussing primarily on free model parameters.

Setup

atmosentry is now published on pypi and can therefore be installed simply as:

• pip install atmosentry

Alternatively (for developing atmosentry):

• Clone the Github repository
• Navigate to the project directory (/atmosentry)
• Important: Ensure you are using a Python version between 3.8-3.10
• Install required packages
  • pip3 install -r requirements.txt
• Install the package
  • pip3 install .

How to use atmosentry

The examples/ sub-directory contains several ipython notebooks that demonstrate the basic functionality of atmosentry.

Model description

atmosentry includes specific semi-analytical prescriptions for the ablation, deformation, and fragmentation of comets as they travel through the atmosphere.

Atmospheric deceleration

Assuming the comet arrives at the top of the atmosphere at an initial angle $\theta$ wrt. the local horizontal, and velocity $\mathbf{v}=(v_x,v_y,v_z)$, its deceleration is given by

$$m\dfrac{d\mathbf{v}}{dt} = -\dfrac{1}{2}C_D\rho_{\rm atm}(z)A|\mathbf{v}|\mathbf{v} -g(z)\mathbf{\hat{e}}_z,$$

where $C_D$ is the comet's drag coefficient, which is left as a free parameter. The comet's position is tracked through the atmosphere, and evolves as

$$\dfrac{d\mathbf{x}}{dt} = \mathbf{v}.$$

As isothermal atmospheric profile is assumed with scale height $H$,

$$\rho_{\rm atm} = \rho_{\rm atm,0}\exp{\left(-\dfrac{z}{H}\right)},$$

where the surface atmospheric density $\rho_{\rm atm, 0}$ is also left as a free parameter.

Mass ablation

Mass loss due to ablation is described by the classical Bronshten (1983) parameterisation,

$$\xi\dfrac{dm}{dt} = -A\,\text{min}\left(\dfrac{1}{2}C_H\rho_{\rm atm}v^3,\sigma_{\rm SB}T^4\right),$$

where $T \simeq 25000,{\rm K}$ is the temperature of the shocked gas at the leading edge of the comet. The heat transfer coefficient ($C_H$) is left as a free parameter.

Deformation

Given the friable, highly porous nature of cometary impactors, we adopt the progressive fragmentation described in Chyba et al., (1993), in which the comet deforms into a cylinder of height $h=m/(\pi\rho_mr^2)$. Its radius increases according to

$$r\dfrac{d^2r}{dt^2} = \dfrac{C_D}{2}\left(\dfrac{\rho_{\rm atm}}{\rho_{\rm m}}\right)v^2.$$

Fragmentation

This deformation will not continue indefinitely, with 3D simulations demonstrating that Rayleigh-Taylor instabilities drive the fragmentation of the comet. Comets break-up after $N_{\rm RT}$ Rayleigh-Taylor growth timescales, which is left as a free parameter in the model. The number of fragments ($n$) produced during fragmentation remains poorly constrained, and is also left as a free parameter. The masses of child fragments are chosen proportional to a random variable

$$\dfrac{m_i}{m_{\rm parent}} = x, \hspace{1em} \text{where}~x\sim\mathcal{U}[0,1],$$

and normalised such that

$$\sum_{i=1}^n{m_i} = m_{\rm parent}.$$