GPU-searches for broadband extended emission in gravitational waves in nearby energetic core-collapse supernovae
As a parent population to long gamma-ray bursts (LGRBs), energetic core-collapse supernovae (CC-SNe) are leading candidates as multi-messenger sources of electromagnetic and gravitational-wave emission for LIGO-Virgo and KAGRA. While their central engines are currently unknown, this outlook derives from a general association with newly born neutron stars, black holes and high-density accretion disks that may extend down to the Inner Most Stable Circular Orbit (ISCO) of the latter. We here highlight the capability of heterogeneous computing for deep searches for broadband extended gravitational-wave emission (BEGE) from non-axisymmetric accretion flows onto rotating black holes with durations of tens of seconds similar to Extended Emission in LGRBs and SGRBEEs. Specific attention is paid to electromagnetic priors derived from BATSE, BeppoSAX and Swift and data-analysis by GPU-accelerated butterfly filtering with over one million chirp templates per second. In deep searches using banks of up to 8 million chirp templates, the challenge is to identify signals of astrophysical origin in a background of pronounced correlations between the LIGO detectors H1 and L1. As the parent population of normal LGRBs, relatively more frequent supernovae of type Ib/c are of particular interest to blind all-sky searches, in archive LIGO S6 or real-time observation runs concurrently with electromagnetic observations covering the Local Universe up to about 100 Mpc at upcoming Advanced LIGO sensitivity. Detection of their output in gravitational waves is expected to unambiguously determine the nature of their central engines and, by implication, that of GRBs.
Maurice H.P.M. van Putten
0000-0002-0786-0000]Maurice H.P.M. van Putten
- 1 Introduction
- 2 Long GRB-supernovae and SGRBEEs
- 3 Extended emission from rotating black holes
- 4 Ascending and descending chirps in accretion flows
- 5 GPU-accelerated searches for broadband extended gravitational-wave emission
- 6 Summary and future prospects
- A Appendix A. Gravitational radiation
- B Appendix B. Relativistic frame dragging
The recent LIGO detection GW150914 poses a dramatic opening to a whole new window to the Universe (LIGO-Virgo, 2016). Together with the upcoming commissioning of Virgo and KAGRA, we will now be in a position to pursue observations well beyond the limits of electromagnetic radiation, neutrinos and (ultra-)high-energy cosmic rays. As broadband detectors covering 30 - 2000 kHz, LIGO-Virgo and KAGRA offer unprecedented power of discovery relevant to an exceptionally broad class of astrophysical sources (Sathyaprakash & Schutz, 2009; Cutler & Thorne, 2002). While the black hole merger event GW150914 was unexpected and left no conclusive signature in the electromagnetic spectrum (Kalogera, 2017), it nevertheless offered new results of direct astronomical interest with estimates of mass and spin of the black hole progenitor,
that run counter to familiar observations on stellar mass black holes in X-ray binaries in the Milky Way. The inferred high mass of the black holes may originate from core-collapse of Population III stars (Kinugawa et al., 2014; Inayoshi et al., 2017) and their slow dimensionless spin may indicate a process of spin down soon after birth such events (van Putten & Della Valle, 2017).
Gravitational radiation has long since been known to be important in binary evolution of compact stars, as may be seen by long time observations of binary evolution in the electromagnetic spectrum (Verbunt, 1997). Notable examples are Hulse-Taylor pulsar PSR B1913+16 (Taylor & Weissberg, 1989; Taylor, 1994; Weisberg et al., 2010), the double pulsar PSR J0737-3039 (Lyne et al., 2004), and ultra-short period cataclysmic variables with He mass transfer from a degenerate dwarf directly onto a companion (low mass) white dwarf (Smal, 1967; Paczyński, 1967; Faulkner, 1971; Faulkner et al., 1972; Nelemans, 2005; Postnov & Yungelson, 2006; Bidsten et al., 2006). For instance, AM CVn ES Cet ( pc) has an orbital period of about 10 min, a mass ratio of the binary with a white dwarf of mass and a luminosity erg s (Woudt & Warner, 2003; Espaillat et al., 2005). Its gravitational wave-to-electromagnetic luminosity satisfies . At an orbital period of about 5 min, current data on RX J0806 (Bidsten et al., 2006) suggest that it conceivably satisfies
These exceptional cases, therefore, demonstrate genuinely relativistic evolution that ultimately terminates in a binary merger. GW150914 is the most extreme example to-date. In terms of the unit of luminosity
where is Newton’s constant and is the velocity of light , it featured a peak luminosity of about . In this light, PSR B1913+16 is remarkably gentle with .
Multi-messenger output in electromagnetic and gravitational radiation is expected from neutron star-neutron star (NS-NS) or neutron star-black hole (NS-BH) mergers. These mergers are widely considered to explain the most relativistic transients in the sky: cosmological gamma-ray bursts (GRBs), discovered serendipitously by nuclear treaty monitoring satellites (Klebesadel et al., 1973). Observationally, we infer their origin in a compact relativistic inner engines from the dimensionless parameter (van Putten, 2000)
for burst energies erg and variability times ms, where denotes Newton’s constant and is the velocity of light. The observed isotropic equivalent energies erg s and variability times down to 0.1 ms show up to . Such values are extremely large compared to those of other transients, including GRB 980425 associated with SN 1998bw (Galama et al., 1998) and galactic sources such as GRS 1915+105 (Mirabel et al., 1994). It implies inner engines in the form of neutron stars or stellar mass black holes, more likely so than aforementioned white dwarfs in CVs. Neutron star masses tend to cluster around (Thorsett & Chakrabarty, 1999), from 1.25 of PSR J0737-303B (Lyne et al., 2004) to 2.1 in the NS-WD binary PSR J075+1807 (Nice et al., 2004); masses of black hole candidates in X-ray novae are broadly distributed between about 5-20 (Bailyn et al., 1998).
GRBs show anomalous Eddington luminosities of , given their limited durations of typically less than one minute (Fig. 1). These super-Eddington luminosities defy an origin in electromagnetic interactions in a baryonic energy source. The only physical processes known that might circumvent these limitations are neutrino emissions and gravitational interactions allowed by the theory of general relativity. In anisotropic emission, the true energy in gamma-rays , e.g., when GRBs are produced in jet-like outflows at finite opening angles. Even thus, some events have erg. Typical values of events that reveal collimation show a relatively narrow distribution around (Frail et al., 2001; Ghirlanda et al., 2006, 2013)
Normal long GRBs have an accompanying supernova explosion with kinetic energies typically greater than . In exceptionally energetic events, points to a required energy reservoir that exceeds the maximal spin energy of a rapidly rotating neutron star (van Putten et al., 2011b). These events probably mark the birth of a black hole, rather than a neutron star. Following the Burst and Transient Source Experiment (BATSE) classification of short (SGRB) and long GRBs (LGRB) with durations s and, respectively, s (Fig. 1), Swift discovered short GRBs with Extended Emission (SGRBEE) lasting tens of seconds to well over a minute. Their soft EE is very similar to long GRBs with accompanying supernova. In attributing SGRBs to mergers, SGRBEEs defy the dynamical time scale ms of NS-NS or NS-BH mergers by a large factor.
These electromagnetic observations introduce the mystery of the physical nature of GRBs by extreme values of (5) and
GRB inner engines hereby should be ultra-relativistic, conceivably operating by strong gravitational interactions with high density matter on the scale of their Schwarzschild radius , defined as twice the gravitational radius
for a mass . If so, their inner engines may well be luminous in gravitational waves over the lifetime of the inner engine, i.e., up to tens of seconds indicated by long GRBs (van Putten, 2001b). Consequently, GRBs are of considerable interest as candidate sources of gravitational radiation that may be probed by upcoming detectors LIGO-Virgo in the US and Europe and KAGRA in Japan. “If gravitational waves are detected from one or more gamma-burst triggers, the waves will almost certainly reveal the physical nature of the trigger” (Cutler & Thorne, 2002).
However, GRB triggers within the sensitivity distance of LIGO-Virgo and KAGRA are rare and they are difficult to detect due to beaming. Even corrected for beaming, the true GRB event rate is about one per year within a distance of 100 Mpc. Practically, it is rather similar to the event rate of double neutron star coalescence. To within the distance to Virgo Mpc), it implies about one event per century. Beaming is less severe in afterglow emission that follows the prompt phase decreases as the blast wave slows down and, at late times, the emission is ultimately roughly isotropic. In such cases, an observer might detect an orphan afterglow emission at radio wavelengths (Levinson et al., 2002), a few months after the explosion. Identifying GRBs by afterglow emissions leaves uncertain the true time-of-onset of the trigger, however, hampering efficient search for an accompany gravitational wave burst. For SGRBs from mergers, considerable improvement in sensitivity will be realised in the upcoming advanced generation of LIGO-Virgo and KAGRA at frequencies up to a few hundred Hz by advanced seismic suspension. However, at higher frequencies expected to be relevant to LGRBs from CC-SNe, improvement in sensitivity requires high laser power expected in next generation detectors. For instance, a sensitivity distance out to 35 Mpc by advanced VIRGO-LIGO and KAGRA may include the LLGRB event GRB 980425/SN1998bw (Galama et al., 1998). Our perspectives hereby improve but not substantially with an anticipated rate of one detectable GRB-SN every few years.
To circumvent the above mentioned observational limitations to detect long GRBs, we propose a focus on type Ib/c supernovae (Maeda et al., 2002, 2008; Fruchter et al., 2006), that are far more numerous given their relatively small branching ratio of about 1% into long GRBs. Core-collapse supernovae (CC-SNe) form a remarkably heterogenous class of events (Fig. 1), and the most energetic events of type Ib/c stand out as the parent population of normal LGRBs.
The small branching ratio of CC-SNe into successful GRBs is commonly attributed to the challenge of creating an energetic inner engine sufficiently long lived, perhaps intermittently, for its ultra-relativistic outflows to successfully break out of the progenitor remnant envelope. Unsuccessful jet breakout from the stellar envelope in a CC-SN event (Mazzali et al., 2008; Couch et al., 2011; Bromberg et al., 2012) will lead to so called “choked GRB.” Such supernovae may appear as a low-luminosity long GRB or, more broadly, as a class of X-ray transients (Soderberg et al., 2008). Conceivably, therefore, the formation of energetic inner engines is more frequent than successful GRB-SNe. In this review, we shall therefore focus on the outlook on gravitational wave emissions from such energetic inner engines with or without a successful long GRB. Similar considerations might apply to their emission in neutrinos (Mészaros & Waxman, 2001).
For energetic type Ib/c supernovae, we set out to develop an outlook and search for broadband extended gravitational-wave emission (BEGE) by the nature of black hole formation and evolution in CC-SNe.
Our outlook is modelled based on current phenomenology of GRBs and accompanying hyper-energetic supernovae. Detailed spectral and temporal analysis of GRBs from BATSE, BeppoSAX and Swift combined points to long-lived inner engines comprising rotating black holes, that appear common endpoints to energetic core-collapse events and mergers of neutron stars with neutron stars or stellar mass black holes alike. They hereby define a leading candidate as a universal inner engine to LGRBs and the Swift class of SGRBEE and LGRBNs (van Putten et al., 2014b). In interaction with high density accretion flows, potentially powerful gravitational wave emission may ensue, powered by accretion or the angular momentum of the black hole mediated by relativistic frame-dragging. The existence of frame dragging is not in doubt: recent measurements of non-relativistic frame dragging around the Earth are in excellent agreement with general relativity (Ciufolini et al., 2004, 2007; Ciofolini et al., 2009; Everitt et al., 2011). (Gravity Probe-B measurement is equivalent to that at 5 million Schwarzschild radii of a black hole at extremal spin with the same angular momentum as the Earth.) Specifically, accretion flows onto rotating black holes offer a window to broadband extended gravitational-wave emission, from non-axisymmetric accretion flows and high density matter accumulated at the Inner Most Stable Circular Orbit (ISCO), contemporaneously with two-component relativistic outflows that may drive an accompanying supernova explosion and GRB. Some of these model considerations can be confronted with data from GRB catalogues of BATSE, BeppoSAX and Swift. The resulting outlook on long duration ascending and descending chirps from accretion flows onto rotating black holes suggests searches for BEGE, accelerated by recent developments in high performance computing.
The prospect for long duration gravitational-wave bursts from accretion flows onto rotating black holes core-collapse of massive stars highligted here is aimed at broadening our outlook beyond various existing discussions on gravitational waves from CC-SNe, much of which focused on complex short duration bursts from core-collapse and core-bounce in the first one or two seconds producing neutron stars (Ott, 2009) with a LIGO sensitivity distance limited to a few Mpc (Röver et al., 2009). Their connection to GRB-supernovae and extremely energetic supernovae, however, is not obvious (Burrows et al., 2007; Dessart et al., 2008). In contrast, the universal appearance of Extended Emission in LGRBs and SGREEs indicates central engine lifetimes of tens of seconds that may be at work in the more frequent group of energetic type Ib/c supernovae. It therefore appears opportune to search for gravitational-wave bursts with extended emission of potentially similar durations from, broadly speaking, nearby energetic core-collapse supernovae and to develop the required near-optimal search algorithms to achieve maximal sensitivity distance.
The energetic output in BEGE may be large by the ample energy reservoir in angular momentum of rotating black holes, exceeding that of rotating neutron stars by some two orders of magnitude opens a radically new window to energetic bursts in gravitational waves with durations up to minutes. If detected, LIGO-Virgo and KAGRA probes may reveal rotating black holes by calorimetry on their output in gravitational waves (van Putten & Levinson, 2002). In general terms, gravitational radiation from non-axisymmetries associated with core-collapse of high angular momentum progenitors and non-axisymmetric collapse has been well appreciated (Bekenstein, 1973; Thuan & Ostriker, 1974; Novikov, 1975; Epstein, 1976; Detweiler & Lindblom, 1981), see further (e.g. Detweiler & Lindblom, 1981; Kotake et al., 2006; Ott, 2009; Fryer & New, 2011). Here, we emphasise potentially extreme luminosities from non-axisymmetric accretion flows down to ISCO powered by the angular momentum of the central black hole (van Putten, 2001b), and hence the need for a general search method for both ascending chirps and descending chirps from accretion flows onto rotating black holes (Levinson et al., 2015).
Energetic type Ib/c supernova have an event rate of about 100 per year within a distance of 100 Mpc, and they are readily found in optical surveys using moderately sized telescopes. As targets of opportunity for gravitational wave bursts, they are hereby competitive with mergers, whenever the fraction successfully producing a gravitational wave burst exceeds 1% (Heo et al., 2015). Additionally, nearby galaxies such as M51 ( Mpc) and M82 Mpc) each with an event rate of over one core-collapse supernova per decade. By their proximity, these events appear of interest as well, independently of any association with type Ib/c supernovae or GRBs (Ando et al., 2013; Aasi et al., 2014). While CC-SNe define the most energetic transients in the Universe, the dimensionless strain amplitude of any accompanying gravitational waves will be small by the time it reaches the detector and by a possibly prolonged duration of emission. To extract signals deeply within the detector noise, it is desirable to take full advantage of high performance computing on Graphics Processor Units (GPUs), to search for essentially un-modelled emission with near-optimal detection sensitivity by matched filtering against a large bank of chirp templates.
Given the current quest for a multi-messenger source of gravitational radiation, we believe it to be opportune to highlight prospects and search for gravitational radiation from energetic type Ib/c supernovae as a parent population of long GRBs, of interest to LIGO-Virgo and KAGRA up to distances of about 100 Mpc at advanced detector sensitivity.
1.1 Quadrupole gravitational radiation
Normal long GRBs, SGRBs with Extended Emission, energetic core-collapse SNe and possibly superluminous SNe are all likely powered by neutrons stars or stellar mass black holes. From their generally aspherical output in electromagnetic radiation, it may be inferred that their putative inner engine should be rich in angular momentum. Angular momentum serves as a reservoir of energy that, in collapse, points to the formation of an accretion disk. In the present context, the density of any such disk will be high. Any non-axisymmetry introduces a multipole mass moment, that will inevitably luminous in gravitational waves.
Non-axisymmetries in mass-flow may result from instabilities (van Putten, 2002; Kobayashi & Meszaros, 2003; van Putten & Levinson, 2003; Piro & Pfahl, 2007) due to cooling in self-gravitating disks (e.g. (Gamma, 2001; Rice et al., 2005; Mejia et al., 2005; Lovelace et al., 2014; Hadley et al., 2014)), magnetic stresses (Tagger et al., 1990; Tagger & Pellat, 1999; Tagger, 2001; Lovelace et al., 2014), that may account for high frequency QPOs in mciro-quasars (Tagger & Verni’ere, 2006) or flaring in SgrA* (Tagger & Mella, 2006), or enhanced pressure by heating or magnetic fields due to feedback by a rotating black hole (van Putten & Levinson, 2003; Bromberg et al., 2006). In addition, intermittent accretion onto the black hole may lead once more to aforementioned excitation of QNM ringing.
Gravitational radiation is essentially inevitable from extreme transient events forming neutron stars and black holes, arising from non-axisymmetric mass-motion on the Schwarzschild radius of the system, e.g., a wobbling neutron star or a non-axisymmetric accretion flow onto the black holes. Its basic premises derive from dimensional analysis and, with no small parameters, the gravitational wave luminosity will be a fraction of in (13).
Gravitational radiation is a key prediction of general relativity as a mixed elliptic-hyperbolic theory of gravitation described by a metric with associated Riemann tensor (Pirani, 1957, 2009; Trautman, 2009) coupled to matter. In what follows, we shall change to geometrical units and denote the gravitational radius (8) by . Equivalently, we put in (8). Thus, parametrizes perturbations in space-time at a distance in terms of a dimensionless strain
where is the strain amplitude in gravitational radiation. At large distances, satisfies the linearized Einstein equations in vacuo, given by a second order wave equation for small amplitude perturbations that satisfies the same dispersion relation as electromagnetic waves (Appendix A).
At the lowest frequency, gravitational radiation is described by the quadruple gravitational-wave formula, that may be derived from the rotating tidal field in a binary system. This time harmonic excitation acts as a source terms to gravitational wave emission. More generally, tidal fields arise from multipole mass moments , where and refer to the poloidal and azimuthal quantum numbers of spherical harmonics. Thorne (Thorne, 1980) gives a comprehensive overview of gravitational wave luminosity in above from multipole mass moments defined by projections on the spherical harmonics ,
where over the source region expressed in spherical coordinates as before.
In contrast, radial motion introduces time-dependence with which, by (10-11), does not tap into the angular momentum of the source. Gravitational wave emission from axisymmetric sources tends to be remarkably inefficient. Illustrative is the gravitational wave output of about 0.2% from head-on collisions of two black holes (Anninos et al., 1993) (cf. (Gibbons, 1972)). This low efficiency reflects the effective regularization by black hole event horizons of the singular behavior of Newton’s law between point particles (van Putten, 2012b). In contrast, the tidal fields in binary mergers shows appreciable efficiency up to about 2% (e.g. Kyutoku (2013); Szilágyi et al. (2015)) and slightly more in neutron star-neutron star coalescence (Bernuzzi et al., 2015b).
In a binary with binary separation much larger than the Schwarzschild radius of the system, the gravitational potential at the root of the metric is the Newtonian potential along with an orbital frequency , . The total luminosity in gravitational radiation, dimensionless in geometrical units, hereby satisfies for some , taking into account scaling with dimensionless orbital frequency . In the distant radiation field, in terms of the radiation intensity for some constant . In geometrical units, is of dimension cm. The angular frequency of a tidal field is twice the angular velocity of the binary motion, i.e., . Since and are both dimensionless, factors over the Newtonian scale factor and (9), i.e., . Hence with the familiar result (e.g. Wald, 1984)
For a binary of two masses in circular motion, a detailed derivation obtains the quadrupole formula of gravitational radiation (Appendix A)
further replacing with the chirp mass An extension to non-circular orbits by incorporating enhanced emission at higher frequency harmonics obtains by including a factor as a function of ellipticity (Peters & Mathews, 1963; Postnov & Yungelson, 2006). It has been verified experimentally in long-term radio observations of the orbital decay of the Hulse-Taylor binary PSR 1913+16 to better than 0.1% (Taylor, 1994) by the additional factor of for the observed ellipticity . At the distance of 6.4 kpc, its erg s produces an instantaneous dimensionless strain at the Earth that, as such, may be evaluated directly in geometrical units as
based on previous arguments with (Appendix A). As a relatively compact binary, the Hulse-Taylor binary coalesces in about 310 Myr (Postnov & Yungelson, 2006).
Coincidentally, (14) is very similar to the scale for the maximal strain produced in the final merger of a circular binary of two neutron stars of total mass in the Local Universe. In this event, defines the observed strain amplitude for an equal mass binary. Following averaging over the orientation of the source (e.g., (Postnov & Yungelson, 2006) for a more general discussion)
where we dropped the subscript . It explicitly shows that is the product of the Newtonian specific binding energy and the scale factor (see also (Sathyaprakash & Schutz, 2009)). Here, we expand the result to the gravitational wave frequency in terms of the orbital frequency . That is (e.g. (Thorne, 1992; Ju et al., 2000; Postnov & Yungelson, 2006)),
In NS-NS coalescence, the chirp (16) holds true up to the instant when peaks at Hz (Baiotti et al., 2008). Numerical simulations show that the neutron stars subsequently break up, and merge into a hyper massive object (e.g. (Bernuzzi et al., 2015a)) followed by collapse into a stellar mass black hole accompanied by a burst of quasi-normal mode (QNM) ringing. The result is a rapidly rotating low-mass black hole of close to mass with an accretion disk of about 0.01-0.1 (Baiotti et al., 2008). It may give rise to a short GRB, but perhaps also a SGRB with Extended Emission (SGRBEE) (van Putten et al., 2014b).
1.2 Multi-messenger emission from SN1987A
SN1987A in the Large Magellanic Cloud (LMC, kpc (Figs. 2-1) stands out as the first genuine multi-messenger event by a luminous output in electromagnetic radiation and MeV neutrinos. Characteristic for a core-collapse supernova, SN 1987A was radio-loud (Turtle, 1987) and aspherical (Papaliosis et al., 1989). It also featuring relativistic jets (Nisenson & Papaliosios, 1999) with possible black hole remnant, based on a lack of detection of a neutron star and on evidence for a black hole in the rather similar type IIL event SN1979C (Mattei et al., 1979; Pagnaude et al., 2011). Collectively, core-collapse supernova form a rather heterogeneous group (Filippenko, 1997), that may be broadly partitioned in narrow line and broad line events (Fig. 1), where the latter tend to be relatively more energetic featuring relativistic ejection velocities. SN1987A belongs to a class with a relatively massive progenitor (Gilmozzi et al., 1987; Kirshner et al., 1987) powered by a probably angular momentum rich inner engine based on the dramatically aspherical supernova remnant (Fig. 1).
Its output erg in MeV neutrinos offered our most direct view yet on the inner-most workings of a CC-SN. It may, in fact, have produced a stellar mass rotating black hole, as may be inferred from the aspherical remnant seen today. Spectroscopic observations of SNe-Ibc (Mazzali et al., 2005; Tauberger et al., 2009; Modjaz et al., 2014) reveal that the geometry of ejecta of stripped envelope supernovae is, in about 50% of the observed events, is strongly asymmetric. Any non-axisymmetric angular momentum rich explosion mechanism inevitably produce gravitational waves, which may be generic to energetic supernovae.
is particularly relevant as evidence of the formation of high density matter that, combined with ample angular momentum in the progenitor as may be inferred from the aspherical supernova remnant, are just the kind of conditions leading up to an additional output in gravitational radiation, provided this collapse event developed canonical non-axisymmetric mass-motion at its core. Such output will be especially luminous, whenever such mass motion takes place on the Schwarzschild scale of the system, e.g., the Inner Most Stable Circular Orbit (ISCO) around a newly formed black hole. By virtue of the large value of in (4), the quadrupole formula (12) predicts an appreciable luminosity even when in (13) is small, e.g.,
by in (13) is on par with the observed luminosities in the electromagnetic radiation and neutrino emissions of SN1987A. This outlook opens a broad window to observationally relevant gravitational wave luminosities, even in the face of considerable model uncertainties and chirp masses small relative to the central object.
To be specific, consider a mass-inhomogeneity with gravitation radius about a mass with the aforementioned chirp mass in the limit of much smaller than . By virtue of (4), reaches luminosities on par with SN1987A’s neutrino luminosity already for orbiting at a few times the Schwarzschild radius . As a mass perturbation in a torus or inner disk of mass , the gravitational wave luminosity (13) of satisfies in the limit of a small chirp mass. Expressed in terms of the dimensionless inhomogeneity and mass , we have
where denotes the orbital separation. The observed dimensionless strain at a source distance satisfies
Generalized to a similar event in the Local Universe, e.g., SN1979C (Pagnaude et al., 2011), scaled to a distance of 20 Mpc, we have
where in the Newtonian approximation and .
With a focus on multi-messenger emission from energetic type Ib/c supernovae powered by black hole inner engines, our roadmap is as follows.
§2 discusses evidence for black holes as a common inner engine to LGRBs and SGRBEEs from detailed analysis of BATSE data of long GRBs. In particular, LGRBs and SGRBEEs may share a common central engine in the form of a rotating black hole, and normal LGRBs may be associated with the formation of near-extremal black holes.
§3 highlights the likely complex process of birth and evolution of rotating black holes in core-collapse supernovae, various stages of accretion therein each with their own outlook on gravitational radiation with extended emission in the form of ascending and descending chirps.
§4 gives a general framework for BEGE from non-axisymmetric accretion onto rotating black holes. Specifically, we identify extended emission currently observed in GRBs with the lifetime of black hole spin, , as a secular time scale extending to tens of seconds relevant to normal long GRBs and SRBEEs. We identify ascending and descending chirps with non-axisymmetric waves in accretion flows. In the Kerr metric (Kerr, 1963), we model the latter by ISCO waves, extended by feedback over an inner torus magnetosphere with an expanding ISCO during black hole spin-down. Thus, a central engine conceivably emits simultaneously descending and ascending chirps from accretion onto rotating black holes (van Putten, 2003; Levinson et al., 2015).
§5 Given the outlook on extended emission in gravitational waves, we introduce a new GPU-accelerated pipeline of butterfly filtering enabling deep searches for BEGE by matched filtering against over banks of millions of chirp templates in real-time, the results of which would appears as tracks in a chirp-based spectrograms. This approach differs from Fourier-based spectrograms (Sutton et al., 2010; Prestegard & Thrane, 2012; Thrane & Coughlin, 2013, 2014; Coughlin et al., 2015; Abbott et al., 2015; Gossan et al., 2015) by bandpass filtering signals with finite slope for some (van Putten et al., 2014a) (Fig. 8, Fig. 13).
§6 summarises our proposed search strategy to probe nearby energetic core-collapse supernovae for BEGE, by LIGO-Virgo and KAGRA in blind all-sky searches or by follow-up of triggers from optical-radio transients surveys. The latter may be obtained from any of the existing (Drout et al., 2011; Li et al., 2011a) or upcoming all sky optical surveys such as Pan-STARRs (Scolnic et al., 2011) or the planned Caltech Zwicky Transient Facility (Kulkarni et al., 2014; Belkin, 2015). Searches for their contribution to the stochastic background in gravitational waves may be pursued by multi-year correlations between two or more gravitational wave detectors (e.g. (Sathyaprakash & Schutz, 2009)). Existing observations of LGRBs and SGRBEEs justify a vigorous probe of the inner most workings of energetic CC-SNe which, if successful, may identify rotating black holes by true calorimetry on their evolution over times scales of tens of seconds.
2 Long GRB-supernovae and SGRBEEs
The association of normal LGRBs with supernovae and shared spectral properties in prompt GRB-emission with Extended Emission to SGRBEEs discovered by Swift, poses novel questions on a common inner engine to both, even as the latter derives from mergers. In what follows, we review some of the observational highlights on these two classes of GRBs.
2.1 Hyper-energetic GRB-supernovae
Aspherical CC-SNe (Papaliosis et al., 1989; Höfflich et al., 1999; Maeda et al., 2008) such as SN1987A derive from relatively massive progenitors that are unlikely produced by their associated MeV neutrino burst. Instead, they may be powered by an internal magnetic wind (Bisnovatyi-Kogan, 1970) or an internal relativistic jet (MacFadyen & Woosley, 1999) derived from a central engine. In core-collapse following a drop in thermal pressure at the end of nuclear burning or associated with pair-instability if the mass of the star is exceptionally large (Bisnovatyi-Kogan et al., 1966; Barkat et al., 1967; Gal-Yam et al., 2009; Chardonet et al., 2010), the central object thus produced is either a (rotating) neutron star or black hole.
The energy in a supernova explosion powered by angular momentum is constrained by the maximal rotational energy of the engine, i.e., a (proto-)neutron star or black hole, and the efficiency in expulsion of the remnant stellar envelope by a putative internal wind or jet. The maximal rotational energy of a neutron star is attained at its break up frequency whereas the same of a black hole of mass is attained when its angular momentum reaches . Canonical bounds for the rotational energy of the inner engine of a CC-SN are
for a rotating neutron star, respectively, black hole. Here, there is some uncertainty in the bound due to the equation of state of neutron stars. The efficiency in the expulsion of the envelope with kinetic energy by a wind or jet with energy depends on the baryon loading of the wind, i.e., (van Putten et al., 2011b)
where denotes the observed velocity of the ejected envelope relative to the velocity of light . The efficiency increases with baryon loading, as the outflow velocity becomes moderately relativistic. The efficiency reduces to in the limit of baryon-poor jets, whose velocity approaches . By the above, is bounded by or .
Jet powered supernovae are of particular interest to the diversity in CC-SNe in long GRBs (Fig. 1) as well as a diversity in their associated GRBs. Certain types of supernova explosions may lead to a relativistic shock breakout that may explain (nearby) low-luminosity GRBs (LLGRBs) but not the prompt GRB emission of normal long GRBs (Nakar & Sari, 2012). The latter class is thought to be produced by collimated ultra-relativistic baryon-poor jets (BPJ) that penetrate through the stellar envelope. Failure to breakout the stellar envelope leads to a ”chocked GRB,” which is considered the leading candidate for LLGRBs (Nakar & Sari, 2012).
For long GRBs, the association with massive stars is now supported by four pieces of evidence:
supernovae (SNe) accompanying a few nearby events (Hjörth et al., 2011);
The fact that is about two orders of magnitude larger than in (21) allows for to be considerably larger than even at modest efficiency. Additionally, black hole-disk systems can produce two-component outflows comprising an ultra-relativistic jet along their spin axis surrounding by a baryon-rich and possibly collimating disk wind. The first offers the potential for high energy emissions upon breakout from the stellar envelope, whereas the second offers the potential for an efficient explosion. In contrast, neutron stars may produce a one-component magnetic outflow, that may facilitate either one but not both.
Exceptional ’s are observed in GRB 031203/SN2003lw and 030329/SN2003dh with erg and erg, respectively (Table 1). Like SN1987A, supernovae accompanying LGRBs are aspherical and radio-loud. Hyper-energetic events with (see (21)) are no exception. In the model of (Bisnovatyi-Kogan, 1970), these explosive events are attributed to magnetic winds powered by angular momentum extraction of a compact object, i.e., a PNS or magnetar (e.g. (Woosley, 2010; Kasen & Bildsten, 2010) in SN2007bi (Nicholl et al., 2013)) or a rotating black hole-disk system (BHS, (van Putten & Levinson, 2003)). Taking into account a finite efficiency for the conversion of angular momentum to a (largely radial) explosion, , we determined that aforementioned two events require a central energy in angular momentum exceeding the maximal spin energy of a rapidly rotating neutron star by a factor of 10 and, respectively, 5.3 (Table 1). With a total output of about erg in optical emission alone, SN2015L (Dong et al., 2015) likewise defies the limit in the face of reasonable efficiencies and finite efficiency in dissipating kinetic energy to electromagnetic radiation.
Given uncertainties in the observed explosion energy by a factor of no more than a few, it appears that, in light of (21), these two events cannot be attributed to spin down of PNS, unless the efficiency is at least 100 %. For this reason, the central engine of these two events stand out as candidate BHS, powering the explosion by the spin energy of a black hole. If so, the required explosion efficiency is brought back to a reasonable few %. In particular, we have a wind energy that may derive from disk winds or black hole spin energy satisfying
for rapidly spinning black hole of mass parameterized by the ratio of the angular velocity of a torus about the ISCO to the angular velocity of the black hole. The fiducial scale of 0.1 in (23) is rather conservative.
2.2 Local event rates of energetic CC-SNe
As a parent population of long GRBs, nearby energetic core-collapse supernovae define targets of opportunity (TOOs) to LIGO-Virgo (Abramovici et al., 1992; Acernese et al., 2006, 2007) and KAGRA (Somiya, 2012; KAGRA, 2014). Current GRB and SN rates measurements point to a branching ratio
covering a conservative (van Putten, 2004; Ghirlanda et al., 2013) to a more optimistic estimate (Guetta & Della Valle, 2007). As targets of opportunity for LIGO-Virgo and KAGRA, the event rate of SN Ib/c is larger than GRB-SNe by .
The origin of the small value of in (24) is not well understood. Evidently, an observable GRB event requires the formation of an inner engine sufficiently powerful for its energetic outflows to overcome various adverse conditions out of which it emerged, namely a high density environment formed in core-collapse of a massive progenitor star, perhaps in a short period binary (Paczyński, 1998). A possible additional factor is the time of residence of the newly formed black hole in the center of the star, that may be sufficiently long only when the kick velocity is low. The latter may be rare. Alternatively, it may reflect the small probability of forming nearly extreme Kerr black holes, i.e., about the Thorne limit reached along a modified Bardeen trajectory as the initial condition for long GRBs (van Putten, 2015c).
We estimate the event rate of Type Ib/c supernovae within a distance in the Local Universe to be
based on a weighted average of the volumetric rates derived from Asiago (Capellaro et al., 1999; Barbon et al., 1999) and Lick surveys (Li et al., 2011a, b). In a 5 year observational window, we expect about 4, 15 and 35 asymmetric Type Ib/c explosions in within a distance of 20, 30 and 40 Mpc respectively. These numbers offer a realistic perspective on simultaneous detections of GWBs and electromagnetic radiation.
The event rate (25) refers to regular Type Ib/c supernovae. Broad line events (cf. Fig. 1) associated with normal LGRBs are more rare by an order of magnitude. Even so, the event rate of these energetic events is a few per year within 100 Mpc, and hence more numerous than the true event rate of LGRBs (corrected for beaming) by up to one order of magnitude.
The relatively high event rate (25) should be viewed in light of the anticipated high frequency in gravitational waves, where LIGO-Virgo and KAGRA sensitivity is limited by photon shot-noise. The shot-noise dominated output of these detectors is above the frequency around 100-200 Hz of minimal (thermal) noise, below which sensitivity is limited by seismic noise. By frequency alone, GWBs from Type Ib/c supernovae are less suitable as gravitational wave sources for these detectors than mergers of double neutron star binaries (§2). This drawback is considerably ameliorated by the relatively high event rate (25), that brings Type Ib/c supernovae statistically more nearby by a factor of about 4.8.
Detecting energetic supernovae such as Type Ib/c events is very easy, especially in the Local Universe within 100 Mpc. In contrast, electromagnetic counterparts to mergers of double neutron star binaries appear to be quite challenging (kasen et al., 2013; Barnes & Kasen, 2013; Tanaka & Hotokezaka, 2013) and may be seen only in the most fortuitous of cases (Tanvir et al., 2013).
2.3 GRBs in the Swift era
Calorimetry on the kinetic energy in supernovae and the prompt GRB emission offers our most prominent views yet on the inner engine of GRB-SNe, in addition to the MeV neutrino burst from SN1987A. We next review the present classification, spectral and temporal properties of GRBs relevant to the question whether their inner engine is a black hole or neutron star. Particularly relevant are the catalogues of BATSE, BeppoSAX and Swift of long and short GRBs.
Immediately following the serendipitous discovery of GRBs, Stirling Colgate suggested an association to supernovae - gamma-ray flashes from type II supernova shocks (Colgate, 1968, 1970, 1974) - now seen by the association of normal long GRBs with core-collapse of massive stars (Woosley & Bloom, 2006). Indeed, shock breakout in regular CC-SNe is likely to produce high energy emission in UV light (Gezari, 2008), X-rays (Campana et al., 2006) up to gamma-rays (Weaver, 1976; Höfflich et al., 2009; Katz et al., 2010; Nakar & Sari, 2010; Svirski et al., 2012). While conceivably relevant to low luminosity (long) GRBs (LLGRBs), the prompt GRB emission from normal long GRBs is now understood to derive, instead, from dissipation in ultra-relativistic BPJs (below).
BATSE identified short and long GRBs by the observed bimodal distribution in durations in a large number of events (Fig. 1). They are now associated with, respectively, mergers of the NS-NS (Eichler et al., 1989) or NS-BH (Paczyński, 1991) variety, albeit with a large overlap between these two populations (Bromberg et al., 2012, 2013). is defined by the time interval covering a 90 percentile in total photon count (Kouveliotou et al., 1993). BATSE identified a mostly non-thermal spectrum, which is typically well described by a smoothly broken power-law (Band spectrum (Band et al., 1993)).
BeppoSAX seminal discovery of X-ray afterglow emission to GRB 970228 by (Costa et al., 1997) allowed rapid follow-up by optical observations (van Paradijs et al., 1997), providing a first cosmological redshift ( of GRB 970508) in optical absorption lines of FeII and MgII (Metzger et al., 1997; Amati et al., 1998). When detected, afterglow emission of short GRBs tends to be very weak compared to those of LGRBs, consistent with less energy output and burst locations outside star forming regions. Weak X-ray afterglow emission discovered by Swift in the High Energy Transient Explorer-2 (HETE II) event GRB 050507 (Fox et al., 2005) and the Swift event GRB 050509B (Gehrels et al., 2005) were anticipated for GRBs from rotating black holes (van Putten & Ostriker, 2001). Following GRB 970508, BeppoSAX, HETE II and Swift provided a growing list of GRBs with measured redshifts. Presently, the total number of redshifts identified is about 350 with 287 due to Swift alone. Fig. 3 shows the distribution of the latter.
Swift identified the new class of short GRBs with Extended Emission (SGRBEEs). GRB060614 (=102 s) has no detectable supernova (Della Valle et al., 2006; Fynbo et al., 2006; Gal-Yam et al., 2006) and GRB 050724 is a SGRB with Extended Emission (SGRBEE) with an overall emission time =69 s in an elliptical host galaxy (Berger et al., 2005, 2007). Neither is readily associated with a massive star. Since then, the list of SGRBEEs has grown considerably (Table 2). Table 2 further shows a few long GRBs with no apparent association to SNe (LGRBNs). SGRBEE and LGRBNs challenge the BATSE classification into short and long events. Though both show an initial hard pulse, characteristic of short GRBs, a subsequent long duration soft tail features a spectral peak energy ()-radiated energy () correlation that satisfies the Amati-correlation holding for normal long GRBs. This “hybrid” structure of observational properties of SGRBEE and LGRBNs suggests that they share the same astronomical origin as short GRBs with the same physics in the central engine as normal long GRBs, albeit with somewhat smaller values of .
The prompt GRB emission has a characteristic peak energy at which the photon spectrum peaks in the cosmological rest-frame. It typically ranges from tens of keV to thousands of keV. If the isotropic-equivalent energy is the radiation output by a GRB during its whole duration (assuming spherical symmetry), it is found that , commonly used in the absence of reliable information on the degree of collimation in individual GRB events, correlates with (see Fig. 5). This correlation, now known as the Amati relation, is well established for long GRBs, while short GRBs do not appear to satisfy this Amati-correlation ((Amati et al., 2006) and references therein).
To quantify our level of confidence in the merger origin of SGRBEE and LGRBNs, we recently considered the mean values of the observed redshifts (Fig. 4), i.e., of LGRBNs, of SGRBEEs, of SGRBs and of LGRBs, and concluded that they satisfy
where , , , and based on the redshifts shown in Table 2.
By a Monte Carlo test, we determined the probability that, from the mean redshift, the Swift samples of SGRBEE (), SGRB () and LGRBNs () are drawn from the observed distribution of LGRBs (). Because of the small samples and the broad distribution of redshifts of LGRBs (with an observational bias towards low ), we proceed with Monte Carlo test by drawing samples of size ( from the distribution of the redshifts of the latter. Doing so times for large obtains distributions of averages of the redshifts in these small samples under the Bayesian null-hypothesis of coming from the distribution of redshifts of LGRBs. We find (van Putten et al., 2014b)
For SGRBs, (27) is consistent with a relatively low redshift origin inferred from identification of host galaxies in the local Universe (Tanvir et al., 2005). At a level of confidence exceeding , SGRBEE and LGRBNs have inner engines originating in mergers in common with normal long GRBs originating in CC-SNe, given that both share the Amati-correlation in the long/soft tail.
Our results (27) show with relatively high confidence that the enigmatic LGRBN GRB060614 is a merger event, suggested earlier based on other arguments (van Putten, 2008; Caito et al., 2010b), whose long durations in soft extended emission can be identified with the lifetime of spin of a rotating black hole (§2); see (Zhang, 2006; Zhang et al., 2007) for various other explanations of extended emissions from mergers. Baryon-rich jets such as shown in Fig. LABEL:fig:jet from accretion disks produced in naked inner engines formed in mergers may dissipate into lower energy emissions, perhaps including a radio burst (van Putten, 2009).
2.4 Prompt GRB emission
Three main stages are involved in the generation of the prompt GRB emission: (i) extraction of energy and formation of outflows, (ii) dissipation of the outflow bulk energy, and (iii) conversion by dissipation into electromagnetic radiation. These processes are most likely interrelated. Successful breakout of the jet from the stellar envelope is a necessary condition for producing a GRB. Due to the compactness of the energy source, the largely non-thermal electromagnetic emission originates from large radii and, therefore, does not provide a direct probe of the central engine. Nevertheless, some of the temporal properties of the activity of the engine may be imprinted in the light curve of the prompt emission (Kumar et al., 2008a; van Putten & Gupta, 2009).
The conventional wisdom has been that GRB jets are powered by magnetic extraction of the rotational energy of a magnetar (Usov, 1994; Metzger et al., 2011) or a hyper-accreting black hole, where the latter is a particularly attractive alternative to account for low baryon-loading (Levinson & Eichler, 1993; Eichler, 2011). In some cases (van Putten et al., 2011b), evidence is tilting towards an association to black holes rather than neutron stars. At sufficiently high accretion rates, annihilation of neutrinos that originate from the hot matter surrounding a Kerr black hole can also power a GRB outflow (Zalamea & Beloborodov, 2011; Levinson & Glubus, 2013), although magnetic extraction seems favorable. In the latter case, it is believed to form an outgoing Poynting flux which, on large enough scales, is converted somehow into kinetic energy in baryonic contaminants. This conversion process has not been identified yet, but it is generally believed to involve gradual acceleration of the flow (e.g., (Bogovalov, 1995; Chiueh et al., 1991; Heyvaerts & Norman, 1989; Lyubarsky, 2009)), impulsive acceleration (Granot et al., 2011; Lyutikov, 2011), magnetic reconnection (Giannios & Spruit, 2007; Levinson & van Putten, 1997; Lyubarsky, 2010; Lyutikov & Blandford, 2003; Zhang & Yahn, 2011; McKinney et al., 2012), and/or current driven instabilities (Levinson & Begelman, 2013).
The production of high energy emission requires substantial dissipation above, or just below the photosphere. It most likely results from the formation of internal (Mészaros & Rees, 1993; Rees & Mészaros, 1992) and/or collimation (Bromberg & Levinson, 2007; Lazzati et al., 2009) shocks in cases where the flow is hydrodynamic in the vicinity of the photosphere, or magnetic reconnection (Giannios & Spruit, 2007; McKinney et al., 2012) if the flow remains highly magnetized at large radii. Dissipation at very large optical depths will merely lead to re-acceleration of the flow, or in case of magnetic extraction to a transition to kinetic energy dominated outflows (Granot et al., 2011; Levinson & Begelman, 2013). It can, nonetheless, help increasing the specific entropy, which seems to be required by the observed SED peaks.
The nature of the prompt emission mechanism is yet an open issue. The emitted spectrum, although exhibiting notable variations from source to source, can generally be described by a broken power law (Band function (Band et al., 1993)), with some exceptions, e.g., GRB 090902B. It has been originally proposed that the observed spectrum is produced by synchrotron emission of non-thermal electrons accelerated at internal collisionless shocks (for reviews see (Piran, 1999, 2004)). However, subsequent analysis (e.g., (Beloborodov, 2013; Crider et al., 1997; Eichler & Levinson, 2000; Preece et al., 1998)) indicated that the synchrotron model has difficulties accounting for some common properties exhibited by the GRB population, specifically, the clustering of peak energies around 1MeV, the hardness of the spectrum below the peak, and the high efficiencies inferred from the observations. At the same time, it has been argued (Ryde, 2004, 2005) that a thermal component appears to be present in some bursts, which may be transient as in the BeppoSAX event GRB 990712 (Frontera et al., 2001). These developments, and the recent detection of some GRBs with a prominent thermal component (e.g., GRB 090902B) or multiple peaks (e.g., GRB 110721A, GRB 120323A) have motivated a reconsideration of photospheric emission (Beloborodov, 2013; Eichler & Levinson, 2000; Giannios, 2012; Peer et al., 2006; Ryde & Peer, 2009; Vurm et al., 2013).
On theoretical grounds, one naively anticipates a significant dissipation of the bulk energy of a GRB outflow just below the photosphere, either by internal (Eichler, 1994; Bromberg et al., 2011b; Morsony et al., 2010) or collimation shocks (Bromberg & Levinson, 2007; Lazzati et al., 2009). They are mediated by radiation and their typical size is on the order of a few Thomson depths (Budnik et al., 2010; Katz et al., 2010; Levinson & Brombert, 2008; Levinson, 2012), larger than any kinetic scale by many orders of magnitudes. Their structure and emission are, therefore, vastly different than those of collisionless shocks that can only form above the photosphere, where the Thomson optical depth is well below unity. The large shock width strongly suppresses particle acceleration (Levinson & Brombert, 2008; Katz et al., 2010), yet a non-thermal spectrum can be produced inside the shock via bulk Comptonization (Budnik et al., 2010) and formation of a Band-like spectrum is conceivable (Keren & Levinson, 2014). Alternatively, sub-photospheric dissipation may be accomplished through magnetic reconnection if the flow remains highly magnetized at mild optical depths, in which case particle acceleration may ensue. Under such conditions, formation of a Band spectrum is also plausible (Beloborodov, 2013; Giannios, 2012; Vurm et al., 2013).
Observationally, a photospheric model (black body plus power law) or a Band function provides a satisfactory fit to most BATSE GRB light curves. However, extending spectra to the low energy range of 2-28 keV (of the BeppoSAX Wide Field Cameras) poses challenges in a number of cases. For the extended energy range of 2-2000 keV, a Comptonization model appears more robust in producing satisfactory fits (Frontera et al., 2013). The low energy window is consistent with Comptonization of black body background photons by an initially non-relativistic expanding outflow, perhaps representative of the initial launch at stellar breakout of the outflow creating the GRB. A particular example, the breakout of a striped MHD jet, computed using numerical simulations, is here presented in §5.2.
The prompt GRB emission is often followed by afterglow emissions at lower energies, especially in X-rays down to radio in some cases. Afterglow emission was anticipated based on the GRB association with ultra-relativistic outflows, further enabling identifying host properties and, in some cases, calorimetry on the total energy output. We refer the reader to existing reviews on this subject (Piran, 1999, 2004). Swift made a key discovery with the identification of long duration X-ray tails, that appear to represent latent activity of the remnant inner engine (e.g. (Chincarini et al., 2010; Bernardini et al., 2011)). Remarkably, these X-ray tails, when observed, are very similar to short and long GRBs, lending some support for a common engine remnant.
2.5 Kolmogorov spectra in BeppoSAX
To probe for high frequency signatures in the prompt GRB emission and, possibly, any intermittency or quasi-periodic behavior in the inner engine, the BeppoSAX catalogue of 2 kHz light curves offers a unique window to broadband spectral analysis. As mentioned above, prompt GRB emission probably originates from ultra-relativistic, baryon poor jets, launched from a compact stellar mass object (Sari & Piran, 1997; Piran & Sari, 1997) (see also (Kobayashi et al., 1997; Nakar & Piran, 2002)), commonly believed to be black holes or neutron stars (Thompson, 1994; Metzger et al., 2011).
Shock induced emission predicts a spectrum that is a power law in energy (e.g. (Sari et al., 1998; Thompson et al., 2007)) and turbulent in temporal behavior. Indeed, a Fourier analysis reveals a Kolmogorov spectrum in the BATSE and BeppoSAX catalogs of light curves of long GRBs (Beloborodov et al., 1998, 2000; Guidorzi et al., 2012; Dichiara et al., 2013a, b). The index of power law behavior in the observed PSD spectra is broadly distributed about the Kolmogorov value of 5/3 with a negative gradient as a function of energy (Fig. 6). Conceivably, this spectral-energy gradient might be due to scale dependent dissipation in turbulent flows, which is only beginning to be explored by high resolution numerical simulations in the approximation of relativistic hydrodynamics (Zrake & MacFadyen, 2013) (see also (Calafut & Wiita, 2014)).
However, Fourier spectra are limited to tens of Hz due to strong Poisson noise in high frequency sampled gamma-ray light curves. The Kolmogorov spectrum is expected to continue to higher frequencies. This has recently been identified in broadband spectra obtained by a chirp search method. The method uses matched filtering using chirp templates with frequencies slowly moving up or down of 1 second duration (Appendix D). Applied to 2 kHz sampled BeppoSAX light curves of long GRBs (7), an approximately Kolmogorov spectrum is found to extend to 1 kHz in the observer’s frame or, equivalently, a few kHz in the source frame (Fig. 8).
The above gives considerable evidence for LGRBs produced by successful breakout of ultra-relativistic jets emerging from an energetic CC-SNe (and LLGRBs as their failed-to-breakout counterparts). While the latter may be powered by an associated baryon-rich collimating wind, the GRB is attributed to dissipation in internal and/or collimation shocks in the former, that may be the result of intermittency at the source.
The preceding data point to a common origin in mergers of SGRBEE, LGRBNs and normal LGRBs: their soft/long tail sharing the same Amati-relation (Fig. 5) and the Kolmogorov spectrum of gamma-ray fluctuations is smooth with no evidence for a bump that might indicate the formation of proto-pulsars. These hints point to a common engine producing soft extended emission, and probably so from black holes in mergers and CC-SNe alike. Additionally, rotating black holes have ample energy to account for the most energetic GRB-SNe (Table 1). Apart from the low number counts, the only reservation would be extremely sub-luminous CC-SNe (cf. (Pastorello et al., 2007)), that would be undetectable in our sample LGRBNs (Fig. 4).
On the premise of black holes unifying the soft extended emission in normal LGRBs (in core-collapse of massive stars) and SGRBEEs (from mergers), we next turn to a model for extended emission from rotating black holes, parameterised largely by black hole mass, defined by a secular time scale of spin down against surrounding high density matter rather than any time scale of accretion or free fall.
3 Extended emission from rotating black holes
The exact Kerr (1963) solution of rotating black holes is parameterised by mass , angular momentum and electric charge . Rotation is commonly expressed by the dimensionless parameter , where denotes the specific angular momentum. According to the Kerr solution, , allowing in terms of (van Putten, 1999). Spacetime about a rotating black holes is dragged into rotation at an angular velocity , that may be observed as the angular velocity of test particles (at constant radial distance and poloidal angle) with vanishing angular momentum as measured at infinity. The angular velocity of the black hole is defined as the limit of as one approaches the black hole that, by the no-hair theorem, reduces to a constant on the event horizon. At a corresponding spin frequency ,
the total energy in angular momentum satisfies , i.e.,
3.1 Secular time scale of black hole spin
To be specific, we propose that BATSE durations of their prompt emission (Fig. 1) represents a proxy for the lifetime of the engine (van Putten, 1999; van Putten & Ostriker, 2001; van Putten & Levinson, 2003), i.e.,
while , where is the angular velocity of matter at the ISCO for prograde (+) and retrograde (-) orbital motion (e.g. Shapiro & Teukolsy, 1983). The inequality is readily satisfied. According to the Kerr metric, it holds whenever their rotational energy exceeds about 5.3% of their maximal spin energy (for a given black hole mass-at-infinity ).
In the proposed identification (30), provides a unique signature of the inner engine of LGRBs and SGRBEEs, where the latter derives from the merger of a neutron star with another neutron star or rotating companion black hole. We herein identify SGRBs (without EE) with hyper-accretion onto slowly rotating black holes, produced in mergers of neutron stars with a slowly spinning black hole companion (van Putten & Ostriker, 2001) (Fig. 9).
In (30), black holes are envision to be losing angular momentum primarily to surrounding matter about the ISCO, leaving a minor release about the spin axis in open outflows powering the baryon-poor ultra-relativistic jets (BPJ) seen in gamma-rays with luminosity (van Putten & Levinson, 2003; van Putten, 2009)
For rapidly rotating black holes, along open magnetic flux tubes is supported by Carter’s magnetic moment of the black hole (Carter, 1968; Cohen et al., 1973; Wald, 1974), in equilibrium with the external magnetic field supported by the surrounding inner disk or torus in a state of suspended accretion (van Putten & Ostriker, 2001; van Putten & Levinson, 2003).
Fig. 10 illustrates in poloidal cross-section the structure of open outflows in a suspended accretion state, allowing the black hole to lose angular momentum to surrounding matter. Like their supermassive counter parts (e.g. Macchetto et al., 1997; Walsh et al., 2013) or galactic stellar mass black holes in micro-quasars such as GRS 1915+105 (Mirabel et al., 1994; Greiner et al., 2001), accretion flows in catastrophic events are believed to be likewise magnetised, exposing the central black hole to a finite magnetic flux by accretion (Ruffini & Wilson, 1975; Bisnovatyi-Kogan et al., 1976; Blandford & Znajek, 1977) or the formation of a torus magnetosphere (van Putten, 1999). Strong magnetic fields may derive from the magneto-rotational instability (MRI, Balbus & Hawley (1991); Lubow et al. (1994); Globus & Levinson (2014)), whose component of the infrared spectrum of MHD turbulence represent a net poloidal flux. In turbulent accretion (Bisnovatyi-Kogan et al., 1976) or by forcing (van Putten, 1999), will follow changes in sign in the part of the infrared MHD spectrum on an Alfvén crossing time scale. Exposed to a finite variance in poloidal magnetic flux, a rapidly rotating black hole develops a finite magnetic moment that preserves maximal magnetic flux through the event horizon at all spin rates. This holds true especially at maximal spin (Wald, 1974; Dokuchaev, 1986; van Putten, 2001a). In the absence of a small angular parameter in the connection of magnetic flux from the latter to the former, the result is an Alvén wave over an inner torus magnetosphere, allowing black holes losing angular momentum to a torus about the ISCO. In this process, the latter is heated and expected to be driven non-axisymmetric instabilities balanced by cooling in gravitational radiation (van Putten, 2012a). The strength in poloidal magnetic flux may be derived from a magnetic stability limit of energy of the poloidal magnetic field to the kinetic energy in the inner disk or torus (van Putten & Levinson, 2003). Conceivably, this bound may be circumvented by strongly intermittent inner engines (van Putten, 2015b), see also (McKinney et al., 2012). As a result, a key parameter setting the lifetime of rapid spin of the black hole is the mass in the torus.
The output (31) is robust in being a consequence of differential frame-dragging. ( decays to zero at infinity from on the black hole.) Locally, the effect is manifest in Papapetrou forces (Papapetrou, 1951; Pirani, 1956) acting on the canonical angular momentum of charged particles supporting a Poynting flux-dominated outflow. The line-integral thereof is a potential energy (van Putten & Gupta, 2009) . For charged particles, is defined by total magnetic flux on the flux-surface at hand (which is an adiabatic invariant). In super-strong magnetic fields typically considered in models of GRB inner engines, assumes energies on the scale of Ultra-High Energy Cosmic Rays (UHECRs). This may be processed downstream to gamma-ray emission in relativistic shocks or, for intermittent sources, into UHECRs by acceleration of ionic contaminants ahead of outgoing Alfvén fronts (van Putten & Gupta, 2009).
The jet luminosity (31) differs from the open model of force-free flux surfaces rotating at one-half the angular velocity of the black hole envisioned in (with in Blandford & Znajek, 1977), in that only a minor fraction of the black hole luminosity channeled in an open outflow whenever . In van Putten (2015c), we consider positively correlated to the ISCO: and, since is dimensionless in geometrical units, for a correlation to the ISCO. Consequently, in a Taylor series expansion in , where denotes the ISCO radius around the black hole with angular velocity . Numerical integration of the equations of suspended accretion (with fixed points at extremal and slow spin) obtains a light curve from (31), providing a template suitable for normalising light curves by matched filtering (van Putten, 2012a; van Putten & Della Valle, 2017). If represents an opening outflow supported by horizon flux over the full hemisphere of the black hole event horizon, will be a substantial fraction of . For GRBs, however, this runs counter to a generically small fraction of true energy in prompt GRB outflows relative to of a black hole (van Putten & Levinson, 2003; van Putten, 2015c).
Immediately after birth, a black hole in core-collapse grows by Bondi accretion (Bondi, 1952; Shapiro & Teukolsy, 1983), up to the moment that an accretion disk first forms by angular momentum hang-up about the ISCO of the newly formed rotating black hole. Subsequently, Bardeen (1970) accretion is expected to ensue (McKinney, 2005; Kumar et al., 2008b; King & Pringle, 2006) - modified by open outflows (van Putten, 2015c) - driving the black hole to a near-extremal state, provided there is sufficient mass infall to reach this state. As accretion rates become sub-critical in the sense of Globus & Levinson (2014), such near-extremal black hole may experience angular momentum loss to surrounding matter at the ISCO through Alfvén waves in an inner torus magnetosphere, until its angular velocity drops to of matter orbiting at the ISCO - a stable fixed point in the equations of suspended accretion (van Putten, 2008).
Fig. 11 illustrates the complex sequence of different types of accretion, over the course of which the black grows in mass and spins down (Bondi accretion), grows in mass and spins up (Bardeen accretion), and loses mass-energy and spins down (suspended accretion). The latter introduces a radically new secular time-scale (van Putten & Levinson, 2003; van Putten & Della Valle, 2017)
defined by the ratio of the mass of a torus at the ISCO to and its normalised radius . According to (32), the process of losing angular momentum to matter at the ISCO can extend to ultra-long durations when is small, e.g.,
which time scale can be found in superluminous supernovae such as SN2015L (van Putten & Della Valle, 2017).
The process of black holes losing angular momentum to matter at the ISCO is expected especially from a fully developed turbulent disk. Exposed to a finite variance in poloidal magnetic flux, a rapidly rotating black hole develops a finite magnetic moment that preserves maximal magnetic flux through the event horizon at all spin rates. This holds true especially at maximal spin (Wald, 1974; Dokuchaev, 1986; van Putten, 2001a). Fig. 12 shows the overall efficiency of radiation thus catalytically converted from black hole spin.
3.2 Observational evidence of black hole spin down
Normalized light curves (nLC) extracted from the BATSE catalogue of LGRBs allow a confrontation with model templates of spindown, of black holes against high density matter at the ISCO and (proto-)neutron stars by magnetic winds. In making the connection to the observed GRB emission, we consider a linear correlation between ultra-relativistic baryon-poor outflows and the observed prompt GRB emission. Fig. 13 shows match between nLC and model templates. The results favour the first, especially so for very long duration events with exceeding tens of seconds. Similar results obtain for nLC extract from Swift (Gupta & van Putten, 2012).
Noticeable also is an improvement in the fit for relatively long duration events with s (van Putten, 2009). We attribute this to the time scale of jet breakout in a remnant stellar envelope for the majority of long GRBs originating in CC-SNe (van Putten, 2012a), possibly further in association with the most rapidly spinning black holes (van Putten, 2009). Based on different observations related to the relatively flat distribution of below 20 s, a similar conclusion obtains (Bromberg et al., 2013).
Eq.(30) may be contrasted with various time scales of accretion, generally associated with growth and spin-up of the central black hole. In Kumar et al. (2008b), a distinction is outlined between fall-back at high and low (down to zero) accretion rates. The first implies an initial for the first ten seconds or so in transition to on the time scale of one hundred seconds. The second implies with , depending on the detailed radial profile of mass-loss in winds. Assuming a linear correlation between black hole luminosity powering the prompt GRB emission and accretion rate (Kumar et al., 2008b), the same procedure applied to these accretion models shows matches vastly sub-par to those shown in Fig. 13 (van Putten & Della Valle, 2017). For power law accretion profiles, discrepant behavior appears notably in a spike between the nLC and the model light curves, characterized by a prompt switch-on (cf. short GRBs). In contast, Fig. 13, shows a satisfactory match the nLC with the model light curve of black holes losing angular momentum against matter at the ISCO across the full duration of the bursts. The results for s provide some support for very long GRBs commencing from near-extremal rotating black holes, perhaps in the Thorne limit of the Bardeen trajectory of evolution (van Putten, 2015c). Furthermore, extreme luminosities in GRBs can derive from a nonlinear response to intermittent accretion about the ISCO (van Putten, 2015b), perhaps stimulated by feedback from the black hole starting from aforementioned nearly extremal spin.
3.3 Slow rotating remnants
A principle outcome of black hole evolution shown in Fig. 11 is a slowly rotating remnant, whose angular velocity has reached the fixed point in the equations of suspended accretion, satisfying
as a black hole gradually lost most of its angular momentum, and the surrounding Kerr space time relaxed to the space time of a slowly spinning black hole. Just such slow spin appears to be present in the progenitor binary estimates (2) of GW150914.
As a stable fixed point, the black hole luminosity will reach a plateau with finite luminosity in open outflows, provided there is a continuing (latent) accretion. In attributing SN2015L to black hole spin down following (33), just such plateau is seen at late times in the optical light curve. Following (32), it may signal X-ray tails (XRT) over time scales of thousands of seconds, discovered by Swift, that are remarkably universal to LGRBs and SGRBs alike, pointing to a common remnant (Eichler et al., 2009). We here identify this remnant with slowly rotating black holes about the stable fixed point (34), as a sure outcome regardless of prior formation and evolution history and progenitor (Fig. 14). In the present context, XRT’s may possibly be accompanied by long lasting low luminosity gravitational wave emission. As a common endpoint, this may appear both to normal LGRBs and SGRBs originating in mergers, following messy break-up of neutron stars in the tidal field of a companion black hole (Lee & Kluzniak, 1998; Lee & Kluznian, 1999) or in the merger of two neutron stars (Rosswog, 2007).
We estimate the resulting release in X-rays to have a luminosity for an accretion rate . Accompanying gravitational wave emissions should be very weak with negligible increase in black hole mass and angular momentum in view of the observed X-ray luminosities, e.g., erg s in GRB060614 (Mangano et al., 2007). If unsteady, large amplitude flaring may occur in, e.g., GRB050502B (Gehrels et al., 2009) by fluctuations between feedback of the black hole or accretion . See also (Lei et al., 2008).
In this broad outlook on “multi-phase multi-messenger” emissions in core-collapse events, we shall focus on a general framework for BEGE from accretion onto rotating black holes and a specific connection to the amply energy in angular momentum of rapidly spinning black holes following Fig. 11.
4 Ascending and descending chirps in accretion flows
The relatively high densities anticipated in accretion flows in catastrophic events such as mergers and core-collapse of massive stars forms a promising starting point for broadband extended gravitational-wave emission. In essence, we expect gravitational radiation derived from accretion flows and, possibly, ISCO waves excited by input from the black hole, converting angular momentum in orbital motion and, respectively, spin of the central black hole. A key pre-requisite for this outlook is the onset of non-axisymmetric waves.
4.1 Alpha-disk model
The alpha-disk model allows us to give a general frame work for mass-inhomogeneities in accretion flows. We consider a disk with the following properties:
A kinematic viscosity expressed in terms of a dimensionless parameter given by
using for the sound speed in terms of orbital angular velocity . Here, is the radial distance to the black hole of mass and, typically, . Where accretion flows are governed by viscous torques, the surface density of the disk satisfies (Pringle, 1981) for an accretion rate with asymptotic radial migration velocity , i.e.,
As shown below, under certain conditions, there exists a critical radius in (55) within which angular momentum loss is dominated by gravitational radiation;
A Lagrangian disk partition, given by annular rings of radius , radial width and mass , here in the approximation that is similar to the vertical scale height of the disk. A ring is parametrised by its mass inhomogeneity, total energy and gravitational wave luminosity
in terms of the dimensionless parameter (Appendix A), where is not necessarily small, in a local Keplerian approximation in the angular velocity distribution
We shall cover gravitational radiation from mass-inhomogeneities in accretion flows down to the ISCO. By self-gravity, these may appear as instabilities driven by cooling, wave-like or as fragments, when cooling times are on the order of the orbital period (Gamma, 2001; Rice et al., 2005). In accretion flows onto rotating black holes, a crucial condition is that such instabilities set in at a radius outside the ISCO. In this event, accretion may be driven by angular momentum loss in gravitational radiation rather than viscous torques across some critical radius greater than . Although the detailed origin and structure of mass-inhomogeneities formed is uncertain, we shall, for illustrative purposes, discuss these in the quadrupole approximation. In this approximation, migration of mass-inhomogeneities is described by (A29-A31) of Appendix A.
Spiral in of inhomogeneities by gravitational radiation dominated angular momentum loss may commence at radii large compared to . In this event, the luminosity in gravitational waves at a given mass accretion rate
For illustrative purposes, we express (40) in a Newtonian approximation of the gravitational binding energy at the ISCO to the central black hole. A more precise estimate for the latter is given by , where denotes the specific energy of orbiting matter in the Kerr metric given. Our aim here is to develop leading order estimates within a factor of a few. Accretion onto the ISCO may be followed by a plunge into the black hole or mass ejection in the form of a disk wind.
The scale (40) points to a potentially substantial energy output in gravitational waves, provided that a window or for gravitational radiation dominated angular momentum transport exists. As the following two sections show, this depends on cooling, viscous transport by random walks of large scale eddies describes by the alpha disk model (2) above and mass-inhomogeneities parameterized by . The and are probably inversely correlated, although a detailed description thereof is not known. For instance, small disks have relatively high density and/or low temperature, by which they are prone to a variety of self-gravity and wave-like instabilities that may produce .
to reflect the ratio of gravitational radiation-to-viscous mediated angular momentum transport. effectively acts as an efficiency parameter in the gravitational wave output from the extended disk in the alpha model, assumed to hold for . In this region, the efficiency in gravitational radiation is relatively low and the approximation in (36) gives the mass density profile
Accordingly, (37) implies
Adopting a scaling , the total disk luminosity , , satisfies
where and associated with a fiducial value .
Based on these preliminaries, we next turn to some specific estimates of and .
4.2 Fragmentation chirps
In self-gravitating accretion flows, a possible origin of mass inhomogeneities is fragmentation when the cooling time of the accreted matter in the instability zone is on the order of or shorter than the orbital time (e.g., (Gamma, 2001; Rice et al., 2005; Mejia et al., 2005)). The disk is unstable to axisymmetric perturbations if (Toomre, 1964; Goldrech & Lynden-Bell, 1965)
and to non-axisymmetric perturbations at slightly larger values, (e.g. (Griv, 2011)).
adopting at this radius (Popham et al., 1999; Chen & Beloborodov, 2007) with the fiducial scale for the relatively colder disk flow further out. The characteristic wavelength of the fastest growing mode is of the order of , and its mass is .
Cooling may derive from several channels. Among electron-positron pair annihilation to neutrinos, URCA process, and photo-disintegration of He, it has been argued that the latter may be most effective one in the instability zone (Piro & Pfahl, 2007). Rapid cooling may thus lead to fragmentation into a gravitationally bound clumps of mass up to a few percent of the mass of the black hole, i.e. (Piro & Pfahl, 2007):
It is unclear how many fragments are produced in this process. In (Piro & Pfahl, 2007), it is suggested that if multiple fragments form, they may merge into a mass of . Fragments thus produced will subsequently migrate inwards, initially so by viscous stresses. Any gravitational wave emission hereby derives its energy from the accretion flow. The characteristic strain amplitude hereby scales with the instantaneous strain amplitude, i.e., (cf. 20). When it reaches small enough radius with associated transition frequency