Periodic long-term X-ray and radio variability of Cygnus X-1

Abstract

We present a comprehensive analysis of long-term periodic variability of Cyg X-1 using the method of multiharmonic analysis of variance (mhAoV) applied to available monitoring data since 1969, in X-rays from Vela 5B, Ariel 5, Ginga, CGRO and RXTE satellites and in radio from the Ryle and Green Bank telescopes. We confirm a number of previously obtained results, and, for the first time, find an orbital modulation at 15 GHz in the soft state and show the detailed non-sinusoidal shape of that modulation in the hard state of both the 15-GHz emission and the X-rays from the RXTE/ASM. We find the CGRO/BATSE data are consistent with the presence of a weak orbital modulation, in agreement with its theoretical modelling as due to Compton scattering in the companion wind. We then confirm the presence of a ~150-d superorbital period in all of the data since ~1976, finding it in particular for the first time in the Ariel 5 data. Those data sets, covering >65 superorbital cycles, show a remarkable constancy of both the period and the phase. On the other hand, we confirm the presence of a ~290-d periodicity in the 1969-1979 Vela 5B data, indicating a switch from that period to its first harmonic at some time <~1980. We find the superorbital modulation is compatible with accretion disc precession. Finally, we find a significant modulation in the RXTE/ASM data at a period of 5.82-d, which corresponds to the beat between the orbital and superorbital modulations provided the latter is prograde.Comment: MNRAS, in pres

A ~4.6 h quasi-periodic oscillation in the BL Lacertae PKS 2155-304?

“…For strictly sinusoidal flux variability with period P, the SF has minima for τ equal to P and its subharmonics (e.g., Lachowicz et al 2006). Thus, an SF allows for quick confirmation of the findings provided by the periodogram techniques.…”

“…It can be directly calculated as P 1 = 1 − F(n , n ⊥ /n corr ; Θ AoV /n corr ) where n ⊥ = n − n and n corr defines a number of consecutive observations being correlated (see Sect. 3.1.4 of Lachowicz et al 2006). A direct derivation of P 1 returns the significance of the periodogram peak (centered at the frequency f 0 ) only under the assumption that any modulation detected has a period, P 0 = 1/ f 0 , which is known in advance.…”

“…In practice, when a set of N eff frequencies in a band, Δ f , is scanned for significant periodicities, a selected peak's significance level should be corrected for multiple trials, so P N eff = 1 − (1 − P 1 ) N eff . Since there is no analytical method that determines N eff , we follow Lachowicz et al (2006) and assume a simple estimate,…”

“…An extensive description of mhAoV with its statistical advantages over the classical Lomb-Scargle method, and examples of applications to X-ray time-series analyses can be found in Lachowicz et al (2006). In the periodogram calculations for the signal x, we employed Szegö orthogonal trigonometric polynomials as model functions, x .…”

Gamma rays detected from Cygnus X-1 with likely jet origin

“…The existence of the radio modulation supports the idea that radio emission comes from a continuous jet versus discrete ejections. Another type of periodical behaviour is observed in Cygnus X-1 both at X-ray and radio frequencies, a superorbital modulation of ∼140 d Pooley et al 1999), although such a value is rather unstable and it has been recently showed to be doubled (Lachowicz et al 2006;Rico 2008;Zdziarski et al 2011). The superorbital modulation is possibly related to the precession of the disk-jet system , or alternatively to a variable mass accretion rate (Brocksopp et al 2001), and its period possibly varies when an X-ray spectral state change occurs (Rico 2008).…”