In-plasma study of opacity relevant for compact binary ejecta
Angelo Pidatella, Sergio Cristallo, Alessio Galat?, Marco La Cognata, Maria Mazzaglia, Albino Perego, Roberta Spart?, Aurora Tumino, Diego Vescovi, David Mascali
aa r X i v : . [ a s t r o - ph . H E ] J a n IL NUOVO CIMENTO
Vol. ?, N. ? ? In-plasma study of opacity relevant for compact binary ejecta
A. Pidatella ( )( ∗ ) , S. Cristallo ( )( ) , A. Galat`a ( ) , M. La Cognata ( ) , M. Mazzaglia ( ) ,A. Perego ( )( ) , R. Spart`a ( ) , A. Tumino ( )( ) , D. Vescovi ( )( ) , and D. Mascali ( ) ( ) INFN, LNS - Catania, Italy ( ) INAF, Osservatorio Astronomico d’Abruzzo - Teramo, Italy ( ) INFN, Sezione di Perugia - Perugia, Italy ( ) INFN, LNL - Legnaro, Italy ( ) Dipartimento di Fisica, Universit`a di Trento - Trento, Italy ( ) TIFPA, INFN - Trento, Italy ( ) Facolt`a di Ingegneria e Architettura, Universit`a degli Studi di Enna ”Kore” - Enna, Italy ( ) Goethe University Frankfurt - Frankfurt am Main, Germany
Summary. — In the context of the INFN project
PANDORA Gr3 ( P lasmafor A strophysics, N uclear D ecays O bservation and R adiation for A rchaeometry)and of multi-messenger astronomy, we propose a feasibility study for in-laboratoryplasma’s opacity investigation, in an environment resembling thermodynamic con-ditions typical of the ejecta of compact binary mergers containing at least a neutronstar. We aim to advance knowledge on the physics of kilonovae , the electromag-netic transients following a merger, which are relevant for the study of the origin ofheavy nuclei in the Universe produced via r -process nucleosynthesis. In this paper,we present preliminary results of numerical simulations for some physics cases con-sidered in the light of a possible experimental setup for future in-laboratory opacityspectroscopic measurements.
1. – Introduction
Binary neutron star (BNS) and black hole-neutron star (BH-NS) mergers can ex-pel rapidly expanding matter, usually referred to as compact binary ejecta (CBE). Atinitial stages, CBE are very rich in neutrons and have peculiar thermodynamic condi-tions which are compatible with being among the major sources of cosmic rapid neutroncapture nucleosynthesis ( r -process) [1]. This matter, enriched in freshly synthesized ra-dioactive isotopes, powers electromagnetic transient emissions known as kilonovae [2].These signals (from UV to near-IR) represent one of the primary electromagnetic coun-terparts of gravitational-wave events produced by the merging, as it occurred for the ( ∗ ) [email protected] © Societ`a Italiana di Fisica A. PIDATELLA ETC.
GW170817 event [3]. A kilonova arises from a translucent stage of the expanding ejecta,when thermal radiation can escape. Its energy results from a balance between thermal-ization processes and the radioactive warm-up due to nuclear fissions and decays [4, 5].As a result of the non-trivial merging dynamics, several ejection episodes can occur and,depending on the ejecta neutron richness, both heavy and light elements are synthesizedvia the r -process. The presence of heavy and light r -process elements can be disen-tangled by analysing the kilonova light curve. Previous studies of the bolometric andbroad band light curves of AT2017gfo (GW170817 kilonova) [2] have stressed the pres-ence of at least two ejecta’s components (in terms of mass, velocity, and composition)[6]. Due to this complex composition, the wavelength, intensity, and evolution time-scaleof the kilonova light curve are strongly affected by the ejecta opacity [6, 7, 8]. Opacity, κ ( ν ) ∼ N ij σ phj → k ( ν ), with N ij being the atomic level population of excited level j ofion stage i , and σ phj → k ( ν ) being the cross section for the atomic transition from level j to level k , regulates the energy exchange between radiation and plasma. It arises fromthe blending of millions of atomic line transitions, and considers multiple absorption-scattering processes involved in the radiation transport from its nucleation place to theedge of the ejecta. Here, opacity can differ of several orders of magnitudes: ejecta enrichedin light r -process elements have relatively low opacity ( κ . − ), radiating optical light that fades in days, while heavy r -process elements enlarges the opacity ( κ ≈
10 cmg − ), with redder light curves lasting even for weeks, depending on the complexity ofcontributing atomic sub-shells [6]. State-of-the-art works point to the necessity to makeprogress in opacity modelling [8, 9, 10] for more correct kilonova light curve predictions.Available models of these objects are often oversimplified and can result incomplete orinconsistent when compared with observational data. A more detailed knowledge of ki-lonovae events is important both for astrophysics and nuclear astrophysics to quicklyidentify related gravitational-wave events, and also to draw quantitative conclusions onthe r -process nucleosynthetic yield from observations, relevant in the study of the cosmicorigin of r -process nuclei.In the context of the INFN project PANDORA Gr3 [11], we propose a feasibilitystudy of CBE plasma opacity evaluation. We aim at designing an experimental setupfor in-laboratory opacity measurements, relevant for kilonovae light curve predictions. Inthe following, we present preliminary results of numerical simulations aiming at locatingreproducible plasma conditions of CBE in the laboratory, and estimates of their nucleiabundances according to the r -process nucleosynthesis. These studies permit to selectsome remarkable physical cases, for which a systematic numerical spectral analysis hasbeen carried out. This investigation has provided stronger bases to further proceed withthe experimental design of opacity measurements.
2. – Modelling of kilonova-emitting CBE and r -process nucleosynthetic yields Inside the PANDORA Gr3 compact magnetic trap, a dense and hot plasma, made ofmulti-charged ions in a cloud of energetic electrons is confined in a so-called minimum-Bmagnetic profile, and heated by microwave power, according to the electron cyclotronresonance (ECR) mechanism [11]. The generated ECR plasmas can reach electron dens-ities up to ∼ cm − and energies in the range of 1 eV −
10 keV. As first step ofthis study, we have located the CBE stage at which plasma conditions are reproduciblein laboratory plasma. For this purpose, modelling of time evolution of CBE has beencarried out considering homologous expansion of a fluid element under adiabatic con-
N-PLASMA STUDY OF OPACITY RELEVANT FOR COMPACT BINARY EJECTA Figure 1. – ( a ) Evolution of ejecta parameters in the electron density n e [cm − ] vs. energy [ keV](computed as k B T ) plane, for ejecta moving with velocity v = 0 . c . ( b ) Time-evolution ofelectron density of ejecta adiabatically expanding at v = 0 . c . Different colors refer to differentejecta masses M and initial electron fraction Y e . Dashed coloured boxes locate laboratory feas-ibility conditions. ( c ) Elements abundances for r -process nucleosynthesis assuming different Y e as calculated with the SKYNET [14] nuclear network. ditions [1]. Initial conditions for the mass M , temperature T , velocity v , and electronfraction Y e - the latter indicative of the initial neutron richness - were assumed fromthe state-of-the-art numerical simulations outcome for BNS mergers [12, 13]. Some res-ults are shown in figs. 1( a,b ). The expected evolution in the density-energy plane infig. 1( a ) suggests that ejecta resemble ECR plasmas densities in an energy range of afew eV. These plasma parameters, as suggested by fig. 1( b ), fit better the conditions ofearly-stage kilonova emission, i.e. , between 10 − − days after merger. This earlyphase of the signal ( blue-kilonova emission ) has its peak at optical frequencies, morelikely due to the ejecta’s light component featuring a low degree of opacity. Assumingthose plasma conditions for CBE, we have determined the main atomic abundances inthe astrophysical environment, according to the r -process nucleosynthesis, in order toconstrain relevant elements for in-laboratory measurements. The neutron richness of theejecta plays a fundamental role in determining the nucleosynthesis outcome. In fig. 1( c )we report on several r -process yields distributions computed by means of the SKYNETnuclear network [14] as a function of Y e . It can be evinced that light r -process elementsproduction dominates for Y e ≥ .
25, where large Y e ’s are expected for early-days bluekilonova (being a reproducible experimental condition as shown in figs. 1( a,b )). On thisbasis, and since the blue-kilonova emission is more likely shaped by light r -process ele-ments [10, 15, 16], we have initially considered elements going from selenium to rhodium as eligible for our experimental campaign.
3. – Numerical simulations about opacity in PANDORA Gr3 plasmas
In addition to considering the abundances of light r -process elements in CBE cor-responding to early-epochs kilonova emission, we have also based the choice of plasmaspecies for experiments on their contribution to opacity. For this purpose, a campaign ofnumerical simulations to explore the expected opacity contribution in the visible (VIS)range has been performed by using FLYCHK [17], a population kinetics and spectralmodelling code that can evaluate plasma opacity, according to the degree of plasmaionization and atomic level population distribution. These aspects strongly depend on A. PIDATELLA ETC.
Figure 2. – ( a ) Opacity (cm g − ) vs. wavelength (nm) for NLTE optically thick selenium plasma, at density ρ = 10 cm − and various energies k B T (eV). ( b ) Frequency-integratedmean opacity (cm g − ) vs. plasma temperature T (K), for all single-species NLTE plasmas, at ρ = 10 cm − . Optical thin (dashed-line, circle marker) and thick (solid-line, square marker)cases are shown. ( c ) Weighted opacity log( α ), in the atomic elements - Y e plane, for NLTEoptically-thick plasmas, at ρ = 10 cm − and energy k B T = 0 .
644 eV. the plasma parameters. The code accounts both for finite-size plasma and differentplasma models, such as local thermodynamic equilibrium (LTE) and non-LTE (NLTE),to produce theoretical synthetic spectra, given plasma density ρ , energy k B T , and op-tical thickness τ . As a first study, single-species self-emitting plasmas made of Se, Sr,Zr, Nb, Mo, Tc, Ru, and Rh have been considered. Both LTE and NLTE regimes wereinvestigated, for ρ ∼ ÷ cm − , k B T ∼ . ÷ τ = 1 µ m ,
10 cm. Someof the numerical results are shown in figs. 2( a-c ). Figure 2( a ) shows an example of opa-city spectrum from simulations for NLTE optically thick Se plasma, at fixed density andvarious energies. Several contributions to opacity in the VIS are present. Comparisonwith the LTE counterpart has evinced a better resolution of the self-consistent interplaybetween rate and radiative transport equations, whilst thicker plasma contributes withlarger opacities than thin plasmas. To describe the plasma’s tendency in absorbing ra-diation in the studied spectral range, frequency-integrated opacity, i.e. , mean opacity ,has been evaluated. An example of mean opacity calculations is shown in fig. 2( b ), forall single-species plasmas. There is a small group of few elements, i.e. , Se, Sr, Zr, andNb, exhibiting larger mean opacity at the temperature condition of early-epochs kilonova( . · K). In view of these numerical results, with the purpose of selecting the mostsuitable species for our experimental measurements, we have defined a weighted opacity parameter α , i.e. , species’ mean opacity weighted by their abundances at a given Y e , asgiven by SKYNET results shown in fig. 1( c ). Results shown in fig. 2( c ) suggest, for Y e ≥ .
25 and T typical of blue-kilonova emission, selenium plasma as one of the mostfavoured for the experiment.
4. – Conclusion
The presented study has provided bases for future experimental activity on plasmaopacity for kilonova light curve predictions. It has especially given constraints in termsof plasma species eligible for being studied in the laboratory, plasma conditions, spectralrange and expected features. This information turns out to be useful for optimizing theexperimental setup. One important aspect is the strong impact of NLTE thermodynamicconditions on plasma spectral features, where the astrophysical scenario is often assumedin LTE [10, 15, 18]. While theoretical expectations based only on r -process abundancesand number of transition lines make elements as Mo, Tc, Ru, and Rh the most opaques N-PLASMA STUDY OF OPACITY RELEVANT FOR COMPACT BINARY EJECTA among those considered [10], their resulting mean opacities are several orders of mag-nitude lower than those for Se or Sr NLTE plasma. Thus, thermodynamic conditions canplay an important role in determining opacity of elements. To conclude, further numer-ical investigations are planned, in view of future measurements, exploring the impact ofmultiple-species plasma and external radiation field on the plasma spectra. ∗ ∗ ∗ The authors wish to thank support of INFN through the project PANDORA Gr3funded by 3rd Nat. Sci. Comm..
REFERENCES[1]
Korobkin O. et al. , Mon. Not. R. Astron. Soc. , (2012) 3-1940:1949.[2] Arcavi I. et al. , Nature , (2017) 7678-64:66.[3] LIGO Scientific Collaboration and Virgo Collaboration , Phys. Rev. Lett. , (2017) 161101.[4] Li L. and
Paczynski, B. , Astrophys. J. , (1998) 59:62.[5] Metzger B. D. et al. , Mon. Not. R. Astron. Soc. , (2010) 2650–2662.[6] Kasen D. et al. , Nature , (2017) 80:84.[7] Barnes J. et al. , Astrophys. J. , (2013) 18.[8] Kasen D. et al. , Astrophys. J. , (2013) 25.[9] Barnes J. et al. , Astrophys. J. , (2016) 110.[10] Tanaka M. et al. , arXiv:1906.08914.[11]
Mascali D. et al. , Eur. Phys. J. A , (2017) 145.[12] Martin D. et al. , Astrophys. J. , (2015) 1-2.[13] Radice D. et al. , Astrophys. J. , (2018) 2-130.[14] Lippuner J. et al. , Astrophys. J. Supplements , (2017) 18.[15] Kasen D. et al. , Astrophys. J. , (2013) 1-9.[16] Watson D. et al. , Nature , (2019) 7779-497:500.[17] Chung H.-K. et al. , High Energy Density Phys. , (2005) 3.[18] Pinto P. A. et al. , Astrophys. J. ,530