On the possibility of GRB forecasting algorithm and alert system for future gravitational wave detectors

G. DEBRECZENI Wigner Research Centre for Physics, 2g_33 Konkoly- Thege M. u,

1121, Budapest, Hungary

Modern gravitational wave (GW) detectors are hunting for GWs originating from various sources. It is assumed that in some cases it is the coalescence (merging) of binary neutron stars (BNS) which is responsible for gamma-ray burst (GRB). Since already well before their merging, during the inspiral phase the BNS system emits GW s, these signals could be used to predict, in advance the time and sky location of a GRB and set up constraints on the physical parameters of the system. There exists no such prediction algorithm, as of today. Despite the fact that it is not yet feasible to use this new method with the current GW detectors, it will be of utmost importance in the late-Advanced LIGO /Virgo era and definitely for Einstein Telescope. The very goal of the research presented in this paper is to develop the above described zero-latency, BNS coalescence forecastingmethod and design the associated alert system to be used by next generation of GW detectors and collaborating EM observatories.

1 Introduction

Gravitational waves originating from inspiraling binary black holes or binary neutron stars are the most widely believed candidates for the first direct detection of gravitational waves predicted by Einstein's theory of General Relativity. In the following couple of years, the current and next generation of ground-based interferometric gravitational wave detectors (the advanced detectors) will have non-negligible chance to perform the first direct observation of such inspiraling events. It is believed that in some cases it is the inspiraling (merger) of such binary neutron star system which is responsible for the production of (a class of) GRBs - routinely observed by electromagnetic observatories.

1 . 1 About Gamma Ray Bursts and gravitational waves

GRBs are unrepeatable astrophysical events happening at quasi random distances and sky lo­cations. As a consequence their observation is performed on a probabilistic basis. A network of ground based detector and space horned satellites is watching the sky with the biggest possible coverage in 24/7 waiting for events. Despite all this effort a fraction of GRBs remains unde­tected due to various reasons (for example incomplete sky coverage) . Even with this approach we have already detected a lot of events and extracted meaningful physics from it, but there are important cases (for example in observing the early light curve of afterglows) when the prior knowledge of the exact or approximate time and sky location of a GRB would tremendously help us performing much more precise, prepared and targeted observations.

A class of GRB is produced by the merger of BNS which is producing gravitational waves in its inspiraling phase. Being able to observere these GWs in advance the electromagnetic burst would allow us not only to reposition our electromagnetic detectors to point to correct sky

locations, but to determine several of the properties of the GRB in advance the electromagnetic observation and examine the dependency of burst properties on BNS system parameters.

1. 2 Feasibility

When such a GW based GRB forecasting alert system is in operation, it is important not to send too many false alarm to the telescopes, since their preparation and/or repositioning needs time and could be expensive. Since this prediction algorithm is intended to be a generic solution - not only restricted to the GRB mass range - it is important to examine which are those parameter spaces where the algorithm can accumulate enough confidence sufficient time before the merger to generate a trigger and send out and alert. A gravitational wave signal is considered to be detected - apart from many other kind of condition - if its SNR is larger than 8.0. The accumulation of SNR over time depends on the shape and duration (Figure 1 b., Eq. 1) of the GW signal, the lower frequency cutoff (10 Hz in this analysis) , and on the sensitivity curve of the detector1 (Figure 1 a.).

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10

" c

10"+02 .g � 0

10"-23 10"+00 10"-24 ���-��-10 100 1000 Frequency [HzJ 10000 10 15 20 25 30

M1 [Msun]

Figure 1 - a.) The designed sensitivity of the advanced LIGO detector without the signal recycling mirror applied. The straight lines represents the analytically fitted approximations used in this analysis. b.) Duration of gravitational wave signal from 10 Hz to fr sea emitted by a non-spinning, circular binary neutron star system.

The duration of a gravitational wave emitted by a circular, non-spinning binary from flow to fisco can be approximated by

T( ,1 ) _ _ 5_ GM [v-8 + (743

+ 1 1 "') v_6 _ 327r

v_5 +

J ,ow - 256TJ c3 low 252 3 ., low 5 low

where (GM )1/3 V[ow = �7r flow '

(3058673 5429 617 2) -4 ] 508032 + 504 T/ + 7277 vlow '

(1)

(2)

However what does really matter is the accumulation of the SNR over time. Figure 2 a. shows the accumulation of SNR over time for a typical 1.4 - 1.4 solar mass BNS. It is visible that despite the very long duration of this signal from the nominal 10 Hz lower frequency cut-off it is only the last (few) hundreds of seconds when significant signal accumulation does indeed happen. If we EM telescopes needs in the order of 100 second for preparation for observations, than it follows that since at time t=-100 only the 0.2 of the total SNR is available the algorithm requires strong signals with total SNR in the order of SNRrot = 8 / 0.2 = 40 to ensure low false alarm probability.

Having determined the above constraints we can now focus on the details of the forecasting algorithm presented in the next section.

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a: 0.7 z 0.6 (/) � 0.5 0 t5 0.4 !<! LL 0.3

0.2 0.1 ----�

0 -1 000 -800 -600 -400 ·200 Time [s]

Figure 2 - Accumulation of the SNR (in units of total SNR of the waveform) as a function of time-to-coalescence for a typical 1.4 - 1.4 solar mass binary neutron star system. b.) The bird-eye view of the architecture of the forecasting pipeline.

2 The forecasting algorithm

One could imagine many different implementation of a forecasting algorithm in question. Our goal here is not to develop a unique implementation but instead, to determine the general characteristics and limitations of such a pipeline.

We choose the usual template bank based matched-filter with the necessary modifications. As a prototype algorithm one could think of the following solution:

1. Generate a template bank in the usual way for a specific parameter space.

2. a. ) Split all the templates of the template bank into equal-time chunks, chunk duration corresponds to a pre-fixed time window size, to be optimized later.

b.) Split all the template of a template bank into different size chunks the time duration of which corresponds to integer multiples of the above mention window size.

3. Match the template chunks of the template bank against the data strain using matched­filter.

4. From the parameters of the template chunks the SNR of which exceeded a given threshold build an N dimensional histogram. One of the simplest - in case of non-spinning, circular binaries - would be a 3 dimensional m1, m2, tcoal histogram, where m1 and m2 are the parameters of template chunk and tcoal is the estimated coalescence time calculated from the position of the maximum match of the chunk with the data and from the position of the chunk relative to its 'parent' template.

5. Perform continuous clustering and max finding on the resulted histogram, and whenever a consistent accumulation of peak for specific parameter set is observed generate a trigger.

2. 1 Estimation of coalescence time

Let's examine how accurately the coalescence time of a binary neutron star merger can be predicted in advance and how the accuracy of the prediction improves over time using the above described algorithm. For this purpose we inject a gravitational wave signal (m1 = 1 .4, m2 = 1 .4) into a simulated gaussian noise with various amplitudes. After that we apply the algorithm and determine the mean and variance of the time parameter of any peak accumulated in the constructed histogram at various times prior to the known coalescence of the injected signal. The estimates are shown on Figure 3.

20 15 Estimated coalescence time as a function of time 10

J!E 5 Q) 0 E ;:: -5

-10 -15 -20 1000 800 600 400 200 0

Time [s]

Figure 3 - Improvement of arrival time estimation as a function of time-to-coalescence of injected signals.

2.2 Estimation of sky location Sky location can be derived using the simple triangulation formula. For the case of the two LIGO detector the theoretical maximum precision of sky localization (Figure 4 a.) and the precision of sky localization in presence of timing inaccuracies (Figure 4 b.) are shown. It is immediately visible that very good coalescence time estimation is necessary for usable sky location estimates some ten or hundred sec before the merger.

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1.5

0.5

Simple timing - sky location for the two UGO detector

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delta_t [s]

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Time difference of GW signal (s]

1.6

1.4

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.§ 0.8 � 0.6 � ];; 0.4 t 0.2

Figure 4 - a.) Theoretical maximum precision of sky localization (0 angle estimate) as a function of arrival time difference for the two LIGO detectors using the simple triangulation. b.) Precision of sky localization as a function of arrival time difference and timing accuracy.

3 Summary and future plans

A novel GRB forecasting algorithm has been presented. The algorithm will be usable when relatively strong GW signals will been seen by GW detectors. It is capable of predicting the estimated coalescence time and sky location of such events, however the precision and early availability of accurate sky location estimates still need to be improved which is the subject of our future research.

Acknowledgements

This research was supported by the GPU Laboratory of Wigner Research Centre.

References

1 . LIGO sensitivity curves: https : //dee . ligo . org/LIGO-T0900288/publie