Nuclear Adiabatic Effects of Electron-Positron Pairs on the Dynamical Instability of Very-Massive Stars


  • Lurwan Garba Yusuf Maitama Sule University
  • Firas A. Ahmed University of Diyala



Massive stars, pair-production, stellar instability


The adiabatic effects of electron-positron pair-production on the dynamical instability of very-massive stars is investigated from stellar progenitors of carbon-oxygen cores within the range of 64 M < MCO < 133 M  both with and without rotation. At a very high temperature and relatively low density; the production of electron-positron pairs in the centres of massive stars leads the adiabatic index to below 4/3. The adiabatic quantities are evaluated by constructing a model into a thermodynamically consistent electron-positron equation of state (EoS) table. It is observed that the adiabatic indices in the instability regions of the rotating models are fundamentally positive with central temperature and density. Similarly, the mass of the oxygen core within the instability region has accelerated the adiabatic indices in order to compress the star, while the mass loss and adiabatic index in the non-rotating model exponentially decay. In the rotating models, a small amount of heat is required to increase the central temperature for the end fate of the massive stars. The dynamic of most of the adiabatic quantities show a similar pattern for all the rotating models. The non-rotating model may not be suitable for inducing the instability. Many adiabatic quantities have shown great effects on the dynamical instability of the massive stars due to electron-positron pair-production in their centres. The results of this work would be useful for better understanding of the end fate of very-massive stars.


J.R. Bond, W.D. Arnett, and B.J. Carr, The Astrophyaical Journal 280 (1984) 825.

P. Ledoux, On the dynamical stability of stars, The Astrophysical Journal 104 (1946) 333,

R. Kippenhahn, A. Weigert, and A. Weiss, Stellar structure and evolution, (Springer, 1990), Vol. 192.

D. Beule, W. Ebeling, and A. Forster, Adiabatic equation ¨of state and ionization equilibrium of dense plasma, Physica A: Statistical Mechanics and its Applications 241 (1997) 719,

O. Pols, Asrronomical Institute Uttecht (2011).

W. A. Fowler, The stability of supermassive stars, The Astnophysical Journal 144 (1966) 180,

G. Rakavy and A. Shaviv, Instabilitiesin highly evolved stellar models, The Astrophysical Journal 148 (1967) 803,

N. Kiriakidis, K. Fricke, and W. Glatzel, The stability of massive stars and its dependence on metallicity and opacity,

MNRAS 264 (1993) 50,

G. Bisnovatyi-Kogan, Dynamic stability of compact stars, in: D. Blaschke, D. Sedrakian (eds), Superdense QCD Matter and

Compact Stars NATO Science Series II: Mathematics, Physics and Chemistry 197 (2006) Springer, Dordrecht,

K. J. Chen, MPLA 30 (2015).

N. Yusof, H. Abu Kassim, L. Garba, and N. Ahmad, The neutrino emission from thermal processes in very massive stars in the local universe, MNRAS 503 (2021) 5965,

N. Smith et al., SN 2006gy: Discovery of the Most Luminous Supernova Ever Recorded, Powered by the Death of an Extremely Massive Star like η Carinae, The Astrophysical Journal 666 (2007) 1116,

A. Gal-Yam et al., Supernova 2007bi as a pair-instability explosion, Nature 462 (2009) 624,

C.C. Joggerts and D.J. Whalen, The early evolution of primordial pair-instability supernovae, The Astrophysical Journal 728 (2011) 129,

J. Cooke et al., Superluminous supernovae at redshifts of 2.05 and 3.90, Nature 491 (2012) 228,

T. Pan, D. Kasen and A. Loeb, Pair-instability supernovae at the epoch of reionization, MNRAS 422 (2012) 2701,

T. Pan, A. Loeb and D. Kasen, Pair-instability supernovae via collision runaway in young dense star clusters, MNRAS 423 (2012) 2203,

K.J. Chen, S. Woosley, A. Heger, A. Almgren and D.J. Whalen, Two-dimensional simulations of pulsational pair-instability supernovae, The Astrophysical Journal 792 (2014) 28,

A. eozyrKva, 2014.

J. Smidt et al., Population III hipernovae, The Astrophysical Journal 799 (2015) 18,

E. Chatzopoulos et al., Emission from pair-instability supernovae with rotation, The Astrophysical Journal 799 (2015) 18,

K. Belczynski et al., The effect of pair-instability mass loss on black-hole mergers, Astronomy and Astrophysics 594 (2016) A97,

G. S. Stringfellow and S. E. Woosley, Origin and Distribution of the Elements, ed. G. J. Mathews (Singapore: World Scientific

Publishing), 467.

B.J. Carr, J.R. Bond and W.D. Arnett, Cosmological consequences of population III stars, The Astrophysical Journal 277 (1984) 445,

W.W. Ober, M.F. El Eid and K.J. Fricke, Evolution of massive pregalactic stars, Astronomy and Astrophysics 119 (1983) 61,

J.C. Wheeler, Final evolution of stars in the range 103 −104 M¯, Ap& SS 50 (1977) 125,

M.F. El Eid and E.R. Hilf, Equation of state for hot an dense n; p; e-mixture with zero charge density, Astronomy and Astrophysics 57 (1977) 243,

G.S. Fraley, Supernovae explosions induced by pair-production instability, The Astrophysical Journal 2 (1968) 96,

Z. Barkat, G. Rakavy, and N. Sack, Dynamics of Supernova Explosion Resulting from Pair Formation, PRL 18 (1967) 379,

P.J. Montero, H.-T. Janka and E. Muller, Relativistic collapse and explosion of rotating supermassive stars with thermonuclear effects, The Astrophysical Journal 749 (2012) 37,

A. Maeder, Physics, formation and evoiution of rotating stars (Springer science & Business Media, 2008).

C. J. Hansen, S. D. Kawaler, and V. Trimble, in Stellar Interiors (Springer, 2004), pp. 431.

S.E. Woosley, A. Heger, and T.A. Weaver, The evolution and explosion of massive stars, Rev. Mod. Phys. 74 (2002) 1015,

E. Chatzopoulos and J.C. Wheeler, Effects of rotation on the minimum mass of the primordial progenitors of pair-instability supernovae, The Astrophysical Journal 748 (2012) 42,

A. Heger, C.L. Fryer, S.E. Woosley, N. Langer, and D.H. Hartmann, How massive single stars end their life, The Astrophysical Journal 591 (2003) 288,

N. Langer, C.A. Norman, A. de Koter, J.S. Vink, M. Cantiello, and S.-C. Yoon, Pair creation supernovae at low and high redshift, Astronomy and Astrophysics 475 (2007) L19,

A. Kozyreva, S.-C. Yoon, and N. Langer, Explosion and nucleosynthe- sis of low-redshift pair-instability supernovae, Astronomy and Astrophysics 566 (2014) A146,

J.S. Vink et al., Wind modelling of very massive stars up to 300 solar masses, Astronomy and Astrophysics 531 (2011) A132,

N. Yusof et al., Evolution and fate of very massive stars, The Astrophysical Journal 433 (2013) 1114,

S.E. Woosley, Pulsational pair-instability supernovae, The Astrophysical Journal 836 (2017) 244,

A.C. Phillips, The Physics of Stars, (John Wiley & Sons, 2013).

P. Eggenberger et al., The Geneva stellar evolution code, in M.J.P.F.G. Monteiro, Evolution and seismic tools for stellar astrophysics, (Springer, 2008), pp. 43-54.

T.A. Weaver, G.B. Zimmerman, and S.E. Woosley, KEPLER: General purpose 1D multizone hydrodynamics code, Astrophysics Source Code Library, ascl:1702.007,

F.X. Timmes and F.D. Swesty, The Accuracy, Consistency, and Speed of an Electron-Positron Equation of State Based on Table Interpolation of the Helmholtz Free Energy, The Astrophysical Journal Supplement Series 126 (2000) 501,

F.X. Timmes and D. Arnett, The Accuracy, Consistency, and Speed of Five Equations of State for Stellar Hydrodynamics,

The Astrophysical Journal Supplement Series 125 (1999) 277,




How to Cite

L. Garba and F. A. . Ahmed, “Nuclear Adiabatic Effects of Electron-Positron Pairs on the Dynamical Instability of Very-Massive Stars”, Rev. Mex. Fís., vol. 68, no. 1 Jan-Feb, pp. 011403 1–, Jan. 2022.



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