Following the previous research on epicyclic oscillations of accretion disks around black holes (BHs) and neutron stars (NSs), a new model of high-frequency quasi-periodic oscillations (QPOs) has been proposed (CT model), which deals with oscillations of fluid in marginally overflowing accretion tori (i.e., tori terminated by cusps). According to preliminary investigations, the model provides better fits of the NS QPO data compared to the relativistic precession (RP) model. It also implies a significantly higher upper limit on the Galactic microquasars BH spin. A short analytic formula has been noticed to well reproduce the model's predictions on the QPO frequencies in Schwarzschild spacetimes. Here we derive an extended version of this formula that applies to rotating compact objects. We start with the consideration of Kerr spacetimes and derive a formula that is not restricted to a particular specific angular momentum distribution of the inner accretion flow, such as Keplerian or constant. Finally, we consider Hartle-Thorne spacetimes and include corrections implied by the NS oblateness. For a particular choice of a single parameter, our relation provides frequencies predicted by the CT model. For another value, it provides frequencies predicted by the RP model. We conclude that the formula is well applicable for rotating oblateness NSs and both models. We briefly illustrate application of our simple formula on several NS sources and confirm the expectation that the CT model is compatible with realistic values of the NS mass and provides better fits of data than the RP model.
In this work I report on the stochastic X-ray variability of the 340 Hz accreting millisecond pulsar MAXI J0911-655. Analyzing pointed observations of the XMM-Newton and NuSTAR observatories I find that the source shows broad band-limited stochastic variability in the $0.01-10$ Hz range, with a total fractional variability of $\sim24\%$ rms in the $0.4-3$ keV energy band, which increases to $\sim40\%$ rms in the $3-10$ keV band. Additionally a pair of harmonically related quasi-periodic oscillations are discovered. The fundamental frequency of this harmonic pair is observed between frequencies…
We consider the behavior of matter in the accretion column that emerges under accretion in binary systems near the surface of a white dwarf. The plasma heated in a standing shock wave near the white dwarf surface efficiently radiates in the X-ray energy band. We suggest a method for estimating post-shock plasma parameters, such as the density, temperature, and height of the hot zone, from the power spectrum of its X-ray luminosity variability. The method is based on the fact that the flux variability amplitude for the hot region at various Fourier frequencies depends significantly on its cooli…
We extract the spectra of the fastest variability (above 10 Hz) from the black hole XTE J1550-564 during a transition from hard to soft state on the rise to outburst. We confirm previous results that the rapid variability contains no significant disc component despite this being strongly present in the total spectrum of the softer observations. We model ionised reflection significantly better than previous work, and show that this is also suppressed in the rapid variability spectrum compared to the total emission. This is consistent with the fast variability having its origin in a hot inner fl…
We investigate the aperiodic variability for a relatively large sample of accreting neutron stars and intermediate polars, focusing on the properties of the characteristic break commonly observed in power spectra of accreting objects. In particular, we investigate the relation of the break frequency and the magnetic field strength, both of which are connected to the size of the magnetosphere. We find that for the majority of objects in our sample the measured break frequency values indeed agree with estimated inner radii of the accretion disc, which allows to use observed break frequencies to …
This work presents an investigation of the stochastic X-ray variability from the 164 Hz accreting millisecond pulsar IGR J17062-6143, based on regular observations collected with the Neutron Star Interior Composition Explorer between 2017 July and 2020 August. Over this period, the power density spectrum showed a stable morphology, with broad $\sim25\%$ rms band-limited noise below 16 Hz. Quasi-periodic oscillations (QPOs) were occasionally observed, with the most notably detections including a low-frequency QPO centered at 2.7 Hz and a sharp QPO centered at 115 Hz that may be a 2:3 resonance …
In addition to coherent pulsation, many accreting neutron stars exhibit flaring activity and strong aperiodic variability on time scales similar to or shorter than their pulsation period. Such a behavior shows that the accretion flow in the vicinity of the accretor must be highly non-stationary. Although from the theoretical point of view the problem of non-stationary accretion has been addressed by many authors, observational study of this phenomenon is often problematic as it requires very high statistics of X-ray data and a specific analysis technique. In our research we used high-resolutio…
We derive the conditions for shock formation in a quasi-spherical, slightly rotating flows. We verify the results of semi-analytical, stationary calculations with the time evolution studied by numerical hydro-simulations, and we study the oscillations of the shock position. We also study the behaviour of flows with varying specific angular momentum, where the 'hysteresis' type of loop is found when passing through the multiple sonic points region. Our results are in agreement with the timescales and shapes of the luminosity flares observed in Sgr A*. These models may also be applicable for the…
We analyzed 39 ks NuSTAR observation data of the high mass X-ray binary Cen X-3 in order to investigate the orbital- and spin-phase spectral variability. The observation covers the orbital phase of $Φ=0.199$-$0.414$ of the source, where $Φ=0$ corresponds to the mid-eclipse. The orbital-phase-resolved spectroscopy revealed that low energy photons are more dominant for the spectral fluctuation, and a large part of the variability can be explained in terms of absorption by clumps of stellar wind. The spin-phase-resolved spectroscopy together with energy-resolved pulse profiles, on the other hand,…
We develop a Monte Carlo Comptonization model for the X-ray spectrum of accretion-powered pulsars. Simple, spherical, thermal Comptonization models give harder spectra for higher optical depth, while the observational data from Vela X-1 show that the spectra are harder at higher luminosity. This suggests a physical interpretation where the optical depth of the accreting plasma increases with mass accretion rate. We develop a detailed Monte-Carlo model of the accretion flow, including the effects of the strong magnetic field ($\sim 10^{12}$ G) both in geometrically constraining the flow into an…
On the basis of data from an energy-conserving 3D general relativistic MHD simulation, we predict the statistical character of variability in the coronal luminosity from accreting black holes. When the inner boundary of the corona is defined to be the electron scattering photosphere, its location depends only on the mass accretion rate in Eddington units (\dot{M}). Nearly independent of viewing angle and \dot{M}, the power spectrum over the range of frequencies from approximately the orbital frequency at the innermost stable circular orbit (ISCO) to ~100 times lower is well approximated by a p…
Accreting black holes show characteristic reflection features in their X-ray spectrum, including an iron K$α$ line, resulting from hard X-ray continuum photons illuminating the accretion disk. The reverberation lag resulting from the path length difference between direct and reflected emission provides a powerful tool to probe the innermost regions around both stellar-mass and supermassive black holes. Here, we present for the first time a reverberation mapping formalism that enables modeling of energy dependent time lags and variability amplitude for a wide range of variability timescales, ta…
Structured jets are recently invoked to explain the complex emission of gamma ray bursts, such as GW 170817. Based on the accretion simulations, the jets are expected to have a structure that is more complex than a simple top-hat. Also, the structure of launching regions of blazar jets should influence their large scale evolution. This is recently revealed by the interactions of jet components in TXS 0506+056, where the jet is observed at a viewing angle close to zero. Observational studies have also shown an anti-correlation between the jet variability, measured e.g. by its minimum variabilit…
We have analyzed the time variability of the wide-band X-ray spectrum of Vela X-1, the brightest wind-fed accreting neutron star, on a short timescale of 2 ks by using {\it Suzaku} observations with an exposure of 100 ks. During the observation, the object showed strong variability including several flares and so-called "low states", in which the X-ray luminosity decreases by an order of magnitude. Although the spectral hardness increases with the X-ray luminosity, the majority of the recorded flares do not show any significant changes of circumstellar absorption. However, a sign of heavy abso…
Multiwavelength variability data, combined with spectral-timing analysis techniques, provides information about the causal relationship between different physical components in accreting black holes. Using fast-timing data and long-term monitoring, we can probe the behaviour of the same components across the black hole mass scale. In this chapter we review the observational status of multiwavelength variability in accreting black holes, from black hole X-ray binaries to AGN, and consider the implications for models of accretion and ejection, primarily considering the evidence for accretion dis…
We present a new release of the RELTRANS model to fit the complex cross-spectrum of accreting black holes as a function of energy. The model accounts for continuum lags and reverberation lags self-consistently in order to consider the widest possible range of X-ray variability timescales. We introduce a more self-consistent treatment of the reverberation lags, accounting for how the time variations of the illuminating flux change the ionisation level of the accretion disc. This process varies the shape of the reflection spectrum in time causing an additional source of lags besides the light cr…
There is strong observational evidence that many active galactic nuclei (AGNs) harbour supermassive black holes (SMBHs), demonstrating multi-accretion episodes during their lifetime. In such AGNs, corotating and counterrotating tori, or strongly misaligned disks, as related to the central SMBH spin, can report traces of the AGNs evolution. Here we concentrate on aggregates of accretion disks structures, ringed accretion disks (RADs) orbiting a central Kerr SMBH, assuming that each torus of the RADs is centered in the equatorial plane of the BH, tori are coplanar and axisymmetric. Many RAD aspe…
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 upp…
We use Rossi X-ray Timing Explorer observations to conduct a population study of the timing properties of accretion-powered neutron star Low Mass X-ray Binaries (LMXBs), following a model-independent approach that was originally applied to black hole systems. The ratios of integrated power in four equally spaced Fourier frequency bands allow power spectral shapes to be parameterised with two `power colour' values, providing a simple way of tracking the evolution in timing properties across observations. We show that neutron star LMXBs follow a remarkably similar power spectral evolution to bla…
AIMS: A few well studied cataclysmic variables (CVs) have shown discrete characteristic frequencies of fast variability; the most prominent ones are around log(f/Hz) $\simeq$ -3. Because we still have only small number statistics, we obtained a new observation to test whether this is a general characteristic of CVs, especially if mass transfer occurs at a high rate typical for dwarf nova in outbursts, in the so called "high state". METHODS: We analyzed optical Kepler data of the quiescent nova and intermediate polar V4743 Sgr. This system hosts a white dwarf accreting through a disk in the hig…
We perform magnetohydrodynamic simulations of accreting, equal-mass binary black holes in full general relativity focusing on the effect of spin and minidisks on the accretion rate and Poynting luminosity variability. We report on the structure of the minidisks and periodicities in the mass of the minidisks, mass accretion rates, and Poynting luminosity. The accretion rate exhibits a quasi-periodic behavior related to the orbital frequency of the binary in all systems that we study, but the amplitude of this modulation is dependent on the existence of persistent minidisks. In particular, syste…
Cataclysmic variable stars are in many ways similar to X-ray binaries. Both types of systems possess an accretion disk, which in most cases can reach the surface (or event horizon) of the central compact object. The main difference is that the embedded gravitational potential well in X-ray binaries is much deeper than those found in cataclysmic variables. As a result, X-ray binaries emit most of their radiation at X-ray wavelengths, as opposed to cataclysmic variables which emit mostly at optical/ultraviolet wavelengths. Both types of systems display aperiodic broad-band variability which can …
We report the discovery of extreme X-ray variability in a type 1 quasar: SDSS J$075101.42+291419.1$. It has a black hole mass of $1.6\times 10^7~\rm M_\odot$ measured from reverberation mapping (RM), and the black hole is accreting with a super-Eddington accretion rate. Its XMM-Newton observation in 2015 May reveals a flux drop by a factor of $\sim 22$ with respect to the Swift observation in 2013 May when it showed a typical level of X-ray emission relative to its UV/optical emission. The lack of correlated UV variability results in a steep X-ray-to-optical power-law slope ($α_{\rm OX}$) of -…
Accreting compact objects show variations in source flux over a broad range of timescales and in all wavebands. The light curves typically show a lognormal distribution of flux and a linear relation between flux and rms. It has been demonstrated that an exponential transform of an underlying (and unobserved) Gaussian stochastic process provides a very good description of the light curves with these observed properties. Recently, a non-stationary power spectrum was observed on fast timescales (~ days) in the active galaxy, IRAS 13224--3809, as well as a non-lognormal flux distribution and non-l…
We introduce a new method for analysing the aperiodic variability of coherent pulsations in accreting millisecond X-ray pulsars. Our method involves applying a complex frequency correction to the time-domain light curve, allowing for the aperiodic modulation of the pulse amplitude to be robustly extracted in the frequency domain. We discuss the statistical properties of the resulting modulation spectrum and show how it can be correlated with the non-pulsed emission to determine if the periodic and aperiodic variability are coupled processes. Using this method, we study the 598.88 Hz coherent p…
HETE J1900.1--2455 is a peculiar accreting millisecond X-ray pulsar (AMXP) because it has shown intermittent pulsations after 22 days from the beginning of its outburst. The origin of intermittent pulses in accreting systems remains to be understood. To better investigate the phenomenon of intermittent pulsations here we present an analysis of 7 years of X-ray data collected with the Rossi X-Ray Timing Explorer and focus on the aperiodic variability. We show that the power spectral components follow the same frequency correlations as the non-pulsating atoll sources. We also study the known kHz…
Context: In addition to coherent pulsation, many accreting neutron stars exhibit flaring activity and strong aperiodic variability on time scales comparable to or shorter than their pulsation period. Such a behavior shows that the accretion flow in the vicinity of the accretor must be highly non-stationary. Observational study of this phenomenon is often problematic as it requires very high statistics of X-ray data and a specific analysis technique. Aims: In our research we used high-resolution data taken with RXTE and INTEGRAL on a sample of bright transient and persistent pulsars, to perform…
The central engines of disc-accreting stellar-mass black holes appear to be scaled down versions of the supermassive black holes that power active galactic nuclei. However, if the physics of accretion is universal, it should also be possible to extend this scaling to other types of accreting systems, irrespective of accretor mass, size, or type. We examine new observations, obtained with Kepler/K2 and ULTRACAM, regarding accreting white dwarfs and young stellar objects. Every object in the sample displays the same linear correlation between the brightness of the source and its amplitude of var…
X-ray variability of accreting black hole binaries is believed to be produced by the fluctuations propagating towards the compact object. Observations suggest the light curves in different energy bands are connected, but the fluctuations at harder energies are delayed with respect to the softer ones. The standard interpretation involves dependence of the X-ray spectral hardness on the radial distance, with harder spectra emitted closer to the black hole. Recently, a number of challenges to this scenario have been found, both at qualitative and quantitative level. The model does not predict the…
X-ray variability of active galactic nuclei (AGN) and black hole binaries can be analysed by means of the power spectral density (PSD). The break observed in the power spectrum defines a characteristic variability timescale of the accreting system. The empirical variability scaling that relates characteristic timescale, black hole mass, and accretion rate ($T_B \propto M_{BH}^{2.1}/\dot{M}^{0.98}$) extends from supermassive black holes in AGN down to stellar-mass black holes in binary systems. We suggest that the PSD break timescale is associated with the cooling timescale of electrons in the …
A universal relationship between the variability timescale and black hole mass in black hole jetted and non-jetted accreting systems
Qujing Normal University（曲靖师范学院）；Nanjing University（南京大学）；Anqing Normal University（安庆师范大学）；Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台）
The phenomenology of anomalous X-ray pulsars is usually interpreted within the paradigm of very highly magnetized neutron stars, also known as magnetars. According to this paradigm, the persistent emission of anomalous X-ray pulsars (AXPs) is powered by the decay of the magnetic field. However, an alternative scenario in which the persistent emission is explained through accretion is also discussed in literature. In particular AXP 4U 0142+61has been suggested to be either an accreting neutron star or a white dwarf. Here we rule out this scenario based on the the observed X-ray variability prop…
The notion of source states characterizing the X-ray emission from black hole binaries has revealed to be a very useful tool to disentangle the complex spectral and aperiodic phenomenology displayed by those classes of accreting objects. We seek to use the same tools for Ultra-Luminous X-ray (ULX) sources. We analyzed the data from the longest observations obtained from the ULX source in NGC 5408 (NGC 5408 X-1) taken by XMM-Newton. We performed a study of the timing and spectral properties of the source. In accordance with previous studies on similar sources, the intrinsic energy spectra of th…
Flickering, and more specifically aperiodic broad-band variability, is an important phenomenon used in understanding the geometry and dynamics of accretion flows. Although the inner regions of accretion flows are known to generate variability on relatively fast timescales, the broad-band variability generated in the outer regions have mostly remained elusive due to their long intrinsic variability timescales. Ultra-compact AM CVn systems are relatively small when compared to other accreting binaries and are well suited to search and characterise low frequency variability. Here we present the f…
Many upcoming surveys, particularly in the radio and optical domains, are designed to probe either the temporal and/or the spatial variability of a range of astronomical objects. In the light of these high resolution surveys, we review the subject of ultra-luminous X-ray (ULX) sources, which are thought to be accreting black holes for the most part. We also discuss the sub-class of ULXs known as the hyper-luminous X-ray sources, which may be accreting intermediate mass black holes. We focus on some of the open questions that will be addressed with the new facilities, such as the mass of the bl…
IGR J18245-2452 is the fifteenth discovered accreting millisecond X-ray pulsar and the first source of this class showing direct evidence for transition between accretion and rotational powered emission states. These swing provided the strongest confirmation of the pulsar recycling scenario available so far. During the two XMM-Newton observations that were carried out while the source was in outburst in April 2013, IGR J18245-2452 displayed a unique and peculiar variability of its X-ray emission. In this work, we report on a detailed analysis of the XMM- Newton data and focus in particular on …
Aperiodic broad-band variability (also known as flickering) is observed throughout all types of accreting compact objects. Many statistical properties of this variability can be naturally explained with the fluctuating accretion disk model, where variations in the mass-transfer rate through the disk are modulated on the local viscous timescale and propagate towards the central compact object. Here, a recently developed implementation of the model is applied for the first time to the time-averaged, high-frequency variability of a cataclysmic variable star (MV Lyrae) observed with the Kepler sat…
Accretion discs around black holes power some of the most luminous objects in the Universe. Discs that are misaligned to the black hole spin can become warped over time by Lense-Thirring precession. Recent work has shown that strongly warped discs can become unstable, causing the disc to break into discrete rings producing a more dynamic and variable accretion flow. In a companion paper, we present numerical simulations of this instability and the resulting dynamics. In this paper, we discuss the implications of this dynamics for accreting black hole systems, with particular focus on the varia…
Jets are observed as radio emission in active galactic nuclei and during the low/hard state in X-ray binaries (XRBs), but their contribution at higher frequencies has been uncertain. We study the dynamics of jets in XRBs using the general-relativistic magnetohydrodynamic code HARM. We calculate the high-energy spectra and variability properties using a general-relativistic radiative transport code based on grmonty. We find the following signatures of jet emission (i) a significant gamma-ray peak above ~10^22 Hz, (ii) a break in the optical/UV spectrum, with a change in luminosity from L ~ nu^0…
The X-ray emission from accreting black-holes and neutron stars features strong variability on sub-second time scales, with very complex and broad phenomenology. From high-frequency quasi-periodic oscillations to rapidly changing X-ray burst oscillations to millisecond pulsations, these are weak signals immersed in strong noise and their study is pushing instrument capabilities to their limit. The scientific significance of fast time variability studies are both astronomical (properties of accretion flows, nature and evolution of sources) and physical (effects of General Relativity, equation o…
We present an analysis of the X-ray spectrum and long-term variability of the nearby dwarf starburst galaxy Henize 2-10. Recent observations suggest that this galaxy hosts an actively accreting black hole with mass ~10^6 M_sun. The presence of an AGN in a low-mass starburst galaxy marks a new environment for active galactic nuclei (AGNs), with implications for the processes by which "seed" black holes may form in the early Universe. In this paper, we analyze four epochs of X-ray observations of Henize 2-10, to characterize the long-term behavior of its hard nuclear emission. We analyze observa…
Accretion-powered X-ray pulsars exhibit significant variability of the Cyclotron Resonance Scattering Feature (CRSF) centroid energy on pulse-to-pulse timescales, and also on much longer timescales. Two types of spectral variability are observed. For sources in group 1, the CRSF energy is negatively correlated with the variable source luminosity, and for sources in group 2, the opposite behavior is observed. The physical basis for this bimodal behavior is currently not understood. We explore the hypothesis that the accretion dynamics in the group 1 sources is dominated by radiation pressure ne…
A0538-66 is a Be/X-ray binary (Be/XRB) hosting a 69 ms pulsar. It emitted bright X-ray outbursts with peak luminosity up to $\sim 10^{39}$ erg/s during the first years after its discovery in 1977. Since then, it was always seen in quiescence or during outbursts with $L_x \lesssim 4 \times 10^{37}$ erg/s. In 2018 we carried out XMM-Newton observations of A0538-66 during three consecutive orbits when the pulsar was close to periastron. In the first two observations we discovered a remarkable variability, with flares of typical durations between $\sim$2-50 s and peak luminosities up to $\sim 4\ti…
LS 5039 is one of the few X-ray binaries detected at VHE, and potentially contains a young non-accreting pulsar. The outflow of accelerated particles emitting synchrotron emission can be directly mapped with high resolution radio observations. The morphology of the radio emission strongly depends on the properties of the compact object and on the orbital parameters of the binary system. We present VLBA observations of LS 5039 covering an orbital cycle, which show morphological and astrometric variability at mas scales. On the other hand, we discuss the possible association of LS 5039 with the …
We present X-ray, ultraviolet, and optical observations of 1RXS J154439.4-112820, the most probable counterpart of the unassociated Fermi LAT source 3FGL J1544.6-1125. The optical data reveal rapid variability, which is a feature of accreting systems. The X-rays exhibit large-amplitude variations in the form of fast switching (within ~10 s) between two distinct flux levels that differ by a factor of $\approx$10. The detailed optical and X-ray behavior is virtually identical to that seen in the accretion-disk-dominated states of the transitional millisecond pulsar binaries PSR J1023+0038 and XS…
We present a detailed X-ray timing analysis of the highly variable NLS1 galaxy, IRAS 13224-3809. The source was recently monitored for 1.5 Ms with XMM-Newton which, combined with 500 ks archival data, makes this the best studied NLS1 galaxy in X-rays to date. We apply standard time- and Fourier-domain in order to understand the underlying variability process. The source flux is not distributed lognormally, as would be expected for accreting sources. The first non-linear rms-flux relation for any accreting source in any waveband is found, with $\mathrm{rms} \propto \mathrm{flux}^{2/3}$. The lig…
Accreting X-ray pulsars (XRPs) undergo luminous X-ray outbursts during which the luminosity-dependent spectral and timing features of the neutron star's emission can be analyzed in detail, thus shedding light on the accretion regime at work. We took advantage of a monitoring campaign performed with NuSTAR, Swift/XRT, AstroSat and NICER, to follow the Be/X-ray Binary 2S 1553-542 along one of its rare outbursts and trace its spectral and timing evolution. We report the discovery of a luminosity-dependent cyclotron line energy for the first time in this source. The pulse profiles and pulsed fract…
In this paper, we report on the analysis of the peculiar X-ray variability displayed by the accreting millisecond X-ray pulsar IGR J00291+5934 in a 80 ks-long joint NuSTAR and XMM-Newton observation performed during the source outburst in 2015. The light curve of the source was characterized by a flaring-like behavior, with typical rise and decay time scales of ~120 s. The flares are accompanied by a remarkable spectral variability, with the X-ray emission being generally softer at the peak of the flares. A strong quasi periodic oscillation (QPO) is detected at ~8 mHz in the power spectrum of …
Kilohertz-scale quasi-periodic oscillations (kHz QPOs) are a distinct feature of the variability of neutron star low-mass X-ray binaries. Among all the variability modes, they are especially interesting as a probe for the innermost parts of the accretion flow, including the accretion boundary layer (BL) on the surface of the neutron star. All the existing models of kHz QPOs explain only part of their rich phenomenology. Here, we show that some of their properties may be explained by a very simple model of the BL that is spun up by accreting rapidly rotating matter from the disk and spun down b…
Accreting black hole sources show a wide variety of rapid time variability, including the manifestation of time lags during X-ray transients, in which a delay (phase shift) is observed between the Fourier components of the hard and soft spectra. Despite a large body of observational evidence for time lags, no fundamental physical explanation for the origin of this phenomenon has been presented. We develop a new theoretical model for the production of X-ray time lags based on an exact analytical solution for the Fourier transform describing the diffusion and Comptonization of seed photons propa…
Strong X-ray Variability of I Zwicky 1: Obscuration from Clumpy Accretion-Disk Winds
Nanjing University（南京大学）；Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education（教育部现代天文与天体物理重点实验室（南京大学））；The Pennsylvania State University（宾夕法尼亚州立大学）；Institute for Gravitation and the Cosmos, The Pennsylvania State University（宾夕法尼亚州立大学引力与宇宙学研究所）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Max-Planck-Institut für extraterrestrische Physik (MPE)（马克斯·普朗克地外物理学研究所）
