To Mars and Beyond: A Coder's Guide to Modelling the Red Planet's Ionosphere

Hello, future planetary scientists and fellow space enthusiasts! We’ve spent some time exploring the Earth’s ionosphere, but today, we're setting our sights on a new frontier: Mars. The Red Planet's atmosphere is a thin, chilly veil, but it has a surprisingly active ionosphere. Understanding it is key to future missions, and we're going to build a model to do just that, inspired by the work of Professor R.P. Singhal of Banaras Hindu University.

Professor Singhal is a leading expert in a technique called the "Analytical Yield Spectrum (AYS)" method. We now know from his book, Elements of Space Physics (2022), that AYS is a way to calculate how charged particles deposit energy into an atmosphere, creating a bustling layer of ions and electrons. While on Earth this is driven by solar winds and our magnetic field, on Mars, it's a different story. The Red Planet lacks a global magnetic field, so its ionosphere is a more direct product of the sun's extreme ultraviolet (EUV) radiation and soft electron precipitation.

We’re going to adapt our previous algorithm to model this unique Martian environment, stepping through the dimensions from 2D all the way to a speculative 5D.

Step 1: Adjusting Our Toolkit for Mars

The fundamental physics remains the same, but the parameters change. We'll be using the same Python libraries—NumPy, SciPy, and Matplotlib—but we need to adjust our physical models to fit the Martian reality.

• Atmosphere: Mars' atmosphere is mostly carbon dioxide ($CO_2$). We'll use a simple $CO_2$-based exponential density model, with a reference altitude that matches Mars' ionospheric peak, which is higher than Earth's.
• Ionisation Energy: The energy required to create an ion pair in $CO_2$ is slightly different from air. We'll use the value of 33 eV.
• Particle Rain: Instead of Earth's auroral electron flux, we'll model the photoelectron flux created by the sun's EUV radiation hitting the Martian atmosphere.

import numpy as np
from scipy.integrate import quad
import matplotlib.pyplot as plt

# Martian parameters
W = 33.0  # eV per ion pair (for CO₂)
h0 = 120.0  # Reference altitude (km)
H = 8.0    # Scale height (km)
E0 = 50.0  # Reference electron energy (eV, for photoelectrons)

# Martian atmosphere model (CO₂-based)
def neutral_density(h):
    return 1e11 * np.exp(-(h - h0) / H)

# Energy loss specific to CO₂
def energy_loss(E, h):
    return 2e-3 * neutral_density(h) * E**0.5

# Electron flux for Mars (photoelectrons)
def electron_flux(E, E0=E0):
    return 1e7 * (E / E0) * np.exp(-E / E0)

Step 2: The 2D Snapshot

Our simplest model is a side-on view of the Martian ionosphere. We'll plot ionisation rates as a function of latitude and altitude, giving us a quick overview of where the action is happening. This is a foundational step, and the principles are directly from Professor SIN's AYS method.

# Our 2D Martian canvas
lat = np.linspace(-60, 60, 50)  # degrees
alt = np.linspace(80, 300, 100)  # km
LAT, ALT = np.meshgrid(lat, alt)

# The core calculation for our 2D model
def ionization_rate_2d(lat, alt):
    q = np.zeros_like(lat)
    for i in range(lat.shape[0]):
        for j in range(alt.shape[1]):
            # Integrate over all possible electron energies
            q[i, j], _ = quad(lambda E: electron_flux(E) * energy_loss(E, alt[i, j]) / W, 10, 1e3)
    return q

# Let's run and visualise it
q_2d = ionization_rate_2d(LAT, ALT)
plt.contourf(lat, alt, q_2d, cmap='viridis')
plt.colorbar(label='Ionisation Rate (ion pairs/cm³/s)')
plt.xlabel('Latitude (deg)')
plt.ylabel('Altitude (km)')
plt.title('2D AYS Ionisation Rate (Mars)')
plt.show()

Step 3 & 4: From 3D to 4D

To build our 3D model, we'll add longitude. Since Mars' ionosphere is directly tied to the sun's illumination, we'll introduce a Solar Zenith Angle (SZA) factor to our electron flux. This ensures that the ionisation rate is highest on the dayside, where the sun is directly overhead, and non-existent on the nightside.

For our 4D model, we add time. This allows us to track the ionosphere's diurnal cycle—the daily change as Mars rotates. We'll use a time-dependent SZA to show how the peak ionisation region moves across the Martian globe as the day progresses.

Step 5: The Fifth Dimension (Speculative)

The concept of a 5D AYS model isn't documented in Professor SIN's work, but it's an exciting theoretical leap. Our 5D model would add particle energy as the fifth dimension. Instead of integrating over all energies, we'd calculate the ionisation rate for specific energy levels. This would give us an incredibly detailed look at how different components of the solar wind and radiation contribute to the ionosphere's structure.

The Next Frontier: Validation with Real Data

A model is only as good as its validation. For our Martian model, we can't use Earth data from BHU's ionosonde. Instead, we'd need to use data from missions like NASA's MAVEN (Mars Atmosphere and Volatile Evolution) orbiter. MAVEN's NGIMS instrument has provided invaluable data on the density of Mars' atmosphere, which we could use to make our model even more accurate. Similarly, we could validate our results against MAVEN's electron density profiles, checking if our calculated peak ionisation altitudes and rates match real-world observations.

The AYS method, as detailed by Professor SIN, provides a powerful framework for these explorations. It shows us how a deep understanding of fundamental physics can be scaled up to model complex, dynamic systems across our Solar System. From a simple 2D view to a speculative 5D model, we're using mathematics and code to bring the invisible forces of the cosmos to light.

References

• Mukundan, V., & Bhardwaj, A. (2019). The dayside ionosphere of Mars: Comparing a one-dimensional photochemical model with MAVEN Deep Dip campaign observations. Monthly Notices of the Royal Astronomical Society, 497(2), 2239-2248.
• Nagy, A. F., T. E. Cravens, & T. I. Gombosi. (1990). The ionospheres of the planets and comets. Advances in Space Research, 10(1), 1-13.
• Schunk, R. W., & A. F. Nagy. (2009). Ionospheres: Physics, Plasma Physics, and Chemistry. Cambridge University Press.
• Singhal, R. P. (2022). Elements of Space Physics (2nd ed.). NOPR.
• Stankov, S. M., et al. (2022). The Neustrelitz Electron Density Model (NEDM2020) and its evaluation. Space Weather and Space Climate, 16(2), 333-356.

Comments

[shemith mohanan]

Absolutely fascinating read 🚀! I love how you connected planetary science with practical coding — turning something as complex as the Martian ionosphere into a Python model is just brilliant. The AYS method and the 5D speculative leap blew my mind 🤯. This kind of crossover between programming and astrophysics makes learning both fields so exciting. Incredible work — bookmarked for a re-read! 🔥