arXiv subjects

Avishay Gal-Yam

Publications and source records attributed to Avishay Gal-Yam.

At least 127 records · Page 7Linked to original sources

arXiv2018

Multi-Messenger Astrophysics: Harnessing the Data Revolution

The past year has witnessed discovery of the first identified counterparts to a gravitational wave transient (GW 170817A) and a very high-energy neutrino (IceCube-170922A). These source identifications, and ensuing detailed studies, have realized longstanding dreams of astronomers and physicists to routinely carry out observations of cosmic sources by other than electromagnetic means, and inaugurated the era of "multi-messenger" astronomy. While this new era promises extraordinary physical insights into the universe, it brings with it new challenges, including: highly heterogeneous, high-volume, high-velocity datasets; globe-spanning cross-disciplinary teams of researchers, regularly brought together into transient collaborations; an extraordinary breadth and depth of domain-specific knowledge and computing resources required to anticipate, model, and interpret observations; and the routine need for adaptive, distributed, rapid-response observing campaigns to fully exploit the scientific potential of each source. We argue, therefore, that the time is ripe for the community to conceive and propose an Institute for Multi-Messenger Astrophysics that would coordinate its resources in a sustained and strategic fashion to efficiently address these challenges, while simultaneously serving as a center for education and key supporting activities. In this fashion, we can prepare now to realize the bright future that we see, beyond, through these newly opened windows onto the universe.

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arXiv2018

iPTF 16hgs: A double-peaked Ca-rich gap transient in a metal poor, star forming dwarf galaxy

Calcium rich gap transients represent an intriguing new class of faint and fast evolving supernovae that exhibit strong [Ca II] emission in their nebular phase spectra. In this paper, we present the discovery and follow-up observations of iPTF 16hgs -- an intermediate luminosity and fast evolving transient that exhibited a double peaked light curve. Exhibiting a typical Type Ib spectrum in the photospheric phase and an early transition to a [Ca II] dominated nebular phase, we show that iPTF 16hgs shows properties consistent with the class of Ca-rich gap transients, with two interesting exceptions. First, while the second peak of the light curve is similar to other Ca-rich gap transients (suggesting $M_{ej}$ of 0.4 M$_\odot$ and peak luminosity of $3 \times 10^{41}$ ergs s$^{-1}$), we show that the first blue and fast declining (over $2$ days) peak is unique to this source. Second, with Integral Field Unit observations of the host galaxy, we find that iPTF 16hgs occurred in the outskirts (projected offset of $6$ kpc $ = 1.9 R_{eff}$) of a low metallicity (0.4 Z$_\odot$), star forming, dwarf spiral galaxy. Using deep late-time VLA and uGMRT observations, we place stringent limits on the local environment of the source, ruling out a large parameter space of circumstellar densities and mass loss environments of the progenitor. If iPTF 16hgs shares explosion physics with the class of Ca-rich gap transients, the presence of the first peak can be explained by enhanced mixing of 0.01 M$_\odot$ of $^{56}$Ni into the outer layers the ejecta, reminiscent of some models of He-shell detonations on WDs. On the other hand, if iPTF 16hgs is physically unrelated to the class, the first peak is consistent with shock cooling emission (of an envelope with a mass of 0.08 M$_\odot$ and radius of 13 R$_\odot$) associated with a core-collapse explosion of a highly stripped massive star in a close binary system.

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arXiv2018

A Significantly off-center Ni56 Distribution for the Low-Luminosity Type Ia Supernova SN 2016brx from the 100IAS survey

We present nebular-phase spectra of the Type Ia supernova (SN Ia) 2016brx, a member of the 1991bg-like subclass that lies at the faint end of the SN Ia luminosity function. Nebular spectra are available for only three other 1991bg-like SNe, and their Co line centers are all within <~ 500 km/s of each other. In contrast, the nebular Co line center of SN 2016brx is blue-shifted by >1500 km/s compared to them and by ~1200 km/s compared to the rest frame. This is a significant shift relative to the narrow nebular line velocity dispersion of <~ 2000 km/s of these SNe. The large range of nebular line shifts implies that the Ni56 in the ejecta of SN 1991bg-like events is off-center by ~1000 km/s rather than universally centrally confined as previously suggested. With the addition of SN 2016brx, the Co nebular line shapes of 1991bg-like objects appear to connect with the brighter SNe Ia that show double-peak profiles, hinting at a continuous distribution of line profiles among SNe Ia. One class of models to produce both off-center and bi-modal Ni56 distributions is collisions of white dwarfs with unequal and equal masses.

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arXiv2018

Spectra of Hydrogen-Poor Superluminous Supernovae from the Palomar Transient Factory

Most Type I superluminous supernovae (SLSNe-I) reported to date have been identified by their high peak luminosities and spectra lacking obvious signs of hydrogen. We demonstrate that these events can be distinguished from normal-luminosity SNe (including Type Ic events) solely from their spectra over a wide range of light-curve phases. We use this distinction to select 19 SLSNe-I and 4 possible SLSNe-I from the Palomar Transient Factory archive (including 7 previously published objects). We present 127 new spectra of these objects and combine these with 39 previously published spectra, and we use these to discuss the average spectral properties of SLSNe-I at different spectral phases. We find that Mn II most probably contributes to the ultraviolet spectral features after maximum light, and we give a detailed study of the O II features that often characterize the early-time optical spectra of SLSNe-I. We discuss the velocity distribution of O II, finding that for some SLSNe-I this can be confined to a narrow range compared to relatively large systematic velocity shifts. Mg II and Fe II favor higher velocities than O II and C II, and we briefly discuss how this may constrain power-source models. We tentatively group objects by how well they match either SN 2011ke or PTF12dam and discuss the possibility that physically distinct events may have been previously grouped together under the SLSN-I label.

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arXiv2018

SN 2017dio: a type-Ic supernova exploding in a hydrogen-rich circumstellar medium

SN 2017dio shows both spectral characteristics of a type-Ic supernova (SN) and signs of a hydrogen-rich circumstellar medium (CSM). Prominent, narrow emission lines of H and He are superposed on the continuum. Subsequent evolution revealed that the SN ejecta are interacting with the CSM. The initial SN Ic identification was confirmed by removing the CSM interaction component from the spectrum and comparing with known SNe Ic, and reversely, adding a CSM interaction component to the spectra of known SNe Ic and comparing them to SN 2017dio. Excellent agreement was obtained with both procedures, reinforcing the SN Ic classification. The light curve constrains the pre-interaction SN Ic peak absolute magnitude to be around $M_g = -17.6$ mag. No evidence of significant extinction is found, ruling out a brighter luminosity required by a SN Ia classification. These pieces of evidence support the view that SN 2017dio is a SN Ic, and therefore the first firm case of a SN Ic with signatures of hydrogen-rich CSM in the early spectrum. The CSM is unlikely to have been shaped by steady-state stellar winds. The mass loss of the progenitor star must have been intense, $\dot{M} \sim 0.02$ $(ε_{Hα}/0.01)^{-1}$ $(v_\textrm{wind}/500$ km s$^{-1}$) $(v_\textrm{shock}/10 000$ km s$^{-1})^{-3}$ $M_\odot$~yr$^{-1}$, peaking at a few decades before the SN. Such a high mass loss rate might have been experienced by the progenitor through eruptions or binary stripping.

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arXiv2017

Energetic eruptions leading to a peculiar hydrogen-rich explosion of a massive star

Every supernova hitherto observed has been considered to be the terminal explosion of a star. Moreover, all supernovae with absorption lines in their spectra show those lines decreasing in velocity over time, as the ejecta expand and thin, revealing slower moving material that was previously hidden. In addition, every supernova that exhibits the absorption lines of hydrogen has one main light-curve peak, or a plateau in luminosity, lasting approximately 100 days before declining. Here we report observations of iPTF14hls, an event that has spectra identical to a hydrogen-rich core-collapse supernova, but characteristics that differ extensively from those of known supernovae. The light curve has at least five peaks and remains bright for more than 600 days; the absorption lines show little to no decrease in velocity; and the radius of the line-forming region is more than an order of magnitude bigger than the radius of the photosphere derived from the continuum emission. These characteristics are consistent with a shell of several tens of solar masses ejected by the star at supernova-level energies a few hundred days before a terminal explosion. Another possible eruption was recorded at the same position in 1954. Multiple energetic pre-supernova eruptions are expected to occur in stars of 95-130 solar masses, which experience the pulsational pair instability. That model, however, does not account for the continued presence of hydrogen, or the energetics observed here. Another mechanism for the violent ejection of mass in massive stars may be required.

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arXiv2017

Exploring the efficacy and limitations of shock-cooling models: new analysis of Type II supernovae observed by the Kepler mission

Modern transient surveys have begun discovering and following supernovae (SNe) shortly after first light---providing systematic measurements of the rise of Type II SNe. We explore how analytic models of early shock-cooling emission from core-collapse SNe can constrain the progenitor's radius, explosion velocity, and local host extinction. We simulate synthetic photometry in several realistic observing scenarios and, assuming the models describe the typical explosions well, find that ultraviolet observations can constrain the progenitor's radius to a statistical uncertainty of $\pm10-15\%$, with a systematic uncertainty of $\pm 20\%$. With these observations the local host extinction ($A_V$) can be constrained to a factor of two and the shock velocity to $\pm 5\%$ with a systematic uncertainty of $\pm 10\%$. We also re-analyze the SN light curves presented in Garnavich et al. (2016) and find that KSN 2011a can be fit by a blue supergiant model with a progenitor radius of $R_s < 7.7 + 8.8 {\rm (stat)} + 1.9 {\rm (sys)}R_\odot$, while KSN 2011d can be fit with a red supergiant model with a progenitor radius of $R_s = 111_{-21 {\rm (stat)}}^{+89 {\rm (stat)}} \phantom{}_{-1{\rm (sys)}}^{+49 {\rm (sys)}}$. Our results do not agree with those of Garnavich et al. (2016). Moreover, we re-evaluate their claims and find that there is no statistically significant evidence for a shock breakout flare in the light curve of KSN 2011d.

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arXiv2017

Quantitative Classification of Type I Supernovae Using Spectroscopic Features at Maximum Brightness

We present a set of new quantitative classification criteria for major subclasses of Type I Supernovae (SNe). We analyze peak spectra of 146 SNe Ia from the Berkeley Supernova Ia Program (BSNIP), 12 SNe Ib, 19 SNe Ic (including 5 SNe Ic-BL) and 4 SNe Ib/c. All the spectra are within 5 days of maximum light. We study their absorption line depths relative to the pseudo-continuum at around observed wavelength 6150Å, attributed to Si II 6355Å for SNe Ia and Ic and to hydrogen for SNe Ib, and O I $λ7774$Å observed around $λ7500$Å. We found that Type I SNe could be quantitatively classified using the line depths at these two absorption regions. Type Ia SNe, including normal SNe Ia, Ia-1991bg and Ia-1999aa, show strong signatures of Si II near peak with relative line depth values of $a{\rm (\lambda6150Å)>0.35}$. Only SNe Ia-2002cx (Iax) do not satisfy this criterion, while the $a{\rm (O\ I\ λ7774Å)}$ index can separate SNe Ia-1991bg and Ia-1999aa cleanly. Type Ib SNe satisfy that $a{\rm (\lambda6150Å)<0.35}$ and $a{\rm (\lambda6150Å)} / a{\rm (O\ I\ λ7774Å)>1}$, while regular Type Ic SNe show $a{\rm (\lambda6150Å)<0.35}$ but $a{\rm (\lambda6150Å)} / a{\rm (O\ I\ λ7774Å)<1}$. These quantitive classification criteria work well for the majority of normal Type I SN subclasses. Peculiar SNe Ia-2002cx and SNe Ic-BL are the exception. We apply these criteria to provide clear identifications to intermediate or unclear SNe Ib/c. The results show good consistency with classification using specific spectral line features. Though there are still some puzzles about the physical mechanisms driving the diverse line ratios, our method is an accurate empirical method to identify the majority of Type I SNe.

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arXiv2017

Type Ia supernovae with and without blueshifted narrow Na I D lines - how different is their structure?

In studies on intermediate- and high-resolution spectra of Type Ia supernovae (SNe Ia), some objects exhibit narrow Na-I D absorptions often blueshifted with respect to the rest wavelength within the host galaxy. The absence of these in other SNe Ia may reflect that the explosions have different progenitors: blueshifted Na-I D features might be explained by the outflows of 'single-degenerate' systems (binaries of a white dwarf with a non-degenerate companion). In this work, we search for systematic differences among SNe Ia for which the Na-I D characteristics have been clearly established in previous studies. We perform an analysis of the chemical abundances in the outer ejecta of 13 'spectroscopically normal' SNe Ia (five of which show blueshifted Na lines), modelling time series of photospheric spectra with a radiative-transfer code. We find only moderate differences between 'blueshifted-Na', 'redshifted-Na' and 'no-Na' SNe Ia, so that we can neither conclusively confirm a 'one-scenario' nor a 'two-scenario' theory for normal SNe Ia. Yet, some of the trends we see should be further studied using larger observed samples: Models for blueshifted-Na SNe tend to show higher photospheric velocities than no-Na SNe, corresponding to a higher opacity of the envelope. Consistently, blueshifted-Na SNe show hints of a somewhat larger iron-group content in the outer layers with respect to the no-Na subsample (and also to the redshifted-Na subsample). This agrees with earlier work where it was found that the light curves of no-Na SNe - often appearing in elliptical galaxies - are narrower, i.e. decline more rapidly.

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arXiv2017

Spatially resolved analysis of Superluminous Supernovae PTF~11hrq and PTF~12dam host galaxies

Superluminous supernovae (SLSNe) are the most luminous supernovae in the universe. They are found in extreme star-forming galaxies and are probably connected with the death of massive stars. One hallmark of very massive progenitors would be a tendency to explode in very dense, UV-bright, and blue regions. In this paper we investigate the resolved host galaxy properties of two nearby hydrogen-poor SLSNe, PTF~11hrq and PTF~12dam. For both galaxies \textit{Hubble Space Telescope} multi-filter images were obtained. Additionally, we performe integral field spectroscopy of the host galaxy of PTF~11hrq using the Very Large Telescope Multi Unit Spectroscopic Explorer (VLT/MUSE), and investigate the line strength, metallicity and kinematics. Neither PTF~11hrq nor PTF~12dam occurred in the bluest part of their host galaxies, although both galaxies have overall blue UV-to-optical colors. The MUSE data reveal a bright starbursting region in the host of PTF~11hrq, although far from the SN location. The SN exploded close to a region with disturbed kinematics, bluer color, stronger [OIII], and lower metallicity. The host galaxy is likely interacting with a companion. PTF~12dam occurred in one of the brightest pixels, in a starbursting galaxy with a complex morphology and a tidal tail, where interaction is also very likely. We speculate that SLSN explosions may originate from stars generated during star-formation episodes triggered by interaction. High resolution imaging and integral field spectroscopy are fundamental for a better understanding of SLSNe explosion sites and how star formation varies across their host galaxies.

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arXiv2017

A spectroscopic search for White Dwarf companions to 101 nearby M dwarfs

Recent studies of the stellar population in the solar neighborhood (<20 pc) suggest that there are undetected white dwarfs (WDs) in multiple systems with main sequence companions. Detecting these hidden stars and obtaining a more complete census of nearby WDs is important for our understanding of binary and galactic evolution, as well as the study of explosive phenomena. In an attempt to uncover these hidden WDs, we present intermediate resolution spectroscopy over the wavelength range 3000-25000 Å of 101 nearby M dwarfs (dMs), observed with the Very Large Telescope X-Shooter spectrograph. For each star we search for a hot component superimposed on the dM spectrum. X-Shooter has excellent blue sensitivity and thus can reveal a faint hot WD despite the brightness of its red companion. Visual examination shows no clear evidence of a WD in any of the spectra. We place upper limits on the effective temperatures of WDs that may still be hiding by fitting dM templates to the spectra, and modeling WD spectra. On average our survey is sensitive to WDs hotter than about 5300 K. This suggests that the frequency of WD companions of T<5300 K with separation of order <50 AU among the local dM population is <3% at the 95% confidence level. The reduced spectra are made available on via WISeREP repository.

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arXiv2017

Time-resolved polarimetry of the superluminous SN 2015bn with the Nordic Optical Telescope

We present imaging polarimetry of the superluminous supernova SN 2015bn, obtained over nine epochs between $-$20 and $+$46 days with the Nordic Optical Telescope. This was a nearby, slowly-evolving Type I superluminous supernova that has been studied extensively and for which two epochs of spectropolarimetry are also available. Based on field stars, we determine the interstellar polarisation in the Galaxy to be negligible. The polarisation of SN 2015bn shows a statistically significant increase during the last epochs, confirming previous findings. Our well-sampled imaging polarimetry series allows us to determine that this increase (from $\sim 0.54\%$ to $\gtrsim 1.10\%$) coincides in time with rapid changes that took place in the optical spectrum. We conclude that the supernova underwent a `phase transition' at around $+$20 days, when the photospheric emission shifted from an outer layer, dominated by natal C and O, to a more aspherical inner core, dominated by freshly nucleosynthesized material. This two-layered model might account for the characteristic appearance and properties of Type I superluminous supernovae.

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arXiv2017

Type Ibn Supernovae Show Photometric Homogeneity and Spectral Diversity at Maximum Light

Type Ibn supernovae (SNe) are a small yet intriguing class of explosions whose spectra are characterized by low-velocity helium emission lines with little to no evidence for hydrogen. The prevailing theory has been that these are the core-collapse explosions of very massive stars embedded in helium-rich circumstellar material (CSM). We report optical observations of six new SNe Ibn: PTF11rfh, PTF12ldy, iPTF14aki, iPTF15ul, SN 2015G, and iPTF15akq. This brings the sample size of such objects in the literature to 22. We also report new data, including a near-infrared spectrum, on the Type Ibn SN 2015U. In order to characterize the class as a whole, we analyze the photometric and spectroscopic properties of the full Type Ibn sample. We find that, despite the expectation that CSM interaction would generate a heterogeneous set of light curves, as seen in SNe IIn, most Type Ibn light curves are quite similar in shape, declining at rates around 0.1 mag/day during the first month after maximum light, with a few significant exceptions. Early spectra of SNe Ibn come in at least two varieties, one that shows narrow P Cygni lines and another dominated by broader emission lines, both around maximum light, which may be an indication of differences in the state of the progenitor system at the time of explosion. Alternatively, the spectral diversity could arise from viewing-angle effects or merely from a lack of early spectroscopic coverage. Together, the relative light curve homogeneity and narrow spectral features suggest that the CSM consists of a spatially confined shell of helium surrounded by a less dense extended wind.

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arXiv2016

On the early-time excess emission in hydrogen-poor superluminous supernovae

We present the light curves of the hydrogen-poor superluminous supernovae (SLSNe-I) PTF12dam and iPTF13dcc, discovered by the (intermediate) Palomar Transient Factory. Both show excess emission at early times and a slowly declining light curve at late times. The early bump in PTF12dam is very similar in duration (~10 days) and brightness relative to the main peak (2-3 mag fainter) compared to those observed in other SLSNe-I. In contrast, the long-duration (>30 days) early excess emission in iPTF13dcc, whose brightness competes with that of the main peak, appears to be of a different nature. We construct bolometric light curves for both targets, and fit a variety of light-curve models to both the early bump and main peak in an attempt to understand the nature of these explosions. Even though the slope of the late-time light-curve decline in both SLSNe is suggestively close to that expected from the radioactive decay of $^{56}$Ni and $^{56}$Co, the amount of nickel required to power the full light curves is too large considering the estimated ejecta mass. The magnetar model including an increasing escape fraction provides a reasonable description of the PTF12dam observations. However, neither the basic nor the double-peaked magnetar model is capable of reproducing the iPTF13dcc light curve. A model combining a shock breakout in an extended envelope with late-time magnetar energy injection provides a reasonable fit to the iPTF13dcc observations. Finally, we find that the light curves of both PTF12dam and iPTF13dcc can be adequately fit with the circumstellar medium (CSM) interaction model.

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arXiv2016

Observational and Physical Classification of Supernovae

This chapter describes the current classification scheme of supernovae (SNe). This scheme has evolved over many decades and now includes numerous SN Types and sub-types. Many of these are universally recognized, while there are controversies regarding the definitions, membership and even the names of some sub-classes; we will try to review here the commonly-used nomenclature, noting the main variants when possible. SN Types are defined according to observational properties; mostly visible-light spectra near maximum light, as well as according to their photometric properties. However, a long-term goal of SN classification is to associate observationally-defined classes with specific physical explosive phenomena. We show here that this aspiration is now finally coming to fruition, and we establish the SN classification scheme upon direct observational evidence connecting SN groups with specific progenitor stars. Observationally, the broad class of Type II SNe contains objects showing strong spectroscopic signatures of hydrogen, while objects lacking such signatures are of Type I, which is further divided to numerous subclasses. Recently a class of super-luminous SNe (SLSNe, typically 10 times more luminous than standard events) has been identified, and it is discussed. We end this chapter by briefly describing a proposed alternative classification scheme that is inspired by the stellar classification system. This system presents our emerging physical understanding of SN explosions, while clearly separating robust observational properties from physical inferences that can be debated. This new system is quantitative, and naturally deals with events distributed along a continuum, rather than being strictly divided into discrete classes. Thus, it may be more suitable to the coming era where SN numbers will quickly expand from a few thousands to millions of events.

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arXiv2016

Host-Galaxy Properties of 32 Low-Redshift Superluminous Supernovae from the Palomar Transient Factory

We present ultraviolet through near-infrared photometry and spectroscopy of the host galaxies of all superluminous supernovae (SLSNe) discovered by the Palomar Transient Factory prior to 2013, and derive measurements of their luminosities, star-formation rates, stellar masses, and gas-phase metallicities. We find that Type I (hydrogen-poor) SLSNe are found almost exclusively in low-mass (M < 2x10^9 M_sun) and metal-poor (12+log[O/H] < 8.4) galaxies. We compare the mass and metallicity distributions of our sample to nearby galaxy catalogs in detail and conclude that the rate of SLSNe-I as a fraction of all SNe is heavily suppressed in galaxies with metallicities >0.5 Z_sun. Extremely low metallicities are not required, and indeed provide no further increase in the relative SLSN rate. Several SLSN-I hosts are undergoing vigorous starbursts, but this may simply be a side effect of metallicity dependence: dwarf galaxies tend to have bursty star-formation histories. Type-II (hydrogen-rich) SLSNe are found over the entire range of galaxy masses and metallicities, and their integrated properties do not suggest a strong preference for (or against) low-mass/low-metallicity galaxies. Two hosts exhibit unusual properties: PTF 10uhf is a Type I SLSN in a massive, luminous infrared galaxy at redshift z=0.29, while PTF 10tpz is a Type II SLSN located in the nucleus of an early-type host at z=0.04.

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arXiv2016

SN2002es-like Supernovae From Different Viewing Angles

In this letter, we compare optical light curves of two SN2002es-like Type Ia supernovae, iPTF14atg and iPTF14dpk, from the intermediate Palomar Transient Factory. Although the two light curves resemble each other around and after maximum, they show distinct early-phase rise behavior in the $\textit{r}$-band. On the one hand, iPTF14atg revealed a slow and steady rise which lasted for 22 days with a mean rise rate of $0.2\sim0.3\,\textrm{mag}\,\textrm{day}^{-1}$, before it reached the $R$-band peak ($-18.05\,$mag). On the other hand, iPTF14dpk rose rapidly to $-17\,$mag within a day of discovery with a rise rate $>1.8\,\textrm{mag}\,\textrm{day}^{-1}$, and then rose slowly to its peak ($-18.19\,$mag) with a rise rate similar to iPTF14atg. The apparent total rise time of iPTF14dpk is therefore only 16 days. We show that emission from iPTF14atg before $-17\,$days with respect to its maximum can be entirely attributed to radiation produced by collision between the SN and its companion star. Such emission is absent in iPTF14dpk probably because of an unfavored viewing angle, provided that SN2002es-like events arise from the same progenitor channel. We further show that a SN2002es-like SN may experience a dark phase after the explosion but before its radioactively powered light curve becomes visible. This dark phase may be hidden by radiation from supernova-companion interaction.

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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.

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