p-capture reaction cycles in rotating massive stars and their impact on elemental abundances in globular cluster stars: A case study of O, Na and Al

Elemental abundance patterns of globular cluster stars can provide important clues for understanding cluster formation and early chemical evolution.The origin of the abundance patterns,however,still remains poorly understood.We have studied the impact of p-capture reaction cycles on the abundances of oxygen,sodium and aluminium considering nuclear reaction cycles of carbon-nitrogenoxygen-fluorine,neon-sodium and magnesium-aluminium in massive stars in stellar conditions of temperature range 2×107to 10×107K and typical density of 102gm cc-1.We have estimated abundances of oxygen,sodium and aluminium with respect to Fe,which are then assumed to be ejected from those stars because of rotation reaching a critical limit.These ejected abundances of elements are then compared with their counterparts that have been observed in some metal-poor evolved stars,mainly giants and red giants,of globular clusters M3,M4,M13 and NGC 6752.We observe an excellent agreement with[O/Fe]between the estimated and observed abundance values for globular clusters M3 and M4 with a correlation coefficient above 0.9 and a strong linear correlation for the remaining two clusters with a correlation coefficient above 0.7.The estimated[Na/Fe]is found to have a correlation coefficient above 0.7,thus implying a strong correlation for all four globular clusters.As far as[Al/Fe]is concerned,it also shows a strong correlation between the estimated abundance and the observed abundance for globular clusters M13 and NGC 6752,since here also the correlation coefficient is above 0.7 whereas for globular cluster M4 there is a moderate correlation found with a correlation coefficient above 0.6.Possible sources of these discrepancies are discussed.

On the magnetic fields of ultraluminous X-ray pulsars

So far quite a few ultraluminous X-ray(ULX) pulsars have been discovered.In this work,we construct a super-Eddington,magnetic accretion disk model to estimate the dipole magnetic field of eight ULX pulsars based on their observed spin-up variations and luminosities.We obtain two branches of dipole magnetic field solutions.They are distributed in the range of B-(0.156-64.5) × 10^(10) G and-(0.275-79.0) × 10^(13) G corresponding to the low-and high-B solutions respectively.The low magnetic field solutions correspond to the state that the neutron stars are far away from the spin equilibrium,and the high magnetic field solutions are close to the spin equilibrium.The ultra-strong magnetic fields derived in Be-type ULX pulsars imply that the accretion mode in Be-type ULX pulsars could be more complicated than in the persistent ULX pulsars and may not be accounted for by the magnetized accretion disk model.We suggest that the transition between the accretor and the propeller regimes may be used to distinguish between the low-and high-B magnetic field solutions in addition to the detection of the cyclotron resonance scattering features.