Origin of the long-term modulation of radio emission of LS I +61°303

¹ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
e-mail: mmassi@mpifr-bonn.mpg.de
² INAF – Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, Firenze, Italy
e-mail: torricel@arcetri.astro.it

Received: 10 July 2015
Accepted: 26 October 2015

Abstract

Context. One of the most unusual aspects of the X-ray binary LS I +61°303 is that at each orbit (P₁ = 26.4960 ± 0.0028 d) one radio outburst occurs whose amplitude is modulated with P_long, a long-term period of more than 4 yr. It is still not clear whether the compact object of the system or the companion Be star is responsible for the long-term modulation.

Aims. We study here the stability of P_long. Such a stability is expected if P_long is due to periodic (P₂) Doppler boosting of periodic (P₁) ejections from the accreting compact object of the system. On the contrary it is not expected if P_long is related to variations in the mass loss of the companion Be star.

Methods. We built a database of 36.8 yr of radio observations of LS I +61°303 covering more than 8 long-term cycles. We performed timing and correlation analysis. We also compared the results of the analyses with the theoretical predictions for a synchrotron emitting precessing (P₂) jet periodically (P₁) refilled with relativistic electrons.

Results. In addition to the two dominant features at P₁ and P₂, the timing analysis gives a feature at P_long = 1628 ± 48 days. The determined value of P_long agrees with the beat of the two dominant features, i.e. P_beat = 1 / (ν₁−ν₂) = 1626 ± 68 d. Lomb-Scargle results of radio data and model data compare very well. The correlation coefficient of the radio data oscillates at multiples of P_beat, as does the correlation coefficient of the model data.

Conclusions. Cycles in varying Be stars change in length and disappear after 2-3 cycles following the well-studied case of the binary system ζ Tau. On the contrary, in LS I +61°303 the long-term period is quite stable and repeats itself over the available 8 cycles. The long-term modulation in LS I +61°303 accurately reflects the beat of periodical Doppler boosting (induced by precession) with the periodicity of the ejecta. The peak of the long-term modulation occurs at the coincidence of the maximum number of ejected particles with the maximum Doppler boosting of their emission; this coincidence occurs every $\frac{\mathrm{1}}{{\mathit{\nu }}_{\mathrm{1}}\mathrm{-}{\mathit{\nu }}_{\mathrm{2}}}$ and creates the long-term modulation observed in LS I +61°303.