Astronomy & Astrophysics manuscript no. 4u1636_11_VII c ESO 2016 July 19, 2016 Long-term quasi-periodicity of 4U 1636–536 resulting from accretion disc instability Mateusz Wi´ sniewicz 1 , Dorota Gondek-Rosi ´ nska 1 , Agnieszka Slowikowska 1 , Andrzej A. Zdziarski 2 , and Agnieszka Janiuk 3 1 Janusz Gil Institute of Astronomy, University of Zielona Góra, Szafrana 2, PL-65-516 Zielona Góra, Poland e-mail: mateusz@astro.ia.uz.zgora.pl 2 Centrum Astronomiczne im. M. Kopernika, Bartycka 18, PL-00-716 Warszawa, Poland 3 Centre for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, PL-02-668 Warsaw, Poland July 19, 2016 ABSTRACT We present the results of a study of the low-mass X-ray binary 4U 1636–536. We have performed temporal analysis of all available RXTE/ASM, RXTE/PCA, Swift/BAT and MAXI data. We have confirmed the previously discovered quasi-periodicity of ≃ 45 d present during ∼2004, and we have found it continued to 2006. At other epochs, the quasi-periodicity is only transient, and the quasi-period, if present, drifts. We have then applied a time-dependent accretion disc model to the interval with the significant X- ray quasi-periodicity. Although 4U 1636–536 is persistent, the observed quasi-periodicity can be well modelled by the hydrogen thermal-ionization instability occurring in outer regions of the accretion disc. For our best model, the period and the amplitude of the theoretical light curve agree well with those observed. The model parameters are the average mass accretion rate (estimated from the light curves), and the accretion disc viscosity parameters, α cold and α hot , for the hot and cold phases, respectively. Our best model gives relatively low values of α cold ≃ 0.01 and α hot ≃ 0.03. Key words. accretion, accretion discs – instabilities – stars: individual: (4U 1636–536, V801 Ara) – X-rays: binaries 1. Introduction 4U 1636–536 is a low-mass X-ray binary (LMXB) discovered by Willmore et al. (1974). The photometry of the optical coun- terpart (V801 Ara) shows a short orbital period of 3.79 h (Giles et al. 2002). The binary system consists of a late-type, low- mass (≃ 0.3–0.4M ⊙ ) donor, which transfers mass onto a neu- tron star (Fujimoto & Taam 1986; van Paradijs et al. 1990). Gal- loway et al. (2006) estimated the distance to 4U 1636–536 to be D = 6.0 ± 0.5 kpc from Eddington limited X-ray bursts, as- suming the neutron star mass of 1.4M ⊙ and the stellar radius of 10 km. According to Casares et al. (2006), the mass function and mass ratio of 4U 1636–536 are f ( M) = 0.76 ± 0.47 M ⊙ and M 2 /M NS ≃ 0.21–0.34, respectively, where M NS is the mass of the neutron star and M 2 is the mass of the donor. They also es- timated the inclination angle as i ≃ 36 ◦ –60 ◦ . The binary is a persistent X-ray source, although it shows significant flux varia- tions on both long and short time scales. On time scales of hours, its flux varies by a factor of ∼2–3 (Hoffman et al. 1977; Ohashi et al. 1982; Breedon et al. 1986; Hasinger & van der Klis 1989). The presence of kHz quasi-periodic oscillations, which are also visible in the system during X-ray bursts, shows that the neu- tron star has been spun-up through accretion (Zhang et al. 1996; Strohmayer 1999). 4U 1636–536 has been monitored daily in the 1.3–12.2 keV energy range by the All Sky Monitor (ASM) on-board of the Rossi X-ray Timing Explorer (RXTE) from 1996 until 2011. Dur- ing the first four years of RXTE/ASM observations (1996–2000) the source count rate was relatively stable at ∼ 15 cts s −1 , see the upper panel of Fig. 1. After 2000, it started to gradually decline and occasionally show a statistically significant quasi-periodic 10 Rate (cts s -1 ) 1996 1998 2000 2002 2004 2006 2008 2010 2012 Year 50000 51000 52000 53000 54000 55000 56000 MJD (days) 200 Rate (cts s -1 ) Fig. 1. Top: The 50-d average RXTE/ASM light curve of 4U 1636–536 in the energy range of 1.3–12.2 keV from January 1996 to November 2011. Bottom: The 50-d average RXTE/PCA light curve in the energy range of 2–60 keV for the same range of time. variability (Shih et al. 2005). Those authors reported the pres- ence of a long-period, ≃ 47 d, quasi-periodic variability in the 2004 light curve. They suggested that the observed flux variabil- ity is caused by the variability of the accretion flow related to X-ray irradiation of the disc. From March 2005 to September 2006, Belloni et al. (2007) performed RXTE/PCA monitoring campaign of 4U 1636–536, finding the light curves to display Article number, page 1 of 8