The various Python projects I have completed during my degree at Queen Mary University of London. This includes the code for visualisations I used in my Master's disseratation, discussing the impact on the Cosmic Microwave Background (CMB) as a result of varying the level of dark matter in the Universe. There are also projects I submitted as part of coursework for computational modules.
I simulated CMB maps for varying levels of dark matter using the Code for Anisotropies in the Microwave Background (CAMB). Following this, I compared these maps to the CMB map generated from theoretical data obtained from the Planck 2018 mission. The theoretical data used as a comparison was read in from the COM_PowerSpect_CMB-base-plikHM-TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt file, also uploaded to this repository.
| Data | Link |
|---|---|
| Theoretical data from Planck 2018 mission | COM_PowerSpect_CMB-base-plikHM-TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt |
- Simulated CMB power spectra and maps for varying dark matter densities.
- Compared theoretical simulations to Planck 2018 datasets to identify discrepancies.
- Used Python libraries like
camb,healpy,numpy,pandasandmatplotlibto process data and visualise results.
Note: The
healpylibrary, essential for handling spherical maps, is supported for macOS and Linux. For Windows users, it is highly recommended to use the Windows Subsystem for Linux (WSL) for the best compatibility.
- Successfully generated CMB maps that reflected the influence of varying dark matter densities.
- Followed Wayne Hu's lecture notes to visualise the effects of dark matter on the third peak of the CMB power spectrum. This emphasised the work from Hu's 2001 paper which explained the change in the height ratios of the second and third peaks due to decay in the gravitational potential during radiation domination.
- Identified consistent patterns between the simulated maps and Planck data, validating the CAMB-based modelling approach.
- Highlighted discrepancies that could point to additional factors or alternative models influencing the CMB.
- Analyse dark matter’s role in shaping the early universe.
- Support cosmological studies by combining observational data and simulations.
- Provide a foundation for further research into alternative dark matter models and their observational signatures.
This work can be extended by:
- Explore alternative dark matter hypotheses using
camb, such as Weakly Interacting Massive Particles (WIMPs) or Primordial Black Holes. - Incorporate datasets from WMAP and upcoming Simons Observatory data, with a particular focus on connecting CMB observations to gravitational wave studies.
- Refinine the simulation process by applying machine learning techniques to extract features, detect anomalies, and improve parameter estimation.
This project focused on detecting and characterising extrasolar planets using radial velocity data obtained through the Doppler technique. I used a variant of the Metropolis-Hastings algorithm to fit circular orbital models to real data, extracting key planetary and orbital parameters. In the table below are the three data files used in the notebook: the first, 51-Peg.dat, is the test radial velocity data where the parameter values were known prior, while the remaining two files (star-01.dat and star-02.dat) have unkown parameters which are estimated with the method here. With this, the code can be validated against known reults, improving its reliability for the other two data files.
| Data | Link |
|---|---|
| 51-Pegasi | 51-Peg.dat |
| Star 1 | star-01.dat |
| Star 2 | star-02.dat |
- Translated orbital mechanics equations into code and implemented MCMC methods for parameter estimation.
- Analysed real radial velocity datasets from stars like 51 Pegasi to infer planetary characteristics.
- Visualised phase-folded radial velocity data to identify trends and features.
- Successfully detected exoplanetary signatures from radial velocity datasets, including identifying potential orbital periods and planetary masses.
- Demonstrated that the Metropolis-Hastings algorithm can effectively estimate parameters with reasonable computational efficiency.
- Highlighted the strengths of the Doppler technique, particularly for characterising larger, closer planets with significant gravitational influence.
This project fits into the broader context of missions like Kepler, TESS, and the James Webb Space Telescope, which aim to characterise exoplanetary systems. Through this project and the 4th-year module 'Extrasolar Planets and Astrophysical Discs' I later took, I learned more about (and was able to demonstrate):
- A method for refining orbital parameters like semi-major axis, period, and planetary mass.
- The ability to compare the Doppler technique to other detection methods, such as the transit method and direct imaging.
- Insights into planetary system diversity and habitability.
- Add interactivity to the notebook, allowing users to adjust orbital parameters via sliders and visualise how changes affect radial velocity curves.
- Extend the analysis to multi-planet systems and non-circular orbits for more complex scenarios.
I simulated the orbital dynamics of two- and three-body systems, specifically the Earth-Sun and Mercury-Earth-Sun systems. I implemented and compared three numerical integration methods: the fourth-order Runge-Kutta (RK4) method, scipy.integrate.ode, and scipy.integrate.odeint.
- Translated the equations of motion for gravitational interactions in two- and three-body systems into code.
- Implemented multiple numerical integrators to solve ODEs.
- Visualised orbital trajectories, energy and angular momentum, and evaluated the accuracy of each method.
- Found that the RK4 method provided high accuracy but required careful step-size adjustment to maintain stability.
- Observed computational efficiency advantages in scipy.integrate.ode and odeint, particularly for longer simulations.
- Demonstrated how different numerical methods yield varying trade-offs between accuracy and computational efficiency.
This project has real-world relevance in:
- Space mission planning, satellite trajectory design, and spacecraft navigation.
- Studying planetary stability, orbital resonance, and gravitational interactions in multi-body systems.
- Understanding celestial mechanics for applications like asteroid deflection or interplanetary travel.
- Include more complex scenarios, such as non-circular or eccentric orbits.
- Compare numerical methods using additional metrics, such as energy conservation and computational efficiency.
- Implement advanced integrators, like symplectic methods, for better long-term stability in simulations.