Twin kHz QPOs Research Articles

A possible explanation of the parallel tracks in kilohertz quasi-periodic oscillations from low-mass-X-ray binaries

We recalculate the modes of the magnetohydrodynamics (MHD) waves in the MHD model (Shi, Zhang & Li 2014) of the kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low mass X-ray binaries (NS-LMXBs), in which the compressed magnetosphere is considered. A method on pointby- point scanning for every parameter of a normal LMXBs is proposed to determine the wave number in a NS-LMXB. The dependence of the twin kHz QPO frequencies on accretion rates ( DOt(M) ) is obtained with the wave number and magnetic field (B?) determined by our method. Based on the MHD model, a new explanation of the parallel tracks, i.e. the slowly varying effective magnetic field leads to the shift of parallel tracks in a source, is presented. In this study, we obtain a simple power-law relation between the kHz QPO frequencies and Dot(M) /B^2 ? in those sources. Finally, we study the dependence of kHz quasi-periodic oscillation frequencies on the spin, mass and radius of a neutron star. We find that the effective magnetic field, the spin, mass and radius of a neutron star lead to the parallel tracks in different sources.

Correlations between the frequencies of twin kHz QPOs and spins of neutron stars in LMXBs

We investigate the correlation between the frequencies of the twin kilohertz quasi-periodic oscillations (kHz QPOs) and the neutron star (NS) spins in low mass X-ray binaries (LMXBs), based on the data sets of 12 sources with simultaneously detected twin kHz QPOs and NS spins, and find that the histogram of the ratio between the frequency difference of twin kHz QPOs ({\Delta}{\nu} = {\nu}2 - {\nu}1) and NS spin {\nu}s shows a non-uniform distribution with a gap at {\Delta}{\nu}/{\nu}s ~ 0.65. We try to classify the 12 sources into two categories according to this gap: (I) The slow rotators with <{\nu}s> ~ 311 Hz, XTE J1807.4-294, 4U 1915-05, IGR J17191-2821, 4U 1702-43, 4U 1728-34 and 4U 0614+09 follow a relation {\Delta}{\nu}/{\nu}s > 0.65; (II) The fast rotators with <{\nu}s> ~ 546 Hz, SAX J1808.4-3658, KS 1731-260, Aql X-1, 4U 1636-53, SAX J1750.8-2900 and 4U 1608-52 satisfy the relation {\Delta}{\nu}/{\nu}s < 0.65. However, the linear fittings of {\Delta}{\nu} versus {\nu}s relations of group (I) and (II) are unsatisfactory to ensure any certain correlations. We suggest that this phenomenon may arise from the fact that most measured kHz QPOs and spins satisfy the conditions of 1.1 {\nu}s < {\nu}2 < 1300Hz and {\Delta}{\nu} decreasing with {\nu}2. Apparently, the diversified distribution of {\Delta}{\nu}/{\nu}s refutes the simple beat-frequency model, and the statistical correlations between the twin kHz QPOs and NS spins may arise from the magnetosphere-disk boundary environments, e.g., co-rotation radius and NS radius, that modulate the occurrences of X-ray signals. Furthermore, we also find that the distribution of the ratio of {\nu}2 to {\nu}1 clusters around the value of <{\nu}2/{\nu}1> ~ 3 : 2, which shows no obvious correlation with NS spins.

Probing the accretion disc structure by the twin kHz QPOs and spins of neutron stars in LMXBs

We analyze the relation between the emission radii of twin kilohertz quasi-periodic oscillations (kHz QPOs) and the co-rotation radii of the 12 neutron star low mass X-ray binaries (NS-LMXBs) which are simultaneously detected with the twin kHz QPOs and NS spins. We find that the average co-rotation radius of these sources is r_co about 32 km, and all the emission positions of twin kHz QPOs lie inside the corotation radii, indicating that the twin kHz QPOs are formed in the spin-up process. It is noticed that the upper frequency of twin kHz QPOs is higher than NS spin frequency by > 10%, which may account for a critical velocity difference between the Keplerian motion of accretion matter and NS spin that is corresponding to the production of twin kHz QPOs. In addition, we also find that about 83% of twin kHz QPOs cluster around the radius range of 15-20 km, which may be affected by the hard surface or the local strong magnetic field of NS. As a special case, SAX J1808.4-3658 shows the larger emission radii of twin kHz QPOs of r about 21-24 km, which may be due to its low accretion rate or small measured NS mass (< 1.4 solar mass).

Application of the relativistic precession model to the accreting milisecond X‐ray pulsar IGR J17511–3057

AbstractThe observation of a pair of simultaneous twin kHz QPOs in the power density spectrum of a neutron star or a black hole allows its mass‐angular‐momentum relation to be constrained. Situations in which the observed simultaneous pairs are more than one allow the different models of the kHz QPOs to be falsified. Discrepancy between the estimates coming from the different pairs would call the used model into question. In the current paper, the relativistic precession model is applied to the twin kHz QPOs that appear in the light curves of three groups of observations of the accreting millisecond X‐ray pulsar IGR J17511–3057. It was found that the predictions of one of the groups are practically in conflict with the other two. Another interesting result is that the region in which the kHz QPOs have been born is rather broad and extends quite far from the ISCO. (© 2016 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

THE APERIODIC X-RAY VARIABILITY OF THE ACCRETING MILLISECOND PULSAR SAX J1808.4−3658

We have studied the aperiodic variability of the 401 Hz accreting millisecond X-ray pulsar SAX J1808.4-3658 using the complete data set collected with the Rossi X-ray Timing Explorer over 14 years of observation. The source shows a number of exceptional aperiodic timing phenomena that are observed against a backdrop of timing properties that show consistent trends in all five observed outbursts and closely resemble those of other atoll sources. We performed a detailed study of the enigmatic ~410 Hz QPO, which has only been observed in SAX J1808.4-3658. We find that it appears only when the upper kHz QPO frequency is less than the 401 Hz spin frequency. The difference between the ~410 Hz QPO frequency and the spin frequency follows a similar frequency correlation as the low frequency power spectral components, suggesting that the ~410 Hz QPO is a retrograde beat against the spin frequency of a rotational phenomenon in the 9 Hz range. Comparing this 9 Hz beat feature with the Low-Frequency QPO in SAX J1808.4-3658 and other neutron star sources, we conclude that these two might be part of the same basic phenomenon. We suggest that they might be caused by retrograde precession due to a combination of relativistic, classical and magnetic torques. Additionally we present two new measurements of the lower kHz QPO, allowing us, for the first time, to measure the frequency evolution of the twin kHz QPOs in this source. The twin kHz QPOs are seen to move together over 150 Hz, maintaining a centroid frequency separation of $(0.446 \pm 0.009) \nu_{spin}$.

LOW-FREQUENCY QPOS AND POSSIBLE CHANGES IN THE ACCRETION GEOMETRY DURING THE OUTBURSTS OF AQUILA X−1

We have studied the evolution of the Low Frequency Quasi-Periodic Oscillations (LFQPOs) during the rising phase of seven outbursts of the neutron star Soft X-ray Transient (SXT) Aql X$-$1 observed with the \textit{Rossi X-ray Timing Explorer (RXTE)}. The frequency correlation between the low frequency break and the LFQPO sampled on the time scale of $\sim$2 days was seen. Except for the peculiar 2001 outburst, the frequency of the LFQPOs increased with time before the hard-to-soft state transition up to a maximum $\nu_{max}$ at $\sim$31 Hz, a factor of $\sim$5 higher than those seen in black hole transients such as GX 339$-$4, making the maximum QPO frequency a likely indicator of the mass of the central compact object. The characteristic frequencies increased by around ten percent per day in the early rising phase and accelerated to nearly one hundred percent per day since $\sim$2 days before the hard-to-soft state transition. We examined the dependence of the frequency $\nu_{LF}$ on the source flux $f$ and found an anti-correlation between the maximum frequency of the LFQPOs and the corresponding X-ray luminosity of the hard-to-soft transition (or outburst peak luminosity) among the outbursts. We suggest that X-ray evaporation process can not be the only mechanism that drives the variation of the inner disk radius if either of the twin kHz QPO corresponds to the Keplerian frequency at the truncation radius.

THE MAGNETOHYDRODYNAMICAL MODEL OF KILOHERTZ QUASI-PERIODIC OSCILLATIONS IN NEUTRON STAR LOW-MASS X-RAY BINARIES (II)

We study the kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low mass X-ray binaries (LMXBs) with a new magnetohydrodynamics (MHD) model, in which the compressed magnetosphere is considered. The previous MHD model (Shi \& Li 2009) is re-examined and the relation between the frequencies of the kHz QPOs and the accretion rate in LMXBs is obtained. Our result agrees with the observations of six sources (4U 0614+09, 4U 1636--53, 4U 1608--52, 4U 1915--15, 4U 1728--34, XTE 1807--294) with measured spins. In this model the kHz QPOs originate from the MHD waves in the compressed magnetosphere. The single kHz QPOs and twin kHz QPOs are produced in two different parts of the accretion disk and the boundary is close to the corotation radius. The lower QPO frequency in a frequency-accretion rate diagram is cut off at low accretion rate and the twin kHz QPOs encounter a top ceiling at high accretion rate due to the restriction of innermost stable circular orbit.

Statistical properties of twin kilohertz quasi‐periodic oscillations in neutron star low‐mass X‐ray binaries

AbstractWe collect the data of twin kilohertz quasi‐periodic oscillations (kHz QPOs) published before 2012 from 26 neutron star (NS) low‐mass X‐ray binary (LMXB) sources, then we analyze the centroid frequency (ν) distribution of twin kHz QPOs (lower frequency ν1 and upper frequency ν2) both for Atoll and Z sources. For the data without shift‐and‐add, we find that Atoll and Z sources show different distributions of ν1, ν2 and ν2/ν1, but the same distribution of Δν (difference of twin kHz QPOs), which indicates that twin kHz QPOs may share the common properties of LXMBs and have the same physical origins. The distribution of Δν is quite different from a constant value, so is ν 2/ν1 from a constant ratio. The weighted mean values and maxima of ν1 and ν2 in Atoll sources are slightly higher than those in Z sources. We also find that shift‐and‐add technique can reconstruct the distributions of ν1 and Δν. The K‐S test results of ν1 and Δν between Atoll and Z sources from data with shift‐and‐add are quite different from those without it, and we think that this may be caused by the selection biases of the sample. We also study the properties of the quality factor (Q) and the root‐meansquared (rms) amplitude of 4U 0614+09 with data from the two observational methods, but the errors are too big to make a robust conclusion. The NS spin frequency (νs) distribution of 28 NS‐LMXBs show a bigger mean value (∼408 Hz) than that (∼281 Hz) of the radio binary millisecond pulsars (MSPs), which may be due to the lack of the spin detections from Z sources (systematically lower than 281 Hz). Furthermore, on the relations between the kHz QPOs and NS spin frequency νs, we find the approximate correlations of the mean values of Δν with NS spin and its half, respectively. (© 2014 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

An Attempt to Describe Frequency-Correlations among kHz QPOs and HBOs by Two-Armed Vertical p-Mode Oscillations: Case of No Magnetic Field

The trapping of two-armed ($ m$$ =$ 2) vertical p-mode oscillations in relativistic disks is examined. The disks are assumed to be isothermal in the vertical direction, but are truncated at a certain height by the presence of corona. The same issues were examined in a previous paper (Kato 2012a). In this paper, unlike the previous paper, however, we do not use the approximation that the oscillations are nearly vertical, but limit to a simpler case of no magnetic field. As in the previous paper, the results suggest that the two basic oscillation modes [both are the fundamental ($ n$$ =$ 1) in the vertical direction, but in the horizontal direction one is the fundamental ($ n_{\rm r}$$ =$ 0) and the other the first overtone ($ n_{\rm r}$$ =$ 1)] correspond to the twin kHz QPOs. Second, the oscillation mode, which is the first overtone ($ n$$ =$ 2) in the vertical direction and the fundamental in the horizontal direction ($ n_{\rm r}$$ =$ 0), will correspond to the horizontal branch oscillation (HBO) of Z-sources. The latter suggests that the horizontal branch of Z-sources is a sequence of temperature change in disks whose vertical thickness is strongly terminated. The temperature increases leftward along the sequence from the apex between the normal and horizontal branches.

Parameter constrain in neutron star by twin kHz QPOs

AbstractWe use data on twin kHz QPOs and measured neutron star (NS) masses to test the relation between the lower (ν1) and upper (ν2) peak frequencies predicted with the MHD Alfvén wave oscillation model (AWOM) and the general relativistic precession model (GRPM). In the context of AWOM, the NS radius can be constrained from kHz QPO data and a measured NS mass.

Distribution of twin kHz QPOs in LMXBs

AbstractWith kilohertz quasi-periodic oscillation (kHz QPO) sources in neutron star low mass X-ray binaries (NS-LMXBs) published up to now, we analyze the centroid frequency (ν) distribution of twin kHz QPOs. We find that Atoll and Z sources show the similar distributions of ν1 and ν2, which indicate that twin kHz QPOs may be the common property of NS-LXMBs and have the similar physical origins. The mean values of ν1 and ν2 in Atoll sources are higher than those in Z sources, and we consider that this may because the QPO signals are sheltered by the thicken accretion disk or corona in Z sources. The maximums of ν2 in both Atoll and Z sources are the same order as the Keplerian orbital frequency of the NS surface, so kHz QPOs could occur near the NS surface.

The kHz QPOs of Neutron Stars and Millisecond Pulsars and Implications

AbstractThe kilohertz quasi-periodic oscillations (kHz QPOs) have been found in neutron star low mass X-ray binaries (NS-LMXBs), which present the millisecond timing phenomena close to the surface of the compact objects. We briefly summarize the following contents: (1). The correlations and distributions of twin kHz QPOs; (2). The relations of high-low frequency QPOs; (3). The QPO properties of NS Atoll and Z sources; (4). No clear direct correlations between NS spins and QPOs; (5). The mechanisms of kHz QPOs; (6). The implications of kHZ QPOs, e.g., NS mass and radius, disk thickness and magnetic field of Atoll and Z source.

Predicting neutron star spins from twin kHz QPOs

We briefly review the proposed relations between the frequencies of twin kilohertz quasi-periodic oscillations (kHz QPOs) and the spin frequencies in neutron star low-mass X-ray binaries (NSLMXBs). To test the validity of the proposed models, we estimate the spin frequencies under these theoretical relations and compare them with the measured ones. It seems that magnetohydrodynamic (MHD) oscillations are more promising to account for the kHz QPOs.

The emission positions of kHz QPOs and Kerr spacetime influence

Based the Alfven wave oscillation model (AWOM) and relativistic precession model (RPM) for twin kHz QPOs, we estimate the emission positions of most detected kHz QPOs to be at r=18+-3 km (R/15km) except Cir X-1 at r = 30\+-5 km (R/15km). For the proposed Keplerian frequency as an upper limit to kHz QPO, the spin effects in Kerr Spacetime are discussed, which have about a 5% (2%) modification for that of the Schwarzchild case for the spin frequency of 1000 (400) Hz.The application to the four typical QPO sources, Cir X-1, Sco X-1, SAX J1808.4-3658 and XTE 1807-294, is mentioned.

Reversal of the amplitude difference of kHz QPOs in six atoll sources

AIMS: For six neutron-star atoll sources (4U 1608-52, 4U 1636-53, 4U 0614+09, 4U 1728-34, 4U 1820-30 and 4U 1735-44) we investigate the relationship between the observed fractional rms amplitudes of the twin kHz QPOs. We discuss whether this displays features that could have a physical meaning in terms of the proposed QPO models. METHOD: We consider the difference in rms amplitude between the upper and lower kHz QPOs, as a function of the frequency ratio R. We compare two data sets. Set I is a collection taken from published data. Set II has rms amplitude values obtained by automatic fitting of continuous segments of RXTE-PCA observations. RESULTS: For each of the six sources, we find that there is a point in the R domain around which the amplitudes of the two twin kHz QPOs are the same. We find such a point located inside a narrow interval R=1.5 +-3%. Further investigation is needed in the case of two sources to explore this finding, since we have not determined this point in Set II. There is evidence of a similar point close to R = 1.33 or R = 1.25 in the four sources. We suggest that some of these points may correspond to the documented clustering of the twin kHz QPO frequency ratios. CONCLUSIONS: For the sources studied, the rms amplitudes of the two kHz peaks become equal when the frequencies of the oscillations pass through a certain ratio R, which is roughly the same for each of the sources. In terms of the orbital QPO models, with some assumptions concerning the QPO modulation, this finding implies the existence of a specific orbit at a common value of the dimensionless radius, at which the oscillations corresponding to the two peaks come into balance. In a more general context, the amplitude difference behaviour suggests the possible existence of an energy interchange between the upper and lower QPO modes.

The magnetohydrodynamics model of twin kilohertz quasi-periodic oscillations in low-mass X-ray binaries

We suggest an explanation for the twin kilohertz quasi-periodic oscillations (kHz QPOs) in low-mass X-ray binaries (LMXBs) based on magnetohydrodynamics (MHD) oscillation modes in neutron star magnetospheres. Including the effect of the neutron star spin, we derive several MHD wave modes by solving the dispersion equations, and propose that the coupling of the two resonant MHD modes may lead to the twin kHz QPOs. This model naturally relates the upper, lower kHz QPO frequencies with the spin frequencies of the neutron stars, and can well account for the measured data of six LMXBs.

FREQUENCY VARIATION OF THE KILOHERTZ QUASI-PERIODIC OSCILLATIONS AND THE FLUX OF THE BAND-LIMITED NOISE IN SCORPIUS X-1

We study the kilohertz quasi-periodic oscillations (kHz QPOs) and the band-limited noise (BLN) in the 0.5–16 Hz range observed simultaneously on the horizontal branch (HB) and on the upper normal branch (NB) of the brightest neutron star low-mass X-ray binary Scorpius X-1 with observations performed with the Rossi X-Ray Timing Explorer. We find that the twin kHz QPO frequencies are positively correlated with the flux variations taking place on the BLN timescales on the HB, in contrast to the anticorrelation held on the timescale of the normal-branch oscillation (NBO) on the NB reported previously, suggesting that although they occur in sequence along the color–color tracks, the BLN and the NBO are of different origin. We also present evidence that the frequency separation between the twin kHz QPOs decreases with the flux by 2–3 Hz on the BLN timescales, which is consistent with the trend on the longer timescale that the Z source traces on the HB. This further suggests that the flux variation associated with the BLN originates from the mass accretion rate variation in the disk accretion flow. We discuss the implications of these results for our understanding of the BLN.

Discovery of the Spin Frequency of 4U 0614+09 with theSwiftBurst Alert Telescope

We report the discovery of burst oscillations at 414.7 Hz during a thermonuclear X-ray burst from the low mass X-ray binary (LMXB) 4U 0614+091 with the Burst Alert Telescope (BAT) onboard SWIFT. In a search of the BAT archive, we found two burst triggers consistent with the position of 4U 0614+091. We searched both bursts for high frequency timing signatures, and found a significant detection at 414.7 Hz during a 5 s interval in the cooling tail of the brighter burst. This result establishes the spin frequency of the neutron star in 4U 0614+091 as 415 Hz. The oscillation had an average amplitude (rms) of 14%, These results are consistent with those known for burst oscillations seen in other LMXBs. The inferred ratio of the frequency difference between the twin kHz QPOs, and the spin frequency in this source is strongly inconsistent with either 0.5 or 1, and tends to support the recent suggestions by Yin et al., and Mendez & Belloni, that the kHz QPO frequency difference may not have a strong connection to the neutron star spin frequency.

Coupling between the 45 Hz Horizontal-Branch Oscillation and the Normal-Branch Oscillation in Scorpius X-1

The observations of the bright persistent neutron star low-mass X-ray binary (LMXB) Sco X-1 performed with the Rossi X-Ray Timing Explorer (RXTE) show a ~6 Hz normal-branch oscillation (NBO), a ~45 Hz horizontal-branch oscillation (HBO), and twin kilohertz quasi-periodic oscillations (kHz QPOs) on its normal branch simultaneously. We have found that the fractional amplitude of the HBO corresponding to the NBO phase of high flux is 1.1%, while that of the NBO phase of low flux is undetectable, with a 3 σ upper limit of 0.4%, implying that the HBO strength varies with the NBO phase in a manner opposite that of the lower kHz QPO previously found, and suggests that the condition for the generation of the HBO is met when the NBO flux is high. The 6 Hz NBO in Sco X-1 connects the 45 Hz HBO and the twin kHz QPO together, showing a unique picture indicating a coupling between the QPOs, which has never been observed in other neutron star LMXBs. We discuss the implications for current models of the 45 Hz HBO, the 6 Hz NBO, and the twin kHz QPOs.

Discovery of Twin kHz QPOs in the Peculiar X‐Ray Binary Circinus X‐1

We report the discovery with the RXTE PCA of twin kHz QPOs in the peculiar X-ray binary Circinus X-1. Eleven cases of simultaneous double QPOs occurred, with significances of up to 6.3 and 5.5 σ and centroid frequencies ranging between approximately 56 and 225 and 230 and 500 Hz for the two QPO peaks, respectively, i.e., for the most part at frequencies well below those of other sources. The QPO properties clearly indicate that these double peaks are the kHz QPOs known from low magnetic field neutron stars, and not black hole high-frequency QPOs, confirming that Cir X-1 is a neutron star, as suspected since the detection of type I X-ray bursts from the field of the source 20 years ago. The kHz QPO peak separation varies over a wide range, ~175-340 Hz, and increases as a function of kHz QPO frequency. This is contrary to what has been observed in other sources but in good agreement with predictions of the relativistic precession model and Alfven wave models; beat-frequency models require modification to accommodate this. In other observations, single kHz QPOs can be seen down to frequencies as low as ~12 Hz, as well as a strong low-frequency quasi-periodic oscillation (LF QPO) between 1 and 30 Hz. The relations between the kHz QPOs and the LF QPO are in good agreement with those found previously in Z sources, confirming that Cir X-1 may be a peculiar Z source. We suggest that the low-frequency range over which the kHz QPOs occur in Cir X-1 and to a lesser extent in (other) Z sources, might be due to a stronger radial accretion flow relative to the disk flow than in other kHz QPO sources, possibly related to the nature of the companion star.