# The Central Engine of GRB170817A and the Energy Budget Issue: Kerr Black Hole versus Neutron Star in a Multi-Messenger Analysis

## Abstract

**:**

## 1. Introduction

## 2. Gravitational Collapse of an HMNS to a Kerr Black Hole

## 3. Event Timing in Multi-Messenger Observations

#### 3.1. The Gap Time ${t}_{g}$ between GRB170817A and Its Progenitor GW170817

#### 3.2. Event Timing by the Trigger Time ${t}_{s}$ of GRB170817A

**Box 1.**The delayed trigger time ${t}_{s}$ of GRB170817A.

- GW170817 initially produced an HMNS, evidenced by the kilonova AT2017gfo, followed by GRB170817A across a duration gap of ${t}_{g}={t}_{GRB}-{t}_{m}\simeq 1.7\phantom{\rule{0.166667em}{0ex}}$s, containing the time of the gravitational collapse of the HMNS to a BH, ${t}_{s}$.
- The black hole is initially rapidly spinning, as evidenced by an output ${\mathcal{E}}_{GW}\simeq 3.5\%{M}_{\odot}{c}^{2}$ in ${f}_{GW}\lesssim 700\phantom{\rule{0.166667em}{0ex}}$Hz, exceeding the spin energy ${E}_{J}^{-}$ of the HMNS.

## 4. Observations of GW Transient Emission in Time-Symmetric Spectrograms

#### 4.1. Butterfly Matched Filtering

#### 4.1.1. Sensitivity Gain over the Time-Sliced Fourier Analysis

#### 4.1.2. Application to Gravitational-Wave Data

**one decade improvement in LIGO sensitivity**.

**Box 2.**High-resolution spectrograms: Fourier versus Butterfly matched filtering.

- GW transients may be ascending or descending chirps in gravitational radiation of mergers and, respectively, the spin-down of a compact object.
- GW transients can be searched for in high-resolution spectrograms covering the bandwidth of sensitivity of LVK over a time scale $\tau $ of time-slicing.
- A gain in sensitivity (23) obtains in Butterfly matched filtering over a bank of time-symmetric chirp-like templates densely covering a region of $\left(f,\dot{f}\right)$ spaces.

## 5. Ascending–Descending GW Transient Emission during GW170817-GRB170817A

#### 5.1. Observation in H1L1 Data

#### 5.2. Calibrated Response Curves

**Box 3.**What is the central engine of GRB170817A?

- The ascending–descending chirp in GW170817 represents a merger followed by delayed spin-down of a Kerr black hole during GRB170817A.
- This observation is seen in spectrograms generated by Butterfly matched filtering calibrated by signal injection experiments.
- EM-GW event timing shows consistency between ${T}_{90}^{8-70\mathrm{keV}}=\left(2.9\pm 0.3\right)\phantom{\rule{0.166667em}{0ex}}$s of GRB170817A [90], ${T}_{GW}\simeq 3.7\phantom{\rule{0.166667em}{0ex}}$s and time scale of descent ${\tau}_{s}=\left(3.0\pm 0.1\right)\phantom{\rule{0.166667em}{0ex}}$s.

## 6. Exascale Computing by Synaptic Parallel Processing

#### 6.1. Acceleration by High-Performance Computing

- Efficient evaluation in the Fourier domain using the fast Fourier transform (FFT);
- Heterogeneous computing by offloading inverse FFTs to graphics processor units (GPUs);
- Distributed computing on a platform, load-balanced by synaptic parallel processing.

#### 6.2. Dynamical Load Balancing by Synaptic Parallel Processing

## 7. Parameter Estimation in an Extended Foreground of (H1,L1)-Spectrograms

#### 7.1. PDFs from the Extended Foreground Analysis over Small Time Slides

#### 7.2. Clustering in Parameter Space

**Box 4.**High-resolution event timing in the extended foreground by the exascale HPC.

- Exascale HPC is achieved by synaptic parallel processing on a heterogeneous compute platform [162] in the mixed F90/C++/C99 using OpenCL and bash.

## 8. Consistent Event Timing in Independent H1 and L1 Analyses

**Box 5.**Statistically independent PFAs of the trigger time ${t}_{s}$ of GRB170817A.

- Independent event timings derive from the mean and difference in ${t}_{s}$, equivalent to a unitary transformation of H1 and L1 data, here obtained from merged and individual H1 and L1 spectrograms.

## 9. Conclusions and Outlook

#### 9.1. Principal Results

#### 9.2. Outlook on Upcoming LVK Observations

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

OpenCL | open compute language |

GPU | graphics processor unit |

PCIe | peripheral computer interface express |

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**Figure 1.**Schematic of event timing in GW170817-GRB170817A, where ${t}_{m}$ denotes the merger time and ${t}_{GRB}$ is the time-of-onset of the accompanying GRB170817A following a gap ${t}_{g}\simeq 1.7$ s (bottom). By causality, the central engine of GRB170817A forms in this gap: ${t}_{m}<{t}_{s}<{t}_{GRB}$, with a potentially accompanying output ${\mathcal{E}}_{GW}$, provided ${t}_{s}$ is resolved at a sufficiently high resolution $({\sigma}_{{t}_{s}}\ll {t}_{g}$). The initial HMNS formed in the immediate aftermath of GW170817 experiences gravitational collapse to a black hole disk or torus system if ${\mathcal{E}}_{GW}$ exceeds the canonical bounds on the maximal spin energy of the HMNS, given the observed frequency in gravitational radiation (4). (Reprinted from [109]).

**Figure 2.**PDF(${t}_{s}$) (blue) of the start time ${t}_{s}$ in a descending chirp in gravitational radiation with duration ∼$3.7\phantom{\rule{0.166667em}{0ex}}$s contemporaneous with GRB170817A (${T}_{90}^{8-70\mathrm{keV}}\simeq \left(2.9\pm 0.3\right)\phantom{\rule{0.166667em}{0ex}}$s [90]). The delay time ${t}_{s}-{t}_{m}\simeq 0.92\phantom{\rule{0.166667em}{0ex}}$s (updated from [118]) satisfies causality (11) with ${\sigma}_{{t}_{s}}\ll {t}_{g}$, carrying PFA (14). This delay is consistent with the lifetime of the HMNS (green, [129]). By energy ${\mathcal{E}}_{GW}$ and frequency ${f}_{GW}$, it reveals black hole spin-down in the central engine of GRB170817A, following rejuvenation in gravitational collapse of the initial HMNS. Estimates of the lifetime of the HMNS are included (as reviewed in [9]). (Reprinted from [109]).

**Figure 3.**(

**Upper and middle panels**) Spectrograms (32 s) of about GW170817 for H1 and L1 were generated by conventional time-sliced FFT (using GWXplore [149]). The ascending chirp produced by the merger in the run-up to coalescence is clearly expressed. Following the coalescence event, a descending chirp can be distinguished during GRB170817A. (

**lower panel**) This outcome serves as an illustration of a time-symmetric, unmodeled observation of a transient GW event. (Reprinted from [149]).

**Figure 4.**(

**Left panel**) Butterfly matched filtering schematically indicated by patterns (“green”) with a minimum slew rate $\delta $ at each point $(t,f(t\left)\right)$ in the time–frequency domain. It is realized by a dense bank of chirp-like time-symmetric templates of intermediate duration. (Reprinted from [155]). Signal tracks pass through the green butterfly patterns and are suppressed otherwise. In particular, horizontal tracks of constant frequency signals are suppressed, whereby butterfly matched filtering is complementary to conventional Fourier–based filtering methods. (

**Right panel**) Broadband Kolmogorov spectrum in an ensemble-averaged spectrum, extending to the Nyquest frequency of 1 kHz of 42 bright long GRBs in the BeppoSAX catalog, by filtering over a dense bank of 8.64 million templates (purple line). By displaying the extension of the Kolmogorov spectrum into high frequencies, this result demonstrates a sensitivity to turbulence that is more than an order of magnitude superior to the conventional Fourier analysis (blue). (Reprinted from [101]).

**Figure 5.**The ascending–descending emission during GW170817-GRB170817A in merged (

**top panel**) and individual (

**middle panels**) H1,L1 spectrograms, where merging is by frequency coincidences $\left|{f}_{H1}-{f}_{L1}\right|<10\phantom{\rule{0.166667em}{0ex}}$Hz (

**top panel**). Included is GRB170817A (

**lower panel**). (Reprinted from [109]).

**Figure 6.**(

**Top left panel**) Response curves from modeled merger plus (delayed) post-merger signals by injection experiments on H1L1 data containing GW170817 with parameter recovery (

**top right panel**) by $\widehat{\chi}$ image analysis of (H1,L1)-spectrograms merged by frequency coincidences (

**lower panel**). Response curves cover descending chirps with ${\mathcal{E}}_{gw}$ of a few $\%{M}_{\odot}{c}^{2}$ and time scales of descent ${\tau}_{s}$ covering the post-merger emission feature in GW170817. The dashed line indicates the mean $\widehat{\chi}$ peaks, averaged over time slices $\Delta t$ that are within the 10 ms light-travel time between the H1 and L1 detectors (Reprinted from [109]). (A movie showcasing the injection experiments can be found at https://zenodo.org/record/4390382, accessed on 25 May 2023).

**Figure 7.**(

**Left panel**) Emulation of gain increase with the array size in matched filtering, evaluated by FFT versus direct evaluation. (

**Right panel**) Benchmark of the OpenCL routine clFFT in CSP/OutOfPLace as a function of the array size N for two batch sizes measured by allocation M in global memory. Array sizes exceeding ${2}^{12}$ require calls to global memory due to the limited size of the local memory in the matrix transpose, causing a drop in performance limited by 1 TB/s of bandwidth in HBM. clButterfly [102] uses a default segment of $N={2}^{17}$ samples (32 s at a 4096 Hz sampling rate with a batch size over $M=128$ per 4096 s frame). (Reprinted from [109], https://zenodo.org/record/6475673, https://zenodo.org/record/1242679, accessed on 25 May 2023).

**Figure 8.**PDF$({t}_{s},{\tau}_{s})$ in (24) from the $\chi $ image analysis of (H1,L1)-spectrograms over $Q=161$ time slides. Extremal clustering (100%) of the global maximum ${\widehat{\chi}}^{*}=8.76$ appears in the extended foreground over ${N}_{c}$ small time slides (26). PDF(${t}_{s}$) shows a time delay ${t}_{s}-{t}_{m}=\left(0.86\pm 0.1\right)\phantom{\rule{0.166667em}{0ex}}$s (${t}_{m}=1842.43$ s) of a descending chirp, satisfying ${C}_{1}$, signaling the gravitational collapse to a Kerr black hole that triggers GRB170817A in (3). The PDF(${\tau}_{s}$) is consistent with ${T}_{90}^{8-70\mathrm{keV}}=2.9\pm 0.3\phantom{\rule{0.166667em}{0ex}}$s of GRB170817A [90], identified with the lifetime of black hole spins interacting with surrounding high-density matter. (Reprinted from [109]).

**Figure 9.**The extremal clustering in ${t}_{s}$ and ${\tau}_{s}$ of the descending chirp in (H1,L1)-spectrograms, merged by frequency coincidences $\left|{f}_{H1}-{f}_{L1}\right|<10\phantom{\rule{0.166667em}{0ex}}$Hz, is unique in clustering considered among all 1024) cells of $w=2$ s covering $[0,T]$. (Reprinted from [109]).

**Figure 10.**One sample of PDF$({t}_{s},{\tau}_{s})$ comprising $nm=320$ elements from individual H1 and L1 analyses, shown around the merger time ${t}_{m}=1842.43$ s. Over $T=2048\phantom{\rule{0.166667em}{0ex}}$ s of data, time differences $\left[{t}_{s}\right]={t}_{s,H1}^{*}-{t}_{s,L1}^{*}$ and $\left[{\tau}_{s}\right]={\tau}_{s,H1}^{*}-{\tau}_{s,L1}^{*}$ are at local maxima of $\widehat{\chi}\left({t}_{s},{\tau}_{s}\right)$ over 64 segments of 32 s. These two trials are uncorrelated, evidenced by a correlation ${\rho}_{\left[{t}_{s}\right],\left[{\tau}_{s}\right]}=1.29\times {10}^{-4}$. (Reprinted from [109]).

**Figure 11.**PDFs(${t}_{s})$ of H1 and L1 centered around ${t}_{s}-{t}_{m}=\left(0.92\pm 0.09\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{s}$ and ${\tau}_{s}=\left(3.00\pm 0.09\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{s}$. Binned over $\delta {t}_{rew}=0.025\phantom{\rule{0.166667em}{0ex}}$s, the cross-correlation (over each segment covering the snippet of H1L1 data of $T=2048$ s) uniquely identifies a global maximum in segment 58 corresponding GW170817, consistent with a zero time difference in the bin $\delta {t}_{res}$. (Reprinted from [109]).

**Figure 12.**Chronicle of GW170817 with merger time ${t}_{m}$ and start time ${t}_{m}<{t}_{s}<{t}_{g}$ of a descending branch signaling the birth of the central engine of GRB170817A with delayed time-of-onset $\Delta {t}_{GRB}={t}_{GRB}-{t}_{s}\simeq 0.8\phantom{\rule{0.166667em}{0ex}}\mathrm{s}$ (10). The energy reservoir in the angular momentum ${E}_{J}$ is rejuvenated in the (delayed) gravitational collapse of the initial HMNS at ${t}_{s}$, producing ${E}_{J}^{+}$ of the black hole, exceeding the physical limits of the HMNS. (Reprinted and revised from [109]).

**Table 1.**Event timing of ${\mathcal{E}}_{GW}$ (5) in (3) with type I error statistics, independently in causality (${C}_{1}$: ${p}_{1}$) and consistency (${C}_{2}$: ${p}_{2}$) in independent H1 and L1 analyses over a duration T. Central values and uncertainties refer to the mean and standard deviations of PDFs. (Reprinted from [109]).

H1 | L1 | H1 | L1 | H1,L1 | H1,L1 | Merged (H1,L1) | Merged (H1,L1) |
---|---|---|---|---|---|---|---|

${t}_{s}-{t}_{m}$ [s] | ${t}_{s}-{t}_{m}$ [s] | ${\tau}_{s}$ [s] | ${\tau}_{s}$ [s] | ${t}_{s}-{t}_{m}$ [s] | ${\tau}_{s}$ [s] | ${t}_{s}-{t}_{m}$ [s] | ${\tau}_{s}$ [s] |

$0.9130\pm 0.1366$ | $0.9234\pm 0.1122$ | $3.1\pm 0.1$ | $2.9\pm 0.2$ | $0.92\pm 0.08$ | $3.00\pm 0.09$ | $0.86\pm 0.10$ | $2.91\pm 0.17$ |

T [s] | ${p}_{1}$ | FAR${}_{1}^{-1}$ | ${p}_{2}$ | FAR${}_{2}^{-1}$ | ${p}_{1}\times {p}_{2}$ | FAR${}^{-1}$ | |

2048 | $1.7/2048$ | 1 month | $0.1/2048$ | 1.4 yr | $4.05\times {10}^{-8}$ | 1.6 kyr | |

204,800 | 1.7/204,800 | 782 yr | $0.1/2048$ | 1.4 yr | $4.05\times {10}^{-10}$ | >$160$ kyr |

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**MDPI and ACS Style**

van Putten, M.H.P.M.
The Central Engine of GRB170817A and the Energy Budget Issue: Kerr Black Hole versus Neutron Star in a Multi-Messenger Analysis. *Universe* **2023**, *9*, 279.
https://doi.org/10.3390/universe9060279

**AMA Style**

van Putten MHPM.
The Central Engine of GRB170817A and the Energy Budget Issue: Kerr Black Hole versus Neutron Star in a Multi-Messenger Analysis. *Universe*. 2023; 9(6):279.
https://doi.org/10.3390/universe9060279

**Chicago/Turabian Style**

van Putten, Maurice H. P. M.
2023. "The Central Engine of GRB170817A and the Energy Budget Issue: Kerr Black Hole versus Neutron Star in a Multi-Messenger Analysis" *Universe* 9, no. 6: 279.
https://doi.org/10.3390/universe9060279