Monthly Archives: February 2016

Observing gravitational waves from core-collapse supernovae in the advanced detector era

Observing gravitational waves from core-collapse supernovae
in the advanced detector era

[This file has been copied from PDF to Word without format conversion. The source of the article is Physical Review D, February 5, 2016. We are in the process of doing rudimentary formatting by hand to make the text more readable. The equations and tables cannot be formatted. — Integrative*Mind editor]

S. E. Gossan,1,2 P. Sutton,4 A. Stuver,5,6 M. Zanolin,3 K. Gill,3 and C. D. Ott2
1 LIGO—California Institute of Technology, Pasadena, California 91125, USA
2 TAPIR, MC 350-17, California Institute of Technology, Pasadena, California 91125, USA
3 Embry Riddle Aeronautical University, 3700 Willow Creek Road, Prescott, Arizona 86301, USA
4 Cardiff University, Cardiff, CF24 3AA, United Kingdom
5 LIGO Livingston Observatory, Livingston, Louisiana 70754, USA
6 Louisiana State University, Baton Rouge, Louisiana 70803, USA
(Received 9 November 2015; published 5 February 2016)

Abstract
The next galactic core-collapse supernova (CCSN) has already exploded, and its electromagnetic (EM) waves, neutrinos, and gravitational waves (GWs) may arrive at any moment.We present an extensive study on the potential sensitivity of prospective detection scenarios for GWs from CCSNe within 5 Mpc, using realistic noise at the predicted sensitivity of the Advanced LIGO and Advanced Virgo detectors for 2015, 2017, and 2019. We quantify the detectability of GWs from CCSNe within the Milky Way and Large Magellanic Cloud, for which there will be an observed neutrino burst. We also consider extreme GW emission scenarios for more distant CCSNe with an associated EM signature. We find that a three-detector network at design sensitivity will be able to detect neutrino-driven CCSN explosions out to ∼5.5 kpc, while rapidly rotating core collapse will be detectable out to the Large Magellanic Cloud at 50 kpc. Of the phenomenological models for extreme GWemission scenarios considered in this study, such as long-lived bar-mode instabilities and disk fragmentation instabilities, all models considered will be detectable out to M31 at 0.77 Mpc, while the most extreme models will be detectable out to M82 at 3.52 Mpc and beyond.

DOI: 10.1103/PhysRevD.93.042002

I. INTRODUCTION
Core-collapse supernovae (CCSNe) are driven by the release of gravitational energy in the core collapse of massive stars in the zero-age-main-sequence mass range 8M⊙ ≲ M ≲ 130M⊙. The available energy reservoir of ∼300 Bethe (B, 1B ¼ 1051 erg) is set by the difference in gravitational binding energy of the precollapse core (R ∼ 1000–2000 km, M ∼ 1.4M⊙) and the collapsed remnant (R ∼ 10–15 km). Much of this energy is initially stored as heat in the protoneutron star and most of it (∼99%) is released in the form of neutrinos, ∼1% goes into the kinetic energy of the explosion, ∼0.01% is emitted across the electromagnetic (EM) spectrum, and an uncertain, though likely smaller, fraction will be emitted in gravitational waves (GWs) [1,2].

Distant CCSNe are discovered on a daily basis by astronomers. Neutrinos from CCSNe have been observed once, from the most recent nearby CCSN, SN 1987A [3,4], which occured in the Large Magellanic Cloud (LMC), roughly 52 kpc from Earth [5]. GWs1 are—at lowest and likely dominant order—emitted by quadrupole massenergy dynamics. In the general theory of relativity, GWs have two polarizations, denoted plus (þ) and cross (×). Passing GWs will lead to displacements of test masses that are directly proportional to the amplitudes of the waves and, unlike EM emission, not their intensity. GWs have not yet been directly detected.

GWs, much like neutrinos, are emitted fromthe innermost region (the core) of the CCSN and thus convey information on the dynamics in the supernova core to the observer. They potentially carry information not only on the general degree of asymmetry in the dynamics of the CCSN, but also more directly on the explosion mechanism [1,10,11], on the structural and compositional evolution of the protoneutron star [12–15], the rotation rate of the collapsed core [16–19], and the nuclear equation of state [17,20,21].

A spherically symmetric CCSN will not emit GWs. However, EM observations suggest that many, if not most, CCSN explosions exhibit asymmetric features (e.g., [22–26]). This is also suggested by results of multidimensional CCSN simulations (e.g., [27–35] and references therein). Spherical symmetry should be robustly broken by stellar rotation, convection in the protoneutron star and in the region behind the CCSN shock, and by the standing accretion shock instability (SASI [36]). The magnitude and time variation of deviations from spherical symmetry, and thus the strength of the emitted GW signal, are uncertain and likely vary from event to event [1,13].

State-of-the-art models, building upon an extensive body of theoretical work on the GW signature of CCSNe, predict GW strains—relative displacements of test masses in a detector on Earth—h of order 10−23–10−20 for a core 1For detailed reviews of GW theory and observation, we refer the reader to Refs. [6–9].

PHYSICAL REVIEW D 93, 042002 (2016)
2470-0010=2016=93(4)=042002(24) 042002-1 © 2016 American Physical Society collapse event at 10 kpc, signal durations of 1 ms − few s, frequencies of ∼1 − few 1000 Hz, and total emitted energies EGW of 1041–1047 erg (corresponding to 10−12−10−7M⊙c2) [1,13,14,17,27,29,37–40].

More extreme phenomenological models, such as long-lasting rotational instabilities of the proto-neutron star and accretion disk fragmentation instabilities, associated with hypernovae and collapsars, suggest much larger strains and more energetic emission, with EGW perhaps up to 1052 erg (∼0.01M⊙c2) [41–44].Attempts to detect GWs from astrophysical sources were spearheaded byWeber in the 1960s [45]. Weber’s detectors and other experiments until the early 2000s relied primarily on narrow-band (≲10 s of Hz) resonant bar or sphere detectors (e.g., [46]). Of these, NAUTILUS [47], AURIGA [48], and Schenberg [49] are still active. The era of broadband GW detectors began with the kilometer-scale first-generation laser interferometer experiments. The two 4-km LIGO observatories [50] are in Hanford, Washington, and Livingston, Louisiana, hereafter referred to as H1 and L1, respectively. A second 2-km detector was located in Hanford, referred to as H2, but was decommissioned at the end of the initial LIGO observing runs. The 3-km Virgo detector [51] is located in Cascina, Italy. Other GWinterferometers are the 300-m detector TAMA300 [52] in Mitaka, Japan, and the 600-m detector GEO600 [53] in Hanover, Germany. The second generation of groundbased laser interferometric GW detectors, roughly 10 times more sensitive than the first generation, are under construction. The two Advanced LIGO detectors [54] began operation in late 2015 at approximately one-third of their final design sensitivity, jointly with GEO-HF [55]. Advanced Virgo [56] will commence operations in 2016, followed by KAGRA [57] later in the decade. LIGO India [58] is under consideration, and may begin operations c. 2022.

Typically, searches for GW transients must scan the entire GW detector data set for signals incident from any direction on the sky (e.g., [59,60] and references therein) unless an external “trigger” is available. The observation of an EM or neutrino counterpart can provide timing and/or sky position information to localize the prospective GW signal (e.g., [61–63] and references therein). The sensitivity of GW searches utilizing external triggers can be more sensitive by up to a factor of ∼2, as constraints on time and sky position help reduce the background noise present in interferometer data (e.g., [61,64]). In both cases, networks of two or more detectors are typically required to exclude instrumental and local environmental noise transients that could be misindentified as GW signals. This is particularly important in the case where there is no reliable model for the GW signal, such as for CCSNe.

Arnaud et al. [65] were the first to make quantitative estimates on the detection of GWs from CCSNe. They studied the detectability of GW signals from axisymmetric rotating core collapse [66], by means of three different filtering techniques. The authors showed that, in the context of stationary, Gaussian noise with zero-mean, the signals should be detectable throughout the galaxy with initial Virgo [51]. Ando et al. [67], using single-detector data taken with the TAMA300 interferometer, were the first to carry out an untriggered all-sky blind search specifically for GWs from rotating core collapse. These authors employed a modelindependent approach which searches for time-frequency regions with excess power compared to the noise background (called an “excess power method” (e.g., [68–71]). They employed rotating core-collapse waveforms from Dimmelmeier et al. [72] to place upper limits on detectability and rate of core collapse events in the Milky Way. Unfortunately, these upper limits were not astrophysically interesting due to the high false alarm rate of their search, caused by their single-detector analysis and the limited sensitivity of their instrument.

Hayama et al. [73] studied the detectability of GWs from multidimensional CCSN simulations from [38,74–76]. Using the coherent network analysis network pipeline RIDGE [77], signals in simulated Gaussian noise for a four-detector network containing the two Advanced LIGO detectors, AdvancedVirgo, and KAGRA are considered. The authors find that GWs from the neutrino-driven explosions considered are detectable out to ∼ð2–6Þ kpc, while GWs from rapidly rotating core-collapse and nonaxisymmetric instabilities are detectable out to between ∼ð11–200Þ kpc.

In this article, we describe a method for the detection of GWs from CCSNe in nonstationary, non-Gaussian data recolored to the predicted sensitivity of the secondgeneration interferometers. Since GW emission from CCSNe may be very weak (but can vary by orders of magnitudes in strain, frequency content, and duration), we follow a triggered approach and employ X-Pipeline [78], a coherent analysis pipeline designed specifically to detect generic GW transients associated with astrophysical events such as gamma-ray bursts and supernovae using data from networks of interferometers. We consider (1) CCSNe within ∼50 kpc with sky position and timing localization information provided by neutrinos (e.g., [79–81]). At close source distances, we hope to detect GWs from CCSNe in current scenarios predicted by state-of-the-art multidimensional numerical simulations. (2) Distant CCSNe with sky position and timing localization information provided by EM observations. At distances greater than ∼ð50–100Þ kpc, we do not expect to detect GWs from the conservative emission scenarios predicted by multidimensional CCSN simulations. Instead, we consider more extreme, phenomenological emission models. These may be unlikely to occur, but have not yet been constrained
observationally.

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042002-2

We consider GW emission from “garden-variety” CCSNe (e.g. convection, SASI, and rotating core collapse and bounce) with waveform predictions from multidimensional CCSN simulations, in addition to extreme postcollapseGW emission mechanisms. In addition, we consider for both scenarios sine-Gaussian GW bursts as an ad hoc model for GW signals of central frequency f0 and quality factor Q, which are frequently used to assess the sensitivity of searches for generic GW bursts of unknown morphological
shape [59,60].

This paper is organized as follows. In Sec. II, we discuss the challenges associated with observing GWs from CCSNe. We outline our strategies to overcome these challenges and introduce the observational scenarios considered in this study in Sec. III. We review the waveforms+ from multidimensional hydrodynamic simulations and phenomenological waveform models used in this study in Sec. IV. In Sec. V, we give details of our analysis approach and lay out how we establish upper limits for detectability. We present the results of our analysis and provide quantitative estimates for the distances out to which GWs may be observed for each of the considered waveform models and detector sensitivity in Sec. VI. We summarize and conclude in Sec. VII.

II. CHALLENGES
GW astronomers looking for short-duration GW transients emitted from CCSNe face multiple challenges.

A. The rate of observable events is low If GW emission in standard, “garden-variety” CCSNe occurs at the strains and frequencies predicted by current models, simple estimates of signal-to-noise ratios (SNRs) suggest that even second-generation detectors may be limited to detecting core-collapse events in the Milky Way and the Small and Large Magellanic Clouds [1,12,14,29]. The expected rate of CCSNe in the Milky Way is ∼ð0.6 − 10.5Þ × 10−2 CCSNe yr−1, (e.g., [82–87]), and it is ∼ð1.9 − 4.0Þ × 10−3 CCSNe yr−1 in the combined Magellanic Clouds [82,84,88]. Similar SNR estimates for extreme GWemission models for CCSNe suggest that they may be observable throughout the Local Group and beyond (D ≲ 20 Mpc). Within the Local Group (D ≲ 3 Mpc), the CCSN rate is ∼9 × 10−2 CCSNe yr−1, with major contributions from Andromeda (M31), Triangulum (M33), and the dwarf irregular galaxy IC 10, IC 1613, and NGC 6822 [82,84,89,90]. Outside of the Local Group, the CCSN rate increases to ∼0.15 CCSNe yr−1 within D ∼ 5 Mpc, including IC342, theM81 group,M83, andNGC253 as significant contributors to theCCSNrate [91–96].WithinD ¼ 10 Mpc, the CCSN rate is ∼0.47 CCSNe yr−1, while it increases to ∼2.1 CCSNe yr−1 within D ¼ 20 Mpc [91,94–96].

B. The duty cycle of the detectors is not 100% The fraction of time interferometers are operating and taking science-quality data is limited by several factorsincluding commissioning work (to improve sensitivity and stability) and interference due to excessive environmental noise. For example, consider LIGO’s fifth science run (S5), the data from which we use for the studies in this paper. S5 lasted almost two years between November 15, 2005 and November 2, 2007, and the H1, H2, and L1 detectors had duty cycles of 75%, 76%, and 65%, respectively. The duty cycle for double coincidence (two or more detectors taking data simultaneously) was 60%, and the triple coincidence duty cycle was 54% [97,98]. The risk of completely missing a CCSN GW signal is mitigated by having a larger network of detectors. In addition, resonant bar and sphere detectors do provide limited backup [47–49].

C. The noise background in the GW data is non-Gaussian and nonstationary Noise in interferometers arises from a combination of instrumental, environmental, and anthropomorphic noise sources that are extremely difficult to characterize precisely [50,99–101]. Instrumental “glitches” can lead to large excursions over the time-averaged noise and may mimic the expected time-frequency content of an astrophysical signal [50,102]. Mitigation strategies against such noise artifacts include
(1) Coincident observation with multiple, geographically separated detectors (2) Data quality monitoring and the recording of instrumental and environmental vetos derived from auxiliary data channels such as seismometers, magnetonometers, etc. (3) Glitch-detection strategies based on Bayesian inference (e.g., [103,104]) or machine learning (e.g., [104,105]) (4) Using external triggers from EM or neutrino observations to inform the temporal “on-source window” in which we expect to find GW signals and consequently reduce the time period searched.

D. The gravitational wave signal to be expected from a core-collapse event is uncertain The time-frequency characteristics of the GW signal from a core-collapse event is strongly dependent on the dominant emission process and the complex structure, angular momentum distribution, and thermodynamics of the progenitor star. In the presence of stochastic emission processes (e.g., fluid instabilities such as convection and SASI), it is impossible to robustly predict the GW signal. As a result, the optimal method for signal extraction, matched (Wiener) filtering [106], cannot be used, as a robust, theoretical prediction of the amplitude and phase of …

OBSERVING GRAVITATIONAL WAVES FROM CORE- … PHYSICAL REVIEW D 93, 042002 (2016) 042002-3

… the GW signal is required. Matched filtering is typically used in searches for GWs from compact binary coalescence, for which robust signal models exist. The “excess-power” approach [69–71] is an alternative to matched filtering for signals of uncertain morphology.

Searching for statistically significant excesses of power in detector data in the time-frequency plane, prior information on the sky position, time of arrival, and polarization of the targeted GW source can be exploited to reduce the noise background and, consequently, the detection false alarm rate. It can be shown that, in the absence of any knowledge of the signal other than its duration and frequency bandwidth, the excess-power method is Neyman-Pearson optimal in the context of Gaussian noise [69].

III. OBSERVATIONAL SCENARIOS
Core-collapse events are the canonical example of multimessenger astrophysical sources and, as such, are particularly suited to externally triggered GW searches. In this section, we describe four potential observational scenarios for CCSNe in the local Universe.

A. Location of SNe
We consider CCSNe in four galaxies that contribute significantly to the CCSN rate in the Local Group and Virgo cluster. The Milky Way, a barred spiral galaxy, is the galaxy that houses our solar system. For the purposes of this study, we consider a CCSN in the direction of the Galactic center, at right ascension (RA) 17h47m21:5s and declination (Dec) −5°3209.600 [107], located ∼9 kpc from Earth. This is motivated by the work of Adams et al. ([87]), in which the probability distribution for the distance of galactic CCSN from Earth is shown to peak around ∼9 kpc, and the CCSN location distribution is assumed to trace the disk of the galaxy. The galactic CCSN rate is estimated at ð0.6 − 10.5Þ × 10−2 CCSNe yr−1 [87], and the youngest known galactic CCSN remnant, Cassiopeia A, is believed to be ∼330 yrs old [108].

The Large Magellanic Cloud (LMC) is home to the most active star-formation region in the Local Group, the Tarantula Nebula [109]. Located at RA 5h23m34:5s and Dec −69°4502200 [110], the LMC is an irregular galaxy located ∼50 kpc from Earth [111,112], and is estimated to have a CCSN rate of ð1.5 − 3.1Þ × 10−3 CCSNe yr−1 [82,84]. The last CCSN observed in the LMC was SN1987A, a type II-pec SN first detected on February 23, 1987, by Kamiokande II via its neutrino burst [3]. The M31 galaxy, also referred to as Andromeda, is the most luminous galaxy in the Local Group. Located at RA 0h42m44:4s andDec 41°1608.600 [113],M31 is a spiral galaxy located ∼0.77 Mpc from Earth [114], and is estimated to have a CCSN rate of ∼2.1 × 10−3 CCSNe yr−1 [82,84]. No CCSNe have yet been observed from M31.

The M82 galaxy, five times brighter than the Milky Way, exhibits starburst behavior incited by gravitational interaction with M81, a neighboring galaxy [115]. Located at RA 9h55m52:7s and Dec 69°4004600 [116], M82 is an irregular starburst galaxy at a distance ∼3.52 Mpc from Earth [117]. Its CCSN rate is estimated to be ∼ð2.1 − 20Þ × 10−2 CCSNe yr−1 [118,119]. The most recent CCSN in M82 was SN2008iz, a Type II SN first observed on May 3, 2008 [120]. We summarize the relevant information on the aforementioned
galaxies in Table I.

B. Analysis times
The SuperNova Early Warning System (SNEWS) [121] Collaboration aims to provide a rapid alert for a nearby CCSN to the astronomical community, as triggered by neutrino observations. CCSNe within ∼100 kpc will have an associated neutrino detection. The Large Volume Detector (LVD), a kiloton-scale liquid scintillator experiment [122], and Super-Kamiokande (Super-K), a waterimaging Cerenkov-detector [123], will be able to detect neutrinos from a CCSN with full detection probability (100%) out to 30 kpc and 100 kpc, respectively [123,124]. BOREXINO (a 300-ton liquid scintillator experiment [125]) is able to detect all galactic CCSNe [126], while IceCube (a gigaton-scale long string particle detector made of Antarctic ice [127]) can detect a CCSN in the Large Magellanic Cloud at 6σ confidence. For CCSNe within ∼0.66 kpc, KamLAND (a kiloton-scale liquid scintillator detector [128]) will be able to detect neutrinos from pre-SN stars at 3σ confidence [129]. Pagliaroli et al. [80] were the first to make quantitative statements on the use of neutrino detection from CCSNe as external triggers for an associated GW search, in the context of an analytical approximation for the anti-electron neutrino luminosity, L¯νe , as a function of time. More realistic models for Lν (see, e.g. [130,131]) suggest that over ∼95% of the total energy in neutrinos is emitted …

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TABLE I. Summary of the location, distance, and CCSN rate of the four host galaxies considered. Galaxy name Right ascension (degrees) Declination (degree) Distance [Mpc] CCSN rate [×10−2 yr−1] References Milky Way 266.42 −29.01 0.01 0.6–10.5 [87] LMC 80.89 −69.76 0.05 0.1–0.3 [82,84,110,112] M31 10.69 41.27 0.77 0.2 [82,84,113,114] M82 148.97 69.68 3.52 2.1–20 [116–119] S. E. GOSSAN et al. PHYSICAL REVIEW D 93, 042002 (2016) 042002-4

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… within ∼10 s of core bounce. Given the neutrino observation time, t0, we consider a 60 s on-source window, aligned ½−10; 50_ s about t0. We note that a more detailed neutrino light curve will allow the time of core bounce to be localized to ∼few ms [132]. This would permit the use of a much shorter on-source window, resulting in a lower background rate and higher detection sensitivity. For more distant CCSNe, the neutrino burst from core collapse will likely not be detected, but an EM counterpart will be observed. The on-source window derived from the EM observation time is dependent on progenitor star characteristics (i.e. progenitor star radius, shock velocity), as well as the observation cadence. The first EM signature of a CCSN comes at the time of shock breakout, tSB, when the shock breaks through the stellar envelope. Type Ib and type Ic SNe, hereafter referred to jointly as type Ibc SNe, have very compact progenitors (R_ ∼ fewð1 − 10ÞR⊙) and have been stripped of their stellar envelopes through either intense stellar winds (i.e. Wolf- Rayet stars) or mass transfer to a binary companion [133,134]. Li ([135]) studied the properties of shock breakout for a variety of type Ibc SN progenitor models in the context of semianalytic density profiles and found shock breakout times in the range tSB ∈ ½1; 35_s. As a conservative estimate, we choose tSB;min ¼ 60 s.

For type II SNe, however, the progenitors are supergiant stars. Type II-pec SNe, such as SN1987A, have blue supergiant progenitors, with typical stellar radii of ∼25R⊙. More typically, the progenitors are red supergiant stars,with typical stellar radii of ∼ð100–1000ÞR⊙ [133,134]. Hydrodynamic simulations of type II-P SN progenitors from Bersten et al. [136] andMorozova et al. [137] show typical breakout times of tSB ∼ few10 h. As a conservative estimate, we consider the unstripped type II-P progenitor from Morozova et al. [137] and use tSB;max ¼ 50 h. In addition to theoretical predictions of the time to shock breakout, the cadence of observations of the CCSN host galaxy must be considered when deriving the on-source window. For actively observed galaxies, we expect to have no greater than ∼24 h latency between pre- and post-CCSN observations. We consider two observational scenarios in which the time scale between pre- and post-CCSN images are tobs ∼ 1 h and 24 h, for sources in M31 and M82, respectively. We construct the on-source window assuming that shock breakout occurs immediately after the last pre-SN image. Given the time of the last pre-SN observation, the EM trigger time t0, we consider an on-source window of length tSB þ tobs, aligned ½−tSB; tobs_ about t0. We summarize the on-source windows used for all observational scenarios considered in Table II. The strain detected by a GW interferometer, hðtÞ, is given by hðtÞ ¼ Fþðθ;Φ; ψÞhþðtÞ þ F×ðθ;Φ; ψÞh×ðtÞ; ð1Þ where Fþ;×ðθ;Φ; ψÞ are the antenna response functions of the detector to the two GW polarizations, hþ;×ðtÞ. For a source located at sky position ðθ;ΦÞ in detector-centered coordinates, and characterized by polarization angle ψ, Fþ;× are given by Fþ ¼ 12ð1 þ cos2θÞ cos 2ϕ cos 2ψ − cos θ sin 2ϕ sin 2ψ; F× ¼ 12 ð1 þ cos2θÞ cos 2ϕ sin 2ψ − cos θ sin 2ϕ cos 2ψ: ð2Þ

The antenna response of the detectors is periodic with an associated time scale of one sidereal day, due to the rotation of the Earth. As a consequence, the sensitivity of GW searches using on-source windows much shorter than this time scale will be strongly dependent on the antenna response of the detectors to the source location at the relevant GPS time. In Fig. 1, we show the sum-squared antenna response for each detector over one sidereal day, for sources located at the Galactic center, LMC, and M31. As the sensitivity of the detector network is a function of time, we wish to choose a central trigger time t0 for which the antenna sensitivity is representative of the average over time. To represent the time-averaged sensitivity of the detector network, we choose GPS trigger times of t0 ¼ 871645255, t0 ¼ 871784200, and t0 ¼ 871623913 for the Galactic, LMC, and M31 sources, respectively. For CCSNe in M82, relying on low-cadence EM triggers, the shortest considered on-source window is longer than one sidereal day and, as such, the entire range of antenna responses is encompassed during the on-source window. We choose GPS trigger time t0 ¼ 871639563 for the M82 source, such that the 74 h on-source window is covered by the 100 h stretch of S5 data recolored for this study.

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TABLE II. Summary of the observational counterpart used to derive the on-source window, in addition to the associated on-source
window, for type Ibc and type II SNe in the four considered host galaxies. Galaxy name Observational counterpart On-source window for type Ibc [s] On-source window for type II [s] Milky Way Neutrino, EM ½−10;þ50_ ½−10;þ50_ LMC Neutrino, EM ½−10;þ50_ ½−10;þ50_ M31 EM ½−60;þ3600_ ½−180000;þ3600_ M82 EM ½−60;þ86400_ ½−180000;þ86400_ OBSERVING GRAVITATIONAL WAVES FROM CORE- … PHYSICAL REVIEW D 93, 042002 (2016) 042002-5

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C. Detector networks
As mentioned previously, the GW detector noise will be
non-Gaussian and nonstationary. To this end, we use real
GW data from the fifth LIGO science run (S5) and the first
Virgo science run (VSR1), recolored to the target noise
amplitude spectra densities (ASDs)2 for the considered
observational scenarios. See Sec. VB for technical details
on the recoloring procedure used.
We consider a subset of the observing scenarios outlined
in Aasi et al. [138] to explore how the sensitivity of the
Advanced detectors to CCSNe will evolve between 2015
and 2019. For all these cases, we characterize the detector
sensitivity by the single-detector binary neutron star (BNS)
range, dR. The BNS range is the standard figure of merit
for detector performance, and is defined as the sky
location- and orientation-averaged distance at which a
ð1.4; 1.4ÞM⊙ BNS system can be detected with an SNR,
ρ ≥ 8. The 2015 scenario assumes a two-detector network
comprised of the two Advanced LIGO detectors (H,L)
operating with BNS range dR;HL ¼ 54 Mpc and is hereafter
referred to as the HL 2015 scenario. The 2017 scenario
assumes a three-detector network comprised of the two
Advanced LIGO detectors (H,L) operating with BNS range
dR;HL ¼ 108 Mpc, and the Advanced Virgo detector operating
with BNS range of dR;V ¼ 36 Mpc, and is hereafter
referred to as the HLV 2017 scenario. In 2019, we consider
a three-detector network, HLV, with the two Advanced
LIGO detectors operating with BNS range dR;HL ¼
199 Mpc, and the Advanced Virgo detector operating with
BNS range dR;V ¼ 154 Mpc, referred to as the HLV 2019
observational scenario [56,138]. Figure 2 shows the onesided
ASDs
ffiffiffiffiffiffiffiffiffiffiffi
ShðfÞ
p
of Advanced LIGO and Advanced
Virgo as used to recolor the data for each observational
scenario considered.
IV. GRAVITATIONAL WAVES FROM
CORE-COLLAPSE SUPERNOVAE:
CONSIDERED EMISSION MODELS
A broad range of multidimensional processes may emit
GWs during core collapse and the subsequent postbounce
CCSN evolution. These include, but are not necessarily
limited to, turbulent convection driven by negative entropy
or lepton gradients and the SASI (e.g., [12–14,21,37]),
rapidly rotating collapse and bounce (e.g., [17,39,75]),
postbounce nonaxisymmetric rotational instabilities (e.g.,
[38,44,139,140]), rotating collapse to a black hole (e.g.,
[40]), asymmetric neutrino emission and outflows [12–14],
and, potentially, rather extreme fragmentation-type instabilities
occuring in accretion torii around nascent neutron
stars or black holes [43]. A more extensive discussion of
GWemission from CCSNe can be found in recent reviews
on the subject in Refs. [1,2,141]. Most of these emission
FIG. 1. The sum-squared antenna response, F2 ¼ F2
þ þ F2
×,
over one mean sidereal day for the two Advanced LIGO detectors
(H,L), and the Advanced Virgo detector, V, for sources located
toward the Galactic center (top), LMC (middle), and M31
(bottom). For each galaxy, we indicate the chosen GPS trigger
time t0 with a dashed black line.
FIGffiffiffi.ffiffiffiffi2ffiffiffi.ffiffi The predicted amplitude spectral densities (ASDs),
ShðfÞ
p
of the Advanced LIGO and Advanced Virgo detector
noise for the considered 2015, 2017, and 2019 detector
networks [56,138].
2The one-sided amplitude spectral density is the square root of
the one-sided power spectral density, ShðfÞ.
S. E. GOSSAN et al. PHYSICAL REVIEW D 93, 042002 (2016)
042002-6
mechanisms source GWs in the most sensitive frequency
band of ground-based laser interferometers (∼50–
1000 Hz). Exceptions (and not considered in this study)
are black hole formation (fpeak ∼ few kHz), asymmetric
neutrino emission, and asymmetric outflows (fpeak≲10 Hz).
For the purpose of this study, we consider a subset of the
above GWemission mechanisms and draw example waveforms
from two-dimensional (2D) and three-dimensional
(3D) CCSN simulations (we refer to these waveforms as
numerical waveforms in the following). In addition, we
construct analytical phenomenological waveforms that
permit us to constrain extreme emission scenarios. We
consider GW emission in the quadrupole approximation,
which has been shown to be accurate to within numerical
error and physical uncertainties for CCSNe [142]. In
Tables III and IV, we summarize key properties of the
selected numerical and phenomenological waveforms,
respectively, including the total energy emitted in GWs,
EGW, the angle-averaged root-sum-squared GW strain,
hhrssi, and the peak frequency of GW emission, fpeak.
We define fpeak as the frequency at which the spectral GW
energy density, dEGW=df, peaks.
We compute EGW as in [6] from the spectral GWenergy
density, dEGW=df, as
EGW ¼
Z

0
df
dEGW
df
; ð3Þ
where
dEGW
df
¼ 2
5
G
c5
ð2πfÞ2j ~̈I
ijj2; ð4Þ
and
~̈I
ijðfÞ ¼
Z

−∞
dẗI
ijðtÞe−2πift ð5Þ
is the Fourier transform of ̈I
ijðtÞ, the second time derivative
of the mass-quadrupole tensor in the transverse-traceless
gauge.
To construct the strain for different internal source
orientations, we present the projection of GW modes,
HlmðtÞ, onto the -2 spin-weighted spherical harmonic basis,
−2Ylmðι; ϕÞ [145]. Using this, we may write
TABLE III. Key characteristics of “numerical” waveforms from multidimensional CCSN simulations. EGW is the energy emitted in
GWs, hhrssi is the angle-averaged root-sum-square strain [Eq. (11)], and fpeak is the frequency at which the spectral GW energy
dEGW=df peaks.
Waveform type Ref. Waveform name hhrssi [10−22 at 10 kpc] fpeak [Hz] EGW [M⊙c2]
2D neutrino-driven convection and SASI [14] yak 1.89 888 9.08 × 10−9
3D neutrino-driven convection and SASI [37] müller1 1.66 150 3.74 × 10−11
3D neutrino-driven convection and SASI [37] müller2 3.85 176 4.37 × 10−11
3D neutrino-driven convection and SASI [37] müller3 1.09 204 3.25 × 10−11
3D neutrino-driven convection and SASI [29] ott 0.24 1019 7.34 × 10−10
2D rotating core collapse [17] dim1 1.05 774 7.69 × 10−9
2D rotating core collapse [17] dim2 1.80 753 2.79 × 10−8
2D rotating core collapse [17] dim3 2.69 237 1.38 × 10−9
3D rotating core collapse [143] sch1 5.14 465 2.25 × 10−7
3D rotating core collapse [143] sch2 5.80 700 4.02 × 10−7
TABLE IV. Key characteristics of the considered waveforms from phenomenological models. EGW is the energy emitted in GWs,
hhrssi is the angle-averaged root-sum-square strain [Eq. (11)], and fpeak is the frequency at which the spectral GW energy density
dEGW=df peaks.
Waveform type Ref. Waveform name hhrssi [10−20 at 10 kpc] fpeak [Hz] EGW [M⊙c2]
Long-lasting bar mode [144] longbar1 1.48 800 2.98 × 10−4
Long-lasting bar mode [144] longbar2 4.68 800 2.98 × 10−3
Long-lasting bar mode [144] longbar3 5.92 1600 1.90 × 10−2
Long-lasting bar mode [144] longbar4 7.40 800 7.46 × 10−3
Long-lasting bar mode [144] longbar5 23.41 800 7.45 × 10−2
Long-lasting bar mode [144] longbar6 14.78 1600 1.18 × 10−1
Torus fragmentation instability [43] piro1 2.55 2035 6.77 × 10−4
Torus fragmentation instability [43] piro2 9.94 1987 1.03 × 10−2
Torus fragmentation instability [43] piro3 7.21 2033 4.99 × 10−3
Torus fragmentation instability [43] piro4 28.08 2041 7.45 × 10−2
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hþ − ih× ¼ 1
D
X∞
l¼2
Xl
m¼−l
HlmðtÞ−2Ylmðι; ϕÞ; ð6Þ
where ðι; ϕÞ are the internal source angles describing
orientation.
It has been shown that for CCSN systems, the quadrupole
approximation method of extracting GWs is sufficiently
accurate [142]. As such, we consider only the l ¼ 2
mode and can write the mode expansion as
Hquad
20
¼
ffiffiffiffiffiffiffiffi
32π
15
r
G
c4
_
̈I
zz − 1
2
ð̈I
xx þ ̈I
yyÞ
_
;
Hquad
2_1
¼
ffiffiffiffiffiffiffiffi
16π
5
r
G
c4
ð∓̈I
xz þ ïI
yzÞ;
Hquad
2_2
¼
ffiffiffiffiffiffi

5
r
G
c4
ð̈I
xx − ̈I
yy∓2ïI
xyÞ; ð7Þ
and
−2Y20
¼
ffiffiffiffiffiffiffiffi
15
32π
r
sin2ι;
−2Y2_1
¼
ffiffiffiffiffiffiffiffi
5
16π
r
sin ιð1 _ cos ιÞe_iϕ;
−2Y2_2
¼
ffiffiffiffiffiffiffiffi
5
64π
r
ð1 _ cos ιÞ2e_2iϕ: ð8Þ
The root-sum-square strain, hrss, is defined as
hrss ¼
_Z

−∞
dt½h2
þðt; ι; ϕÞ þ h2
×ðt; ι; ϕÞ_
_
1=2
: ð9Þ
Using the mode decomposition introduced previously, we
construct an explicit angle-dependent expression for hrss,
whichwe analytically average over all source angles.Defining
hhrssi ¼
ZZ
dΩhrss; ð10Þ
we obtain
hhrssi ¼ G
c4
1
D
_
8
15
Z

−∞
dt½̈I
2
xx þ ̈I
2
yy þ ̈I
2
zz
− ð̈I
xẍI
yy þ ̈I
xẍI
zz þ ̈I
yÿI
zzÞ
þ 3ð̈I
2
xy þ ̈I
2
xz þ ̈I
2
yzÞ_
_
1=2
: ð11Þ
A. Numerical waveforms
1. Gravitational waves from convection and SASI
Postbounce CCSN cores are unstable to convection. The
stalling shock leaves behind an unstable negative entropy
gradient, leading to a burst of prompt convection soon after
core bounce. As the postbounce evolution proceeds, neutrino
heating sets up a negative entropy gradient in the region of net
energy deposition (the gain layer) behind the shock, leading to
neutrino-driven convection. Simultaneously, neutrino diffusion
establishes a negative lepton gradient in themantle of the
proto-neutron star (NS), leading to proto-NS convection. The
GW signal from these convective processes has a broad
spectrum. The prompt convection GW emission occurs at
frequencies in the range 100–300 Hz, while neutrino-driven
convection at later times sources GWemission with significant
power at frequencies between∼300–a1000 Hz (increasing
with time [12–15]). Proto-NS convection contributes at
the highest frequencies (≳1000 Hz). While the frequency
content of the signal is robust, the phase is stochastic due to
the chaotic nature of turbulence [1,74].
In addition to convection, depending on progenitor
structure (and, potentially, dimensionality of the simulation;
cf. [29,31,146–148]), the shock front may become
unstable to SASI, which leads to large-scale modulations of
the accretion flow. This results in sporadic large amplitude
spikes in the GW signal when large accreting plumes are
decelerated at the edge of the proto-NS (e.g., [12,13]).
We draw sample waveforms for GWs from nonrotating
core collapse from the studies of Yakunin et al. [14], Müller
et al. [37], and Ott et al. [29]. Yakunin et al. performed 2D
simulations of neutrino-driven CCSNe. We choose a waveform
obtained from the simulation of a 15M⊙ progenitor star
(referred to as yak in the following). Due to axisymmetry, the
extracted waveform is linearly polarized. Müller et al. performed
3D simulations of neutrino-driven CCSNe with a
number of approximations to make the simulations computationally
feasible. Importantly, they started their simulations
after core bounce and assumed a time-varying inner boundary,
cutting out much of the proto-neutron star. Prompt and
proto-neutron star convection do not contribute to their
waveforms, and higher frequencyGWemission is suppressed
due to the artificial inner boundary.As the simulations are 3D,
the Müller et al. waveforms have two polarizations, and we
usewaveforms ofmodels L15-3,W15-4 (two different 15M⊙
progenitors), and N20-2 (a 20M⊙ progenitor). We refer to
these waveforms as müller1, müller3, and müller2,
respectively. Ott et al. performed 3D simulations of neutrinodriven
CCSNe. The simulations are general-relativistic and
incorporate a three-species neutrino leakage scheme. As the
simulations are 3D, the Ott et al. waveforms have two
polarizations, and we use the GW waveform from model
s27fheat1.05 (a 27M⊙ progenitor).We hereafter refer to this
waveform as ott.We plot the GWsignal for the ott model
in the top panel of Fig. 3.
2. Gravitational waves from rotating core
collapse and bounce
Rotation leads to oblateness (an l ¼ 2,m ¼ 0 quadrupole
deformation) of the inner quasihomologously collapsing
core. Extreme accelerations experienced by the inner core
at bounce lead to a large spike in the GW signal at bounce,
followed by ringdown of the proto-neutron star as it settles to
its new equilibrium state (see, e.g., [1,17,149] for a detailed
S. E. GOSSAN et al. PHYSICAL REVIEW D 93, 042002 (2016)
042002-8
discussion). The GWsignal is dependent on the mass of the
inner core, its angular momentum distribution, and the
equation of state of nuclear matter. There are significant
uncertainties in these and it is difficult to exactly predict the
time series of the GW signal. Nevertheless, work by several
authors [11,16,20,149–152] has demonstrated that GW
emission from rotating core collapse and bounce has robust
features that can be identified and used to infer properties of
the progenitor core.
We draw three sample waveforms from the axisymmetric
general-relativistic (conformally flat) simulations of
Dimmelmeier et al. [17]. All were performed with a
15-M⊙ progenitor star and the Lattimer-Swesty equation
of state [153]. The three linearly polarized waveforms
drawn from [17], s15A2O05-ls, s15A2O09-ls, and
s15A3O15-ls, differ primarily by their initial rotation rate
and angular momentum distribution. We refer to them as
dim1 (slow and rather uniform precollapse rotation),
dim2 (moderate and rather uniform precollapse rotation),
and dim3 (fast and strongly differential precollapse rotation),
respectively. We plot the GW signal for the dim2
model in the middle panel of Fig. 3.
Shortly after core bounce, nonaxisymmetric rotational
instabilities driven by rotational shear (e.g., [38,41,
139,143,154]) or, in the limit of extreme rotation, by a
classical high-T=jWj instability at T=jWj ≳ 25 − 27%
[155], where T is the rotational kinetic energy and W is
the gravitational energy, may set in. The nonaxisymmetric
deformations may lead to a signficant enhancement of the
GW signal from the postbounce phase of rotating CCSNe.
We choose two sample waveforms from the 3D Newtonian,
magnetohydrodynamical simulations of Scheidegger et al.
[143], which use a neutrino leakage scheme. All were
performed with a 15M⊙ progenitor star, and the Lattimer-
Swesty equation of state [153]. Due to the 3D nature of the
simulations, the Scheidegger et al. waveforms have two
polarizations.We employ waveforms for models R3E1ACL
(moderate precollapse rotation, toroidal/poloidal magnetic
field strength of 106G=109G), and R4E1ACL (rapid precollapse
rotation, toroidal/poloidal magnetic field strength
of 1012G=109G). We hereafter refer to these waveforms as
sch1 and sch2, respectively. We plot the GW signal for
the sch1 model in the bottom panel of Fig. 3.
B. Phenomenological waveforms
1. Gravitational waves from long-lived
rotational instabilities
Proto-neutron stars with ratio of rotational kinetic energy
T to gravitational energy jWj, β ¼ T=jWj ≳ 25–27%
become dynamically unstable to nonaxisymmetric deformation
(with primarily m ¼ 2 bar shape). If β ≳ 14%, an
instability may grow on a secular (viscous, GW backreaction)
time scale, which may be seconds in protoneutron
stars (e.g., [156]). Furthermore, proto-neutron stars
are born differentially rotating (e.g., [157]) and may thus be
subject to a dynamical shear instability driving nonaxisymmetric
deformations that are of smaller magnitude than in
the classical instabilities, but are likely to set in at much
lower β. Since this instability operates on differential
FIG. 3. The time domain GW strain for representative models
of convection and standing accretion-shock instability (ott; top
panel), bounce and ringdown of the proto-neutron star (dim2;
middle panel), and non-axisymmetric rotational instabilities
(sch1; bottom panel) as seen by an equatorial (ι ¼ π=2;
ϕ ¼ 0) observer at 10 kpc. We note that the typical GW strain
from rotating core collapse is roughly an order of magnitude
larger than the typical GW strain from neutrino-driven explosions.
In addition, the typical GW signal duration of bounce and
ringdown of the proto-neutron star is ∼ few 10 ms, compared to
the typical GW signal duration of ∼ few 100 ms for neutrinodriven
explosions. Non-axisymmetric rotational instabilities,
however, may persist for ∼ few 100 ms.
OBSERVING GRAVITATIONAL WAVES FROM CORE- … PHYSICAL REVIEW D 93, 042002 (2016)
042002-9
rotation, it may last for as long as accretion maintains
sufficient differential rotation in the outer proto-neutron star
(e.g., [38,139,143,154,158,159] and references therein).
For simplicity, we assume that the net result of all these
instabilities is a bar deformation, whose GW emission we
model in the Newtonian quadrupole approximation for a
cylinder of length l, radius r and mass M in the x–y plane,
rotating about the z axis. We neglect spin-down via GW
backreaction. The second time derivative of the bar’s
reduced mass-quadrupole tensor is given by
̈I
ij ¼ 1
6
Mðl2 − 3r2ÞΩ2
_
−cos 2Ωt sin 2Ωt
sin 2Ωt cos 2Ωt
_
; ð12Þ
where Ω ¼ 2πf is the angular velocity of the bar (see, e.g.,
[144] for details). We then obtain the GW signal using the
quadrupole formula in Eq. (7) [7,145].
We generate representative analytic bar waveforms by
fixing the bar length to 60 km, its radius to 10 km and
varying the mass in the deformationM, the spin frequency f,
and duration of the bar mode instability Δt. In practice,
we scale the waveforms with a Gaussian envelope
∝ expð−ðt − ΔtÞ2=ðΔt=4Þ2) to obtain nearly zero amplitudes
at start and end of the waveforms, resulting in
waveforms of sine-Gaussian morphology. In this study,
we consider three bars of mass M ¼ 0.2M⊙, with ðf;ΔtÞ¼
ð400 Hz; 0.1sÞ, ð400 Hz; 1sÞ, and ð800 Hz; 0.1sÞ (hereafter
referred to as longbar1, longbar2, and longbar3,
respectively), and three bars of mass M ¼ 1M⊙ with
ðf;ΔtÞ ¼ ð400 Hz; 0.1sÞ, ð400 Hz; 1sÞ, and ð800 Hz;
0.025sÞ (hereafter referred to as longbar4, longbar5,
and longbar6, respectively).We choose these parameters
to explore the regime of strong bar-mode GW emission
with the constraint that the strongest signal must emit less
energy than is available in collapse, EGW ≲ 0.15M⊙c2.
Values of hhrssi, fpeak, and EGW for the six representative
waveforms used in this study are shown in Table IV.We plot
the GW signal for the longbar1 model in the top panel
of Fig. 4.
2. Disk fragmentation instability
If the CCSN mechanism fails to reenergize the stalled
shock (see, e.g., [160]), the proto-neutron star will collapse
to a black hole on a time scale set by accretion (e.g., [161]).
Provided sufficient angular momentum, a massive selfgravitating
accretion disk/torus may form around the
nascent stellar-mass black hole with mass MBH. This
scenario may lead to a collapsar-type gamma-ray burst
(GRB) or an engine-driven SN [162].
The inner regions of the disk are geometrically thin due to
efficient neutrino cooling, but outer regions are thick and may
be gravitationally unstable to fragmentation at large radii
[43,163]. We follow work by Piro and Pfahl ([43]), and
consider the case in which a single gravitationally bound
fragment forms in the disk and collapses to a low-mass
neutron star withMf ∼ 0.1 − 1M⊙ ≪ MBH. We then obtain
the predicted GW signal using Eq. (7) [7,145], assuming the
fragment is orbiting in the x–y plane, such that
̈I
ij ¼2
MBHMf
ðMBHþMfÞr2Ω2
_
−cos2Ωt −sin2Ωt
−sin2Ωt cos2Ωt
_
: ð13Þ
For more technical details, including the waveform generation
code, we direct the reader to [43,164]. We consider
waveforms from four example systems with ðMBH;MfÞ ¼
ð5M⊙; 0.07M⊙Þ, ð5M⊙; 0.58M⊙Þ, ð10M⊙; 0.14M⊙Þ, and
ð10M⊙; 1.15M⊙Þ (hereafter denoted piro1, piro2,
piro3, and piro4, respectively). Values of hhrssi, fpeak,
and EGW for the four representative waveforms used in this
study are shown in Table IV. We plot the GW signal for the
piro2 model in the bottom panel of Fig. 4.
3. Ad hoc signal models
It is possible that there are GW emission mechanisms
from CCSNe that we have not considered. In this case, it is
instructive to determine the sensitivity of our GW search to
short, localized bursts of GWs in time-frequency space. For
this reason, we include ad hoc signal models in our signal
injections, in addition to the aforementioned physically
motivated signal models. We take motivation from the allsky,
all-time searches for GW bursts performed in the intial
FIG. 4. The time domain GW strain for representative models
of bar-mode instability (longbar1; top panel) and disk fragmentation
instability (piro2; bottom panel), as seen by a polar
(ι ¼ 0; ϕ ¼ 0) observer at 10 kpc.
S. E. GOSSAN et al. PHYSICAL REVIEW D 93, 042002 (2016)
042002-10
detector era [59,165], and consider linearly and elliptically
polarized sine-Gaussian GW bursts. Characterized by
central frequency, f0, and quality factor, Q, the strain is
given by
hþðtÞ ¼ A
_
1 þ α2
2
_
expð−2πf20
t2=Q2Þ sinð2πf0tÞ;
h×ðtÞ ¼ Aα expð−2πf20
t2=Q2Þ cosð2πf0tÞ; ð14Þ
where A is some common scale factor, and α is the
ellipticity, where α ¼ 0 and 1 for linearly and circularly
polarized waveforms, respectively. Assuming isotropic
energy emission, we may compute the energy in GWs
associated with a sine-Gaussian burst as
EGW ¼ π2c3
G
d2f20
h2
rss; ð15Þ
where d is the distance at which hrss is computed. In
Table V, we list the f0, Q, and α values for all sine-Gaussian
waveforms considered in this study.
V. DATA ANALYSIS METHODS
A. X-Pipeline: A search algorithm for gravitational
wave bursts
X-Pipeline is a coherent analysis pipeline used to
search for GW transient events associated with CCSNe,
gamma-ray bursts (GRBs), and other astrophysical triggers.
X-Pipeline has a number of features designed specifically
to address the challenges discussed in Sec. II.
For example, since the signal duration is uncertain,
X-Pipeline uses multiresolution Fourier transforms to
maximize sensitivity across a range of possible signal
durations. The pixel clustering procedure applied to
time-frequency maps of the data is designed to find
arbitrarily shaped, connected events [166]. The potentially
nonstationary data is whitened in blocks of 256 s duration,
removing the effect of variations in background noise levels
which typically happen on longer time scales. Shortduration
noise glitches are removed by comparing measures
of interdetector correlations to a set of thresholds that
are tuned using simulated GW signals from the known sky
position of the CCSNe and actual noise glitches over the
on-source window. The thresholds are selected to satisfy
the Neyman-Pearson optimality criterion (maximum detection
efficiency at fixed false-alarm probability), and are
automatically adjusted for the event amplitude to give
robust rejection of loud glitches. We provide a brief
overview of the functionality of X-Pipeline here,
specifically in the context of CCSN searches, and direct
the reader to the X-Pipeline technical document for a
more in-depth description [78].
As previously introduced in Sec. III B, an external EM or
neutrino trigger at time t0 can be used to define an
astrophysically motivated on-source window, such that
the expected GW counterpart associated with the external
trigger is enclosed within the on-source window. For the
purposes of this study, we choose four distinct on-source
windows centered about t0—see Sec. III B for detailed
information. Given a specified external source location,
ðα; δÞ, the N data streams observed from an N-detector
network are time-shifted, such that any GW signals present
will arrive simultaneously in each detector. The timeshifted
data streams are then projected onto the dominant
polarization frame, in which GW signals are maximized,
and null frame, in which GW signals do not exist by
construction [167,168].
The data streams in the dominant polarization frame are
processed to construct spectrograms, and the 1% of timefrequency
pixels with the largest amplitude are marked as
candidate signal events. For each cluster, a variety of
information on the time and frequency characteristics is
computed, in addition to measures of cluster significance,
which are dependent on the total strain energy jhj2, of the
cluster. For the purposes of this study, a Bayesian likelihood
statistic is used to rank the clusters. We direct the
reader to [64,78] for a detailed discussion of the cluster
quantities used by X-Pipeline.
For statements on the detection of GWs to be made,
we must be able to show with high confidence that
candidate events are statistically inconsistent with the
background data. To do this, we consider the loudest
event statistic, where the loudest event is the cluster in the
on-source with the largest significance; we hereafter
denote the significance of the loudest event Son
max
[169,170]. We estimate the cumulative distribution of
the loudest significances of background events, CðSmaxÞ,
and set a threshold on the false alarm probability (FAP)
TABLE V. Key characteristics of the ad hoc sine-Gaussian
waveforms employed in this study. f0 is the central frequency, Q
is the quality factor, and α is the ellipticity. See Eq. (14) in
Sec. IV B 3 for details.
Model name f0 [Hz] Q α
sglin1, sgel1 70 3 0,1
sglin2, sgel2 70 9 0,1
sglin3, sgel3 70 100 0,1
sglin4, sgel4 100 9 0,1
sglin5, sgel5 153 9 0,1
sglin6, sgel6 235 3 0,1
sglin7, sgel7 235 9 0,1
sglin8, sgel8 235 100 0,1
sglin9, sgel9 361 9 0,1
sglin10, sgel10 554 9 0,1
sglin11, sgel11 849 3 0,1
sglin12, sgel12 849 9 0,1
sglin13, sgel13 849 100 0,1
sglin14, sgel14 1053 9 0,1
sglin15, sgel15 1304 9 0,1
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that the background could produce an event cluster in the
on-source with significance Son
max. If CðSon
maxÞ is greater than
the threshold imposed, we admit the loudest event as a
potential GW detection candidate. For the purposes of this
study, we impose FAP ¼ 0.1%, which corresponds to
∼3.3σ confidence.
For Gaussian noise, the significance distribution of
background events can be estimated analytically, but as
mentioned in Sec. II C, glitches produce excess-power
clusters in the data that may be mistaken for a GW event.
However, the method used by X-Pipeline to construct
the dominant polarization frame results in strong correlations
between the incoherent energy I (from the individual
data streams) and the coherent energy E (from the combined
data streams) for glitches [171]. A comparison of I
and E for candidate events can thus be used to veto events
that have the same statistical properties as the background
noise. A threshold curve in ðI;EÞ space is defined, and veto
tests may be one-sided (all events on one side of the curve
are vetoed), or two-sided (events within some band
centered on the I ¼ E diagonal are vetoed). The threshold
curve is chosen to optimize the ratio of glitch rejection to
signal acceptance.
In practice, the statistics of the distribution of background
events in the data are determined by applying unphysically
large time-shifts, hereafter referred to as “lags,” to the
detector streams. Additionally, we generate known signal
events by injecting simulated GW signals into the data
streams. The background and signal events are split into two
sets, used for pipeline tuning and testing detection performance,
respectively. A large range of trial threshold cuts are
applied for the background rejection test, and the statistics of
the background events computed. The minimum injection
amplitude for which 50% of the injections (1) survive the
threshold cuts and (2) have a FAP ≤ 0.1%, h50%
rss , for a given
family of GW signal models is computed. This is known as
the upper limit on hrss at 50%confidence—see Sec.VD. The
optimal threshold cut is defined as that for which h50%
rss is
minimized at the specified FAP. Unbiased statements on the
background distribution andwaveform detectability can then
be made by processing the tuning set events with the
thresholds obtained previously.
B. Recoloring of GW detector data
The many methods used to detect GW transients can
often be proven to be near optimal in the case of stationary,
Gaussian noise. Data from the GW detectors, however, is
not expected to be stationary or Gaussian, and as such, it is
important to test the efficacy of one’s detection method in
nonstationary and non-Gaussan noise. To this end, we
utilize observational data taken by the Hanford and
Livingston LIGO detectors during the S5 science run, in
addition to data taken by the Virgo detector during the
VSR1 science run. The S5 data is now publically available
via the LIGO Open Science Center (LOSC) [172].
Recoloring of these data to the predicted power spectral
densities (PSDs) of the Advanced detectors during different
stages during the next five years (see Sec. III C) permits a
more realistic estimation of the sensitivity of the advanced
detectors to CCSNe.
We recolor the GW data using the gstlal software
packages [173,174], following the procedure outlined below:
(i) Determine PSD of original data.
(ii) Whiten data using a zero-phase filter created from
the original PSD.
(iii) Recolor whitened data to desired PSD.
This method provides non-Gaussian, nonstationary detector
data including noise transients, tuned to any sensitivity
desired. For specific details on the detector networks, and
noise PSDs considered, see Sec. III C. For the purposes of
this study, we recolor 100 hours of data from the H1 and L1
detectors during the S5 science run, and the V1 detector
during the VSR1 science run.
C. Injection of known signal events
As mentioned previously in Sec. VA, it is a wellestablished
practice to inject known signal events into
detector data for analysis (see, e.g., [175]). This process
permits the estimation of detection efficiency for GWs from
signal models of varying time-frequency characteristics.
A GW source can be characterized by five angles—ðι; ϕ;
θ;Φ; ψÞ, where ðθ;Φ; ψÞ describe the sky location and
polarization of the source, while ðι; ϕÞ describe the internal
orientation of the source relative to the line of sight of the
observer. In this study, the source location in Earth-centered
coordinates ðθ;ΦÞ are fixed by right ascension α, and
declination δ of the source, in addition to the GPS time at
geocenter of the injected signal—see Sec. III for more
detailed information. The polarization angle ψ relating the
source and detector reference frames is distributed uniformly
in ½0; 2π_ for all injections. For CCSN systems, it is not
possible to know the inclination angle ι and azimuthal angle
ϕ. To represent this, we inject signals with many different
ðι; ϕÞ, to average over all possible internal source
orientations.
As mentioned previously in Sec. IV, we may construct
the strain for different internal source orientations by
projecting the mode coefficients HlmðtÞ onto the −2
spin-weighted spherical harmonics, −2Ylmðι; ϕÞ. Making
use of geometric symmetries for different astrophysical
systems permits the use of polarization factors to describe
hþ;×ðι; ϕÞ as a function of hþ;×;0
¼ hþ;×ðι ¼ 0; ϕ ¼ 0Þ.
Defining polarization factors nþ;×ðι; ϕÞ, we may write the
strain at an arbitrary internal orientation as
hþðι; ϕÞ ¼ nþðι; ϕÞhþ;0; ð16Þ
h×ðι; ϕÞ ¼ n×ðι; ϕÞh×;0; ð17Þ
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where the form of nþ;×ðι; ϕÞ is dependent on the symmetries
of the system considered.
For linearly polarized signals (e.g., linear sine-Gaussian
injections), we apply
nlin
þ ¼ 1; ð18Þ
nlin
× ¼ 0: ð19Þ
For elliptically polarized signals (e.g., bar-mode instability,
disk fragmentation instability, and elliptical sine-
Gaussian injections), we apply
nel
þ ¼ 1
2
ð1 þ cos ιÞ2; ð20Þ
nel
× ¼ cos ι: ð21Þ
For the 2D CCSN emission models, the axisymmetric
system results in a linearly polarized GW signal. The
system has azimuthal symmetry, resulting in zero amplitude
for all GW modes except H20. From Eq. (6), we see
that the strain hþ varies with ι as
hþðιÞ ¼ heq
þ sin2 ι;
where heq
þ is the strain as seen by an equatorial observer.We
are thus able to apply SN polarization factors:
nSN
þ ¼ sin2ι;
nSN
× ¼ 0:
For the 3D CCSN emission models, the GW polarizations
are nontrivially related to the internal source
angles, and as such, the hþ and h× strains must be
computed for specific internal configurations using
Eq. (6). No additional polarization factors are applied
for these waveforms.
For all emission models for which nþ;× can be defined,
we inject signals uniform in cos ι ∈ ½−1; 1_. For the 3D
CCSN emission models, we inject signals uniformly drawn
from a bank of 100 realizations of ðcos ι; ϕÞ, where cos ι ∈
½−1;−7=9;…; 1_ and ϕ ∈ ½0; 2π=9;…; 2π_.
For each observational scenario, we inject 250 injections
across the considered on-source window.
D. Upper limits and detection efficiencies
To make detection statements and set upper limits on the
GWs emitted from CCSNe, we must compare the cumulative
distribution of background event significance,
CðSmaxÞ, estimated from off-source data, to the maximum
event significance in the on-source data Son
max. If no onsource
events are significant, we may instead proceed to set
frequentist upper limits on the GWs from the CCSN of
interest, given the emission models considered.
As alluded to previously in Sec. VA, we may define the
50% confidence level upper limit on the signal amplitude
for a specific GW emission model as the minimum
amplitude for which the probability of observing the signal,
if present in the data, with a cluster significance louder than
Smax
on is 50%. In this study, we aim to determine the 50%
upper limit, as defined here, as a function of
(i) Source distance d50%, in the context of astrophysically
motivated signal models.
(ii) Root-sum-square amplitude h50%
rss , in the context of
linear and elliptical sine-Gaussian waveforms. It is
more relevant, astrophysically to consider the corresponding
50% upper limit on the energy emitted in
GWs, E50%
GW , which we compute from h50%
rss using
Eq. (15).
After the on-source data has been analyzed and Smax
on
computed, we inject a large number of known signal events
for families of waveforms for which h50%
rss and d50% (where
applicable) are desired. For a single waveform family, we
outline the upper limit procedure:
(i) Inject many waveforms at different times during the
on-source window and with a broad range of
polarization factors.
(ii) Compute the largest significance S of any clusters
associated with the injected waveforms (observed
within 0.1 seconds of the injection time) that have
survived after application of veto cuts.
(iii) For all injections, compute the percentage of injections
for which S > Smax
on . This is called the
“detection efficiency,” E.
(iv) Repeat procedure, modifying the injection amplitude
of each waveform by a scaling factor.
The final goal is to produce a plot of the detection
efficiency as a function of hrss or distance d for each
waveform family, such that one may place upper limits on
the GW emission models considered. From the efficiency
curve, one may determine h50%
rss as
Eðhrss ¼ h50%
rss Þ ¼ 0.5: ð22Þ
Given an astrophysical signal injected at hinj
rss corresponding
to fiducial distance dinj, we may define d50% as
d50% ¼
_
h50%
rss
hinj
rss
_
dinj: ð23Þ
We note that X-Pipeline rescales the detection efficiency
to account only for injections placed at times at which
detector data is available. Without this correction, the
efficiencies computed asymptote to the duty cycle fraction
for the on-source window considered. For the data considered
in this study, the total duty cycle is typical of the S5 and
VSR1 science runs, which is described in detail in Sec. II B.
E. Systematical uncertainties
The uncertainties in the efficiencies, upper limits and
exclusion capabilities of our analysis method are related to
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non-Gaussian transients in the data, in addition to calibration
uncertainties. There are a number of systematic
uncertainties present in this study that will non-negligibly
affect the results. We consider only a short period of
recolored data from LIGO’s S5 and Virgo’s VSR1 datataking
runs, over which the frequency and character of non-
Gaussian transients changed non-negligibly. The noise
transients in advanced LIGO data are also significantly
different to those in initial LIGO data, and the non-
Gaussianities are not yet understood well enough to make
quantitative statements on the statistical behavior of the
data. For these reasons, we only quote results to two
significant figures in this study. The statistical uncertainty
in detector calibration can be characterized by the 1σ
statistical uncertainty in the amplitude and phase of the
signal. Uncertainties in phase calibration can be estimated
by simulating its effect on the ability to recover test
injections. We direct the reader to Kalmus [176], in which
it is shown that phase uncertainties contribute negligibly to
the total systematic error, and thus we only consider
amplitude uncertainties in this study. The target design
amplitude uncertainties in the frequency range 40–2048 Hz
for Advanced LIGO and Advanced Virgo are 5% at 2σ
confidence [177]. As such, the upper limits for h50%
rss and
d50% obtained from a search for GWs from CCSNe in the
Advanced detector era will have intrinsic ∼5% uncertainties.
For comparison, typical amplitude uncertainties due to
calibration in S5 were below 15% [98].
VI. RESULTS
In this section, we present the results for the detectability
of the consideredGWemission models described in Sec. IV.
We consider realistic waveform models from numerical
simulations of core collapse. For the ‘garden-variety’
CCSN models considered (müller1, müller2,
müller3, ott, and yak), convection and SASI are the
dominant GW emission processes. For rotating core collapse,
we choose models where bounce and ringdown of
the proto-neutron star (dim1, dim2, and dim3), and
nonaxisymmetric rotational instabilities (sch1 and
sch2) are the dominant GWemission processes. As these
waveforms will only be detectable from CCSNe at close
distances (d ≲ 100 kpc), we consider CCSNe in the direction
of the Galactic center and LMC, for which the
coincident neutrino signal will be detected. We use a
conservative on-source window of ½−10;þ50_ s about
the time of the initial SNEWS trigger.
For more distant CCSNe, we consider more speculative,
extreme phenomenological GW emission models for longlived
bar-mode instabilities (longbar1, longbar2,
longbar3, longbar4, longbar5, and longbar6)
and disk fragmentation instabilities (piro1, piro2,
piro3, and piro4). More distant CCSNe will not be
detectable via neutrinos, but the EM counterpart will be
observed. We consider CCSNe in M31 and M82, and use
on-source windows assuming a compact, stripped progenitor
star of 61 minutes and 24 hour 1 minute, respectively.
For an extended, red supergiant progenitor, we use onsource
windows of 51 hours and 74 hours for M31 and
M82, respectively.
For all host galaxies, we consider ad hoc sine-Gaussian
bursts to assess the sensitivity of our analysis to localized
bursts of energy in time-frequency space.
We remind the reader of the large systematic uncertainties
associated with these results and, as such, quote all
results to two significant figures.
A. Numerical waveforms
We present the distances d50% at which 50% detection
efficiency is attained (the measure we use for ‘detectability’)
for the considered numerical waveforms in Table VI,
for CCSNe in the direction of the Galactic center and LMC,
in the context of a 60-second on-source window.
For CCSNe in the direction of the Galactic center, we see
that emission from neutrino-driven convection and SASI is
detectable out to ∼ð1.0–2.4Þ kpc with the HL 2015
TABLE VI. The distance in kpc at which 50% detection efficiency is attained, d50% for the numerical corecollapse
emission models considered using the HL 2015, HLV 2017, and HLV 2019 detector networks, for
CCSNe in the direction of the Galactic center and the LMC.
d50% [kpc] for Galactic center d50% [kpc] for LMC
Waveform HL 2015 HLV 2017 HLV 2019 HL 2015 HLV 2017 HLV 2019
müller1 2.3 3.3 4.7 2.5 3.8 5.3
müller2 1.0 1.5 2.2 1.2 1.8 2.5
müller3 1.2 1.5 2.4 1.4 1.6 2.7
ott 2.4 3.4 5.5 3.2 4.9 7.2
yak 1.5 1.8 5.1 1.6 2.1 6.2
dim1 7.0 9.1 17 7.4 10 18
dim2 11 17 29 13 20 32
dim3 13 21 38 18 32 50
sch1 31 43 78 36 48 90
sch2 35 50 98 45 56 120
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detector network. This increases to ∼ð1.5–3.4Þ kpc and
∼ð2.2–5.5Þ kpc with the HLV 2017 and HLV 2019
detector networks, respectively.
Similarly, we see that emission from bounce and ringdown
of the central proto-neutron star core is detectable out
to ∼ð7.0–13.4Þ kpc for CCSNe in the direction of the
Galactic center with the HL 2015 detector network. This
increases to ∼ð9.1–21Þ kpc and ∼ð17–38Þ kpc with the
HLV 2017 and HLV 2019 detector networks, respectively.
Emission from nonaxisymmetric rotational instabilities
from CCSNe in the direction of the Galactic center is
detectable out to ∼ð31–35Þ kpc with the HL 2015 detector
network. This increases to∼ð43–50Þ kpc and∼ð78–98Þ kpc
with the HLV 2017 and HLV 2019 detector networks,
respectively.
Assuming the fiducial distance of a galactic CCSN to be
∼9 kpc, this suggests that we will be able to detect emission
from the more extremely rapidly rotating CCSN waveforms
considered with the HL 2015 detector network, while all
considered rapidly rotating waveforms will be detectable
for CCSNe in the direction of the Galactic center with the
HLV 2017 and HLV 2019 detector networks. We will be
limited to detection of nonrotating CCSNe within 5.5 kpc
with the most sensitive HLV 2019 detector network.
Considering CCSNe in the direction of the LMC, we see
that emission from neutrino-driven convection and SASI is
detectable out to ∼ð1.2–3.2Þ kpc with the HL 2015
detector network. This increases to ∼ð1.6–4.9Þ kpc
and ∼ð2.5–7.2Þ kpc with the HLV 2017 and HLV 2019
detector networks, respectively. Given that the LMC
is ∼50 kpc away, this shows that emission from
neutrino-driven convection and SASI will not be detectable
from CCSNe in the LMC.
Emission from bounce and ringdown of the central protoneutron
star core is detectable out to ∼ð7.4–18Þ kpc and
∼ð11–32Þ kpc for CCSNe in the direction of the LMC with
the HL2015andHLV2017 detector networks, respectively.
This increases to ∼ð18–50Þ kpcwith the HLV 2019 detector
network. This suggests that emission from the bounce and
subsequent ringdown of the proto-neutron star may not be
detectable fromCCSNe in theLMCfor even themost rapidly
rotating waveform considered with the HLV 2019 detector
network.
We see that emission from nonaxisymmetric rotational
instabilities from CCSNe in the direction of the LMC
is detectable out to∼ð36–45Þ kpcwith the HL 2015 detector
network. This increases to∼ð48–56Þkpc and∼ð90–120Þ kpc
with the HLV 2017 and HLV 2019 detector networks,
respectively. This suggests we will be able to detect
emission from nonaxisymmetric rotational instabilities
for CCSNe in the LMC with the HLV 2017 detector
network.
FIG. 5. The detection efficiency as a function of distance for the numerical waveforms in this study, in the context of a 1 minute onsource
window and the HLV 2019 detector network. The top row is for galactic sources, and the bottom row is for sources in the Large
Magellanic Cloud. In each plot, 50% and 90% detection efficiency is marked with a dashed black line, and the distance to the host galaxy
is marked with a vertical blue line.
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Figure 5 presents the detection efficiency as a function
of distance, for the numerical waveforms considered,
for CCSNe directed toward theGalactic center and theLMC.
B. Extreme phenomenological models
We present the distances at which 50% detection
efficiency is attained d50% (the measure we use for
“detectability”) for the considered phenomenological
waveforms in Table VII, for CCSNe in the direction of
M31, in the context of 61-minute and 51-hour on-source
windows, and M82, in the context of 24-hour 1-minute and
74-hour on-source windows.
For CCSNe in the direction of M31, we see that emission
from long-lived bar-mode instabilities will be detectable
out to ∼ð0.5–5.2Þ Mpc [∼ð0.2–2.7Þ Mpc] when using a
61-minute [51-hour] on-source window, with the HL 2015
detector network. The distances at which 50% detection
efficiency is reached, d50%, increase to ∼ð0.8–8.6Þ Mpc
[∼ð0.3–3.4Þ Mpc] and ∼ð1.6–18Þ Mpc (∼ð0.8–9.9Þ Mpc)
when using a 61-minute [51-hour] on-source window, with
the HLV 2017 and HLV 2019 detector networks,
respectively.
Emission from disk fragmentation instabilities will be
detectable out to ∼ð0.9–12Þ Mpc [∼ð0.6–6.5Þ Mpc] and
∼ð1.3–19Þ Mpc [∼ð0.6–6.1Þ Mpc] when using 61-minute
[51-hour] on-source windows with the HL 2015 and
HLV 2017 detector networks, respectively, for CCSNe
in the direction of M31. These distances increase to
∼ð2–28Þ Mpc [∼ð1.4–18Þ Mpc] when using a 61-minute
[51-hour] on-source window, with the HLV 2019 detector
network.
Assuming a fiducial distance of 0.77 Mpc for a CCSN in
M31, this suggests that we will be able to detect emission
from all considered long-lived bar-mode instability waveforms
with the HLV 2019 detector network, while the
detectable fraction of considered waveforms with the HL
2015 and HLV 2017 detector networks is strongly
dependent on the on-source window length. Taking the
51-hour on-source window as the most pessimistic scenario,
∼50% and ∼67% of the considered bar-mode
instability waveforms are detectable with the HL 2015
and HLV 2017 detector networks, respectively.
Similarly, emission from the considered disk fragmentation
instabilities waveforms will be detectable for a
CCSN in M31 with the HLV 2019 detector network for
all considered on-source windows. For the 51-hour onsource
window, we see that ∼75% of the considered diskfragmentation
instability waveforms are detectable with
both the HL 2015 and HLV 2017 detector networks.
We note that, for some models, the d50% values computed
for the M31 source, when using a 51-hour on-source
window, are smaller for the HLV 2017 detector network
than the HL 2015 network. While this might at first seem
counter-intuitive, this is due to the requirement for coincident
data between detectors to run a coherent analysis. The
lower sensitivity of the HV and LV detectors for the data
analyzed, compared with the sensitivity of the HL detectors,
reduces the effective total sensitivity of the network. We
include the third detector, however, as it increases the
overall duty cycle of the network.
For CCSNe in the direction of M82, we see that emission
from long-lived bar-mode instabilities will be detectable out
to ∼ð0.3–3Þ Mpc [∼ð0.4–4.3Þ Mpc] and ∼ð0.3–3.4Þ Mpc
[∼ð0.4–5.2Þ Mpc] using a 24 hour 1 minute [74 hour]
on-source window, with the HL 2015 and HLV 2017
detector networks. This increases to ∼ð1–9.7Þ Mpc
[∼ð0.7–8.3Þ Mpc] for a 24 hour 1 minute [74 hour] onsource
window, with the HLV 2019 detector network.
For emission from disk fragmentation instabilities for
CCSNe in the direction of M82, the distance reach is
∼ð0.5–6.4Þ Mpc [∼ð0.7–7.5Þ Mpc] when using a 24-hour
1-minute [74-hour] on-source window with the HL 2015
detector network. This increases to ∼ð0.7–8.6Þ Mpc
[∼ð0.8–9.5Þ Mpc] and ∼ð1.3–16Þ Mpc [∼ð1.3–15Þ Mpc]
for the HLV 2017 and HLV 2019 detector networks,
respectively.
TABLE VII. The distance in Mpc at which 50% detection efficiency is attained, d50% for the numerical core-collapse emission models
considered using the HL 2015, HLV 2017, and HLV 2019 detector networks, for CCSNe in the direction of M31 and M82, in the
context of 61-minute (51-hour) and 24-hour 1-minute (74-hour) on-source windows, respectively.
d50% [Mpc] for M31 d50% [Mpc] for M82
Waveform HL 2015 HLV 2017 HLV 2019 HL 2015 HLV 2017 HLV 2019
longbar1 0.5 [0.2] 0.8 [0.3] 1.6 [0.8] 0.3 [0.4] 0.3 [0.4] 1.0 [0.7]
longbar2 1.5 [0.7] 2.5 [0.9] 4.8 [2.8] 0.9 [1.1] 1.0 [1.2] 3.0 [2.1]
longbar3 1.0 [0.6] 1.6 [0.6] 3.6 [2.2] 0.8 [0.8] 0.7 [0.8] 2.4 [1.8]
longbar4 2.0 [1.1] 2.8 [1.2] 6.0 [3.8] 1.1 [1.5] 1.4 [1.5] 3.9 [2.8]
longbar5 5.2 [2.7] 8.6 [3.4] 18 [9.9] 3.0 [4.3] 3.4 [5.2] 9.7 [8.3]
longbar6 2.1 [1.1] 3.4 [1.1] 6.7 [4.7] 1.4 [1.9] 1.4 [1.7] 4.4 [3.7]
piro1 0.9 [0.6] 1.3 [0.6] 2.0 [1.4] 0.5 [0.7] 0.7 [0.8] 1.3 [1.3]
piro2 3.9 [2.2] 6.3 [2.6] 9.4 [5.8] 2.2 [3.2] 3.0 [3.8] 5.7 [5.8]
piro3 1.9 [1.3] 3.4 [1.8] 4.9 [3.7] 1.1 [1.3] 1.5 [1.9] 2.8 [3.1]
piro4 12 [6.5] 19 [6.1] 28 [18] 6.4 [7.5] 8.6 [9.5] 16 [15]
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Given a fiducial distance of ∼3.52 Mpc for CCSNe in
M82, we note that only the most extreme waveform
considered for both long-lived bar-mode instabilities and
disk fragmentation instabilities are detectable with the HL
2015 detector network. Of the considered long-lived barmode
instability waveforms, only the most extreme emission
model is detectable with the HLV 2017 detector
network, while 50% of the waveforms will be detectable
with the HLV 2019 detector network. For emission from
disk-fragmentation instabilities, we see that only 50% of
the waveforms considered will be detectable out to M82
with the HLV 2017 and HLV 2019 detector networks.
We note that the distance reach for these models
increases with the larger on-source window for the M82
source. This is due to the properties of the data over the two
considered on-source windows. As previously mentioned,
real data from GW detectors is not stationary, and as such,
the PSD of the data is a function of time. Time periods over
which the detector data is glitchy will have locally have
significantly decreased sensitivity when compared to a
much larger time period over which the detector is more
well behaved. This means that if the on-source window
derived happens to lie in a glitchy period of detector data,
the sensitivity of the detector network will, unfortunately,
be decreased. In repeating the search for a larger on-source
window, over which the average sensitivity is much greater,
the distance reach for the emission models considered may
appear to increase. The detectability of the waveforms
considered in this study is established by injecting a
number of waveforms over the full on-source window
considered. The distance reach for the longer on-source
window in this case appears to increase because we inject
waveforms uniformly across the on-source window, meaning
that many “test” signals are placed at times in the data
stretch where the sensitivity is greater, in addition to the
shorter, more glitchy, time period where the sensitivity is
not as great. This is a great example of how realistic noise
can significantly affect the detectability of GWs from
CCSNe at different times, and is motivation for improving
active noise suppression techniques for the detectors.
Figures 6 and 7 present the detection efficiency as a
function of distance for the considered phenomenological
extreme emission models, for CCSNe in the direction of
M31 and M82 for the HLV 2019 detector network, using
on-source windows motivated by type Ibc and Type II
CCSNe, respectively.
C. Sine-Gaussian waveforms
The energy emitted in GW, E50%
GW , required to attain the
root-sum-squared strain at 50% detection efficiency, h50%
rss ,
for the sine-Gaussian bursts considered is presented in
FIG. 6. The detection efficiency as a function of distance for the phenomenological waveforms considered in this study, in the context
of the on-source window astrophysically motivated by a stripped envelope type Ibc SN progenitor and the HLV 2019 detector
configuration. The top row is for sources in M31 with an on-source window of 61 minutes, and the bottom row is for sources in M82
with a 24-hour 1-minute on-source window. In each plot, 50% and 90% detection efficiency is marked with a dashed black line, and the
distance to the host galaxy is marked with a vertical blue line.
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Fig. 8 for sources in the direction of the Galactic center,
LMC, M31, and M82.
For the ad hoc sine-Gaussian bursts considered, we use
E50%
GW as the figure of merit for detection.
For CCSNe in the direction of the Galactic center, we see
that the typical E50%
GW values are ∼ð8–110Þ × 10−10M⊙ for
sine-Gaussian bursts with central frequencies of
∼ð554–1304Þ Hz, the typical frequencies of emission for
CCSNe, using a 60-second on-source window with the HLV
2019 detector network. For CCSNe in the direction of the
LMC, we find E50%
GW ∼ ð1–20Þ × 10−8M⊙ in the same frequency
range. We remind the reader that for the numerical
waveforms considered, EGW∼ð0.1–4000Þ×10−10M⊙. This
is consistent, as X-Pipeline is more sensitive to sine-
Gaussian bursts, and we find that only the more rapidly
rotating models considered are detectable.
For CCSNe in the direction of M31, we find typical E50%
GW
values of ∼ð7–100Þ × 10−6M⊙ across the frequency range
considered, using a 51-hour on-source window with the
HLV 2019 detector network. For CCSNe in the direction of
M82, we find E50%
GW ∼ ð3–60Þ × 10−4M⊙ across the same
frequency range. We remind the reader that for the
extreme phenomenological waveforms considered,
EGW∼ð2–600Þ×10−4M⊙. This is again consistent with
our previous results, as we find that all waveforms are
detectable for CCSNe in M31 with the HLV 2019 detector
network, but only the more extreme cases are detectable out
to M82.
VII. DISCUSSION
The next galactic CCSN will be of great importance to
the scientific community, allowing observations of unprecedented
accuracy via EM, GW, and neutrino messengers.
Using GW waveform predictions for core collapse from
state-of-the-art numerical simulations, and phenomenological
waveform models for speculative extreme GWemission
scenarios, we make the first comprehensive statements on
detection prospects for GWs from CCSNe in the Advanced
detector era.
Given a known sky location,we outline a search procedure
for GW bursts using X-Pipeline, a coherent network
analysis pipeline that searches for excess power in timefrequency
space, over some astrophysically motivated time
period (or on-source window). The GWdetector data is non-
Gaussian, nonstationary, and often contains loud noise
transients. For this reason, it is beneficial to minimize the
on-source window to reduce the probability of glitchiness or
extreme Gaussian fluctuations being present in the detector
data.
FIG. 7. The detection efficiency as a function of distance for the phenomenological waveforms considered in this study, in the context
of the on-source window astrophysically motivated by a type II SN progenitor and the HLV 2019 detector configuration. The top row is
for sources in M31 with an on-source window of 51 hours, and the bottom row is for sources in M82 with a 74-hour on-source window.
In each plot, 50% and 90% detection efficiency is marked with a dashed black line, and the distance to the host galaxy is marked with a
vertical blue line.
S. E. GOSSAN et al. PHYSICAL REVIEW D 93, 042002 (2016)
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For CCSNe within ∼100 kpc, the coincident neutrino
signal will be detected, allowing the time of core collapse to
be determined to within a few tens of milliseconds. Using
an conservative asymmetric on-source window of
½−10;þ50_ seconds around the start time of the neutrino
signal, we consider hypothetical CCSNe in the direction of
the Galactic center and the LMC. We find that neutrinodriven
CCSN explosions, believed to account for ∼99% for
CCSNe, will be detectable within 2.4 kpc, 3.5 kpc, and
5.5 kpc in 2015, 2017, and 2019, respectively. Rapidly
rotating CCSNe, however, will be detectable throughout
the galaxy from 2017, and the most rapidly rotating model
considered will be detectable out to the LMC in 2019.
Rapidly rotating CCSNe with nonaxisymmetric rotational
instabilities will be detectable out to the LMC and beyond
from 2015.
More distant CCSNe will not have coincident neutrino
observations, and so the on-source window must be derived
using EM observations. Using recent studies of light curves
for type Ibc and type II CCSNe (see, e.g. [135–137]), we
assume that, if the time of shock breakout tSB is observed,
the time of core collapse can be localized to between
1 minute and 50 hours. Unfortunately, shock breakout is
rarely observed, and an observation cadence time delay,
FIG. 8. The energy emitted in GW, E50%
GW , required to attain the root-sum-squared strain at 50% detection efficiency, h50%
rss , for the sine-
Gaussian bursts considered in this study, in the context of the HLV 2019 detector network. The top row is for sources directed toward the
Galactic center (left) and the Large Magellanic Cloud (right), for both of which a 1-minute on-source window is used. The middle row is
for sources in M31, considering 61-minute and 51-hour on-source windows (left and right plots, respectively). The bottom row is for
sources in M82, considering on-source windows of 24 hours and 1 minute, and 74 hours (left and right plots, respectively). Distances of
10 kpc, 50 kpc, 0.77 kpc, and 3.52 Mpc are used to compute E50%
GW for sources in the galaxy, Large Magellanic Cloud, M31, and M82,
respectively.
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tobs, between the last pre-CCSN and first post-CCSN
images is introduced. Given this, we construct an on-source
window of ½−tSB; tobs_ about the time of the last pre-CCSN
image. Frequently observed galaxies, such as those for
which the CCSN rate is high, are likely to have CCSNe
detected within one day of shock break-out. As such, we
consider two observational scenarios where tobs ¼ 1 hour
and 24 hours for hypothetical CCSNe in M31 and M82,
respectively. In the context of EM observations of type Ibc
CCSNe, we use on-source windows of 61 minutes and
24 hour 1 minute for CCSNe in M31 and M82, respectively.
Correspondingly for type II CCSNe, we use onsource
windows of 51 hours and 74 hours for CCSNe in
M31 and M82, respectively. We find that most of the
extreme GW emission models considered are observable
out to M31 with the HL 2015 detector network when using
a 61-minute on-source window, while all models are
observable when using the 51 hour on-source window in
2019. Only the most extreme emission models considered
are observable out to M82 with the HL 2015 detector
network, but approximately half of the models considered
will be detectable out to M82 and beyond in 2019. This
allows us to either detect events associated with or exclude
such extreme emission models for CCSNe in M31 and M82
with the HLV 2019 detector network.
In anticipation of unexpected GW emission from
CCSNe, we additionally consider sine-Gaussian bursts
across the relevant frequency range for all observational
scenarios studied. We find that the sensitivity of our search
method is comparable, if not slightly improved, to that
found for the realistic waveform models considered. This is
to be expected as X-Pipeline, and other clusteringbased
burst search algorithms, are most sensitive to short
bursts of GW energy localized in frequency space. It
should be noted, however, that such simple waveform
morphologies are more susceptible to being confused for
noise transients. As such, a more complicated waveform
morphology, as found for realistic GW predictions for
CCSNe, can actually improve detectability [178].
Detection prospects for GWs from CCSNe can be
improved by refining light curve models for CCSNe,
and increasing observation cadence, so as to reduce the
on-source window as derived from EM observations as
much as possible. Improvement of stationarity and glitchiness
of detector data, in addition to increasing the detector
duty cycle, will improve detectability of GWs from
CCSNe. Further to this, more second-generation GW
detectors such as KAGRA and LIGO India will improve
the overall sensitivity of the global GW detector network
and could potentially allow for neutrino-driven CCSN
explosions to be observable throughout the Galaxy.
ACKNOWLEDGMENTS
The authors thank Alan Weinstein, Peter Kalmus, Lucia
Santamaria, Viktoriya Giryanskaya, Valeriu Predoi, Scott
Coughlin, James Clark, MichałWąs, Marek Szczepanczyk,
Beverly Berger, and Jade Powell for many fruitful discussions
that have benefitted this paper greatly. We thank
the CCSN simulation community for making their gravitational
waveform predictions available for this study.
LIGO was constructed by the California Institute of
Technology and Massachusetts Institute of Technologywith
funding from the National Science Foundation, and operates
under cooperative agreement No. PHY-0757058. Advanced
LIGO was built under Award No. PHY-0823459. C. D. O. is
partially supported by National Science Foundation Grants
No. PHY-1404569 and No. CAREER PHY-1151197 and by
the Sherman Fairchild Foundation. This paper carries LIGO
Document No. LIGO-P1400233.
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Zakharchenko: Ukraine Hangs Between Dictatorship and Counterrevolution

By Alexander Zakharchenko

Zakharchenko Official Website
Edited autotranslation by Quemado Institute
February 21, 2016

Alexander Zakharchenko

Alexander Zakharchenko

The anniversary of the coup in Kiev was marked by new riots, and promises another Maidan.

First you need to remember that these events are taking place against the backdrop of a deep political crisis, the degradation of the economy and monstrous decline in living standards of Ukrainian citizens. Why is this happening? Because as a result of the coup and the violent overthrow of the legitimate authorities, whcih in Kiev is called “revolution”, processes of destruction were launched that no one can stop. It happens to all revolutions. They all ran to the people and the state of self-destruction process [sic]. That is why we are against any revolutions, according to their version. And the Russian and Ukrainian peoples have exhausted the limit on revolutions.

Where is the exit? Historically, there have been only two. Either the victory of the counter-revolution, or the victory of the revolutionary dictatorship, which then, painfully, through blood and sweat, the people return to public life. Here we are just at the limit of the second option and the Russian and Ukrainian people are exhausted. Many intelligent people in Russia and Ukraine said and say that the people and the state will not survive another revolution. Here we see the result in Ukraine. The process of self-destruction is happening on the Maidan, and Ukraine will not survive.

About dictatorship in Kiev, I do not believe it, because, firstly, there are no candidates for the role of dictator. Well, certainly not Poroshenko! And secondly, the people will not accept dictatorship, if there were another coup and the henchmen of Bandera and neo-Nazis come to power.

So I do not have any optimism about the development of the situation in Ukraine. And I have is no cause for joy. Because Ukrainians are a sorry, sorry people. On this I will have to remind you that we did not fight, and do not fight, with the Ukrainian people. We are fighting against Bandera and their accomplices, who have usurped power in Kiev.

Is a counter-revolution possible? Of course. But it depends on whether the Ukrainian people gather together to overthrow entrenched usurpers in Kiev, and whether there are leaders who will bring the Ukrainian people to a return to common sense, traditional moral values and economic revival. That is, leaders who will not make the Ukrainians become someone else—the Europeans, for example— once again become themselves, with their real history, real culture, and real heroes.

So I was quite surprised by the pogroms in Kiev. It is clear that now, after the authorities, who were initially illegitimate from the point of view of the law, have lost the moral legitimacy, and the Maidan flywheel [tr?] will go the next round and eventually destroy Ukraine, or the Ukrainian people will stop it and return to normal life. We in Donbass have already made our choice and are ready to render assistance to the Ukrainian people, if they will gather to stop the Maidan flywheel and return to normal life.

–February 21, 2016, Donetsk.

Source: av-zakharchenko.su/ru/news/aleksandr-zaharchenko-ukraina-nahoditsya-mezhdu-diktaturoy-i-kontrrevolyuciey

Editor’s note: please excuse possible errors in translation.