Millihertz Quasi-periodic Oscillations Research Articles

EOS-dependent millihertz quasi-periodic oscillation in low-mass X-ray binary

ABSTRACT We studied the frequency and critical mass accretion rate of millihertz quasi-periodic oscillations (mHz QPOs) using a one-zone X-ray burst model. The surface gravity is specified by two kinds of equation of states: neutron star (NS) and strange star (SS). The base flux, Qb, is set in the range of 0–2 MeV nucleon−1. It is found that the frequency of mHz QPO is positively correlated to the surface gravity but negatively to the base heating. The helium mass fraction has a significant influence on the oscillation frequency and luminosity. The observed 7–9 mHz QPOs can be either explained by a heavy NS/light SS with a small base flux or a heavy SS with a large base flux. As base flux increases, the critical mass accretion rate for marginally stable burning is found to be lower. Meanwhile, the impact of metallicity on the properties of mHz QPOs was investigated using one-zone model. It shows that both the frequency and critical mass accretion rate decrease as metallicity increases. An accreted NS/SS with a higher base flux and metallicity, combined with a lower surface gravity and helium mass fraction, could be responsible for the observed critical mass accretion rate ($\dot{m}\simeq 0.3\dot{m}_{\rm Edd}$). The accreted fuel would be in stable burning if base flux is over than ∼2 MeV nucleon−1. This finding suggests that the accreting NSs/SSs in low-mass X-ray binaries showing no type I X-ray bursts possibly have a strong base heating.

Detection of millihertz quasi-periodic oscillations in the low-mass X-ray binary 4U 1730–22 with NICER

ABSTRACT We report the discovery of millihertz quasi-periodic oscillations (mHz QPOs) from the neutron star (NS) low-mass X-ray binary 4U 1730–22 using the Neutron Star Interior Composition Explorer (NICER). After being inactive for almost 50 years, 4U 1730–22 went into outburst twice between June and August 2021, and between February and July 2022. We analyse all the NICER observations of this source, and detect mHz QPOs with a significance > 4 σ in 35 observations. The QPO frequency of the full data set ranged between ∼ 4.5 and ∼ 8.1 mHz with an average fractional rms amplitude of the order of ∼2 per cent. The X-ray colour analysis strongly suggests that 4U 1730–22 was in a soft spectral state during the QPO detections. Our findings are consistent with those reported for other sources where the mHz QPOs have been interpreted as the result of a special mode of He burning on the NS surface called marginally stable nuclear burning (MSNB). We conclude that the mHz QPOs reported in this work are also associated with the MSNB, making 4U 1730–22 the eighth source that shows this phenomenology. We discuss our findings in the context of the heat flux from the NS crust.

High energy millihertz quasi-periodic oscillations in 1A 0535 + 262 with Insight-HXMT challenge current models

ABSTRACT We studied the millihertz quasi-periodic oscillation (mHz QPO) in the 2020 outburst of the Be/X-ray binary 1A 0535 + 262 using Insight-HXMT data over a broad energy band. The mHz QPO is detected in the 27–120 keV energy band. The QPO centroid frequency is correlated with the source flux and evolves in the 35–95 mHz range during the outburst. The QPO is most significant in the 50–65 keV band, with a significance of ∼8σ, but is hardly detectable (<2σ) in the lowest (1–27 keV) and highest (>120 keV) energy bands. Notably, the detection of mHz QPO above 80 keV is the highest energy at which mHz QPOs have been detected so far. The fractional rms of the mHz QPO first increases and then decreases with energy, reaching the maximum amplitude at 50–65 keV. In addition, at the peak of the outburst, the mHz QPO shows a double-peak structure, with the difference between the two peaks being constant at ∼0.02 Hz, twice the spin frequency of the neutron star in this system. We discuss different scenarios explaining the generation of the mHz QPO, including the beat frequency model, the Keplerian frequency model, the model of two jets in opposite directions, and the precession of the neutron star, but find that none of them can explain the origin of the QPO well. We conclude that the variability of non-thermal radiation may account for the mHz QPO, but further theoretical studies are needed to reveal the physical mechanism.

The Harmonic Component of the Millihertz Quasi-periodic Oscillations in 4U 1636–53

Abstract We studied the harmonics of the millihertz quasi-periodic oscillations (mHz QPOs) in the neutron star low-mass X-ray binary 4U 1636–53 using the Rossi X-ray Timing Explorer observations. We detected the harmonics of the mHz QPOs in 73 data intervals, with most of them in the transitional spectra state. We found that the ratio between the rms amplitude of the harmonic and that of the fundamental remains constant in a wide range of the fundamental frequency. More importantly, we studied, for the first time, the rms amplitude of the harmonics versus energy in 4U 1636–53 in the 2–5 keV range. We found that the rms amplitude of both the harmonic and the fundamental shows a decreasing trend as the energy increases, which is different from the behaviors reported in QPOs in certain black hole systems. Furthermore, our results suggest that not all observations with mHz QPOs have the harmonic component, although the reason behind this is still unclear.

Drifts of the marginally stable burning frequency in the X-ray binaries 4U 1608–52 and Aql X–1

ABSTRACT We detect millihertz quasi-periodic oscillations (mHz QPOs) using the Rossi X-ray Time Explorer (RXTE) from the atoll neutron-star (NS) low-mass X-ray binaries 4U 1608–52 and Aql X–1. From the analysis of all RXTE observations of 4U 1608–52 and Aql X–1, we find mHz QPOs with a significance level >3σ in 49 and 47 observations, respectively. The QPO frequency is constrained between ∼4.2 and 13.4 mHz. These types of mHz QPOs have been interpreted as being the result of marginally stable nuclear burning of He on the NS surface. We also report the discovery of a downward frequency drift in three observations of 4U 1608–52, making it the third source that shows this behaviour. We only find strong evidence of frequency drift in one occasion in Aql X–1, probably because the observations were too short to measure a significant drift. Finally, the mHz QPOs are mainly detected when both sources are in the soft or intermediate states; the cases that show frequency drift only occur when the sources are in intermediate states. Our results are consistent with the phenomenology observed for the NS systems 4U 1636–53 and EXO 0748–676, suggesting that all four sources can reach the conditions for marginally stable burning of He on the NS surface. These conditions depend on the source state in the same manner in all four systems.

Phase-resolved Analyses of Millihertz Quasi-periodic Oscillations in 4U 1636-53 using the Hilbert–Huang Transform

Abstract We present phase-resolved spectroscopy based on the Hilbert–Huang transform (HHT) for millihertz quasi-periodic oscillations (mHz QPOs) in 4U 1636-53. The ∼8 mHz QPO can be detected approximately several thousand seconds before a type-I X-ray burst. It has been interpreted as marginally stable burning on the neutron-star surface. In this study, we use the HHT to analyze the data collected by XMM-Newton between 2007 and 2009. The HHT is a powerful tool that enables us to obtain instantaneous frequency, amplitude, and phase of phenomena with nonstationary periodicity, such as QPOs. With well-defined phases, the oscillation profile of the ∼8 mHz QPO for 4U 1636-53 can be precisely revealed. In addition to the oscillation profile, phase-resolved spectra for the complete cycle are constructed. From the correlation between spectral parameters and fluxes, we find that the oscillation is mainly attributed to variations in the area emitting blackbody radiation in three out of four observations with mHz QPO detections, whereas the other one shows a concurrent variation of temperature and flux with a constant emitting area. Although the cause of the difference is not clear, it might be related to the spectral state of the source that can be observed from a hard color difference in the color–color diagram.

XMM-Newton and NICER Measurement of the Rms Spectrum of the Millihertz Quasiperiodic Oscillations in the Neutron-star Low-mass X-Ray Binary 4U 1636–53

Abstract We used two XMM-Newton and six Neutron Star Interior Composition Explorer observations to investigate the fractional rms amplitude of the millihertz quasiperiodic oscillations (mHz QPOs) in the neutron-star low-mass X-ray binary 4U 1636–53. We studied, for the first time, the fractional rms amplitude of the mHz QPOs versus energy in 4U 1636–53 down to 0.2 keV. We find that, as the energy increases from ∼0.2 to ∼3 keV, the rms amplitude of the mHz QPOs increases, different from the decreasing trend that has been previously observed above 3 keV. This finding has not yet been predicted by any current theoretical model; however, it provides an important observational feature to speculate whether a newly discovered mHz oscillation originates from the marginally stable nuclear burning process on the neutron-star surface.

Discovery of an Accretion-rate Independent Absolute RMS Amplitude of Millihertz Quasi-periodic Oscillations in 4U 1636-53

Abstract We investigate the frequency and amplitude of the millihertz quasi-periodic oscillations (mHz QPOs) in the neutron-star low-mass X-ray binary 4U 1636–53 using Rossi X-ray Timing Explorer observations. We find that no mHz QPOs appear when the source is in the hard spectral state. We also find that there is no significant correlation between the frequency and the fractional RMS amplitude of the mHz QPOs. Notwithstanding, for the first time, we find that the absolute rms amplitude of the mHz QPOs is insensitive to the parameter S a , which measures the position of the source in the color–color diagram and is usually assumed to be an increasing function of mass accretion rate. This finding indicates that the transition from marginally stable burning to stable burning or unstable burning could happen very rapidly since, before the transition, the mHz QPOs do not gradually decay as the rate further changes.

Discovery of millihertz quasi-periodic oscillations in the X-ray binary EXO 0748−676

Abstract We report the discovery of millihertz quasi-periodic oscillations (mHz QPOs) from the bursting, high-inclination atoll neutron star low-mass X-ray binary (NS LMXB) EXO 0748−676 with the Rossi X-ray Time Explorer (RXTE). This class of QPO, originally discovered in three NS LMXBs, has been interpreted as a consequence of a special mode of nuclear burning on the NS surface. Using all the RXTE archival observations of the source, we detected significant (>3σ) mHz QPOs in 11 observations. The frequency of the oscillations was between ∼5 and ∼13 mHz. We also found a decrease of the QPO frequency with time in two occasions; in one of these the oscillations disappeared with the onset of an X-ray burst, similar to what was reported in other sources. Our analysis of the X-ray colours revealed that EXO 0748−676 was in a soft spectral state when it exhibited the QPOs. This makes EXO 0748−676 the sixth source with mHz oscillations associated with marginally stable burning, and the second one that shows a systematic frequency drift. Our results suggest that the mechanism that produces the drift might always be present if the mHz QPOs are observed in the so-called intermediate state.

X-Ray Timing Analysis of Cyg X-3 Using AstroSat/LAXPC: Detection of Milli-hertz Quasi-periodic Oscillations during the Flaring Hard X-Ray State

Abstract We present here results from the X-ray timing and spectral analysis of the X-ray binary Cyg X-3 using observations from the Large Area X-ray proportional Counter on board AstroSat. Consecutive light curves observed over a period of one year show the binary orbital period of 17253.56 ± 0.19 s. Another low-amplitude, slow periodicity of the order of 35.8 ± 1.4 days is observed, which may be due to the orbital precession as suggested earlier by Molteni et al. During the rising binary phase, power density spectra from different observations during the flaring hard X-ray state show quasi-periodic oscillations (QPOs) at ∼5–8 mHz, ∼12–14 mHz, and ∼18–24 mHz frequencies at the minimum confidence of 99%. However, during the consecutive binary decay phase, no QPO is detected up to 2σ significance. Energy-dependent time-lag spectra show soft lag (soft photons lag hard photons) at the mHz QPO frequency and the fractional rms of the QPO increases with the photon energy. During the binary motion, the observation of mHz QPOs during the rising phase of the flaring hard state may be linked to the increase in the supply of the accreting material in the disk and corona via stellar wind from the companion star. During the decay phase, the compact source moves in the outer wind region causing the decrease in supply of material for accretion. This may cause weakening of the mHz QPOs below the detection limit. This is also consistent with the preliminary analysis of the orbital phase-resolved energy spectra presented in this paper.

Millihertz quasi-periodic oscillations in 4U 1636−53 associated with bursts with positive convexity only

We investigated the convexity of all type I X-ray bursts with millihertz quasi-periodic oscillations (mHz QPOs) in 4U 1636-53 using archival observations with the Rossi X-ray Timing Explorer. We found that, at a 3.5 $\sigma$ confidence level, in all 39 cases in which the mHz QPOs disappeared at the time of an X-ray burst, the convexity of the burst is positive. The convexity measures the shape of the rising part of the burst light curve and, according to recent models, it is related to the ignition site of bursts on the neutron star surface. This finding suggests that in 4U 1636-53 these 39 bursts and the marginally-stable nuclear burning process responsible for the mHz QPOs take place at the neutron-star equator. This scenario could explain the inconsistency between the high accretion rate required for triggering mHz QPOs in theoretical models and the relatively low accretion rate derived from observations.

Spectral and timing analysis of the mHz QPOs in the neutron-star low-mass X-ray binary 4U 1636–53

We investigate the spectral and timing properties of the millihertz quasi-periodic oscillations (mHz QPOs) in neutron-star low-mass X-ray binary 4U 1636-53 using XMM-Newton and Rossi X-ray Timing Explorer (RXTE) observations. The mHz QPOs in the XMM-Newton/RXTE observations show significant frequency variation and disappear right before type I X-ray bursts. We find no significant correlation between the mHz QPO frequency and the temperature of the neutron-star surface, which is different from theoretical predictions. For the first time we observed the full lifetime of a mHz QPO lasting 19 ks. Besides, we also measure a frequency drift timescale around 15 ks, we speculate that this is the cooling timescale of a layer deeper than the burning depth, possibly heated by the previous burst. Moreover, the analysis of all X-ray bursts in this source shows that all type I X-ray bursts associated with the mHz QPOs are short, bright and energetic, suggesting a potential connection between mHz QPOs and He-rich X-ray bursts.

Millihertz quasi-periodic oscillations and broad iron line from LMC X-1

We study the temporal and energy spectral characteristics of the persistent black hole X-ray binary LMC X-1 using two XMM-Newton and a Suzaku observation. We report the discovery of low frequency (~ 26-29 mHz) quasi-periodic oscillations (QPOs). We also report the variablity of the broad iron K-alpha line studied earlier with Suzaku. The QPOs are found to be weak with fractional rms amplitude in the ~ 1-2 % range and quality factor Q~2-10 . They are accompanied by weak red noise or zero-centered Lorentzian components with rms variability at the ~ 1-3 % level. The energy spectra consists of three varying components - multicolour disk blackbody (kT_{in} ~ 0.7-0.9 keV), high energy power-law tail (Gamma ~ 2.4 - 3.3) and a broad iron line at 6.4-6.9 keV. The broad iron line, the QPO and the strong power-law component are not always present. The QPOs and the broad iron line appear to be clearly detected in the presence of a strong power-law component. The broad iron line is found to be weaker when the disk is likely truncated and absent when the power-law component almost vanished. These results suggest that the QPO and the broad iron line together can be used to probe the dynamics of the accretion disk and the corona.

Discovery of a correlation between the frequency of the mHz quasi-periodic oscillations and the neutron-star temperature in the low-mass X-ray binary 4U 1636–53

We detected millihertz quasi-periodic oscillations (QPOs) in an XMM–Newton observation of the neutron-star low-mass X-ray binary 4U 1636−53. These QPOs have been interpreted as marginally stable burning on the neutron-star surface. At the beginning of the observation the QPO was at around 8 mHz, together with a possible second harmonic. About 12 ks into the observation a type I X-ray burst occurred and the QPO disappeared; the QPO reappeared ∼25 ks after the burst and it was present until the end of the observation. We divided the observation into four segments to study the evolution of the spectral properties of the source during intervals with and without mHz QPO. We find that the temperature of the neutron-star surface increases from the QPO segment to the non-QPO segment, and vice versa. We also find a strong correlation between the frequency of the mHz QPO and the temperature of a blackbody component in the energy spectrum representing the temperature of neutron-star surface. Our results are consistent with previous results that the frequency of the mHz QPO depends on the variation of the heat flux from the neutron-star crust, and therefore supports the suggestion that the observed QPO frequency drifts could be caused by the cooling of deeper layers.

A 400-solar-mass black hole in the galaxy M82.

M82 X-1, the brightest X-ray source in the galaxy M82, has been thought to be an intermediate-mass black hole (100 to 10,000solar masses) because of its extremely high luminosity and variability characteristics, although some models suggest that its mass may be only about 20solar masses. The previous mass estimates were based on scaling relations that use low-frequency characteristic timescales which have large intrinsic uncertainties. For stellar-mass black holes, we know that the high-frequency quasi-periodic oscillations (100-450hertz) in the X-ray emission that occur in a 3:2 frequency ratio are stable and scale in frequency inversely with black hole mass with a reasonably small dispersion. The discovery of such stable oscillations thus potentially offers an alternative and less ambiguous means of mass determination for intermediate-mass black holes, but has hitherto not been realized. Here we report stable, twin-peak (3:2 frequency ratio) X-ray quasi-periodic oscillations from M82 X-1 at frequencies of 3.32±0.06hertz and 5.07±0.06hertz. Assuming that we can extrapolate the inverse-mass scaling that holds for stellar-mass black holes, we estimate the black hole mass of M82 X-1 to be 428±105solar masses. In addition, we can estimate the mass using the relativistic precession model, from which we get a value of 415±63solar masses.

MILLIHERTZ QUASI-PERIODIC OSCILLATIONS AND THERMONUCLEAR BURSTS FROM TERZAN 5: A SHOWCASE OF BURNING REGIMES

We present a comprehensive study of the thermonuclear bursts and millihertz quasi-periodic oscillations (mHz QPOs) from the neutron star (NS) transient and 11 Hz X-ray pulsar IGR J17480-2446, located in the globular cluster Terzan 5. The increase in burst rate that we found during its 2010 outburst, when persistent luminosity rose from 0.1 to 0.5 times the Eddington limit, is in qualitative agreement with thermonuclear burning theory yet opposite to all previous observations of thermonuclear bursts. Thermonuclear bursts gradually evolved into a mHz QPO when the accretion rate increased, and vice versa. The mHz QPOs from IGR J17480-2446 resemble those previously observed in other accreting NSs, yet they feature lower frequencies (by a factor ~3) and occur when the persistent luminosity is higher (by a factor 4-25). We find four distinct bursting regimes and a steep (close to inverse cubic) decrease of the burst recurrence time with increasing persistent luminosity. We compare these findings to nuclear burning models and find evidence for a transition between the pure helium and mixed hydrogen/helium ignition regimes when the persistent luminosity was about 0.3 times the Eddington limit. We also point out important discrepancies between the observed bursts and theory, which predicts brighter and less frequent bursts, and suggest that an additional source of heat in the NS envelope is required to reconcile the observed and expected burst properties. We discuss the impact of NS magnetic field and spin on the expected nuclear burning regimes, in the context of this particular pulsar.

X-RAY BURSTS FROM THE TERZAN 5 TRANSIENT IGR J17480-2446: NUCLEAR RATHER THAN GRAVITATIONAL

The 2010 outburst of the transient neutron star low-mass X-ray binary IGR J17480-2446 has exhibited a series of unique X-ray bursts, as well as millihertz (mHz) quasi-periodic oscillations (QPOs) related to these bursts. It has been recently proposed that these are type-II bursts, powered by the gravitational energy. This implies that the current nuclear-burning based model of mHz QPOs is not correct, and this timing feature cannot be used as a tool to measure the neutron star parameters. We report the analysis of the Rossi X-ray Timing Explorer data of IGR J17480-2446 to show that the burst properties of this source are quite different from the properties of the type-II bursts observed from the rapid burster and GRO J1744-28. For example, the inferred ratio (~ 50-90) of the non-burst fluence to burst fluence is consistent with the thermonuclear origin of IGR J17480-2446 bursts, and is significantly different from this ratio (< 4) for type-II bursts. Our results suggest that the bursts and the mHz QPOs from IGR J17480-2446 are powered by the nuclear energy.

Millihertz Oscillation Frequency Drift Predicts the Occurrence of Type I X-Ray Bursts

The millihertz quasi-periodic oscillations (mHz QPOs) discovered in three neutron star low-mass X-ray binaries have been suggested to be a mode of marginally stable nuclear burning on the neutron star surface. We show that, close to the transition between the island and the banana state, 4U 1636–53 exhibits mHz QPOs whose frequencies systematically decrease with time, until the oscillations disappear and a type I X-ray burst occurs. There is a strong correlation between the QPO frequency ν and the occurrence of X-ray bursts: when ν 9 mHz, no bursts occur, whereas ν 9 mHz does allow the occurrence of bursts. The mHz QPO frequency constitutes the first identified observable that can be used to predict the occurrence of X-ray bursts. If a systematic frequency drift occurs, then a burst happens within a few kiloseconds after ν drops below 9 mHz. This observational result confirms that the mHz QPO phenomenon is intimately related to the processes that lead to a thermonuclear burst.

Large X-Ray Flares from LMC X-4: Discovery of Millihertz Quasi-periodic Oscillations and Quasi-periodic Oscillation–Modulated Pulsations

We report the discovery of millihertz (mHz) quasi-periodic oscillations (QPOs) and QPO-modulated pulsations during large X-ray flares from the high-mass X-ray binary pulsar LMC X-4 using data from the Rossi X-Ray Timing Explorer. The light curves of flares show that, in addition to ~74 mHz coherent pulsations, there exist two more time-varying temporal structures at frequencies of ~0.65-1.35 and ~2-20 mHz. These relatively long term structures appear in the power density spectra as mHz QPOs and also as well-developed sidebands around the coherent pulse frequency, indicating that the amplitudes of the coherent pulsation are modulated by those of the mHz QPOs. One interesting feature is that, while the first flare shows symmetric sidebands around the coherent pulse frequency, the second flare shows significant excess emission in the lower frequency sidebands due to the ~2-20 mHz QPOs. We discuss the origin of the QPOs using a combination of the beat-frequency model and a modified version of the Keplerian-frequency model. According to our discussion, it seems possible to attribute the origin of the ~0.65-1.35 and ~2-20 mHz QPOs to the beating between the rotational frequency of the neutron star and the Keplerian frequency of large accreting clumps near the corotation radius and to the orbital motion of clumps at Keplerian radii of (2-10) × 109 cm, respectively.