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Register a new userA maximum likelihood estimate of the parameters of the FRB population
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Added by
Siddhartha Bhattacharyya
Publication date
2021
fields
Physics
and research's language is
English
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We consider a sample of $82$ non-repeating FRBs detected at Parkes, ASKAP, CHIME and UTMOST each of which operates over a different frequency range and has a different detection criteria. Using simulations, we perform a maximum likelihood analysis to determine the FRB population model which best fits this data. Our analysis shows that models where the pulse scatter broadening increases moderately with redshift ($z$) are preferred over those where this increases very sharply or where scattering is absent. Further, models where the comoving event rate density is constant over $z$ are preferred over those where it follows the cosmological star formation rate. Two models for the host dispersion measure ($DM_{rm host}$) distribution (a fixed and a random $DM_{rm host}$) are found to predict comparable results. We obtain the best fit parameter values $alpha=-1.53^{+0.29}_{-0.19}$, $overline{E}_{33}=1.55^{+0.26}_{-0.22}$ and $gamma=0.77pm 0.24$. Here $alpha$ is the spectral index, $gamma$ is the exponent of the Schechter luminosity function and $overline{E}_{33}$ is the mean FRB energy in units of $10^{33} , {rm J}$ across $2128 - 2848; {rm MHz}$ in the FRB rest frame.
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We examine the spectra of 23 fast radio bursts detected in a flys-eye survey with the Australian SKA Pathfinder, including those of three bursts not previously reported. The mean spectral index of $alpha = -1.6_{-0.2}^{+0.3}$ ($F_ u propto u^alpha$) is close to that of the Galactic pulsar population. The sample is dominated by bursts exhibiting a large degree of spectral modulation: 17 exhibit fine-scale spectral modulation with an rms exceeding 50% of the mean, with decorrelation bandwidths (half-maximum) ranging from $approx$ to 49 MHz. Most decorrelation bandwidths are an order of magnitude lower than the $gtrsim 30,$MHz expected of Galactic interstellar scintillation at the Galactic latitude of the survey, $|b| = 50 pm 5 deg$. A test of the amplitude distribution of the spectral fluctuations reveals only 12 bursts consistent at better than a 5% confidence level with the prediction of 100%-modulated diffractive scintillation. Moreover, five of six FRBs with a signal-to-noise ratio exceeding 18 are consistent with this prediction at less than 1% confidence. Nonetheless, there is weak evidence (88-95% confidence) that the amplitude of the fine-scale spectral modulation is anti-correlated with dispersion measure (DM) that would suggest it originates as a propagation effect. This effect appears to be corroborated by the smoothness of the higher-DM Parkes FRBs, and could arise due to quenching of diffractive scintillation (e.g. in the interstellar medium of the host galaxy) by angular broadening in the intergalactic medium.
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Astrophysical sources are now observed by many different instruments at different wavelengths, from radio to high-energy gamma-rays, with an unprecedented quality. Putting all these data together to form a coherent view, however, is a very difficult task. Each instrument has its own data format, software and analysis procedure, which are difficult to combine. It is for example very challenging to perform a broadband fit of the energy spectrum of the source. The Multi-Mission Maximum Likelihood framework (3ML) aims to solve this issue, providing a common framework which allows for a coherent modeling of sources using all the available data, independent of their origin. At the same time, thanks to its architecture based on plug-ins, 3ML uses the existing official software of each instrument for the corresponding data in a way which is transparent to the user. 3ML is based on the likelihood formalism, in which a model summarizing our knowledge about a particular region of the sky is convolved with the instrument response and compared to the corresponding data. The user can choose between a frequentist analysis, and a Bayesian analysis. In the former, parameters of the model are optimized in order to obtain the best match to the data (i.e., the maximum of the likelihood). In the latter, the priors specified by the user are used to build the posterior distribution, which is then sampled with Markov Chain Monte Carlo or Multinest. Our implementation of this idea is very flexible, allowing the study of point sources as well as extended sources with arbitrary spectra. We will review the problem we aim to solve, the 3ML concepts and its innovative potential.
We present a novel technique for estimating disk parameters (the centre and the radius) from its 2D image. It is based on the maximal likelihood approach utilising both edge pixels coordinates and the image intensity gradients. We emphasise the following advantages of our likelihood model. It has closed-form formulae for parameter estimating, requiring less computational resources than iterative algorithms therefore. The likelihood model naturally distinguishes the outer and inner annulus edges. The proposed technique was evaluated on both synthetic and real data.
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