ABSTRACT 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: (1) is mathematically proven to be the optimal transient detection statistic in the limit of background-dominated noise, (2) is numerically stable, (3) for accurately registered, adequately sampled images, does not leave subtraction or deconvolution artifacts, (4) allows automatic transient detection to the theoretical sensitivity limit by providing credible detection significance, (5) has uncorrelated white noise, (6) is a sufficient statistic for any further statistical test on the difference image, and, in particular, allows us to distinguish particle hits and other image artifacts from real transients, (7) is symmetric to the exchange of the new and reference images, (8) is at least an order of magnitude faster to compute than some popular methods, and (9) 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 modeled. In addition, we show that the optimal way to prepare a reference image is the proper image coaddition presented in Zackay & Ofek. We demonstrate this method on simulated data and real observations from the PTF data release 2. We provide an implementation of this algorithm in MATLAB and Python.
The localization of the repeating fast radio burst (FRB), FRB 121102, suggests that it is associated with a persistent radio-luminous compact source in the FRB host galaxy. Using the FIRST radio ...catalog, I present a search for luminous persistent sources in nearby galaxies, with radio luminosities of the FRB 121102 persistent source luminosity. The galaxy sample contains about 30% of the total galaxy g-band luminosity within Mpc, in a footprint of 10,600 deg2. After rejecting sources likely due to active galactic nuclei activity or background sources, I am left with 11 candidates that are presumably associated with galactic disks or star-formation regions. At least some of these candidates are likely to be due to chance alignment. In addition, I find 85 sources within of galactic nuclei. Assuming that the radio persistent sources are not related to galactic nuclei and that they follow the galaxy g-band light, the 11 sources imply a 95% confidence upper limit on the space density of luminous persistent sources of Mpc−3, and that at any given time only a small fraction of galaxies host a radio-luminous persistent source ( ). Assuming a persistent source lifetime of 100 years, this implies a birth rate of yr−1 Mpc−3. Given the FRB volumetric rate, and assuming that all FRBs repeat and are associated with persistent radio sources, this sets a lower limit on the rate of FRB events per persistent source of yr−1. I argue that these 11 candidates are good targets for FRB searches and I estimate the FRB event rate from these candidates.
We discuss the late-time (tens of days) emission from the radioactive ejecta of mergers involving neutron stars, when the ionization energy loss time of beta-decay electrons and positrons exceeds the ...expansion time. We show that if the e are confined to the plasma (by magnetic fields), then the time dependence of the plasma heating rate, , and hence of the bolometric luminosity , are given by , nearly independent of the composition and of the instantaneous radioactive energy release rate, . This universality of the late-time behavior is due to the weak dependence of the ionization loss rate on composition and on e energy. The late-time IR and optical measurements of GW170817 are consistent with this expected behavior provided that the ionization loss time exceeds the expansion time at t > t 7 days, as predicted based on the early (few day) electromagnetic emission.
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 nontrivial. We present image coaddition methods that maximize the signal-to-noise ratio (S/N) and optimized for source detection and flux measurement. 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 the 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% 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 these algorithms in MATLAB.
The mass of single neutron stars (NSs) can be measured using astrometric microlensing events. In such events, the center-of-light motion of a star lensed by an NS will deviate from the expected ...nonlensed motion and this deviation can be used to measure the mass of the NS. I search for future conjunctions between pulsars, with measured proper motion, and stars in the GAIA-DR2 catalog. I identify two candidate events of stars involving lensing by a foreground pulsar in which the estimated light deflection of the background star will deviate from the nonlensed motion by more than 10 as. PSR J185635−375435 passed ≅4 1 from a 19.4 G magnitude star on J2014.9 with an estimated deflection of 13 as, while PSR J084606−353340 may pass ∼0 2 from a 19.0 G magnitude star on J2022.9 with an estimated deflection of 91 as. However, the proper motion of the second event is highly uncertain. Therefore, additional observations are required in order to verify this event. I briefly discuss the opposite case, in which a pulsar is being lensed by a star. Such events can be used to measure the stellar mass via pulsar timing measurements. I do not find good candidates for such events with predicted variations in the pulsar period derivative ( ), divided by 1 s, exceeding 10−20 s−1. Since only about 10% of the known pulsars have measured proper motions, there is potential for an increase in the number of predicted pulsar lensing events.
ABSTRACT Astronomical radio signals are subjected to phase dispersion while traveling through the interstellar medium. To optimally detect a short-duration signal within a frequency band, we have to ...precisely compensate for the unknown pulse dispersion, which is a computationally demanding task. We present the "fast dispersion measure transform" algorithm for optimal detection of such signals. Our algorithm has a low theoretical complexity of , where Nf, Nt, and NΔ 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 a two-dimensional fast Fourier transform, indicating that incoherent dedispersion can now be considered a nonissue while planning future surveys. We further present a fast algorithm for sensitive detection of pulses shorter than the dispersive smearing limits of incoherent dedispersion. In typical cases, this algorithm is orders of magnitude faster than enumerating dispersion measures and coherently dedispersing 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 dispersed pulses are feasible using existing facilities. We provide an implementation of these algorithms in Python and MATLAB.
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 operations for a N × N image, the fast Radon transform has a complexity of . 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.
Abstract
We report our Spitzer Space Telescope observations and detections of the binary neutron star merger GW170817. At 4.5 μm, GW170817 is detected at 21.9 mag AB at +43 days and 23.9 mag AB at ...+74 days after merger. At 3.6 μm, GW170817 is not detected to a limit of 23.2 mag AB at +43 days and 23.1 mag AB at +74 days. Our detections constitute the latest and reddest constraints on the kilonova/macronova emission and composition of heavy elements. The 4.5 μm luminosity at this late phase cannot be explained by elements exclusively from the first abundance peak of the r-process. Moreover, the steep decline in the Spitzer band, with a power-law index of 3.4 ± 0.2, can be explained by a few of the heaviest isotopes with half-life around 14 d dominating the luminosity (e.g. 140Ba, 143Pr, 147Nd, 156Eu, 191Os, 223Ra, 225Ra, 233Pa, 234Th) or a model with lower deposition efficiency. This data offers evidence that the heaviest elements in the second and third r-process abundance peak were indeed synthesized. Our conclusion is verified by both analytics and network simulations and robust despite intricacies and uncertainties in the nuclear physics. Future observations with Spitzer and James Webb Space Telescope will further illuminate the relative abundance of the synthesized heavy elements.
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 perform 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 that 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 coadded 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 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.
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