# Localisation of gamma-ray bursts from the combined SpIRIT+HERMES-TP/SP nano-
satellite constellation

M. Thomas  School of Physics, The University of Melbourne, VIC 3010, Australia
[ M. Trenti  School of Physics, The University of Melbourne, VIC 3010,
Australia  A. Sanna  Dipartimento di Fisica, Università degli Studi di
Cagliari, SP Monserrato-Sestu km 0.7, I-09042 Monserrato, Italy  R. Campana
INAF - Osservatorio di Astrofisica e Scienza dello Spazio, Via Gobetti 93/3,
40129 - Bologna, Italy  G. Ghirlanda  INAF - Osservatorio Astronomico di
Brera, Via E. Bianchi 46, 23807 Merate (LC), Italy  J. Řípa  Masaryk
University, Faculty of Science, Department of Theoretical Physics and
Astrophysics, Kotlářská 2, Brno, Czech Republic, 611 37  L. Burderi
Dipartimento di Fisica, Università degli Studi di Cagliari, SP Monserrato-
Sestu km 0.7, I-09042 Monserrato, Italy  F. Fiore  INAF - Osservatorio di
Astrofisica e Scienza dello Spazio, Via Gobetti 93/3, 40129 - Bologna, Italy
Y. Evangelista  INAF - Istituto di Astrofisica e Planetologia Spaziali, Via
del Fosso del Cavaliere, 100, 00133 Roma RM, Italy  L. Amati  INAF -
Osservatorio di Astrofisica e Scienza dello Spazio, Via Gobetti 93/3, 40129 -
Bologna, Italy  S. Barraclough  School of Physics, The University of
Melbourne, VIC 3010, Australia  K. Auchettl  OzGrav, School of Physics, The
University of Melbourne, Parkville, Victoria 3010, Australia.  M. O. del
Castillo  School of Physics, The University of Melbourne, VIC 3010, Australia
A. Chapman  Department of Mechanical Engineering, School of Engineering, The
University of Melbourne, Australia  M. Citossi  INAF - Osservatorio
Astronomico di Trieste, Via GB Tiepolo, 11 I-34143 Trieste, Italy  A.
Colagrossi  Department of Aerospace Science and Technology, Politecnico di
Milano, Via La Masa 34, 20156 Milano, Italy  G. Dilillo  INAF - Istituto di
Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere, 100, 00133
Roma RM, Italy  N. Deiosso  Dipartimento di Fisica, Università degli Studi di
Cagliari, SP Monserrato-Sestu km 0.7, I-09042 Monserrato, Italy  E. Demenev
FBK - Sensors and Devices, Micro Nano Facility, via Sommarive, 18 38123 Povo,
Trento, Italy  F. Longo  Department of Physics, University of Trieste, via
Valerio 2, Trieste, Italy  A. Marino  Institute of Space Sciences (ICE, CSIC),
Campus UAB, Carrer de Can Magrans s/n, E-08193 Barcelona, Spain  J. McRobbie
School of Physics, The University of Melbourne, VIC 3010, Australia  R. Mearns
School of Physics, The University of Melbourne, VIC 3010, Australia  A.
Melandri  INAF - Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807
Merate (LC), Italy  A. Riggio  Dipartimento di Fisica, Università degli Studi
di Cagliari, SP Monserrato-Sestu km 0.7, I-09042 Monserrato, Italy  T. Di
Salvo  Università degli Studi di Palermo, Dipartimento di Fisica e Chimica,
via Archirafi 36 - 90123 Palermo, Italy  S. Puccetti  ASI - Agenzia Spaziale
Italiana, Via del Politecnico s.n.c., 00133 Roma, Italy  M. Topinka  INAF –
Istituto di Astrofisica Spaziale e Fisica Cosmica, Via A. Corti 12, I-20133
Milano, Italy

(dd Mmm YYYY; dd Mmm YYYY; dd Mmm YYYY)

###### Abstract

Multi-messenger observations of the transient sky to detect cosmic explosions
and counterparts of gravitational wave mergers critically rely on orbiting
wide-FoV telescopes to cover the wide range of wavelengths where atmospheric
absorption and emission limit the use of ground facilities. Thanks to
continuing technological improvements, miniaturised space instruments
operating as distributed-aperture constellations are offering new capabilities
for the study of high energy transients to complement ageing existing
satellites. In this paper we characterise the performance of the upcoming
joint SpIRIT and HERMES-TP/SP constellation for the localisation of high-
energy transients through triangulation of signal arrival times. SpIRIT is an
Australian technology and science demonstrator satellite designed to operate
in a low-Earth Sun-synchronous Polar orbit that will augment the science
operations for the equatorial HERMES-TP/SP constellation. In this work we
simulate the improvement to the localisation capabilities of the HERMES -
TP/SP constellation when SpIRIT is included in an orbital plane nearly
perpendicular (inclination = 97.6°) to the HERMES - TP/SP orbits. For the
fraction of GRBs detected by three of the HERMES satellites plus SpIRIT, we
find that the combined constellation is capable of localising $60\%$ of long
GRBs to within $\sim 30$ deg2 on the sky, and $60\%$ of short GRBs within
$\sim 1850$ deg2 ($1\sigma$ confidence regions), though it is beyond the scope
of this work to characterise or rule out systematic uncertainty of the same
order of magnitude. Based purely on statistical GRB localisation capabilities
(i.e., excluding systematic uncertainties and sky coverage), these figures for
long GRBs are comparable to those reported by the Fermi Gamma Burst Monitor
instrument. These localisation statistics represents a reduction of the
uncertainty for the burst localisation region for both long and short GRBs by
a factor of $\sim 5$ compared to the HERMES-TP/SP alone. Further improvements
by an additional factor of $2$ (or $4$) can be achieved by launching an
additional 4 (or 6) SpIRIT-like satellites into a Polar orbit respectively,
which would both increase the fraction of sky covered by multiple satellite
elements, and also enable localisation of $\geq 60\%$ of long GRBs to within a
radius of $\sim 1.5\degree$ (statistical uncertainty) on the sky, clearly
demonstrating the value of a distributed all-sky high energy transient monitor
composed of nano-satellites.

###### doi:

10.1017/pasa.2020.32

###### keywords:

Time domain astronomy; X-ray transient sources; Gamma ray transient sources;
Space telescopes

M<EMAIL_ADDRESS>Australian Research Council Centre
of Excellence for All-Sky Astrophysics in 3-Dimensions, Australia INFN –
Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy INFN -
Sezione Tor Vergata, Via della Ricerca Scientifica, I-00133 Rome, Italy
Australian Research Council Centre of Excellence for All-Sky Astrophysics in
3-Dimensions, Australia Department of Astronomy and Astrophysics, University
of California, Santa Cruz, CA 95064, USA INFN, sezione di Trieste, via Valerio
2, Trieste, Italy Institute for Fundamental Physics of the Universe (IFPU),
via Beirut 2, Trieste, Italy Institut d’Estudis Espacials de Catalunya (IEEC),
E-08034 Barcelona, Spain INAF/IASF Palermo, via Ugo La Malfa 153, I-90146 -
Palermo, Italy INAF/IASF Palermo, via Ugo La Malfa 153, I-90146 - Palermo,
Italy dd Mmm YYYY

##  1 Introduction

The ability to localise gamma ray bursts (GRBs) from their prompt X-ray/gamma-
ray emission is a critical step in the identification and follow-up
observation of these cosmic explosions. GRB afterglows are so faint that until
the advent of large-aperture, wide-field, deep optical/infrared imaging
telescopes (e.g., the Vera Rubin Observatory - albeit with a limited FoV; see
LSST Science Collaboration et al. 2017), the location of the burst must be
determined purely from its prompt high energy photon emission.

Accurate GRB localisations and subsequent afterglow follow-up observations are
desirable across many areas of astronomy. Observations of long GRB afterglows
offer many opportunities to study the high redshift universe, and can be used
in the study of the cosmic star formation rate (e.g., Robertson & Ellis 2012;
Trenti et al. 2013; Petrosian et al. 2015, Chary et al. 2016; Lloyd-Ronning et
al. 2019), investigating the luminosity function of high redshift galaxies
(e.g., Trenti et al. 2012; Tanvir et al. 2012; Salvaterra et al. 2012; McGuire
2016), characterising the interstellar medium in distant galaxies (e.g., Klose
et al. 2004; Berger et al. 2005; Vreeswijk et al. 2007; Fox et al. 2008;
Prochaska et al. 2008; Thöne et al. 2013; Wiseman et al. 2017) and measuring
the neutral hydrogen fraction along the line of sight (e.g., Miralda‐Escude
1998; Mesinger & Furlanetto 2008; McQuinn et al. 2008; Hartoog et al. 2015;
Melandri et al. 2015; Lidz et al. 2021).

Furthermore, observations of prompt and afterglow emission from both long and
short GRBs provide unique insights into the physics of energy transport and
dissipation within relativistic jets (see e.g., Kumar & Zhang 2015; Miceli &
Nava 2022 for review articles). For example, the very recent opening of the
so-called VHE (Very High Energy) window, with the detection of TeV emission
from GRB afterglows (MAGIC Collaboration et al., 2019; Abdalla et al., 2019;
H.E.S.S. Collaboration et al., 2021), provides us with a new tool to
understand the physics of particle acceleration in weakly magnetised ultra-
relativistic shocks, and may in future also enable a better understanding of
highly magnetised mildly relativistic shocks with VHE observations of GRB
prompt emission.

More recently, GRB localisations have become useful tools in the field of
gravitational wave (GW) science due to the association between short GRBs and
compact object mergers (Eichler et al., 1989; Perna & Belczynski, 2002;
Belczynski et al., 2006). The nearly simultaneous detection of a short GRB
within the same localisation region as a GW event provides unique insight into
the true nature of these high energy explosions, as illustrated by the
simultaneous observations of the binary neutron star (BNS) coalescence event
GW170817, and the short gamma-ray burst GRB170817A (Abbott et al., 2017) which
solidified the link between short GRBs and binary neutron star mergers. In the
future, accurate localisations of short GRBs from their high energy photon
emission may also assist in more precise localisation of GW transient events
in the case where the uncertainty region from the GW signal is large.

A well-established method to localise high energy EM transients is
triangulation, whereby the source position in the sky is determined by
measuring the arrival time difference of light at each detector (see, e.g.,
Hurley et al. 2013). This method has been used to localise GRBs since they
were first discovered by the Vela satellites in 1969 (Klebesadel et al.,
1973), and has been used for the last several decades since 1976 by the Inter-
Planetary Network (IPN) (NASA/GSFC Interplanetary Gamma-Ray Burst Timing
Network111https://heasarc.gsfc.nasa.gov/docs/heasarc/missions/ipn.html), an
evolving group of independent, separately executed satellite missions all
carrying high energy photon detectors, the data from which can be combined in
order to accurately localise GRBs and other high energy transients (Hurley et
al., 1999, 2013, 2017).

Due to the cost-effectiveness of CubeSat technology in achieving specific
science goals and the potential benefit to the field of GRB science, many
nano-satellite missions and mission concepts are under development to take
advantage of this emergent new technology. Such missions include the GRID
mission (Wen et al., 2019; Wang et al., 2021), CAMELOT (Werner et al., 2018),
GECAM (Zhang et al., 2019), BurstCube (Racusin et al., 2017), EIRSAT-1 (Murphy
et al., 2021), and MoonBEAM (Hui & MoonBEAM Team, 2021). Similarly, small
hosted payload instruments on a constellation of larger satellites have been
proposed (Greiner et al., 2022).

When combined together, all these upcoming instruments for high energy
astrophysics have the potential to significantly contribute to and improve the
existing network of GRB satellites within the next decade. In fact, they could
establish an all-sky X/gamma-ray monitor capable of high precision
localisations and low-latency communications with the ground (given many
elements would be in low Earth orbit), which would dramatically increase the
number of GRBs identified in near-real time and thus accessible for rapid
afterglow follow-up observations.

The HERMES - TP/SP (High Energy Rapid Modular Ensemble of Satellites -
Technologic/Scientific Pathfinder) is a constellation of six 3U nano-
satellites (the size of small standardized-form-factor satellites is measured
in ‘Units’ U, where 1U $\approx 10\times 10\times 10$ cm3), hosting innovative
wide field-of-view (FOV) X-ray detectors for the monitoring and localisation
of GRBs and high energy transients (Fiore et al., 2020). Each satellite will
be launched into an equatorial low Earth orbit (LEO), and the constellation is
designed to not only triangulate GRBs and high-energy transients on the sky
(Sanna et al., 2020) but also to probe the quantum structure of spacetime
thanks to sub $\mu s$ timing resolution of the HERMES instrument (Burderi et
al., 2020). The HERMES - TP/SP is designed to demonstrate accurate GRB
localisation mainly in the right ascension coordinate - the equatorial orbit
of the pathfinder satellites imposes inherent geometrical limitations on
triangulation which means that GRBs will be only loosely constrained in the
declination coordinate (Sanna et al., 2020). This limitation is expected to be
addressed in a future HERMES Full Constellation (FC), which is envisioned to
consist of tens of satellites into several different orbital planes to achieve
accuracy of localising bright long GRBs better than $15^{\prime}$ (Fiore et
al., 2020).

As a first step to demonstrate the potential of the HERMES FC, the SpIRIT
(Space Industry Responsive Intelligent Thermal) nano-satellite is an
Australia-Italy nano-satellite mission planned for launch in 2023 which will
operate as part of the HERMES - TP/SP, forming a combined constellation of
seven satellites designed to detect and localise high energy transient events.
SpIRIT will be the only satellite among the HERMES Pathfinder to be launched
into a Polar orbit, which will enable improved localisation in the declination
coordinate due to SpIRIT’s large baseline perpendicular to the equatorial
plane. In this capacity, SpIRIT will act as a proof-of-concept for the HERMES
FC to demonstrate the GRB localisation capabilities with satellites in
different orbital planes.

In this paper we simulate the localisation capabilities of the combined SpIRIT
+ HERMES - TP/SP constellation in order to understand the improvement gained
by having a single satellite element in Polar orbit. As an extension, we
further investigate the localisation capabilities of a combined constellation
with as many as six additional satellites launched into Polar orbit.

This paper is organised as follows: Section 2 provides a brief background to
the HERMES Technologic/Scientific Pathfinder mission and gives details
regarding the HERMES X-ray instrument. Section 3 introduces the SpIRIT nano-
satellite mission. Section 4 describes our simulation framework and modelling
assumptions, as well as the mathematical techniques used for the triangulation
and localisation of GRBs. In Section 5 we compare the GRB localisation
capabilities and the sky coverage statistics of the HERMES - TP/SP with and
without the SpIRIT satellite, and with a larger number of polar nano-
satellites. The main conclusions from this work are presented in Section 6.

##  2 HERMES-Technologic and Scientific Pathfinder

The HERMES - TP/SP is a constellation of six 3U nano-satellites being
developed with funding from the Italian Space Agency and the Italian Ministry
for education, University and Research (PI: Burderi) and from the European
Union’s Horizon 2020 Research and Innovation Program (PI Fiore; see Fiore et
al. (2020) for further details). The HERMES - TP/SP is an in-orbit
demonstration of the capabilities of distributed aperture astronomy in the
field of GRB science. It is designed as an intrinsically modular experiment
which can later be naturally expanded to provide a global, sensitive all-sky
monitor for high-energy transients (the HERMES - FC; see e.g., Fuschino et al.
2019 for discussion).

The HERMES - TP/SP mission is in advanced stages of development. The critical
design review was successfully passed in late 2020 (Fiore et al., 2020), and
integration and testing of flight units has been taking place since mid-2021.
Integration and testing is continuing throughout 2022, and the constellation
is expected to be launched to a nearly equatorial (inclination $\leq
20\degree$) low Earth orbit (Fiore et al., 2021).

Each satellite hosts a miniaturised X-ray detector - the HERMES instrument -
based on the so-called ‘siswich’ concept of silicon drift detectors (SDD’s)
coupled with scintillator crystals. The instrument has a burst sensitivity of
2 photons/cm2/s for $E\leq 20$keV and 1 photon/cm2/s for $50\leq E\leq 300$keV
(which is comparable to the Fermi GBM burst sensitivity of $<0.5$
photons/cm2/s between 50-300 keV (NASA/GSFC Fermi Gamma-ray Space Telescope
GBM Specifications &
Performance222https://fermi.gsfc.nasa.gov/science/instruments/table1-2.html)),
and low background for its size (Evangelista et al., 2020; Campana et al.,
2020). Its two operative modes – direct X-ray absorption on the SDD or
scintillation light readout from the GAGG crystals – cover a wide energy range
(3-60 keV and 20-2000 keV, respectively; Fuschino et al. 2020). The instrument
has excellent temporal resolution ($<400$ns), and has been designed for
detection of cosmic high energy transients (such as GRBs) and for the
determination of their positions through triangulation via the distributed
detector architecture.

The response function of the HERMES instrument depends on both the energy of
the incoming photon and its incident angle on the detector relative to the
line of sight (LOS), and we refer to Campana et al. (2020) for a plot of the
instrument response as a function of photon energy and incident angle. The
response of the HERMES instrument as a function of incident angle for energies
between $50-300$ keV can be approximated by a cosine profile with respect to
the LOS, meaning that the full width at half maximum (FWHM) of the instrument
is 120deg, corresponding to an effective FOV of 3.2sr FWHM or, equivalently, a
circular FOV with a radius $60\degree$ (Colagrossi et al., 2020; Evangelista
et al., 2020). In this work we adopt the use of a cosine profile out to a
radius of 80 degrees for the instrument response (IR):

####

$IR(\theta)=\begin{cases}\cos\theta&,\theta<80\degree\\\
0&,\theta>80\degree\\\ \end{cases}\\\ $ (1)

The 80 degree cutoff is motivated as approximately representative of the
physical obstructions to the detector field of view, given how the instrument
is mounted on the SpIRIT satellite. We note that we have assumed that the
aluminum chassis of the satellite and the tungsten shielding of the instrument
block all radiation coming from incident angles $>80\degree$ \- in reality
this may not be the case, and a more detailed procedure – or ultimately in-
orbit verification against GRBs with known localisation – would be needed to
determine which satellites observe the GRB within their FOV and which observe
it off-axis. In the context of this work, the approximation given in Equation
1 is sufficient for quantifying the improvement in GRB localisations gained by
augmenting the HERMES - TP/SP with satellites in polar orbit.

##  3 SpIRIT Nano-Satellite

The SpIRIT satellite is an Australia-Italy mission supported in Australia by
the Australian Space Agency International Space Investment - Expand Capability
scheme. SpIRIT is a 6U CubeSat with $\sim 11.5~{}\mathrm{kg}$ mass and linear
dimensions of approximately $30\times 20\times 10~{}\mathrm{cm}$ when stowed
in the launch dispenser. SpIRIT will be launched in a Polar Sun-synchronous
orbit with $\sim 550~{}\mathrm{km}$ altitude and approximately 1:30pm LTDN
(Local Time at the Descending Node), and has a target main mission lifetime of
24 months including commissioning.

Figure 1: Diagram of the SpIRIT nano-satellite, demonstrating the orientation
of the solar panels (facing away from the view on the right) relative to the
HERMES instrument (located on the top face near the left). Also visible on the
left side are the deployable thermal radiators.

SpIRIT is being developed by an Australian consortium led by the University of
Melbourne (PI: Michele Trenti), which is responsible for the project
management and mission design, as well as for the development of four
subsystems:

  1. 1.

The Payload Management System (PMS), a dedicated computer that manages
operations of all payloads and related data processing. This system is based
on a SmartFusion2 System on Chip (SoC) Field Programmable Gate Array (FPGA)
which includes a Cortex-M3 microprocessor and FPGA logic. A Graphic Processing
Unit is also part of PMS for additional on-board data processing capabilities
(including a progressive compression algorithm for improved performance in
imaging data downlink). PMS also includes a Power Management Module with
multiple supercapacitors to guarantee up to 60 seconds of uninterrupted power
supply to the HERMES instrument and allow it to transition to a safe mode in
case of temporary power failure at the platform level.

  2. 2.

The Thermal Management Integrated System (TheMIS), a subsystem for precision
thermal management and active cooling of payloads that includes (a) a Stirling
cycle cryocooler capable of achieving $T=80~{}\mathrm{K}$ cold-tip
temperature, (b) custom-developed control electronics designed for space
operations, (c) multiple temperature monitoring sensors, (d) and deployable
thermal radiators.

  3. 3.

Mercury, a low-latency communication subsystem that combines Iridium and
Globalstar user terminals to provide capability of sending and receiving short
burst data packets (e.g. target of opportunity commands or burst alerts).

  4. 4.

LORIS, a set of visible and near-infrared inspection cameras that will monitor
and characterise key elements of the spacecraft, including one mounted on a
deployable arm, seen on the bottom of the satellite in Figure 1.

The main scientific payload of SpIRIT is a HERMES instrument unit, identical
to the ones that will fly on the HERMES - TP/SP satellites. The HERMES
instrument on SpIRIT will accumulate a higher total ionizing dose compared to
a satellite in an equatorial orbit due to its repeated passage over the South
Atlantic Anomaly and the Poles. To reduce the resultant buildup of leakage
current and mitigate the performance degradation of the instrument (Dilillo et
al., 2020), SpIRIT will feature active thermal management conducted by the
TheMIS payload, with a target operating temperature of $T=245\pm
1~{}\mathrm{K}$. The lower the temperature the greater the benefit, and TheMIS
would, in principle, be capable of cooling a well-insulated instrument to
cryogenic temperatures ($T\sim 80~{}\mathrm{K}$), but the HERMES instrument
electronics in the current design are only rated to $T\gtrsim
240~{}\mathrm{K}$. A CAD illustration of the satellite is shown in Figure 1.

All of these elements make SpIRIT a mission designed to demonstrate new
technologies in orbit and the scientific operation and performance of the
HERMES instrument in high inclination orbits.

##  4 Simulating GRB Triangulation

In this Section we introduce our analysis framework to simulate and localise
GRBs using the HERMES (+ SpIRIT) nanosatellite constellation.

###  4.1 Satellite Orbits

Using as a starting point of our analysis the orbital configuration and
pointing strategy presented in Colagrossi et al. (2020), we simulate each of
the six satellites in the HERMES - TP/SP as being uniformly spaced around the
same circular 550km equatorial orbit ($\text{inclination}=0$,
$\text{eccentricity}=0$).

For simplicity we presume that the satellites maintain their equidistant
spacing over time, neglecting environmental perturbations to each spacecraft’s
orbit. We note that this configuration is close to the optimal configuration
of the HERMES - TP/SP as it maintains a large baseline between neighbouring
satellites, meaning that our results will show an idealised comparison between
the HERMES - TP/SP and SpIRIT + HERMES - TP/SP constellations.

We model the SpIRIT satellite in a 550km Polar sun-synchronous circular orbit
($\text{inclination}=97.6\degree$, $\text{eccentricity}=0$) with a 1:30pm
LTDN. When modelling several SpIRIT-like satellites in Polar orbit, we
position them equally around a 550km Polar sun-synchronous orbit, just as the
HERMES-TP/SP is uniformly spaced around an equatorial orbit. The spacing of
the satellites around a Polar orbit depends on how many satellites are in this
orbital plane, e.g., two satellites in Polar orbit will be on opposite sides
of the globe, but four satellites will only be a quarter of the way around the
globe from their nearest neighbour.

Figure 2: Particle background maps (in Earth coordinates) for a satellite in
550km low Earth orbit, obtained using the AP8MIN (protons) and AE8MAX
(electrons) models included in ESA’s SPENVIS system. Note that the South
Atlantic Anomaly (the high particle flux region around lat $\sim-45$, lon
$\sim 0$) features in both the electron and proton flux maps. The high-flux
bars across the top and bottom of the e- map reflect the rings around Earth’s
poles. In the colour scheme, black indicates regions with zero integral flux.

###  4.2 Particle Background Modeling

The scientific operations of the HERMES and SpIRIT satellites are highly
dependent on the high energy particle flux in low-Earth orbit. Space radiation
can not only damage the solid-state sensors (Ripa et al., 2020), but it also
increases the level of background noise in the HERMES instrument (Dilillo et
al., 2020, 2022), making it more difficult to detect faint GRBs and increasing
the signal cross-correlation uncertainty when trying to triangulate a burst.
While the influence of high energy particles is minimal for satellites in low-
altitude equatorial orbit, they will have a substantial impact on SpIRIT which
– due to its Polar orbit – will traverse multiple times a day both of the high
flux regions around the poles as well as the South Atlantic Anomaly (SAA).
While there is still a background flux of particles outside of the SAA and the
poles (see e.g., Ling 1975; Cumani et al. 2019), the flux is low enough that
it does not prohibit the detection of GRBs or pose a risk to the operation of
the detector.

In this work we make use of particle background maps from ESA’s Space
Environment Information System333https://www.spenvis.oma.be/credits.php
(SPENVIS), specifically the time-averaged electron integral flux above 0.04MeV
and the proton integral flux above 0.1MeV obtained using the AP8MIN and AE8MAX
models included in SPENVIS (Figure 2). Conservatively, we assume that SpIRIT
and the HERMES satellites will not operate the HERMES instrument while
travelling through a region with non-zero particle background in the maps
considered (non-black regions in Figure 2), and we take this into account in
the orbital simulations presented in Section 4.4. With this assumption, and
taking into account the orbits defined in Section 4.1, we find that on average
each satellite in the HERMES - TP/SP has approximately a $\sim 92\%$ duty
cycle, while SpIRIT (and any satellite in Polar orbit) has a $\sim 65\%$ duty
cycle.

As a consistency check for the duty cycle and particle background modeling, we
considered in-flight data from VZLUSAT-2 (Granja et al., 2022) (mission
overview available online at the VZLUSAT-2 website444
https://www.vzlusat2.cz/.) and GRBAlpha (Pál et al., 2020), two satellites
that carry a similar detector to the HERMES instrument. Here we computed the
fraction of their orbits where the instrument noise is below the threshold to
detect a typical long GRB at $S/N>5$ (i.e. assuming a GRB flux greater than
$1.19~{}\mathrm{ph/cm^{2}/s}$ for energy $E>30~{}\mathrm{keV}$) using the
simulation framework outlined in Galgóczi et al. (2021). After mapping those
results to the expected orbit of SpIRIT (taking advantage of the similarity
with VZLUSAT-2, which is also in a Polar orbit, and rescaling for the
sensitivity of HERMES) we estimate a 67% duty cycle for SpIRIT, which is in
very good agreement with the estimate derived using the particle background
maps.

Figure 3: Left column: 3D representation of the pointing strategy of the
combined SpIRIT + HERMES - TP/SP constellation (not to scale). Note that for
each constellation the satellites in a given orbital plane are uniformly
spaced around their orbit. Note that for a satellite with $n$ elements in
Polar orbit, the maximum number of Polar-orbiting satellites which can
simultaneously detect a GRB is $n/2$ (with the exception of the case of a
single Polar satellite). Right column: Sky-coverage analysis of the
corresponding constellation demonstrating the probability that a random GRB
will be detected by $n$ satellites (taking into account satellite FOV, the
nominal flux limit of the HERMES instrument, and satellite passage through
regions of high particle flux) generated from $10^{4}$ simulated trials.

###  4.3 Satellite Pointing Strategy

The pointing direction of SpIRIT is constrained by several factors. The first
constraint is the requirement to keep its solar panels illuminated by the Sun
(i.e. within $\pm 20\degree$ of the Sun normal vector), which in turn
restricts the direction that the on board HERMES detector - located on a face
orthogonal to the solar panel - can point at, since the solar panels are fixed
(see Figure 1). Secondly, it is undesirable to point the HERMES instrument
within a $90\degree$ angle of the Sun, as this would cause the detector to be
directly illuminated by sunlight. The final constraint that we impose on
SpIRIT’s pointing in this work is the requirement to align its field of view
with that of the HERMES - TP/SP to ensure the concurrent detection of GRB
events.

A full optimisation of the pointing strategy of a nano-satellite constellation
which combines satellites in equatorial and Polar orbits with additional
astrophysical constraints (i.e. preference for avoidance of the galactic
plane) is beyond the scope of this work. Instead, we adopt a simplified
framework (Figure 3) taking advantage of the pointing strategy optimisation
already carried out by the HERMES - TP/SP team (Colagrossi et al., 2020; Sanna
et al., 2020):

  * •

The six satellites in the HERMES - TP/SP follow the optimal pointing strategy
outlined in Sanna et al. (2020), where the constellation is arranged into two
co-pointing groups of three satellites. In this work we orient those two co-
pointing groups at right angles to the sun, towards the coordinates
$(\alpha,\delta)=(\alpha_{\text{sun}}+90\degree,0\degree)$ or
$(\alpha_{\text{sun}}-90\degree,0\degree)$. While the satellites orbit around
the globe they will re-orient themselves to point at whichever field of view
is not obstructed by the Earth. This results in both pointing directions being
constantly observed by three HERMES - TP/SP satellites at any given time.

  * •

The SPIRIT nano-satellite will align its field of view with one of the HERMES
- TP/SP triplets at any given point in time, pointing at either
$(\alpha,\delta)=(\alpha_{\text{sun}}+90\degree,0\degree)$ or
$(\alpha_{\text{sun}}-90\degree,0\degree)$. As SpIRIT crosses the Earth’s
poles, it will re-orient itself to point in the opposite direction such that
its field of view is always minimally obstructed by Earth. In the case of
additional Polar satellites similar to SpIRIT, each satellite will
independently follow this strategy such that every satellite is co-pointing
with one of the HERMES - TP/SP triplets at any given point in time.

Note that for the actual HERMES - TP/SP constellation in orbit (or for any
constellation of Polar-orbiting satellites) the satellites will drift over
time in absence of active orbital control maneuvers, hence the pointing
strategy of the satellite triplets would have to be constantly updated and
optimised based on the actual positions of the satellites (Sanna et al.,
2020). However, in this work we neglect satellite drift, using instead the
simplified configuration with constant relative orbital phases as outlined
above.

###  4.4 Simulation Method

We model the orbits of each satellite as defined in Section 4.1. We ignore the
Moon in our simulations since it occupies such a small fraction ($\sim
0.25\degree$ radius) of the sky, and likewise the influence of the Sun is not
relevant as our satellites point at a $90\degree$ offset from the Sun and
their FoV only has a $80\degree$ radius. However, we do track the position of
Earth for LoS obstruction calculations; from a 550km LEO, Earth has an angular
diameter of $\sim 134\degree$, meaning that Earth will maximally encroach on
one side of the satellite’s FOV by $\sim 47\degree$ when Earth is
perpendicular to the satellite’s pointing direction (assuming the HERMES
instrument’s FOV has a radius of $80\degree$). We additionally track the
operational status of the HERMES instrument on board each satellite based on
the particle background maps presented in Section 4.2.

To compare the localisation capabilities of different sized nano-satellite
constellations, we generate a random sample of $10^{4}$ long and $10^{4}$
short GRB events for each constellation that we test. The procedure for
simulating each GRB is as follows:

  1. 1.

Each GRB is generated with a random right ascension and declination (sampled
from a uniform distribution across the celestial sphere), and occurs at a
random time in the year.

  2. 2.

We generate the flux, $F_{GRB}$, of the GRB by selecting a random burst from
the Fermi GBM catalog (FERMIGBRST - Fermi GBM Burst
Catalog555https://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html;von
Kienlin et al. 2020; Gruber et al. 2014; von Kienlin et al. 2014; Bhat et al.
2016). Specifically, we randomly select one of the ‘Flnc_Band_Phtfluxb’ values
(the average photon flux, in photon/cm2/s between 50 and 300 keV, for a Band
function law fit to a single spectrum over the duration of the burst. For long
GRBs, we sample from the set of bursts with $T90>2$ seconds (as reported by
the catalog), and for short GRBs we take those with $T90<2$ seconds, where
$T90$ is defined as the time interval over which the GRB emits 90% of the
total energy of its prompt emission phase.

  3. 3.

If the GRB occurs within the FOV of one of the co-pointing groups in the
constellation, we check whether each satellite has LOS to the coordinates of
the GRB or whether they are occulted by the Earth.

For each satellite that has LOS to the burst we calculate the observed GRB
flux, $F_{obs}$, based on the incident angle of the GRB to the detector
(Equation 1). Note that we do not include Poisson noise on the observed flux
of the GRB.

We model the flux sensitivity of the HERMES instrument as four times less
sensitive than Fermi GBM (as per Section 2). Given we are sampling
‘Flnc_Band_Phtfluxb’ values from the Fermi GBM database, this corresponds to:

$F_{\text{lim}}=\begin{cases}0.463\text{\,ph}/\text{cm}^{2}/\text{s}&,\text{Long
GRBs}\\\ 1.861\text{\,ph}/\text{cm}^{2}/\text{s}&,\text{Short
GRBs}\end{cases}$ (2)

We consider a satellite to detect a GRB if it has LOS to the burst and
$F_{\text{obs}}>F_{\text{lim}}$.

Note that in the simplified context of our simulation the value of $F_{obs}$
is the same for all co-pointing satellites in the constellation, since we
model them as pointing at the exact same coordinates. In reality this issue is
far more complex - the pointing of each satellite will drift slightly, the
response function of each HERMES instrument may differ slightly in shape or
absolute value, and there will be incident-angle dependent energy dispersion
which scatters high energy photons down to lower energies, influencing the
number of photons in the chosen energy band.

  4. 4.

We compute the standard deviation on cross-correlation uncertainty
$\sigma_{cc}$ according to the observed flux $F_{obs}$ using the power-law
fits plus Gaussian scatter model detailed in Table 1.

We note that this method contains several large simplifications regarding the
photon energy, noise treatment, and incident angle response of the HERMES
instrument and the relation between GRB flux and cross-correlation
uncertainty, both of which will impact the accuracy of the results presented
in this work. However, as the purpose of this work is to demonstrate the
improved localisation performance gained by launching a satellite into a
different orbital plane, we proceed with these simplifying assumptions and
highlight that our results should only be considered an approximate estimate
of the nano-satellite constellation’s GRB localisation capabilities to within
a factor $\approx 2$ of precision.

####  4.4.1 Subsample of ”observable” GRBs

By construction, the method presented above includes the generation of GRB
events that cannot be observed by the nano-satellite constellation (either
because they are too faint or occur outside the FOV of the constellation), or
that are otherwise unsuitable for localisation if too few satellites detect
the burst. For these reasons, and to aid in the clarity of our results, we
define the following additional conditions that must be met in order to
include a GRB in our sample of $10^{4}$ events that we use as base for our
analysis:

  * •

The GRB must occur within the FOV of one of the co-pointing groups in the
constellation:

$\text{Burst incident angle }\theta\leq 80\degree.$

Since the nano-satellite constellation is divided into two co-pointing groups
each pointing in opposite directions the burst can only ever be detected by
one co-pointing group at a time.

  * •

The observed flux of the GRB must be higher than the nominal flux limit of the
HERMES instrument:

$F_{\text{obs}}=F_{\text{GRB}}\times\cos{\theta}\geq F_{\text{lim}}.$

  * •

At least three satellites in the constellation must directly detect the burst:

$N_{\text{det}}\geq 3.$

In order to localise the burst using triangulation techniques at least three
independent detections are needed (see Section 4.5). Note that we do not
enforce that every satellite in the co-pointing group detects the GRB, since
Earth may reduce the effective field of view of some elements, and a non-
detection in this context can still contribute to the burst localisation (see
Section 4.5.3 for further discussion).

  * •

Every satellite in the co-pointing group must be operational at the time of
the burst (i.e., not travelling through a region of high particle flux). We
impose this restriction because the GRB localisation capabilities of an
n-satellite constellation with one satellite missing are approximately
equivalent to localisation statistics reported by an (n-1) satellite
constellation (not taking into account the FOV and orbital position of each
satellite). Therefore, to avoid such overlap in our results we enforce that
every co-pointing satellite is operational at the time of the burst.

  * •

In the case of the SpIRIT + HERMES - TP/SP constellation (i.e., a
constellation with only one satellite in Polar orbit) we impose one additional
condition that SpIRIT is part of the co-pointing group that detects the GRB.
Without this condition, the localisation capabilities presented for the SpIRIT
+ HERMES - TP/SP constellation would consist both of bursts that are observed
by SpIRIT + 3 HERMES satellites, as well as bursts that are observed by only 3
HERMES satellites, the latter of which would be identical to the localisation
capabilities presented for the HERMES - TP/SP constellation alone. Therefore
we ensure that SpIRIT is part of the co-pointing group that detects the GRB,
which is only true for $\sim 50\%$ of bursts (since SpIRIT can only point
towards one of the two fields at any given time). Note that we do not enforce
that SpIRIT detects the GRB; we only impose that it is co-pointing with other
satellites that detect the GRB.

If a simulated GRB meets these conditions, then we include it in our sample
and perform the localisation technique described in the following section.

###  4.5 Triangulating GRBs

####  4.5.1 Triangulation Method

In this work we follow the localisation method used in Sanna et al. (2020),
which utilises the arrival time difference of photons at each detector in
order to triangulate the position of the GRB. This technique has been used for
decades by the IPN to triangulate the positions of GRBs (see e.g., Hurley et
al. 1999, 2013), and as such is appropriate for our estimation purposes,
despite some limitations discussed more in Section 4.5.2. Here, we provide a
brief outline of the method, referring the reader to the work referenced above
for full details.

As GRBs occur at cosmological distances, one can represent the gamma ray
photons from the burst as a narrow plane wave travelling through space. Given
a network of $n$ detectors distributed throughout space (i.e., a satellite
constellation), this plane wave will pass over each detector $i$ at a
different global time $t_{i}$ depending on the coordinates of each detector
$\vec{r}_{i}$.

If the GRB occurred at right ascension $\alpha$ and declination $\delta$, its
Cartesian direction can be represented by unit vector d̂:

$\textbf{\^{d}}(\alpha,\delta)=\\{\cos{\alpha}\cos{\delta},\sin{\alpha}\cos{\delta},\sin{\delta}\\}.$
(3)

Defining $t_{0}$ as the time the GRB signal reaches the origin of the chosen
reference frame, the arrival time of photons at detector $i$ is then given by

$t_{i}=t_{0}-\frac{\vec{r_{i}}\cdot\textbf{\^{d}}}{c},$ (4)

Where $\vec{r_{i}}$ represents the position vector of the $i$-th detector. The
time delay between two satellites will then be:

$\Delta
t_{ij}(\textbf{\^{d}})=\frac{(\vec{r_{j}}-\vec{r_{i}})\cdot\textbf{\^{d}}}{c}.$
(5)

In Equation 5, $\Delta t_{ij}$ represents the difference in arrival time of
the signal at each instrument due purely to satellite geometry. The measured
value of time delay $\Delta\tau_{ij}$ will depend on this intrinsic time delay
plus some offset due to measurement uncertainty:

$\Delta\tau_{ij}(\textbf{\^{d}}_{GRB})=\Delta
t_{ij}(\textbf{\^{d}}_{GRB})+\mathcal{N}(0,\sigma_{cc}),$ (6)

where the term $\mathcal{N}(0,\sigma_{cc})$ represents the uncertainty on the
measurement of the arrival time difference. This timing uncertainty is
discussed in detail in Sections 4.5.2 and 4.5.3.

To estimate the true position of the GRB, we compare the measured time-delay
pairs $\Delta\tau_{ij}(\textbf{\^{d}}_{GRB})$ from each satellite that
detected the GRB to the time delays that would be measured if the GRB were
coming from some guess direction, $\Delta t_{ij}(\textbf{\^{d}}_{guess})$. In
this work we perform this comparison using a non-linear least squares method:
we define the $\chi^{2}(\textbf{\^{d}}_{guess})$ function as the sum of the
squares of the differences between the expected and measured time delays
divided by the uncertainty on the signal alignment after cross-correlation:

$\chi^{2}(\textbf{\^{d}}_{guess})=\\\
\sum_{i=0}^{n-2}\sum_{j=i+1}^{n-1}\frac{(\Delta\tau_{ij}(\textbf{\^{d}}_{GRB})-\Delta
t_{ij}(\textbf{\^{d}}_{guess})^{2}}{\sigma_{\text{cc}}^{2}}.$ (7)

The coordinates of the GRB can then be estimated by finding the value of
$\textbf{\^{d}}_{guess}$ which minimise the $\chi^{2}$ function. Equation 7
takes the form of a ‘minimum $\chi^{2}$’ function with two degrees of freedom
(right ascension and declination), and so we estimate the $68\%$ and $90\%$
confidence region of the source localisation as the set of all values of
$\alpha,\delta$ where (Avni, 1976):

$\chi^{2}(\alpha,\delta)-\chi^{2}_{\text{min, sky}}<=\begin{cases}2.3&,68\%\\\
4.61&,90\%\end{cases}$ (8)

Note that Equation 8 is a linear approximation for determining the $68\%$ and
$90\%$ confidence intervals. In fact this equation is only asymptotically
correct for linear models, and as triangulation is a non-linear problem, the
degrees of freedom are not necessarily exactly 2. In fact, the exact value of
the degrees of freedom depends on data quality and predictiveness of the fit
parameters (e.g., Janson et al. 2013).

Finally, we consider the sky coverage and LOS of each satellite in the co-
pointing group, which influences GRB localisation depending on whether each
satellite directly detects the GRB:

  * •

If a satellite detects the GRB, we exclude all directions
$\textbf{\^{d}}_{guess}$ from the localisation region that are either outside
that satellites FOV or obstructed by the Earth from that satellite’s
perspective.

  * •

If one satellite in a co-pointing group does not detect the GRB, but other
satellites in that co-pointing group detect the burst, then we only consider
possible burst directions $\textbf{\^{d}}_{guess}$ that were obstructed by
Earth from the non-detecting satellite’s perspective.

####  4.5.2 Signal Cross-Correlation Uncertainty

The triangulation method for GRB localisation relies heavily on an accurate
estimation of $\Delta\tau_{ij}$ \- the measured time difference between the
signal arriving at each detector in the network. Classically, this time
difference has been computed by binning the light curves observed by each
detector with some temporal resolution (which usually depends on the flux of
the GRB - brighter bursts can be binned with finer resolution), and then using
a cross-correlation algorithm to determine the time offset between the two
observed signals (Hurley et al., 1999, 2013; Sanna et al., 2020). Note that
Equation 7 therefore presumes that the only source of timing uncertainty is in
the signal cross-correlation, which is a valid approximation in our case as
the uncertainty on cross-correlation is of the order $\sim 1$ ms (Sanna et
al., 2020) whereas the positional uncertainty on the satellite is $<30$ m
(translating to a temporal accuracy of $<20$ ns; Fiore et al. 2020) and the
detector has an absolute timing accuracy lower than $0.4\,\mu$s (Evangelista
et al., 2020).

Figure 4: Black points: Standard deviation in the cross-correlation
uncertainty ($\sigma_{\text{cc}}$) calculated for a sample of 100 long and 100
short GRBs from Sanna et al. (2020). Red line: Best-fit power-law to the black
data points, where the $1\sigma$ interval is shown in light red.

It has been shown by Burgess et al. (2021) that this ‘classical’ triangulation
method has limitations, especially for faint bursts when the number of photons
per time bin is small. When compared to a full Bayesian treatment of
statistical uncertainties, Burgess et al. (2021) shows that the classic cross-
correlation approach results in an overconfidence of the $1\sigma$ uncertainty
on time delay by a factor of $\sim 2-3$, which translates directly into an
overconfidence on the burst localisation. Nevertheless, given this paper is a
continuation of the work performed in Sanna et al. (2020) and given the
computational benefits in our Monte Carlo simulation approach, we use the
classic cross-correlation approach, and note that our results may contain a
systematic uncertainty of 2-3 times our reported statistical localisations for
the faintest bursts.

Table 1: Power-law fits to the data presented in Sanna et al. (2020) used to calculate the uncertainty in signal arrival-time from the average flux of the GRB between 50-300kev. | Line of Best Fit | Standard Deviation
---|---|---
Long GRBs | $\log\sigma_{cc}=-0.88\log(F)-3$ | $\pm 0.22$
Short GRBs | $\log\sigma_{cc}=-1.02\log(F)-1.33$ | $\pm 0.33$

In order to determine the impact that GRB flux has on time-delay uncertainty,
we adopt the work of Sanna et al. (2020), where the standard deviation in the
cross-correlation uncertainty, $\sigma_{\text{cc}}$ is reported as a function
of average GRB flux for a random sample of 100 long and 100 short GRBs
observed by Fermi GBM. Specifically, in this work we use the
‘Flnc_Band_Phtfluxb’ data type from the Fermi GBM catalog (Gruber et al.,
2014; von Kienlin et al., 2014; Bhat et al., 2016; von Kienlin et al., 2020),
which is a quantity related to the burst photon flux between 50-300keV. The
results from Sanna et al. (2020) are reported here in Figure 4 as black data
points. In this figure, each data point represents the results from 1000
Monte-Carlo (MC) simulations which calculated the difference between the true
arrival time delay and the value inferred from cross-correlation methods. The
resulting distribution of time-offset values is then fit with a Gaussian
function with a mean of zero and a standard deviation $\sigma_{cc}$. To
perform 1000 MC trials for each burst, the GRB light curve observed by Fermi
GBM is used as a template from which unique GRB light curves can be generated
by both rescaling the detector effective area to match that of the HERMES
instrument and applying a Poissonian randomisation of the counts contained in
each bin of the template.

To generalise the results of Sanna et al. (2020) we construct a power-law fit
to this data (Figure 4, red lines), assuming that the residuals follow a
Gaussian distribution. The parameters for our fits are given in Table 1.

We use these relations to compute the uncertainty on signal cross-correlation,
$\sigma_{cc}$, given the observed flux of a burst, which depends not only on
the flux of the GRB as seen from LEO, but also on the incident angle of the
burst to the detector ($F_{obs}=F_{GRB}\cos\theta$).

Figure 5 plots the results from $10^{4}$ Mote-Carlo trials using this method
to calculate the standard deviation on cross-correlation uncertainty. As
expected, the satellites in our simulated constellation observe a lower GRB
flux on average than those bursts used by Sanna et al. (2020) (black
points/curves), since we take into account the HERMES instruments’ approximate
cosine dependence on photon incident angle. Otherwise we find good agreement
with the results presented in Sanna et al. (2020).

Note that this method contains several assumptions, justified by our aim to
forecast performance of a future constellation rather than a detailed
characterisation of the localisation algorithm applied to actual data.
Firstly, we are assuming that average GRB flux is as accurate predictor of
cross-correlation uncertainty. For a more realistic simulation, one could
follow the same procedure as performed in Sanna et al. (2020) and perform the
cross-correlation of GRB light curves to determine the ‘measured’ arrival time
difference.

Secondly, our simulation assumes that the uncertainty on signal cross-
correlation between two detectors $\sigma_{cc,ij}$ is uncorrelated between
pairs of detectors. In reality, we would expect this quantity to have some
correlation between pairs of satellites, e.g., $\sigma_{cc,ij}$ should have
some relation to $\sigma_{cc,ik}$ since both involve the signal observed by
detector $i$. However, understanding these correlations is non-trivial, and
beyond the scope of this work.

####  4.5.3 Simulating GRB Localisation

For each GRB that meets the conditions defined in Section 4.4 we perform the
triangulation procedure described in Section 4.5.1. We start by constructing a
set of ‘measured’ time-difference pairs $\Delta\tau_{ij}=\Delta
t_{ij}(\textbf{\^{d}}_{GRB})+\mathcal{N}(0,\sigma_{cc})$ between each
satellite which detected the event, where $\mathcal{N}(0,\sigma_{cc})$
represents a random variable sampled from a Gaussian distribution with a mean
of zero and standard deviation $\sigma_{cc}$, as defined above.

Using these values we calculate Equation 7 for each point on the sky, where we
represent the whole sky using a grid of $660048$ points uniformly distributed
on the celestial sphere (giving each point an area of $\sim 0.0625$ deg2),
with positions generated by the Fibonacci lattice method (González, 2009). For
computational efficiency, in cases where the localisation is not expected to
reach $<1$ deg2 (e.g., when localising short GRBs, or when testing
constellations with fewer satellites in Polar orbit), a grid of 41,253 points
($1$ deg2 resolution), or $165012$ points ($0.25$ deg2 resolution) is used.

Finally, we determine the $68\%$ or $90\%$ localisation confidence regions
using the values defined in Equation 8, excluding those points that are
disallowed by LOS arguments as defined in Section 4.5.1.

Figure 5: Scatter plot showing the relation between the observed flux of the
GRB ($F_{obs}=F_{GRB}\cos\theta$) and the expected standard deviation on
timing uncertainty after cross-correlation $\sigma_{cc}$ from $10^{4}$ MC
trials. The top panel plots the distribution of observed average GRB fluxes,
and right hand panel show histograms for the resulting distribution of cross-
correlation uncertainty as derived from the given flux distributions. For
comparison, in black we also plot the 100 long GRBs (circles, solid
histograms) and 100 short GRBs (triangles, dashed histograms) from Sanna et
al. (2020) which were used as a basis for our model. We have arbitrarily
scaled the histograms of the Sanna et al. (2020) data by eye so that they
match the scale of our simulated data.

We note here that when calculating the time-difference pairs $\Delta\tau_{ij}$
and the timing uncertainty on the signal cross-correlation $\sigma_{cc}$, we
presume that the satellites are stationary for the duration of the burst. In
reality, the relative motion of each satellite introduces a small difference
in the arrival time of photons at each detector. We estimate that as a worst-
case scenario - a satellite in LEO moving at $10$km/s in the direction of the
burst - would detect the final photon from a typical long GRB (approximately
$\sim 10$ sec) $0.3$ ms before a stationary satellite, meaning that the moving
satellite would effectively observe the signal of the GRB ‘compressed’ in time
by $0.3$ ms, which is comparable to the cross-correlation accuracy achieved
for the brightest $\sim 20$% of long GRBs. However, given the position and
velocity of each satellite in the SpIRIT + HERMES constellation are known to a
high accuracy, in principle this effect is entirely deterministic and can be
accounted for in a sufficiently sophisticated cross-correlation algorithm. For
this reason we choose to neglect the relative motion of each satellite in this
work, leaving its inclusion to a future simulation of the HERMES
constellation’s localisation capabilities, and note that this assumption may
introduce some systematic uncertainty into our results for the best localised
long GRBs.

##  5 Results and Discussion

Following the method outlined in Section 4.4, we simulate the localisation
capabilities of HERMES - TP/SP, as well as SpIRIT + HERMES - TP/SP and
constellations featuring additional SpIRIT-like satellites in Polar orbit. The
following sections present the localisation results for a sample of $10^{4}$
long and $10^{4}$ short GRBs.

###  5.1 Constellation Sky Coverage

Figure 3 demonstrates that the combined SpIRIT + HERMES - TP/SP constellation
is only able to detect a maximum of $60\%$ of long GRBs and $\sim 50\%$ of
short GRBs, which is to be expected since the FWHM of the HERMES instrument is
$60\degree$ meaning that each FOV covers $\sim 25\%$ of the sky at FWHM, and
the constellation is divided into two co-pointing groups. We note that the
constellation is able to detect a higher fraction of long GRBs than short GRBs
because of the different limits we have placed on the average flux sensitivity
for the two types of burst (see Section 4.4).

We find that for a constellation with a single satellite in polar orbit,
approximately $\sim 10\%$ of bursts can be detected by four orbital elements
simultaneously (SpIRIT + all three satellites in one of the HERMES triplets).
This low fraction is both due to the transit of each orbital element through
high particle flux regions (e.g., SpIRIT over the poles and through the SAA;
HERMES through the edge of the SAA), as well as in part of each satellite’s
FOV being obstructed by the Earth at the point in its orbit when Earth is
perpendicular to its LOS.

For a constellation of 4 Polar satellites + HERMES - TP/SP we find similarly
that only $\sim 10\%$ of GRBs can be detected by the all 5 of the co-pointing
satellites (2 Polar satellites + 3 HERMES - TP/SP satellites), while $\sim
25\%$ of bursts are detected by four satellites (1 Polar satellite + 3 HERMES
- TP/SP, or two Polar satellites + 2 HERMES - TP/SP), with one satellite
missing the observation due to crossing a high particle flux region or LOS
obstruction. The case is similar for six Polar satellites, where $\lesssim
10\%$ of bursts are detected by all of the co-pointing satellites due to the
intermittent passage of each orbital element through a region of high particle
flux.

In the case of launching additional Polar satellites, the benefit comes from
the fact that each burst is detected by a larger number of satellites on
average. For example, in the case of a single Polar satellite, only $10\%$ of
bursts are detected by four satellites, while with six Polar satellites $\sim
40\%$ of GRBs are detected by four or more satellites, enabling more accurate
burst localisations on average despite the fact that not all Polar satellites
are observing the event.

Figure 6: Comparison of the $68\%$ (yellow) and $90\%$ (teal) confidence
regions for the location of a long GRB as measured by the HERMES - TP/SP and
by the SpIRIT + HERMES - TP/SP constellations for one realisation in our Monte
Carlo simulation. The red cross denotes the location of the GRB on the sky.
The grey lines represent the $1\sigma$ error annuli between each pair of
satellites in the HERMES constellation. The gold lines represent the error
annuli for the three additional satellite pairs that can be made when SpIRIT
is included in the HERMES - TP/SP.

###  5.2 SpIRIT + HERMES - TP/SP Localisation

The primary advantage of augmenting the HERMES-TP/SP constellation with the
SpIRIT satellite is that the additional detector in Polar orbit greatly
reduces the localisation degeneracy in declination when SpIRIT is located at
high latitudes.

Because each satellite in the HERMES - TP/SP constellation orbits in the
equatorial plane and align their LOS in the same direction, there is limited
accuracy and intrinsic degeneracy in the declination coordinate of the burst -
for example, it is equally possible that a burst came from declination
$\delta=30\degree$ or $\delta=-30\degree$. However, SpIRIT’s Polar orbit gives
a large average baseline perpendicular to the orbital plane of the HERMES -
TP/SP, which allows for the degeneracy in declination to be broken if SpIRIT
is able to detect the event. Indeed, even if SpIRIT doesn’t directly detect
the event while co-pointing with the other observing satellites, a non-
detection would still provide useful information to rule out uncertainty
regions enclosed in SpIRIT’s FoV. An example uncertainty region for HERMES -
TP/SP and SpIRIT + HERMES - TP/SP is given in Figure 6, which demonstrates the
increased localisation accuracy in the declination coordinate when including
SpIRIT.

It should be noted that another way to resolve this degeneracy is by adjusting
the pointing direction of each satellite so that they do not co-point at the
same field. Doing so could allow the constellation to exploit the HERMES
instruments’ cosine dependence on photon incident angle to localise bursts by
taking into account the ratio of GRB fluence at each detector. However, this
would lead to a trade-off between GRB localisation accuracy and number of GRBs
localised, since a smaller fraction of the sky would be observed by all three
satellites. This trade-off is something that will be explored in future work.

Figure 7 plots the area of the $1\sigma$ localisation region for long GRBs
detected by SpIRIT + 3 HERMES - TP/SP satellites against SpIRIT’s distance
from the equatorial plane, where we have colour-coded each data point by the
average flux of the GRB. While the localisation accuracy depends strongly on
the flux of the GRB, we find that SpIRIT’s polar orbit is able to dramatically
improve burst localisations, such that the constellation’s capabilities
improve by a factor of $\sim 5$ when SpIRIT is over the poles compared to when
it is at the equator. When SpIRIT is close to its maximum distance from the
equatorial plane, we expect to achieve statistical burst localisations within
$\sim 10$ deg2 for $50\%$ of long GRBs, and localisations within a few square
degrees for bursts with an observed time-averaged flux higher than $\sim
5$ph/cm2/s ($\sim 15\%$ of long GRBs).

Note that while in the context of our simulation the constellation achieves
localisations $<1$ deg2 for very bright bursts when SpIRIT is near the poles,
quantifying with precision such cases goes beyond the simplifying assumptions
upon which our framework is based.

Figure 7: Plot of the $1\sigma$ localisation region for $\sim 10^{4}$
simulated long GRB events observed by the SpIRIT + HERMES - TP/SP
constellation. The x-axis shows SpIRIT’s baseline perpendicular to the
equatorial plane for each burst normalised by its maximum baseline (maximum
baseline = Earth radius + 550km orbital altitude). Note here that ‘baseline’
refers to SpIRIT’s distance perpendicular to the equatorial plane. The black
line shows the median of the data points within the bin (binned into intervals
of 0.05 on normalised polar baseline), and the grey region contains the
central $68\%$ of data in each bin. Individual data points are shown for
outliers, with the colour denoting the average flux of the GRB.

In the following analysis we divide our results into long and short GRBs.

####  5.2.1 Long GRBs

Figure 8 compares the cumulative distributions of the $1\sigma$ localisation
region for $10^{4}$ long GRBs localised by HERMES - TP/SP and SpIRIT + HERMES
- TP/SP. For comparison we also plot the $68\%$ statistical sky area
uncertainties reported in the fourth Fermi/GBM catalog (von Kienlin et al.,
2020). Note here that we are comparing the statistical GRB localisation
capabilities only - while both instruments also have an associated systematic
uncertainty, we cannot estimate these for the nano-satellite constellation
since to do so would require in-flight data, which is impossible since the
constellation has not been launched yet. For reference, the systematic
uncertainty for Fermi GBM is approximately $\sim 2-4\degree$ (Goldstein et
al., 2020), and it will likely be comparable to this for the nano-satellite
constellation.

Figure 8: Cumulative probability of localising a long GRB within a given
$1\sigma$ region on the sky for $n$ SpIRIT-like satellites in Polar orbit +
HERMES - TP/SP. The $n_{\text{polar}}=0$ constellation (blue line) represents
the HERMES - TP/SP constellation operating alone.

(a) 68% Confidence Interval

(b) 90% Confidence Interval

Figure 9: Cumulative probability of localising a short GRB within a given area
on the sky for $n$ SpIRIT-like satellites in Polar orbit + HERMES - TP/SP. The
$n_{\text{polar}}=0$ constellation (blue line) represents the HERMES - TP/SP
constellation operating alone. Left: 68% confidence intervals. Right: 90%
confidence intervals. The dashed lines represent the highest expected
localisation capabilities of the advanced LIGO Hanford and Livingstone,
advanced VIRGO and KAGRA GW detectors to localise BNS coalescences in O3 and
O4 respectively (note that for O3, detector sensitivities were taken to be
representative of the first 3 months of observations for aLIGO Hanford and
Livingston, and AdV, and the highest expected O3 sensitivity for KAGRA). See
(Abbott et al., 2020) Figure 6 for details). The two vertical grey lines
represent the prompt reported 90% confidence regions for the two binary
neutron star coalescences observed to date; GW170817, and GW190425.

The inclusion of SpIRIT greatly enhances the accuracy of GRB localisations
compared to the HERMES - TP/SP alone. SpIRIT + HERMES - TP/SP is able to
localise $60\%$ of long GRBs within $\sim 28$ deg2, which corresponds to an
uncertainty radius on the sky of $\sim 3\degree$ (presuming the uncertainty
region is circular), and $90\%$ of long GRBs within $150$ deg2 ($\sim
7\degree$ radius). In reality the uncertainty regions are irregular in shape,
but a circle is a good approximation when the burst is relatively well
localised. This represents an improvement by a factor of $\sim 5$ over the
HERMES - TP/SP alone, which is only able to localise $\sim 50\%$ of GRBs to
within $100$ deg2 on the sky.

Figure 8 shows that the combined SpIRIT + HERMES - TP/SP constellation will
have statistical GRB localisation capabilities comparable to those reported by
Fermi GBM. This result demonstrates the potential cost-effectiveness of using
modular nano-satellite astronomy to achieve specific science goals, as a
constellation of several relatively inexpensive nano-satellites is expected to
achieve a localisation accuracy similar to the substantially more complex and
expensive Fermi GBM. In fact, estimating an approximate cost of US $150M for
the Fermi GBM instrument ($\sim 25\%$ of the total cost of the mission (Fermi
Gamma-ray Space Telescope Q&A on the GLAST
Mission666https://www.nasa.gov/mission_pages/GLAST/main/questions_answers.html))
and of US $2.5M for each element of the nano-satellite constellation, there is
a possible factor 10x in savings using a distributed aperture solution for
localising long GRB afterglows. We note however that the disadvantage to using
a HERMES-like distributed aperture solution with the current design is sky
coverage: the Fermi GBM can observe over half the sky at any time (i.e., the
whole sky not obstructed by the Earth (Meegan et al., 2009)), whereas the FoV
of a single HERMES instrument only achieves $\sim 25\%$ sky coverage at FWHM,
meaning that achieving all-sky coverage with a nano-satellite constellation
with overlapped FoV’s would partially offset the cost savings (although there
would be further gains from mass production of the constellation elements).
Furthermore, it is non-trivial to achieve maximal overlap of the FOV of each
nano-satellite element, as it requires continual optimisation of the pointing
directions of each satellite to account for orbital drift and different
orbital configurations (Colagrossi et al., 2020).

####  5.2.2 Short GRBs

Figure 9 compares the localisation capabilities of the HERMES - TP/SP and
combined SpIRIT + HERMES - TP/SP constellations to both the Fermi GBM (where
we have plot the Fermi localisation uncertainty using same method as discussed
in Section 5.2.1) and to the theoretical current and future localisation
capabilities of the Advanced LIGO Hanford and Livingston, Advanced VIRGO and
KAGRA gravitational wave detectors (Abbott et al. (2020); $90\%$ confidence
regions, Figure 9(b)). Note that this reflects the predicted performance of
the four gravitational wave detectors operating concurrently during O3 and O4
- in reality KAGRA did not participate in O3, but is planned for joint
operation in O4. We have also included the reported prompt localisations for
both of the BNS coalescences observed by GW detectors; GW170817 (Abbott et
al., 2020) and GW190425 (Abbott et al., 2021). While the error box for
GW190425 was later refined, here we compare the prompt localisation capability
to ensure a fair comparison to a nano-satellite constellation. Note that the
HERMES - TP/SP constellation is less effective at localising short GRBs
compared to long GRBs due to the increased difficulty in precise signal cross-
correlation for short GRBs, although a future instrument redesign with
increased collecting area would mitigate this current limitation (Sanna et
al., 2020).

The addition of SpIRIT to HERMES - TP/SP is able to substantially improve the
localisation of short GRBs. HERMES - TP/SP alone has a 90% $1\sigma$
localisation range of $\sim 215-13000$ deg2, while the SpIRIT + HERMES - TP/SP
constellation’s 90% $1\sigma$ range is $\sim 50-8450$ deg2, where we have
defined the 90% $1\sigma$ localisation interval as the range of $1\sigma$
confidence regions spanning 5% to 95% of the cumulative distribution.

Despite this improvement in the constellation’s ability to localise short
GRBs, in terms of multi-messenger observations of short GRBs/BNS coalescences
the combined SpIRIT + HERMES-TP/SP constellation is not expected to
dramatically improve upon existing capabilities to localise these sources. Not
only is the Fermi GBM more effective by a factor of $\sim 5-10\times$ at the
EM localisation of short GRBs, but current-generation GW instruments are
theoretically capable of localising $>50\%$ of short GRBs within $\sim 200$
deg2 (and within $\sim 40$ deg2 in the future O4 observing runs) from the GW
signal alone (Abbott et al., 2020), which exceeds the localisation
capabilities of the nano-satellite constellation. Therefore, in the domain of
multi-messenger astronomy the utility of the SpIRIT + HERMES - TP/SP
constellation will be in the constellation’s sky coverage ($\sim 50\%$) and
flux sensitivity, which gives it a high probability of detecting the
electromagnetic counterpart to a compact binary event observed by GW
detectors. Such dual detections are critically needed to improve our
understanding of these compact binary mergers, as currently only one
simultaneous detection of the GW signal from a BNS merger (GW170817) and a
short GRB (GRB170817A) has been recorded to date (Abbott et al., 2017).

Figure 10: Localisation histograms for the sample of $10^{4}$ GRBs detected by
the SpIRIT + HERMES - TP/SP Constellation. The blue curve represents the full
sample of simulated GRBs, while the orange and green curves compare the
localisation capabilities of the constellation when SpIRIT either detects or
does not detect the burst. Left: Long GRB sample. Right: Short GRB sample.

####  5.2.3 Utilising SpIRIT Non-Detections

The inclusion of SpIRIT into the HERMES - TP/SP enables improvements to the
GRB localisation capabilities of the HERMES - TP/SP both when SpIRIT directly
detects the burst, but also when SpIRIT does not directly detect the burst.
The improvement in the latter case is a product of SpIRIT’s high inclination
orbit, since when SpIRIT is over the poles then a considerable section of the
HERMES triplet’s FOV is obstructed by the Earth from SpIRIT’s perspective.
This means that a SpIRIT non-detection can impose relatively strong
constraints on possible source location under these conditions, assuming that
SpIRIT is co-pointing at the same field as the HERMES triplet that detects the
burst, and that the noise level is low enough for SpIRIT that we would expect
to detect the GRB signal.

Figure 10 compares the size of the $1\sigma$ confidence region for long and
short GRBs, where the results have been divided depending on whether SpIRIT
detects the GRB or not. Note that in all cases, SpIRIT is co-pointing with the
HERMES triplet that detects the GRB. In both cases, we find that SpIRIT makes
a direct detection of the GRB for $\sim 85\%$ of bursts in our ‘observable’
sample, which represents the average fraction of the HERMES triplet’s FOV that
is simultaneously observed by SpIRIT.

In the case of long GRBs we find that the size of the $1\sigma$ localisation
region is always smaller when SpIRIT directly detects the burst compared to
when SpIRIT does not detect the GRB. This is to be expected, since for HERMES
- TP/SP the typical size of the long GRB localisation region is much lower
than the sky coverage of the triplet, meaning that a SpIRIT non-detection will
only improve the source localisation in the unlikely case that the burst
occurs at coordinates close to the edge of Earth as seen from SpIRIT’s
perspective.

Conversely, in the case of short GRBs we find that in some cases it is
possible to achieve more accurate GRB localisations when SpIRIT does not
detect the burst. These cases arise for faint short GRBs where the typical
uncertainty on signal cross-correlation is large, meaning that the typical
$1\sigma$ localisation region is comparable to the sky coverage of the
constellation ($\geq 10^{4}$ deg2). In such cases, SpIRIT non-detections
enable more accurate GRB localisations as they restrict the possible location
of the GRB to those regions of sky that are obstructed by the Earth at the
time of the burst, which is why there are practically no bursts with $1\sigma$
localisation regions larger than $\sim 5\times 10^{3}$ deg2 in the green curve
in Figure 10 (right panel).

###  5.3 Additional Polar Satellites

After demonstrating the benefits of adding one Polar satellite to the HERMES -
TP/SP constellation, it is natural to investigate the localisation potential
of launching additional satellites into Polar orbit.

Specifically, we compare constellations featuring 2, 4 and 6 SpIRIT-like
satellites in Polar orbit (plus HERMES - TP/SP), since these constellations
ensure that either one, two or three Polar satellites are observing each of
the co-pointing directions of the HERMES - TP/SP. For example, the
localisation capabilities that we present for the $n_{\text{polar}}=4$
constellation are a product of observation from 3 equatorial HERMES - TP/SP
satellites plus 2 Polar SpIRIT-like satellites (see Figure 3).

####  5.3.1 Long GRBs

Figure 8 demonstrates that a constellation of four Polar satellites plus
HERMES - TP/SP would improve the localisation capabilities of the
constellation by a factor of $\sim 2$ over the case of a constellation with
only one Polar satellite, and would be capable of localising $60\%$ of long
GRBs to within $\sim 10$ deg2 of random uncertainty on the sky ($\sim
2\degree$ radius). A constellation of six Polar satellites would reflect a
further improvement by an additional factor of $\sim 1.5$ (or equivalently a
$4\times$ improvement over the case of a single Polar satellite), and could
enable the localisation of $\sim 50\%$ of long GRBs to within a radius of
$1\degree$ on the sky.

Despite the substantial improvement over the case of a single Polar-orbiting
satellite, GRB localisations with an error radius of $\sim 1\degree$ are not
accurate enough to enable reliable afterglow follow-up observations from
existing ground or space-based observatories, most of which have a FoV of the
order $10\times 10$ arcmin2, e.g., GROND: $10^{\prime}\times 10^{\prime}$
(Greiner et al., 2008), Swift UVOT: $17^{\prime}\times 17^{\prime}$ (Troja,
2020), Gemini Multi-Object Spectrograph (GMOS): $5^{\prime}.5\times
5^{\prime}.5$ (Hook et al., 2004). Taking effective advantage of these GRB
detections at high energy for infrared follow-up may, however, be possible in
the future with $\gtrsim 1$ deg2 FoV space-based telescopes with rapid
repointing capabilities, such as the SkyHopper nano-satellite concept (Thomas
et al., 2022).

####  5.3.2 Short GRBs

As Figure 9 demonstrates, launching a constellation of 4 or 6 Polar orbiting
satellites into Polar orbit can improve short GRB localisations by a factor of
$\sim 2-4$ over a constellation with a single Polar satellite, achieving a 90%
$1\sigma$ short GRB localisation range between $\sim 20-4100$ deg2 (4 Polar)
and $12-2850$ deg2 (6 Polar) respectively. These improvements enable the
statistical localisation of short GRBs with an accuracy close to that reported
by Fermi GBM for a small fraction of the best-localised bursts, meaning that
such an expanded nano-satellite constellation could be valuable in the near
real-time localisation of EM counterparts to BNS coalescences, especially in
cases where a short GRB is observed by both Fermi GBM and the nano-satellite
constellation (which is likely, given Fermi GBM observes such a large fraction
of the sky).

At the time of writing, real time triggers and $1\sigma$ localisations for
short GRBs can be obtained with accuracies $<10$’s of square degrees (e.g.,
Fermi GBM (Goldstein et al., 2020), the Neil Gehrels Swift Observatory
(Gehrels et al., 2004; Troja, 2020), the Gravitational wave high-energy
Electromagnetic Counterpart All-sky Monitor (GECAM; Zhao et al. (2021)). To
localise a substantial fraction of short GRBs to this accuracy with the
current design of the HERMES instrument (and under the assumption that the
satellites are uniformly distributed around equatorial and Polar orbits), at
least 20 satellites divided evenly between equatorial and Polar orbit all
observing the same field are required (i.e., combined detection from at least
10 HERMES instruments with large baselines in both the equatorial and Polar
planes). On the other hand, the performance forecast for the localisation of
long GRBs indicates that with an increase in the effective area of the
detector, a constellation with a smaller number of elements would have a
strong potential to provide state-of-the-art and cost effective all-sky
monitoring and localisation of short GRBs/gravitational wave counterparts. A
detailed investigation on the trade off between detector collecting area and
number of constellation elements in the HERMES constellation is beyond the
scope of this work (though the reader is directed to Greiner et al. 2022,
where a similar study for a hosted instrument on the Galileo constellation is
presented).

##  6 Conclusion

In this paper we characterise the GRB localisation capabilities of the SpIRIT
+ HERMES - TP/SP mini-constellation using temporal triangulation techniques.
We design a simplified mission simulation based on an optimised mission
scenario for the HERMES - TP/SP outlined in Sanna et al. (2020) and specific
assumptions regarding SpIRIT’s orbit and pointing strategy in order to
estimate the burst localisation capabilities of the combined constellation.

We find that the SpIRIT + HERMES - TP/SP constellation is able to localise
$60\%$ of long GRBs within a $1\sigma$ confidence region of $28$ deg2 on the
sky, and $90\%$ of long GRBs within $150$ deg2. These confidence regions
represent an improvement by a factor of $\sim 5$ over the HERMES - TP/SP
alone, and are comparable to the statistical burst localisation capabilities
of the Fermi GBM (excluding systematic uncertainties for all satellites). The
increased performance of SpIRIT + HERMES - TP/SP compared to HERMES - TP/SP
alone is due to SpIRIT’s Polar orbit, which affords it a large baseline
perpendicular to the equatorial orbit of the six HERMES - TP/SP satellites. We
find that when SpIRIT is over the poles, the localisation capabilities of the
combined constellation improve by a factor of $\sim 5$ compared to when SpIRIT
is at the equator.

The short GRB localisation capabilities of SpIRIT + HERMES - TP/SP reflect a
similar improvement by a factor of $\sim 5$ over HERMES - TP/SP alone, with
the combined constellation localising $60\%$ of short GRBs within $\sim 1850$
deg2 and $90\%$ of short GRBs within $6000$ deg2 (1$\sigma$ confidence
regions). In fact, for some faint short GRBs the constraint on the source’s
position from statistical localisation techniques is so loose that
constellation achieves more accurate GRB localisations when SpIRIT does not
detect the burst, as this restricts the search region to the fraction of the
sky that is obstructed by the Earth from SpIRIT’s perspective at the time of
the burst. The short GRB localisation capabilities of the constellation is
greatly reduced compared to long GRBs due to the limited precision in the
signal cross-correlation between satellites, which could be addressed by
increasing the collecting area of the HERMES instrument. While this forecast
performance is not competitive with state-of-the-art localisation of Fermi
GMB, the combined SpIRIT + HERMES - TP/SP is still expected to provide a
meaningful contribution to multi-messenger astrophysics. This will be both for
events that might be missed by Fermi due to Earth occultation, as well as
through the unique time resolution of the HERMES instrument, which would
enable novel investigation into rapid variability of the high energy emission.

In order to further augment the capabilities of the HERMES - TP/SP, we
investigated the localisation capabilities of an expanded nano-satellite
constellation which includes additional satellites in Polar orbit. We find
that a constellation covering two nearly orthogonal orbital planes comprising
of 4 or 6 nano-satellites in each plane is capable of effectively localising
$60\%$ of long GRBs within $\sim 5-10$ deg2, and $60\%$ of short GRBs to
within $\sim 550-850$ deg2, which may enable an expanded nano-satellite
constellation to aid in the timely localisation of bright short GRBs/GW
transients. Furthermore, a constellation with 6 elements in Polar orbit
enables $50\%$ of long GRBs to be localised to within a statistical $68\%$
uncertainty radius of $\sim 1\degree$ on the sky, which may enable systematic
afterglow follow-up observations from future instruments with FoV’s $\geq 1$
deg2. Furthermore, it will be possible to integrate the expanded HERMES nano-
satellite constellation into the IPN in order to achieve even more accurate
sky localisations for both long and short GRBs, though this improved
localisation would only be available at later times since the IPN latency can
be substantial.

Therefore, after successful on-orbit demonstration of the concept that is
expected to be achieved by the SpIRIT + HERMES - TP/SP satellites, augmenting
further the elements in Polar orbit would be an ideal next step towards
achieving an all-sky X-ray/gamma-ray monitor based on distributed aperture
detectors to complement future gravitational wave detection campaigns.

##  7 Acknowledgements

MTh. acknowledges support from an Australian Government Research Training
Program (RTP) Scholarship. This research is supported in part by the
Australian Research Council Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D), through project number CE170100013. Parts of this
research were supported by the Australian Research Council Centre of
Excellence for Gravitational Wave Discovery (OzGrav), through project number
CE170100004. GG acknowledges PRIN-MUR 2017 (grant 20179ZF5KS). JR acknowledges
support by the European Union’s Horizon 2020 Programme under the AHEAD2020
project (grant agreement n. 871158).

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