A simple analytic description is provided of the rate of energy deposition by $β$-decay electrons in the homologously expanding radioactive plasma ejected in neutron star mergers, valid for a wide range of ejecta parameters -- initial entropy, electron fraction $\{s_0,Y_e\}$ and density $ρt^3$. The formulae are derived using detailed numerical calculations following the time-dependent composition and $β$-decay emission spectra (including the effect of delayed deposition). The deposition efficiency depends mainly on $ρt^3$ and only weakly on $\{s_0,Y_e\}$. The time $t_e$ at which the ratio between the rates of electron energy deposition and energy production drops to $1-e^{-1}$, is given by $t_e=t_{0e}\Big(\frac{ρt^3}{0.5(ρt^3)_0}\Big)^a$, where $(ρt^3)_0=\frac{0.05M_{\odot}}{4π(0.2c)^3}$, $t_{0e}(s_0,Y_e)\approx17$ days and $0.4\le a(s_0,Y_e)\le0.5$. The fractional uncertainty in $t_e$ due to nuclear physics uncertainties is $\approx10\%$. The result $a\le0.5$ reflects the fact that the characteristic $β$-decay electron energies do not decrease with time (largely due to "inverted decay chains" in which a slowly-decaying isotope decays to a rapidly-decaying isotope with higher end-point energy). We provide an analytic approximation for the time-dependent electron energy deposition rate, reproducing the numerical results to better than $50\%$ (typically $<30\%$, well within the energy production rate uncertainty due to nuclear physics uncertainties) over a 3-4 orders-of-magnitude deposition rate decrease with time. Our results may be easily incorporated in calculations of kilonovae light curves (with general density and composition structures), eliminating the need to numerically follow the time-dependent electron spectra. Identifying $t_e$, e.g. in the bolometric light curve, will constrain the (properly averaged) ejecta $ρt^3$.
Spectroscopic r-Process Abundance Retrieval for Kilonovae II: Lanthanides in the Inferred Abundance Patterns of Multi-Component Ejecta from the GW170817 Kilonova
Impact of in situ nuclear networks and atomic opacities on neutron star merger ejecta dynamics, nucleosynthesis, and kilonovae
Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）；Università di Trento（特伦托大学）；INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（意大利国家核物理研究所-特伦托基础物理与应用研究所）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Contribution to the 2025 Gravitation session of the 59th Rencontres de Moriond: Limits on the Ejecta Mass During the Search for Kilonovae Associated with Neutron Star-Black Hole Mergers
Ultraviolet Signatures of Jet-Ejecta Interaction in Early Kilonovae: Prediction from Realistic Atomic Opacities
Technische Universität Darmstadt（达姆施塔特工业大学）；Tohoku University（东北大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
Plasma Instabilities Dominate Radioactive Transients Magnetic Fields: The self-confinement of leptons in Type Ia and Core-Collapse Supernovae, and Kilonovae
Spectroscopic r-Process Abundance Retrieval for Kilonovae III: Linking Spectral and Light Curve Modeling of the GW170817 Kilonova
Trottier Space Institute at McGill, McGill University（麦吉尔大学特罗蒂尔空间研究所）；Department of Physics, McGill University（麦吉尔大学物理系）；Department of Physics and Astronomy, Bishop’s University（主教大学物理与天文系）；David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto（多伦多大学大卫·A·邓普天文学与天体物理学系）；Department of Physics, University of Alberta（阿尔伯塔大学物理系）
Exploring the diversity of kilonovae with 3D radiative transfer I. The polar direction
Trinity College Dublin, The University of Dublin（都柏林三一学院，都柏林大学）；Astrophysics Research Centre, School of Mathematics and Physics, Queens University Belfast（贝尔法斯特女王大学数学与物理学院天体物理研究中心）；GSI Helmholtzzentrum für Schwerionenforschung（GSI亥姆霍兹重离子研究中心）
Heavy-element dust as an explanation for the late-time kilonova spectra
The University of Tokyo（东京大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Lanthanide Impact on the Infra-Red Spectra of Nebular Phase Kilonovae
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Astronomical Institute, Graduate School of Science, Tohoku University（东北大学理学研究科天体物理研究所）；Frontier Research Institute of Interdisciplinary Sciences (FRIS), Tohoku University（东北大学前沿跨学科科学研究院）；Oskar Klein Center, Department of Astronomy, Stockholm University（斯德哥尔摩大学天文系奥谢·克莱因中心）；Theoretical Astrophysics, Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文系理论天体物理学）
The imprint of individual neutron star spins on ejecta, $r$-process nucleosynthesis, and kilonovae in binary neutron star mergers
University of Southampton（南安普顿大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；University of British Columbia（不列颠哥伦比亚大学）；University of Illinois（伊利诺伊大学）；University of Edinburgh（爱丁堡大学）
2D End-to-End Modeling of Kilonovae from Binary Neutron Star Merger Remnants
University of Amsterdam（阿姆斯特丹大学）；Oregon State University（俄勒冈州立大学）；Anton Pannekoek Institute for Astronomy（安东·潘内克天文研究所）；Institute of High-Energy Physics, University of Amsterdam（阿姆斯特丹大学高能物理研究所）；Department of Physics, University of California, Berkeley（加州大学伯克利分校物理系）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Theoretical Astrophysics Center, University of California, Berkeley（加州大学伯克利分校理论天体物理中心）
Beta-Particle Transport and Thermalization in Kilonova Ejecta with Detailed Atomic Microphysics
Princeton University（普林斯顿大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；The George Washington University（乔治华盛顿大学）；Obsidian Research（黑曜石研究）；University of Notre Dame（圣母大学）
Self-consistent 3D radiative transfer for kilonovae: directional spectra from merger simulations
GSI Helmholtzzentrum für Schwerionenforschung（GSI亥尔姆霍兹重离子研究中心）；Department of Physics and Astronomy, Ruprecht-Karls-Universität Heidelberg（海德堡大学物理与天文系）；Astrophysical Big Bang Laboratory, RIKEN Cluster for Pioneering Research（理化学研究所先锋研究集群大爆炸天体物理实验室）；Institut für Kernphysik (Theoriezentrum), Technische Universität Darmstadt（达姆施塔特工业大学核物理研究所（理论中心））
Limits on the Ejecta Mass During the Search for Kilonovae Associated with Neutron Star-Black Hole Mergers: A case study of S230518h, GW230529, S230627c and the Low-Significance Candidate S240422ed
