scholarly journals A non-linear mathematical model for the X-ray variability classes of the microquasar GRS 1915+105 – I. Quiescent, spiking states, and quasi-periodic oscillations

2020 ◽  
Vol 495 (1) ◽  
pp. 1110-1121 ◽  
Author(s):  
E Massaro ◽  
F Capitanio ◽  
M Feroci ◽  
T Mineo ◽  
A Ardito ◽  
...  
Keyword(s):  
Differential Equations ◽  
Equilibrium Points ◽  
Low Frequency ◽  
Input Function ◽  
Light Curves ◽  
Stable Region ◽  
Periodic Oscillations ◽  
X Ray ◽  
Unstable Solutions ◽  
Unified View

ABSTRACT The microquasar GRS 1915+105 is known to exhibit a very variable X-ray emission on different time-scales and patterns. We propose a system of two ordinary differential equations, adapted from the Hindmarsh–Rose model, with two dynamical variables x(t), y(t), and an input constant parameter J0, to which we added a random white noise, whose solutions for the x(t) variable reproduce consistently the X-ray light curves of several variability classes as well as the development of low-frequency quasi-periodic oscillations (QPO). We show that changing only the value of J0, the system moves from stable to unstable solutions and the resulting light curves reproduce those of the quiescent classes like ϕ and χ, the δ class and the spiking ρ class. Moreover, we found that increasing the values of J0 the system induces high-frequency oscillations that evolve into QPO when it moves into another stable region. This system of differential equations gives then a unified view of the variability of GRS 1915+105 in term of transitions between stable and unstable states driven by a single input function J0. We also present the results of a stability analysis of the equilibrium points and some considerations on the existence of periodic solutions.

scholarly journals A non-linear mathematical model for the X-ray variability of the microquasar GRS 1915+105 – III. Low-frequency quasi-periodic oscillations

2020 ◽  
Vol 497 (1) ◽  
pp. 405-415
Author(s):  
E Massaro ◽  
F Capitanio ◽  
M Feroci ◽  
T Mineo
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Low Frequency ◽  
Input Function ◽  
Power Density Spectrum ◽  
Periodic Oscillations ◽  
Density Spectrum ◽  
X Ray ◽  
Almost All ◽  
The Mathematical Model

ABSTRACT The X-ray emission from the microquasar GRS 1915+105 shows, together with a very complex variability on different time-scales, the presence of low-frequency quasi-periodic oscillations (LFQPOs) at frequencies lower than ∼30 Hz. In this paper, we demonstrate that these oscillations can be consistently and naturally obtained as solutions of a system of two ordinary differential equations, which is able to reproduce almost all variability classes of GRS 1915+105. We modified the Hindmarsh–Rose model and obtained a system with two dynamical variables x(t), y(t), where the first one represents the X-ray flux from the source, and an input function J(t), whose mean level J0 and its time evolution is responsible of the variability class. We found that for values of J0 around the boundary between the unstable and the stable interval, where the equilibrium points are of spiral type, one obtains an oscillating behaviour in the model light curve similar to the observed ones with a broad Lorentzian feature in the power density spectrum and, occasionally, with one or two harmonics. Rapid fluctuations of J(t), as those originating from turbulence, stabilize the LFQPOs, resulting in a slowly amplitude modulated pattern. To validate the model, we compared the results with real RXTE data, which resulted remarkably similar to those obtained from the mathematical model. Our results allow us to favour an intrinsic hypothesis on the origin of LFQPOs in accretion discs ultimately related to the same mechanism responsible for the spiking limit cycle.

scholarly journals A non-linear mathematical model for the X-ray variability classes of the microquasar GRS 1915+105 – II. Transition and swaying classes

2020 ◽  
Vol 496 (2) ◽  
pp. 1697-1705 ◽  
Author(s):  
E Massaro ◽  
F Capitanio ◽  
M Feroci ◽  
T Mineo ◽  
A Ardito ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Input Function ◽  
Unstable Equilibrium ◽  
Light Curves ◽  
Extended Model ◽  
X Ray ◽  
Non Linear ◽  
Non Linear System

ABSTRACT The complex time evolution in the X-ray light curves of the peculiar black hole binary GRS 1915+105 can be obtained as solutions of a non-linear system of ordinary differential equations derived from the Hindmarsh–Rose model and modified introducing an input function depending on time. In the first paper, assuming a constant input with a superposed white noise, we reproduced light curves of the classes ρ, χ, and δ. We use this mathematical model to reproduce light curves, including some interesting details, of other eight GRS 1915+105 variability classes either considering a variable input function or with small changes of the equation parameters. On the basis of this extended model and its equilibrium states, we can arrange most of the classes in three main types: (i) stable equilibrium patterns (classes ϕ, χ, α″, θ, ξ, and ω) whose light curve modulation follows the same time-scale of the input function, because changes occur around stable equilibrium points; (ii) unstable equilibrium patterns characterized by series of spikes (class ρ) originated by a limit cycle around an unstable equilibrium point; and (iii) transition pattern (classes δ, γ, λ, κ, and α′), in which random changes of the input function induce transitions from stable to unstable regions originating either slow changes or spiking, and the occurrence of dips and red noise. We present a possible physical interpretation of the model based on the similarity between an equilibrium curve and literature results obtained by numerical integrations of slim disc equations.

scholarly journals High‐ and Low‐Frequency Quasi‐periodic Oscillations in the X‐Ray Light Curves of the Black Hole Transient H1743−322

2005 ◽  
Vol 623 (1) ◽  
pp. 383-391 ◽  
Author(s):  
Jeroen Homan ◽  
Jon M. Miller ◽  
Rudy Wijnands ◽  
Michiel van der Klis ◽  
Tomaso Belloni ◽  
...  
Keyword(s):  
Black Hole ◽  
Low Frequency ◽  
Light Curves ◽  
Periodic Oscillations ◽  
X Ray

Low frequency quasi-periodic oscillations in the hard X-ray emission from Cygnus X-1

2000 ◽  
Vol 25 (3-4) ◽  
pp. 429-432
Author(s):  
B. Paul ◽  
P.C. Agrawal ◽  
A.R. Rao
Keyword(s):  
Low Frequency ◽  
Periodic Oscillations ◽  
X Ray

scholarly journals Wave modes from the magnetorotational instability in accretion discs

2012 ◽  
Vol 8 (S290) ◽  
pp. 201-202
Author(s):  
Giuseppe Di Bernardo ◽  
Ulf Torkelsson
Keyword(s):  
Three Dimensional ◽  
Accretion Disc ◽  
Light Curves ◽  
Accretion Discs ◽  
Magnetorotational Instability ◽  
Periodic Oscillations ◽  
X Ray ◽  
Black Hole Binaries ◽  
Angular Momentum Transport ◽  
Magnetohydrodynamic Simulations

AbstractThe magnetorotational instability (MRI) is widely believed to be the source of turbulence in accretion discs. This turbulence is responsible for the anomalous angular momentum transport in accretion discs. The turbulence will affect other aspects of the dynamics of the disc as well, and we will concentrate on two such issues: a) what kind of oscillations can be excited by the turbulence itself, and b) how the turbulence is interacting with modes that have been excited by some other agent. This is of interest in understanding the quasi-periodic oscillations (QPOs) that have been observed in the X-ray light curves of accreting neutron star and black hole binaries. We carry out local three dimensional (3D) magnetohydrodynamic simulations of a keplerian differentially rotating accretion disc, using a shearing box configuration taking in account the effects of the vertical stratification.

An X‐Ray Timing Study of XTE J1550−564: Evolution of the Low‐Frequency Quasi‐periodic Oscillations for the Complete 2000 Outburst

2004 ◽  
Vol 612 (2) ◽  
pp. 1018-1025 ◽  
Author(s):  
J. Rodriguez ◽  
S. Corbel ◽  
E. Kalemci ◽  
J. A. Tomsick ◽  
M. Tagger
Keyword(s):  
Low Frequency ◽  
Periodic Oscillations ◽  
X Ray
Sign in / Sign up

Export Citation Format

Share Document