Nonlinear Time-Varying Studies Of Low-Mass X-Ray Binaries

The study of the time variation of X-ray binaries has been a very hot research topic since its discovery in the 1960s～1970s.In particular,various models have been proposed to explain the quasi-periodic oscillation(QPO)phenomenon in burst out processes.The method for studying the time variation of X-ray binaries is usually Fourier transform,which is still an important mathematical tool in the field of astronomy up to now.However,there is an obvious nonlinear component in the broadband noise in the power spectrum of black hole X-ray binaries,which indicates that we need a means to study the nonlinear process to make sense of the mechanism of X-ray generation.The Hard X-ray Modulation Telescope(Insight-HXMT)is Chinese first space Xray astronomical satellite,successfully launched at Jiuquan Satellite Launch Center on June 15,2017,marking China’s entry into the forefront of the world in the space X-ray field.The main scientific objectives of HXMT include:searching for new transient sources on the galactic disc and monitoring known sources of change;observing X-ray binaries to study the motion and radiation mechanisms in strong gravitational or magnetic fields;monitoring and studying electromagnetic counterparts of gamma ray bursts and gravitational waves.Relying on the characteristics of broad energy band and large field of view,a large number of achievements have been achieved since its launch.Bispectrum is a very prominent method for studying quasi-periodic oscillations in nonlinear time-varying X-ray binaries.Similar to the cross-coherence function,there is also the concept of double coherence in bispectrum,which is a measure of phase coupling at different Fourier frequencies.In this paper,using the HXMT data analysis software,we first produced advanced data products,including light curves and corresponding backgrounds,spectra and corresponding backgrounds,and response files.Then,using this tool,we conducted a time series analysis of the nonlinear changes of two black hole low-mass X-ray binaries,MAXI J1820+070 and MAXI J1535-571,and plotted the power spectrum and bispectrum diagrams of the light curves of each exposure file.Low frequency QPO is generally divided into three types:A,B,and C.Type A QPO often appears during the peak stage of the burst,with a high count rate and accompanied by weak red noise components.Type B QPO appears in the soft intermediate state,with weak power-law noise.Type C QPO appears in the low hard state and hard intermediate state at the beginning of the burst,with strong band-limited noise.When the count rate of the source changes,the type of QPO will transition.The rigid body like precession between the outer geometrically thin accretion disc and the inner geometrically thick thermal accretion flow produces LFQPO.For inclined accretion flow,spin affects the position of the sudden drop in density on the disk surface,thereby affecting the QPO frequency.At the same time,the truncation radius is also affected by the accretion rate,leading to changes in the spectral state,resulting in three low-frequency QPO transitions.In addition,the oscillation of the disk structure and the oscillation of the corona transition layer also generate LFQPO.We found that low-frequency QPO has different modes in different burst states,such as "cross" mode and "hypotenuse" mode.When they can be clearly distinguished,the bicoherence modes are similar in the broad energy range of 1-100 keV.Interestingly,in some type C QPOs,we have found patterns commonly observed in type B QPOs.On the contrary,the "hypotenuse" pattern is a characteristic of type C QPO,and we have also detected it in type B QPO.This indicates that different types of QPOs can derive from similar potential mechanisms.In the process of black hole X-ray binary burst,the changes in the source state are also reflected in the changes in the bicoherence mode.This indicates a gradual change in the accretion disc.In different states,the dominant positions of the blackbody component and the power-law component are different,resulting in different modulation effects on high frequency signals and low frequency signals,forming three modes:"hypotenuse","cross",and "web".We also performed preliminary calculations on the data of the MAXI J1348-630 during the burst period,but no significant bicoherence pattern was found.This may be due to the fact that the exposure light curve contains too many types of QPOs,which inhibits the coupling of a single QPO and broadband noise.In summary,bispectral analysis is a very important method for studying nonlinear processes.This method can inspire us to distinguish between QPO models with different interactions between broadband noise and QPO components.For example,in the accretion ejection instability model(AEI),QPO is associated with broadband noise,resulting in harmonics that are the result of rotational instability;Under the LenseThirring precession framework,the different bicoherence modes of QPO may be explained by the change of light depth with the state of accretion disc,or by the joint action of jet,corona and accretion disc.