An overview of neutron star mergers

NUCLEAR ASTRO SUMMER SCHOOL

(15-MAY-2025)

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illustration: NASA Goddard

ATUL KEDIA

POSTDOC @

NORTH CAROLINA STATE UNIVERSITY

ASKEDIA@NCSU.EDU

Lecture outline

1. Neutron stars (NS) and NS mergers (NSM)
1. Gravitational Wave
2. Numerical Relativity simulation�
2. r-process nucleosynthesis�
3. Kilonova
• Observation
• Simulation
• Angular dependence

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Neutron Star

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Yunes, Miller and Yagi, Nature Rev. Phys. (2022)

Neutron Stars:

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Compact remnant of Supernovae

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Mass ~ Mass of Sun

Size ~ 9-13 km radius

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Gravitational pressure balanced by repulsive strong nuclear force, neutron degeneracy pressure

Neutron Star above Athens, Ohio

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Radius ~12km ~ 7 mi

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Visualization from https://ns-in-my-city.daniel-wysocki.info/

AT2017gfo / GW170817

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Neutron Star merger

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LIGO (Laser Interferometer [for] Gravitational wave observation)

https://phys.org/news/2019-05-ligo-virgo-neutron-star-smash-ups.html

LIGO-Livingston-Louisiana, LIGO-Hanford-Washington, Virgo-Italy, KARGA-Japan, upcoming LIGO-India (2030s)

Timeline of LVK observational runs

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Detection rate�projection

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Credit: Broekgaarden

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Future NS observations

*O4 LIGO-Virgo-KAGRA (ongoing)

*3^rd Generation GW detectors

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More measurements from�NICER: such as PSR-J0437

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(Next gen pulse-profiling via Strobe-X)

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ATUL KEDIA – NCSU

Sign up for GW Alerts with GraceDB

• Grace DB Link: https://gracedb.ligo.org/
• GCN : https://gcn.nasa.gov/circulars
• O4 resuming in June and will go on until October in 2025.

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Gravitational Wave

Far from the binary neutron stars (or any compact merger, BBH, NS-BH), the weak field regime is valid, and the Einsteins equations reduce to the Linearized Einstein equation

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Also see visualization here:

http://www.tapir.caltech.edu/~teviet/Waves/gwave.html

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Flow for Gravitational wave detection

GR: 3+1 (space-time) split and BSSN formalism.

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Dynamics: Relativistic hydrodynamics (to describe the flow of matter) + Equations of State (“Close” the equations)

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Numerical relativity codes that do this: Einstein Toolkit, Dendro-GR, GR-Athena++, SpECTRE, SPHINCS_BSSN, a few others.

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(See Foucart et al. Snowmass white paper, arXiv:2203.08139 [gr-qc])

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Numerical Relativity

Neutron Star merger

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Top-Down view

Cross-section Edge-on view

AK et al., PRD (2022)

Impact of the EoS on the Postmerger

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AK et al., PRD (2022)

Max density in the system in NR simulation

Impact of the EoS on the remnant

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AK et al., PRD (2022)

Dietrich et al. GRG (2020)

EoS softness

Waveform differences

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Scenarios of NSM: mass dependence

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Bartos, Brady, and Marka (2013).

Neutron star merger ejecta contributing to the abundance

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Radice et al ApJ (2018)

Fujibayashi et al, ApJ (2023)

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Flow of Nucleosynthesis

Stellar chemical composition

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• Fig. from Lippuner (2018)

and r-process

Some Nomenclature

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Calculation done on PRISM (reaction network)

ng -> neutron capture

gn -> photodissociation (neutron removal)

beta -> beta decay

Uncertainties in neutron capture rate

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Uncert. for near stability isotopes

Uncert. away from stability

N-cap uncertainties propagated to abundances

Neutron star merger ejecta contributing to the kilonova

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Radice et al ApJ (2018)

Kilonova is a multi-physics problem

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Simulation setup

• Radiative transfer software using tabulated binned opacities on SuperNu. (Wollaeger et al 2013, 2014)
• Composition and radioactive heating from r-process elements, nucleosynthetic results from WinNet. (Winteler et al. 2012)
• Nuclear model
• Heating rates (Korobkin et al. 2012)
• Thermalization model of (Barnes et al. (2016))
• Atomic opacities (Fontes et at. 2020)
• Reprocessing of light from one component to another.

(Wollaeger et al 2013, 2014, 2018, 2021)

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Broadband filters

Visible

Fig from Ristic et al PRR (2023)

Lanthanide curtaining

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Wollaeger et al ApJ 2021; See also Korobkin+2021, Kasen+2015

More equatorial

A smoking gun for r-process

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Curtaining of low wavelength (“blue”) light by Lanthanides (present in the “red” ejecta) produced by the nucleosynthesis.

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Top panel: Ejecta more spherically symmetric and less obstructed by the “red” component. Therefore, there is virtually no angular dependence.

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Bottom: “Red” component travels further and obstructs light emitted along the equator. Therefore, Lanthanide curtaining is observed.�Low wavelength light is suppressed substantially along the equator.

High wavelength light passes unaffected (spherically symmetric).

Impact of velocity distribution

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Fryer, .., AK et al, ApJ, (2024) ; similar conclusions by Tak et al, ApJ (2023)

AT2017gfo / GW170817

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Villar et al ApJL 2017

Abbott et al PRL 2017 , LIGO+Virgo

sGRB ~ 2s

NGC 4993

Multi-Messenger Inference

• Fig. Credit: Raaijmakers et al, ApJ (2021) ; modified here

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Radiative transfer

simulations

Kilonova modelling

BNS merger modelling (Numerical relativity)

Nucleosynthesizing ejecta material

EM v GW ejecta�tension

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Kilonova approach

🡨 Assuming(Torus, Peanut morphology )

GW approach

Ejecta properties (Kilonova approach) != Ejecta properties (GW approach)

NICER – Pulse Profile

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Lightcurve model

EoS properties: Mass-Radius relation

Riley et al. 2019, 2021

NASA’s Neutron star Interior Composition ExploRer at the International Space Stn.

Credit: NASA Goddard

Equation of State (EoS)

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Yunes, Miller and Yagi, Nature Rev. Phys. (2022)

Baym, Furusawa, Hatsuda et al. ApJ (2019) 885:42

Bayesian Inference

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(Bayes’ theorem)

(TOV solver using: RePrimAnd)

Posterior

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Prior

10,000 EoSs

Extra :EOS inference

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Extra slides

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EM v GW ejecta estimates

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Nedora et al ApJ (2021)

Siegel EPJA (2019)

Henkel, PRD (2023)

Ejecta masses and velocities

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Darker shade signifies more mass ;

longer arrows indicate faster moving ejecta

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NS Prior effect

HyperPipe – (RIFT)�HyperPosterior Pipeline -�Rapid parameter inference on gravitational �wave sources �via Iterative �FiTting

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Start

Construct Initial grid

Input Grid

EoS generation for row #1 9.882e+01 …

EoS generation for row #2 1.856e-01 …

EoS generation for row #3, and so on

Join (all Likelihoods above)

Unify

Posterior generation (MC Integrator)

Posterior Samples

Sample Randomizer (Puff-ing)

All sample Likelihoods

https://rift-documentation.readthedocs.io/en/latest/hyperpipe.html�https://rift-documentation.readthedocs.io/en/latest/overview.html

iteration i

# lnL sigma_lnL g0 g1 g2 g3

0 0 9.882e-01 1.770e-01 2.720e-02 …

0 0 1.856e-01 1.389e-01 1.916e-02 ….

….

Posterior

# lnL sigma_lnL g0 g1 g2 g3

0 0 2.413e-01 1.055e-01 1.596e-02 …

0 0 1.647e-01 2.853e-01 2.107e-02….

….

e.g.

Internal book-keeping steps

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Gaussian iterative fit (bimodal)

Y

Y

Z

Z

X

Three plausible/astrophysical priors for 170817

• Uniform : m1,m2 uniform; s1z, s2z using the 'z prior', with max magnitude <=0.05
• Extreme q: as above, but requiring the mass-ratio q<0.6. motivated by kilonova.
• Positive spin, comparable q: q>0.9 and s_{iz} >0, motivated by galactic pulsars

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GW prior effect

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• PRISM: Portable Routines for Integrated nucleoSynthesis Modeling  (Sprouse & Mumpower (NCSU alum))
• Purpose – Reaction network code for astrophysical abundance yield calculation
• Execution – for (Z_R1,A_R1) +...+ (Z_RN,A_RN) → (Z_P1,A_P1) +...+ (Z_PM,A_PM)
• Solves for Y(Z_i,A_i,t) from 
• (P(i) = probability for �each isotope formation)
• �Inputs – 
• Nuclear data – for reactions rates(Optical Model Potential, Gamma strength function, level densities), decays probabilities. In the form of reaction rates for Alpha decay, beta decay, neutron capture, fission,�
• Astrophysical data – Tracer particle - Initial abundance, Evolution of the packet in time, temperature, density

Reaction Network

LIGO-Virgo-KAGRA observation rate

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Credit: Broekgaarden

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Flow of Physics