The Advanced Spectral Leakage (ASL) scheme for simulations of merging neutron stars

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The Advanced Spectral Leakage (ASL) scheme for simulations of merging neutron stars

Davide Gizzi

Davide Gizzi The Advanced Spectral Leakage (ASL) scheme for simulations of merging neutron stars

Department of Astronomy

ISBN 978-91-7911-466-4

Davide Gizzi

Bachelor in Physics (2014) and Master in Astrophysics (2016) at the University of Rome La Sapienza.

Neutrinos play a primary role in binary neutron star mergers. They are produced in copious amounts in the hot merger environment, and given the large densities they interact with matter. Neutrino absorption via charged-current interactions powers an ejecta component called neutrino-driven wind, and changes the composition of the ejected material. This consequently impacts the r-process nucleosynthesis and the matter opacity, leaving an imprint in the macronova signal arising from the decay of the unstable r-process nuclei. With the prospect of future macronovae detections, modelling neutrino transport in mergers is therefore paramount to understand the variety of macronovae light curves. In this thesis we describe a new, efficient implementation of the Advanced Spectral Leakage (ASL), an approximation to the neutrino transport ideal to systematically extract neutrino-driven wind profiles in dynamical simulations of merging neutron stars.

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The Advanced Spectral Leakage (ASL) scheme for simulations of merging neutron stars

Davide Gizzi

Academic dissertation for the Degree of Doctor of Philosophy in Astronomy at Stockholm University to be publicly defended on Tuesday 18 May 2021 at 14.00 in Oskar Kleins

auditorium (FR4), AlbaNova universitetscentrum, Roslagstullsbacken 21, and online via Zoom, public link is available at the department website.

Abstract

The detection of a blue macronova following the event GW170817 has emphasized the role that neutrinos play in merging neutron stars. In particular, neutrinos are able to drive mass ejection, the so-called neutrino-driven winds, and change the neutron richness of the matter by absorption. Since the amount of neutrons in the ejecta sets the r-process nucleosynthesis and the matter opacity, the macronova signal arising from the decay of unstable r-process nuclei in the wind carries the signature of weak interactions in mergers as it shines in the optical wavelength band. However, other mass ejection channels have been shown to potentially contribute to this optical counterpart of the macronova. Looking forward to future, new macronovae detections, it is therefore important to systematically explore the impact of neutrino-driven winds in shaping macronovae light curves. For this purpose, in this thesis we introduce a computationally efficient neutrino scheme, called Advanced Spectral Leakage (ASL), that, together with hydrodynamic simulations of binary neutron star mergers, will allow to characterize macronovae and link the physics of binary neutron star mergers with observations.

Keywords: hydrodynamics, radiative transfer, neutrinos, stars: neutron, supernovae: general.

Stockholm 2021

http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-191475

ISBN 978-91-7911-466-4 ISBN 978-91-7911-467-1

Department of Astronomy

Stockholm University, 106 91 Stockholm

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THE ADVANCED SPECTRAL LEAKAGE (ASL) SCHEME FOR SIMULATIONS OF MERGING NEUTRON STARS

Davide Gizzi

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The Advanced Spectral Leakage (ASL) scheme for simulations of merging neutron stars

Davide Gizzi

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©Davide Gizzi, Stockholm University 2021

ISBN print 978-91-7911-466-4 ISBN PDF 978-91-7911-467-1

Cover image: distribution of the change in internal energy (top) and electron fraction (bottom) of the matter due to weak interactions in the neutrino-driven wind region of a binary neutron star merger, obtained with a Monte Carlo neutrino transport approach (left), the Advanced Spectral Leakage (ASL, middle) and a two-moment scheme (M1, right). The snapshot is obtained from a dynamical simulation of a binary neutron star merger with the smoothed-particle hydrodynamics.

The figure was produced by the author.

Printed in Sweden by Universitetsservice US-AB, Stockholm 2021

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List of papers

Paper I: D. Gizzi, E. O’Connor, S. Rosswog, A. Perego, R. M. Cabezon, L.

Nativi. A multi-dimensional implementation of the Advanced Spectral neutrino Leakage scheme, Monthly Notices of the Royal Astronomical Society, 490(3):4211- 4229, October 2019.

Paper II: D. Gizzi, C. Lundman, E. O’Connor, S. Rosswog, A. Perego. Exten- sion of the Advanced Spectral Leakage scheme for neutron star merger simulations, submitted to Monthly Notices of the Royal Astronomical Society, February 2021.

Paper III: L. Nativi, M. Bulla, S. Rosswog, C. Lundman, G. Kowal, D. Gizzi, G. P. Lamb, A. Perego. Can jets make the radioactively powered emission from neutron star mergers bluer?, Monthly Notices of the Royal Astronomical Society, 500(2):1772-1783, January 2021.

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Declaration

Summary of project

The neutrino scheme I have developed is based on the initial work by Albino Perego (Perego et al., 2016), who designed the so-called Advanced Spectral Leakage (ASL) for dynamical simulations of spherically symmetric core-collapse supernovae (CC- SNe). I have extended this scheme to binary neutron star (BNS) mergers and performed a detailed testing of its accuracy. The implementation of this new ASL is such that, coupled with the smoothed-particle hydrodynamics (SPH), the calcu- lation of the neutrino quantities is fully Lagrangian. In this way, the scheme can be used as a poweful tool to include neutrino effects in dynamical simulations of BNS mergers with SPH, allowing for a characterization of macronovae by means of different binary neutron star masses, different equations of state (EoSs), as well as in the context of jet-wind interactions.

Contribution to papers

Paper I: I have implemented the mathematical model to extend the original ASL scheme to BNS mergers. I have run the simulations to test the model over a snapshot of a merger remnant, and compared against a two-moment (M1) approach to test the accuracy of the scheme. The outputs from the simulations with M1 were given to me by prof. Evan O’Connor. I have carried out the whole comparison analysis in the paper.

Paper II: I have implemented the strategy for calibrating the ASL parameters.

I have collected the data from the other neutrino transport approaches and led the whole analysis. Data from the Monte Carlo (MC) code Sedonu and from M1 have been given to me by dr. Christoﬀer Lundman and prof. Evan O’Connor respectively. In addition, the paper contains a new, mesh-free algorithm to calculate optical depths on SPH conﬁgurations. The intuition for this approach came by prof.

Stephan Rosswog, and I subsequently implemented it into the code, as well as com- paring the results of this approach with a standard, grid-based approach adopted in most of the literature to date.

Paper III: I have provided functions to extract the thermodynamical proﬁle of the neutrino-driven wind, and use it as initial condition to run the subsequent simulations. I have tested these functions earlier on in the context of both CCSNe and

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BNS mergers. The extraction of the neutrino-driven wind properties required the usage of a nuclear equation of state (EoS), which I have provided and which was also tested. Once the neutrino-driven wind profile was ready, the subsequent simulations involved as first step the wind expansion with an Eulerian hydrodynamics code, as well as the jet launching and propagation through the wind, and as second step the radiative transfer calculations to extract macronovae light curves. Both first and second step were carried out by Lorenzo Nativi and dr. Mattia Bulla, respectively.

Reused and new material in the thesis

This thesis is a completion of the work initiated in Gizzi (2019). Therefore, I have reused chapter 2 entirely. This chapter introduces weak interactions and the main neutrino transport approaches, both used in papers I and II of the list. Chapters 1 and 3 are instead new. The former chapter is used to provide an overview of the physics of neutron star mergers, including the diﬀerent mass ejection channels, the associated r-process nucleosynthesis and macronovae, and the EoS. In the context of describing the properties of blue macronovae and constraining the EoS, the role of neutrino-driven winds is outlined. In the same way, the role of relativistic jets in characterising the diversity of macronovae light curves, which is the core of paper III, is also explained. The latter chapter describes the punchlines of both paper I and II, to which the reader is referred for more details.

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Acronyms

ASL Advanced Spectral Leakage

AT Astronomical transient

BNS Binary neutron star

BNSs Binary neutron stars CCSN Core-collapse supernova CCSNe Core-collapse supernovae CPU Central processing unit

EM Electromagnetic

EOB Eﬀective one-body

EoS Equation of state

EoSs Equations of state

GRB Gamma-ray burst

GRBs Gamma-ray bursts

GW Gravitational wave

GWs Gravitational waves

IAU International Astronomical Union

MC Monte Carlo

MGFLD Multi-group ﬂux limited diﬀusion

MHD Magneto-hydrodynamics

M0 One-moment

M1 Two-moment

NSE Nuclear statistical equilibrium O2 Second observational run O3 Third observational run O4 Fourth observational run

PN Post-Newtonian

QCD Quantum chromodynamics

sGRB Short gamma-ray burst sGRBs Short gamma-ray bursts

SPH Smoothed-particle hydrodynamics

SSS Swope Supernova Survey

TOV Tolman-Oppenheimer-Volkoﬀ

UV Ultraviolet

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List of Figures

1.1 Summary of the diﬀerent mass ejection channels and the corresponding timescales, taken from Shibata and Hotokezaka (2019) . . . 8 1.2 Sketch of the oﬀ-axis jet model associated to GRB170817A, taken

from Troja et al. (2017) . . . 11 1.3 Fading of the optical transient AT2017gfo from the blue to the red

band. Image credit: 1M2H Team/UC Santa Cruz & Carnegie Obser- vatories/Ryan Foley . . . 14 Electron fraction (

1.4 Ye) proﬁles of a cold, neutrino-less, -equilibrium neutron star. Figure is taken from Rosswog and Davies (2002). . . 17 r-process nuclei abundances for diﬀerent trajectories of a BNS merger 1.5

environment, resulting in diﬀerent mass-weighted electron fractions (Martin et al., 2018). . . 18 a) Nuclear heating rate

1.6 q obtained by running nuclear network calcu-_ lations, compared to the one associated to GW170817. b) Mass fraction of r-process nuclei obtained from nuclear network calculations, for three diﬀerent trajectories, two of which associated to a nuclear heating rate in agreement with the observed one from GW170817.

Figures are from Rosswog et al. (2018) . . . 20 1.7 Mass-radius relations for diﬀerent EoSs, for cold, non-rotating neu-

tron stars(Demorest et al., 2010) . . . 22 3.1 top: particle-based and bottom: grid-based approaches for calcu-

lating optical depths in a BNS merger remnant. The sketch is taken from paper II . . . 45 3.2 Luminosity per solid angle as a function of the polar angle for

both electron neutrinos (blue) and electron anti-neutrinos (red), for a snapshot of an equal mass BNS merger taken from the dynamical simulations of Rosswog et al. (2017). The ﬁgure is taken from paper I 46 Density maps on the x-z plane for the snapshot of the BNS merger 3.3

remnant studied in paper I. Green curves represent the location of the neutrino surfaces for some energies of the spectrum . . . 49 3.4 Inverse of the ﬂux factor for diﬀerent neutrino energies and for

both electron neutrinos (top) and electron anti-neutrinos (bottom) along the radius of a CCSN snapshot taken from the simulations of Perego et al. (2016). The ﬁgure is taken from paper I . . . 50 3.5 Speciﬁc, energy-integrated heating rate maps for a snapshot taken

from the simulations of Rosswog et al. (2017), used to calibrate the parameter p entering Eq. (3.9) for our new ASL. . . 52

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3.6 Initial conditions on the x-y plane for the three snapshots of BNS mergers taken from the dynamical simulations of Rosswog et al. (2017) and used for the ASL parameters calibration . . . 55 3.7 Initial conditions on the x-z plane for the three snapshots of BNS

mergers taken from the dynamical simulations of Rosswog et al. (2017) and used for the ASL parameters calibration . . . 56 Plots reported to show that a) the analytical closure in M1 leads to an 3.8

excess of neutrinos along the polar axis with respect to the reference solution from Sedonu. b) the 2D averaging can impact luminosities considerably when post-processing 3D snapshots at early times after merger. In addition, the assumption of axially symmetric ﬂuxes for the computation of the neutrino heating in the ASL is validated by the limited variation of the neutrino ﬂux with the azimuthal angle at each polar angle, in the bulk of the neutrino-driven winds. Figures are from paper II . . . 57 3.9 SPH maps of the rate of change of the matter internal energy and of

the electron fraction in the neutrino-driven wind region of the 1.4-1.4 M binary, for the diﬀerent neutrino approaches explored. Figures are from paper II . . . 58

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List of Tables

1.1 Subset of data taken from Radice et al. (2018a), showing properties of dynamical ejecta in dynamical simulations of merging neutron stars. 7 1.2 Summary of masses and velocities of the secular ejecta, component

by component. Data are taken from Ciolﬁ and Kalinani (2020); Fu- jibayashi et al. (2020); Perego et al. (2014); Nedora et al. (2019) . . . 15 2.1 Summary of the weak interactions included in the ASL scheme (Perego

et al., 2016) . . . 41 3.1 Values of neutrino luminosities and average energies with the ASL

for both prescriptions of ﬂux factors, for a snapshot of a CCSN taken from Perego et al. (2016). The data are taken from paper I . . . 51 Accuracy on neutrino luminosities and mean energies recovered from 3.2

the ASL with respect to the reference solution, using the best parameter set resulting from the calibration process. Data are taken from paper II . . . 57

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Introduction

Neutron stars are among the most dense (core densities several times the nuclear saturation density _sat 3 10¹⁴g cm ³) and compact (radii R 10 km) objects in the Universe. They represent, together with black holes, the end stage of the evolution of massive (M& 8 M) zero-age main sequence stars (Kippenhahn et al., 2012). Neutron stars are typically observed through X-ray and radio observations (Lattimer, 2012; Lorimer and Kramer, 2004) and are either isolated or found in multiple (i.e. binary, triple, quadruple etc.) systems. The discovery of the binary pulsar PSR B1913+16 by Hulse and Taylor (Hulse and Taylor, 1975) and the conse- quent study of its orbital evolution (Taylor and Weisberg, 1982) was paramount to demonstrate indirectly for the ﬁrst time the existence of gravitational waves (GWs).

The coalescence of two neutron stars is astrophysically relevant due to the variety of electromagnetic (EM) signals arising from the merger and post-merger phases (Fernández and Metzger, 2016; Nakar, 2020; Ascenzi et al., 2021; Margutti and Chornock, 2020). In particular, when two neutron stars merge and in the subsequent post-merger phase mass ejection occurs via several channels (see Sec. 1.1 for details) (Rosswog et al., 1999; Radice et al., 2018a; Shibata and Hotokezaka, 2019;

Bernuzzi, 2020). Due to the neutron-rich environment, a key parameter to describe the amount of neutrons in each ejecta component is the electron fraction Ye. The large ( several tens of MeV) temperatures achieved when two neutron stars merge lead to a re-processing of the initial, -equilibrium Ye. 0:1 to higher values up to Ye 0:4 for most of the ejecta components. This change in Yeis partially ascribed by neutrinos largely produced at those temperatures, and which interact with the matter while escaping because of the large (& 10⁹g cm ³) densities involved. De- spite the increase in Ye, mass ejecta from the merger host the favourable physical conditions to synthesize the heaviest elements in the Universe by r-process nucleosynthesis (see Sec. 1.4 for details) (Lattimer and Schramm, 1974; Eichler et al., 1989; Rosswog et al., 1999; Freiburghaus et al., 1999; Thielemann et al., 2017). The observational signature of the presence of r-process elements comes from the decay of the unstable nuclei, which powers a transient called macronova or kilonova (Ross- wog, 2005; Metzger et al., 2010; Rosswog et al., 2017; Grossman et al., 2014; Kasen et al., 2013; Kasen and Barnes, 2019; Shibata and Hotokezaka, 2019) (see Sec. 1.3 for details), making binary neutron star (BNS) mergers one, and likely the major, astrophysical event contributing to the chemical enrichment by r-process nuclei in the Universe (Cowan et al., 2021). Radiative transfer models predict that a blue macronova arises from the decay of nuclei in lanthanide-poor (Ye & 0:25) ejecta, whereas a red-infrared macronova comes from the decay of nuclei in lanthanide-rich (Ye . 0:25) ejecta (Korobkin et al., 2012). Given that neutrino irradiation is the

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cause for Y_e> 0:1, detecting a blue macronova is thus an imprint of the role of weak interactions occurring during and after the merger.

The first observational evidence of BNS mergers as ideal site for r-process nucleosynthesis came from the first detection of a BNS merger via GWs, the event GW170817, detected on the 17th of August 2017 by the LIGO and Virgo collaboration (Abbott et al., 2017b) during the second observational run (O2). In particular, due to its nearby location ( 40 Mpc), EM counterparts were detected in several wavebands following the gravitational wave (GW) signal (Abbott et al., 2017a; Pian, 2021), with a short gamma-ray burst (sGRB) detected 1:74 s after merger (Savchenko et al., 2017; Goldstein et al., 2017; Kasliwal et al., 2017), followed by a macronova (Arcavi et al., 2017; Chornock et al., 2017; Kilpatrick et al., 2017; Kasen et al., 2017; Pian et al., 2017; Smartt et al., 2017; Coulter et al., 2017; Tanvir et al., 2017), as well as X-ray and radio signals from a sGRB afterglow (Troja et al., 2017; Margutti et al., 2017; Haggard et al., 2017; Alexander et al., 2017; Hallinan et al., 2017). Beside assessing the role of BNS mergers as site for the synthesis of lanthanides and actinides (Rosswog et al., 2018; Kasen et al., 2017; Drout et al., 2017; Watson et al., 2019), this event allowed to answer other questions of astrophysics. For example, the long- standing, unconfirmed association between compact binaries and short gamma-ray bursts (sGRBs) (Narayan et al., 1992; Paczynski, 1986) became a clear evidence for the first time. In addition, the event GW170817 has contributed to set important constraints on the equation of state (EoS) (Most et al., 2018; De et al., 2018; Abbott et al., 2018; Radice et al., 2018a; Radice and Dai, 2019; Coughlin et al., 2019; Kiuchi et al., 2019; Bauswein et al., 2017; Jiang et al., 2019, 2020; Nicholl et al., 2021), to provide and independent measurement of the Hubble constant (Abbott et al., 2017c;

Dhawan et al., 2020; Wang and Giannios, 2021) and to test the theory of General Relativity (Abbott et al., 2019; Wei et al., 2017). We discuss more about the event GW170817 and the corresponding EM counterparts in chapter 1.

After GW170817, astronomers were longing for new exciting detections of macronovae during the third observational run (O3). Despite the initial 14 new merger alerts issued and involving at least a neutron star, later including also the events GW190425 (Abbott et al., 2020a) and GW190814 (Abbott et al., 2020b), no macronovae were detected by optical sky surveys, as a consequence of the large distances (> 100 Mpc) associated to the events, and pointing to the need of deeper limiting magnitudes in future surveys (Sagués Carracedo et al., 2021).

While waiting for the fourth observational run (O4) to start and possibly delivering new macronovae data, more eﬀort needs to be invested into simulations in order to fully understand macronovae properties. Even just looking back at GW170817, models struggle in explaining some properties of the associated macronova, especially the blue component (Ciolﬁ, 2020a) (see more in Sec. 1.3). Predicting macronovae properties depends on the EoS, the binary parameters, and to a large extent on the role of weak interactions, neutrino transport and ejecta geometry and composition (Perego et al., 2017a; Radice et al., 2018b; Even et al., 2020).

This thesis focuses on the problem of neutrino transport in mergers (see chapter 2.2). In particular, modelling neutrinos is computationally expensive (see Mezza- cappa et al. (2020) for a recent review) and requires the need of approximations. Our attention is on the modelling of an ejecta component launched by neutrino absorp-

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tion and called neutrino-driven winds, which is thought to be one of the potential candidates behind the blue macronova associated to GW170817 and for which a systematic study in simulations of BNS mergers is still missing (see more in Sec. 1.3.2 about this). The neutrino transport physics has been so far mainly explored in core-collapse supernovae (CCSNe) simulations (e.g. Buras et al. (2006); O’Connor and Ott (2010); O’Connor and Couch (2018); Roberts et al. (2016); O’Connor and Ott (2012); Müller (2016); Ebinger et al. (2018); Curtis et al. (2018); Ebinger et al.

(2020); Liebendörfer et al. (2001); Perego et al. (2015); Pan et al. (2019); Powell and Müller (2020); Harada et al. (2020); Walk et al. (2020); Burrows and Vartanyan (2021); Iwakami et al. (2020); Akaho et al. (2021); Pan et al. (2020)). The mechanism responsible for the explosion of massive stars is indeed a long-standing, still unresolved open question in astrophysics (e.g. Colgate and White (1966); Bethe and Wilson (1985); Janka et al. (2007, 2016); Woosley et al. (2002); Müller (2020)), and neutrino absorption behind the shock is thought to be an important ingredient in this respect (e.g. Colgate and White (1966); Bethe and Wilson (1985); Müller (2019); Janka (2017); Matsumoto et al. (2020)). The first dynamical simulations of BNS mergers with the inclusion of a neutrino transport approach were typically adopting a grey leakage scheme (Rosswog and Liebendörfer, 2003), an approximation where a spectral (i.e. energy-dependent) treatment of the weak interactions was neglected. However, neutrinos of different energies interact differently with matter, and capturing this feature is a key ingredient when modelling outflows like neutrino- driven winds (Foucart et al., 2016). Simulations involving neutrinos of different energies have been performed more recently, either using a moment approximation (e.g.

Dessart et al. (2009), see Sec. 2.2.3 for details) or a spectral leakage (e.g. Perego et al.

(2014)). In spite of this, the usage of an analytical closure in a moment approach has been shown to be problematic for accurately modelling neutrino-driven winds, and therefore for predicting macronovae light curves (Foucart et al., 2018), although the recent work Foucart et al. (2020) claims that a two-moment (M1) scheme care- fully treating the energy spectrum approximates the exact solution of the transport within 10 20% accuracy. Moreover, the work presented in Perego et al. (2014) requires large computational resources to model the neutrino absorption responsible for launching the winds. For this reason, we base our work on the original scheme developed for CCSNe simulations by A. Perego (Perego et al., 2016), called Advanced Spectral Leakage (ASL) (see Sec. 2.2.4), and extend it to obtain a computationally eﬃcient neutrino treatment suitable for systematic studies of neutrino-driven winds in BNS mergers (see chapter 3). The design of the scheme constitutes the heart of paper I, which includes a careful testing over a BNS snapshot, and is described in Sec. 3.1 in its main ideas. As a further step, we deepen the analysis of the scheme by calibrating the leakage parameters for BNS merger simulations against both a Monte Carlo (MC) neutrino transport code called Sedonu (Richers et al., 2015) and the M1 scheme implemented in the Eulerian hydrodynamics code FLASH (Fryxell et al., 2000; O’Connor, 2015; O’Connor and Couch, 2018) (paper II, but see also Sec. 3.2 for a summary). In the same paper we additionally introduce a novel, mesh-free implementation to calculate optical depths with smoothed-particle hydrodynamics (SPH) (Rosswog, 2015a, 2009; Monaghan, 2005; Rosswog, 2015b, 2020) setups (see Sec. 3.1 for details). Both papers provide a complete description of the new ASL,

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suitable for fully Lagrangian, dynamical simulations of binary neutron stars (BNSs) with neutrino transport, and constitute the major part of the thesis.

Beside the composition of the neutrino-driven winds, the properties of macronovae can be further characterized by adding physical eﬀects occurring after the merger.

In particular, relativistic jets launched at the merger time and drilling through the wind affect the macronova signal by altering the distribution of the ejected material. We have explored this effect in paper III. With the efficient ASL presented in this thesis it will be possible to explore the contribution of neutrino-driven winds in shaping macronovae light curves, for a variety of binary configurations as well as jet properties.

The structure of the thesis contains three chapters whose content is relevant for understanding the papers in the list. Chapter 1 constitutes an overview of binary neutron star mergers, and it is also meant to introduce the properties of neutrino- driven winds, which we model in paper I and II, as well as the role of jets and their impact on the macronova, extensively discussed in paper III. We additionally include details of the event GW170817 for completeness. Since the PhD project was focused on neutrino transport in mergers, we devote two chapters to this topic.

In particular, chapter 2 describes more in detail how to model neutrinos in a BNS merger environment. It contains both a summary of relevant weak interactions that are used in both paper I and II, as well as a description of the neutrino transport approaches being adopted. On the other hand, chapter 3 is more focused on describing the core of paper I and II, speciﬁcally, the novelties introduced in the ASL for modelling neutrino-driven winds.

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Chapter 1 Merging neutron stars: overview

1.1 Mass ejection

When two neutron stars merge, mass ejection occurs via different channels and on different timescales. In particular, ejecta can be classified either as dynamical ejecta, which forms within timescales of a few ms, or secular ejecta, which forms on longer timescales from several tens of ms to s. In the following, we will go through both classes, discussing key properties of the ejecta useful for understanding macronovae (Sec. 1.3).

1.1.1 Dynamical ejecta

Dynamical ejecta masses and velocities inferred from simulations span the ranges of a few [10 ⁴; 10 ²] Mand [0:1; 0:3] c respectively, c being the speed of light (Radice et al., 2018a; Bauswein et al., 2013; Bovard et al., 2017; Lehner et al., 2016; Sekiguchi et al., 2015; Bernuzzi, 2020; Bernuzzi et al., 2020). Two types of dynamical ejecta can be identiﬁed: tidal ejecta and shock-heated ejecta. The former arises from tidal torques operating in the last phases prior to the merger and it is distributed along the equatorial plane of the binary (polar angle =2), while the latter arises from shocked material getting squeezed and unbound when the two stars get in contact with each other, and has a more isotropic distribution. Overall, the bulk of the dynamical outﬂow is comprised within an angle of =3 from the equatorial plane.

The diversity of masses and velocities of dynamical ejecta comes from the dependence of the dynamical ejection on the masses of the two neutron stars, the mass ratio and the EoS. Indeed, for a given EoS and assuming the central remnant to be a massive neutron star, high-mass neutron star binaries eject more mass than low mass binaries, and this is even stronger if the mass ratio is diﬀerent from unity, because of the least massive star being tidally deformed by the more massive one (Rosswog et al., 2000), with the dynamical ejecta mass reaching 10 ²Mfor large ratios q 1:7 1:8 (Bernuzzi et al., 2020). If we ﬁx the mass ratio still assuming the central remnant to be a massive neutron star, soft equations of state (EoSs)

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lead generally to larger masses and ejecta velocities than stiﬀ EoSs ¹. This is a consequence of the fact that soft EoSs imply more compact stars, and therefore the merger occurs at shorter relative distances and is more violent (Vincent et al., 2020;

Radice et al., 2018a). If the EoS is very soft, the central remnant undergoes prompt collapse to a black hole. In this case, the shock-heated component is suppressed and only a few 10 ⁴M, mainly coming from the tidal component, is ejected. In terms of composition, while tidal ejecta maintain the electron fraction Ye. 0:1 of a neutrino-less, -equilibrium, cold neutron star, shock-heated ejecta experience a re-process of this electron fraction up to Ye > 0:25 because of weak interactions triggered by the large temperatures achieved at merger in the shocked material.

Recently, dynamical simulations of merging neutron stars have shown the appear- ance of a third, fast (velocities 0:6c) and light (masses 10 ⁶ 10 ⁴M) ejecta component, named fast moving ejecta (Radice et al., 2018a; Bauswein et al., 2013;

Metzger et al., 2015). Given the relativistic speed involved, this material might keep a large fraction of free neutrons, which after decaying might power an early ultraviolet(UV)-optical transient on timescale of minutes to hours from the merger (Kulkarni, 2005; Metzger et al., 2015). However, given the rather small mass, it is not yet clear whether this channel is physical or if it is of numerical origin. At last, in Radice et al. (2018b) viscously-driven outﬂows appearing on dynamical timescales and generated by thermalization of mass exchange streams between the two merging neutron stars have been addressed in unequal mass binaries as additional channel to increment the total dynamical ejecta mass up to a factor of a few. Similarly to the fast moving ejecta, asymptotic velocities can reach up to& 0:6c, with a broad distribution of Ye2 [0:1; 0:3]. We show in table 1.1 a subset of the data taken from table 2 of Radice et al. (2018a), with a summary of the properties of dynamical ejecta from a set of simulations involving 4 nuclear EoSs and 35 binaries with total mass M 2 [2:4; 3:4] Mand mass ratio q 2 [0:85; 1].

1.1.2 Secular ejecta

Secular ejecta comprise the largest fraction of mass that is unbound from a BNS merger remnant. It originates from the disk around the central object, and is often referred to as winds. Typical disk masses are of the order of a few 10 ¹Mfor suﬃciently stiﬀ EoSs (Vincent et al., 2020), while they reduce to a few 10 ³M

for very soft EoSs leading to a prompt collapse of the remnant to a black hole.

Compared to the equal mass cases, unequal mass binaries develop a more massive disk for a given EoS (Vincent et al., 2020), as a consequence of the tidal deformation of the least massive star, which allows more material to settle around the central object after the merger. In particular, a few 10 ¹Mare seen for large mass ratios q 1:7 1:8 (Bernuzzi et al., 2020).

There are three types of wind-outflows: magnetically-driven, neutrino-driven, and viscously-driven winds. Magnetically-driven winds (Ciolfi et al., 2017; Ciolfi and Kalinani, 2020) have masses of a few 10 ²M and velocities of 0:2c. Long- term (& 100 ms), magneto-hydrodynamic (MHD) simulations show that this wind

1Soft EoSs are generally deﬁned as those EoSs supporting lower maximum masses and providing smaller neutron star radii than stiﬀ EoSs.

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Table 1.1: Subset of data taken from Radice et al. (2018a), showing properties of dynamical ejecta in dynamical simulations of merging neutron stars. From left to right: model considered, time before collapse to black hole, disk mass, dynamical ejecta mass, fast moving ejecta mass, mass-averaged electron fraction of dynamical ejecta and asymptotic velocity. Each model is labelled with the name of the EoS used followed by the masses of the two stars. For example, BHB135135 refers to a model with the BHB EoS (Banik et al., 2014) and an equal mass binary where both stars have masses of 1:35M. The neutrino transport treatment for all models is a leakage, and it is chosen to be the same for a better comparison. The BHB

and the SFHo (Steiner et al., 2013) predict radii of a 1:4M neutron star of 13.2 and 11.9 respectively, therefore we refer to them as the stiﬀ and the soft EoS case respectively.

Model tblack hole Mdisk Mej M_ej^v0:6c hYei vej

[ms] [10 ²M] [10 ²M] [10 ⁵M] [c]

BHB135135 > 21.3 14.45 0.07 0.746 0.15 0.17 BHB140120 > 23.7 20.74 0.11 0.229 0.11 0.16

BHB150150 2.3 1.93 0.05 0.727 0.17 0.23

SFHo135135 12.0 6.23 0.35 1.924 0.17 0.24

SFHo140120 > 24.3 11.73 0.12 1.302 0.14 0.20

SFHo146146 0.7 0.02 0.00 0.000 - -

originates on timescales of a few tens of ms from the extremely large (& 10¹⁵ G) magnetic fields achieved during the merger, which drive wind outflows due to the large magnetic pressures involved. Simulations show that since the magnetic field structure is initially disordered, the wind distribution is roughly isotropic, until the magnetic field acquires a helical structure around the remnant spin axis. At this point, a faster component of the outflow arises along the poles. Neutrino-driven winds (Perego et al., 2014; Martin et al., 2015) originate over timescales of 100 ms from the partial re-absorption of neutrinos in the outer layers of the disk. Their mass is estimated to be a few 10 ³M, with velocities of 0:1c at the most, and the bulk of the emission is located at polar angles. =3 from the poles of the remnant. Both magnetically-driven and neutrino-driven winds share electron fractions Ye& 0:25 as a consequence of the change in the composition due to weak interactions. However, while the main source of power for the magnetically-driven wind is the presence of a strong magnetic field, and for this reason the central remnant does not have to necessarily be a massive neutron star, neutrino-driven winds might be suppressed in case the central remnant promptly collapses to a black hole, as the presence of a hot remnant neutron star is most likely an important source of neutrino irradiation. However, since most of the total neutrino luminosity actually comes from the disk (Perego et al., 2014), the presence of a remnant neutron star might not be paramount, as recent simulations of black hole-accretion disk systems with neutrino transport have shown (Miller et al., 2019). From the above argument, it is clear that the EoS, which defines the nature of the remnant central object and the properties of the surrounding disk, has an impact on the properties of neutrino-

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Figure 1.1: Summary of the diﬀerent mass ejection channels and the corresponding timescales, taken from Shibata and Hotokezaka (2019). Two cases are shown: case a) corresponds to a massive neutron star remnant, while case b) to a prompt collapse of the central remnant to black hole.

driven winds (see also Sec. 1.5.2).

Viscously-driven winds are powered over timescales of a few 0:1 1 s by viscous heating and nuclear recombination occurring in the disk (Fernández and Metzger, 2013; Fernández et al., 2019; Fujibayashi et al., 2018, 2020; Siegel and Metzger, 2017). They can unbind up to 40% of material from the initial disk mass, with velocities of 0:1 0:2c. Unlike the previous two types of winds, the electron fraction distribution is rather broad, with Ye2 [0:1; 0:4], depending on the role of weak interactions occurring in the diﬀerent parts of the disk over its dynamics. In particular, the high-electron fraction material is located into a funnel above the disk mid-plane, while the low-electron fraction one at equatorial latitudes.

A diﬀerent type of wind has been advocated recently (Nedora et al., 2019, 2021) by means of long term ( 100 ms) general relativistic, hydrodynamic simulations.

In particular, oscillations in the newly formed, central massive neutron star remnant drive density waves propagating through the disk and unbinding 10 ²M

of material with velocities 0:2c and electron fraction Yemostly distributed above 0.25. This wind is able to last as long as the central remnant does not collapse to a black hole, and, unlike the other types of wind, it is mostly distributed along the equatorial plane, regardless of the EoS and the mass ratio.

To provide a visual summary of the main mass ejection channels explored so far and of the relative timescales, we show ﬁg. 1.1 taken from Shibata and Hotokezaka (2019).

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1.2 Short gamma-ray bursts (sGRBs)

1.2.1 Overview

Gamma-ray bursts (GRBs) are rapid, bright flashes of radiation peaking in the gamma-rays. They are isotropically distributed in the sky, and occur at an average rate of one event per day. Typically, a gamma-ray burst (GRB) has a prompt phase characterized by a collimated, relativistic outflow pushing through the interstellar medium and powering radiation in the gamma-rays, followed by an afterglow phase shining in the X-ray, optical and radio bands for weeks and months. The relativistic outflow, called jet, is launched by the central engine. sGRBs are a class of GRBs with duration T90. 2 s, being T⁹⁰the time for the burst to reach 95% of the observed fluence from 5% in the canonical energy range 50-300 keV. Typical isotropic energies and luminosities of sGRBs are in the range 10⁴⁹ 10⁵¹ erg and 10⁵¹ 10⁵²erg s ¹ respectively (Nakar, 2007; Ghirlanda et al., 2011, 2009; D’Avanzo, 2015). Their host galaxies have a low star formation rate and an old stellar population (Berger, 2008;

Leibler and Berger, 2010; Fong and Berger, 2013). Compact binaries involving neutron stars have been for long associated to sGRBs (Narayan et al., 1992; Paczynski, 1986; Eichler et al., 1989; Nakar, 2007), but no direct identiﬁcation of the source was possible until very recently, with the detection of the ﬁrst BNS merger event via GWs, the event GW170817 (see Sec. 1.2.2).

Perhaps the most puzzling question related to sGRBs is the mechanism powering the jet. The first proposed models involved either neutrino-anti-neutrino annihilation into electron-positron pairs or extraction of energy from the central object via magnetic processes (see Rosswog et al. (2003) and references therein). However, recent studies show that neutrino-anti-neutrino annihilation might not be strong enough to explain the observed sGRBs luminosities alone (Perego et al., 2017b). Moreover, the most common engines associated to extraction of magnetic energy come from the magnetar object (Mösta et al., 2020; Ciolfi et al., 2019; Ciolfi, 2020b) and the Blandford-Znajek mechanism (Lee et al., 1999; Blandford and Znajek, 1977). Sev- eral studies move in favour of the latter mechanism (e.g. Ciolfi et al. (2019); Ciolfi (2020b)), although no definitive answer is available at the moment. For example, Mösta et al. (2020) have shown that also magnetized neutron stars are able to launch relativistic outflows.

1.2.2 The event GRB170817A

After 1:74 s from the peak of the GW emission, a gamma-ray signal of duration T90 2 s was detected at the same sky location of GW170817, and called GRB170817A (Savchenko et al., 2017; Goldstein et al., 2017). Moreover, on timescales of several days since merger a X-ray, optical and radio afterglow was also detected (Abbott et al., 2017a; Pian, 2021; Kasliwal et al., 2017; Troja et al., 2017; Margutti et al., 2017; Haggard et al., 2017; Alexander et al., 2017; Hallinan et al., 2017).

Although initially classiﬁed as a sGRB due to its duration, other properties of GRB170817A were remarkably in disagreement with the known population of sGRBs (Bhat et al., 2016; Gruber et al., 2014; D’Avanzo, 2015; Ghirlanda et al., 2009). For

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instance, the hardness ratio is one of the softest with respect to the catalogs (Gold- stein et al., 2017). Moreover, the isotropic energy and luminosity are lower by several orders of magnitudes (Zhang et al., 2018; Pozanenko et al., 2018). However, these properties were in the end explained by considering an observer viewing angle

v 15 35with respect to the jet axis, which prevents from receiving the emission of the jet core (He et al., 2018; Zhang et al., 2018; Granot et al., 2018; Kasliwal et al., 2017; Mooley et al., 2018; Lazzati et al., 2017; Gottlieb et al., 2018; Piro and Kollmeier, 2018; Kasliwal et al., 2017). The conﬁrmation of this scenario came also from the modelling of the afterglow emission, whose signal showed a rise for about

100 150 days followed by a decline both in the X-ray and radio bands (Margutti et al., 2018; Mooley et al., 2018; Ruan et al., 2018; Dobie et al., 2018; D’Avanzo et al., 2018; Alexander et al., 2018; Nynka et al., 2018; Nathanail et al., 2021). In particular, the X-ray signal would come from the jet interacting with the interstellar medium, and the delay in the detection ( 9 days since merger) would be consistent with an oﬀ-axis observer receiving such a signal only when the jet has decelerated enough in the medium so that beaming eﬀects reduce and the beaming cone include the observer itself (Troja et al., 2017). Furthermore, models of the decaying trend of the late (from 1 to 3.5 years since merger) (Lazzati et al., 2018; Troja et al., 2019;

Mooley et al., 2018; Troja et al., 2020; Makhathini et al., 2020; Hajela et al., 2019;

Balasubramanian et al., 2021) afterglow signal favour the oﬀ-axis jet scenario over others. At last, independent estimates of the observer viewing angle coming from studies of the properties of the macronova signal (see Sec. 1.3) and its polarization (Bulla et al., 2019; Bulla, 2019) are in support of the oﬀ-axis jet model as well.

Fig. 1.2 shows a sketch of this model taken from Troja et al. (2017), highlighting the diﬀerent macronova signal an observer would detect at diﬀerent viewing angles.

1.3 Macronova

As we shall see in Sec. 1.4, BNS mergers host the ideal physical conditions for the nucleosynthesis of the heaviest elements in the Universe via rapid neutron captures (i.e.

the r-process). The observational signature of the presence of these elements comes from the decay of the unstable r-process nuclei, which powers a transient peaking in the UV-optical-infrared bands and called macronova or kilonova (Metzger, 2019).

The ﬁrst studies of compact binaries as major sources of r-process nucleosynthesis are from Lattimer and Schramm (1974); Rosswog et al. (1999); Eichler et al. (1989);

Freiburghaus et al. (1999). Conversely, the ﬁrst toy model of macronova light curves is from Li and Paczyński (1998) (see below for a similar one), where the authors concluded that the ejecta from merging compact binaries, given its mass and velocity, becomes quickly transparent to its own radiation such that a transient appears on timeascales of about a day (faster than supernovae, for which typical timescales are of the order of& weeks).

In the following, we ﬁrst describe a typical toy model to characterize macronovae via order of magnitude estimates, following Metzger et al. (2010); Metzger (2019) (Sec. 1.3.1). We then dedicate a section to the macronova associated to the event GW170817 (Sec. 1.3.2).

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Figure 1.2: Sketch of the off-axis jet model associated to GRB170817A, taken from Troja et al. (2017). An off-axis observer with a viewing angle v 20 30 with respect to the jet axis receives a fainter gamma-ray signal not coming from the core of the jet, as well as a late afterglow signal resulting from a decreasing beaming effect due to the interaction and deceleration of the jet with the interstellar medium.

A viewing angle v 20 30 is also consistent with the temporal and spectral evolution of the observed macronova light curve (see Sec. 1.3.2). In particular, an observer looking at the binary system edge-on would not be able to detect any blue macronova because of the shielding from the lanthanide-rich component of the ejecta.

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1.3.1 Toy model

Let’s consider a spherically symmetric ejecta of total mass M , expanding with a constant velocity v such that the mean radius at time t is R vt. The ejecta expelled from the merging stars is rather hot at the beginning, but its thermal energy cannot be radiated away due to the high optical depths at early times:

' R = 3M

4R² ' 70 M 10 ²M

1 cm²g ¹

v 0:1c

2 t 1 day

2

; (1.1) and to the long photon diﬀusion timescale:

tdi 'R

c = 3M

4cR= 3M

4cvt: (1.2)

In the above equations is the opacity of the matter, is its density and c is the speed of light. Given the tdi / t ¹, the diﬀusion timescale decreases as the ejecta expands, until photons escape when tdi= t (Arnett, 1982). This condition deﬁnes the timescale for the light curve to peak:

tpeak 2:7 days M 10 ²M

1=2 v 0:1c

1=2 1 cm²g ¹

1=2

: (1.3)

From Eq. 1.3 we can clearly see that the larger the mass M and/or the opacity the longer the time needed for radiation to escape. On the other hand, the faster the ejecta the shorter the timescale for the light curve to peak.

The energy injected by radioactive decay is initially trapped by the high-opacity material and partially lost in adiabatic expansion of the ejecta. Therefore, only a fraction thermalizes and powers the EM transient. Assuming a radioactive rate Q t_ , with < 2, we approximate the energy released at tpeakas:

Qpeak _Qpeaktpeak= f M c²; (1.4) where f is a fraction 1 which can be estimated by running nuclear network calculations involving -decay, -decay and ﬁssion. This results in f 10 ⁶ and 1:1 1:4 (Metzger et al., 2010). We can then estimate the bolometric luminosity at tpeakas:

LpeakQpeak

tpeak

10⁴¹erg s ¹ f 10 ⁶

v 0:1c

1=2 M 10 ²M

1=2

; (1.5)

and assuming a black-body emission, the eﬀective temperature at the photosphere as:

Te = Lpeak

4R²_peak

1=4

; (1.6)

where Rpeak vtpeakand is the Stefan-Boltzmann constant. From Eq. 1.5 we see that faster and more massive ejecta are also brighter. Typical values of Te are of order 10⁴K, which implies the radiation to peak in the UV-optical bands.

Although the analytical toy model above provides a ﬁrst insight to the macronova

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properties, the ultimate task is to predict light curves and spectra of observed macronovae by means of realistic models, from which we can extract ejecta properties such as masses, velocities and composition, and consequently track back and understand the physics and dynamics of the merger. However, accurate models of light curves and spectra require the knowledge of physical ingredients for which the lack of exper- imental data forces us to introduce model assumptions and make approximations.

For example, a key quantity to describe macronovae is the opacity (Kasen et al., 2013), which allows one to quantify the abundances of heavy r-process elements in the ejecta (Even et al., 2020). Opacity estimates require the knowledge of the nuclear composition to deﬁne the distribution of r-process nuclei, and then the modelling of line transitions for the resulting, complex atomic structures. For the former, nuclei with extreme neutron excess such as those synthesized in BNS mergers cannot be reproduced in the laboratory, and therefore nuclear network calculations rely largely on model assumptions to determine the structure of the elements (Cowan et al., 2021; Zhu et al., 2021; Barnes et al., 2020). For the latter, there is no available list of atomic lines for heavy ions, and consequently ab initio calculations are the standard approach. Even then, modelling all the possible line transitions of r-process atomic nuclei is prohibitively expensive given their open f-shells (Fontes et al., 2020;

Kasen et al., 2013). At last but not least, radiative transfer calculations are needed to describe the temporal behaviour of the macronova light curve and to get spectra.

The variety of macronovae light curves and spectra is also geometry-dependent (Ko- robkin et al., 2020; Darbha and Kasen, 2020; Heinzel et al., 2021). While the simple toy model above assumes spherical symmetry, realistic models need to account for asymmetries induced by the diﬀerent ejection channels and their spatial distribu- tions (Sec. 1.1). The impact of the geometry on peak luminosity and time is by orders of magnitude, leading to potentially wrong estimates of masses and velocities of the ejecta components. It is also important to notice that realistic models of macronovae should account for the interplay between the mass ejecta distribution and the relativistic jet launched from the merger, as the jet pushing through the material makes the EM signal bluer for observers viewing angles close to face-on (see paper III for details, but also Klion et al. (2021)). This could contribute in explaining the large mass and velocity of the blue macronova inferred from the event GW170817, both of which are not yet fully explained by dynamical simulations of BNS mergers (see Sec 1.3.2). Moreover, simple multi-component macronova models where the diﬀerent components are assumed to have no mixing in their composition need further improvement, as the matter distribution can be sensitively impacted by the jet.

1.3.2 The macronova of GW170817: AT2017gfo

The ﬁrst signal associated to the macronova AT2017gfo was detected by the Swope telescope in Las Campanas Observatory in Chile, about 10.9 hrs after the GW trig- ger (Coulter et al., 2017). The transient, initially designated as Swope Supernova Survey (SSS) 2017a, was later called AT2017gfo in the IAU² designation. After- wards, many other teams announced the detection of optical (Soares-Santos et al.,

2International Astronomical Union

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Figure 1.3: Fading of the optical transient AT2017gfo from the blue to the red band.

Image credit: 1M2H Team/UC Santa Cruz & Carnegie Observatories/Ryan Foley

2017; Lipunov et al., 2017; Arcavi et al., 2017) and UV-infrared signals (Evans et al., 2017; Smartt et al., 2017) at the same sky location. Overall, these observations have shown a dimming in the UV-blue emission over a couple of days, followed by a brightening of the near-infrared emission lasting for a few weeks (see ﬁg. 1.3).

The properties of the spectrum from blue to infrared were in agreement with models involving mass ejection from neutron star mergers (Kasen et al., 2013), leading to the identiﬁcation of the transient as a macronova (Tanvir et al., 2017; Ross- wog et al., 2018; Drout et al., 2017; Cowperthwaite et al., 2017). In particular, a multi-component ejecta model was needed to ﬁt the data. Existing models either involve three contributions, with a "blue" (mean opacity 1 cm²g ¹), a "purple"

( 3 cm²g ¹) and a "red" ( 10 cm²g ¹) component, or just two contributions ("blue" and "red"). Nevertheless, data are well reproduced if the total ejecta mass is Mej 0:05 0:06 M and the velocities are vej 0:1 0:3 c. Within the simple, spherically symmetric, two-component light curve model, inferred masses and velocities of ejecta are Mblue 0:025 M, vblue 0:3c, Mred 0:04 M, vred 0:1c (Kasen et al., 2017). These numbers are clearly not always in agreement with ejecta properties derived from dynamical simulations of BNS mergers (Fujibayashi et al., 2018; Radice et al., 2018a; Perego et al., 2014; Nedora et al., 2019; Dietrich and Ujevic, 2017; Kasen et al., 2017), pointing to the need for both more accurate dynamical simulations and more realistic macronovae models. However, there is a general consensus on the role of secular ejecta, particularly viscously-driven and magnetically-driven winds, as necessary ingredient to achieve ejecta masses of a few 10 ²M(e.g. Ciolfi and Kalinani (2020); Nedora et al. (2021)). On the other hand, no systematic study of neutrino-driven winds has been performed yet. Although their masses and velocities might not be high enough to explain the blue component of AT2017gfo alone, their contribution is still crucial to define the opacity of the material and needs further investigation. At last, the still uncertain EoS is definitely a limitation for current simulations, as its impact on the dynamics of the merger

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Table 1.2: Summary of masses and velocities of the diﬀerent secular ejecta components. For each one we take data from representative dynamical simulations of BNS mergers. In particular, Ciolﬁ and Kalinani (2020) for the magnetically- driven, Fujibayashi et al. (2020) for the viscously-driven, Perego et al. (2014) for the neutrino-driven and Nedora et al. (2019) for the spiral wind. Note that unlike for the other components, there are no recent simulations systematically studying neutrino-driven winds yet.

Wind component Mej[10 ²M] vej[c]

Magnetically-driven & 1 . 0:2 Viscously-driven & 1 . 0:1 Neutrino-driven 0:1 . 0:1

Spiral & 1 0:2

is primary (see Sec. 1.5). Table 1.2 summarizes typical masses and velocities of ejecta for the diﬀerent wind components obtained from dynamical simulations, to be compared with those inferred from the AT2017gfo macronova mentioned above.

1.4 R-process nucleosynthesis

In the following, we ﬁrst describe the basics of the r-process nucleosynthesis following Thielemann et al. (2017) (Sec. 1.4.1), and subsequently we focus on the event GW170817 and the inferred abundances of r-process elements (Sec. 1.4.2).

1.4.1 Conditions for making the heaviest elements The production of r-process elements occurs in a two stages process: explosive burning at high temperatures until charged-particle freeze-out, and neutron capture from seed nuclei.

Explosive burning and charged-particle freeze-out

Let’s consider some expanding ejecta at an initial, high temperature T . If the material has T & 0:5 MeV its chemical composition is set by the nuclear statistical equilibrium (NSE). This means that for a nucleus i with proton number Zi, neutron number Ni and mass number Ai= Zi+ Ni the chemical potential Ai is set by the equilibrium condition:

Ai= Zip+ Nin; (1.7) where pand nare the proton and the neutron chemical potentials. Moreover, the nucleus abundance Y_i is deﬁned by the Boltzmann distribution:

Yi= Gi(NA)^Aⁱ ¹A³⁼²_i 2^Aⁱ

2~² mukBT

3(Ai 1)=2

exp Bi

kBT

Y_n^NⁱY_p^Zⁱ: (1.8)

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In Eq. 1.8, G_i is the partition function, the matter density, N_A the Avogadro’s number, mu the nuclear mass unit, ~ the Planck constant, k^B the Boltzmann constant, Bi the nuclear binding energy, Ypthe fraction of protons and Yn the fraction of neutrons. Moreover, we can see that the ^Aⁱ ¹dependence favor large Yiabun- dances for a given T , while large temperatures favor light nuclei for a given because of (kbT ) ^3=2(Aⁱ ¹⁾. The term exp(Bi=kbT ) favors nuclei with the highest binding energies in an intermediate regime of T and , which translates into elements of the iron-group.

Since we are assuming large temperatures at the beginning, the ejecta chemical composition is initially made of mainly neutrons, protons and alpha particles because of photo-disintegration of forming nuclei. As the ejecta expands and cools (but still with T & 0:5 MeV), heavier nuclei can be synthesized in NSE via the reactions + + !¹²C and + + n !⁹Be. However, this requires ﬁrst overpassing the synthesis of⁸Be via + $⁸Be, but⁸Be is highly unstable due to the short half life (1=2= 6:7 10 ¹⁷s). Therefore, only at suﬃciently high densities the synthesis of

12C and⁹Be occurs, but most of the ejecta has still an rich composition. At some point during the expansion, every part of the ejecta reaches temperatures below the NSE limit, and in combination with the unstable⁸Be the so-called rich freeze-out condition is reached. At this stage, only those nuclei that overpassed the bottleneck caused by⁸Be had the chance to build up elements with mass number in the range A 2 [50 100]. The only subsequent, possible way of synthesizing elements below NSE is via rapid neutron capture, or r-process.

Rapid neutron capture

If the amount of free neutrons in the ejecta is large, nuclei with A 2 [50 100] act as a seed for the synthesis of the heaviest elements in the periodic table. The nucleosynthesis process involves rapid and continuous captures of free neutrons by the already formed nuclei, until neutrons begin to run out. In particular, if the neutron- to-seed ratio is& 150, which translates into an electron fraction Y^e= _Y^Y^p

n+Yp . 0:1, elements of the lanthanide (Zi 2 [57; 71]) and actinide (Zi 2 [89; 103]) groups are produced.

Three parameters deﬁne a strong r-process nucleosynthesis (Arcones and Thiele- mann, 2013): large entropies, short expansion timescale of the ejecta, and most importantly, the neutron richness (i.e. low Ye). High entropies allow the ejecta material to keep a small amount of seed nuclei at the end of the NSE in comparison to free neutrons, protons and particles. A short expansion timescale allows to reach the -rich freeze-out earlier, avoiding more material to overpass the⁸Be-bottleneck.

A low Yeallows for more neutrons to be caught by seed nuclei, therefore building up heavier elements. While CCSNe do not meet the low Yerequirement to synthesize the heaviest elements (Arcones and Thielemann, 2013), but can only allow for the synthesis of nuclei as heavy as Strontium (Sr, Z = 38), Yttrium (Y, Z = 39) and Zir- conium (Zr, Z = 40), BNS mergers, thanks to ejecta components that keep Ye. 0:1 (like the tidal ejecta, see Sec. 1.1), host the ideal conditions for a strong r-process.

Values of Ye . 0:1 are standard in pre-merger, cold, -equilibrium neutron star proﬁles, as can be seen in ﬁg. 1.4 from Rosswog and Davies (2002). Fig. 1.5 from

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Figure 1.4: Electron fraction (Ye) profiles of a cold, neutrino-less, -equilibrium neutron star, obtained by solving the Tolman-Oppenheimer-Volkoff (TOV) equations with the Shen EoS (Shen et al., 1998), for three different equal-mass binaries where each star in the binary has a mass of 0.8 M, 1.4 M and 2.0 M. The Y_eprofile decreases from values 0:1 in the core down to 0:01 moving towards the neutron star surface. Only 1% of the neutron star mass at the surface has increasing Y_e up to 0:45. Figure is taken from Rosswog and Davies (2002).

Martin et al. (2018) shows an example of r-process nuclei abundances obtained from nuclear network calculations in a BNS merger environment, for diﬀerent trajectories resulting in diﬀerent values of the mass-weighted electron fraction hY_ei. As long as hYei < 0:25, elements with mass number A & 130 can be synthesized, whereas if neutrinos re-process the initial composition such that hY_ei & 0:25, only elements with A . 130 are produced (Martin et al., 2018; Shibata and Hotokezaka, 2019;

Wanajo et al., 2014). As source of comparison, black dots show the solar r-process abundances. The rather good agreement with the nuclear network calculations show that BNS mergers contribute to the chemical enrichment by r-process nuclei in the Universe.

1.4.2 The event GW170817: implications for cosmic nucleosynthesis

What has been described above in Sec. 1.4.1 was also confirmed with the detection of GW170817. In particular, running nuclear network calculations spanning the parameter space [v=c] Ye= [0:1; 0:2; 0:3; 0:4] [0:1; 0:2; 0:3; 0:4] (Rosswog et al., 2018) have shown that trajectories with Ye . 0:3 are the only ones providing nuclear heating rates in agreement with the trend of the observed bolometric luminosity (fig. 1.6a). In addition, trajectories with Ye< 0:3 are necessary to produce elements with A& 130 (fig. 1.6b).

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Figure 1.5: r-process nuclei abundances for diﬀerent trajectories of a BNS merger environment, resulting in diﬀerent mass-weighted electron fractions (Martin et al., 2018). Black dots show the solar r-process abundances. The higher the electron fraction content due to weak interactions, the lower the chance to synthesize the heaviest r-process nuclei.

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Although the transient AT2017gfo allowed to record for the first time spectra of a macronova, there was no robust identification of any element at the beginning. Only with a later re-analysis the element Strontium (Sr, Z = 38) was clearly identified, belonging to the first peak of the r-process abundances (A 80) (Watson et al., 2019). This identification undoubtedly establishes the role of merging neutron stars as ideal site for r-process nucleosynthesis.

Whether BNS mergers are suﬃcient to explain all the chemical abundances of observed r-process nuclei in the Universe is still matter of debate, as there are challenges that BNSs face in this respect, related to observed r-process abundances in ultrafaint dwarf galaxies (Ji et al., 2016; Hansen et al., 2017), in Galactic metal-poor halo stars and disk stars (Sneden et al., 2008; Cowan et al., 2021; Côté et al., 2017; Hotokezaka et al., 2018; Schönrich and Weinberg, 2019; Cavallo et al., 2021; Holmbeck et al., 2021), as well as in globular clusters (Sneden, 1999; Roederer, 2011; Sobeck et al., 2011; Worley et al., 2013; Zevin et al., 2019). Other proposed astrophysical sources include collapsars (Nomoto et al., 2006; Nomoto, 2017; Nakamura et al., 2001; Na- gataki, 2011; Sekiguchi and Shibata, 2011; Nagataki et al., 2007; MacFadyen et al., 2001; MacFadyen and Woosley, 1999; Siegel, 2019; Siegel et al., 2019; Brauer et al., 2020; Yamazaki et al., 2021) and MHD-driven supernovae (Kasen and Bildsten, 2010; Greiner et al., 2015; Nicholl et al., 2017; Symbalisty et al., 1985; Winteler et al., 2012; Nishimura et al., 2015, 2017; Reichert et al., 2021). Future detections of macronovae from merging binaries will be deﬁnitively helpful in better assessing the role of BNS mergers in this picture.

1.5 Equation of State (EoS)

1.5.1 Neutron star structure

An EoS is a relation between thermodynamical quantities describing the thermodynamical state of matter. When it comes to compact objects like neutron stars, knowing the properties of matter under extreme conditions of density, temperature and electron fraction is one of the hottest topics in current stellar astrophysics. The neutron star EoS has indeed been mostly constrained from laboratory experiments up to densities 20, being 0 = 2:7 10¹⁴g cm ³ the nuclear saturation density (Oertel et al., 2017; Gordon et al., 2018). The structure of matter beyond the laboratory limits is currently unknown, and guesses must rely on model predictions.

What we certainly know is that the pressure supporting neutron stars against gravitational collapse comes from strong interactions occurring in the inner core (Shapiro and Teukolsky, 1983). This implies that realistic models of the EoS in the core need to make use of the quantum chromodynamics (QCD) theory of strong interactions. Several nuclear EoSs have been modelled (Oertel et al., 2017) via diﬀerent techniques to deal with many-body strong interactions, and which provide a precise relation between the gravitational mass M and the radius R of a neutron star (see ﬁg. 1.7 from Demorest et al. (2010) for an example of mass-radius relations). A way of testing nuclear EoS models is by means of astrophysical observations of neutron stars that allow to constrain both M and R (Lattimer, 2012; Ozel and Freire, 2016).

Before the beginning of the GW era, measurements of masses and radii of neutron

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(a)

(b)

Figure 1.6: a) Nuclear heating rate _q obtained by running nuclear network calculations with a trajectory parameter space [v=c] Ye = [0:1; 0:2; 0:3; 0:4] [0:1; 0:2; 0:3; 0:4]. Yellow dots describe an estimate for the observed nuclear heating rate associated to GW170817, obtained by dividing the bolometric luminosity for a lower limit of the ejecta mass of 1:5 10 ²M. b) Mass fraction of r-process nuclei obtained from nuclear network calculations, for three diﬀerent trajectories. The red and orange ones are associated to a nuclear heating rate in agreement with the observed rate from GW170817. Blue dots describe the corresponding solar abundances.

Both ﬁgures are taken from Rosswog et al. (2018). Trajectories with Ye. 0:3 are the only ones providing nuclear heating rates in agreement with the trend of the observed bolometric luminosity, as well as synthesized elements with mass number A & 130.

The Advanced Spectral Leakage (ASL) scheme for simulations of merging neutron stars

The Advanced Spectral Leakage (ASL) scheme for simulations of merging neutron stars

Davide Gizzi

Department of Astronomy

The Advanced Spectral Leakage (ASL) scheme for simulations of merging neutron stars

Davide Gizzi

Davide Gizzi

The Advanced Spectral Leakage (ASL) scheme for simulations of merging neutron stars

Davide Gizzi

List of papers

Declaration

Summary of project

Contribution to papers

Reused and new material in the thesis

Acronyms

List of Figures

List of Tables

Contents

Introduction

Chapter 1

Merging neutron stars: overview

1.1 Mass ejection

1.2 Short gamma-ray bursts (sGRBs)

1.3 Macronova

1.4 R-process nucleosynthesis

1.5 Equation of State (EoS)