A First Targeted Search for Gravitational-Wave Bursts from Core-Collapse Supernovae in Data of First-Generation Laser Interferometer Detectors

LIGO Scientific Collaboration and Virgo Collaboration (Dated: 3 March 2014)

We present results from a search for gravitational-wave bursts in coincidence of 4 core collaplse optical supernovae observed during the fifth and sixth LIGO scientific runs, the Virgo second sci- ence run and astrowatch data. The analysis searches for transients of duration . 1 s over the frequency band 64–2048 Hz, without other assumptions on the signal waveform, polarization or specific occurrence time in the onsource window.

PACS numbers: 04.80.Nn, 07.05.Kf, 95.30.Sf, 95.85.Sz

I. INTRODUCTION example of such constraints. Satellite detectors observe unpredictable bursts of soft gamma-rays from neutron with extreme magnetic fields, known as . The physics of core-collapse supernovae cannot be fully The hypothesis that a GW arrives within ±2 s of such understood from electromagnetic signatures because the a gamma-ray burst was tested by looking for transient photons tipically leave the source after being absorbed excess power in the GW data within this signal region, and emitted many times. An important alternative a and comparing to the background [? ]. On this basis source of information can be provided by transient grav- the hypothesis of a GW signal in the data was rejected. itational waves (of duration of 1 s) which are expected . The loudest transient event in the signal region was then to be emitted by core-collapse supernovae [? ]. compared to simulated GW signals predicted by models This paper reports on a search for GW bursts occurring of the damping of non-radial global stellar modes, in coincidence of nearest optically observed Core Collapse constraining those models via estimation of upper limits supernovae explosions during the S5, S6 runs from the on emitted GW energy. LIGO scientific collaboration and VRS1 VRS2 runs from the VIRGO scientific collaboration. More specifically S5 So long as the signal region duration t is much lasted from 04 November 2005 to 30 September 2007, S6 s less than the from July 7th, 2009 and Oct. 20, 2010, VSR2 started characteristic duration of the time windows of contin- with S6 and ended on Jan.8, 2010, and VSR3 started on uous data aquisition t , model exclusion from individual Jun. 26, 2010 and ended with S6. d null detections can proceed as described above. However, This search makes use of the observed source sky loca- when ts  td the situation is more complicated. In this tion, and uses constraints on the signal arrival time. case, the detectors may have outages during the signal As explained in [? ] and the references within, the region, and the data will have gaps. A short burst of gravitational wave signal to be expected from a core signal falling into a gap will be missed. collapse event is uncertain. Its overall strength and char- For this reason a new strategy different from the stan- acteristics (duration, frequency content, polarization, dard All-sky and targeted searches needs to be emplyed etc.) will depend on the dominant emission process and in order to search for GW transients in correspondence the complex structure, rotation, and thermodynamics with CCSN EM triggers. of the progenitor . It is impossible to robustly predict the signal’s detailed time series, since most of the processes driving the emission have stochastic character II. TRIGGERS: CONSIDERED OPTICAL (e.g., convection/turbulence, rotational instabilities). CORE-COLLAPSE SUPERNOVAE This is true even if the full set of parameters influencing the overal signal characteristics were known, understood,  [TODO: CDO: Much of this section is incorrect and and the space spanned by them covered with detailed must be fixed by CDO. PLEASE DO NOT TOUCH.] computational models. More than 100 core-collapse supernovae were discov- Even if indirect evidence of gravitational waves (GW) ered in the optical by amateurs and professional as- has been observed in like PSR B1913+16 tronomers (e.g., [? ]) during the S5/S6 LIGO and the The global network of gravitational wave (GW) laser VSR2/VSR3 Virgo data taking periods. interferometers [? ] has yet to directly detect a signal. For our search it is important to have an estimate of Nevertheless coincident searches of GW signal in laser the time of core collapse in a considered core-collapse interferometers data when triggers from other observa- . This time coincides (within ∼1 − few s; e.g., tion channels were available have already constrained [? ]) with the time of strongest GW emission. The better astrophysical models. flares provide an the estimate of the core collapse time, the smaller the on- 2

TABLE I: Core-collapse supernovae selected as triggers for the GW search carried out in this study. Distance gives the best current estimate for the distance to the host . t1 and t2 are the UT dates delimiting the on-source window. ∆t is the temporal extent of the on-source window. LIGO/Virgo run indicates during which data taking campaign the supernova exploded, and Detectors list the first-generation interferometers active at least during parts of the on-source window. See text for details and references.  [TODO: add detector coverage fractions!]

SN Type Host Galaxy Distance t1 t2 ∆t LIGO/Virgo run Detectors coverage [Mpc] [days] 2011dh IIb M51 8.40 ± 0.70 2011 May 30.37 2011 May 31.89 1.52 S6E/VSR3 G1,V1 36% 2008bk IIP NGC 7793 3.53 +0.41 −0.29 2008 Mar 13.50 2008 Mar 25.14 12.64 A5 G1,H2 2008ax IIb NGC 4490 9.64 +1.38 −1.21 2008 Mar 2.19 2008 Mar 3.45 1.26 A5 G1,H2 2007gr Ic NGC 1058 10.55 ± 1.95 2007 Aug 10.39 2007 Aug 15.51 5.12 S5/VSR1 H1,H2,L1,V1 75.9%

source window of detector data that must be searched ∼10−15 Mpc. Since GWs from core-collapse supernovae and the smaller the confusion background due to non- are most likely very weak and because the observable GW Gaussian non-stationary detector noise. amplitude scales with one-over-distance, nearer events The time of core collapse can be estimated based on are greatly favored. (ii) Well constrained time of explo- estimates of the explosion time and the radius of the sion leading to an uncertainty in the time of core collapse progenitor. The explosion time is defined as the time of less than ∼2 weeks. (iii) At least partial availability of at which the supernova shock breaks out of the stel- science-quality data from more than one interferometer lar surface and the EM emission of the supernova sets. in the on-source window. Basic information about the progenitor can be obtained The core-collapse supernovae making these cuts are SN from the lightcurve and spectrum of the supernova (e.g., 2007gr, SN 2008ax, SN 2008bk, and SN 2011dh. Table I [? ]). Much more information can be obtained if pre- summarizes key properties of these supernovae and we explosion imaging of the progenitor is available (e.g., [? discuss each in more detail in the following. ]). A red supergiant progenitor with a typical radius of SN 2007gr, a Type Ic supernova, was discovered on few 100 − 1500 R produces a Type IIP supernova and 2007 August 15.51 UT [? ]. A pre-discovery empty image has an explosion time of order 1 day after core collapse [? taken by KAIT [? ] on August 10.44 UT provides a base- ? ]. A Wolf-Rayet star progenitor, giving rise to a Type line constriant on the explosion time. The progenitor of Ib/c supernova, has been stripped of its hydrogen (and this supernova was a compact stripped-envelope star [? helium) envelope by stellar winds or binary interactions ?? ] through which the supernova shock propagated and has a radius of only few − 10 R and shock breakout within tens of seconds. In order to be conservative, we occurs within ∼10 − 100 s of core collapse [?? ]. add an additional hour to the interval between discovery The breakout of the supernova shock through the sur- and last non-detection and arrive at a GW on-source win- face of the progenitor star leads to a short-duration high- dow of 2007 August 10.39 UT to 2007 August 15.51 UT. burst of EM radiation with a spectral peak de- The sky location of SN 2007gr is R.A. = 02h43m27s.98, pendent on the radius of the progenitor. The burst from Decl.= +37◦2004400.7 [? ]. The host galaxy is NGC 1058. shock-breakout preceeds the rise of the optical lightcurve Schmidt et al. [? ] used the EPM to determine the dis- which occurs on a timescale of days after shock break- tance to SN 1969L, which exploded in the same galaxy. out [? ]. With the exception of very few serendipitous They found D = (10.6 + 1.9 − 1.1) Mpc. This is broadly discoveries of shock breakout bursts (e.g., [?? ]), core- consistent with the more recent Cepheid-based distance collapse supernovae are usually discovered days after ex- estimate of D = (9.29 ± 0.69) Mpc to NGC 925 by [? ]. plosion and their explosion time is constrained by one This galaxy is in the same galaxy group as NGC 1058 and or multiple of (i) the most recent non-detection, i.e., thus presumed to be in close proximity. For the purpose by the date of observation of the host galaxy without of this study, we use the conservative combined distance the supernova present, (ii) by comparison of observed estimate of D = (10.55 ± 1.95 Mpc). lightcurve and spectra with those of other supernovae for SN 2008ax, a Type IIb supernova [? ], was discov- which the explosion time is well known, (iii) by lightcurve ered by KAIT on 2008 March 3.45 UT [? ]. The for- extrapolation [? ], or, (iv), for type IIP supernovae, tuitous non-detection observation made by Arbour on via lightcurve modeling using the expanding 2008 March 3.19 UT [? ], a mere 6.24 h before the SN method (EPM; e.g., [?? ]). discovery, provides an excellent baseline estimate of the In order to select optically discovered core-collapse su- explosion time. The spectral type of SN 2008ax indicates pernovae as triggers for this search, we imposed the fol- that the progenitor was at least partially stripped of its lowing criteria: (i) Distance from Earth not greater than hydrogen envelope, but reliable information on the pro- 3 genitor’s radius are not available [? ]. To be conservative, variations [? ] or the Tully-Fisher relation [? ] are less we add an additional day to account for the uncertainty reliable, but give a somewhat lower distance estimate of in shock propagation time and define the GW on-source D = 7.7 ± 0.9 and D = 7.7 ± 1.3, respectively. We adopt window as 2008 March 2.19 UT to 2008 March 3.45 UT. the farther distance D = 8.4 ± 0.7 Mpc for the purpose The coordinates of SN 2008ax are R.A.= 12h30m40s.80, of this study. ◦ 0 00 Decl.= +41 38 14 .5 [? ]. Its host galaxy is NGC 4490,  [TODO: Discuss detector uptime vs. on-source window which together with NGC 4485 forms a pair of interacting plot.] with a relatively high rate. We adopt the distance D = (9.64+1.38−1.21) Mpc given by Pastorello et al. [? ], who obtained it by averaging over III. SEARCH OVERVIEW a number of Tully-Fisher/sosie estimates (see, e.g., [?? ] for a description of these methods). In this analysis, we considered four CCSN when some SN 2008bk, a Type IIP supernova, was discovered on of the Laser interferometers were collecting data and 2008 March 25.14 UT [? ]. Its explosion time is poorly for each of them we processed separately the different constrained by a pre-explosion image taken on 2008 Jan- fractions of time where a specific combination of de- uary 2.74 UT [? ]. Morrell & Stritzinger [? ] compared tectors was operational. Specifically for SN2007gr we a spectrum taken of SN 2008bk on 2008 April 12.4 UT processed data when the following network were avail- to a library of SN spectra [? ] and found a best fit able H1H2L1V1, H1H2L1, H1H2V1, H1H2, L1V1, for to the spectrum of SN 1999em taken at 36 days after SN2008ax G1H2, for SN2008bk G1H2, and for SN2011dh explosion [? ]. However, the next other spectra avail- G1V1. able for SN 1999em are from 20 and 75 days after ex- Two search algorithms are employed in this study: X plosion, so the uncertainty of this result is rather large. pipeline and Coherent Waveburst. While the two al- EPM modeling by Dessart [? ] suggests an explosion ghorithms produced background runs separately as well time of March 19.5 ± 5 UT, which is broadly consistent as establishing the significance of the loudest event in with the lightcurve data and hydrodynamical modeling the foreground (by comparing it with the probability of presented in [? ]. The progenitor of SN 2008bk was obtaining an equally loud or louder event in a compara- most likely a red supergiant with a radius of ∼500 R ble duration of background run - False alarm probability [??? ], which suggests an explosion time of .1 day (FAP)), the results were combined for the production of after core collapse [?? ]. Hence, we assume a con- the efficiency curves and establishing the model exclusion servative on-source window of 2008 March 13.5 UT to capabilities. 2008 March 25.14 UT. The coordinates of SN 2008bk are The general procedure for determining the efficiency R.A. = 23h57m50s.42, Decl. = −32◦3302100.5[ ? ]. Its curves is described in the following: (a) Each of the two host galaxy is NGC 7793, which is located at a Cepheid- pipelines established a relationship between the param- distance D = (3.44 + 0.21 − 0.2) Mpc [? ]. This distance eter used to quantify the ’loudness’ of an event and the estimate is consistent with D = (3.61 + 0.13 − 0.14) Mpc probability that an even equally loud or louder is pro- obtained by [? ] based on the tip of the branch. duced in a background run. (b) The loudest event of For the purpuse of this study, we use a conservative av- the 2 pipelines was converted into a FAP and the small- eraged estimate of D = (3.53 + 0.21 − 0.29) Mpc. est of the two became the threshold used by the two SN 2011dh, a type IIb supernova, has an earlierst alghorithms to derive the efficiencies. Only CAT2 data discovery date by amateur astronomers in the literature was processed. of 2011 May 31.893 [???? ]. An earlier discov- ery date of 2011 May 31.840 is given by Alekseev [? ] and a most recent non-detection by Dwyer on 2011 May A. Search Algorithm 31.365 [? ]. The progenitor of SN 2011dh was with high probability a yellow [? ] with a large This search is based on the Xpipeline and coherent radius of a few 100 R [??? ] for type IIb super- WaveBurst (cWB) algorithm [? ]. with a partially stripped envelope. We conserva- The cWB analysis is performed in several steps. First, tively estimate an earliest time of core collapse of a day detector data is decomposed into a time-frequency repre- before the most recent non-detection by Dwyer and use sentation and then whitened and conditioned to remove an on-source window of 2011 May 30.365 to 2011 May narrow-band noise features. Events are identified by 31.893. SN 2011dh’s location is R.A. = 13h30m05s.12, clustering time-frequency pixels with significant energy Decl. = +47◦1001100.30 [? ] in the nearby spiral galaxy which is coherent among detectors and characterized us- M51. The best estimates for the distance to M51 come ing test statistics derived from the likelihood (which is Vink´o et al. [? ], who give D = 8.4 ± 0.7 Mpc on the also a measure of the signal energy detected in the net- basis of EPM modeling of SN 2005cs and SN 2011dh. work and is calculated as described in [? ]). The primary This is in agreement with Feldmeier et al. [? ], who give statistics are the network correlation coefficient cc, which D = 8.4 ± 0.6 Mpc on the basis of lumi- is a measure of the degree of correlation between the de- nosity functions. Estimates using the surface brightness tectors, and the coherent network amplitude η, which 4 is proportional to the signal-to-noise ratio and is used totally (with 3D simulations). The waveforms belonging to rank events within a homogeneous sub-period. Both to this group (see (REF and the references within)) of these statistics are described in detail in [? ]. The are related to the following mechanisms (a) convection application of the event selection criteria is thoroughly and SASI (b) rotating core collapse and bounce (c) described in [?? ]. CWB scans a patch of a radius of Protoneutron star pulsations. 0.4 degrees around the correct location. CWB processed segments that are at least 600 second II) Semianalytic waveforms models that encompass long. some of the the most optimistic scenario. These include ADD DESCRIPTION OF X PIPELINE X pipeline (a) Long lasting rotational instabilities of the protoneu- uses the correct location to combine the streams in a tron star and (b) Torus fragmentation instabilities. ”scalar” search over which thresholds are applied. III) Ad Hoc signal models (sine Gaussians) that probe certain regions of the time frequency plane and that allow to produce upper limits in the amount of energy produced by the source for test directionalities B. Background Estimation of emission. Such upper limit would not make sense for the scenarios I and II where the total energy emission is We estimate the distribution of background events by one of the output of the calculations. performing the analysis on time-shifted data, typically in ∼ 1 s steps. The shifts minimize the chance of drawing an The polarization status that was adopted for the actual GW into the background sample. To accumulate a different simulated waveforms is elliptical for sources sufficient sampling, this shifting procedure is performed assumed to be rotating and not axisymmetric The hundreds or thousands of times without repeating the injected waveforms can be parametrized as: same relative time shifts among detectors. Background " # " 2 # " # h (t) 1+α H (t) events corresponding to times which are flagged by CAT2 + = A × 2 × + , (3.1) data quality studies are discarded, just as an event candi- h×(t) α H×(t) date from the foreground would be. X pipeline performs 2000 time lags with shifts of one second while CWB per- where A is the amplitude, α the ellipticity is the cosine forms 200 timelags with a shift of one second and analizes of the source inclination angle, i.e. the angle between all resulting segments longer than 600 seconds. the source rotational axis and the line of sight to Earth. and H+/× are the waveforms for the two independent polarizations. C. Simulated Signals and Detection Efficiencies For 2-D and axisymmetric models we used simulated signals that were linearly polarized. This follows from the fact that the emitted gravitational waves in terms of The primary goal of this study is to use the temporal spin-weighted tensor spherical harmonics [?? ] with and geographycal information of the closest CCSNs source-frame angles θ and φ needs to be independent of so that we can search deeper in the noise for GW φ. In fact if the following decomposition signals generated by these astronomical events. In the ∞ ` case of a non detection we can use the data and the M X X h − ih = H (t) −2Y (θ, φ) , (3.2) search alghorithms to quantify our capability to detect + × r `m `m representative CCSN waveforms and discuss if certain `=2 m=−` models can be experimentally discarded. −s has to be independent of φ than m=0 because Ylm is given by a real number times eimφ. In this case the The main figures of merit that are used in these quadrupole component of H`m(t) is real and therefore, to kinds of analyses are efficiency curves describing the quadrupole order h× is zero. The table 1 and 2 describe probability of the alghorithms to detect injected signals the waveforms adopted in this study. For the produc- with respect to certain scale factors. The pool of signals tion of the efficiencies, waveforms were added in the data adopted here mirrors the families of signals identified every 100 seconds plus a random time contained in the as interesting and representative in a companion paper interval [−10s, 10s]. The relative delays of the two po- [REf]. larizations for elliptical signals were consitent with the sky location of the CCSN at that specific sidereal time The waveforms can be loosely organized in 3 groups: as well as the antenna patterns. The ad Hoc waveforms were modelled accordingly to: I) waveforms generated numerically by applying numerical relativity evolution schemes that break the • Sine-Gaussian: spherical symmetry of the source either partially (by 2 2 H+(t) = exp (−t /τ ) sin(2πf0t) (3.3) preserving the axial symmetry of the ellipsoid of inertia 2 2 with respect to the original rotational axis of the star) or H×(t) = exp (−t /τ ) cos(2πf0t) (3.4) 5

Waveform Type Ref. Model Name hrss fpeak egw Polarizations −22 −8 2 [10 @10 kpc] [Hz] [10 M c ] Rotating Core Collapse [? ] Dim-s15A2O05ls + Rotating Core Collapse [? ] Dim-s15A2O09ls + Rotating Core Collapse [? ] Dim-s15A3O15ls + 2D Convection [? ] Yakunin-s15 + 3D Convection [? ] M¨uller-L15-3 +, × 3D Convection [? ] M¨uller-N20-2 +, × 3D Convection [? ] M¨uller-W15-4 +, × Protoneutron Star Pulsations [? ] Ott-s15 + −19 2 ciao [10 @10 kpc] [M c ]

TABLE II:  [TODO: Table data to be updated; not final.] The model name, maximum gravitational wave strain (|h|max), peak frequency of gravitational wave emission (fpeak) and total energy emitted in gravitational waves (EGW) for the numerical waveform injections utilised in this paper.

Waveform Type Ref. Model Name hrss EGW −19 2 [10 @10 kpc] [M c ] Long-lasting Bar Mode [? ] M0p2L60R10f400t100 WAITING ON ANGLE-AVG 2.88 × 10−4 Long-lasting Bar Mode [? ] M0p2L60R10f400t1000 WAITING ON ANGLE-AVG 2.89 × 10−3 Long-lasting Bar Mode [? ] M0p2L60R10f800t100 WAITING ON ANGLE-AVG 1.68 × 10−2 Long-lasting Bar Mode [? ] M1p0L60R10f400t100 WAITING ON ANGLE-AVG 7.20 × 10−3 Long-lasting Bar Mode [? ] M1p0L60R10f400t1000 WAITING ON ANGLE-AVG 7.21 × 10−2 Long-lasting Bar Mode [? ] M1p0L60R10f800t25 WAITING ON ANGLE-AVG 1.04 × 10−1 Torus Fragmentation Instability [? ] piroM5.0eta0.3fac0.2 WAITING ON ANGLE-AVG 1.78 × 10−3 Torus Fragmentation Instability [? ] piroM5.0eta0.6fac0.2 WAITING ON ANGLE-AVG 2.87 × 10−2 Torus Fragmentation Instability [? ] piroM10.0eta0.3fac0.2 WAITING ON ANGLE-AVG 4.75 × 10−3 Torus Fragmentation Instability [? ] piroM10.0eta0.6fac0.2 WAITING ON ANGLE-AVG 7.96 × 10−2 Sine-Gaussian [? ] 235HzQ8d9linear Sine-Gaussian [? ] 1304HzQ8d9linear Sine-Gaussian [? ] 235HzQ8d9elliptical Sine-Gaussian [? ] 1304HzQ8d9elliptical

TABLE III:  [TODO: Table data to be updated; not final] The model name, root sum square gravitational wave strain (hrss) and total energy emitted in gravitational waves (EGW) for the numerical waveform injections utilised in this paper.

√ where τ = Q/( 2πf0). position (Θ, Φ), and on the polarization angle ψ. The sky positions of simulated signals are distributed accord- The simulated signals were injected with many ampli- ing to the recorded sky location. tude scale factors to trace out the detection efficiency as The detection efficiency is defined as the fraction of a function of signal strength. The amplitude of the sig- signals successfully recovered using the same selection nal is expressed in terms of the root-sum-square strain thresholds and DQFs. The detection efficiency of the amplitude (h ) arriving at the Earth, defined as: rss search depends on the network configuration and the se- lection cuts used in the analysis. sZ 2 2 hrss = |h+(t)| + |h×(t)| dt (3.5) D. Systematic Uncertainties The signal amplitude at a detector is modulated by the detector antenna pattern functions, expressed as follows: The most relevant systematic uncertainty in the astro- physical interpretation of our results is due to the cal- h (t) = F (Θ, Φ, ψ)h (t) + F (Θ, Φ, ψ)h (t) (3.6) det + + × × ibration error on the strain data produced by each de- where F+ and F× are the antenna pattern functions, tector [?? ]. The effect of calibration systematics on which depend on the orientation of the wavefront rela- network detection efficiency has been estimated by dedi- tive to the detector, denoted here in terms of the sky cated simulations of GW signals in which the signal am- 6

SN Network hrss SGlin2 piro5 numerical3 SGel2 Acknowledgments 2007gr H1H2L1V1 50% 1.4e-21 2.8e-22 2.1e-22 1.3e-21 90% 2.1e-20 1.4e-21 8e-21 4.9e-20 We thank L. Dessart for applying the expanding pho- H1H2L1 50% 1.7e-21 2.9e-22 2.5e-22 1.5e-21 tosphere method to SN 2008bk to derive an approximate 90% 1.2e-20 1.4e-21 8.9e-21 4.5e-21 explosion date and A. Howell for access to his supernova spectra fit software superfit. The authors gratefully ac- H1H2V1 50% 1.7e-21 3e-22 2.6e-22 1.6e-21 knowledge the support of the United States National Sci- 90% 1.4e-20 1.5e-21 NaN 4.1e-21 ence Foundation for the construction and operation of the H1H2 50% 1.7e-21 3.6e-22 3.1e-22 1.5e-21 LIGO Laboratory, the Science and Technology Facilities 90% 9.8e-21 1.7e-21 8.8e-21 4.3e-21 Council of the United Kingdom, the Max-Planck-Society L1V1 50% 1.9e-20 9.1e-22 6.8e-21 4.3e-21 and the State of Niedersachsen/Germany for support of 90% NaN 5.5e-21 NaN 1.2e-20 the construction and operation of the GEO 600 detector, 2008ax pending and the Italian Istituto Nazionale di Fisica Nucleare and 2008bk pending the French Centre National de la Recherche Scientifique for the construction and operation of the Virgo detec- 2011dh G1V1 pending tor. The authors also gratefully acknowledge the sup- port of the research by these agencies and by the Aus- tralian Research Council, the Council of Scientific and Industrial Research of India, the Istituto Nazionale di plitude and phase at each detector is randomly jittered Fisica Nucleare of Italy, the Spanish Ministerio de Edu- according to the modeled distribution of calibration er- caci´ony Ciencia, the Conselleria d’Economia Hisenda i rors for that detector. The resulting network detection Innovaci´oof the Govern de les Illes Balears, the Foun- efficiency marginalizes the effect of the systematic uncer- dation for Fundamental Research on Matter supported tainties over the observation time. The main effect can by the Netherlands Organisation for Scientific Research, be parametrized as an overall shift of the detection effi- the Polish Ministry of Science and Higher Education, the ciency curves along the signal strength axis. The largest FOCUS Programme of Foundation for Polish Science, the effect over the injected signal waveforms was a 8% in- Royal Society, the Scottish Funding Council, the Scottish crease of the hrss amplitude at fixed detection efficiency. Universities Physics Alliance, the National Aeronautics To produce the astrophysical limits shown in Section IV, and Space Administration, the Carnegie Trust, the Lev- we use the reduced detection efficiency curves obtained erhulme Trust, the David and Lucile Packard Founda- by shifting the original fits from Subsection III C and the tion, the Research Corporation, and the Alfred P. Sloan results in Tables to 8% larger hrss values. Foundation. This document has been assigned LIGO Laboratory document number LIGO-P1100118-v16.

APPENDIX A: DATA QUALITY FLAGS IV. SEARCH RESULTS

Data Quality Flags (DQFs) are intended to indicate The results for the two different pipelines will be pre- periods of data taking which suffer from environmental sented side by side. and instrumental effects inducing noise into the data [? ]. We followed the DQF strategy used in previous searches [??? ], organizing DQFs into 3 categories. The dif- ferent categories reflect the level of understanding of the V. SUMMARY AND DISCUSSION detectors’ performances as well as of the relation between disturbances in the data set and environmental or instru- mental causes. This paper reports the results achieved by the LIGO Category 1 DQFs mark segments of time (typically and Virgo detectors in the search for GW transients in more than tens of seconds) when disturbances make anal- coincidence of optically observed Core Collapse SNs. ysis unfeasible. Data segments remaining after their ap- The long baseline interferometric detectors LIGO and plication are used in the analysis. Virgo are currently being upgraded to their advanced Category 2 DQFs are connected to well-understood configurations, and the next joint observation is planned short duration (typically a few seconds) periods of noise for 2015. Another advanced detector, LCGT [?? ], is transients. Data segments flagged by this category can be being built in Japan, and there are proposals to realize used for data conditioning and noise property estimation, an additional advanced LIGO detector outside the USA. but events emerging from these periods are discarded as These advanced detectors should achieve strain sensitiv- very likely originating from the detector environment. ities a factor of ten better than the first-generation de- Finally, Category 3 DQFs denote periods that are tectors. only weakly correlated to environmental and instrumen- 7 tal monitors and were not used in this analysis (similarly the observable of interest is typically either root-sum- to the traditional GRB searches). square GW strain at the detector (hrss) , GW emission −1 energy EGW, or source distance (d ∝ hrss ). The signal is convoluted with the detector’s response function and APPENDIX B: MODEL EXCLUSION METHOD noises and may produce an “analysis event.” In general an analysis event is anything interesting in the analyzed data, and could be a time- and frequency-limited burst In this appendix we describe a simple and general of excess power, for example [? ]. An analysis event in method for quantifying the confidence of null-detection the signal region might correspond to either noise or a model exclusion statements given non-stationary detec- transient GW signal that is not strong enough to claim tors (or detector networks) and multiple observational a detection. The analysis must define a ranking statistic events. We illustrate the method with a hypothetical with which to calculate the ‘loudness’ of analysis events. search for GWs from CCSNe. The conclusion we draw from P (x) depends on a par- In this paper the upper limit constructions are used ticular model M. If M predicts the value of the observ- mainly for excluding a particular model of emission in the able of interest associated with the observational event, case of one or multiple non detections. This usage is also xM , then we can state the exclusion confidence P (xM ). determined by the fact that in externally triggered SN If M predicts a range in x, we may be able to exclude searches we usually know the distance and the models of a region of model-space. We can find the 90% detection emission provided by the numerical relativity community efficiency loudest event upper limit x90%, which is the have a fixed total GW energy emission. Standard upper value of x at which 90% of analysis events associated limits could be interesting to be produce, however, if ap- with simulations predicted by M would be louder than plied to the content in particular time frequency regions the loudest signal region event. This results in the 90% (by injecting for example sine gaussian waveforms in the confidence limit for the model M and the observational data). event, the red construction in Figure ??. We see that loud It is worth noticing that the idea of producing upper analysis events in the signal region diminish the excluding limits on some rescaling parameters with targeted SN power of the data (but have a larger likelihood of being searches was proposed in [? ], even if the article does not GW signals). adress how to deal with long onsource regions with gaps or on how to combine results from different SNs. It is also worth mentioning the work [? ] which introduced 2. Non-stationary detector observing one event the usage of the inverse of the probability of obtaining a trigger with a given loudness as a ranking measure for the triggers of different data segments. The advantage of We now discuss the case of one observational event this approach is that it prevents that the loudest events with a model-predicted signal region covered by a non- in noisy data damage the efficiencies produced in quieter stationary detector. A detector is non-stationary if its data simultaneously analyzed. In [? ] it is suggested that properties change over time. Here, we consider changes even in the case of a detection it is possible to produce in detector sensitivity, or the detector turning on and off. upper limits on some parameters. In this case the most A network of multiple detectors independently turning common approach is the one of performing parameter on and off can be thought of as a single non-stationary estimation and model selection as described in [? ]. detector comprised of the individual instruments. Finally we envision that that in the detection era, when This case can be analyzed in the same way as the sim- SN signal will be regularly observed, both detections and pler single detector, 100% duty cycle case introduced non detections in fragmented on source data segments above: add simulated signals randomly into the entire could be used to constrain where the GW emission is signal region and construct the efficiency curve. The pro- more likely to have happened within the window of un- cedure requires no modification. Simulated signals which certainty that comes from the electromagnetic observa- fall into regions where no detector is observing will, of tions. course, not be detected, and will not be counted in the detected fraction of the efficiency curve. While in this example the detectors change discretely, the same proce- dure will also work in the case of continuously changing 1. Loudest event limits detectors. (In practice, GW detectors change continu- ously.) We begin by reviewing the frequentist loudest event We assume a flat probability density function for limit construction, consistent with procedures described the location of the observational event (for example, a in [?? ] and used in astrophysical GW searches for CCSN) within this signal region. We can make an ex- burst-like signals such as [???? ]. Any physical ob- clusion statement for a model M, which predicts a sig- servable which can be expressed as a monotonic function nal from the event with some specific value xM for the of the signal amplitude may be constrained; we refer to it observable of interest (which could correspond to the as the observable of interest. In the case of GW searches, CCSN GW strain, for example) following the procedure 8 in Section B 1, except in this case the efficiency curve will lar GW emission pattern during the CCSN event. We asymptote to the overal duty cycle P (x = ∞) = 0.8. We can constrain the model using observations from multi- could make a statement such as,“We exclude the model ple CCSN events at known distances di. M with 80% exclusion confidence” if xM were greater First, efficiency curves are constructed for the indi- than three, for example. With a single event this is the vidual events, Pi(d). Here, the observable of interest is best we can do. For any value of xM predicted by the source distance, d, and the amplitudes of the simulations model, we can find the corresponding fraction detected, predicted by MSN are scaled according to the inverse of which can be interpreted as the exclusion confidence. the hypothetical distance to the CCSN (we imagine let- We note that the method can be generalized to the case ting the source distance vary). Then the known distance where the probability density function for the event loca- to the source di is drawn as a vertical line on the curve tion with the signal region ts is assigned a non-flat prior. and the model exclusion confidence Pi(di) is read off from In this case the time location for each simulated signal the y-axis. within the signal region is chosen randomly according to These Pi(di) are combined into the overall exclusion the prior PDF, whatever that may be. No other change confidence, : is necessary. N Y  = 1 − (1 − Pi(di)) (B3) 3. Multiple events i=1

Consider two independent but identical astrophysical if we multiply all the distances for a rescaling factor α events, occurring within distinct signal regions each with which aquires its physical value at 1. We can calculate  detector duty cycle of 0.5, neither of which is detected. as a function of α. The probability of missing detectable signals from both events is 1/4, and we can exclude the model M with up to We are free to choose a different observable of in- 75% exclusion confidence. In general, for N independent terest for the same physical processes. In the case of unmodlelled waveforms we could equally well begin by observational events with duty cycles Ci (the fraction of the signal region observed by the detector for the ith constructing efficiency curves for the individual obser- event), the maximum exclusion confidence is vational events using emitted GW energy, EGW. These individual efficiency curves Pi(EGW) are combined into N the total exclusion confidence curve, P(EGW) via Y max = 1 − (1 − Ci). (B1) N i=1 Y PT (EGW) = 1 − [1 − Pi(EGW)] (B4) It is possible that some of the null detections from i=1 these observational events will not fully constrain the model, given the detector sensitivity. In this case, we PT (EGW) gives the exclusion confidence as a proba- construct the individual efficiency curves and find the bility as a function of EGW, which folds in the known values Pi(xM ) for each observational event. Then the distances di: observational exclusion confidence is 3 Z ∞ 2 c  ˙ 2 ˙ 2 N EGW = 4πdi (hi+) + (hi×) dt. (B5) Y 16πG −∞  = 1 − (1 − Pi(xM )). (B2) i=1 M Then the energy predicted by the model M, EGW, is For example, consider a CCSN model MSN which pre- drawn as a vertical line on the curve and the total model dicts an energy of GW emission EGW and a particu- exclusion confidence  is read off from the y-axis.