Cygnus X-1 is a well-studied persistent black hole X-ray binary. Recently, the three parameters needed to estimate the black hole spin of this system, namely the black hole mass $M$, the orbital inclination $i$ and the source distance $D$, have been updated. In this work we redetermine the spin parameter using the continuum-fitting technique for those updated parameter values. Based on the assumption that the spin axis of the black hole is aligned with the orbital plane, we fit the thermal disk component to a fully relativistic thin accretion disk model. The error in the spin estimate arising from the combined observational uncertainties is obtained via Monte Carlo (MC) simulations. We demonstrate that, without considering the counteracting torque effect, the new spin parameter is constrained to be a$_* > 0.9985$ (3$σ$), which confirms that the spin of the black hole in Cygnus X-1 is extreme.
We report the appearance of a new radio source at a projected offset of 460 pc from the nucleus of Cygnus A. The flux density of the source (which we designate Cygnus A-2) rose from an upper limit of <0.5 mJy in 1989 to 4 mJy in 2016 (nu=8.5 GHz), but is currently not varying by more than a few percent per year. The radio luminosity of the source is comparable to the most luminous known supernovae, it is compact in VLBA observations down to a scale of 4 pc, and it is coincident with a near-infrared point source seen in pre-existing adaptive optics and HST observations. The most likely interpre…
We utilize the joint capabilities of IBIS and SPI to perform a state-resolved 20--2000\,keV analysis of the microquasar Cygnus X-1. In both LHS and HSS, the spectral analysis reveals the presence of a high-energy tail above 400\,keV in addition to a standard, Compton-like continuum in the 20--400\,keV range. We study the polarisation properties of the hard X-ray radiation, as well as of the polarisation of this high-energy tail. Polarisation is detected in the LHS in agreement with previous work. We find potential variations of the LHS polarisation with time and no polarisation detection in th…
Because of their inherently high flux allowing the detection of clear signals, black hole X-ray binaries are interesting candidates for polarization studies, even if no polarization signals have been observed from them before. Such measurements would provide further detailed insight into these sources' emission mechanisms. We measured the polarization of the gamma-ray emission from the black hole binary system Cygnus X-1 with the INTEGRAL/IBIS telescope. Spectral modeling of the data reveals two emission mechanisms: The 250-400 keV data are consistent with emission dominated by Compton scatter…
The evolution of massive stars is influenced by the mass lost to stellar winds over their lifetimes. These winds limit the masses of the stellar remnants (such as black holes) that the stars ultimately produce. We use radio astrometry to refine the distance to the black hole X-ray binary Cygnus X-1, which we find to be $2.22^{+0.18}_{-0.17}$ kiloparsecs. When combined with previous optical data, this implies a black hole mass of $21.2\pm2.2$ solar masses, higher than previous measurements. The formation of such a high-mass black hole in a high-metallicity system constrains wind mass loss from …
Cygnus X-1 is the candidate with the highest probability of containing a black hole among the X-ray binary systems in the Galaxy. It is also by far the most often studied of these objects. Recently, the International Gamma-Ray Astrophysics Laboratory Imager onboard then Integral satellite ({\it INTEGRAL}/IBIS) detected strong polarization in the high-energy radiation of this source, between 400 keV and 2 MeV. This radiation has been attributed to a jet launched by the black hole. We consider whether the corona around the black hole might be the site of production of the polarized emission inst…
The bright and highly variable X-ray and radio source known as Cygnus X-3 was among the first X-ray sources discovered, yet it remains in many ways an enigma. Its known to consist of a massive, Wolf-Rayet primary in an extremely tight orbit with a compact object. Yet one of the most basic of parameters - the mass of the compact object - is not known. Nor is it even clear whether its is a neutron star or a black hole. In this Paper we present our analysis of the broad-band high-energy continua covering a substantial range in luminosity and spectral morphology. We apply these results to a recent…
In 2015, a radio transient named Cygnus A-2 was discovered in Cygnus A with the Very Large Array. Because of its radio brightness ($νF_ν \approx 6 \times 10^{39}$ erg s$^{-1}$), this transient likely represents a secondary black hole in orbit around the AGN. Using {\it Chandra} ACIS observations from 2015 to 2017, we have looked for an X-ray counterpart to Cygnus A-2. The separation of 0.42 arcsec means that Cygnus A-2 can not be spatially resolved, but by comparing the data with simulated \texttt{marx} data, we put an upper limit to the 2-10 keV X-ray luminosity of Cygnus A-2 of $1 \times 10^…
Cygnus X-1 is a binary star system that is comprised of a black hole and a massive giant companion star in a tight orbit. Building on our accurate distance measurement reported in the preceding paper, we first determine the radius of the companion star, thereby constraining the scale of the binary system. To obtain a full dynamical model of the binary, we use an extensive collection of optical photometric and spectroscopic data taken from the literature. By using all of the available observational constraints, we show that the orbit is slightly eccentric (both the radial velocity and photometr…
Black-hole binary (BHB) systems comprise a stellar-mass black hole and a closely orbiting companion star. Matter is transferred from the companion to the black hole, forming an accretion disk, corona and jet structures. The resulting release of gravitational energy leads to emission of X-rays. The radiation is affected by special/general relativistic effects, and can serve as a probe of the properties of the black hole and surrounding environment, if the accretion geometry is properly identified. Two competing models describe the disk-corona geometry for the hard spectral state of BHBs, based …
To date, there have been several detections of high-mass black hole binaries in both the Milky Way and other galaxies. For some of these, the spin parameter of the black hole has been estimated. As many of these systems are quite tight, a suggested origin of the spin is angular momentum imparted by the synchronous rotation of the black hole progenitor with its binary companion. Using Cygnus X-1, the best studied high-mass black hole binary, we investigate this possibility. We find that such an origin of the spin is not likely, and our results point rather to the spin being the result of proces…
The X-ray luminosity of black holes is produced through the accretion of material from their companion stars. Depending on the mass of the donor star, accretion of the material falling onto the black hole through the inner Lagrange point of the system or accretion by the strong stellar wind can occur. Cygnus X-1 is a high mass X-ray binary system, where the black hole is powered by accretion of the stellar wind of its supergiant companion star HDE226868. As the companion is close to filling its Roche lobe, the wind is not symmetric, but strongly focused towards the black hole. Chandra-HETGS ob…
We present the analysis of an extended \textit{INTEGRAL} dataset of the high-mass microquasar Cygnus X-1. We first classify, in a model-independent way, all the \textit{INTEGRAL} individual pointings taken between 2003 and 2016 in three basic spectral states. This, in particular, allows us to triple the exposure time of the soft state in comparison with previous publication. We then study the spectral properties of the 5--400 keV stacked spectra of the soft and hard states and provide the parameters obtained with our modelling. Using a refined alternative method of extracting the Compton doubl…
In general, it is very difficult to test the Kerr-nature of an astrophysical black hole candidate, because it is not possible to have independent measurements of both the spin parameter $a_*$ and possible deviations from the Kerr solution. Non-Kerr objects may indeed look like Kerr black holes with different spin. However, it is much more difficult to mimic an extremal Kerr black hole. The black hole candidate in Cygnus X-1 has the features of a near extremal Kerr black hole, and it is therefore a good object to test the Kerr black hole paradigm. The 3$σ$-bounds $a_* > 0.95$ and $a_* > 0.983$ …
Cygnus X-1 was the first X-ray source widely accepted to be a black hole candidate and remains among the most studied astronomical objects in its class. The detection of non-thermal radio, hard X-rays and gamma rays reveals the fact that this kind of objects are capable of accelerating particles up to very high energies. In order to explain the electromagnetic emission from Cygnus X-1 in the low-hard state we present a model of a black hole corona with both relativistic lepton and hadron content. We characterize the corona as a two-temperature hot plasma plus a mixed non-thermal population in …
We report the detection of a short-lived narrow quasi-periodic oscillation (QPO) at ~88 mHz in an Insight-HXMT observation during the soft state of the persistent black hole high mass X-ray binary Cygnus X-1. This QPO is significantly detected in all the three instruments of Insight-HXMT, so in the broad energy range 1-250 keV. The fractional rms of the QPO does not show significant variations above 3 keV (~5%) while decreases at lower energy (~2%). We show that this QPO is different from the type-A, -B, and -C QPOs usually observed in black hole X-ray binaries. We compare QPOs at similar freq…
Recent observations of the high-mass X-ray binary Cygnus X-1 have shown that both the companion star (41 solar masses) and the black hole (21 solar masses) are more massive than previously estimated. Furthermore, the black hole appears to be nearly maximally spinning. Here we present a possible formation channel for the Cygnus X-1 system that matches the observed system properties. In this formation channel, we find that the orbital parameters of Cygnus X-1, combined with the observed metallicity of the companion, imply a significant reduction in mass loss through winds relative to commonly us…
Astrophysical black holes are ideal laboratories for testing Einstein's theory of general relativity in the strong field regime. In this manuscript, we present an analysis of Suzaku and NuSTAR spectra of the black hole binary Cygnus X-1 using RELXILL_NK. Unlike our previous study on Cygnus X-1 with NuSTAR data, here we are able to constrain the Johannsen deformation parameter $α_{13}$. However, despite the high energy resolution near the iron line provided by Suzaku, our constraints on the Kerr metric from Cygnus X-1 are not very stringent in comparison with those that have been obtained from …
The knowledge of the spectral state of a black hole is essential for the interpretation of data from black holes in terms of their emission models. Based on pointed observations of Cyg X-1 with the Rossi X-ray timing Explorer (RXTE) that are used to classify simultaneous RXTE-ASM observations, we develop a scheme based on RXTE -ASM colors and count rates that can be used to classify all observations of this canonical black hole that were performed between 1996 and 2011. We show that a simple count rate criterion, as used previously, leads to a significantly higher fraction of misclassified obs…
We present the analysis of the broadened, flourescent iron Kalpha line in simultaneous XMM-Newton and RXTE data from the black hole Cygnus X-1. The XMM-Newton data were taken in a modified version of the timing mode of the EPIC-pn camera. In this mode the lower energy threshold of the instrument is increased to 2.8 keV to avoid telemetry drop outs due to the brightness of the source, while at the same time preserving the signal-to-noise ratio in the Fe Kalpha band. We find that the best-fit spectrum consists of the sum of an exponentially cut off power-law and relativistically smeared, ionized…
Recent observations of AdLIGO and Virgo have shown that the spin measurements in binary black hole (BH) systems are typically small, which is consistent with the predictions by the classical isolated binary evolution channel. In this standard formation channel, the progenitor of the first-born BH is assumed to have efficient angular momentum transport. The BH spins in high-mass X-ray binaries (HMXBs), however, have been found consistently to be extremely high. In order to explain the high BH spins, the inefficient angular momentum transport inside the BH progenitor is required. This requiremen…
The galactic black hole candidate Cygnus X-1, one of the brightest sources in the sky, is the first ever black hole candidate to be discovered. Despite being a very well-studied object due to its persistent brightness in X-rays, there has been much difficulty in determining its mass since its discovery. In spite of continuous efforts since the early nineteen seventies, there is yet no concensus on its mass for nearly four decades. The uncertainties in the mass measurements are due to the high degree of error involved in the measurement of its distance. In 2011, Orosz et al. constrained the mas…
Aims: Probe the high-energy ($>$60 MeV) emission from the black hole X-ray binary system, Cygnus X-1, and investigate its origin. Methods: We analysed 7.5 yr of data by Fermi/LAT with the latest PASS8 software version. Results: We report the detection of a signal at $\sim$8 $σ$ statistical significance spatially coincident with Cygnus X-1 and a luminosity above 60 MeV of 5.5$\times$10$^{33}$ erg s$^{-1}$. The signal is correlated with the hard X-ray flux: the source is observed at high energies only during the hard X-ray spectral state, when the source is known to display persistent, relativis…
The high-mass microquasar Cygnus X-1, the best-established candidate for a stellar-mass black hole in the Galaxy, has been detected in a flaring state at very high energies (VHE), E > 200 GeV, by the Atmospheric Cherenkov Telescope MAGIC. The flare occurred at orbital phase 0.91, where phase 1 is the configuration with the black hole behind the companion high-mass star, when the absorption of gamma-ray photons by photon-photon annihilation with the stellar field is expected to be highest. We aim to set up a model for the high-energy emission and absorption in Cyg X-1 that can explain the natur…
We present the first X-ray reverberation mass measurement of a stellar-mass black hole. Accreting stellar-mass and supermassive black holes display characteristic spectral features resulting from reprocessing of hard X-rays by the accretion disc, such as an Fe K$α$ line and a Compton hump. This emission probes of the innermost region of the accretion disc through general relativistic distortions to the line profile. However, these spectral distortions are insensitive to black hole mass, since they depend on disc geometry in units of gravitational radii. Measuring the reverberation lag resultin…
We present simultaneous multi-band radio and X-ray observations of the black hole X-ray binary Cygnus X-1, taken with the Karl G. Jansky Very Large Array and the Nuclear Spectroscopic Telescope Array. With these data, we detect clear flux variability consistent with emission from a variable compact jet. To probe how the variability signal propagates down the jet flow, we perform detailed timing analyses of our data. We find that the radio jet emission shows no significant power at Fourier frequencies $f\gtrsim0.03$ Hz (below $\sim30$ sec timescales), and that the higher frequency radio bands (…
The black hole binary Cygnus X-1 was observed in late-2012 with the Nuclear Spectroscopic Telescope Array (NuSTAR) and Suzaku, providing spectral coverage over the ~1-300 keV range. The source was in the soft state with a multi-temperature blackbody, power-law, and reflection components along with absorption from highly ionized material in the system. The high throughput of NuSTAR allows for a very high quality measurement of the complex iron line region as well as the rest of the reflection component. The iron line is clearly broadened and is well-described by a relativistic blurring model, p…
0.1-10 MeV observations of the black hole microquasar Cygnus X-1 have shown the presence of a spectral feature in the form of a power law in addition to the standard black body and Comptonization components observed by INTEGRAL. This so-called "high-energy tail" has recently been shown to be strong in its hard spectral state and interpreted as high-energy part of the emission from a compact jet. This result was, however, obtained from a data set dominated by hard state observations. In the soft state, only upper limits on the presence and hence the potential parameters of a high-energy tail co…
The compact primary in the X-ray binary Cygnus X-1 was the first black hole to be established via dynamical observations. We have recently determined accurate values for its mass and distance, and for the orbital inclination angle of the binary. Building on these results, which are based on our favored (asynchronous) dynamical model, we have measured the radius of the inner edge of the black hole's accretion disk by fitting its thermal continuum spectrum to a fully relativistic model of a thin accretion disk. Assuming that the spin axis of the black hole is aligned with the orbital angular mom…
We present a timing analysis of threeRossi X-ray Timing Explorer observations of the black hole binary Cygnus X-1 with the propagating mass accretion rate fluctuations model PROPFLUC. The model simultaneously predicts power spectra, time lags, and coherence of the variability as a function of energy. The observations cover the soft and the hard state of the source, and the transition between the two. We find good agreement between model pre-dictions and data in the hard and in the soft state. Our analysis suggests that in the soft state the fluctuations propagate in an optically thin hot flow …
We present a detailed study of the X-ray dust scattering halo of the black hole candidate \cygx1 based on two \chandra\ HETGS observations. Using 18 different dust models, including one modified by us (dubbed XLNW), we probe the interstellar medium between us and this source. A consistent description of the cloud properties along the line of sight that describes at the same time the halo radial profile, the halo lightcurves, and the column density from source spectroscopy is best achieved with a small subset of these models. Combining the studies of the halo radial profile and the halo lightcu…
We present a new analysis of NuSTAR and Suzaku observations of the black hole Cygnus X-1 in the intermediate state. The analysis uses kerrC, a new model for analyzing spectral and spectropolarimetric X-ray observations of black holes. kerrC builds on a large library of simulated black holes in X-ray binaries. The model accounts for the X-ray emission from a geometrically thin, optically thick accretion disk, the propagation of the X-rays through the curved black hole spacetime, the reflection off the accretion disk, and the Comptonization of photons in coronae of different 3-D shapes and physi…
We present observations of a transient He-like Fe K alpha absorption line in Suzaku observations of the black hole binary Cygnus X-1 on 2011 October 5 near superior conjunction during the high/soft state, which enable us to map the full evolution from the start and the end of the episodic accretion phenomena or dips for the first time. We model the X-ray spectra during the event and trace their evolution. The absorption line is rather weak in the first half of the observation, but instantly deepens for ~10 ks, and weakens thereafter. The overall change in equivalent width is a factor of ~3, pe…
Ultralight scalars, if they exist as theorized, could form clouds around rapidly rotating black holes. Such clouds are expected to emit continuous, quasimonochromatic gravitational waves that could be detected by LIGO and Virgo. Here we present results of a directed search for such signals from the Cygnus X-1 binary, using data from Advanced LIGO's second observing run. We find no evidence of gravitational waves in the 250-750 Hz band. Without incorporating existing measurements of the Cygnus X-1 black hole spin, our results disfavor boson masses in $6.4 \leq μ/(10^{-13} {\rm eV}) \leq 8.0$, a…
In Gou et al. (2011), we reported that the black hole primary in the X-ray binary Cygnus X-1 is a near-extreme Kerr black hole with a spin parameter a*>0.95(3σ). We confirm this result while setting a new and more stringent limit: a*>0.983 at the 3σ(99.7%) level of confidence. The earlier work, which was based on an analysis of all three useful spectra that were then available, was possibly biased by the presence in these spectra of a relatively strong Compton power-law component: The fraction of the thermal seed photons scattered into the power law was f_s=23-31%, while the upper limit for re…
The accretion onto the black hole in the system HDE 226868/Cygnus X-1 is powered by the strong line driven stellar wind of the O-type donor star. We study the X-ray properties of the stellar wind in the hard state of Cyg X-1 as determined with data from the Chandra High Energy Transmission Gratings. Large density and temperature inhomogeneities are present in the wind, with a fraction of the wind consisting of clumps of matter with higher density and lower temperature embedded in a photoionized gas. Absorption dips observed in the light curve are believed to be caused by these clumps. This wor…
We show that the jet power $P_j$ and geometrically corrected $γ$-ray luminosity $L_γ$ for the X-ray binaries (XRBs) Cygnus X-1, Cygnus X-3, and V404 Cygni, and $γ$-ray upper limits for GRS 1915+105 and GX339-4, follow the universal scaling for the energetics of relativistic jets from black hole (BH) systems found by Nemmen et al. (2012) for blazars and GRBs. The observed peak $γ$-ray luminosity for XRBs is geometrically corrected; and the minimum jet power is estimated from the peak flux density of radio flares and the flare rise time. The $L_γ-P_j$ correlation holds across $\sim 17$ orders of…
XRISM High-Resolution X-ray Spectroscopy of Cygnus X-1 -- Orbital and Short-Term Variability of Iron Absorption
Tokyo University of Science（东京科学大学）；Rikkyo University（立教大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；SRON Netherlands Institute for Space Research（荷兰空间研究所）；California Institute of Technology（加州理工学院）；University of Michigan（密歇根大学）；Massachusetts Institute of Technology（麻省理工学院）；Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA)（日本宇宙航空研究开发机构宇宙科学研究所）
Orbital variability has been found in the X-ray hardness of the black hole candidate Cygnus X-1 during the soft/high X-ray state using light curves provided by the Rossi X-ray Timing Explorer's All Sky Monitor. We are able to set broad limits on how the mass-loss rate and X-ray luminosity vary between the hard and soft states. The folded light curve shows diminished flux in the soft X-ray band at phase 0 (defined as the time of of the superior conjunction of the X-ray source). Models of the orbital variability provide slightly superior fits when the absorbing gas is concentrated in neutral clu…
We present an analysis of three Chandra High Energy Transmission Gratings observations of the black hole binary Cyg X-1/HDE 226868 at different orbital phases. The stellar wind that is powering the accretion in this system is characterized by temperature and density inhomogeneities including structures, or "clumps", of colder, more dense material embedded in the photoionized gas. As these clumps pass our line of sight, absorption dips appear in the light curve. We characterize the properties of the clumps through spectral changes during various dip stages. Comparing the silicon and sulfur abso…
State-Dependent X-ray Variability in Cygnus X-1: A 12-Year NuSTAR Timing Study of Accretion Flow Geometry
Boston University（波士顿大学）；Raman Research Institute（拉曼研究所）；Indian Institute of Science Education and Research Bhopal（印度科学教育与研究学院博帕尔分校）；Florida International University（佛罗里达国际大学）；Miami Dade College（迈阿密戴德学院）；Osmania University（奥斯曼尼亚大学）；Physical Research Laboratory（物理研究实验室）；UN Center for Space Science and Technology Education in Asia and Pacific (CSSTEAP)（联合国亚洲及太平洋空间技术和外空活动教育训练中心）；Sardar Vallabhbhai National Institute of Technology, Surat（萨达尔·瓦拉巴伊国立技术学院苏拉特分校）；Pondicherry University（本地治里大学）；School of Sciences, JAIN (Deemed-to-be University), Bengaluru（JAIN（视为大学）班加罗尔理学院）；Janusz Gil Institute of Astronomy, University of Zielona Góra（绿山大学扬努什·吉尔天文学研究所）
A black hole x-ray binary (XRB) system forms when gas is stripped from a normal star and accretes onto a black hole, which heats the gas sufficiently to emit x-rays. We report a polarimetric observation of the XRB Cygnus X-1 using the Imaging x-ray Polarimetry Explorer. The electric field position angle aligns with the outflowing jet, indicating that the jet is launched from the inner x-ray emitting region. The polarization degree is (4.01+-0.20)% at 2 to 8 kiloelectronvolts, implying that the accretion disk is viewed closer to edge-on than the binary orbit. The observations reveal that hot x-…
Using Suzaku and the Rossi X-ray Timing Explorer, we have conducted a series of four simultaneous observations of the galactic black hole candidate Cyg X-1 in what were historically faint and spectrally hard low states. Additionally, all of these observations occurred near superior conjunction with our line of sight to the X-ray source passing through the dense phases of the focused wind from the mass donating secondary. One of our observations was also simultaneous with observations by the Chandra-High Energy Transmission Grating. These latter spectra are crucial for revealing the ionized abs…
Binary black holes as the recently detected sources of gravitational waves can be formed from massive stellar binaries in the field or by dynamical interactions in clusters of high stellar density, if the black holes are the remnants of massive stars that collapsed without natal kicks that would disrupt the binary system or eject the black holes from the cluster before binary black hole formation. Here are summarized and discussed the kinematics in three dimensions of space of five Galactic black hole X-ray binaries. For Cygnus X-1 and GRS 1915+105 it is found that the black holes of ~15 and ~…
Although General Relativity had provided the physical basis of black holes, evidence for their existence had to await the Space Era when X-ray observations first directed the attention of astronomers to the unusual binary stars Cygnus X-1 and A0620-00. Subsequently, a number of faint Ariel 5 and Uhuru sources, mainly at high Galactic latitude, were found to lie close to bright Seyfert galaxies,suggesting the nuclear activity in AGN might also be driven by accretion in the strong gravity of a black hole. Detection of rapid X-ray variability with EXOSAT later confirmed that the accreting object …
Binary systems with an accreting compact object are a unique chance to investigate the strong, clumpy, line-driven winds of early type supergiants by using the compact object's X-rays to probe the wind structure. We analyze the two-component wind of HDE 226868, the O9.7Iab giant companion of the black hole Cyg X-1 using 4.77 Ms of RXTE observations of the system taken over the course of 16 years. Absorption changes strongly over the 5.6 d binary orbit, but also shows a large scatter at a given orbital phase, especially at superior conjunction. The orbital variability is most prominent when the…
We address the problem where the X-ray emission lines are formed and investigate orbital dynamics using Chandra HETG observations, photoionizing calculations and numerical wind-particle simulations.The observed Si XIV (6.185 A) and S XVI (4.733 A) line profiles at four orbital phases were fitted with P Cygni-type profiles consisting of an emission and a blue-shifted absorption component. In the models, the emission originates in the photoionized wind of the WR companion illuminated by a hybrid source: the X-ray radiation of the compact star and the photospheric EUV-radiation from the WR star. …
In this review, I have tried to focus on the development of the field, from the first speculations to the current lines of research. According to Einstein's theory of general relativity, black holes are relatively simple objects and completely characterized by their mass, spin angular momentum, and electric charge, but the latter can be ignored in the case of astrophysical macroscopic objects. Search for black holes in the sky started in the early 1970s with the dynamical measurement of the mass of the compact object in Cygnus X-1. In the past 10-15 years, astronomers have developed some techn…
Light speed is assumed as a constant in Einstein's general relativity theory. In this paper, the polarized light from black hole Cygnus X-1 is found fit well with Cherenkov radiation generated by Faster Than Light movement in vacuum under gravity. Thus, proved the gravitational lens is a real existence, the refractive index of space did increase with the gravity field, and light speed is changeable with gravitational potential energy. Possible experiments to double verify the theory on the earth is discussed. A new way to find more advanced alien civilizations in lower gravitational potential …
