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#### Evaluating radiation transport errors in merger simulations using a Monte-Carlo algorithm

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##### Citation

Foucart, F., Duez, M. D., Kidder, L. E., Nguyen, R., Pfeiffer, H., & Scheel, M. A. (2018).
Evaluating radiation transport errors in merger simulations using a Monte-Carlo algorithm.* Physical
Review D,* *98*(6): 063007. doi:10.1103/PhysRevD.98.063007.

Cite as: https://hdl.handle.net/21.11116/0000-0001-DC1A-B

##### Abstract

Neutrino-matter interactions play an important role in the post-merger

evolution of neutron star-neutron star and black hole-neutron star mergers.

Most notably, they determine the properties of the bright optical/infrared

transients observable after a merger. Unfortunately, Boltzmann's equations of

radiation transport remain too costly to be evolved directly in merger

simulations. Simulations rely instead on approximate transport algorithms with

unquantified modeling errors. In this paper, we use for the first time a

time-dependent general relativistic Monte-Carlo (MC) algorithm to solve

Boltzmann's equations and estimate important properties of the neutrino

distribution function ~10ms after a neutron star merger. We do not fully couple

the MC algorithm to the fluid evolution, but use a short evolution of the

merger remnant to critically assess errors in our approximate gray two-moment

transport scheme. We demonstrate that the analytical closure used by the moment

scheme is highly inaccurate in the polar regions, but performs well elsewhere.

While the average energy of polar neutrinos is reasonably well captured by the

two-moment scheme, estimates for the neutrino energy become less accurate at

lower latitudes. The two-moment formalism also overestimates the density of

neutrinos in the polar regions by ~50%, and underestimates the neutrino

pair-annihilation rate at the poles by factors of 2-3. Although the latter is

significantly more accurate than one might have expected before this study, our

results indicate that predictions for the properties of polar outflows and for

the creation of a baryon-free region at the poles are likely to be affected by

errors in the two-moment scheme, thus limiting our ability to reliably model

kilonovae and gamma-ray bursts.

evolution of neutron star-neutron star and black hole-neutron star mergers.

Most notably, they determine the properties of the bright optical/infrared

transients observable after a merger. Unfortunately, Boltzmann's equations of

radiation transport remain too costly to be evolved directly in merger

simulations. Simulations rely instead on approximate transport algorithms with

unquantified modeling errors. In this paper, we use for the first time a

time-dependent general relativistic Monte-Carlo (MC) algorithm to solve

Boltzmann's equations and estimate important properties of the neutrino

distribution function ~10ms after a neutron star merger. We do not fully couple

the MC algorithm to the fluid evolution, but use a short evolution of the

merger remnant to critically assess errors in our approximate gray two-moment

transport scheme. We demonstrate that the analytical closure used by the moment

scheme is highly inaccurate in the polar regions, but performs well elsewhere.

While the average energy of polar neutrinos is reasonably well captured by the

two-moment scheme, estimates for the neutrino energy become less accurate at

lower latitudes. The two-moment formalism also overestimates the density of

neutrinos in the polar regions by ~50%, and underestimates the neutrino

pair-annihilation rate at the poles by factors of 2-3. Although the latter is

significantly more accurate than one might have expected before this study, our

results indicate that predictions for the properties of polar outflows and for

the creation of a baryon-free region at the poles are likely to be affected by

errors in the two-moment scheme, thus limiting our ability to reliably model

kilonovae and gamma-ray bursts.