GrailQuest & HERMES: Hunting for Gravitational Wave Electromagnetic Counterparts and Probing Space-Time Quantum Foam
L. Burderi, T. Di Salvo, A. Sanna, F. Fiore, A. Riggio, A. F. Gambino, HERMES-TP, HERMES-SP Collaborations
GGrailQuest & HERMES: Hunting for Gravitational WaveElectromagnetic Counterparts and Probing Space-Time QuantumFoam
L. Burderi a , T. Di Salvo b , A. Sanna a , F. Fiore c , A. Riggio a , A. F. Gambino b , F. Amarilli i , L. Amati g ,F. Ambrosino f , G. Amelino-Camelia j,k , A. Anitra a , M. Barbera a , M. Bechini d , P. Bellutti l ,R. Bertacin e , G. Bertuccio m , R. Campana g , J. Cao n , S. Capozziello j , F. Ceraudo f , T. Chen n ,M. Cinelli o , M. Citossi p , A. Clerici q , A. Colagrossi d , E. Costa f , S. Curzel d , M. De Laurentis j , G. DellaCasa p , E. Demenev l , M. Del Santo r , M. Della Valle ν , G. Dilillo p , P. Efremov s , Y. Evangelista f, γ ,M. Feroci f, γ , C. Feruglio c , F. Ferrandi m , M. Fiorini t , M. Fiorito d , F. Frontera ψ , F. Fuschino g ,D. Gacnik u , G. Galg´oczi z , N. Gao n , M. Gandola m , G. Ghirlanda v , A. Gomboc s , M. Grassi w ,C. Guidorzi ψ , A. Guzman x , R. Iaria b , M. Karlica s , U. Kostic q , C. Labanti g , G. La Rosa r , U. LoCicero r , B. Lopez Fernandez h , P. Lunghi d , P. Malcovati w , A. Maselli β , ρ , A. Manca a , F. Mele m ,D. Mil´ankovich y , A. Monge h , G. Morgante g , L. Nava v , B. Negri e , P. Nogara r , M. Ohno z , D. Ottolina d ,A. Pasquale d , A. Pal α , M. Perri β , ρ , M. Piccinin d , R. Piazzolla f , S. Pirrotta e , S. Pliego-Caballero u ,J. Prinetto d , G. Pucacco o , S. Puccetti e , M. Rapisarda f , I. Rashevskaya δ , A. Rashevski δ , J. Ripa z, (cid:15) ,F. Russo r , A. Papitto β , S. Piranomonte β , A. Santangelo x , F. Scala d , G. Sciarrone f , D. Selcan u ,S. Silvestrini d , G. Sottile r , M. Rapisarda f , T. Rotovnik u , C. Tenzer x , I. Troisi d , A. Vacchi p, ζ ,E. Virgilli g , N. Werner z, (cid:15) , L. Wang n , Y. Xu n , G. Zampa η , N. Zampa η , ζ , S. Zane µ , and G. Zanotti da Dipartimento di Fisica, Universit`a degli Studi di Cagliari, SP Monserrato-Sestu km 0.7, I-09042Monserrato, Italy b Dipartimento di Fisica e Chimica, Universit`a degli Studi di Palermo, via Archirafi 36, I-90123Palermo, Italy c INAF-OATS, Via G.B. Tiepolo 11, I-34143, Trieste, Italy d Politecnico di Milano, Via La Masa 34, 20156, Milano, Italy e Agenzia Spaziale Italiana, via del Politecnico snc, 00133 Roma, Italy f INAF-IAPS Rome, Via del Fosso del Cavaliere 100, I-00133, Italy g INAF-OAS Bologna, Via Gobetti 101, I-40129, Bologna, Italy h DEIMOS, Spain i Fondazione Politecnico di Milano, Piazza Leonardo da Vinci, 32 20133 Milano, Italy j Dipartimento di Fisica Ettore Pancini, Universit`a di Napoli “Federico II”, and INFN, Sezione diNapoli, Complesso Univ. Monte S. Angelo, I-80126 Napoli, Italy k INFN, Sezione di Napoli, Complesso Univ. Monte S. Angelo, I-80126 Napoli, Italy l Fondazione Bruno Kessler - FBK, Via Sommarive 18, I-38123 Trento, Italy m Department of Electronics, Information and Bioengineering (DEIB) of Politecnico di Milano, ComoCampus, Via Anzani 42, 22100 Como, Italy n Institute of High Energy Physics, Chinese Academy of Sciences, China o Dipartimento di Matematica, Universit`a di Roma Tor Vergata p Universit`a degli Studi di Udine, Via delle Scienze, 206, 33100 Udine, Italy q Aalta Lab, Slovenia r INAF-IASF Palermo, Via U. La Malfa 153, I-90146 Palermo, Italy s University of Nova Gorica, Slovenia t INAF-IASF Milano, Via Bassini 15, I-20100 Milano, Italy a r X i v : . [ a s t r o - ph . H E ] J a n Skylabs, Slovenia v INAF-OAB,Via E. Bianchi 46, I-23807 Merate, Italy w University of Pavia, Department of Electrical, Computer, and Biomedical Engineering, Via Ferrata5, I-27100, Pavia, Italy x IAAT University of Tuebingen, Sand 1 - 72076 Tuebingen, Germany y C3S, Hungary z ELTE - E¨ot¨ovs Lor´and University, Hungary α Konkoly Observatory, Hungary β INAF - Osservatorio Astronomico di Roma, via Frascati 33, I-00040 Monteporzio Catone, Italy γ INFN δ TIFPA-INFN (cid:15)
Department of Theoretical Physics and Astrophysics, Masaryk University, Brno, Czech Republic ζ INFN Udine, Via delle Scienze 206, I-33100 Udine, Italy η INFN sez. Trieste, Padriciano 99, I-34127 Trieste, Italy ψ Dipartimento di Fisica e scienze della Terra, Universit`a di Ferrara, Italy µ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking,Surrey, RH5 6NT, UK ν Capodimonte Observatory, INAF-Naples , Salita Moiariello 16, 80131-Naples, Italy ρ Space Science Data Center (SSDC) - ASI, via del Politecnico, s.n.c., I-00133, Roma, Italy
ABSTRACT
GrailQuest (Gamma-ray Astronomy International Laboratory for Quantum Exploration of Space-Time) is an ambitiousastrophysical mission concept that uses a fleet of small satellites whose main objective is to search for a dispersion lawfor light propagation in vacuo . Within Quantum Gravity theories, di ff erent models for space-time quantization predictrelative discrepancies of the speed of photons w.r.t. the speed of light that depend on the ratio of the photon energy tothe Planck energy. This ratio is as small as 10 − for photons in the γ − ray band (100 keV). Therefore, to detect thise ff ect, light must propagate over enormous distances and the experiment must have extraordinary sensitivity. Gamma-RayBursts, occurring at cosmological distances, could be used to detect this tiny signature of space-time granularity. This canbe obtained by coherently combine a huge number of small instruments distributed in space to act as a single detector ofunprecedented e ff ective area. This is the first example of high-energy distributed astronomy: a new concept of modularobservatory of huge overall collecting area consisting in a fleet of small satellites in low orbits, with sub-microsecond timeresolution and wide energy band (keV-MeV). The enormous number of collected photons will allow to e ff ectively searchthese energy dependent delays. Moreover, GrailQuest will allow to perform temporal triangulation of impulsive events witharc-second positional accuracies: an extraordinary sensitive X-ray / Gamma all-sky monitor crucial for hunting the elusiveelectromagnetic counterparts of Gravitational Waves, that will play a paramount role in the future of
Multi-messengerAstronomy . A pathfinder of
GrailQuest is already under development through the
HERMES (High Energy Rapid ModularEnsemble of Satellites) project: a fleet of six 3U cube-sats to be launched by the end of 2022.
Keywords:
Gamma-Ray Bursts, X-rays, CubeSats, nano-satellites, temporal triangulation, Quantum gravity, GravitationalWave counterparts, all-sky monitor, Temporal triangulation
1. INTRODUCTION: TWO COMPELLING (ASTRO) − PHYSICAL PROBLEMS FOR THE NEXTDECADES
In this paper we review a new concept of modular observatory for high-energy astronomy from space. This new type ofspace observatory is based on the principle of Distributed Astronomy in which the overall capabilities of the instrument
Further author information:Luciano Burderi: E-mail: [email protected],Andrea Sanna: E-mail: [email protected] rise from the simultaneous use of very small and simple sub-units. This principle allows the construction, in space, ofinstruments with an enormous overall e ff ective area. Distributed Astronomy will allow to tackle two of the most compelling(astro)-physical problems of the next decades: i) The development of multi-messenger astronomy from infancy to maturity . The construction of a very high sensi-tivity all-sky monitor for the accurate localization of transient events in the X- / gamma-ray band is mandatory for thefast identification and localization of the electromagnetic counterparts of some Gravitational Wave Events (GWE). ii) To probe Space-Time granularity down to the Planck scale ( (cid:96) PLANCK = . × − cm ) . The realization of a hugee ff ective area X- / gamma-ray telescope allows to perform an ambitious Quantum Gravity experiment: to search for adispersion law for light in vacuo, that linearly depends on the ratio between photon energy and Planck energy. − Messenger Astronomy and the Multi − Messenger Astronomy Paradox
In August 2017, the first neutron star-neutron star (NS-NS) merger has been discovered by LIGO / Virgo gravitational waveinterferometers [1]. A short Gamma Ray Burst (GRB 170817A), seen o ff jet-axis, was detected 1.7 seconds after theevent, first by the Gamma-ray Burst Monitor (GBM) on board of the Fermi satellite, and later by INTEGRAL and otherobservatories [2, 3]. The intersection of the sky error box of LIGO / Virgo with that of GBM led to the first identification ofan optical transient associated to a short GRB and a GWE, opening, de facto , the era of multi-messenger astronomy [4].The timeline of the multi-wavelength detection is shown in Figure 1.Gravitational-wave interferometers are expected to both expand in number and increase in sensitivity over the next 5-10 years. The first two observing runs included both of the LIGO interferometers as well as the French-Italian Virgointerferometer. The third observing run will likely see the inclusion of a fourth site in Japan, KAGRA [5]. A fifth site inIndia, LIGO-India is in the planning, with a 2024 commissioning date [6]. By the middle of the decade, a five-site world-wide network will be operational, with a detection horizon of approximately 300 Mega-parsecs for binary NS mergers. Onthe other hand, most of the present large Field of View X- / gamma-ray observatories are expected to end operations by 2025.The situation is summarized in Figure 2. While GW170817 was detected with relative ease due to its close by distanceExpected rate of detectable Gravitational Wave EventsObjects Rate (Gpc − yr − )Short − GRBs / kilonovae 1540Long − GRBs / Hypernovae 225SuperLuminousSNe 100CC − SNe about one eventper year within25 Mpc
Table 1. (40 Mega–pc), future detections may not be so easy. This is particularly true as the sensitivity horizon of GravitationalWave detectors spreads out to hundreds of Mega–parsecs, allowing the detection of few NS–NS merger events per year.Indeed for Gravitational Wave detectors we have the following estimates: 1540 ( + + Kilonovae rate. Long-duration GRBs + HNe: 225 events Gpc-3 / yr [7]. Ifwe search for synergy with electromagnetic observations we should rescale this number for a beaming angle of 4- 8 deg.So the electromagnetic rate of long GRBs drastically decreases to about 1 GRB per Gpc-3 / yr. Other catastrophic eventslike Super Luminous SNe producing rapidly rotating black holes. The expected rate is circa 100 events per Gp3 per year.Finally we should include among the potential targets very nearby Core-Collapse Supernovae. The estimated frequencyof occurrence for these objects is about 70,000 Gpc-3 yr-1 [8]. Obviously since far less energy is emitted in GWs by The birth of Multi − Messenger Astronomy
GW170817 • NS-NS merging • Host galaxy NGC 4993 • ~ 40 Mpc •
70 observatories
Figure 1. The birth of multi-messenger astronomy: timeline of multi-wavelength detection of GW170817 / GRB170817A. Figures from[4].
CC-SNe than GRBs (the former phenomena involve -as final product- the formation of neutron stars which are well belowthe energy reservoir in angular momentum of black holes of similar mass, given their limited rotational energy), they canbe detected as GW sources only within the very local universe, likely within the Virgo circle of 20 Mpc, which impliesabout 1 event / yr. These estimates are summarized in the Table 1.Indeed, Fermi-GBM would not have detected the counterpart of an event like GW170817 at distances greater than 60Mega-parsecs. We therefore need an all-sky monitor with an area at least 10 to 100 times larger than GBM for lettingmulti-messenger astronomy to develop from infancy (one event, GW170817 / GRB170817A, detected up to date) to fullmaturity.
In the following we summarize the GRBs phenomenology, highlighting the features most relevant for the present paper: i) sudden and unpredictable bursts of hard-X / soft gamma rays with huge flux ii) most of the flux detected from 10-20 keV up to 10 MeV iii) occurrence rate of very bright GRBs (25 counts cm − s − in the 20 −
300 keV band) is ∼ − . The outlier monsterGRB130427A reached a record flux of ∼
160 counts cm − s − The Multi − Messenger Astronomy Paradox I • LIGO/VIRGO/KAGRA/LIGO-INDIA will detect GW170817 within ~ 300 Mpc with localisation accuracy ~10 deg • FERMI GBM would not have been able to detect GRB 170817A at
D > 60 Mpc
Figure 2. Schematic view of the operative schedule of Gravitational Wave Interferometers and X- / gamma-ray Observatories in theperiod 2000-2040. iv) presence of a bimodal distribution of duration 0 . − . −
100 s (Long GRBs) (see e.g.[9, 10]) v) measured rate (by an all-sky experiments on a LEO satellites) ∼ . / day [11] (estimated true rate ∼ ÷ / day) vi) Long and Short GRB with millisecond time variability are about 40% of bright GRBs. There is evidence ofsub-millisecond variability in some GRBs (see e.g. [12–14]) vii) presence of an afterglow in X-rays, UV, optical, IR, millimeter, radio (see e.g. [15]) viii) redshift measured in afterglow and host galaxies (see e.g. [16] for a review) ix) cosmological origin:spatial isotropy and distance measured from redshifts in afterglows and host galaxies (seee.g. [16] for a review)Proposed GRB progenitors are the collapse of a massive star (Hypernova model for Long GRBs) [17, 18] and the merger(because of gravitational wave emission) of two NSs (Kilonova model for Short GRBs) [19–21]. Both these events createa black hole with a transient disk of material around it that pumps out a jet of material at a speed close to the speed oflight. In the so called
Fireball model , a compact source releases a few 10 ergs within tens of seconds in a 10 km radiusregion. Regardless of the form of energy initially released, a quasi-thermal equilibrium between radiation and matter isreached. This electron-positron plasma, clumped in thin shells and opaque to radiation, accelerates to relativistic velocitieswith Lorentz factors of γ = [1 − ( v / c ) ] − / = ÷ v is the speed of the shell and c is the speed of light) untila considerable fraction of the initial energy has been converted into bulk kinetic energy. The plasma is collimated into ajet of few tens degrees opening angle. Multiple collision of relativistic shells of slightly di ff erent Lorentz factors cause theprompt emission through synchrotron radiation and inverse Compton scattering. Furthermore, shock of outer shells withinterstellar medium originates the so-called afterglow that generates radiations from X-rays down to radio. Long and ShortGRBs progenitors and details of the Fireball model are shown in Figure 3 ong GRB: BH collapse of a massive star short long
Short GRB: NS − NS binary system coalescence (emission of GW)
GRB progenitors
GRB - Fireball model • jet emission (about 10° opening angle) • multiple collision of relativistic shells ( Γ = [1 – (v jet /c) ] − ≥ • explains rapid variability • synchrotron radiation and inverse Compton scattering • energetics: 10 ergs released in 50 s Panel a) Panel b)
Figure 3.
Panel a)
Schematic representation of a Hypernova (top) and of the final phases of a NS-NS merger.
Panel b)
The
Fireball model for GRBs. Credits to NASA / ALBERT EINSTEIN INSTITUTE / ZUSE INSTITUTE BERLIN / M. KOPPITZ AND L. REZZOLLAand JUAN VELASCO)
2. DISTRIBUTED ASTRONOMY IN A NUTSHELL: HERMES AND GRAILQUEST MISSIONS INTHIS CONTEXT
Distributed Astronomy is an e ff ective way to build an all-sky monitor of excellent sensitivity to locate in the sky withgreat accuracy and study fast variability of high-energy transient, and for continuous monitoring of periodic sources. Eachdetector has a half-sky field of view, and localization capabilities are obtained by temporal triangulation of an impulsiveor periodic signal detected by a network of detectors distributed in space (see section 2.1, below).Nano-satellites can host100 cm detector in the keV-MeV range. The advantages of using fleets of nano-satellites reside in the modularity of theexperiment, allowing for: i) build-up a huge overall e ff ective area. ii) mass-production and subsequent cost reduction. iii) quick development and continuous upgrade of the detectors. HERMES (High Energy Rapid Modular Ensemble of Satellite) is a pathfinder experiment consisting of a fleet of six 3Unano-satellites in Low Earth Orbit to be launched by the end of 2022.On the other hand,
GrailQuest (Gamma Ray Astronomy International Laboratory for Quantum Exploration of Space-Time)is a mission concept including a vast fleet of hundreds / thousands of satellites proposed for the Voyage 2050 - long termplan in the ESA science program. A very promising technique for accurate localization of transient astrophysical sources is the so-called
Temporal Trian-gulation . The idea is simple and robust, as outlined in the following. Let us represent the transient event as a narrow-in time- wavefront (pulse) traveling in a given direction. Let us displace a network of detectors in space. The narrowwavefront will hit the detectors of the network at di ff erent times that depend on the spatial position of each detector and thedirection of the wavefront. Consider the simplest case of three detectors ( e.g. A, B, C) displaced on a plane on the vertexof an equilateral triangle, D being the diameter of the circumscribed circumference. The three Time of Arrivals (ToAs,hereafter) of the wavefront on each detector define the absolute ToA of the signal ( e.g. the ToA on the detector A, chosento represent reference of the time axis) and two delays ( i.e. the ToAs on B and C w.r.t. the ToA on A) that uniquely definehe direction of the source in the sky ( e.g. through a system of two equations in the two unknowns α and δ , representing itscelestial coordinates). A simplified bi-dimensional model is shown in Figure 4 In a broad sense, this method constrains the Principles of temporal triangulation
GRB front c dt baseline
Determination of source position through Delays in Time of Arrival (ToA) of an impulsive event (variable signal) over 3 (or more) spatially separate detectors Transient source in the sky defined by time of the event, position in the sky: T , α , δ (3 parameters, N PAR = 3 ) i = 1, …, N
SATELLITES j = 1, …, N
SATELLITES
DEL ij = ToA(i) – ToA(j) DEL ij = − DEL ji ; DEL ii = − DEL jj = 0 Number of (non trivial) different DEL ij : N DELAYS = N
SATELLITES × (N SATELLITES −
1) / 2 Number of independent measurements: N
IND = N
SATELLITES
Statistical accuracy in determining α and δ with N SATELLITES : σ α ≈ σ δ = c σ ToA /
2, since a di ff erence in phase modulus of λ/ D of theorder of the size of the collector of the waves ( e.g. the diameter of the mirror, for optical telescopes) simple trigonometricconsiderations imply ∆ θ ∼ λ/ D . In perfect analogy, in performing a temporal triangulation, we use the ToA of the transientsignal (pulse) as a proxy of the phases of the electromagnetic wave. Given an uncertainty σ ∆ t in the delays of the ToA oftwo detectors, the associated uncertainty in the spatial distance travelled by the pulse, ∆ s = c σ ∆ t , correspond to the limitin sensitivity to phase di ff erences of optical devices. Therefore the ”di ff raction limit” of temporal triangulation techniquesis given by ∆ θ ∼ c σ ∆ t / D , where D is typical distance between the detectors.Pursuing this analogy further, we can understand the paramount di ff erence between di ff erent interferometric techniques.Direct interferometry is the technique adopted in some optical and radio arrays of telescopes, e.g. the optical telescopesof Very Large Telescope, VLT, in the Atacama Desert, Chile, (see e.g. the recent paper on the first direct detection ofan exoplanet by optical interferometry [22]) or the radio telescopes of the Very Large Array, VLA, in Socorro, NewMexico (see e.g. https://public.nrao.edu/telescopes/vla/vla-basics ). In these cases, the optical and radiowaves are allowed to interfere directly through waveguides that convey them appropriately. On the other hand, o ff -lineradio interferometry is adopted for Earth-sized array of radio telescopes, e.g. those of Very Large Baseline Interferometer,VLBI, network (see e.g. ) or in processing data fromthe di ff erent radio and millimeter telescopes of the Event Horizon Telescope (EHT) project, an Earth size telescope arrayconsisting of a global network of radio telescopes with a angular resolution su ffi cient to resolve the event horizon of asupermassive black hole. In 2019 the EHT Collaboration published the first image of the region surrounding the eventhorizon of the supermassive black hole at the center of galaxy Messier 87 [23]. In these cases, the ToA of the phases of thewaves were recorded at each detector and, subsequently, the phases were combined with numerical codes. Direct optical orradio interferometry are complicated versions of optical devices in which scientists content themselves with knowing theoutcome of the interference phenomenon and not the separate values of the phases of the waves in the individual detectors.We want to observe that for an electromagnetic signal that is revealed through the detection of each single quanta ondi ff erent detectors of di ff erent devices, the interference pattern, and therefore the phase of the wave, is lost in the detectionprocess. This is certainly the case for optical light and therefore direct interferometry is, at moment, the only viabletechnique in this case. On the other hand, if the electromagnetic signal can be treated classically, it is possible to recordthe variable (w.r.t. time) amplitude of, e.g. , the electric vector of the wave and therefore the phases can be reconstructed aposteriori. This is the case of VLBI or EHT observations where o ff -line radio interferometry is applicable.Temporal triangulation is the analog of o ff -line radio interferometry where temporal delays play the role of phasei ff erences. It is straightforward that increasing the number of detectors from three to N DET >
3, the number of independentdelays adopted to determine the two quantities that define the position of a source in the sky ( e.g. α and δ , as before) isoverdetermined and equal to N IND = ( N DET − −
2, and the accuracy can be treated in a statistical way. For N DET > σ α STAT ∼ σ δ STAT ∼ c σ ∆ t D − ( N DET − − / . (1)To fully appreciate the potential of temporal triangulation, it is instructive to compare the resolving power of the VLA,27 radio telescopes capable of moving on the radii of a circle with a maximum diameter of 40 km, which operates in theradio band at wavelengths between 0.7 and 400 cm, with that of a configuration of detectors for high-energy photons, inthe keV-MeV band, arranged at distances comparable to those of the Earth-Moon system Lagrangian points, which we willcall Lagrange System, in this example. For the VLA, we adopt an average diameter D VLA =
20 km, an average wavelength λ =
20 km, while for the Lagrange System we adopt an average diameter of D LAG = × km and σ ∆ t = . ff raction limit of the VLA is ∆ θ ∼ λ/ D =
20 cm /
20 km ∼ ff raction limit” of the Lagrange System is ∆ θ ∼ c σ ∆ t D − = × cm / × cm ∼
15 arcsec. This shows that a temporal triangulation system displaced in space around the Earth and the Moon is capable tolocate high-energy transients with a positional accuracy only slightly worse than the VLA.
Here we describe the approach adopted to exploit temporal triangulation capabilities to investigate GRBs. The light-curve of a bright long GRB observed by Fermi-GBM is shown in Figure 5, left panel. The bright Long GRB lasted for ∆ t GRB =
40 s, with an average flux in the 50-300 keV energy band of φ GRB = . / s / cm , and a background flux of φ BCK = . / s / cm . Moreover, the GRB is characterized by variability on timescale of the order of ∼ ff erent Monte-Carlo simulations of a true long GRB C oun t s Time (s)
Monte-Carlo simulations of a true long GRB C oun t s Time (s)
Panel a) Panel b)
Figure 5. GRB130502327 observed by Fermi-GBM.
Panel a)
GRB light-curve.
Panel b)
Template at one millisecond resolution (detailof the main peak). e ff ective areas located in di ff erent positions of space. We performed cross-correlation analysis between pairs of simulatedGRB with the aim to investigate the capability to reconstruct time delays between the observed signals. As an example, thecross-correlation function at 1 µ s resolution for a pair of detectors of 100 m area is shown in Figure 6, left panel. The rightpanel shows the detail of the cross-correlation function around the peak and the best fit Gaussian. To determine a reliableestimation of the accuracy achievable using cross-correlation analysis, we repeated the procedure described 1000 times,and we then fitted the distribution with a Gaussian model, from which we estimated an accuracy of 0 . µ s. Distributionsfor di ff erent e ff ective areas, 56 cm (HERMES), 125 cm (Fermi-GBM), 1 m , 10 m , 50 m , and 100 m , are shown in the ross − correlation analysis of light − curves from two detectors cross − correlation accuracy from Gaussian fit of distribution of 1000 Monte-Carlo simulations: σ CC ≈ Cross-correlation (1µs resolution) of a bright long GRB ( Δ t = 40 s; φ GRB = 6.5 phot/s/cm ; φ BCK = 2.8 phot/s/cm ; variability timescale ≈ effective area detectors (50 −
300 keV band) zoom of 10 ms of cross-correlation centered at the main peak ( ≈ -0.1 -0.05 0 0.05 0.1 C r o ss - c o rr e l a t i on ( a . u . ) Delay (s) Cross-Correlation -0.0001 -5x10 -5
0 5x10 -5 C r o ss - c o rr e l a t i on ( a . u . ) Delay (s) Cross-CorrelationFit
Cross − correlation analysis of light − curves from two detectors -0.0001 -5x10 -5
0 5x10 -5 C r o ss - c o rr e l a t i on ( a . u . ) Delay (s) Cross-CorrelationFit
Panel a) Panel b)
Figure 6. Cross–correlation analysis of a simulated GRB seen by two identical detectors.
Panel a)
Cross–correlation function.
Panel b)
Detail of the cross–correlation function at 1 µ s around the main peak. six panels of Figure 7, top panel. The bottom panel shows the one sigma delay accuracy as a function of the e ff ective area.The accuracy scales as the inverse of the e ff ective area A to the power of 0.6, close but slightly better than the theoreticallower limit of 0.5 (grossly derived from counting statistics).The best fit formula is: σ cross ∼ σ ∆ t = . µ s × (cid:18) A (cid:19) − . . (2)In terms of the number of collected photons N (adopting the same 0 . / . ∼
40% overall background) the formula is: σ cross ∼ σ ∆ t = . µ s × (cid:18) N . × (cid:19) − . . (3)Inserting equation (2) into equation (1), it is possible to obtain the positional accuracy in the celestial coordinates of thebright Long GRB considered, once the average baseline, the e ff ective area of each detector, and their number is known.As an example, we considered the location accuracies of HERMES
Pathfinder, composed of three detectors with 56 cm e ff ective area in the energy band 50 −
300 keV, with an average baseline of 6000 km in case of a standard Long GRB,for which we adopted the rather conservative assumption of σ ∆ t = .
07 ms). In Figure 8, we show the predicted location accuracies obtainedwith
HERMES
Pathfinder ( ∼ The
HERMES
Pathfinder is composed by a fleet of six 3U nano-satellites in equatorial Low Earth Orbit to be launchedby the end of 2022. The structure of a 3U cube-sat is that of a parallelepiped 30 × ×
10 cm, which is the size of achampagne bottle. Figure 9, left panel, shows the chassis of the spacecraft, while the right panel, shows the explodedview of the spacecraft. The
HERMES satellites have full gyroscopic stabilization and pointing capabilities. Data recordingis continuous on internal bu ff er, and each satellite is equipped with S-band and VHF antennas for data download andcommand upload.The scintillator crystal X- / gamma-ray detector is located on top, with the detector window on the small face. It has ahalf-sky FoV (3 steradians FWHM). The solar panels, folded on the side of spacecraft, will be unfolded after the satelliterelease by means of the spring catapult. Figure 10, left panel, shows the exploded view of the payload that is described indetail in an accompanying paper [25]. Gadolinium-Aluminum-Gallium Garnet scintillator crystals (GAGGs, hereafter), ingrey and dark grey in the figure, are arranged in blocks of five, for a total of twelve blocks (sixty crystals), for detection of ccuracy in delays from cross − correlation analysis HERMES -2 -1 0 1 2
Delay (s) -4 O cc u rr en c e Sigma:8.2004e-05data1
GBM -1 0 1 2
Delay (s) -4 O cc u rr en c e Sigma:4.4725e-05
Delay (s) -6 O cc u rr en c e Sigma:3.3162e-06
Delay (s) -6 O cc u rr en c e Sigma:9.0514e-07
Delay (s) -6 O cc u rr en c e Sigma:3.9841e-07
Delay (s) -6 O cc u rr en c e Sigma:2.6554e-07 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
LOG Area (m2) -6.5-6-5.5-5-4.5-4 L OG S i g m a ( s ) y = - 0.58*x - 5.4 linear Best fit formula: σ DELAYS ≈ σ ToA = 3.3 µs × (A/1 m ) − Accuracy in determining delays from a bright long GRB with Δ t = 40 s; φ GRB = 6.5 phot/s/cm ; φ BCK = 2.8 phot/s/cm ; variability timescale ≈ Figure 7. Accuracy in cross correlation derived from Monte-Carlo simulations of GRBs.
Top panel)
Distributions of the delays obtainedfrom cross-correlation analysis between 1000 pairs of simulated light-curves of identical detectors, for di ff erent e ff ective areas, 56 cm (HERMES), 125 cm (Fermi-GBM), 1 m , 10 m , 50 m , and 100 m . Bottom panel)
Logarithmic plot of the one sigma delay accuracyas a function of the e ff ective area and best linear fit. photons in the band 20 keV − −
20 keV) andscintillation optical photons from GAGGs. Passive shielding of the detector box is obtained by means of tungsten layers onbottom and sides to reduce X-ray and particle background. The total e ff ective area is 56 cm and the temporal resolution is ≤ . µ s. The current detector prototype is shown on Figure 10, right panel.The HERMES
Project has been fully financed by the Italian Space Agency (HERMES Technological Pathfinder) andthe European community Horizon 2020 funds (HERMES Scientific Pathfinder) in the last four years, for a total amountjust above eight million Euros. Launch and Operation costs (for a minimum of two years) will be supported by the ItalianSpace Agency.
3. A SHALLOW DIVE INTO QUANTUM GRAVITY: MINIMAL LENGTH HYPOTHESIS,LORENTZ INVARIANCE VIOLATION, AND DISPERSION RELATION FOR PHOTONS IN VACUO
GW Triangulation & EM counterparts (Fermi GBM, INTEGRAL, HERMES Pathfinder)
Figure 8. Accuracy in the location capabilities of LIGO, LIGO + Virgo,
HERMES (red dot, ∼ . HERMES 3U CubeSat
10 HERMES-SP template WP18-20 v20171006 likely associated to optical light produced in the scintillator by an incoming hard X-ray (the set of the four SDD and the scintillator crystal is indicated as a Photon Detector Unit (PDU). The full detector will then be formed by several modules (Modular Detector Unit, MDU), each consisting of four PDUs, as represent schematically in Figure 1. Figure 1 Schematic view of one HERMES modular detector unit (MDU), made by four PDUs. Each module is composed by: • Low energy collimator. A thin optical screen will be mounted on the collimator (not shown) to avoid optical photon load on the SDD • Printed Circuit Board (PCB), on which the collimator is placed; the SDDs are mounted on the back side of the PCB, opposite to the collimator. The pre-amplifiers (preamps, represented by the red cubes), one for each SDD, are mounted on the same side of the collimator. The PCB is pierced in correspondence of the active area of the SDD to allow the bonding between SDDs and preamps and not to impede low energy X radiation • The SDDs • Thin layer of elastic and transparent material for optical contact (silicone) • Scintillator crystals (to be optically coupled to SDDs) and coated with a film that spreads the light (not shown in the drawing) • Case and light screen with the function of pressing the crystals against the SDDs In each HERMES detector 4 MDU (16 PDU) are combined in a 4 × Scintillator . Table below gives the main characteristics of the crystal selected for the HERMES application: GAGG (Gadolinium Aluminium Gallium Garnet). These new crystals are characterised by a fast response (well below 1 μ sec) and high light throughput per keV (~56 photons/keV), which allows reaching a lower energy thresholds with respect to a more standard scintillator of similar density like the BGO (~8 photons/keV). A viable alternative to GAGG is GFAG (Gadolinium Fine Aluminum Gallate), which has similar characteristics. Photo-detector.
The solid-state photo-detector that appears to be the most convenient in the framework of this project is the Silicon Drift Detector (Gatti and Rehak 1984, NIMA 225, 608), a Silicon detector that allows the decoupling of the area of photon collection (hence the Figure 2: Schematic view of the payload • × ×
30 cm • Gyroscope Stability on 3 axes • FoV(FWHM) ≈ • continuous on temporary buffer • trigger capability for data recording • continuous download of data (VHF) for monitoring of known bright sources Data download: • S − band download on ground stations (equatorial orbit) • VHF data transmission • IRIDIUM constellation for data transmission Spacecraft
3U minimum, simplest basic configuration ≤ detector6U more performing configuration ≤ detector, more accurate GPS, more accurate AOCS Panel a) Panel b)
Figure 9. Hermes 3U cubesat.
Left panel)
Chassis of the spacecraft. Credit: Lawrence Livermore National Laboratory.
Right panel)
Exploded view of the spacecraft.
Several theories proposed to describe quantum Space-Time, for instance some String Theories, predict the existence ofa minimal length for space of the order of Planck length, (cid:96)
PLANCK = (cid:112) G (cid:126) / c = . × − cm (see e.g. [26] for a review).This implies the following facts: i) these theories predict a Lorentz Invariance Violation (LIV, hereafter). According to Special Relativity, a properlength, (cid:96) , is Lorentz contracted by a factor γ − = [1 − ( v / c ) ] / when observed from a reference system movingat speed v w.r.t. the reference system in which (cid:96) is at rest. If (cid:96) MIN = α (cid:96) PLANCK (where α ∼ (cid:96) MIN is the String length), no further Lorentz contraction must occur, at this scale. This is a violationof the Lorentz invariance.anel a) Panel b)
Figure 10.
Left panel)
Exploded view of the payload. GAGGs are in grey and dark grey in the figure. SDD Array cells are the greensquares.
Right panel)
Prototype of the HERMES detector. ii)
These theories predict the remarkable fact that the space has, somehow, the structure of a crystal lattice, at Planckscale. iii)
In perfect analogy with the propagation of light in crystals, these theories predict the existence of a dispersion lawfor photons in vacuo [27]. Since, for photons, energy scales as the inverse of the wavelength, this dispersion law canbe expressed as a function of the energy of photons in units of the Quantum Gravity energy scale, which is the energyat which the quantum nature of gravity becomes relevant: E QG = ζ m PLANCK c = ζ E PLANCK , where ζ ∼ α − ∼ m PLANCK = √ c (cid:126) / G = . × − gis the Planck mass, and the Planck energy is E PLANCK = . × GeV: | v PHOT / c − | ≈ α (cid:32) E PHOT ζ m PLANCK c (cid:33) n (4)where α ∼ v PHOT is thegroup velocity of the photon wave-packet, and E PHOT is the photon energy. The index n is the order of the firstrelevant term in the expansion in the small parameter (cid:15) = E PHOT / ( ζ m PLANCK c ). In several theories that predict theexistence of a minimal length, typically, n =
1. Finally, the modulus is present in equation (4) takes into account thepossibility (predicted by di ff erent LIV theories) that higher energy photons are faster or slower than lower energyphotons (discussed as sub-luminal, +
1, or super-luminal, −
1, as in [28].We stress that not all the theories proposed to quantize gravity predict a LIV at some scale. This is certainly the case forLoop Quantum Gravity (see e.g. [29–31]). No LIV is expected as a consequence of the recently proposed Space-TimeUncertainty Principle [32] and in the Quantum Space-Time [33]. In some of these theories it is possible to conceive aphoton dispersion relation that does not violate Lorentz invariance, although the first relevant term is quadratic in the ratiophoton energy over E QG , i.e. n = E QG ∼ GeV, second order e ff ects arealmost not relevant even for photons of at 0 . eV), the highest energy photons ever recorded, recentlyconfirmed to be emitted by the Crab Nebula [34]. Indeed also for these extreme photons ( E PHOT / E QG ) ∼ − . During motion at constant velocity, travel time is the ratio between the distance travelled D TRAV and the speed. Therefore,di ff erences in speed result in di ff erences in the arrival times ∆ t QG of photons of di ff erent energies ∆ E PHOT departing fromthe same point at the same time, such as those emitted during a GRB. For small speed di ff erences, as those predicted byhe dispersion relations discussed above, these delays scales with the same order n – in the ratio ∆ E PHOT / E QG – as thatbetween photon energy and Quantum Gravity energy scale: ∆ t QG = ± ξ (cid:18) D TRAV c (cid:19) (cid:32) ∆ E PHOT ζ m PLANCK c (cid:33) n , (5)where ξ ∼ ± takesinto account the possibility (predicted by di ff erent LIV theories) that higher energy photons are faster or slower than lowerenergy photons respectively, as discussed above [28].On the other hand, the distance traveled has to take into account the cosmological expansion, being a function ofcosmological parameters and redshift. The comoving trajectory of a particle is obtained by writing its Hamiltonian interms of the comoving momentum [35]. The computation of the delays has to take into account the fact that the properdistance varies as the universe expands. Photons of di ff erent energies are a ff ected by di ff erent delays along the path, so,because of cosmological expansion, a delay produced further back in the path amounts to a larger delay on Earth. Takinginto account these e ff ects this modified ”distance traveled” D EXP can be computed [35].More specifically we adopted the so called Lambda Cold Dark Matter Cosmology ( Λ CDM) with the following values [36]: H = . − Mpc − , Ω k =
0, curvature k = Ω R =
0, radiation = w = −
1, negative pressure Equation of State for the so called Dark Energy that implies an acceleratingUniverse, Ω Λ = . Ω Matter = . D EXP c = H (cid:90) z dz (1 + z ) (cid:112) Ω Λ + + (1 + z ) Ω Matter , (6)where z is the redshift.Substituting D TRAV of equation (5) with D EXP derived in equation (6) we finally obtain the delays between the time ofarrival of photons of di ff erent energies as a function of the specific Dispersion Relation adopted, the specific Cosmologyadopted, and the redshift: ∆ t QG = ± ξ H (cid:90) z dz (1 + z ) (cid:112) Ω Λ + + (1 + z ) Ω Matter (cid:32) ∆ E PHOT ζ m PLANCK c (cid:33) n . (7) ff erent redshifts We considered a bright Long GRB lasted for ∆ t GRB =
40 s, with average flux in the 50-300 keV energy band φ GRB = . / s / cm , background flux of φ BCK = . / s / cm , and variability timescale ∼ , the numberof detected photons in each band was computed adopting a Band function, an empirical function that well fits GRB spectra[38]: dN E ( E ) dA dt = F × (cid:16) EE B (cid:17) α exp {− ( α − β ) E / E B } , E ≤ E B (cid:16) EE B (cid:17) β exp {− ( α − β ) } , E ≥ E B , (8)where E is the photon energy, dN E ( E ) / ( dA dt ) is the photon intensity energy distribution in units of photons / cm / s / keV, F is a normalization constant in units of photons / cm / s / keV, E B is the break energy, and E P = [(2 + α ) / ( α − β )] E B is thepeak energy. For most GRBs: α ∼ − β ∼ − . ÷ − .
5, and E B ∼
225 keV that implies E P ∼
150 keV. We considered softand hard cases ( β = − . β = − .
0, respectively). Once the number of photons collected in each band N is computed,the one sigma accuracy in the delays of the ToA of photons in a given energy band, E CC ( N ), is computed adopting theresults of cross-correlation analysis performed on pairs of Monte-Carlo simulated GRBs in section 2.1.1 and expressed inequation (3) adopting the most conservative assumption that E CC ( N ) scales as ( N / . × ) − . (as expected from countingstatistics) and not as ( N / . × ) − . of equation (3). We adopted the geometric mean of the lower and upper limits ofa given energy band, E min and E min respectively, as representative of the average energy of the photons in that given band E AVE = √ E min × E max . With this, the energy di ff erence between photons of di ff erent energy bands w.r.t. photons of very Long GRB ÷ keV) t = 25 s A = cm Energy band E
AVE
N E CC ( N ) N E CC ( N ) T LIV ( ⇠ = . , ⇣ = . )( = . ) ( = . ) MeV MeV photons µ s photons µ s µ s µ s µ s µ sz = . = . = . = . . .
025 0 . . ⇥ .
38 3 . ⇥ .
43 0 .
04 0 .
25 0 .
51 1 . . .
050 0 . . ⇥ .
62 1 . ⇥ .
69 0 .
13 0 .
72 1 .
46 4 . . .
100 0 . . ⇥ .
71 9 . ⇥ .
74 0 .
27 1 .
43 2 .
93 8 . . .
300 0 . . ⇥ .
79 1 . ⇥ .
74 0 .
66 3 .
51 7 .
19 20 . . .
000 0 . . ⇥ .
64 3 . ⇥ .
20 2 .
09 11 .
11 22 .
72 63 . . .
000 1 . . ⇥ .
56 8 . ⇥ .
60 5 .
40 28 .
68 58 .
67 164 . . .
000 3 . . ⇥ .
19 4 . ⇥ .
35 12 .
07 64 .
12 131 .
19 367 . . .
00 15 . . ⇥ .
54 2 . ⇥ .
33 60 .
35 320 .
62 656 .
00 1834 . dN E ( E ) dA dt = F ⇥ EE B ⌘ ↵ exp { ( ↵ ) E / E B } , E E B , ⇣ EE B ⌘ exp { ( ↵ ) } , E E B . (1)where E is the photon energy, dN E ( E ) / ( dA dt ) is the photon intensity energydistribution in units of photons / cm / s / keV, F is a normalization constant in unitsof photons / cm / s / keV, E B is the break energy, and E P = [(2 + ↵ ) / ( ↵ )] E B isthe peak energy. For most GRBs: ↵ ⇠ ⇠ . E B ⇠
225 keV that implies E P = 150 keV. E CC Long = µ s / p N phot / (2)for a Long GRB, and E CC Short = µ s / p N phot / (3)for a Short GRB. References
1. Abbott, B.P. et al., Observation of Gravitational Waves from a Binary Black Hole Merger,Physical Review Letters, 116, 061102 (2016)2. Abbott, B.P. et al., GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coales-cence at Redshift 0.2, Physical Review Letter, 118, 221101 (2017a)3. Abbott, B.P. et al., GW170814 : A three-detector observation of gravitational waves froma binary black hole, Physical Review Letter, 119, 161101 (2017b)4. Abbott, B.P. et al., GW170817: Observation of Gravitational Waves from a Binary NeutronStar Inspiral, Physical Review Letter, 119, 161101 (2017c)5. Abbott, B.P. et al., Gravitational Waves and Gamma-Rays from a Binary Neutron StarMerger: GW170817 and GRB 170817A, Astrophysical Journal Letters, 848, L13 (2017d)6. Abbott, B.P. et al., Multi-messenger Observations of a Binary Neutron Star Merger, As-trophysical Journal Letters, 848, L12 (2017e)7. Abdo, A.A. et al., Fermi observations of high-energy gamma-ray emission fromGRB080916C, Science, 323, 1688 (2009a) σ CC ≈ × (2.6 10 /N) Δ t MP/LIV = ξ (D TRAV /c) [ Δ E phot /(M QG c )] n D TRAV (z)=(c/H ) ∫ d β (1+ β )/[ Ω Λ +(1+ β ) Ω M ] GRBs & Quantum Gravity
Figure 11. Distribution of 219 GRBs detected by Swift as a function of the redshift in bins of ∆ z = .
2. Figure from [37] low energy E AVE ∼
0, are ∆ E PHOT = E AVE . We adopted the cosmology described in section 3.1, a first order dispersionrelation i.e. n =
1, and, finally, ξ = ζ =
1. The Quantum Gravity delays of the time of arrival of photons of di ff erentenergy bands were computed with equation (7), for values of the redshift z = . , . , . , .
0, typical of GRBs as shownin Figure 11. The results are shown in Table 2. Numbers in red and blue refer to delays below and just above one sigmaaccuracy, respectively. Numbers in black are above three sigma.
Because of unknown details on the
Fireball model , intrinsic delays in the emission of photons of di ff erent energy bandsare possible. For a given GRB, these intrinsic delays can mix to, or even mimic, a genuine quantum gravity e ff ect, makingits detection impossible. However, intrinsic delays in the emission mechanism are independent of the distance of the GRB.On the other hand, the delays induced by a photon dispersion law are proportional both to the distance traveled (knownfunction of redshift) and to the di ff erences in energy of the photons. This double dependence on energy and redshift isthe unique signature of a genuine Quantum Gravity e ff ect. This behavior, shown in Table 2, demonstrates that, given anadequate collecting area, GRBs are indeed excellent tools to e ff ectively search for a first order dispersion law for photons,once their redshifts are known.
4. GRB LOCALIZATION AND REDSHIFT MEASUREMENTS
Distributed astronomy o ff ers a double vantage for detecting transient events in the high-energy sky: i) thanks to the possibility of reaching an overall huge collection area, it allows to reach extraordinary sensitivity andto collect an impressive number of photons, resulting in high statistics even at tiny temporal scales; ii) by means of temporal triangulation techniques, it allows for unprecedented accuracies in location capabilities foran all-sky monitor with half-sky field of view and no pointing capabilities.The accuracy in locating the prompt emission of GRBs is particularly relevant as it allows for fast follow-up from largeoptical telescopes and determination, in almost all cases, of the redshift of the host galaxy. As an example, we consider thebright Long GRB described in section 2.1.1, for which we compute the positional accuracy for the following configurationof satellites:uantum Gravity delays predicted with a first order photon dispersion relationEnergy band E AVE
N E CC ( N ) N E CC ( N ) ∆ t QG ( ξ = . , ζ = . β = − .
5) ( β = − . µ s photons µ s µ s µ s µ s µ s z = . z = . z = . z = . . − .
025 0 . . × .
38 3 . × .
43 0 .
04 0 .
25 0 .
51 1 . . − .
050 0 . . × .
62 1 . × .
69 0 .
13 0 .
72 1 .
46 4 . . − .
100 0 . . × .
71 9 . × .
74 0 .
27 1 .
43 2 .
93 8 . . − .
300 0 . . × .
79 1 . × .
74 0 .
66 3 .
51 7 .
19 20 . . − .
000 0 . . × .
64 3 . × .
20 2 .
09 11 .
11 22 .
72 63 . . − .
000 1 . . × .
56 8 . × .
60 5 .
40 28 .
68 58 .
67 164 . . − .
000 3 . . × .
19 4 . × .
35 12 .
07 64 .
12 131 .
19 367 . . − .
00 15 . . × .
54 2 . × .
33 60 .
35 320 .
62 656 .
00 1834 . Table 2. Photon fluence and expected delays induced by a Quantum Gravity first order Dispersion Relation for the bright Long GRBdescribed in section 2.1.1 and observed with a detector of cumulative e ff ective area of 100 m (e.g. obtained by adding the photonscollected by N = nano–satellites of 100 cm each). The GRB is described by a Band function with α = − β = − . ÷ − . E B ∼
225 keV. The modified ”distance traveled” by the photons D EXP described in the text has been computed for each redshiftadopting a Λ CDM cosmology with Ω Λ = . Ω Matter = . D EXP = . z = . D EXP = . z = . D EXP = . z = . D EXP = . z = .
0. Adopting n = ξ = ζ =
1, we found | ∆ t QG | = . µ s × ∆ E PHOT / (1 MeV) for z = . | ∆ t QG | = . µ s × ∆ E PHOT / (1 MeV) for z = . | ∆ t QG | = . µ s × ∆ E PHOT / (1 MeV) for z = . | ∆ t QG | = . µ s × ∆ E PHOT / (1 MeV) for z = . ∆ E PHOT = E AVE = √ E max × E min (see text). The (statistical) cross–correlation accuracies are computed as E CC ( N ) = . µ s (cid:112) . / N , obtained from Monte–Carlosimulations. a) Large fleet of small satellites in Low Earth Orbits: A = ×
30 cm ≈ . that implies σ ∆ t = . µ sAverage baseline D ≈ ,
000 km N DET ≈ σ α STAT ∼ σ δ STAT ≈ b) Three satellites with large detectors in Earth-Moon system Lagrangian points: A = that implies σ ∆ t = . µ s.Average baseline D ≈ ,
000 km N DET = σ α STAT ∼ σ δ STAT ≈ .
5. GRAILQUEST: FIRST QUANTUM-GRAVITY DEDICATED EXPERIMENT
We conceived
GrailQuest as the first large astrophysical experiment dedicated to Quantum Gravity. The main objective ofthis experiment is the e ff ective search for a first order dispersion law for photons in vacuo to explore Space-Time structuredown to the Planck scale.We demonstrated that this ambitious goal is possible with an all-sky monitor of the Gamma-ray sky (50 keV – 50 MeVenergy band) distributed in space, with overall collecting area of the order of several tens of square meters, and very fasttime resolution of ∼ . µ s. Crystal scintillators read by Silicon Photomultiplier or Silicon Drift Detectors are a promisingclass of detectors for this experiment, under study at present moment. Temporal triangulation techniques allow to locateGRBs within few arc-seconds, allowing fast follow-up with optical telescope to obtain redshifts.In order to promote the potential of Distributed Astronomy and to support the GrailQuest project, we submitted a whitepaper in response to an European Space Agency call for the scientific long term plan Voyage 2050, following the last plan,osmic Vision, started in 2004. Voyage 2050, will cover the period from 2035 to 2050. The paper has been accepted to bepublished in a dedicated issue of
Experimental Astronomy [39].A compelling possibility for the future of distributed astronomy and, in particular, for the
GrailQuest project, is tohost the detectors, as symbionts, on the large constellations of satellites on Earth orbit. These constellations (mega-constellations, hereafter) are already under construction, or planned for the immediate future, to provide satellite internetaccess worldwide.
OneWeb * is a constellation of 650 satellites (150 kg each), in a circular Earth orbit, at 1,200km altitude, owned, amongothers, by Virgin Galactic, Arianespace, and Airbus Defence and Space. They started launching satellites in 2019 andat present already 110 satellites are operational. They recently planned to increase the number of satellites up to severalthousands.Boarding a 30 ×
30 cm e ff ective area detectors on each of the originally planned satellites, would result in a ∼
60 m e ff ective area all-sky monitor. Starlink † is a constellation of satellites (12,000 approved by International Telecommunication Union plus 30,000 re-quested and under approval) under construction by Space-X. The satellites (between 100 and 500 kg each) will be deployedin circular orbits between 340 and 1,100 km altitude. Launches started in 2018 and about 1,000 satellites were launched upto date. Even boarding a small 10 ×
10 cm e ff ective area detector on each of the originally planned satellites, would resultin a ∼
120 m e ff ective area all-sky monitor. Kuiper System ‡ , an Amazon project, is a planned constellation of 3,000 satellites in circular orbits at 600 km altitude,proposed in 2019. Also in this case, the detectors of the GrailQuest project could be hosted as symbionts on the satellitesof this constellation.In the name of scientific progress, the companies that are constructing the mega-constellations could bear part ofthe costs of building the detectors and managing the flow of scientific data. Indeed, philanthropy has often aided theadvancement of science and astronomy in particular. The famous Hale reflector in Palomar Observatory (5.1 m in diameter)was funded by Rockefeller Foundation in 1928 on a proposal by the astronomer George Ellery Hale.The last point we want to highlight, here, is another fundamental aspect of distributed astronomy which is that of beingmodular and scalable through the replication of identical and easy to implement detectors. This could allow a sort of massproduction with a massive cut in production costs, in line with the great intuition of Henry Ford, inventor of the assemblyline. A quantum leap for astronomy of the third millennium.
6. GRAILQUEST: CONCLUSIONS
Main conclusions on the
GrailQuest project are shown in Figure 12 and summarized in the following points: i) GrailQuest is a modular astrophysical observatory hosted on hundreds / thousands small satellites. ii) The simultaneous use of very small and simple sub-units allow to reach a huge overall collecting area (hundredsof square meters). iii) GrailQuest is an all-sky monitor for transient events in the X- / gamma-ray band (from few keV to 50 MeV). iv) Extraordinary temporal resolution (0 . µ s) allows, with temporal triangulation techniques, to localize the eventsdown to sub-arcsecond accuracies. v) GrailQuest will be the perfect hunter for the electromagnetic counterparts of Gravitational Wave Events. vi) GrailQuest will perform the first large scale dedicated Quantum Gravity experiment to search for a first order (inthe ratio photon energy over Quantum Gravity energy) dispersion law for photons in vacuo , constraining the Spacegranular structure down to the minuscule Planck length, (cid:96) PLANCK = (cid:112) G (cid:126) / c = . × − cm. vii) Mass production of each module (Assembly Line philosophy) will allow huge reduction of costs. * † ‡ igure 12. The GrailQuest project.
ACKNOWLEDGMENTS
This work has been carried out in the framework of the HERMES-TP and HERMES-SP collaborations. We acknowledgesupport from the European Union Horizon 2020 Research and Innovation Framework Program under grant agreementHERMES-Scientific Pathfinder n. 821896 and from ASI-INAF Accordo Attuativo HERMES Technologic Pathfinder n.2018-10-H.1-2020. LB and AS acknowledge financial contribution from the PRIN 2017 agreement n. 20179ZF5KS. LB,AS and AR acknowledge financial contribution from the FdS 2017, CUP n. F71I17000150002.
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