On Discovering Electromagnetic Emission from Neutron Star Mergers: The Early Years of Two Gravitational Wave Detectors
DDraft version October 29, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
ON DISCOVERING ELECTROMAGNETIC EMISSION FROM NEUTRON STAR MERGERS:THE EARLY YEARS OF TWO GRAVITATIONAL WAVE DETECTORS
Mansi M. Kasliwal & Samaya Nissanke Draft version October 29, 2018
ABSTRACTWe present the first simulation addressing the prospects of finding an electromagnetic (EM) coun-terpart to gravitational wave detections (GW) during the early years of only two advanced interfer-ometers. The perils of such a search may have appeared insurmountable when considering the coarsering-shaped GW localizations spanning thousands of deg using time-of-arrival information alone. Weshow that leveraging the amplitude and phase information of the predicted GW signal narrows thelocalization to arcs with a median area of only ≈
250 deg , thereby making an EM search tractable.Based on the locations and orientations of the two LIGO detectors, we find that the GW sensitivityis limited to one polarization and thus to only two sky quadrants. Thus, the rates of GW eventswith two interferometers is only ≈
40% of the rate with three interferometers of similar sensitivity.Another important implication of the sky quadrant bias is that EM observatories in North Americaand Southern Africa would be able to systematically respond to GW triggers several hours soonerthan Russia and Chile. Given the larger sky areas and the relative proximity of detected mergers,1m-class telescopes with very wide-field cameras are well positioned for the challenge of finding an EMcounterpart. Identification of the EM counterpart amidst the even larger numbers of false positivesfurther underscores the importance of building a comprehensive catalog of foreground stellar sources,background AGN and potential host galaxies in the local universe.
Subject headings: gravitational waves — binaries: close — stars: neutron — surveys — catalogs INTRODUCTION
The advent of advanced ground-based interferometersthis decade is expected to usher in the era of routine grav-itational wave (GW) detection (Barish & Weiss 1999;LIGO Scientific Collaboration 2008; Accadia et al. 2011;Somiya 2012). Binary neutron star (NS) mergers are an-ticipated to be amongst the most numerous and strongestGW sources (Abadie et al. 2010). NS mergers are pre-dicted to produce neutron-rich outflows and emit electro-magnetic (EM) radiation across many wavelengths andtimescales as the ejected debris interacts with its environ-ment — gamma (e.g., Eichler et al. 1989; Paczynski 1991;Narayan et al. 1992), optical (e.g., Li & Paczy´nski 1998;Kulkarni 2005; Metzger et al. 2010; Roberts et al. 2011;Piran et al. 2012; Rosswog 2013), infrared (e.g., Barnes& Kasen 2013; Kasen et al. 2013; Tanaka & Hotokezaka2013; Grossman et al. 2013) and radio (e.g., Hansen &Lyutikov 2001; Pshirkov & Postnov 2010; Nakar & Piran2011).The discovery and characterization of the EM counter-parts to GW detections promises to unravel astrophysicsin the strong field gravity regime. Moreover, such EM-GW events will serve as the litmus test for whether NSmergers are indeed the sites of r-process nucleosynthe-sis (and hence, responsible for producing half the ele-ments heavier than iron including gold, platinum anduranium; e.g. Lattimer & Schramm 1976; Mathews &Cowan 1990). The accompanying surge of excitementin preparation for this endeavor has been described asanalogous to the “gold rush” (Kasliwal 2013). The Observatories, Carnegie Institution for Science, 813Santa Barbara St Pasadena, California 91101 Theoretical Astrophysics, California Institute of Technology,Pasadena, CA 91125, USA
In Nissanke et al. 2013 (hereafter, Paper I), we un-dertook an extensive end-to-end simulation on how toidentify the elusive EM counterpart of a GW detectionof NS mergers. We started with simulated astrophysicalpopulations of NS mergers, evaluated GW detectabilityand considered three critical steps: (1) GW sky local-ization and distance measures using different worldwidenetworks of three to five GW interferometers, (2) sub-sequent EM detectability by a slew of multiwavelengthtelescopes, and (3) identification of the merger counter-part amongst a possible fog of astrophysical false-positivesignatures. We showed how constructing GW volumesand local Universe galaxy catalogs, can help identify andreduce the number of false-positives, thereby enabling asecure EM identification.Paper I simulated mergers detected by a network ofthree to five GW interferometers. However, given pro-jected timescales for construction of advanced GW in-terferometers, it appears that the early years (and pos-sibly the first detections) could be limited to a networkof only two LIGO interferometers (LIGO Scientific Col-laboration 2013).In this letter, we consider new observational challengesspecific to a network of only two GW interferometers. Wederive GW localization arcs ( § § § § § GW METHOD: DETECTION AND SOURCECHARACTERIZATION
As detailed in § × NS-NSbinaries out to a limiting redshift z = 0 .
5. Parametersinclude: binary masses, luminosity distance D L , inclina- a r X i v : . [ a s t r o - ph . H E ] S e p Kasliwal & Nissanketion angle to the observer’s line-of-sight cos ι , GW po-larization angle ψ , and sky position n (where ˆ n ≡ ( θ, φ )is the unit vector pointing to a binary on the sky froma fixed Earth coordinate system, θ is the colatitude and φ is the longitude). We associate each binary with arandom orientation and sky position, and distribute themergers assuming a constant comoving volume densityfor D L >
200 Mpc (ΛCDM, Komatsu et al. 2009) or us-ing a B-band luminosity galaxy catalog (CLU; Kasliwal2011) for D L <
200 Mpc.Next, we select the NS mergers that are detectable withonly the two LIGO interferometers at positions x H and x L (the subscripts denote the Hanford and Livingstonsites, hereafter LIGO-H and LIGO-L). GW detection andsource characterization methods use optimum matchedfiltering between GW predictions and simulated detectorstreams (see § h M at a particular detector x H or x L is the sum ofthe two GW polarizations, h + and h × , each weighted bytheir antenna response functions F + , [ H / L ] and F × , [ H / L ] ,and multiplied by a time-of-flight correction. The timedelay of the signal between the detector and the coor-dinate origin is given by τ [ H / L ] ∼ ˆ n · x [ H / L ] /c , where c is the speed of light. h + and h × are functions of D L ,cos ι , masses, and the GW frequency f . The antennaresponses, F + , [ H / L ] and F × , [ H / L ] , depend on ˆ n and ψ .Based on triangulation with three or more interferom-eters, the time delay factor dominates over amplitudeeffects in the GW waveform when reconstructing sky lo-cation errors for the majority of sources (Nissanke et al.2011; Veitch et al. 2012).For LIGO-H and LIGO-L, we assume two anticipatednoise curves at mid and full sensitivity (the upper redand black lines in Figure 1 of LIGO Scientific Collab-oration 2013) and idealized noise. We define a binaryto be GW detectable if its expected signal-to-noise ratio(SNR) at each detector is > > § Net2a denotesa LIGO-H and LIGO-L network using such a coincidenttrigger, whereas
Net2b corresponds to an expected net-work SNR trigger of > § θ , φ ). We took particular care to start each MCMCchain at random all-sky positions.Finally, to better understand our MCMC derivedmeasures, we also implement two toy models usingamplitude-only GW waveforms. The first model incorpo-rates only time-of-arrival information, whereas the sec-ond incorporates a combination of time-of-arrival andthe detector antenna responses. Our second toy modelassumes a 5-D GW waveform of the form: h T + F ∼ exp i πτf (cid:104) F + (ˆ n , ψ ) (1+cos ι ) D L + F × (ˆ n , ψ ) − ιD L (cid:105) , wherewe take f = 100Hz. By simulating hundreds of noise real-izations, we map out the likelihood function for (cos θ, φ )for randomly orientated and located binaries on the skyat different SNRs [ H / L ] . GW RESULTS: DISTANCE, LOCALIZATION ARCS, ANDSKY SENSITIVITY
In Figure 1(a), we show the cumulative distance dis-tributions of NS mergers detectable using only LIGO-Hand LIGO-L at full-sensitivity. As expected, the distancedistribution of mergers detected by Net2a is similar tothose detected with Net3a-Net5a in § ∼ § compared with 17 deg in Net3a. As in PaperI, we expect NS black-hole (BH) binaries to show a dis-tribution similar to NS-NS. At mid-sensitivity, we expectthe specific distribution in sky localizations to be similarto those at full-sensitivity because the majority of merg-ers will be detected at the SNR threshold (distributionnot shown here due to small number of detections).In Figure 2, we show the localization shapes, ori-entation and sky position of detected mergers at full-sensitivity. Using only time-of-arrival of signals at LIGO-H and LIGO-L, sky localization estimates have so farpredicted annular error rings for non-spinning mergersof several thousand deg (LIGO Scientific Collaboration2013). Instead, we find that inclusion of F + (ˆ n , ψ ) and F × (ˆ n , ψ ) in the GW waveform’s amplitude significantlyimproves localization errors to arcs comprising severalhundred deg . For Net 3–Net 5, we found that degenera-cies between parameters result in non-contiguous areasfor a handful of threshold mergers. (Nissanke et al. 2011).Furthermore, we do not measure mirror-image arcs onthe sky for any of the detected binaries in our small sam-ple. Indeed, for a single spinning NS-BH merger usingtwo initial LIGO sensitivities, Raymond et al. (2009) gen-erated a localization arc by including the BH’s spin.Investigations with our two toy models improve ourunderstanding of the MCMC results. Using only time-of-arrival, averaging over a hundred noise realizations, wefind GW localizations of almost annular rings of 1000sdeg . Adding detector antennae information to the samebinary, we find smaller GW arcs of 100s deg in onlyone sky quadrant as long as the network SNR > SNR crit ,where SNR crit ranges from 8–12 depending on orientationand sky position. Below SNR crit , the shapes depend onindividual noise realizations and we find mirror imagesof GW arcs in different sky quadrants using h T + F .The quadrupolar antenna patterns of LIGO-H andLIGO-L are oriented such that they are sensitive to iden-tical GW polarizations. Figure 2 shows that Net2 havesignificantly reduced sensitivity in two out of four skyquadrants for sources arriving in the plane of the inter-ferometer arms. In contrast to Net3-5, we do not finda strong correlation between the D L and sky error as aresult of the two-quadrant sky sensitivity. We find thattwo binaries at the same distance can have localizationareas differing by an order of magnitude based on skyposition.Out of our underlying population, we find that only17 ± ± ± ±
12 mergers were detected us-arly Years of EM-GW searches 3ing the corresponding Net3a and Net3b respectively (Ta-ble 1 of Paper I). Therefore, Net2 will detect ≈ EM DETECTABILITY (TRIGGERED):RESPONSE-TIME, TILING AND DEPTH
Our GW results, indicating a sky quadrant bias andcoarse arc-shaped localizations, present new challengesfor triggered EM follow-up. (The challenge for contem-poraneous, independent detection in the γ -rays or X-raysor low frequency radio is unchanged.) Given the medianlocalization of 250 deg (at 95% c.r.), we find the tiling iscurrently beyond the scope of existing infrared, ultravio-let and millimeter facilities. Hence, we consider follow-upby a representative set of optical facilities, with telescopeapertures spanning 0.5–8 m and camera angles spanning2–50 deg (see Table 1), and simulate relative detectabil-ity.Due to the Net2 sky quadrant bias (Figure 2), merg-ers are preferentially detected overhead in the north andat hour angles around twelve in the south (relative toLST at LIGO-H/LIGO-L). Consequently, an EM obser-vatory located around the same longitude as LIGO canrespond instantly if located in North America but onlyhalf a day later in Chile (see Table 1). This time-lag inresponse is critical for afterglows, which fade as a power-law in time, and some kilonova models, which fade onfew hours to day timescales. It is not relevant for radiofacilities looking for late-time emission on the months toyear timescale.Due to the elongated arc-shape and the coarser local-ization of hundreds of deg , tiling presents a major chal-lenge. We compute an optimal tiling pattern to coverthe GW localization contour (95% c.r.) for each mergerat each EM facility (Figure 3). While the widest cam-eras need <
20 pointings, other facilities need hundredsof pointings. Naive division of the localization area bythe camera field of view grossly underestimates the actualnumber of pointings required. This tiling inefficiency fac-tor has a median value of 1.6 for BG4/HSC, 1.8 for DE-CAM, 2.0 for LSST/PS1, 2.3 for ATLAS and 2.6 for ZTF.The localization arcs have a median width of 6.5 ◦ (inagreement with time-of-arrival estimates e.g., Fairhurst2010). Narrow-angle cameras can tile more nimbly thanwide-angle cameras (e.g., the BG4 tiling is 30% moreefficient than the contiguous PS1).With the number of pointings in-hand for each binaryand for each EM facility, we compute the maximum ex-posure time (and hence, depth) allowable in a fixed du-ration. We assume three epochs (dithered to cover chipgaps) of one hour each with a detection above 5 σ in atleast two epochs as minimum criterion for EM detection.We take into account overhead between exposures whichis dominated by readout for large mosaic cameras. Giventhe distance to each binary in our simulation, we convertthe apparent magnitude depth to a luminosity.Our detectability simulation results for Net2 are verydifferent from those in Paper I for Net3–5. Figure 4shows that small telescopes with large camera angles(e.g., ZTF) are more competitive than large telescopeswith small camera angles (e.g., HSC) for detecting coun- terparts with an i -band luminosity brighter than M i = − § EM IDENTIFICATION: FALSE POSITIVES
Optical detection of candidate EM counterparts in asingle epoch is only the first step. Multiple epochs areessential to distill the true EM counterpart from thou-sands of astrophysical false positives in the foreground(e.g., moving objects in solar system, variable stars inMilky Way) and background (e.g., supernovae and AGNin higher redshift galaxies). An ongoing survey of thesame sky location to a similar depth would provide ahistoric baseline of variability of unrelated sources andserve as a severe filter.Timely identification of the EM counterpart is criticalfor obtaining spectroscopic and multi-wavelength follow-up before the transient fades. In § A Beamed Merger (391 Mpc):
On account of the skyquadrant bias, this merger is not detected by Net2 de-spite being beamed towards us. Given the lower rate ofmergers detected with Net2 and the small fraction thatis beamed ( < < ◦ ), we maynot have the luxury of the relatively easier search for theEM counterpart of a beamed merger in the early yearsof Net2. A Close-in Merger (69 Mpc):
Net2 localizes thismerger to 23 deg at full sensitivity and 32 deg at mid-sensitivity. This is a factor of ≈
40 – 50 coarser than Net3. Thus, the number of false positives would be propor-tionately larger and it is even more important to havea complete catalog of nearby galaxies. The fraction of“golden” binaries that are closer than 100 Mpc remains ≈ A High Galactic Latitude Merger (139 Mpc):
WhileNet 3 localized this merger to 19.5 deg , Net2 localizesthis to 223 deg at full sensitivity (it is not detected atmid-sensitivity due to its distance). Therefore, there areten times more background sources and it is even moreimportant to have a complete catalog of nearby galaxiesand AGN variability. A Low Galactic Latitude Merger (125 Mpc):
While Net3 localized this merger to 1.8 deg , Net2 localizes this to100 deg and 810 deg at full and mid-sensitivity respec-tively. Thus, the foreground is 55 times larger and it iseven more important to build a catalog of stellar sources. A Galaxy Cluster Merger (115 Mpc): . On account ofthe sky quadrant location, this merger is not detected byNet2 despite being relatively nearby. Kasliwal & Nissanke DISCUSSION
The EM-GW challenge for NS mergers is three-fold:the GW localizations are wide (few hundred deg ) andthe predicted EM counterparts are faint (M i ≈ −
12 to −
16 mag) and fast (few hours to few days). With LIGO-H and LIGO-L, we derive arc-shaped localizations with amedian area of 250 deg that are biased to only two skyquadrants. The rate of GW-detectable mergers is ≈ < to be best positioned forsearching for EM counterparts brighter than M i < − > , is uniquely po-sitioned to find faint EM counterparts. A plannedlarge time investment, facilitation of camera avail-ability and minimization of overheads betweenpointings are recommended to be able to efficientlytile a larger fraction of mergers.Independent of telescope size, the efficiency of a ro-bust, real-time transient detection pipeline is an essen-tial factor in assessing detectability. High quality imagesubtraction requires a deep pre-explosion reference im-age of the same sky location, preferably taken with thesame EM facility. Reliable candidate vetting needs a vet-eran machine learning algorithm, preferably trained ona large set of previous transient detections by the sameEM facility. Thus, two facilities with identical hardwarebut disparate software would have different EM-GW de-tection capabilities.Ongoing surveys have already successfully demon-strated the capability to discover optical transients whichovercome the challenges of wide/faint/fast, but one at atime. For example, the discovery of an afterglow in 71deg addresses the wide challenge (Singer et al. 2013),the discovery of multiple transients spanning kilonovaluminosities addresses the faint characteristic (review inKasliwal 2012) and the discovery of a relativistic explo-sion decaying on an hour timescale addresses the fast evolution (Cenko et al. 2013). Future surveys shouldprepare to simultaneously address all three challenges.In summary, the early years of a small number of coarseGW localizations will be challenging but tractable for anEM search. The combination of camera angle, telescopeaperture, observatory location and survey software foreach EM facility will delineate a different range in EM emission timescale and luminosity. A multi-pronged EMsearch would provide robust constraints on the vast phasespace of kilonovae (ejecta mass, velocity and composi-tion). The findings of early searches will help plan EM-GW identifications to a larger number of better localizedmergers in the era of three to five GW interferometers.We thank C. Hirata and E. S. Phinney for careful read-ing of the manuscript. We acknowledge valuable discus-sions with E. Bellm, J. Bloom, Y. Chen, J. M. D´esert, A.Georgieva, P. Groot, C. Galley, S. Mohta and D. Reitze.We thank D. Kasen for making kilonova models available.MMK acknowledges generous support from the HubbleFellowship and Carnegie-Princeton Fellowship. SMN issupported by the David & Lucile Packard Foundation.arly Years of EM-GW searches 5 TABLE 1
Facility Aperture Field-of-View Exposure Overhead Sensitivity Detectable Fraction Lag(m) (deg ) (sec) (sec) (5 σ , i-mag) ( − − −
12 mag) (hr)Palomar: Zwicky Transient Facility (ZTF) a ± b × × ± c ± d ± e ± f ± g ± a Kulkarni 2012, E. Bellm priv. comm. b c http://pan-starrs.ifa.hawaii.edu d J. Tonry priv. comm. e D. DePoy priv. comm., Bernstein et al. 2012 f g LSST Science Collaborations 2009
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Kasliwal & Nissanke S pe c i f i c D e t e c t ed B i na r y F r a c t i on (a) NS-NS mergers: Luminosity Distance
10 100 1000Area (sq deg)0.00.20.40.60.81.0 S pe c i f i c D e t e c t ed B i na r y F r a c t i on (b) NS-NS mergers: Sky errors Fig. 1.—
Cumulative distribution in luminosity distance (top panel) and 95% confidence sky error (bottom panel) of NS-NS mergers.Red lines denote a network of two GW interferometers. Gray lines denote Net 3–5 as presented in Paper I. We require an expected networkSNR >
12 and normalize to each specific network. arly Years of EM-GW searches 7 ° S 45 ° S 0 ° ° N ° N 0h 12h6h 9h3h 15h 18h 21h 24hGW SNR< 12.012.0 − − −
30> 30
Fig. 2.—
Sky location and localization arcs of mergers detected by LIGO-H and LIGO-L. Color represents expected network SNR. Notethat the quadrupolar antenna pattern has a bias towards two sky quadrants. The rate of detected mergers is ≈
40% of the rate of a threeinterferometer network. The EM observatory location dictates a time lag in response to GW trigger of up to to one day (Table 1).
10 100Number of Pointings0.00.20.40.60.81.0 C u m u l a t i v e F r a c t i on o f M e r ge r s ZTF BG4 DECAMHSCPS1LSSTATLAS
Fig. 3.—
Cumulative distribution of number of pointings necessary to tile localization arcs at all sky positions by LIGO-H and LIGO-L.Color represents telescope diameter: 0.5m-class (green), 1m-class (red), 4m-class (purple) and 8m-class (blue). Line style represents cameraangle: few tens of deg (solid), several deg (dashed) and few deg (dotted). Kasliwal & Nissanke -11 -12 -13 -14 -15 -16 -17EM Counterpart Luminosity (Absolute i-mag)0.00.20.40.60.81.0 E M - G W D e t e c t ab l e F r a c t i on o f M e r ge r s Nickel peak r-proc peak ZTFBG4 DECAMHSCPS1LSSTATLAS
Fig. 4.—
Fraction of mergers detectable by a given EM facility as a function of kilonova luminosity (expressed in absolute i-band ABmagnitude). Color and line-styles are same as in Figure 3. Shaded regions denote theoretical predictions for kilonovae (Barnes & Kasen2013; Kasen et al. 2013) — r-process powered peak (light grey; M ejecta ≈ − –10 − M (cid:12) , v ejecta ≈ ejecta ≈ − –10 − M (cid:12)(cid:12)