Turbulence plays a central role in shaping the structure and dynamics of the interstellar medium (ISM), governing the star formation rate (SFR) and the initial mass function (IMF). A key consequence of turbulence is the generation of density fluctuations, which regulate the amount of dense gas available for star formation. Accurate measurements of the three-dimensional (3D) turbulent density dispersion are therefore essential for understanding molecular-cloud structure and star formation. However, observations typically provide only two-dimensional (2D) column densities and are often affected by measurement/detector noise. The Brunt method estimates the 3D density dispersion from 2D column-density maps, but it does not account for finite signal-to-noise ratio (SNR). Here, we extend the method to recover the 3D turbulent density dispersion from noise-contaminated observations. Using numerical simulations spanning a range of density perturbation amplitudes and noise types, we identify a characteristic noise wavenumber, k_noise, corresponding to the intersection of the signal and noise spectra. Restricting the Brunt reconstruction to wavenumbers below k_noise yields a denoised density-dispersion estimate that closely reproduces the noise-free result. We provide a practical prescription to determine k_noise directly from the measurement SNR and image resolution. Alternatively, if the noise spectrum is known, it can be subtracted directly from the observed spectrum, eliminating the need to estimate k_noise. The proposed correction recovers the noise-free density dispersion with errors of <~5% for SNR>=3 and <~15% for SNR>=1, enabling substantially more reliable estimates of turbulent density fluctuations from noisy column-density data.
The problem of signal detection under an unknown background can be framed as one of inferring the weight of a mixture model with one misspecified component. Banerjee and Algeri (2026) show that, for this problem, the conservativeness of the inference is entirely determined by one single parameter, called the compensator. They demonstrate that, when the data are independent and identically distributed, an inferential approach based on the compensator circumvents the need to estimate the density of the misspecified component and the associated challenges. The main purpose of this manuscript is to broaden the scope of such an approach and extend it to the case in which, as is often encountered in modern experiments in physics and astronomy, the data consist of Poisson counts observed over a large number of bins.
Fast Radio Bursts (FRBs) are millisecond-duration radio transients whose automated detection increasingly relies on highly specialized deep learning models. These detectors achieve exceptional performance, but they require large task-specific training datasets and cannot be redefined without retraining. In this work, we evaluate whether small, open-weight, locally run generalist Vision-Language Models (VLMs) can detect FRBs in dynamic spectra under a zero-shot, prompt-only regime, with no fine-tuning and no labeled examples, returning structured decisions with a natural-language justification. From a controlled set of 3000 simulated L-band dynamic spectra containing FRBs, structured Radio Frequency Interference (RFI), and noise, we draw a balanced binary benchmark of 2000 samples and compare two such VLMs (Gemma 4 2B and 4B), sample by sample, against the state-of-the-art specialized detector SwinYNet. At the default threshold, Gemma 4 2B reaches an accuracy of 93.65%, with no statistically significant difference from SwinYNet (92.90%), while showing a significantly lower false-positive rate on structured RFI (6.4% vs. 25.0%) and no false positives on pure noise. SwinYNet retains a perfect probabilistic ranking on this benchmark (ROC-AUC of 1.0000 vs. 0.9482), a ceiling that the zero-shot VLM approaches from general-purpose pretraining alone. Rewriting the prompt alone reconfigures the same models for three-class FRB/RFI/noise classification on the full set of 3000 spectra, where they reach up to 86% accuracy without a single false FRB.