# Science with the Daksha High Energy Transients Mission

Varun Bhalerao Department of Physics, IIT Bombay, Powai, Mumbai 400076, India
Disha Sawant Department of Physics, IIT Bombay, Powai, Mumbai 400076, India
Archana Pai Department of Physics, IIT Bombay, Powai, Mumbai 400076, India
Shriharsh Tendulkar Department of Astronomy and Astrophysics, Tata Institute
of Fundamental Research, Mumbai, 400005, India  Santosh Vadawale Physical
Research Laboratory, Navrangpura, Ahmedabad 380009, India  Dipankar
Bhattacharya Ashoka University, Sonipat 131029, Haryana, India  Vikram Rana
Raman Research Institute, C. V. Raman Avenue, Sadashivanagar, Bengaluru
560080, India  Hitesh Kumar L. Adalja Physical Research Laboratory,
Navrangpura, Ahmedabad 380009, India  G C Anupama Indian Institute of
Astrophysics, 2nd Block 100 Feet Rd, Koramangala Bengaluru 560 034, India
Suman Bala Department of Physics, IIT Bombay, Powai, Mumbai 400076, India
Smaranika Banerjee Tohoku University, Aoba, Sendai 980-0845, Japan  Stockholm
University, AlbaNova, SE-10691 Stockholm, Sweden  Judhajeet Basu Indian
Institute of Astrophysics, 2nd Block 100 Feet Rd, Koramangala Bengaluru 560
034, India  Hrishikesh Belatikar Department of Electrical Engineering, IIT
Bombay, Powai, Mumbai 400076, India  Paz Beniamini Department of Natural
Sciences, The Open University of Israel, P.O Box 808, Ra’anana 4353701, Israel
Mahesh Bhaganagare  Department of Electrical Engineering, IIT Bombay, Powai,
Mumbai 400076, India  Ankush Bhaskar Space Physics Lboratory, ISRO/Vikram
Sarabhai Space Centre, Thiruvananthapuram 695022, India  Soumyadeep
Bhattacharjee Department of Physics, Indian Institute of Science, Bengaluru,
Karnataka 560012, India  Sukanta Bose Inter-University Center for Astronomy
and Astrophysics, Pune, Maharashtra-411007, India  Washington State
University, Pullman, WA 99164, U.S.A.  Brad Cenko University of Maryland,
College Park, USA  Mehul Vijay Chanda Department of Physics, IIT Bombay,
Powai, Mumbai 400076, India  Gulab Dewangan Inter-University Center for
Astronomy and Astrophysics, Pune, Maharashtra-411007, India  Vishal Dixit
Interdisciplinary Program in Climate Studies, IIT Bombay, Powai, Mumbai
400076, India  Anirban Dutta Raman Research Institute, C. V. Raman Avenue,
Sadashivanagar, Bengaluru 560080, India  Priyanka Gawade Inter-University
Center for Astronomy and Astrophysics, Pune, Maharashtra-411007, India
Abhijeet Ghodgaonkar Department of Physics, IIT Bombay, Powai, Mumbai 400076,
India  Shiv Kumar Goyal Physical Research Laboratory, Navrangpura, Ahmedabad
380009, India  Suresh Gunasekaran  Department of Aerospace Engineering, IIT
Bombay, Powai, Mumbai 400076, India  Guruprasad P J Department of Aerospace
Engineering, IIT Bombay, Powai, Mumbai 400076, India  Manikantan Hemanth Raman
Research Institute, C. V. Raman Avenue, Sadashivanagar, Bengaluru 560080,
India  Kenta Hotokezaka University of Tokyo, Bunkyo City, Tokyo 113-8654
Shabnam Iyyani School of Physics, IISER Thiruvananthapuram, 695551, Kerala
Mansi Kasliwal Division of Physics, Mathematics, and Astronomy, California
Institute of Technology, Pasadena, CA 91125, USA  Jayprakash G. Koyande
Department of Astronomy and Astrophysics, Tata Institute of Fundamental
Research, Mumbai, 400005, India  Salil Kulkarni  Department of Mechanical
Engineering, IIT Bombay, Powai, Mumbai 400076, India  APK Kutty  Department of
Astronomy and Astrophysics, Tata Institute of Fundamental Research, Mumbai,
400005, India  Tinkal Ladiya Physical Research Laboratory, Navrangpura,
Ahmedabad 380009, India  Deepak Marla Department of Mechanical Engineering,
IIT Bombay, Powai, Mumbai 400076, India  Sujay Mate Department of Astronomy
and Astrophysics, Tata Institute of Fundamental Research, Mumbai, 400005,
India  Advait Mehla Department of Physics, IIT Bombay, Powai, Mumbai 400076,
India  N. P. S. Mithun Physical Research Laboratory, Navrangpura, Ahmedabad
380009, India  Surhud More Inter-University Center for Astronomy and
Astrophysics, Pune, Maharashtra-411007, India  Rakesh Mote Department of
Mechanical Engineering, IIT Bombay, Powai, Mumbai 400076, India  Dipanjan
Mukherjee Inter-University Center for Astronomy and Astrophysics, Pune,
Maharashtra-411007, India  Sanjoli Narang Department of Electrical
Engineering, IIT Bombay, Powai, Mumbai 400076, India  Shyama Narendranath
Space Astronomy Group, U R Rao Satellite Centre, ISRO, Bengaluru 560037, India
Ayush Nema Department of Astronomy and Astrophysics, Tata Institute of
Fundamental Research, Mumbai, 400005, India  Sudhanshu Nimbalkar Department of
Electrical Engineering, IIT Bombay, Powai, Mumbai 400076, India  Samaya
Nissanke GRAPPA, Anton Pannekoek Institute for Astronomy and Institute of
High-Energy Physics, University of Amsterdam, Science Park 904, 1098 XH
Amsterdam, The Netherlands 2Nikhef, Science Park 105, 1098 XG Amsterdam, The
Netherlands  Sourav Palit Indian Center for Space Physics, Kolkata, West
Bengal 700084  Jinaykumar Patel Department of Mechanical and Aerospace
Engineering, The University of Texas at Arlington, Arlington, TX 76019, USA
Department of Aerospace Engineering, IIT Bombay, Powai, Mumbai 400076, India
Arpit Patel Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India
Biswajit Paul  Raman Research Institute, C. V. Raman Avenue, Sadashivanagar,
Bengaluru 560080, India  Priya Pradeep  Vikram Sarabhai Space Centre,
Kochuveli, Thiruvananthapuram, 695022, India  Prabhu Ramachandran Department
of Aerospace Engineering, IIT Bombay, Powai, Mumbai 400076, India  Kinjal Roy
Raman Research Institute, C. V. Raman Avenue, Sadashivanagar, Bengaluru
560080, India  B.S. Bharath Saiguhan Physical Research Laboratory,
Navrangpura, Ahmedabad 380009, India  Joseph Saji School of Physics, IISER
Thiruvananthapuram, 695551, Kerala  M. Saleem Chennai Mathematical Institute,
Siruseri 603103, Tamilnadu, India  School of Physics and Astronomy, University
of Minnesota, Minneapolis, MN 55455, USA  Divita Saraogi Department of
Physics, IIT Bombay, Powai, Mumbai 400076, India  Parth Sastry Department of
Physics, IIT Bombay, Powai, Mumbai 400076, India  M. Shanmugam Physical
Research Laboratory, Navrangpura, Ahmedabad 380009, India  Piyush Sharma
Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India  Amit
Shetye  Department of Electrical Engineering, IIT Bombay, Powai, Mumbai
400076, India  Nishant Singh Physical Research Laboratory, Navrangpura,
Ahmedabad 380009, India  Shreeya Singh  Department of Chemical Engineering,
IIT Bombay, Powai, Mumbai 400076, India  Akshat Singhal Department of Physics,
IIT Bombay, Powai, Mumbai 400076, India  S. Sreekumar  Vikram Sarabhai Space
Centre, Kochuveli, Thiruvananthapuram, 695022, India  Srividhya Sridhar
Department of Aerospace Engineering, IIT Bombay, Powai, Mumbai 400076, India
Department of Aerospace, University of Illinois Urbana-Champaign - 61801, US.
Rahul Srinivasan Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS,
Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4,
France  Artemis, Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS,
F-06304 Nice, France  Department of Physics, IIT Bombay, Powai, Mumbai 400076,
India  Siddharth Tallur Department of Electrical Engineering, IIT Bombay,
Powai, Mumbai 400076, India  Neeraj K. Tiwari Physical Research Laboratory,
Navrangpura, Ahmedabad 380009, India  Amrutha Lakshmi Vadladi Department of
Mechanical Engineering, IIT Bombay, Powai, Mumbai 400076, India  C. S.
Vaishnava Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India
Sandeep Vishwakarma Department of Astronomy and Astrophysics, Tata Institute
of Fundamental Research, Mumbai, 400005, India  Gaurav Waratkar Department of
Physics, IIT Bombay, Powai, Mumbai 400076, India

###### Abstract

We present the science case for the proposed Daksha high energy transients
mission. Daksha will comprise of two satellites covering the entire sky from 1
keV to $>1$ MeV. The primary objectives of the mission are to discover and
characterize electromagnetic counterparts to gravitational wave source; and to
study Gamma Ray Bursts (GRBs). Daksha is a versatile all-sky monitor that can
address a wide variety of science cases. With its broadband spectral response,
high sensitivity, and continuous all-sky coverage, it will discover fainter
and rarer sources than any other existing or proposed mission. Daksha can make
key strides in GRB research with polarization studies, prompt soft
spectroscopy, and fine time-resolved spectral studies. Daksha will provide
continuous monitoring of X-ray pulsars. It will detect magnetar outbursts and
high energy counterparts to Fast Radio Bursts. Using Earth occultation to
measure source fluxes, the two satellites together will obtain daily flux
measurements of bright hard X-ray sources including active galactic nuclei,
X-ray binaries, and slow transients like Novae. Correlation studies between
the two satellites can be used to probe primordial black holes through
lensing. Daksha will have a set of detectors continuously pointing towards the
Sun, providing excellent hard X-ray monitoring data. Closer to home, the high
sensitivity and time resolution of Daksha can be leveraged for the
characterization of Terrestrial Gamma-ray Flashes.

Space telescopes (1547) — Time domain astronomy (2109) — Gamma-ray bursts
(629) — Gravitational wave astronomy (675)

††software: Numpy (van der Walt et al., 2011), Matplotlib (Hunter, 2007),
Astropy (Astropy Collaboration et al., 2013, 2018, http://www.astropy.org),
HealPIX (Gorski et al., 2005), Healpy (https://healpy.readthedocs.org/), Ephem
(https://pypi.python.org/pypi/pyephem/), WebPlot Digitizer
https://automeris.io/WebPlotDigitizer, GEANT4 (Agostinelli et al., 2003,
https://geant4.web.cern.ch/)

##  1 Introduction

In the past decade, transient astronomy has received a great boost due to the
expansion from electromagnetic (EM) regime to multi-messenger astronomy by
including gravitational waves (GW), neutrinos, and high-energy cosmic rays.
The joint detection of a faint gamma-ray burst (GRB) coincident with the
gravitational wave detection of a binary neutron star (BNS) merger GW170817
(LIGO Scientific Collaboration et al., 2017; Abbott et al., 2017a) was the
first direct proof of the long hypothesized link between short GRBs and BNS
mergers. This has also provided us with a detailed understanding of the
production of r-process elements in kilonovae (Watson et al., 2019; Kasliwal
et al., 2017a) and independent measurements of the neutron star equation of
state (De et al., 2018).

The GRB counterpart of GW170817, however, was several orders of magnitude
fainter than expected than “classical” GRBs and was barely detected by most
current space-based detectors (Zhang et al., 2018). With the improved
sensitivity of advanced GW detectors, the horizon for detecting compact binary
mergers involving neutron stars (possibly with a stellar mass black hole
companion) will reach farther distances. We will need comparable improvements
in X-ray and gamma-ray telescope sensitivities to be able to fully leverage
the increased number of GW detections. Indeed, after GW170817 (at a distance
of 40 Mpc), the BNS and neutron star black hole (NSBH) events detected in
LIGO–Virgo observing run 3 (O3) where typically at distances $\gtrsim$ 100
Mpc. Despite extensive searches, no EM counterparts were found (see for
instance Hosseinzadeh et al., 2019; Coughlin et al., 2019). Roughly scaling
the flux from GW170817 to these distances, the non-detections are not
unexpected with the current sensitivity of all-sky missions.

X-ray and gamma-ray transient astronomy has been a rich field with missions
such as _BATSE_ (Schönfelder et al., 1984; Band et al., 1993a), _BeppoSAX_
(Boella et al., 1997), Swift (Gehrels et al., 2004; Barthelmy et al., 2005)
and Fermi (Meegan et al., 2009) leading the exploration of GRBs, magnetar
flares, and X-ray binary outbursts. More recently, instruments such as
AstroSat CZTI (Bhalerao et al., 2017), POLAR (Produit et al., 2005), and
IKAROS-GAP (Yonetoku et al., 2011a) have characterized the polarization of
GRBs. Yet, there remain open questions about the detailed emission mechanism,
the jet launching physics, jet composition, the effects of magnetic fields,
and the nature of the remnant and the afterglow (Metzger et al., 2008; Kumar &
Zhang, 2015).

The next generation of transient detection telescopes need to have a much
higher sensitivity and all-sky coverage to match the nearly isotropic
visibility and detection horizons of GW detector networks — aLIGO (LIGO
Scientific Collaboration et al., 2015), adVirgo (Acernese et al., 2015), KAGRA
(KAGRA Collaboration et al., 2020), and LIGO-India (Iyer et al., 2011; Saleem
et al., 2022). These should also provide low-latency alerts in order to
coordinate with new synoptic radio, optical and infrared telescopes that will
coordinate the EM followup response such as the ZTF (Bellm, 2014), Rubin
Observatory (LSST Science Collaboration et al., 2009), Square Kilometer Array
(Dewdney et al., 2009), uGMRT (Gupta et al., 2017), LOFAR (van Haarlem et al.,
2013), ASKAP (Johnston et al., 2007), and IceCube (Aartsen et al., 2017). A
greater sensitivity, especially at lower energies will improve detection rates
of high-redshift GRBs, improving their use as probes of cosmology, star
formation rates etc.

With these considerations, we have proposed Daksha, a broadband high-energy
all-sky mission dedicated to X-ray and gamma-ray transient astronomy. In this
paper, we discuss the science cases enabled by Daksha. The technical details
of Daksha are given in a companion paper (Bhalerao et al, hereafter Paper I),
but we have included a brief summary in Section 2 for completeness. In the
next sections, we discuss the primary and secondary science enabled by Daksha
along with the detection rate estimates and simulations — Section 3 covers the
impact of Daksha for coincident detections of prompt GRB-like counterparts of
GW events expected from upcoming gravitational wave detector networks; Section
4 covers the detection rates, prompt soft spectra, and polarization of GRBs;
Section 5 covers the secondary science cases — X-ray pulsars, magnetar flares,
fast radio burst (FRB) counterparts, primordial blackholes (PBHs), Earth
occultation studies of bright X-ray sources, solar physics, and terrestrial
gamma-ray flares.

##  2 Mission overview

Figure 1: Overall design of a Daksha satellite. The dome-shaped payload has 13
surfaces, each carrying Low-energy (LE) and Medium-energy (ME) detector
packages. Four ME detector packages are mounted under the satellite bus, and
always point directly to the sun. Four High-energy (HE) detector packages are
mounted inside the dome, along with processing electronics.

The mission comprises of two satellites launched in a near-equatorial low-
earth orbit (LEO). The pair of satellites located opposite to each other in
their orbit helps to gain all-sky coverage by mitigating the impact of the
South Atlantic Anomaly and earth occultation in LEO. Daksha satellites use
three types of detectors to cover an energy range from 1 keV to $>1$ MeV
(Figure 1). Silicon Drift Detectors (SDDs) cover the Low Energy (LE) range
from 1–25 keV. Cadmium Zinc Telluride (CZT) detectors provide Medium Energy
(ME) coverage from 20–200 keV. High Energy (HE) sensitivity is provided by NaI
detectors with Silicon Photomultipliers, sensitive from 100 keV to $>1$ MeV.
Details of the instruments and their capabilities are given in Paper I.

Figure 2:  Effective area of Daksha detectors as a function of energy.
Effective areas of Swift-BAT and both NaI and BGO detectors of Fermi-GBM are
shown for comparison. These areas were adapted from (Luo et al., 2020). The
NaI effective area is the averaged over the unocculted sky.

The workhorse of Daksha are the ME detectors, which provide nearly uniform
all-sky coverage with a median effective area of $\sim 1300\mathrm{~{}cm}^{2}$
(Figure 2), and a 5-$\sigma$ sensitivity of 4$\times
10^{-8}~{}\mathrm{\mathrm{erg~{}cm}^{-2}~{}\mathrm{s}^{-1}}$ for 1-second
bursts. Bursts with fluence of about 1$\times
10^{-7}~{}\mathrm{\mathrm{erg~{}cm}^{-2}}$ can be localized with an accuracy
of 10°, with sub-degree localization for brighter bursts.

##  3 Science Driver I: Electromagnetic Counterparts to Gravitational Wave
Sources

On 2017 August 17, gravitational wave detectors had the first direct detection
of coalescing neutron stars. 1.7 s later, a flash of gamma rays was detected
by Fermi and Integral missions (Abbott et al., 2017a; LIGO Scientific
Collaboration et al., 2017). The high energy detection spurred broadband
follow-up observations leading to the discovery of a kilonova (Kilpatrick et
al., 2017), and eventually proving that the merger produced a successful
structured jet (Mooley et al., 2018a, b; Troja et al., 2018). Thanks to an
extensive multi-wavelength data set, significant progress was made on many
unsolved mysteries — proving the connection between neutron star mergers and
short GRBs (Goldstein et al., 2017), establishing that such mergers indeed are
the sites of r-process nucleosynthesis (Kasen et al., 2017; Kasliwal et al.,
2017b), providing an independent measurement of the Hubble constant (Abbott et
al., 2017c), and a measurement of the equation of state of ultra-dense matter
(Abbott et al., 2018a, 2019).

GRB 170817 was peculiar in many ways. It was detected further off axis than
typical GRBs (Mooley et al., 2018c, b; Beniamini & Nakar, 2019). The prompt
emission had soft spectral components which could not be adequately
characterized or explained (Goldstein et al., 2017). While it is the closest
GRB ever detected, it was still faint — and intrinsically the most sub-
luminous of all short GRBs detected to date (Zhang et al., 2018). Had this
event even been 30$\%$ fainter for instance, it would have been missed by
several EM missions (Saleem et al., 2020). This is consistent with studies
conducted in the third observing run of the advanced gravitational wave
detectors (O3): while several neutron star merger events were detected in
gravitational waves, no electromagnetic counterparts were found. A notable
example is the lack of counterparts to BNS event GW190425 at a distance of
$\sim 150$ Mpc (Hosseinzadeh et al., 2019; Coughlin et al., 2020). Besides
sensitivity, GW170817 also underscored the importance of continuous all-sky
coverage: sensitive missions like Swift (Evans et al., 2017) and AstroSat
(Kasliwal et al., 2017a) could not detect the source as it was occulted by the
Earth at that instant.

The peculiarity GRB170817A of having low luminosity but comparable peak energy
as any standard SGRBs (Bégué et al., 2017) posed additional questions: Does
GRB170817A belong to a new, unexplored class of SGRBs? Do we need high soft
X-ray sensitivity to detect and study this class of sources? How would they be
different in terms of source distribution, energetics, spectral properties
etc? Multi-wavelength and multi-messenger studies of more sources are critical
for tackling these questions. Such observations can shed light on the SGRBs
distribution as well as into the physics of SGRB jet structure, energetics
(Hotokezaka et al., 2018; Beniamini et al., 2019).

The interferometric GW detector network is constantly getting upgraded. In
future observing runs, the Advanced LIGO-Virgo detectors will achieve the
sensitive distance reach of $\sim$ 200 Mpc (Abbott et al., 2018b). Additional
advanced detectors such as the Japanese detector KAGRA (Aso et al., 2013) and
the LIGO-India (Saleem et al., 2022) will make the network uniformly sensitive
over the sky, with the localization capability up to ten square degrees (Mills
et al., 2018; Abbott et al., 2020). A growing number of BNS sources will be
detected within a few hundred Mpc (Burns et al., 2019; Petrov et al., 2022).
To maximize the science returns from these detections, we need new higher
sensitivity instruments with all–sky coverage (Abbott et al., 2017a; National
Academies of Sciences Engineering and Medicine, 2021).

###  3.1 Design considerations for EMGW

Daksha has been designed keeping in mind the lessons learnt from the GW
network observing runs and corresponding follow-up programs. Two key features
of Daksha are the higher sensitivity and all-sky coverage, thanks to which we
will detect far more events than other missions (§3.3). On-board algorithms
will detect bursts, localize them, and create coarse light curves and spectra
to be broadcast globally within $\sim 1$ minute of each event. This
information will enable groups to prioritize their resources and start rapid
follow-up observations.

All event-mode data will be downlinked on the next ground-station pass, to
create improved data products. The broad spectral coverage will play a
critical role in modeling spectral components of the prompt emission. A unique
capability for Daksha is its low energy coverage for prompt soft emission,
which we discuss in §3.2. For bright events, Daksha will also be able to
measure polarization of the events, which is discussed in greater detail in
the context of GRBs in §4.6. All bursts detected by Daksha can also be
utilized for “triggered” searches in GW network data for corresponding GW
signals. Our calculations show that this can give a significant boost to the
number of binary neutron star events detected in GW (§3.3; also see
Bhattacharjee et al. in prep).

###  3.2 Probing science of soft X-ray sources: the cocoon shock breakout
model

A SGRB jet propagating inside the merger ejecta forms a cocoon, which
eventually breaks out from the ejecta surface. The emission arising from the
cocoon shock break-out is expected to be composed of an initial hard-spike
followed by a soft-tail (Gottlieb et al., 2018a; Beloborodov et al., 2020a).
The luminosity, duration, and spectral peak of the hard spike and soft tail
depend on the ejecta structure as well as the jet properties such as the
power, opening angle and time delay between the merger and jet launch.

For instance, the emission properties of GRB170817A can be explained with the
cocoon shock breakout model with a breakout radius of $\sim 2\times
10^{11}\,{\rm cm}$, a maximum ejecta velocity of $\sim 0.7c$ (Gottlieb et al.,
2018a). Although these values are expected to be different for different
events, the emission properties must roughly satisfy a closure relation
between the duration, total energy, and the temperature (Nakar & Sari, 2012).
Thus, the cocoon breakout model can be tested by detecting more X-ray flashes
associated with neutron star mergers. Furthermore, by modeling the emission
properties, we will be able to obtain valuable information about the structure
of merger ejecta and the jet formation in neutron star mergers. This in turn
may allow us to constrain the neutron star equation of state (EOS) since the
ejecta profile in the fast tail is sensitive to the EOS (Hotokezaka et al.,
2018a; Radice et al., 2018a)

###  3.3 Rates

The rate of joint EMGW detectors depends on the volumetric BNS merger rate
$\mathcal{R}$, the source emission models, and sensitivities of the GW
detector network and EM satellites. We estimated these rates by injecting BNS
events uniformly randomly in co-moving volume, with random inclination, then
calculating their detectability by the GW network as well as Daksha. A
detailed set of calculations with a variety of emission models will be
presented elsewhere (Bhattacharjee et al., in prep), but we give a quick
overview and present the results here.

We consider a configuration where five GW detectors are operating at their
full sensitivity: “A+” sensitivity for LIGO Hanford, Livingston, and India,
“AdV” sensitivity for Advanced Virgo, and the standard design sensitivity for
Kagra. Following Petrov et al. (2022), we assume that the detectors have a
duty cycle of 70%, and an event is considered to be detected in gravitational
waves if the network signal-to-noise ratio (SNR) is $>8$. We take
$\mathcal{R}=320~{}\mathrm{Gpc^{-3}yr^{-1}}$ from Abbott et al. (2021a).

First, we assume a simplistic EM model where every BNS merger has the same
intrinsic luminosity as GW170817, independent of viewing angle111This implies
that there is no bright jet even for face-on observers.. We assume a
“Comptonized” spectral model with a photon power-law index $\alpha=-0.62$, an
exponential cut-off at $E_{p}=185$ keV, duration $\Delta t=0.576$ s (Goldstein
et al., 2017). The luminosity is calculated to match the observed Fermi flux
of 3.1$\times 10^{-7}~{}\mathrm{~{}\mathrm{erg~{}cm}^{-2}~{}\mathrm{s}^{-1}}$
in the 10–1000 keV band. Using the Daksha sensitivity discussed in Paper I, we
calculate that the pair of Daksha satellites will detect about 0.5 neutron
star merger events per year (after accounting for time lost due to SAA etc),
almost all of which will have a high enough GW amplitude to be detected by GW
networks.

Next, we consider a “Gaussian jet” model from Ioka & Nakamura (2019), where
the jet energy $E_{\gamma}$ and the Lorentz factor $\Gamma$ are given by,

$\displaystyle E_{\gamma}(\theta)$ $\displaystyle=$
$\displaystyle\eta_{\gamma}E_{0}e^{-\theta^{2}/2\theta_{0}^{2}}$ (1)
$\displaystyle\Gamma(\theta)$ $\displaystyle=$ $\displaystyle\Gamma_{\rm
max}/(1+(\theta/\theta_{0})^{\lambda})$ (2)

where $\theta_{0}=0.059$ rad, $\Gamma_{\rm max}=2000$ and $\eta_{\gamma}=0.1$.
The event duration was assumed to be 0.3 s for all the events, the typical
sGRB duration (Kouveliotou et al., 1993). Source energies ($E_{0}$) are drawn
from the Wanderman & Piran (2015a) luminosity function. For this model, we
find that Daksha will obtain 12 joint detections with the GW network per year.
On the other hand, very few events are found despite Daksha’s high
sensitivity, the upper limits from our data will imply that gamma-ray
production efficiency drops beyond the core: thereby giving new insights into
the underlying dissipation and emission mechanisms (Beniamini & Nakar, 2019).

Another key observation in the Gaussian jet simulations is the presence of
several events that are clearly detectable by Daksha, but just below the GW
network SNR of 8. Since the direction and time of the bursts will be known
from Daksha, we can undertake sub-threshold searches for coincident GW events
(see for instance Abbott et al., 2021b, 2022). Considering such sub-threshold
events to be detectable if their GW network SNR is $>6.5$, we find that Daksha
will enable the detection of gravitational waves from an additional seven sub-
threshold neutron star mergers each year.

##  4 Science Driver II: Gamma Ray Burst science

The observed GRBs fall into two broad categories. They are long GRBs (LGRBs)
with duration $T_{90}>2$ sec and short GRBs (SGRBs) with $T_{90}<2$ sec. Long
GRBs are produced by the core collapse SNe of giant star (Bloom et al., 2002;
Hjorth et al., 2003; Hjorth & Bloom, 2012), while, the short GRBs are produced
by the merger of binary compact objects such as binary neutron stars and
neutron star - black hole. The observation of GW170817 confirmed that at least
a class of short GRBs are produced by binary neutron star (BNS) mergers
(Abbott et al., 2017d).

A typical GRB emission consists of two main parts: the prompt phase which
consists of the immediate $\gamma$-rays produced closed to origin of the
burst, and the late time afterglow phase which is produced as the outflow
interacts with ISM surrounding the burst.The afterglow phase is well studied
unlike the prompt phase. The GRB afterglow observations provide the redshift
of the the burst which shed light on the constituents of ISM and the
underlying physical processes (Greiner, J. et al., 2009; Gendre, B. & Boër,
M., 2005; Schady, 2015). The broadband observation of the afterglow phase
conveys broad picture of the energetics and timeline of the underlying
processes.

During the main prompt GRB phase, the source invokes highly relativistic jets
with bulk Lorentz factors of a few hundreds emitting highly energetic photons.
The exact physical mechanism producing such powerful $\gamma$-rays still
remains debated (Kumar & Zhang, 2015). The composition of GRB jets, the
radiative processes giving rise to the prompt $\gamma$-rays are some of the
open ended questions (Kumar & Zhang, 2015). Both in terms of spectral
properties and physical mechanisms, prompt emissions are still comparatively
poorly explored (Zhang, 2011) as opposed to the afterglow phase due to the
transient nature of the event and lack of observations in the soft X-ray band
(Gehrels & Mészáros, 2012; Oganesyan, G. et al., 2018). Daksha is expected to
improve over both these aspects with its all-sky capability and ability to
probe in soft X-ray band and hence improving the population of the GRBs. Owing
to the high sensitivity, Daksha will help towards better understanding of the
transition between the prompt and afterglow emission in GRBs. This is of high
importance — for instance, it will enable the determination of the Lorentz
factor of the external shocked region, and whether the deceleration is
effectively in the “thick shell” or “thin shell” regimes. Below, we highlight
on the GRB science we can probe with the Daksha mission especially in the
prompt phase.

###  4.1 Rates

The distribution of the rate of long gamma ray burst with respect to redshift,
$z$, mainly depends on the star formation rate $R_{GRB}(z)$ and the luminosity
function $\phi(L)$. In case of the distribution of the rate of short GRBs, an
additional factor of time delay ($\Delta t$) relative to the star formation
rate is also considered. We adopt a functional form of broken power law for
both $R_{GRB}(z)$ and $\phi(L)$ as mentioned in Wanderman & Piran (2010),
whereas, a model of lognormal distribution is adopted for the time delay from
Wanderman & Piran (2015b). The various parameters defining $R_{GRB}(z)$,
$\phi(L)$ and $\Delta t$ are evaluated separately using the observed
distribution of the redshift detected long and short GRBs by the Swift mission
during the span of $17.5$ years222Note $\Delta t$ is estimated for the short
GRB distribution only.. During this period, Swift has detected a total of
$1314$ long GRBs and $133$ short GRBs, out of which $350$ long GRBs and $26$
short GRBs are found to have redshift measurements.

Figure 3: The cumulative plot showing the long and short GRB detection rate
(per year) the by Daksha and Swift as a function of redshift.

We use the Swift redshift distributions of long and short GRBs to predict GRB
detection rate of Daksha. Using the obtained fit values and the Daksha
sensitivity of $S=4\times 10^{-8}$
$\mathrm{erg~{}cm}^{-2}~{}\mathrm{s}^{-1}$and spatiotemporal coverage of
$\Omega\,T/(4\pi)=87\%$ (Paper I), we estimate that Daksha can detect nearly
$500$ long GRBs and $46$ short GRBs per year (around $7$ and $2.5$ times
greater than current Swift and Fermi rates respectively). Figure 3 shows the
expected redshift distribution for long and short GRB that would be observed
by Daksha.

###  4.2 Broad-band spectroscopy of the prompt emission

The physical origin of the prompt emission in GRBs is still a subject of
intense debate. In absence of a clear understanding of the processes giving
rise to the prompt emission, its spectrum is typically characterized by an
empirical model consisting of two smoothly joining power-law (Band et al.,
1993a), known as Band model or Band function. The typical GRB spectra in
$\nu$Fν form, shows a peak around energy of $\sim$100 keV, characterized by
the peak energy $E_{p}$, of the Band function. The spectra below and above
$E_{p}$ are characterized by two spectral indices $\alpha$ and $\beta$ of the
Band function. It has been observed that the peak energy is correlated to the
isotropic equivalent energy of GRBs (Amati et al., 2002; Amati, 2006).
Further, it has been found that the isotropic equivalent energy of the prompt
emission is correlated with the Lorentz factor of the outflow (Liang et al.,
2010; Ghirlanda et al., 2012), which may define the other spectral parameters.
Thus, accurate estimation of the GRB spectral parameters is important.

###  4.3 Prompt emission spectral anomaly with soft X-ray studies

A disagreement exists between the observed prompt spectral shape and the
theoretical synchrotron predictions from a non-thermal population of ultra
relativistic electrons in the soft X-ray band (Derishev et al., 2001; Daigne
et al., 2011). The observed GRB prompt spectra consist of a photon index
$\langle\alpha\rangle\sim-1$ which is on the harder side than the value
$\alpha=-1.5$ expected from fast cooling synchrotron radiation. Unfortunately,
the observational statistics for the existing missions in this low energy
prompt phase are really poor.

Several explanations exist in literature to counter this discrepancy. One of
the scenarios is either the cooling frequency $\nu_{c}$ or the self-absorption
frequency $\nu_{sa}$ being comparable to the characteristic synchrotron
frequency $\nu_{m}$ (Daigne et al., 2011; Beniamini & Piran, 2013). Another
possibility points at the low-energy part of the synchrotron spectrum being
modified by the energy-dependent inverse Compton scattering in the Klein-
Nishina regime hence hardening spectral shape (up to $\alpha=-2/3$) (Nakar et
al., 2009). These models assume a constant magnetic field, while some other
models explain the spectral hardening by invoking a non-uniform magnetic field
that depends on the radius and/or the distance from the shock front (Uhm &
Zhang, 2014). Moreover, synchrotron spectra can have photon indices much
harder than –1.5 if the pitch angles of the emitting electrons are distributed
anisotropically (Medvedev, 2006). It is then extremely important to explore
whether these proposed scenarios represent a viable solution and are supported
by observational evidence.

Figure 4: Simulated spectrum of a typical GRB, assuming a Band function
spectrum (Band et al., 1993b) with $\alpha=-1.0$, $\beta=-4.0$, $E_{c}=300$
keV, and a 10 – 1000 keV fluence of $\sim 1\times 10^{-5}$
$\mathrm{erg~{}cm}^{-2}$. Background statistics are not considered in these
simulations. The top panel shows the GRB spectra and the fitted model. In the
Middle panel we have shown the residuals with GBM spectra. Black and Red
colours correspond to single NaI and BGO detectors, respectively. The figure
at the Bottom panel shows the residuals for Daksha. The green, blue and aqua
colours show the spectra obtained using just one each of LEP, MEP and HEP. In
practice, the effective are is much higher when adding the signals from
multiple detector packages, but this example suffices to show the high
sensitivity. The response files used for LEP and MEP assume an on-axis
incidence, while for the HEP we have used a response file with a slightly off-
axis angle of incidence. This approximation does not significantly affect the
results.

Oganesyan et al. (2018) have characterized GRB prompt emission spectra down to
soft X-rays; in their sample of about 34 GRBs, they detect a low energy break
in about 62% of the spectra where the spectra harden below the break energy
(between 3 keV and 22 keV in their sample). However, this sample is small, and
Daksha, with its dedicated detector to measure the soft X-ray spectra of the
prompt emission, is ideally suited to determine the low-energy break for large
number GRBs. Figure 4 shows the simulated spectra of a GRBs with 10–1000 keV
fluence of 1 $\times 10^{-5}~{}\mathrm{\mathrm{erg~{}cm}^{-2}}$ as as detected
by Daksha and Fermi-GBM.

###  4.4 Extended emission and long central engine activity

A fraction of SGRBs are observed to have softer extended emission on time
scales of a few seconds to a hundred seconds. Amongst them, a good fraction of
the SGRBs are followed by a kilonovae e.g. GRB 050724 (Norris et al., 2010),
GRB 060614 (Bostanci et al., 2012), and GRB 080503 (Perley et al., 2009). The
fluence of the extended emission of some of these SGRBs is higher than the
prompt emission (Norris et al., 2010). It is also worth mentioning that the
extended emission was not found in GW170817, suggesting either that NS mergers
with masses similar to GW170817 do not produce extended emission or that it
was produced in GW170817 but was significantly beamed away from the Earth
(Abbott et al., 2017b). These observations pose few important questions: Are
their progenitors different from SGRBs without extended emission? What is the
energy source of long lasting emission if they arise from binary NS mergers?

It has been suggested that the extended emission can be powered by the spin-
down luminosity of a remnant magnetar or the Blandford-Znajek process of a
remnant Kerr black hole in NS mergers (Metzger et al., 2008). The detection of
an extended emission associated with the GW from confirmed BNS merger event
will shine light on this as well as the nature of GRB central object. Daksha,
with its high sensitivity and wide bandpass, particularly extending down to
soft X-rays, is ideally suited to investigate these aspects.

###  4.5 Time-resolved studies

The time resolved prompt emission studies are governed by two distinct
patterns in the evolution of the peak energy $E_{p}$: first the spectral
evolution from hard to soft energies. This can be explained by the matter
dominant jet outflow first giving black body radiation from the collapsing
material (Shemi & Piran, 1990) and then emitting non thermal photons resulting
from interaction of internal shocks interacting with optically thin region
above the photosphere (Daigne & Mochkovitch, 1998). Second, the luminosity
correlation with temperature (Golenetskii et al., 1983) resulting in flux
driven spectra taking into account the local magnetic-energy dissipation in a
Poynting flux dominant outflow fueling the acceleration of the flow to a high
bulk Lorentz factor. For typical GRB parameters, the dissipation takes place
mainly above the photosphere, producing non-thermal radiation (McKinney &
Uzdensky, 2011). In order to understand the underlying emission mechanism and
to reach to a unifying physical model, we need observations with fine time
resolved prompt spectra as well as ample GRBs with soft energy detection.

Even for short GRBs, investigating temporal evolution is of great importance.
The short GRB jet propagating inside the merger ejecta forms a cocoon, which
eventually breaks out from the ejecta surface. The emission arising from the
cocoon shock break-out is expected to be composed of an initial hard-spike
followed by a soft-tail (Gottlieb et al., 2018b; Beloborodov et al., 2020b).
The luminosity, duration, and spectral peak of the hard spike and soft tail
depend on the ejecta structure as well as the jet properties such as the
power, opening angle and time delay between the merger and jet launch. By
modeling the emission properties with time resolved spectroscopy of the prompt
phase, we will be able to obtain valuable information about the structure of
merger ejecta and the jet formation in neutron star mergers. This in turn may
allow us to constrain the neutron star equation of state (EOS) since the
ejecta profile in the fast tail is sensitive to the EOS (Hotokezaka et al.,
2018b; Radice et al., 2018b). Daksha with micro-second time resolution
capabilities and broadband energy coverage (including the soft X-ray energies)
is well suited to probe the temporal evolution of the prompt phase for long as
well as short GRBs.

###  4.6 Polarization from GRBs

Polarization from GRB emission can be an important tool to probe the physics
of emission mechanisms in GRBs, the geometry of the emission region, and the
origin and nature of the magnetic field at the emission region (Covino & Gotz,
2016; Lazzati et al., 2004; Waxman, 2003). Till date polarization has been
detected in only a handful of sources (Gill et al., 2020; Chattopadhyay et
al., 2022; Yonetoku et al., 2011a). There is significant debate in the
literature regarding the source of the polarization e.g. synchrotron with
ordered magnetic fields, synchrotron with random magnetic fields at shocks,
and inverse Compton interactions (Beloborodov, 2011; Toma et al., 2009; Covino
& Gotz, 2016; Gill et al., 2020). Different theoretical models predict varying
degrees of maximum polarization, based on the magnetic field, geometry and the
viewing angle (Ghisellini & Lazzati, 1999; Lazzati et al., 2004; Gill et al.,
2020). If the polarization is due to synchrotron processes, as is often
conjectured (Burgess et al., 2020), then a high polarization fraction would
imply ordered magnetic fields within the jet structure. A disordered magnetic
field structure that many theories propose may arise at the forward shock
(Medvedev & Loeb, 1999) would lower the polarization. Contemporary work on GRB
spectra indicate the prompt emission resulting from synchrotron radiation(non-
thermal) (Burgess et al., 2019; Troja et al., 2017). However, spectral
modeling of photospheric emission(thermal) has also provided adequate fits to
a subset of GRBs (Vianello et al., 2018). A combined study of the GRB spectrum
and polarization will break the degeneracy between various such theoretical
models.

Variation of the GRB polarization degree and the polarization angle has been
observed in very few sources (Götz et al., 2009; Yonetoku et al., 2011b; Zhang
et al., 2019; Sharma et al., 2019; Chattopadhyay et al., 2022). Time-resolved
polarization studies are challenging due to insufficient photon counts during
a GRB outburst. However, such observations can be a valuable tool to
understand the internal structure of the GRB jet and the nature of emission.
Different theoretical models have put forth possible predictions of variation
of the polarization angle, for example, the evolution of viewing angle cone
resulting in observing different magnetic field geometries (Ghisellini &
Lazzati, 1999) or inherently patchy, non-axisymmetric emission due to internal
fluid inhomogeneities (Lazzati & Begelman, 2009). The strength of the observed
polarization fraction and nature of the variation will help distinguish
between such models (e.g. as reported in Yonetoku et al., 2011b; Sharma et
al., 2019), which will provide valuable constraints on the nature of GRB
outflow.

Daksha, with its pixellated CZT detectors with large collecting area will be
able to measure polarization of hard X-rays in the prompt phase for GRBs
having sufficient brightness. Figure 5 shows simulation results showing hard
X-ray polarization measurement capabilities of Daksha. Our preliminary study
finds that the MDP for Daksha will be 0.31 for a fluence of $10^{-4}$
$\mathrm{erg~{}cm}^{-2}$, and we expect to measure polarization for nearly 5 –
8 GRBs per year with a fluence of more than $10^{-4}$
$\mathrm{erg~{}cm}^{-2}$. In the lifetime of Daksha, it will obtain a
homogeneous GRB polarization sample to constrain physical models of GRB prompt
emission. The details of the polarization sensitivity of Daksha (including the
measurement method) will be published in Bala et. al (in prep).

Figure 5: The plot shows hard X-ray polarization measurement capability of
Daksha using GRB 160821A as an example. GRB 160821A had a fluence of
$1.32\times 10^{-4}$ $\mathrm{erg~{}cm}^{-2}$ in the energy range 10 – 1000
keV ($3.64\times 10^{-5}$ $\mathrm{erg~{}cm}^{-2}$ in 20 – 200 keV). The red
point shows the injected GRB with polarization angle (PA) = 25° and a
polarization fraction (PF) of 0.54 while the blue point shows the recovered
value of PA (=23°) and PF (=0.57). The recovered value lies well within
1-$\sigma$ contour.

As an illustration, we consider the case of the polarized GRB 160821A. The GRB
had a 10 – 1000 keV fluence of 1.32$\times
10^{-4}~{}\mathrm{~{}\mathrm{erg~{}cm}^{-2}}$, and a duration $T_{90}=43$ s.
We model the GRB spectrum as a Band function with parameters $\alpha=-1.05$,
$\beta=-2.3$, and $E_{\mathrm{peak}}=941$ keV.

##  5 Additional science goals

As a sensitive all-sky monitor, Daksha data can be used to probe many other
scientific questions. Here, we discuss some of the science cases.

###  5.1 Magnetar Bursts

Magnetars are young (age $\lesssim 10^{4}$ yrs), highly magnetized
($B_{\mathrm{surf}}\sim 10^{13-16}$ G) neutron stars, that are notorious for
their wide variety of high-energy transient phenomena (see Kaspi &
Beloborodov, 2017, for an observational and theoretical review). These include
outbursts which last for months to giant flares that have been known to emit
$10^{46}$ erg in $\approx$100 ms (Hurley et al., 2005). With it’s lower
fluence threshold, wide energy range, and sky coverage Daksha will be a
valuable tool for probing magnetar bursts and flares from the Milky Way
magnetars as well as giant flares from magnetars in nearby galaxies
($d\lesssim 10^{2}\,\mathrm{Mpc}$). The increased volume probed by Daksha will
allow for a better understanding of magnetar burst rates, luminosity
distributions, and the birth-to-death cycle of magnetars.

For brighter bursts, Daksha’s polarization capabilities will allow for the
measurement of linear polarization which is expected to occur due to the
propagation of photons through extremely strong magnetic fields ($B\sim
10^{15}$ G, Taverna & Turolla, 2017). While other planned X-ray polarization
missions aim to study the polarization of persistent emission from magnetars,
Daksha’s polarization measurement capabilities over a near-all-sky field of
view are required for polarization measurements of magnetar bursts.

###  5.2 Fast Radio Burst Counterparts

FRBs are recently discovered millisecond timescale radio transients that are
detected from cosmological distances ($\sim$Gpc). The isotropic burst energies
of FRBs ($10^{38-42}$ ergs) are almost a trillion times higher than the
brightest radio pulses observed from Galactic pulsars. Due to the short
timescale and the luminosity of FRBs, neutron stars, especially magnetars
(e.g. Metzger et al., 2019; Lyutikov & Popov, 2020) are leading candidates for
their origins. Similarly, many FRB models expect prompt radio counterparts to
be emitted with BNS and NSBH mergers (Pshirkov & Postnov, 2010; Totani, 2013;
Mingarelli et al., 2015; Paschalidis & Ruiz, 2019; Rowlinson & Anderson,
2019). From the large volumetric rates of FRBs, compared to those of BNS and
NSBH mergers, it is clear that these would contribute to a small fraction of
observed FRBs. To date, while the observational data is rapidly increasing,
the evidence is heterogenous with a multiple theories (see e.g. Platts et al.,
2019, for a review) and plenty of open questions remain about the origins of
FRBs (Petroff et al., 2019, 2022).

Most mechanisms expect that the radio emission of fast radio bursts is a small
fraction of the total burst energy and prompt counterparts as well as
afterglows are expected in different wavebands, including X-rays. Due to the
extreme sensitivity of radio telescopes compared to X-ray and optical
telescopes, it is expected that most models predict that typical FRBs will not
have detectable high-energy counterparts. By significantly increasing the rate
of X-ray and gamma-ray transients, Daksha will be able to help identify and
constrain X-ray and gamma-ray counterparts of FRBs, a search that has yet been
unsuccessful from existing missions, see e.g. Cunningham et al. (2019);
Anumarlapudi et al. (2020); Guidorzi et al. (2020); Curtin et al. (2022);
Principe et al. (2022).

On 2020 April 28, an energetic radio burst with a total isotropic radio
emission of $10^{34}$ erg from the Galactic magnetar SGR 1935+2154 (CHIME/FRB
Collaboration et al., 2020; Bochenek et al., 2020b) accompanying an X-ray
burst with an energy of $\approx 10^{39}$ erg. The X-ray burst was delayed by
6 ms relative to the radio emission and was significantly harder
($E_{\mathrm{peak}}\sim 65\,$keV) compared to typical magnetar bursts
(Mereghetti et al., 2020). While the radio energy output of this burst was few
orders of magnitude lower than that of typical FRBs, this burst was the
brightest radio transient ever observed and partially bridges the energy gap
between radio pulsars and FRBs. For a 10 ms burst, Daksha has a 5-$\sigma$
fluence sensitivity of 7$\times 10^{-8}~{}\mathrm{~{}\mathrm{erg~{}cm}^{-2}}$.
Given the scarcity of bright FRBs and the faintness of their corresponding
high energy counterparts, Daksha’s broad sky-coverage and low fluence
threshold will be able to detect or rule out high energy counterparts to FRBs
detected by ground-based instruments such as CHIME (CHIME/FRB Collaboration et
al., 2018), ASKAP (Bannister et al., 2017), STARE2 (Bochenek et al., 2020a)
and upcoming telescopes such as BURSTT (Lin et al., 2022).

###  5.3 X-ray pulsars

The accretion powered X-ray pulsars are laboratories for study of various
phenomena involving matter in strong magnetic fields. The accreting matter
imparts or draws out angular momentum from the neutron star. Both the
accretion torque and the X-ray beaming from the neutron star are dependent on
the mass accretion rate and structure of the accretion column on the magnetic
poles of the neutron star. For a neutron star with a supergiant companion
star, the mass accretion from the wind causes these sources to show random
variation in accretion torque. However, these sources occasionally show rapid
spin-up phases, indicating a change in the mode of accretion from wind to a
disk. Study of various pulsar characteristics like pulse shape, pulse fraction
etc. at different accretion torque level measured with Daksha will lead to
better understanding of the relative importance of the two accretion
mechanisms in the persistent accretion powered X-ray pulsars. The neutron
stars with Be-Star companions undergo large outbursts during which the neutron
star shows large spin-up followed by slow spin-down during the quiescence.
Measurement of the accretion torque as a function of the accretion power and
the pulse profiles of X-ray pulsars will therefore be very useful in study of
the accretion processes in high magnetic field neutron stars over a large
range of mass accretion rate. Isolated X-ray pulsars and magnetars can also
undergo discontinuous changes in their rotation rate (glitches and anti-
glitches), some times accompanied by large scale pulse profile and emission
mechanism changes.

As an all sky X-ray sensitive satellite, Daksha will be able to gather time-
tagged photons from all sources in the sky. The absolute timing precision of
Daksha of the time-tagging will be sub-ms. Since individual Daksha detectors
lack directionality, photons from any specific source will be confused.
However, by barycentering the arrival times and optimally combining photon
counts from different detector facets of Daksha, we can search for periodic
astrophysical signals in a frequency–frequency derivative–sky-position phase
space. For known pulsars, we can use Daksha photons to continuously monitor
the spin periods for variations with accretion rates, detect glitches, and
refine their ephemeris. This monitoring can simultaneously cover all the X-ray
bright pulsars in the sky, unlike the monitoring with radio telescopes. In
addition to barycentering the data and combining the signals from different
detectors, Daksha can also use Earth occultation (see Section 5.5) as a method
to distinguish photons from bright sources near the Earth limb.

We calculated the expected source count rates for these sources with Daksha ME
detectors based on the _NuSTAR_ 20–50 keV spectra of several accretion powered
pulsars. We created lightcurves for these pulsars based on the _NuSTAR_ pulse
profiles in the same energy band, scaled appropriately and a background rate
of $\sim 7400\,\mathrm{cts\,s^{-1}}$ (for seven surfaces). We simulated
observations of these pulsars with an integration time of 2.5 days with a duty
cycle appropriate for the low-earth orbit of Daksha. A Lomb-Scargle
periodogram search was used to determine the pulsed flux level required to
detect the pulsation above a 3- and 5-$\sigma$ threshold.

The simulations show that accretion powered pulsars with a flux level above
$2.6\times 10^{-10}(3.1\times 10^{-10})\,\mathrm{ergs\,s^{-1}\,cm^{-2}}$ in
the 20–50 keV band will be detected with Daksha-ME at 3-$\sigma$ (5-$\sigma$)
level in every 2.5 day interval. Figure 6 shows these limits in comparison
with the pulsed flux measurements of GX 301–2 from _Fermi_ -GBM. The detection
threshold depends partly on the pulsed fraction and the pulse shape of each
source. Daksha-ME will therefore be able to carry out continuous monitoring of
the pulsar frequency and pulsed flux history of about 10 persistent X-ray
pulsars. A large number of transient pulsars (about six transient pulsars
every year) will also be monitored during their outbursts. About two new
transient pulsars are expected to be discovered every year. For study of
accretion powered X-ray pulsars, Daksha-ME is at par with _CGRO_ -BATSE and
_Fermi_ -GBM which have been extremely useful for study of this type of
sources in the last three decades.

Figure 6: Pulsed flux of GX 301–2 from _Fermi_ -GBM observations (black dots)
compared to the Daksha-ME detection thresholds (green: 5-$\sigma$, red:
3-$\sigma$)

###  5.4 Primordial black hole abundance

The nature of dark matter remains one of the biggest puzzles in cosmology
today. Primordial black holes (PBHs) that formed very early in the history of
the Universe have been suggested as possible candidates to make up a large
fraction of dark matter (Zel’dovich & Novikov, 1967; Hawking, 1971).
Cosmological observations including the cosmic microwave background, as well
as various microlensing surveys carried out from both ground and space have
ruled out a vast parameter range for the possible masses of such primordial
black holes (see e.g., Carr & Kühnel, 2020). However, there exists a window in
the mass range $[10^{-11}-10^{-16}]M_{\odot}$ where such PBHs remain
unexplored thus far. Such PBHs could even make up the entirety of the dark
matter, thus solving the dark matter puzzle without recourse to any new
particle physics. Such mass scales cannot be explored with light in the
optical wavelength range, as the Schwarzschild radii of such black holes are
smaller than the wavelength of optical light (see e.g. Niikura et al., 2019).
Due to its wide wavelength coverage, Daksha will probe this mass range in its
high energy band. The two Daksha satellites will enable a unique parallax
microlensing experiment for the first time, where the same GRB can be observed
with two different lines-of-sight (see e.g. Jung & Kim, 2020). The PBH will be
at a different impact parameter compared to the GRB for the two different
satellites, thus causing a difference in the measured flux of the GRB. A null
detection of a difference in flux (i.e. no detection of lensed GRBs) can
constrain the PBH abundance in the unexplored mass range. Assuming Daksha
detects a sample of 10000 such GRBs, we can expect to constrain the fraction
of dark matter locked in PBHs in the aforementioned mass range to $f_{\rm
PBH}\leq 0.5$ at 95 percent confidence (Gawade et al., in preparation).
Alternatively, a detection of a difference in the detected fluxes of the same
GRB from the two satellites will open an exciting possibility of finding such
tiny primordial black holes for the very first time. This experiment will
require excellent cross-calibration between the detectors on board the twin
Daksha satellites.

###  5.5 Earth Occultation Studies

Figure 7: Sources whose flux can be monitored daily with Daksha by the Earth
Occultation technique. In addition to these persistent sources, bright
transient sources like novae, X-ray binaries outbursts, etc can also be
detected with this technique.

The background for Daksha arises from the diffuse cosmic X-ray background, a
relatively small contribution from electronic noise, and counts from bright
point sources in the sky. The occultation of these bright sources by the Earth
causes changes in the net count rate, which can be used to monitor the
brightness of these sources (Harmon et al., 2002). We follow the method
defined in Singhal et al. (2021) to calculate the sensitivity of Daksha for
such measurements. The instant of the occultation event (ingress or egress) is
known from the coordinates of the source and the orbital position of the
satellite. We measure the flux levels in 100 s pre– and post– event windows,
and estimate the change in flux from the change in counts. We have to account
for one subtlety in these calculations: source photons are incident on the
projected area of the satellite, while the background rates are determined by
the total physical area of the relevant surfaces. We do these calculations
considering a nominal case with the median effective area (1310 cm2) for the
source and seven surfaces for the background. We calculate that for a single
ingress or egress, the 3-$\sigma$ sensitivity of Daksha is 0.048
$\mathrm{ph~{}cm}^{-2}~{}\mathrm{s}^{-1}$ (186 mCrab) in the 20–200 keV band.
Each satellite completes about 14 orbits per day, with two measurements per
orbit. Combining data from both satellites, the daily averaged sensitivity is
0.0064 $\mathrm{ph~{}cm}^{-2}~{}\mathrm{s}^{-1}$ (25 mCrab).

We used the Swift-BAT catalogue (Oh et al., 2018) to estimate the number of
sources that can be detected every day by Daksha. Using the reported hard
X-ray fluxes and power-law indices, we calculate that Daksha can provide daily
flux measurements of 29 sources: two active galactic nuclei (Cen A, NGC 4151),
the Crab Pulsar, ten High Mass X-ray Binaries, and sixteen Low Mass X-ray
Binaries. As seen in Figure 7, most sources are along the galactic plane. Note
that sources in the $\pm$(60° – 70°) declination range are not occulted in
every satellite orbit, owing to the 6° orbital inclination. Sources close to
the poles are never occulted by the Earth for Daksha, and cannot be monitored
by this method.

###  5.6 Novae

In addition to the study of persistent sources, the Earth occultation
technique can also be used to detect bright transient sources like novae,
outbursts of X-ray binaries, etc. As an illustration, we discuss the hard
X-ray detectability of novae. Soft X-rays have been commonly detected in
novae, but hard X-ray detections remain few in number — and the emission
mechanisms are poorly understood (Senziani et al., 2008a; Gordon et al.,
2021). Theoretical models predict that the early flash may be as bright as 0.1
$\mathrm{ph~{}cm}^{-2}~{}\mathrm{s}^{-1}$ in the 100–200 keV band, with
emission fading rapidly to lower levels over the timescale of a day (Senziani
et al., 2008b, and references therein). However, some novae have been bright
in hard X-rays: for instance, the 2006 outburst of recurrent nova RS Oph was
detected by Swift/BAT (Bode et al., 2006), and the 2015 outburst of GK Per was
detected by Integral (Tuerler et al., 2015). Pointed hard X-ray observations
of novae have led to more detections, with steep power-law spectral slopes:
$\Gamma=-3.6$ for V5855 Sgr (Nelson et al., 2019), $-3.9$ for V906 Car
(Sokolovsky et al., 2020), and $-3.3$ for YZ Ret (Sokolovsky et al., 2022).

Predictions for hard X-ray fluxes of novae are often made by extrapolating the
low-energy models (see for instance Bode et al., 2006). To estimate if RS Oph
would be detectable by Daksha, we follow the approach of Page et al. (2022) by
fitting the Swift-XRT data with an APEC model, and calculating the expected
flux in the Daksha energy band (20-200 keV). We find that the source would
have been detectable to Daksha from day 3–6 of the outburst.

A direct comparison with Swift-BAT lightcurves shows that Daksha can also
detect X-ray novae like MAXI J1828$-$249 (Grebenev et al., 2016), GRS 1739–278
(Mereminskiy et al., 2017) and MAXI J1535$-$571 (Mereminskiy et al., 2018).

###  5.7 Terrestrial Gamma-ray Flashes

The Earth’s atmosphere is populated by processes like thunderstorms,
lightning, and related electrical phenomena which emit X-rays and gamma-rays.
Despite their global occurrences, the underlying science of these critical
electromagnetic phenomena is still poorly understood. One such phenomenon is
Terrestrial gamma-ray flashes (TGFs) which were first detected in 1994 from
space by Compton Gamma Ray Observatory (Fishman et al., 1994). TGFs are
millisecond-duration sudden bursts of gamma-ray radiation having energies
reaching as high as 100 MeV (Tavani et al., 2011). They are observed over
thunderstorms and originate at around 20 km altitude (Carlson et al., 2007).
On average 500 TGFs/day are expected to occur globally but not all get
detected. Moreover, TGFs also produce energetic particles known as Terrestrial
Electron Beams (TEBs) that are composed of mainly secondary electrons and
positrons, which can be observed by spacecraft orbiting in the inner
magnetosphere (Dwyer et al., 2012). Their impact on the inner magnetosphere is
unknown and warrants detailed investigation. The simultaneous conjugate
studies with existing radiation belt missions like the Exploration of
energization and Radiation in Geospace (ERG) /Arase (Miyoshi et al., 2018)
will help to decipher the linkage of the lower atmosphere and inner
magnetosphere coupling.

High energy atmospheric physics is a new domain and evolving, the space-based
continuous observations of gamma rays will assist in deciphering the
unresolved problems of TGFs and TEBs. The microsecond time resolution and high
sensitivity of Daksha in the hard X-ray band makes it a well-suited instrument
for the study of TGFs. At an altitude of 650 km, Daksha can monitor a $\pm
25\arcdeg$ band on the Earth’s surface, corresponding to a footprint of
$\sim$2700 km. Combined with the 6° inclination, the satellites will be able
to detect activity in the latitude range from $-19\arcdeg$ to $+19\arcdeg$ in
each orbit, reaching upto $\pm 31\arcdeg$ in various parts of the Earth on
successive passes.

Key instruments for the study of TGFs inclued Fermi and the Atmosphere-Space
Interactions Monitor (ASIM) instrument on the International Space Station
(ISS). We can compare the TGF capabilities of Daksha directly with the “Low
Energy Detector” (LED) of the Modular X-ray and Gamma-ray Sensor (MXGS) on
ASIM. The LED comprises of CZT detectors covering the energy range from 50 keV
to 400 keV, with an effective area of 400 cm2 at 100 keV and a time resolution
of 1 $\mu$s (Østgaard et al., 2019). Daksha has similar time resolution, and a
much higher effective area: hence will be more sensitive to TGFs. The higher
altitude of Daksha (650 km instead of 400 km) will also allow each Daksha
satellite to view a much larger part of the Earth, while the near-equatorial
orbit (as opposed to 55° orbit of the ISS) ensures that Daksha spends more
time over areas with active thunderstorms, and avoids background
magnetospheric particle fluxes as well as auroral X-ray emission which could
have added to background noise. The orbital inclination is very important, and
has been suggested to be the main reason why ASIM detects only about 260
TGFs/year while Fermi detects close to 800 TGFs/year (Roberts et al., 2018;
Østgaard et al., 2019).The peak count rates reach tens of counts in 10 $\mu$s
intervals, with only a fraction of events yielding over 100 counts. These
rates are easily detectable in Daksha, where individual MEPs will have an
average of 0.03 counts in 10 $\mu$s bins, and are designed to handle might
higher peak count rates. TGFs are expected to have a few percent degrees of
polarization (Bagheri et al., 2019) which varies with source altitude. Daksha
will be able to put stringent observational constraints on the polarization of
the brightest TGFs.

There are several ground-based facilities studying the atmosphere: electric
field measurements, cosmic ray observations,
mesosphere–stratosphere–troposphere (MST) radars, etc. Simultaneous data from
Daksha and such facilities can give great insight in understanding association
of TGFs with convective activities and their evolutions. A particular example
of such a synergy will be joint studies with Daksha, the GRAPES-3 muon
telescope (Hariharan et al., 2019), Equatorial secondary cosmic ray
Observatory, Tirunelveli, India (Vichare et al., 2018), and Indian MST radars
(Uma & Rao, 2009; Subrahmanyam & Kumar, 2022).

###  5.8 Solar Flares

Solar flares are sudden releases of energy in the solar atmosphere leading to
emission across the entire electromagnetic spectrum, and often the release of
energetic particles into the interplanetary medium. According to the standard
flare model, the underlying mechanism powering the flares is magnetic
reconnection that leads to acceleration of particles into non-thermal
distributions and also heating of the plasma to temperatures often exceeding
10 MK (Benz, 2017). While the standard flare model picture explains the
observations in a broader context, several details such as the acceleration
mechanism are still not well understood. As the accelerated electrons emit in
hard X-rays by non-thermal bremsstrahlung, observations of the hard X-ray
spectrum provide the most direct diagnostics of the non-thermal electron
population (Krucker et al., 2008). By modeling the observed hard X-ray
spectrum, the distribution of the non-thermal electron population as well as
quantitative estimates of their total energy content can be obtained. Reuven
Ramaty High-Energy Solar Spectroscopic Imager (RHESSI, Lin et al., 2002) that
observed the Sun in hard X-rays for 16 years until 2018 provided wealth of
information on particle acceleration in solar flares with its broad band
spectroscopic and imaging observations. RHESSI could observe non-thermal
emission up to few tens of keV for flares down to GOES B-class intensities
(Hannah et al., 2008); however, it was not possible to extend this to lower
intensity flares.

Daksha, with its Sunward MEPs, will provide measurements of hard X-ray spectra
of solar flares in 20–200 keV energy band. With 4 MEPs in the Sunward
direction, Daksha will have about an order of magnitude larger effective area
than that of RHESSI in this energy range. With the added advantage of
simultaneous background measurements from other faces, Daksha is expected to
have much better sensitivity than RHESSI for solar flare spectra. Simultaneous
observations of flares by Daksha with instruments at other vantage points such
as the Spectrometer/Telescope for Imaging X-rays (STIX, Krucker et al., 2020)
on Solar Orbiter or various instruments of Aditya-L1 (Seetha & Megala, 2017)
also provides the opportunity to probe hard X-ray directivity.

###  5.9 Earth-Sun interaction

X-ray fluorescence (XRF) emission is triggered by solar X-rays from planetary
atmospheres along with a scattered continuum. The scattered X-ray spectrum
from Earth’s atmosphere in the soft X-ray regime is a representation of the
incident solar spectrum from which solar coronal abundances have been derived
by Katsuda et al. (2020). The LE detector package on Daksha would measure the
scattered solar X-ray spectra over a dynamic range enabling solar coronal
studies. The reduction in intensity by scattering especially during strong
flares would be an advantage here where often sun pointing spectrometers reach
a saturation. In addition, a mapping of the Ar elemental abundance in Earth’s
atmosphere would be possible from its X-ray fluorescence line.

##  6 Summary: the Impact of Daksha

Daksha has unprecedented coverage of the transient high energy sky. As
discussed in Paper I, the overall “grasp” of the mission, defined as the
product of effective area and sky coverage, is higher than any current or
proposed missions. Thanks to this, Daksha will discover the highest number of
high energy counterparts to gravitational wave sources. It will boost our
understanding of GRBs with prompt soft X-ray spectroscopy, highly time-
resolved spectroscopic studies, and polarization measurements.

In addition, Daksha covers a large number of secondary science cases. Compact
object studies will benefit from continuous monitoring of accreting X-ray
pulsars, detection and characterization of magnetar bursts, and the search for
counterparts to FRBs. Daksha can monitor persistent sources and slower
timescale transients like Novae to a sensitivity of 25 mCrab by the Earth
Occultation Technique. The two identical satellites in the mission will allow
us to probe primordial black hole abundance through microlensing. Closer in,
Daksha will provide excellent data for the study the Sun, TGFs, and the
atmospheric response to solar activity.

As mentioned in Paper I, Daksha was proposed in response to the Indian Space
Research Organisation’s Announcement of Opportunity (AO) for Astronomy
missions in 2018. The proposal was shortlisted for further studies, and was
awarded seed funding by the Space Science Program Office for demonstration of
a proof-of-concept. The team has completed the construction and testing of a
laboratory model of the Medium Energy detector Package, as required. Daksha
builds heavily on the legacy of various Indian space science missions, giving
a high technology readiness level to all subsystems. The mission will be
reviewed for full approval, after which we target a development timeline of
three years to launch.

We thank the Space Program Office (SPO) of the Indian Space Research
Organisation for its Announcement of Opportunity for space astrophysics
missions, under which Daksha was proposed. Development of the Daksha MEP
laboratory model was started with funding support from SPO. We thank the
administrative and support staff at all partner institutes for their help in
all Daksha-related matters. DS was supported under the CEFIPRA Grant No.
IFC/5404-1. AP acknowledges the SERB Matrics grant MTR/2019/001096 and SERB-
Power-fellowship grant SPF/2021/000036 of Department of Science and
Technology, India for support.

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