The origin of magnetic fields in massive stars remains enigmatic. Several hypothesis have been proposed. In 2019, Schneider and colleagues analysed a different scenario where strong magnetic fields occur as a result of a merger. They performed 3-dimensional magnetohydrodynamic simulations for the merger of two massive main sequence stars. They noticed that this process produces strong magnetic fields compatible with 9 kG. These strongly magnetised merger products could be the magnetar progenitors. Stellar mergers occur in 22 per cent of all binaries, but it is impossible to quantify currently what fraction of mergers end up strongly magnetised. Therefore, some massive stars could be very different from the bulk population because of their past binary interactions or because of their significant initial magnetisation. Thus, in 2006, Ferrario & Wickramasinghe suggested that magnetars could originate from strongly magnetised massive B stars and radio pulsars are from weakly magnetised ones which they called “the fossil field hypothesis”.
“Stars of spectral types O and B produce neutron stars (NSs) after supernova explosions. Most of NSs are strongly magnetised including normal radio pulsars with 𝐵 ∝ 1012 G and magnetars with 𝐵 ∝ 1014 G. A fraction of 7-12 per cent of massive stars are also magnetised with 𝐵 ∝ 103 G and some are weakly magnetised with 𝐵 ∝ 1 G. It was suggested that magnetic fields of NSs could be the fossil remnants of magnetic fields of their progenitors. Our work is dedicated to study this hypothesis.”— wrote authors of the study
Now, Makarenko and colleagues check this hypothesis by comparing the magnetic field distributions both for massive OB stars and neutron stars (NSs). To do so, they collect all reliable, modern measurements of magnetic fields at surfaces on massive stars of spectral types O, B, A. Then, they developed a maximum likelihood technique to estimate the parameters of the magnetic field distribution. They found that the log-normal distribution describes well measurements of magnetic fields of O and B stars. In the case of A stars, they found significant deviations from the log-normal distribution possibly related to evolution. In the case of B stars, the parameters of the log-normal distribution are as following: 𝜇𝐵 = 2.83±0.1 log10 (G) i.e. ≈ 700 and 𝜎𝐵 = 0.65±0.09 for strongly magnetised and 𝜇𝐵 = 0.14 ± 0.5 log10 (G), 𝜎 = 0.7 for weakly magnetised.
They also noticed that the difference between magnetic field of strongly magnetised B-stars and weakly magnetised B stars is 2.7 DEX and magnetars represent 10 per cent of all young NSs and run population synthesis.
“We found that it is impossible to simultaneously reproduce pulsars and magnetars populations if the difference in their magnetic fields is 2.7 DEX. Therefore, we conclude that the simple fossil origin of the magnetic field is not viable for NSs.”— Makarenko, lead author of the study
In addition, in accordance to the fossil field hypothesis, they assumed that weakly-magnetised B stars produce normal radio pulsars with 𝜇𝐵 = 11.7 and 𝜎𝐵 = 0.7 and strongly magnetised produce magnetars with 𝜇𝐵 = 14.45 and 𝜎𝐵 = 0.7. To check if the resulting population looks anything like an observed population of radio pulsars and magnetars they ran the population synthesis. They found that simple conservation of magnetic field in the core cannot explain the observed value of period and period derivative for normal radio pulsars. The cloud of radio pulsars is shifted towards too small period derivative values. In trying to improve their model, they guess that their original model for magnetic field conservation might be too simplistic. Therefore, they assumed values of 𝜇𝐵 = 12.65, 𝜎𝐵 = 0.7 for 90 per cent of NSs and 𝜇𝐵 = 15.35, 𝜎𝐵 = 0.7 for magnetars to keep 2.7 DEX difference. This model strongly overproduces bright magnetars with fluxes 𝑆𝑋 in the range 10¯10– 10¯8 erg cm¯2 s¯1. This result they found, does not depend on the value of the crust impurity parameter.
Therefore, they concluded that the fossil field hypothesis cannot simply explain NS magnetic field distribution. Finally, they suggested that in order to correct this hypothesis there is a need of a mechanism that decreases the difference of 2.7 DEX between two groups of stars to the difference of ≈ 1 DEX seen between magnetic fields of magnetars and normal radio pulsars. One such mechanism could be the field instability at the proto-NS stage.
“It is interesting to note that even if we miss most of the distribution for weakly magnetised massive stars (e.g. due to instrumental limitations) and estimate only the exponential tail, our conclusion still holds. In this case, the mean value of magnetic fields for weakly magnetised stars is located at even smaller values and the actual difference is more than 2.7 DEX.”— Makarenko, lead author of the study
Featured image: Schematic view of magnetic field lines inside and outside of a massive star. The blue region is a radiative envelope, the grey region is a convective core and solid lines show the magnetic field lines. © Makarenko et al.
Reference: Ekaterina I. Makarenko, Andrei P. Igoshev, A.F. Kholtygin, “Testing the fossil field hypothesis: could strongly magnetised OB stars produce all known magnetars?”, Arxiv, pp. 1-23, 2021. https://arxiv.org/abs/2104.10579
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