arXiv subjects

Barak Zackay

Publications and source records attributed to Barak Zackay.

67 records · Page 4Linked to original sources

arXiv2019

Gravitational-wave-moderated Accretion: The Case of ES Ceti

We show that recent observations of the compact binary, AM CVn type system, ES Ceti are fully consistent with theoretical predictions of stable mass transfer moderated by angular momentum loss due to gravitational-wave radiation. One of the main predictions of this model (for degenerate donors) is a widening of the binary. The mass transfer rate inferred from the observed rate of change in the orbital frequency is consistent with that inferred from the observed flux using the recent Gaia DR2 parallax

astro-ph.HE↗

arXiv2018

Optimal and Efficient Streak Detection in Astronomical Images

Identification of linear features (streaks) in astronomical images is important for several reasons, including: detecting fast-moving near-Earth asteroids; detecting or flagging faint satellites streaks; and flagging or removing diffraction spikes, pixel bleeding, line-like cosmic rays and bad-pixel features. Here we discuss an efficient and optimal algorithm for the detection of such streaks. The optimal method to detect streaks in astronomical images is by cross-correlating the image with a template of a line broadened by the point spread function of the system. To do so efficiently, the cross-correlation of the streak position and angle is performed using the Radon transform, which is the integral of pixel values along all possible lines through an image. A fast version of the Radon transform exists, which we here extend to efficiently detect arbitrarily short lines. While the brute force Radon transform requires an order of N^3 operations for an N by N image, the fast Radon transform has a complexity of the order of N^2 log(N). We apply this method to simulated images, recovering the theoretical signal-to-noise ratio, and to real images, finding long streaks of low-Earth-orbit satellites and shorter streaks of Global Positioning System satellites. We detect streaks that are barely visible to the eye, out of hundreds of images, without a-priori knowledge of the streaks' positions or angles. We provide implementation of this algorithm in Python and MATLAB.

astro-ph.IM↗

arXiv2018

Detecting Lensing-Induced Diffraction in Astrophysical Gravitational Waves

Gravitational waves emitted from compact binary coalescence can be subject to wave diffraction if they are gravitationally lensed by an intervening mass clump whose Schwarzschild timescale matches the wave period. Waves in the ground-based frequency band $f\sim 10$--$10^3\,$Hz are sensitive to clumps with masses $M_E \sim 10^2$--$10^3\,M_\odot$ enclosed within the impact parameter. These can be the central parts of low mass $M_L \sim 10^3$--$10^6\,M_\odot$ dark matter halos, which are predicted in Cold Dark Matter scenarios but are challenging to observe. Neglecting finely-tuned impact parameters, we focus on lenses aligned generally on the Einstein scale for which multiple lensed images may not form in the case of an extended lens. In this case, diffraction induces amplitude and phase modulations whose sizes $\sim 10\%$--$20\%$ are small enough so that standard matched filtering with unlensed waveforms do not degrade, but are still detectable for events with high signal-to-noise ratio. We develop and test an agnostic detection method based on dynamic programming, which does not require a detailed model of the lensed waveforms. For pseudo-Jaffe lenses aligned up to the Einstein radius, we demonstrate that a pair of fully upgraded aLIGO/Virgo detectors can extract diffraction imprints from binary black hole mergers out to $z_s \sim 0.2$--$0.3$. The prospect will improve dramatically for a third-generation detector for which binary black hole mergers out to $z_s \sim 2$--$4$ will all become valuable sources.

gr-qc↗

arXiv2018

A possible advantage of telescopes with a non-circular pupil

Most telescope designs have a circular-shape aperture. We demonstrate that telescopes with an elongated pupil have better contrast, at lower separations, between a bright central star and a faint companion. We simulate images for an elongated-pupil telescope and for a circular-pupil telescope of equal aperture area and integration time, investigating specifically what is the maximal contrast for finding faint companions around bright stars as a function of angular separation. We show that this design gives better contrast at lower separation from a bright star. This is shown for diffraction-limited (for perfect and imperfect optics) and seeing-limited speckle images, assuming equal aperture area and observing time. We also show the results are robust to errors in measurement of the point spread function. To compensate for the wider point spread function of the short axis, images should be taken at different rotation angles, either by rotating the telescope around the optical axis or by allowing a stationary mirror array to scan different parallactic angles with time. Images taken at different rotation angles are added using the proper image coaddition algorithms developed by Zackay & Ofek. The final image has the same contrast in all angles, rather than in specific areas of diffraction nulls. We obtained speckle observations with a small, ground based elongated-aperture telescope and show the results are consistent with simulations.

astro-ph.IM↗

arXiv2018

Relative Binning and Fast Likelihood Evaluation for Gravitational Wave Parameter Estimation

We present a method to accelerate the evaluation of the likelihood in gravitational wave parameter estimation. Parameter estimation codes compute likelihoods of similar waveforms, whose phases and amplitudes differ smoothly with frequency. We exploit this by precomputing frequency-binned overlaps of the best-fit waveform with the data. We show how these summary data can be used to approximate the likelihood of any waveform that is sufficiently probable within the required accuracy. We demonstrate that $\simeq 60$ bins suffice to accurately compute likelihoods for strain data at a sampling rate of $4096\,$Hz and duration of $T=2048\,$s around the binary neutron star merger GW170817. Relative binning speeds up parameter estimation for frequency domain waveform models by a factor of $\sim 10^4$ compared to naive matched filtering and $\sim 10$ compared to reduced order quadrature.

astro-ph.IM↗

arXiv2018

Parameter Estimation for GW170817 using Relative Binning

Relative binning is a new method for fast and accurate evaluation of the likelihood of gravitational wave strain data. This technique can be used to produce reliable posterior distributions for compact object mergers with very moderate computational resources. We use a fast likelihood evaluation code based on this technique to estimate the parameters of the double neutron-star merger event GW170817 using publicly available LIGO data. We obtain statistically similar posteriors using either Markov-chain Monte-Carlo or nested sampling. The results do not favor non-zero aligned spins at a statistically significant level. There is no significant sign of non-zero tidal deformability (as quantified by the Bayesian evidence), whether or not high-spin or low-spin priors are adopted. Our posterior samples are publicly available, and we also provide a tutorial Python code to implement fast likelihood evaluation using the relative binning method.

gr-qc↗

arXiv2017

Optimal matched filter in the low-number count Poisson noise regime and implications for X-ray source detection

Detection of templates (e.g., sources) embedded in low-number count Poisson noise is a common problem in astrophysics. Examples include source detection in X-ray images, gamma-rays, UV, neutrinos, and search for clusters of galaxies and stellar streams. However, the solutions in the X-ray-related literature are sub-optimal -- in some cases by considerable factors. Using the lemma of Neyman-Pearson we derive the optimal statistics for template detection in the presence of Poisson noise. We demonstrate that this method provides higher completeness, for a fixed false-alarm probability value, compared with filtering the image with the point-spread function (PSF). In turn, we find that filtering by the PSF is better than filtering the image using the Mexican-hat wavelet (used by wavedetect). For some background levels, our method improves the sensitivity of source detection by more than a factor of two over the popular Mexican-hat wavelet filtering. This filtering technique can also be used also for fast PSF photometry and flare detection, and it is efficient, as well as straight forward to implement. We provide an implementation in MATLAB.

astro-ph.IM↗

arXiv2017

The detection of an extremely bright fast radio burst in a phased array feed survey

We report the detection of an ultra-bright fast radio burst (FRB) from a modest, 3.4-day pilot survey with the Australian Square Kilometre Array Pathfinder. The survey was conducted in a wide-field fly's-eye configuration using the phased-array-feed technology deployed on the array to instantaneously observe an effective area of $160$ deg$^2$, and achieve an exposure totaling $13200$ deg$^2$ hr. We constrain the position of FRB 170107 to a region $8'\times8'$ in size (90% containment) and its fluence to be $58\pm6$ Jy ms. The spectrum of the burst shows a sharp cutoff above $1400$ MHz, which could be either due to scintillation or an intrinsic feature of the burst. This confirms the existence of an ultra-bright ($>20$ Jy ms) population of FRBs.

astro-ph.HE↗

arXiv2016

Proper image subtraction - optimal transient detection, photometry and hypothesis testing

Transient detection and flux measurement via image subtraction stand at the base of time domain astronomy. Due to the varying seeing conditions, the image subtraction process is non-trivial, and existing solutions suffer from a variety of problems. Starting from basic statistical principles, we develop the optimal statistic for transient detection, flux measurement and any image-difference hypothesis testing. We derive a closed-form statistic that: (i) Is mathematically proven to be the optimal transient detection statistic in the limit of background-dominated noise; (ii) Is numerically stable; (iii) For accurately registered, adequately sampled images, does not leave subtraction or deconvolution artifacts; (iv) Allows automatic transient detection to the theoretical sensitivity limit by providing credible detection significance; (v) Has uncorrelated white noise; (vi) Is a sufficient statistic for any further statistical test on the difference image, and in particular, allows to distinguish particle hits and other image artifacts from real transients; (vii) Is symmetric to the exchange of the new and reference images; (viii) Is at least an order of magnitude faster to compute than some popular methods; and (ix) Is straightforward to implement. Furthermore, we present extensions of this method that make it resilient to registration errors, color-refraction errors, and any noise source that can be modelled. In addition, we show that the optimal way to prepare a reference image is the proper image coaddition presented in Zackay \& Ofek (2015b). We demonstrate this method on simulated data and real observations from the Palomar Transient Factory data release 2. We provide an implementation of this algorithm in MATLAB and Python.

astro-ph.IM↗

arXiv2015

How to coadd images? I. Optimal source detection and photometry using ensembles of images

Stacks of digital astronomical images are combined in order to increase image depth. The variable seeing conditions, sky background and transparency of ground-based observations make the coaddition process non-trivial. We present image coaddition methods optimized for source detection and flux measurement, that maximize the signal-to-noise ratio (S/N). We show that for these purposes the best way to combine images is to apply a matched filter to each image using its own point spread function (PSF) and only then to sum the images with the appropriate weights. Methods that either match filter after coaddition, or perform PSF homogenization prior to coaddition will result in loss of sensitivity. We argue that our method provides an increase of between a few and 25 percent in the survey speed of deep ground-based imaging surveys compared with weighted coaddition techniques. We demonstrate this claim using simulated data as well as data from the Palomar Transient Factory data release 2. We present a variant of this coaddition method which is optimal for PSF or aperture photometry. We also provide an analytic formula for calculating the S/N for PSF photometry on single or multiple observations. In the next paper in this series we present a method for image coaddition in the limit of background-dominated noise which is optimal for any statistical test or measurement on the constant-in-time image (e.g., source detection, shape or flux measurement or star-galaxy separation), making the original data redundant. We provide an implementation of this algorithm in MATLAB.

astro-ph.IM↗

arXiv2015

How to coadd images? II. A coaddition image that is optimal for any purpose in the background dominated noise limit

Image coaddition is one of the most basic operations that astronomers perform. In Paper~I, we presented the optimal ways to coadd images in order to detect faint sources and to perfrom flux measurements under the assumption that the noise is approximately Gaussian. Here, we build on these results and derive from first principles a coaddition technique which is optimal for any hypothesis testing and measurement (e.g., source detection, flux or shape measurements and star/galaxy separation), in the background-noise-dominated case. This method has several important properties. The pixels of the resulting coadd image are uncorrelated. This image preserves all the information (from the original individual images) on all spatial frequencies. Any hypothesis testing or measurement that can be done on all the individual images simultaneously, can be done on the coadded image without any loss of information. The PSF of this image is typically as narrow, or narrower than the PSF of the best image in the ensemble. Moreover, this image is practically indistinguishable from a regular single image, meaning that any code that measures any property on a regular astronomical image can be applied to it unchanged. In particular, the optimal source detection statistic derived in paper~I is reproduced by matched filtering this image with its own PSF. This coaddition process, which we call proper coaddition, can be understood as a the maximum signal-to-noise ratio measurement of the Fourier transform of the image, weighted in such a way that the noise in the entire Fourier domain is of equal variance. This method has important implications for multi-epoch seeing-limited deep surveys, weak lensing galaxy shape measurements, and diffraction-limited imaging via speckle observations. The last topic will be covered in depth in future papers. We provide an implementation of this algorithm in MATLAB.

astro-ph.IM↗

arXiv2014

An accurate and efficient algorithm for detection of radio bursts with an unknown dispersion measure, for single dish telescopes and interferometers

Astronomical radio bursts disperse while traveling through the interstellar medium. To optimally detect a short-duration signal within a frequency band, we have to precisely compensate for the pulse dispersion, which is a computationally demanding task. We present the Fast Dispersion Measure Transform (FDMT) algorithm for optimal detection of such signals. Our algorithm has a low theoretical complexity of 2N_f N_t+ N_t N_d log_2(N_f) where N_f, N_t and N_d are the numbers of frequency bins, time bins, and dispersion measure bins, respectively. Unlike previously suggested fast algorithms our algorithm conserves the sensitivity of brute force dedispersion. Our tests indicate that this algorithm, running on a standard desktop computer, and implemented in a high-level programming language, is already faster than the state of the art dedispersion codes running on graphical processing units (GPUs). We also present a variant of the algorithm that can be efficiently implemented on GPUs. The latter algorithm's computation and data transport requirements are similar to those of two-dimensional FFT, indicating that incoherent dedispersion can now be considered a non-issue while planning future surveys. We further present a fast algorithm for sensitive dedispersion of pulses shorter than normally allowed by incoherent dedispersion. In typical cases this algorithm is orders of magnitude faster than coherent dedispersion by convolution. We analyze the computational complexity of pulsed signal searches by radio interferometers. We conclude that, using our suggested algorithms, maximally sensitive blind searches for such pulses is feasible using existing facilities. We provide an implementation of these algorithms in Python and MATLAB.

astro-ph.IM↗

arXiv2013

The Multiplexed Imaging Method: High-Resolution Wide Field Imaging Using Physically Small Detectors

We present the method of multiplexed imaging designed for astronomical observations of large sky areas in the IR, visible and UV frequencies. Our method relies on the sparse nature of astronomical observations. The method consists of an optical system that directs light from different locations on the focal plane of a telescope onto the same detector area and an algorithm that reconstructs the original wide-field image. In this way we can use a physically small detector to cover a wide field of view. We test our reconstruction algorithm using public space telescope data. Our tests demonstrate the reliability and power of the multiplexed imaging method. Using our method it will be possible to increase the sky area covered with space telescopes by 1-3 orders of magnitude, depending on the specific scientific goal and optical parameters. This method can significantly increase the volume of astronomical surveys, including search programs for exoplanets and transients using space and ground instruments.

astro-ph.IM↗