Browsing by Author "Moodley, Kavilan."

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Aspects of spherically symmetric cosmological models.
(1998) Moodley, Kavilan.; Maharaj, Sunil Dutt.; Govinder, Keshlan Sathasiva.
In this thesis we consider spherically symmetric cosmological models when the shear is nonzero and also cases when the shear is vanishing. We investigate the role of the Emden-Fowler equation which governs the behaviour of the gravitational field. The Einstein field equations are derived in comoving coordinates for a spherically symmetric line element and a perfect fluid source for charged and uncharged matter. It is possible to reduce the system of field equations under different assumptions to the solution of a particular Emden-Fowler equation. The situations in which the Emden-Fowler equation arises are identified and studied. We analyse the Emden-Fowler equation via the method of Lie point symmetries. The conditions under which this equation is reduced to quadratures are obtained. The Lie analysis is applied to the particular models of Herlt (1996), Govender (1996) and Maharaj et al (1996) and the role of the Emden-Fowler equation is highlighted. We establish the uniqueness of the solutions of Maharaj et al (1996). Some physical features of the Einstein-Maxwell system are noted which distinguishes charged solutions. A charged analogue of the Maharaj et al (1993) spherically symmetric solution is obtained. The Gutman-Bespal'ko (1967) solution is recovered as a special case within this class of solutions by fixing the parameters and setting the charge to zero. It is also demonstrated that, under the assumptions of vanishing acceleration and proper charge density, the Emden-Fowler equation arises as a governing equation in charged spherically symmetric models.
Bayesian analysis of cosmological models.
(2010) Moodley, Darell.; Moodley, Kavilan.; Sealfon, C.
In this thesis, we utilise the framework of Bayesian statistics to discriminate between models of the cosmological mass function. We first review the cosmological model and the formation and distribution of galaxy clusters before formulating a statistic within the Bayesian framework, namely the Bayesian razor, that allows model testing of probability distributions. The Bayesian razor is used to discriminate between three popular mass functions, namely the Press-Schechter, Sheth-Tormen and normalisable Tinker models. With a small number of particles in the simulation, we find that the simpler model is preferred due to the Occam’s razor effect, but as the size of the simulation increases the more complex model, if taken to be the true model, is preferred. We establish criteria on the size of the simulation that is required to decisively favour a given model and investigate the dependence of the simulation size on the threshold mass for clusters, and prior probability distributions. Finally we outline how our method can be extended to consider more realistic N-body simulations or be applied to observational data.
Diffuse radio emission in ACTPol clusters.
(2021) Sikhosana, Sinenhlanhla Precious.; Moodley, Kavilan.; Knowles, Kenda Leigh.; Hilton, Matthew James.
Low-frequency radio observations of galaxy clusters reveal cluster-scale diffuse emission that is not associated with individual galaxies. Studying the properties of these diffuse radio sources gives insight into astrophysical processes such as cosmic ray transportation in the intracluster medium (ICM). Observations have linked the formation of radio halos and relics with turbulence caused by cluster mergers and the formation of mini-halos to gas sloshing in cool-core clusters. Statistical studies of large galaxy cluster samples have been used to determine how the radio properties of diffuse emission scale with the mass and X-ray luminosity of the host clusters. Such studies are crucial for refining the formation theories of diffuse emission. New generation telescopes with wide bandwidths and high sensitivity such as the upgraded Giant Metrewave Radio Telescope (uGMRT) andMeerKAT are advantageous for the study of faint extended emission in large cluster samples. The main aim of this thesis was to do an in-depth study of the diffuse radio emission using a cluster sample that spans a wider mass and redshift range compared to the currently studied parameter space. We developed data reduction techniques for calibrating data from telescopes such as uGMRT and MeerKAT. The wide bandwidth of these telescopes introduces directional dependent effects (DDEs) that make the calibration process extremely complicated. However, such observations are excellent for studies of the faint diffuse emission and in-band spectral indices of this emission. In the first part of this thesis, we focused on the study of diffuse radio emission in a Sunyaev- Zeldovich (SZ) selected sample of clusters. These clusters were observed by the Atacama Cosmology Telescope’s Polarimetric extension (ACTPol). We used archival and new GMRT observations for the radio analysis of this sample. We reported newly detected diffuse emission in the following clusters: a radio halo and revived fossil plasma in ACT-CL J0137.4 0827, a radio relic in ACT-CL J2128.4+0135, and a candidate relic in ACT-CL J0022.2 0036. The radio analysis of the full sample revealed that the fraction of clusters in the sample hosting diffuse emission is 26.7% excluding candidate emission and 30% when it is included. The detection rate of the diffuse emission over all categories is lower than the detection rates reported in literature. We note that this may be because the sample comprised high redshift (z ¡ 0.5) and low mass clusters (M500c;SZ 5 1014 Md), though future more sensitive observations of these clusters could reveal fainter diffuse emission structures. We compared our results to the most recent radio halo and radio relic scaling relations. The radio halo P1:4GHz M500 scaling relation plot indicates that a few flatter spectrum radio halos are located in the region previously known to be populated by ultrasteep spectrum radio halos (USSRHs). Finally, we presented preliminary results of the uGMRT wideband backend (GWB) data reduction for ACT-CL J0034.4+0225, ACT-CL J0137.4 0827, and ACT-CL J2128.4+0135. We prioritised these clusters because the narrowband data revealed that they host diffuse emission. However, once the data reduction algorithm is improved, we will reduce the remaining clusters with non-detections. Comparing the GWB results to the narrowband GMRT data, we note that the radio halo observed in ACT-CL J0137.4 0827 is more extended in the GWB data. The diffuse emission is detected at a higher signal-to-noise ratio in the GWB images for the three clusters. We note that an improvement in the GWB reduction algorithm might reveal diffuse emission that was not detected in the narrowband data. In the second part of the thesis, we used MeerKAT observations to study diffuse emission in the Bullet Cluster (1E0657 56), RXCJ1314.4 2515, Abell 3562, and Abell 3558. We detected new extended features in the radio halos hosted by the Bullet cluster and Abell 3562. We assume that the decrement feature in the Bullet cluster might be an indication of a second wave of merger activity. The ridge feature in the peripheral region of the radio halo in Abell 3562 overlaps with the edge of the X-ray emission. Hence, we assume that the feature might be related to a shock region. We also reported the detection of a new mini-halo in Abell 3558. MeerKAT’s sensitivity and wide bandwidth enabled us to perform in-band spectral index studies and produce spectral index maps for the Bullet cluster, RXCJ1314.4 2515, and Abell 3562. The spectral index maps of the relics in the Bullet cluster and RXCJ1314.4 2515 indicate a spectral steepening towards the cluster center, while the spectral index map of the radio halo in the Bullet cluster indicates radial spectral steepening. The spectral index map of Abell 3562 indicates that the radio halo and ridge have similar spectral index variations, which suggests that the ridge feature is related to the radio halo.
Giant radio halos and relics in ACTPol clusters.
(2017) Sikhosana, Sinenhlanhla Precious.; Moodley, Kavilan.; Knowles, Kenda Leigh.
Galaxy clusters are the largest gravitationally-bound structures in the universe. They act as the largest astrophysical laboratories in the universe and are extremely interesting objects to study as they are at crossroads between astrophysics and cosmology. In previous decades the most prominent cluster studies were focused on thermal processes in the intracluster medium (ICM). However, recent studies have shown that non-thermal studies give a different perspective on ICM processes. Giant radio halos and radio relics are examples of this non-thermal diffuse radio emission. Giant radio halos are believed to originate from synchrotron radiation resulting from the re-acceleration of relativistic electrons in the cluster's magnetic field by the turbulent energy following merger activity. Radio relics, another form of non-thermal diffuse radio emission, have been identi ed as possible tracers of merger shock waves. The study of diffuse radio emission has a number of open questions such as; the observed bimodality in the radio power versus X-ray luminosity plot. The bimodality could partly be due to the identi cation of halos and relics in clusters without a well-de ned selection function. In this thesis, we studied giant radio halos and relics in a homogeneous, mass-selected sample of sixteen clusters selected via the Sunyaev- Zel'dovich (SZ) effect by the Atacama Cosmology Telescope (ACT) with polarization sensitive receivers (ACTPol). We carried out a radio wavelength study using data obtained from the Giant Metrewave Radio Telescope (GMRT) for four of these clusters. This subsample of four clusters will be added to the larger sample, eight of which have archival data, and four of which will be proposed for observations in the next GMRT observation cycle. We used the GMRT data at 610 MHz to search for diffuse radio emission in each cluster. We applied various uv-cuts and tapers to isolate the low-resolution emission in the target fi eld. For two of the four observed clusters, we tentatively discovered extended radio emission at a signifi cance level of at least 3o' We then measured radio fluxes for compact sources in the cluster region. We were able to calculate spectral indices for the compact sources that were cross-matched in FIRST.
Gravitational lensing of the cosmic microwave background: techniques and applications.
(2016) Prince, Heather.; Moodley, Kavilan.
We have entered an era of precision cosmology, in which the parameters of the standard cosmological model have been well constrained by observations. The cosmic microwave background (CMB) has played a vital role in providing these constraints, because the primordial CMB is sensitive to many of the cosmological parameters. The observed CMB is modified by secondary effects caused by photon interactions after the surface of last scattering. One such effect is gravitational lensing, the deflection of photons due to the matter that they pass. Gravitational lensing can be used to probe the total matter distribution, which is dominated by dark matter. CMB lensing also provides complementary cosmological information to that obtained from the CMB power spectrum, and can be used to break parameter degeneracies and improve constraints on dark energy and neutrino masses. We explore methods of reconstructing the lensing field from lensed CMB temperature and polarisation maps in real space, as an alternative to the harmonic space estimators currently in use, by extending an existing temperature real space estimator to CMB polarisation. Real space estimators have the advantage of being local in nature and they are thus equipped to deal with the nonuniform sky coverage, galactic cuts and point source excisions found in experimental data. We characterise some of the properties and limitations of these estimators and test them on simulated maps, finding that the reconstructions are accurate for large-scale lensing fields, and that the polarisation reconstructions improve on those from CMB temperature maps. Neutral hydrogen (HI) intensity mapping is expected to be a powerful probe of large scale structure and cosmology, and a number of current and planned experiments will be performing large intensity mapping surveys. HI is a biased tracer of the dark matter distribution, therefore HI observations will be correlated with CMB lensing reconstructions. We investigate the potential for measuring this cross-correlation using CMB lensing reconstructed from Advanced ACTPol observations and HI intensity mapping data from the Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX).We find that the CMB lensing-HI cross-correlation will be detectable with a total signal to noise ratio of between 20 and 50 in each of four bins in the HIRAX frequency range, which will allow us to constrain the HI bias on various scales over a wide redshift range (z = 0.8 to 2.5).
HI intensity mapping and cross-correlation science with HIRAX.
(2020) Naidoo, Warren.; Moodley, Kavilan.
Abstract available in PDF.
Initial conditions of the universe : signatures in the cosmic microwave background and baryon acoustic oscillations.
(2012) Kasanda, Simon Muya.; Moodley, Kavilan.
In this thesis, we investigate the signatures of isocurvature initial conditions in the cosmic microwave background (CMB) through the temperature and polarization anisotropies, and in the large-scale structure distribution through the baryon acoustic oscillations (BAO). The first part of this thesis is a brief review of the standard cosmological model with its underlying linear cosmological perturbation theory. We supplement it with a general discussion on the initial conditions of the primordial fluctuations. In the third chapter, we review the evolution of the perturbations in the adiabatic model. We focus on the evolution of adiabatic perturbations in the photons and baryons from the epoch of initial conditions to the photon-baryon decoupling, as these determine the main features of the primary CMB anisotropies and of the baryon acoustic oscillations. The fourth chapter recalls the theory of the CMB anisotropies in the adiabatic model. We consider the perturbations from the last scattering surface and evolve them through the line of sight integral to get the adiabatic CMB power spectrum. We review the effect of different cosmological parameters on the adiabatic CMB temperature spectrum. In the fifth chapter, we investigate the observational signatures of the isocurvature perturbations in the CMB anisotropies. We first derive simple semi-analytic expressions for the evolution of the photon and baryon perturbations prior to decoupling for the four isocurvature regular modes and show that these modes excite different harmonics which couple differently to Silk damping and alter the form and evolution of acoustic waves. We study the impact of different cosmological parameters on the CMB angular power spectrum through the line of sight integral and find that the impact of the physical baryon and matter densities in isocurvature models differ the most from their effect in adiabatic models. In the last two chapters, we explore in detail the effect of allowing for small amplitude admixtures of general isocurvature perturbations in addition to the dominant adiabatic mode, and their effect on the baryon acoustic oscillations. The sixth chapter focuses on the distortion of the standard ruler distance and the degradation of dark energy constants due to the inclusion of isocurvature perturbations, while the seventh chapter discusses in more detail the sensitivity of BAO dark energy constraints to general isocurvature perturbations. We stress the role played by Silk damping on the BAO peak features in breaking the degeneracy in the peak location for the different isocurvature modes and show how more general initial conditions impact our interpretation of cosmological data in dark energy studies. We find that the inclusion of these additional isocurvature modes leads to a significant increase in the Dark Energy Task Force figure of merit when considered in conjunction with CMB data. We also show that the incorrect assumption of adiabaticity has the potential to substantially bias our estimates of the dark energy parameters. We find that the use of the large scale structure data in conjunction with CMB data significantly improves our ability to measure the contributions of different modes to the initial conditions.
Multi-wavelength study of radio sources in the universe.
(2009) El Bouchefry, Khadija.; Rash, Jonathan Paul Stuart.; Moodley, Kavilan.
This thesis presents a detailed multi-wavelength study of radio sources. A major part of the thesis focuses on radio sources in the FIRST survey while the latter part of the thesis studies low redshift radio galaxies in X-ray selected galaxy clusters. In the first part of the thesis a cross correlation analysis of FIRST radio sources with optical data from the NDWFS and infrared data from the FLAMINGOS survey in the Boötes and Cetus fields was performed. Optical counterparts were found for 76% (688/900) of sources in one band or more i.e., Bw, R, I or K. Photometric redshifts for these sources have been computed using the Hyperz code. The red-shifts obtained are fairly consistent with those expected from the K−z relation for brighter radio sources. A total number of 57 counterparts have extremely red colour (R− K > 5). Photometric redshifts derived using Hyperz imply that these Extremely Red Object (ERO) counterparts to FIRST radio sources are mostly located in the range z ∼ 0.7 −2, with the bulk of the population at z ∼ 1. A total of 25 ERO counterparts to FIRST radio sources were identified in R, J and K bands. These objects were separated into passively-evolving and dusty star-forming galaxies using their R, J and K colours. The relatively blue J − K colour of these galaxies suggest that most (72%, 18/25) are elliptical galaxies rather than dusty starburst galaxies. Using data from the Chandra XBoötes survey, a total of 92 (10%) FIRST radio sources were identified above the X-ray flux limit, fX (0.5 − 7) keV = 8 × 10−15 erg s−1 cm−2, and of these 79 optical counterparts are in common to the radio-X-ray matches. The majority (68%) of the radio-X-ray matched population were found to have −1 < log fX/ fopt < +1 indicative of AGNs. There is a significant population (23%) with high X-ray-to-optical flux ratio (log fX/ fopt > 1), suggesting high redshift and/or dust obscured AGN. In addition, there is also a population of sources that are X-ray faint optically bright sources with log fX/ fopt < −1. Spectroscopic identifications were found for 22 of the 79 sources. These optical spectra were dominated by broad line AGNs and also included narrow emission line galaxies. It was found that many classes of objects contribute to the X-ray/radio emission including quasars, BL Lacs, starburst galaxies, normal galaxies and galaxies with both AGN and starburst activity. This thesis also investigated the clustering analysis of FIRST radio sources optically identified in the SDSS DR6 survey using the two point angular correlation function ω(θ). The matched sources were found to have a larger amplitude of clustering compared to the full catalogue of radio sources consistent with similar studies in the literature. The angular correlation function was measured for different magnitude limited and flux limited subsamples. It was found that the angular correlation function scales with the depth of the optical survey as expected, whereas the amplitude of the angular correlation function increases as the radio flux increases. The last part of this thesis is devoted to studying radio galaxies in galaxy clusters at high frequencies to explore their contamination to the Sunyaev-Zel’dovich effect signal in these clusters. A total of 139 galaxies at low redshift (z < 0.25) in X-ray selected clusters were observed at four frequencies, 4.9, 9, 22, and 43 GHz using the NRAO Very Large Array. It was found that more than half of the observed sources have steep microwave spectra with steep spectral index, α < −0.5, as generally expected. However, about 60% of the unresolved or barely resolved sources have flat or inverted spectra. Most of these sources show an upward turn in flux at ν > 22 GHz, implying a higher flux than would be expected from an extrapolation of the lower frequency flux measurements. Our results quantify the need for careful source subtraction in increasingly sensitive measurements of the Sunyaev-Zel’dovich effect in clusters of galaxies.
Observational probes of merging galaxy clusters.
(2016) Knowles, Kenda Leigh.; Moodley, Kavilan.
Abstract available in PDF file.
Optimisation of the population Monte Carlo algorithm : application to cosmology.
(2015) Moodley, Darell.; Moodley, Kavilan.
In this thesis we study the Population Monte Carlo (PMC) algorithm and utilise simulations to improve the efficiency of the algorithm by optimising the algorithm parameters. We then ap ply these optimisation results to a cosmological parameter estimation problem, specifically that of determining the initial conditions for structure formation. We accomplish this by using cos mic microwave background (CMB) data to constrain models with an admixture of adiabatic and isocurvature modes. We review the standard cosmological model and current cosmological probes used for cosmol ogy and discuss the CMB anisotropy spectrum, which forms the basis for our cosmological parameter estimation study. We briefly outline linear perturbation theory and initial conditions that form the basis of the inflationary models considered in this thesis. We describe the adiabatic and isocurvature perturbations and investigate their effect on the CMB anisotropy spectrum. We outline the Bayesian parameter estimation methodology adopted in our study and review Monte Carlo sampling, specifically the Markov Chain Monte Carlo (MCMC) and PMC algo rithms explaining why these methods are used in Bayesian parameter estimation. We discuss recent developments to the PMC and MCMC algorithms and discuss various applications of these algorithms in cosmology. We focus on optimising the performance of the PMC algorithm with respect to its algorithm pa rameters that are specified initially. However, we first define a measure of efficiency, related to the computational cost of the sampling algorithm and then use simulations to maximise this mea sure with respect to the algorithm parameters. These algorithm parameters include the sample size drawn at each iteration, the number of importance functions used, and the parameters that characterise the importance functions. Before this though, we will first investigate the optimi sation of the PMC algorithm for a multivariate Gaussian target distribution, and present results for choosing the optimal algorithm parameters that maximise efficiency. We will also explore the performance of PMC on more complex distributions such as the banana shaped, bimodal and hypercube distribution, and discuss the advantages and shortfalls for these distributions. We incorporate the results from the previous optimisation study by applying the PMC algorithm to a cosmological parameter estimation problem. We constrain models with an admixture of adiabatic and isocurvature perturbations using the nine-year data release from the Wilkinson Mi crowave Anisotropy Probe (WMAP) experiment. We discuss challenges faced in sampling such complex distributions, the modifications to the PMC sampler needed to achieve convergence, and the efficiencies achieved in sampling these distributions. We present results on the marginal and joint parameter distributions for all possible admixtures of adiabatic and isocurvature modes. We then perform a principal component analysis to determine the degeneracies that arise from the introduction of isocurvature modes. In comparison to similar studies undertaken with the WMAP one-year and three-year datasets, we find that the allowed isocurvature fraction is more tightly constrained than in previous studies.
The thermal Sunyaev-Zel'dovich effect as a probe of cluster physics and cosmology.
(2010) Warne, Ryan Russell.; Moodley, Kavilan.
The universe is a complex environment playing host to a plethora of macroscopic and microscopic processes. Understanding the interplay and evolution of such processes will help to shed light on the properties and evolution of the universe. The juxtaposition is that in order to study small scale effects one needs to observe large scale structure as the latter objects trace the history of our universe. Galaxy groups and clusters are the largest known objects in the universe and thus provide a means to probe the evolution of structure formation in the universe as well as the underlying cosmology. In this thesis we investigate how clusters observed through the Sunyaev-Zel’dovich (SZ) effect can be used to constrain cosmological models. In addition, we present the first results of the Atacama Cosmology Telescope (ACT), a mm-wave telescope measuring the small-scale microwave background anisotropy, and conclude with preliminary SZ cluster detection performed on the latest ACT sky maps. In the first part of this thesis we investigate the ability of high resolution cosmic microwave background (CMB) experiments to detect hot gas in the outer regions of nearby group halos. We construct two hot gas models for the halos; a simpler adiabatic formalism with the gas described by a polytropic equation of state, and a more general gas description which incorporates feedback effects in line with constraints from X-ray observations. We calculate the thermal Sunyaev- Zel’dovich (tSZ) signal in these halos and compare it to the sensitivities of upcoming and current tSZ survey experiments such as ACT, PLANCK and the South Pole Telescope (SPT). Through the application of a multi-frequency Wiener filter, we derive mass and redshift based tSZ detectability limits for the various experiments, incorporating effects of galactic and extragalactic foregrounds as well as the CMB. In this study we find that galaxy group halos with virial masses below 1014M. can be detected at z ~< 0.05 with the mass limit dropping to 3 − 4 × 1013M. at z ~< 0.01. Probing such halos with the tSZ effect allows one to map the hot gas in the outer regions, providing a means to constrain gas processes, such as feedback, as well as the distribution of baryons in the local universe. In the fourth chapter, we extend this analysis and determine the ability of ACT to constrain galactic feedback and star formation in clusters and groups using the tSZ effect. We present a new microwave deblender, which provides a means of extracting accurate halo fluxes and radial profiles from maps of the tSZ effect. Considering various surveys that could be performed by ACT, we use multi-frequency filtering on simulated sky maps to predict how well such surveys will constrain gas properties using a Fisher matrix analysis. We find that the current ACT survey will be unable to constrain any gas parameters. However, if ACT were to survey a smaller area then we will be able to constrain feedback. Furthermore, with greater sensitivity, we will be able to place interesting constraints on the gas feedback, and baryon and stellar fractions. The fifth chapter in this thesis concerns itself with the first results of the Atacama Cosmology Telescope Project. In this section we discuss the map-making method as well as telescope beam characterisation, an understanding of which is important in any subsequent map analyses. In addition, we present maps of eight clusters observed at 148 GHz via the SZ effect, and provide flux and signal to noise estimates of the clusters. In the final chapter we present a preliminary analysis of the latest 148 GHz ACT maps from the 2008 observing season. We study the sky maps using single frequency wiener filtering, allowing for CMB, dust and correlated noise contamination. To substantiate our results, we compare the number counts, recovered fluxes and sample purity from simulated sky maps. The compounding effects of CMB and correlated noise result in high contamination levels below a signal to noise ratio of 6, however our investigation shows that above 8¾ our cluster sample is ¼ 80% pure. A cluster list containing 44 detections, of which 8 are previously known, is also presented, along with a Table listing the candidate cluster positions and fluxes. The candidate cluster catalogue will be used for follow-up studies using optical and X-ray observations.
Weak gravitational lensing in the cosmic microwave background : reconstructing the lensing convergence.
(2012) Ridl, Jethro Venn.; Moodley, Kavilan.
Many of the most significant constraints on the standard model of Cosmology describing the origins, contents and evolution of the Universe arise from the Cosmic Microwave Background (CMB). As we enter an era of precision cosmology, with more sensitive and higher angular resolution ground, balloon and space-based experiments, it is becoming increasingly important to understand the small-scale secondary anisotropies of the CMB. One of the most important of these secondary anisotropies comes from weak gravitational lensing, whereby free-streaming CMB photons are deflected by the gravitational potentials in the large-scale structure of the Universe. This has several important effects including modifications to the CMB power spectrum, the introduction of non-Gaussianities and the generation of B-mode polarization. In principle it is possible to reconstruct the the projection of the gravitational potential on the celestial sphere directly from observations of the CMB temperature anisotropies by examining the distinctive non-Gaussian signature the gravitational lensing imparts on to the CMB. This reconstructed map can be used to constrain the amplitude of the mass fluctuations in the early Universe and contains significant information regarding the dark matter distribution throughout the Universe. After a review of the standard Big Bang cosmological model the phenomenon of gravitational lensing is introduced. Equations for the deflection angle and lensing convergence are derived, as well as their power spectra, and the effect that gravitational lensing has on the CMB is discussed. In the main part of the thesis we study two methods for reconstructing the lensing convergence, the standard harmonic space quadratic estimator and a second estimator which is defined in real space. Each of the estimators is derived and implemented to recover reconstructed lensing convergence maps. The various biases that are inherent in the estimators is discussed, including details of how these biases can be removed. The performance of each of the estimators in reconstructing the lensing convergence is evaluated and contrasted. The final part of this thesis involves an analysis of a non-linear bias which affects both the harii monic space and real space estimators, resulting from a break down of the linear approximation, which arises if the lensing field has a sufficiently large magnitude. The effect of the non-linear bias on the reconstructed lensing field is evaluated, and comparison of these results with the reconstructed lensing amplitude from the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT) lensing measurement provides an estimate for the level of importance of the non-linear bias.