Dr James Allison

Abstract:

We present a Bayesian stacking technique to directly measure the H i mass function (HIMF) and its evolution with redshift using galaxies formally below the nominal detection threshold. We generate galaxy samples over several sky areas given an assumed HIMF described by a Schechter function and simulate the H i emission lines with different levels of background noise to test the technique. We use Multinest to constrain the parameters of the HIMF in a broad redshift bin, demonstrating that the HIMF can be accurately reconstructed, using the simulated spectral cube far below the H i mass limit determined by the 5σ flux-density limit, i.e. down to MHI = 107.5 M⊙ over the redshift range 0 < z < 0.55 for this particular simulation, with a noise level similar to that expected for the MIGHTEE survey. We also find that the constraints on the parameters of the Schechter function, φ⋆, M⋆ and α can be reliably fit, becoming tighter as the background noise decreases as expected, although the constraints on the redshift evolution are not significantly affected. All the parameters become better constrained as the survey area increases. In summary, we provide an optimal method for estimating the H i mass at cosmological distances that allows us to constrain the H i mass function below the detection threshold in forthcoming H i surveys. This study is a first step towards the measurement of the HIMF at high (z > 0.1) redshifts.

Abstract:

Photonic Doppler velocimetry (PDV) is an established technique for measuring the velocities of fast-moving surfaces in high-energy-density experiments. In the standard approach to PDV analysis, the short-time Fourier transform (STFT) is used to generate a spectrogram from which the velocity history of the target is inferred. The user chooses the form, duration, and separation of the window function. Here, we present a Bayesian approach to infer the velocity directly from the PDV oscilloscope trace, without using the spectrogram for analysis. This is clearly a difficult inference problem due to the highly periodic nature of the data, but we find that with carefully chosen prior distributions for the model parameters, we can accurately recover the injected velocity from synthetic data. We validate this method using PDV data collected at the STAR two-stage light gas gun at Sandia National Laboratories, recovering shock-front velocities in quartz that are consistent with those inferred using the STFT-based approach and are interpolated across regions of low signal-to-noise data. Although this method does not rely on the same user choices as the STFT, we caution that it can be prone to misspecification if the chosen model is not sufficient to capture the velocity behavior. Analysis using posterior predictive checks can be used to establish whether a better model is required, although more complex models come with additional computational cost, often taking more than several hours to converge when sampling the Bayesian posterior. We, therefore, recommend it be viewed as a complementary method to that of the STFT-based approach.