Insight-HXMT observations of jet-like corona in a black hole X-ray binary MAXI J1820+070
Bei You, Yuoli Tuo, Chengzhe Li, Wei Wang, Shuang-Nan Zhang, Shu Zhang, Mingyu Ge, Chong Luo, Bifang Liu, Weimin Yuan, Zigao Dai, Jifeng Liu, Erlin Qiao, Chichuan Jin, Zhu Liu, Bozena Czerny, Qingwen Wu, Qingcui Bu, Ce Cai, Xuelei Cao, Zhi Chang, Gang Chen, Li Chen, Tianxiang Chen, Yibao Chen, Yong Chen, Yupeng Chen, Wei Cui, Weiwei Cui, Jingkang Deng, Yongwei Dong, Yuanyuan Du, Minxue Fu, Guanhua Gao, He Gao, Min Gao, Yudong Gu, Ju Guan, Chengcheng Guo, Dawei Han, Yue Huang, Jia Huo, Shumei Jia, Luhua Jiang, Weichun Jiang, Jing Jin, Yongjie Jin, Lingda Kong, Bing Li, Chengkui Li, Gang Li, Maoshun Li, Tipei Li, Wei Li, Xian Li, Xiaobo Li, Xufang Li, Yanguo Li, Zhengwei Li, Xiaohua Liang, Jinyuan Liao, Congzhan Liu, Guoqing Liu, Hongwei Liu, Xiaojing Liu, Yinong Liu, Bo Lu, Fangjun Lu, Xuefeng Lu, Qi Luo, Tao Luo, Xiang Ma, Bin Meng, Yi Nang, Jianyin Nie, Ge Ou, Jinlu Qu, Na Sai, Rencheng Shang, Liming Song, Xinying Song, Liang Sun, Ying Tan, Lian Tao, Chen Wang, Guofeng Wang, Juan Wang, Lingjun Wang, Wenshuai Wang, Yusa Wang, Xiangyang Wen, Baiyang Wu, Bobing Wu, Mei Wu, Guangcheng Xiao, Shuo Xiao, Shaolin Xiong, Yupeng Xu, Jiawei Yang, Sheng Yang, et al. (26 additional authors not shown)
IInsight-HXMT observations of jet-like corona in ablack hole X-ray binary MAXI J1820+070
Bei You , Yuoli Tuo , Chengzhe Li , Wei Wang , Shuang-Nan Zhang , Shu Zhang ,Mingyu Ge , Chong Luo , Bifang Liu , Weimin Yuan , Zigao Dai , Jifeng Liu , ErlinQiao , Chichuan Jin , Zhu Liu , Bozena Czerny , Qingwen Wu , Qingcui Bu , CeCai , Xuelei Cao , Zhi Chang , Gang Chen , Li Chen , Tianxiang Chen , Yibao Chen ,Yong Chen , Yupeng Chen , Wei Cui , Weiwei Cui , Jingkang Deng , Yongwei Dong ,Yuanyuan Du , Minxue Fu , Guanhua Gao , He Gao , Min Gao , Yudong Gu , JuGuan , Chengcheng Guo , Dawei Han , Yue Huang , Jia Huo , Shumei Jia , LuhuaJiang , Weichun Jiang , Jing Jin , Yongjie Jin , Lingda Kong , Bing Li , Chengkui Li ,Gang Li , Maoshun Li , Tipei Li , Wei Li , Xian Li , Xiaobo Li , Xufang Li , Yanguo Li ,Zhengwei Li , Xiaohua Liang , Jinyuan Liao , Congzhan Liu , Guoqing Liu , HongweiLiu , Xiaojing Liu , Yinong Liu , Bo Lu , Fangjun Lu , Xuefeng Lu , Qi Luo , Tao Luo ,Xiang Ma , Bin Meng , Yi Nang , Jianyin Nie , Ge Ou , Jinlu Qu , Na Sai , RenchengShang , Liming Song , Xinying Song , Liang Sun , Ying Tan , Lian Tao , ChenWang , Guofeng Wang , Juan Wang , Lingjun WANG , Wenshuai Wang , Yusa Wang ,Xiangyang Wen , Baiyang Wu , Bobing Wu , Mei Wu , Guangcheng Xiao , ShuoXiao , Shaolin Xiong , Yupeng Xu , Jiawei Yang , Sheng Yang , Yanji Yang , QibinYi , Qianqing Yin , Yuan You , Aimei Zhang , Chengmo Zhang , Fan Zhang ,Hongmei Zhang , Juan Zhang , Tong Zhang , Wanchang Zhang , Wei Zhang , WenzhaoZhang , Yi Zhang , Yifei Zhang , Yongjie Zhang , Yue Zhang , Zhao Zhang , ZiliangZhang , Haisheng Zhao , Xiaofan Zhao , Shijie Zheng , Dengke Zhou , JianfengZhou , Yuxuan Zhu , and Yue Zhu School of Physics and Technology, Wuhan University, Wuhan 430072, People’s Republic of China; Email:[email protected] Astronomical Center, Wuhan University, Wuhan 430072, People’s Republic of China Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing100049, People’s Republic of China University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, People’s Republic ofChina Key Laboratory of Space Astronomy and Technology, Chinese Academy of Sciences, Beijing 100012, China a r X i v : . [ a s t r o - ph . H E ] F e b School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road,Beijing, 100049, People’s Republic of China School of Astronomy and Space Science, Nanjing University, Nanjing 210023, People’s Republic of China Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing100101, China WHU-NAOC Joint Center for Astronomy, Wuhan University, Wuhan, Hubei 430072, China Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China Tuebingen University Department of Astronomy, Beijing Normal University, Beijing 100088, People’s Republic of China Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China Department of Astronomy, Tsinghua University, Beijing 100084, People’s Republic of China Department of Engineering Physics, Tsinghua University, Beijing 100084, People’s Republic of China Computing Division, Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing100049,People’s Republic of China School of Physics and Optoelectronics, Xiangtan University, Yuhu District, Xiangtan, Hunan, 411105, China College of Physics, Jilin University, No.2699 Qianjin Street, Changchun City, 130012, China * Corresponding authors; Email: [email protected], [email protected]
A black hole X-ray binary produces hard X-ray radiation from its corona and disk when the accretingmatter heats up. During an outburst, the disk and corona co-evolves with each other. However, such anevolution is still unclear in both its geometry and dynamics. Here we report the unusual decrease ofthe reflection fraction in MAXI J1820+070, which is the ratio of the coronal intensity illuminating the diskto the coronal intensity reaching the observer, as the corona is observed to contrast during the decayphase. We postulate a jet-like corona model, in which the corona can be understood as a standing shockwhere the material flowing through. In this dynamical scenario, the decrease of the reflection fractionis a signature of the corona’s bulk velocity. Our findings suggest that as the corona is observed to getcloser to the black hole, the coronal material might be outflowing faster. ntroduction During an outburst, a black hole (BH) X-ray binary usually displays transition between hard and softstates, according to the spectral properties of its radiation . In the hard state, usually defined as thephoton index Γ < Γ >
2, the observed radiation then is characterized by astrong (disk) blackbody component below ∼
10 keV and a weak, high-energy tail of ∼
25% of the totalbolometric luminosity
2, 5–8 . MAXI J1820+070 (ASASSN-18ey) is a low-mass black hole X-ray binary,newly discovered in X-rays with MAXI on 2018 March 11 . In addition to X-ray, the source has alsobeen observed in optical and in radio
16, 17 . Low-frequency quasi-periodic oscillations (LFQPOs)were found in both X-ray and optical bands . The measurement of the radio parallax indicates thatthis source is located at a distance of 2 . ± .
33 kpc away from us . Follow-up X-ray observationssince its outburst were carried out by other X-ray telescopes, e.g., Swift , NuSTAR , and NICER .The long-term and high cadence observation of MAXI J1820+070 by Hard X-ray Modulation Telescope(called as Insight-HXMT) was carried from 2018-03-14 (MJD 58191) to 2018-10-21 (MJD 58412) .Figure 1 shows the Insight-HXMT HE (red) / ME (blue) / LE (green) light curves (Figure 1a) and hardnessintensity diagram (Figure 1b) during the whole observations, displaying two outbursts. In the first outburst,MAXI J1820+070 rapidly rose from 2018-03-14 (MJD 58191) to 2018-03-23 (MJD 58200), and thengradually decayed until 2018-06-17 (MJD 58286). During this first burst, the source was in the hard statewith the observed radiation being dominated by the high energy photons ( >
20 keV; purple points inFigure 1b). The second outburst started on 2018-06-19 (MJD 58288), with HE counts rising again to thepeak on MJD 2018-07-01 (MJD 58300). After then, the source started to decay again until 2018-10-21(MJD 58412). In this decay, the source mainly stayed in the soft state in which the LE photon ratesdominated over ME/HE photon rates. The same Insight-HXMT observations have been used recentlyto study the timing properties of the outburst and LFQPOs were discovered above 200 keV, which wasinterpreted as due to the precession of a twisted compact X-ray jet .Spectral and timing analysis of MAXI J1820+070 from MJD 58198 to MJD 58250 based on NICER eported that the profile of broad Fe K emission line was almost unchanged, indicating the inner diskis very close to the black hole (about 2 R g , where R g = GM / c is the gravitational radius) and keepsconstant . Moreover, the thermal reverberation (soft) lags evolved to higher frequencies. Given theseobservational properties, it is suggested that it may be the corona that evolves during the outburst ofthis source, rather than the inner accretion disk, i.e., the corona might be contracting with time . Thedetection energy band of NICER is 0.5-12 keV. However, the reflection component dominates over theX-ray spectra around 20-50 keV. The spectral fitting at this energy range could put crucial constraint onthe reflection parameters , e.g., the reflection fraction and reflection strength, which can be used to probethe inner geometry of the accretion flow . Moreover, the high energy cutoff of the X-ray spectrum can beused to measure the electron temperature which is the important physical parameter to study the evolutionof the accretion flow in the hard state. Insight-HXMT observes the broad-band X-rays from 1-250 keV,which enables us to probe the evolution of the accretion flow in detail by spectral and timing analysis. Inthis paper, we aim to reveal how the physical properties of accretion flow (corona+disk) evolve with time,mainly concentrating on the period when the radiation is dominated by high energy photons most likelyfrom the corona, by fitting the Insight-HXMT spectrum.In this work, we show the evolution of the accretion flow in the hard state when the emission isdominated by high energy photons from the corona, by analysing the observations of the first outburst ofMAXI J1820+070 with Insight-HXMT. The derived reflection fraction R f is found to increase with time inthe rise phase and decrease with time in the decay phase. In the scenario of a dynamical corona, this maysuggest that as the corona contracts, i.e., the dissipation region gets closer to the black hole, the coronalmaterial might be outflowing faster. Results
We found that all spectra of MAXI J1820+070 in the first outburst can be approximately characterizedby an asymptotic power law with cutoff at high energy ≤
100 keV. The broad continuum is thought tooriginate from the thermal Comptonization of the seed photons from the accretion disk by the hot plasma(hereafter corona) near the black hole. Moreover, our preliminary spectral analysis to those spectra withthe simple cut-off powerlaw clearly reveals the line features at about 3-10 keV and the hump above 20 keV, ith respect to the thermal Comptonization (see Fig. 2 and qualitative spectral analysis section in methods).These features may be related to the illumination to the accretion disk. The Comptonized photons whichilluminate the disk are reprocessed within the disk and then reflected off to the observer, resulting inthe reflection with the characteristic iron line and hump features . Therefore, we applied relxillCp toaccount for the reflection model, which is the standard reflection model taking the relativistic effect intoaccount. This reflection model contains both the direct emission from the corona and its reflection on thedisk, which will be used in this work as the basic spectral model to fit the spectra of MAXI J1820+070 inthe first outburst. The parameter settings of the relxillCp model is given in configuration of the spectralfitting model section in methods. relxillCp allows to fit the broad iron K α emission line around 3-10 keV. However, in the residuals, wedetect a clear narrow core to the iron emission ( ∼ andNuSTAR data . This narrow component may also originate from the reflection, but due to photoionizationof neutral material or at least colder gas further from BH. So we additionally include another non-relativistic reflection model xillverCp to account for this narrow line component. Moreover, we include diskbb to account for the accretion disk radiation at low energy ( ∼ tbabs toaccounts for the low galactic extinction of N H ∼ . × cm − . Therefore, the fitting modeling tbabs ∗ ( diskbb + relxillCp + xillverCp ) ∗ constant (1)is applied in the spectral fits.The spectra of 70 epochs, from March 14, 2018 (MJD 58191) to June 17, 2018 (MJD 58286), arefitted with the model described above. The best-fitting results are obtained by implementing a MarkovChain Monte-Carlo (MCMC) algorithm, and all spectra can be fitted well with the reduced χ < . ∼
230 to 50 keV in the rise phase, and starts to lowly increase to ≤
100 keV in the decay phase. This tendency is in agreement with the results based onthe combined spectra of MAXI/GSC and Swift/BAT
37, 38 .Moreover, the best-fitting reflection fraction R f of the X-ray point source steeply increases up to about0.5 in the rise phase and then slowly decreases to about 0.1 in the decay phase. In the reflection model, relxillCp , the reflection fraction is defined as the ratio of the coronal intensity that illuminates the disk tothe coronal intensity that reaches the observer. The reflection fraction as well as some other parameters,e.g., ionization parameters, iron abundance and the emissivity profile, have impacts on the shape of thereflection spectrum. This means that, the increasing fraction of photons from the X-ray source illuminatethe disk in the rise phase while the decreasing fraction of photons from the X-ray source illuminatethe disk in the decay phase. In the hard state of GX 339-4, the reflection fraction is also found to bepositively correlated with the source luminosity . Assuming the X-ray source to be point-like staticlamppost, the height of the X-ray point source can uniquely correspond to the reflection fraction , giventhe configuration of model parameters, i.e., black hole spin, inner/outer radius of the disk. In this case, inthe decay phase, the decrease in the reflection fraction corresponds to the increases of the height.However, the spatial extent of the corona which was estimated by the timing analysis of NICERdata covering the early decay studied in this work, decreases or contracts with time . It was previouslydiscussed that the corona above the disk could be effectively ejected away from the accretion disk by thepressure of the reflected radiation, if the Comptonizing source is dominated by e ± pairs . This scenariohas successfully explained both the weakness of the reflection with the reflection fraction R f < . Γ ∼ .
6, in active galactic nuclei and X-ray binaries. Whenthe corona, if being assumed as the point-like lamppost for simplicity, is accelerated outflowing awayfrom the black hole, the beaming effect will reduce the illuminating flux towards the accretion disk, whichreduces the reflection fraction. In general, the lamppost geometry should be interpreted as a jet base,possibly a standing shock which determines the corona position, but with material flowing throughthe standing shock. So the system should be characterized by two independent parameters: its positionand bulk velocity. The corona position and its evolution with time could be constrained by the timinganalysis . In addition to that, the bulk velocity and its evolution with time can be constrained by thespectral analysis. In order to investigate the effect of the bulk motion of the corona on the reflection raction, we calculate the reflection fraction by applying the package relxilllpionCp of relxill(v1.4.0), withthe X-ray point source being located at height H above a black hole and outflowing with the velocity β = υ / c . The light bending effect is taken into account. In Fig. 4, we plot the reflection fraction R f asa function of height H and the bulk motion velocity β . It can be seen that, the reflection increases asthe height decreases, as we expect in the normal lamppost model. In the mean time, for a given height,the reflection fraction gets smaller if the outflowing velocity increases. During the decaying phase ofMAXI J1820+070 between MJD 58200 and 58286, X-ray timing analysis suggested the contracting ofthe corona with decreasing height , which should enhance the reflection fraction in the static lamppostmodel. However, the broad-band X-ray spectral results suggest that the reflection fraction decreases withtime. Considering the effect of the bulk motion of the corona on the reflection fraction, the timing andspectral properties could be self-consistently explained in the scenario of the outflowing corona.When the corona contracts towards black hole, the decrease in the height will enhance the reflectionfraction. However, the bulk motion of the corona could significantly reduce the reflection. If the bulkmotion effect could dominate over the contracting effect, the contracting corona with the increasing speedof the outflow can explain both the shortening of the time-lag of the X-ray emission observed by NICERand the weakening of the reflection component observed by Insight-HXMT, although the mechanism ofthe contracting/acceleration of the corona is still unknown. For clarity, we also plot the schematic of theevolution of the corona with time in Fig. 5.The corona in the lamppost geometry, should be interpreted as a jet base, possibly a standing shock ,and was discussed in a number of previous studies of AGN and black hole X-ray binary in the low/hardstate ; this probably provides a physical interpretation to the compact X-ray jet revealed by the timinganalysis of the same Insight-HXMT data used here . The evolution of the outflowing corona shouldbe studied in terms of both its position and bulk velocity, which can help us to better understand theacceleration/deceleration of the particles near a black hole. The X-ray temporal/timing analysis canprovide us the spatial information of the relative geometry of the corona. The broad band spectral fittingswhich derived variations of the reflection fraction, help to probe the dynamical properties of the corona,i.e., if the corona is outflowing/inflowing. Therefore, this work discovered that the corona outflows fasteras it contracts towards to black hole, suggesting that the hard X-ray emission region in the jet base or tanding shock is formed at closer distance to the black hole for faster outflow. This scenario could beapplied to other black hole X-ray binaries and AGNs in which the coronas are active, at least to diagnoseif the outflowing/inflowing corona is accelerating or decelerating. Discussion
On the evolution of the spectral parameters
In the relxillCp model, the emissivity profile is assumed to be broken powerlaw of two indexes q and q with the break radius R br . In our spectral fits, for simplicity, we assume the index q = R > R br . The emissivity profile is roughly flattened with the index q < . R br ∼ − R ISCO (where R ISCO ∼ . R g for a = . (e.g., theirFig. 10 and 12), the flattened emissivity profiles suggest that the X-ray corona source might be spatiallyextended with the size of tens of R g in radius. The emissivity profile for a point source is predicted to bemuch steeper with the index q ∼ − R < R g ) before the profile flattens off(where R < R br ). Such a twice-broken power law profile was observed in the narrow-line Seyfert 1 galaxy1H 0707-495 by fitting the relativistically broadened emission lines from the disk . The derived smallindex with q < relxillCp uses a singlebroken-powerlaw, so the index q is the emissivity-weighted value for the region R < R br ; (2) the index q and the inner radius are somewhat degenerated with each other. On one hand, if the emissivity profile fallssteeply with the index q ∼ −
8, then in order to reproduce the flux levels emitted from the innermostregions, the disk must be truncated at a larger radius. On the other hand, if the emissivity profile is flat withsmaller index q <
1, then the disk can extend to the innermost regions with a smaller truncation radius, tomatch the flux levels . In our spectral fits, the inner radius is assumed to be small with R in = R ISCO , forsimplicity. If we assume R in = R g instead and refit the spectra, the emissivity profiles then are requiredto be steep with the index q ∼ − relxillCp is smaller than unity, which requires the spatially extended coronato be relativistically outflowing to overcome the increasingly important light-bending effect, since thecorona is suggested to be contracting from NICER lag-observations . Since the reflection fractiondecreases along with the decay, the corona may be outflowing faster as it contracts over the time. The ime evolution of the ionization parameter log ξ , the abundance A Fe with respect to the solar value, theconstant for ME and the constant for HE are plotted in Supplementary Figure 2. For these parameters,the correlations with respect to each other are also investigated with the Spearman’s rank test, which areplotted in Supplementary Figure 3. The probabilities of null correlation between the reflection fractionand other three parameters ( A Fe , Const ME , Const HE ) are 7.5 × − , 0.02, and 0.02, respectively. The twoconstant factors of ME/HE do not show obvious evolution over the epochs, and the reflection fraction isuncorrelated with the constants of ME/HE. Together with the fact that there is no degeneracy between thereflection fraction and these factors, we conclude that the trend of the reflection fraction reported in thiswork is unlikely associated with the constant factors of ME/HE.The best-fitting values of the iron abundance are high with A Fe ≥
5, and the fits prefer changing iniron abundance which roughly increases along with the decay, resulting in an apparent correction withthe reflection fraction with the p-value of 7.5 × − . Such supersolar abundances also appear in thespectral fitting of other black hole X-ray binaries, e.g., GX 339-4 and Cyg X-1 . It was suggested thatthe derived supersolar abundances are not physical, but may be caused by the limitation of the assumeddensity in the reflection model
46, 47 . Both the density and the iron abundance of the accretion disk haveimpacts on the emergent reflection spectrum. As the density increases, the rise in free-free absorptionleads to an increase in temperature, causing extra thermal emission at soft X-ray energy E <
10 keV .This effect could become significant when the density is high ( n e > cm − ) (see Fig. 7 in ref ),although it was emphasized that the microphysics in the current reflection models is only known to beaccurate up to n e = cm − (see the reference for more details). The effect of the abundance on thereflection spectrum is studied, using the relxillCp model. The increase in the iron abundance from A Fe = A Fe =
10, will also cause the increase in the soft X-ray emission of the reflection for the highly ionizeddisk in the hard state (see Supplementary Figure 4a), mimicking the effect of the disk density increase.Therefore, the soft X-ray emission could be reproduced by either high density or high abundance in theaccretion disk
46, 47 . It was shown that, the high density model with the solar value of iron abundance, orthe low density model with supersolar abundance, could both fit the NuSTAR spectra of Cygnus X-1 . Inthe current reflection model relxillCp which is used in this work, the constant density is fixed at constantvalue n e = cm − , which is much lower than the typical values in the standard thin disk model , e ≥ cm − . Along with the decay of the outburst studied in this work, the radiation pressure in theinner disk should decrease and thus the gas density should increase
46, 49 . Therefore, the spectral fits withthe much lower and constant density in the reflection model should lead to artificially supersolar and alsoincreasing iron abundance along with the outburst decay, consistent with the spectral fitting results in thiswork. Deriving the physical values and evolution of the iron abundance and disk density with the spectralfitting, however, requires new atomic data in high-density to be implemented in the reflection model,which is beyond the scope of this work. Nonetheless, in order to demonstrate that the observed trend of thereflection fraction is physical and independent of the expected artificial correlation between the reflectionfraction and the iron abundance, we tried the case of the constant iron abundance, e.g., A Fe = .
0. In thiscase, the reflection fraction still decreases along with the outburst decay (see Supplementary Figure 4b),although fixing A Fe is not supported by F-test, due to the problems we discussed above.The best-fitting values of the ionization parameter are high with log ξ ≥ .
8. The ionization parameter isdefined as the ratio of the illuminating flux and the electron number density ( n e = cm − ). Accordingto this definition, changing the ionization parameter will not only redistribute the reflected photonsover energy (i.e., reshaping the X-ray spectroscopy), but also the number of the reflected photons (i.e.,increasing/decreasing the spectrum flux). Therefore, in the current relxill model, the reflection spectrum isnormalized to the constant illuminating flux F = ξ n e / π where ξ = − , and the illuminatingflux (which takes the reflection fraction into account) from the nthcomp is normalized to this constantilluminating flux. Then, the total spectrum can be simply calculated by combining the reflection spectrumwith the nthcomp spectrum. After normalizing the spectrum in the relxill model, the ionization parameteris not proportional to the illuminating flux
29, 32 . In photoionization modelling of the relxill model, it isassumed that log ξ completely characterizes the X-ray spectroscopy, regardless of the actual values ofdensity or flux . Therefore, the highly ionized disk in Supplementary Figure 2a is not in conflict with theweak illuminating flux, although the faster outflowing corona provides a weaker illuminating flux. Highlyionized disk for low flux at 3-78 keV was also found in the NuSTAR spectrum of MAXI J1820+070 .Instead, the large values of the ionization parameter is possibly caused by the over-estimateed ironabundance as discussed above. The 0.01-10 keV flux would be reduced due to the increase of thecontinuum opacity, as the iron abundance increases to account for the deficiency of the constant density in he reflection model . In order to compensate for this effect in the spectral fits, the degree of the ionizationin the disk would increase. This is because in the case of high ionization, the illumination continuumwill not be highly absorbed by the photoelectric opacity, which leads to the relatively strong reflectioncontinuum in 0.01-10 keV.The broad component of the iron line visually appears stable throughout the decay, while the strength ofthe narrow core decreases with time, which is consistent with the observations of NICER and NuSTAR
28, 33 .The broadening/narrowing of the broad iron line can also be quantitatively evaluated with the equivalentwidth (EW), a measure of the relative strength of the line profile. The formula of calculating the EW ofthe iron line (including narrow component) is as follows:EW = (cid:90) E max E min F ( E ) − F c ( E ) F c ( E ) dE , (2)where F ( E ) is the total flux and F c ( E ) is the total flux of the continuum under the line. E max and E min are the upper and lower energy band limits of the integration, respectively. F ( E ) is taken from thebest-fitting model spectrum, and the continuum F c ( E ) is approximated by a powerlaw connecting E max and E min32 . Here, we take E min = E max = 10 keV, with the assumption that the iron line takesplace in this region. Note that the simplification of the powerlaw continuum and the particular choiceof integration limits are somewhat arbitrary, mainly considering the decomposition of the best-fittingspectrum (see Supplementary Figure 1) and the ratio plot (see Fig. 2). In Supplementary Figure 5a, weplot the time-evolution of the iron line EW from the best-fitting spectral model ( relxillCp + xillverCp ). Itturns out that the iron line EW is roughly stable with ∼
200 eV during the first half of the decay (coveringthe epochs of NICER in ref ), while there is some scatter.Furthermore, as we discussed above, the X-ray spectroscopy (including the relative strength of the ironline) by relxillCp does not depend on the actual illuminating flux, EW then is insensitive to the reflectionfraction. As discussed above, the broad Fe K α line appears stable throughout the decay, while the relativestrength of the narrow core decreases with time. In order to understand the evolution of the the X-rayspectroscopy of Fig. 2 in terms of the reflection models, in Supplementary Figure 5b and 5c, we plotthe time-evolution of EW from the best-fitting model spectrum of relxillCp , and the normalization of illverCp . It shows that the constant broad iron line can be maintained by the evolution of relxillCp . Theweakening of the narrow line as well as that decrease in the amplitude of the hump are attributed to thedecrease in the normalization of xillverCp .Supplementary Figure 6 plots the time evolution of the diskbb parameters, i.e., the temperature at innerdisk radius T in in units of keV, the normalization and the diskbb flux in units of erg/cm /s. The disk innertemperature increases from 0.4 keV to 0.6 keV during the decay, although there is significant degeneracybetween the inner temperature and the normalization of diskbb . We note that, the seed photon temperature kT bb in relxillCp is fixed at 0.05 keV, which is much lower than the best-fitting values of T in . In order tostudy the effect of kT bb on the results, we freeze kT bb = 0.5 keV. It turns out that the difference in kT bb does not have a strong effect on other parameters. We use cflux in XSPEC to estimate the diskbb flux in0.01 - 100.0 keV and its time-evolution. We found that the disk flux increases with time until around MJD= 58250, and then evidently decreases until the end of the decay. In our spectral model, the inner radius ofthe accretion disk is assumed to be constant at ISCO. We note that the inner radius can be derived from the diskbb parameters, e.g., GX 339-4 and XTE J1550-564 . In ref , the inner radius was estimated withthe photon flux of the direct disk component and the Comptonized disk component, taking into accountthe Comptonized disk photons. In this work, we also estimate the disk inner radius from the spectral fits.Although the observed Comptonization and the reflection flux can be fitted with the reflection model, it ishard to determine the Comptonized disk flux, which depends on the geometry of the corona with respectto the disk. Therefore, we introduce a constant factor λ which is multiplied by the direct disk flux F d toestimate the Comptonized disk flux F c , i.e., F c = λ F d . Then, the inner radius can be calculated as follows(see the Appendix in ref , F d + F c = ( + λ ) F d = . × r cos i ( D /
10 kpc ) × ( T in ) photons s − cm − , (3)where the source distance D = .
96 kpc, i = ◦ are adopted from the observational measurements , andthe direct disk flux in 0.01-100 keV (in units of photons s − cm − ) from diskbb is obtained with the flux command in XSPEC. In Supplementary Figure 6d, we plot the derived R in (in units of R g , assuming BHmass M = M (cid:12) ) along with time, for the case of λ =
0. It can be seen that, if only considering the irect disk flux, the inner radius of the disk is indeed very close to ISCO of BH. And if the Comptonizeddisk flux is comparable or dominates over the direct disk flux, i.e., λ = R in shouldbe enlarged by a factor of ∼ diskbb is trickybecause of strong coupling with the inner disc temperature and the absorption column, and the estimateof the inner radius from diskbb also depends on the boundary condition and the color hardening factor.These may contribute to the uncertainty on the estimate of the inner radius. In ref , the inner radius is oneof the free parameters affecting the shape of the reflection spectrum (not from the disk parameter), whichis fitted to the NuSTAR spectra of MAXI J1820+070.During the decay of MAXI J1820+070, the Comptonization component is softened with the increaseof the photon index, as the reflection fraction decreases with time. Considering the primary X-ray sourceas the blob of the plasma, the photon index of the Comptonized radiation emerging from the blob isdetermined by the Compton amplification factor “ A ” (which is defined as the ratio between the blobluminosity and the disk seed luminosity intercepted by the blob) taken in the plasma’s comoving frame .Moreover, it was shown in ref that this amplification factor depends on not only the blob outflowingvelocity β (as we discussed in this work) but also the geometrical factor µ s of the blob (see their Figure.1). The geometrical factor µ s describes the relative geometry of the blob with respect to the disk, with µ s = µ s = . µ s corresponds to the increasingly strengtheneddisk flux intercepted by the blob. In the decay of MAXI J1820+070, the corona contracts with time ,i.e., the corona getting closer to the disk, strengthening the intercepted disk flux by the corona with thedecrease of the geometrical factor µ s . Therefore, on one hand, the Compton amplification factor candecrease due to the decrease of µ s , leading to the increase of the photon index (see Equation. 10 in ref );on the other hand, the Compton amplification factor can increase due to the increase of the outflowingvelocity β , leading to the decrease of the photon index (see Supplementary Figure 7b). In the decay ofMAXI J1820+070, if the effect of the geometrical factor dominates over that of the outflowing velocity,the resultant photon index will increase, as found in our spectral fitting. n the effect of system parameters In our spectral fits, the black hole spin is fixed at a = . R in = R ISCO , providedthat the inner radius R ISCO is fitted to be around 5 R g over the decay . Spectral fits to NICER data ofMAXI J1820+070 in the soft state suggests a low spin a < . ). In order to study the effect of thelow spin on the evolution of the corona, we refit six observations which cover the decay of this outburstwith the same model, but fixing the spin a = .
5. It turns that the evolution of the corona remains (seeSupplementary Figure 8a), i.e., the reflection fraction is also smaller than unity, and decreases with thedecay, which requires the relativistic outflowing motion of the corona.The inclination is fixed to the constant value θ = ◦ based on the jet/optical measurements. However,the inner disc/jet/orbital plane do not necessarily align. In order to study the constraint of spectral fits onthe inclination and its effect on the evolution of the corona, we refit six observations which covers thedecay of this outburst with the same model, but allowing the inclination to be free. It turns that, the spectralfits with the standard relativistic reflection model relxillCp also prefers to large values of the inclination,and the evolution of the corona remains (see Supplementary Figure 8b and 8c), i.e., the reflection fractionis also small than unity and decreases during the decay phase. Justification of the outflowing corona
Recently, the outflowing velocity of the lamppost X-ray primary source is taken into account in the packagerelxilllpionCp of relxill(v1.4.0). In principle, we could refit the Insight-HXMT data to directly infer theoutflowing velocity and its evolution over time. We found that the outflowing velocity and the heightcannot be uniquely determined in the spectral fits. Therefore, deriving the evolution of the outflowingvelocity may require that the height of the corona can be estimated from other measurements. e.,g., timinganalysis. However, this is difficult to achieve due to the following two facts: (1) the effective area of LEdetector in Insight-HXMT is one order of magnitude smaller than that of NICER, so that the derivedtime-lags in low energy band is not precise enough; (2) converting the lag into a light travel time distancebetween the corona and the accretion disk is not straightforward. A number of effects, e.g., the geometryof the system, the viewing angle to this source and relativistic Shapiro delay, etc, have to be well studied efore the reliable measurement of the light travel time can be derived . Nonetheless, we could fix theheight of the lamppost X-ray source at constant value, e.g., H = R g , and refit the spectra during the decayto directly infer the outflowing velocity and its evolution over time. It is shown in Supplementary Figure7a that the outflowing velocity indeed increases from ∼ c to ∼ c along with time, resulting in thedecrease of the reflection fraction.Moreover, we simulate the energy spectra for NuSTAR observation, as a function of the lamppostheight and outflowing velocity, using the reflection model relxilllpionCp which takes the outflowing of thecorona into account. The EW of these simulated
NuSTAR spectra is then estimated, which turns out tobe fairly constant (see Supplementary Figure 9). Given the simulation results in Supplementary Figure4a and 9, it can be seen that the EW of the iron line depends on not only the height and the outflowingvelocity of the lamppost but also the iron abundance and ionization of the reflection disk . Comparison to NuSTAR spectral analysis
NuSTAR spectra of MAXI J1820+070 in the decay were reported and analysed in ref. . The two lamppostpoint sources ( relxilllpCp ) with different heights, as the reflection model, were used in their spectral fits. Itwas shown that, during the decay, the height of the lower point source remains constant at about ∼ R g ,while the height of the upper point source decreases from 100 R g to a few R g . We also used the twolampposts model to fit Insight-HXMT spectra, and found that the derived height of the upper lamppostdecreases with the decay as well, which is consistent with the results of NuSTAR. Note that, in relxilllp(Cp) and relxilllpion(Cp) , the disk outer radius cannot exceed 1000 R g . Therefore, when the corona is high,e.g., H > R g , a fraction of photons will not hit the disk, which results in the reflection fraction beinglower than unity. This should be distinguished from the case of the corona being relativistically outflowingat low height H < R g . In the latter case, the reflection fraction will also be small with R f <
1, but nowit is due to the beaming effect of the relativistically outflowing motion.However, in the lamppost model relxilllpCp , the corona is assumed to be stationary. The conversionfrom height to reflection fraction is not self-consistent between the stationary corona model ( relxilllpCp )and the moving corona model ( relxilllpionCp ), since the corona discussed in this work might be movingat different heights, along with the evolution of the outburst. Taking the spectrum of the later epoch MJD , we found that, both the stationary corona with the height H ∼ R g using relxilllpCp ,and the outflowing corona at different heights (e.g., H ∼ R g , v ∼ . c ; H ∼ R g , v ∼ . c ) using relxilllpionCp , can provide the equivalently good fits to the data. In the former case, the reflection fractionis high R f = .
3, while in the later case, the reflection fraction is low R f ∼ .
6. These comparison studiesabove confirm that the decrease of the height alone cannot explain the observed reflection evolution, whichalso requires the outflowing corona reported in this work.Meanwhile, in the case of an outflowing corona (relxilllpionCp), the height and the outflowing velocitycannot be uniquely determined from the spectral fits, as discussed above. Nonetheless, at later epoch ofthe outburst (e.g., MJD =58271), the corresponding reflection fractions are roughly the same R f ∼ .
6, andthe fitted velocity is moderate with v ∼ . c . In contrast, at the peak of the outburst, e.g., MJD =58204(obsID = P0114661006), the fitted reflection fraction is R f = .
2, and the corona prefers to be stationary,using relxilllpionCp model. Therefore, although it is not easy to uniquely determine the height and theoutflowing velocity, the resultant reflection fraction decreases during the decay, which is consistent withour results in the spectral fits of Insight-HXMT using relxillCp .Here, we also directly fit the reflection fraction from the spectral fits to NuSTAR data with the relxillCp + xillverCp model, as is done for Insight-HXMT in this work. The inclination angle is fixed at constantlarge value θ = ◦ . The two diskbb components are used to account for the differences between FPMsdue to a thermal blanket tear in FPMA . It turns out that the the reflection model which consists of therelativistic reflection relxillCp and non-relativistic reflection xillverCp can also fit the NuSTAR spectrawell with reduced χ ≤ .
1, and the best-fitting values of the parameters are given in SupplementaryTables 1, 2 and 3. The index of emissivity profile q are pegged at zero. This also suggests that the coronais spatially extended, as seen in Insight-HXMT fits. More importantly, the reflection fraction turns out todecrease with the decay from 0.8 to 0.3 (see Supplementary Figure 10), which has the same trends withthe Insight-HXMT results in this work (see Fig. 3). ethods Data reduction
Insight-HXMT consists of three groups of instruments: High Energy X-ray Telescope (HE, 20-250 keV),Medium Energy X-ray Telescope (ME, 5-30 keV), and Low Energy X-ray Telescope (LE, 1-15 keV).HE contains 18 cylindrical NaI(Tl) / CsI(Na) phoswich detectors with a total detection area of 5000 cm ;ME is composed of 1728 Si-PIN detectors with a total detection area of 952 cm ; and LE uses SweptCharge Device (SCD) with a total detection area of 384 cm . There are three types of Field of View (FoV):1 ◦ × ◦ (FWHM, full-width half maximum) (also called the small FoV), 6 ◦ × ◦ (large FoV), and theblind FoV used to estimate the particle induced instrumental background (see or The Insight-HXMTData Reduction Guide for details). Since its launch, Insight-HXMT went through a series of performanceverification tests by observing blank sky, standard sources and sources of interest. These tests showedthat the entire satellite works smoothly and healthily, and have allowed for the calibration and estimationof the instruments background. The systematic errors of LE are less than 1% at 1–7 keV except the SiK-edge at 1.839 keV. The response model of the energy band 7-10 keV of LE is well calibrated basedon more information of background lines of the detectors; For ME and HE, more accurate backgroundmodels with HXMTDAS (v2.02, which will be public soon) are utilized and the effective area is updated.The systematic errors for ME 20-30 keV are relatively smaller. Fluorescence lines due to the photoelectriceffect of electrons in Silver K-shell are detected by the Si-PIN detectors of ME, which dominates thespectrum over 21-24 keV. Therefore, the spectrum over 21-24 keV is ignored; The systematic errors ofHE, compared to the model of the Crab nebular, are less than 2% at 28-120 keV and 2%-10% above 120keV. According to these calibration results, the energy bands for the spectral fits in this work are 2-10 keVfor LE, 10-30 keV for ME, and 28-200 keV for HE, with a systematic error of 1.5% for LE/ME/HE.We use the Insight-HXMT Data Analysis software (HXMTDAS) v2.0 to analyze all the data, filteringthe data with the following criteria: (1) pointing offset angle < . ◦ ; (2) pointing direction above Earth > ◦ ; (3) geomagnetic cut-off rigidity value >
8; (4) time since SAA passage >
300 s and time to nextSAA passage >
300 s; (5) for LE observations, pointing direction above bright Earth > ◦ . We onlyselect events that belong to the small FoV for LE and ME observations, and for HE we use the events from oth small and large FoV. To improve the signal-to-noise ratio of HE observation, we combine 17 spectraobtained from 15 small FoV and 2 large FoV together using addascaspec script in HEAsoft v6.8. Thecorresponding background spectra and response files are also combined together. Qualitative spectral analysis
The spectra are analyzed using XSPEC version 12.10.0 . In Fig. 2, we plot the ratio of the unfoldedInsight-HXMT spectrum of MAXI J1820+070 to the best-fitting cutoff powerlaw ( cutoffpl in XSPEC)over 2-200 keV, for 2018-03-23 (MJD 58201), 2018-4-25 (MJD 58233), 2018-05-31 (MJD 58269),corresponding to the early, middle and late times of the decay, respectively. There is an increase in fluxat low energies ( ∼ α emission line and a narrow component at around 6.4 keV. The broad component of the iron linevisually appears stable throughout the decay, while the relative strength of the narrow core reduces withtime. This is consistent with what is observed in ref
28, 33 . The hump at 20 - 100 keV is clearly seen in theratio plot. The broad iron K α emission line and the hump indicate the presence of relativistic reflection,as expected from an accretion disc extending close to a black hole . It is found that the amplitude ofthis hump drops along with the decay, while the broad iron line keeps fairly constant. This suggests that,the distant reflection component, which accounts for the narrow Fe K line and contributes to parts of theobserved Compton hump, decreases in the normalization along with the decay. We will discuss this furtherin Supplementary Figure 5. Configuration of the spectral fitting model
In this work, we applied the relativistic model relxillCp which accounts for the reflection with thebroad/high-ionization iron line and the non-relativistic model xillverCp which accounts for the reflectionwith the narrow/low-ionization iron line, to fit Insight-HXMT spectra. For both models, we use thesame nthcomp parameters as the incident spectrum inputs, and the seed photon temperature is fixed at kT bb = .
05 keV. The inner radius, which is derived by fitting the NICER spectra with the relativisticreflection model, is estimated to be less than 2 R g under some assumptions . It was also suggested thatthere is little or no evolution in the truncation radius of the inner disk during the luminous hard state, giventhat the thermal reverberation lags remain throughout all epochs and that the spectral shape of the broad Fe ine component is constant over time. In ref , the inner radius is fitted to be around 5 R g over the decay. Ifassuming the black hole spin a = . R in = R ISCO (cid:39) R g ,where R ISCO is the innermost stable circular orbit, this may imply that the black hole spin is low. Also, fitsto the spectra of NICER in the soft state suggests a low spin . Indeed, fixing R in , spin and inclination atdifferent values, will result in different values for other free parameters, but the time-dependent trends inthe fitted parameters will be preserved. Since in this work we are mainly concerned with the evolution ofthe corona, we assume the black hole spin a = . R in = R ISCO .The effect of the low spin on the evolution of the corona will be discussed below. The outer radius of thereflection disk is fixed at the upper limit of their table model R out = R g .The strong absorption dips were detected by NICER in the outburst of MAXI J1820+070, suggestingthat this source is a high-inclination system
24, 37 . The observed sharp increase in the H α emission lineequivalent width and the absence of X-ray eclipses in MAXI J1820+070 in ref indicated the inclinationangle to be 69 ◦ < i < ◦ . The measurement of the radio parallax indicates that this source is located at adistance of 2 . ± .
33 kpc away from us. Together with the measured proper motions of the approachingand receding jet ejecta in radio, the inclination angle between the jet and the line of sight is estimated to be63 ◦ (see ref ). In this work, we take the inclination angle as 63 ◦ . The free parameters of the relativisticreflection model relxillCp are the emissivity profile q , the reflection fraction R f , the incident photonindex Γ , the Fe abundance relative to the solar value A Fe , the ionization parameter log ξ , and the electrontemperature kT e . The emissivity profile is parameterised in terms of the index q , q and the broken radius R br . For simplicity, the index of the outer disk region is fixed with q = .
0. The index of the innerdisk region q and the broken radius R br are free parameters. As for the non-relativistic reflection model, xillverCp , the spectral fits are insensitive to the ionization parameter, which is evaluated with F-test inXSPEC. Therefore, the ionization parameter are fixed at low value with log ξ = .
0, while the only freeparameter is the normalization. pectral fitting method
The statistical analysis of all the fits are achieved by implementing a Markov Chain Monte-Carlo (MCMC)algorithm. More specifically, we used the MCMC algorithm implemented in XSPEC to create a chain ofparameter values whose density gives the probability distribution for that parameter. For each individualspectrum fitting, two chains of 250000 steps are run with 20 walkers. The first 10 steps of the runningare discarded as burn-in phase. Convergence between these two chains is assessed by Gelman-Rubindiagnostic , which requires | R − | < .
01. The analysis of the probability distributions derived fromthe MCMC chains is implemented using the corner package , to estimate the mean values and errors ofmodel parameters.Supplementary Figure 11 shows an illustration of one and two dimensional projections of the posteriorprobability distributions derived from the MCMC analysis for the parameters in relxillCp , i.e., theemissivity profile q , the photon index Γ , the ionization parameter log ξ , the abundance A Fe with respectto the solar value, the electron temperature kT e , the reflection fraction R f , the normalization, the constantfor ME and the constant for HE. The contours in the two dimensional projections for each set of twoparameters correspond to 1-, 2- and 3- σ confidence interval. The vertical lines in the one dimensionalprojections correspond to the lower, median and upper value of each parameter. The MCMC analysisshown in this figure is produced using the corner package . This illustration corresponds to the spectralfitting (see Supplementary Figure 1) of MJD 58204 (ObsID = P0114661006). Data availability statement
All Insight-HXMT data used in this work are publicly available and can be downloaded from the officialwebsite of Insight-HXMT: http://hxmtweb.ihep.ac.cn/
Code availability
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BY thanks J. Garc´ıa and T. Dauser for helping with the reflection model relxill , and thanks Z. Yan, X.G.Zheng and S.X. Tian for the discussion of the spectral fitting. This work is supported by the NationalProgram on Key Research and Development Project (Grants No. 2016YFA0400803) and the NSFC(11903024, U1931203, 11622326, U1838103, U1838201, and U1838202). This work made use of thedata from the Insight-HXMT mission, a project funded by China National Space Administration (CNSA)and the Chinese Academy of Sciences (CAS).
Author contributions statement
BY, YLT, CZL, WW, SNZ, SZ, CL contributed to spectral analysis and interpretation of results. MYGcontributed to the calibration of Insight-HXMT data. BFL, WMY, ZGD, JFL, ELQ, CCJ, ZL, BCcontributed to interpretation of results. BY, WW and SNZ wrote the paper. TPL is the previous PI(2000-2015) and SNZ is the current PI of Insight-HXMT. QWW, QCB, CC, XLC, ZC, GC, LC, TXC,YBC, YC, YPC, WC, WWC, JKD, YWD, YYD, MXF, GHG, HG, MG, YDG, JG, CCG, DWH, YH, JH,SMJ, LHJ, WCJ, JJ, YJJ, LDK, BL, CKL, GL, MSL, TPL, WL, XL, XBL, XFL, YGL, ZWL, XHL, JYL,CZL, GQL, HWL, XJL, YNL, BL, FJL, XFL, QL, TL, XM, BM, YN, JYN, GO, JLQ, NS, RCS, LMS,XYS, LS, YT, LT, CW, GFW, JW, LJW, WSW, YSW, XYW, BYW, BW, MW, GCX, SX, SLX, YPX,JWY, SY, YJY, QBY, QQY, YY, AMZ, CMZ, FZ, HMZ, JZ, TZ, WCZ, WZ, WZZ, YZ, YFZ, YJZ, YZ,ZZ, ZLZ, HSZ, XFZ, SJZ, DKZ, JFZ, YXZ, YZ contributed to the development and scientific operationof Insight-HXMT. Correspondence should be addressed to Wei Wang ([email protected]) andShuang-Nan Zhang ([email protected]).
Competing interests
The authors declare no competing interests. igure 1.
Insight-HXMT light curves and hardness-intensity diagram. a Insight-HXMT lightcurves (in units of counts per second) of MAXI J1820+070 in HE (red, 20-250 keV), ME (blue, 5-30 keV)and LE (green, 1-15 keV) band. b The Insight-HXMT hardness-intensity diagram, defined as the total2-10 keV count rate (in units of counts per second) versus the ratio of hard (4-10 keV) to soft (2–4 keV)count rates. The purple dots represent the first outburst from MJD 58192 to MJD 58286, which are fittedin this work. b Figure 2.
Ratio of the spectrum to the best-fitting cutoff powerlaw. a Ratio of the spectrum of threeepochs to the best-fitting cutoff powerlaw ( cutoffpl in XSPEC) in 2-200 keV. Time runs from top tobottom, corresponding to the early, middle and late echo of this decay, i.e., 2018-03-23 (MJD =58201,ObsID = P0114661003), 2018-4-25 (MJD = 58233, ObsID = P0114661028), 2018-05-31 (MJD =58269, ObsID = P0114661060). b Ratio of the spectrum of the same epochs to the best-fitting powerlawin 3-10 keV. The vertical dashed line indicates the rest energy (6.4 keV) of the iron line. Fluorescencelines due to the photoelectric effect of electrons in K-shell of silver are detected by the Si-PIN detectors ofME, which dominates the spectrum over 21-24 keV. Therefore, the spectrum over 21-24 keV is ignored. bcd
Time(MJD)
Figure 3.
Time-evolutions of the free parameters in the best-fitting of the spectral model (1) . Theevolution of the dimensionless reflection fraction R f which is defined as the ratio of intensity emittedtowards the disk to that emitted to infinity, the dimensionless index q of the emissivity profile, theelectron temperature T e in units of keV, and the incident photon index Γ , are plotted in subpanels (a), (b),(c), and (d), respectively. Assuming an inclination angle θ = ◦ , the inner/outer radius of the reflectiondisk R in = R ISCO ( R ISCO is innermost stable circular orbit) and R out = R g , the black hole spin a = . corner package to analyse the probabilitydistributions derived from the MCMC chains. The uncertainties of the fitted parameters arise from boththe statistical and systematic uncertainties. .0 0.1 0.2 0.3 0.4 0.5 [ v / c ] H [ R g ] R f = 1.0 Figure 4.
The dependence of the reflection fraction on the corona height and the bulk velocity .The dimensionless reflection fraction R f , is estimated as a function of the corona height H (in units of R g )and the bulk velocity β = υ / c . The dashed line correspond to the reflection fraction R f = 1.0. The colorbar represents the dimensionless reflection fraction, with the minimum and maximum being 0.1 and 6.4,respectively. isk + outflowing corona evolve with timeBlack Hole Accretion Disk Corona Figure 5.
Schematic of the proposed jet-like corona in the decay phase, in which the corona can beunderstood as a standing shock where the material flowing through. The Comptonized hard photons fromthe corona illuminates the accretion disk, resulting in the observed reflection component. As the coronacontracts towards black hole with decreasing height, the fitted reflection fraction decreases, whichsuggests that the bulk motion of the outflowing coronal material gets faster in the deeper gravitationalpotential well. The animation is available: http://youbei.work/research/. upplementary Figure 1.
Unfolded Insight-HXMT spectrum obtained on March 27, 2018 (MJD 58204,ObsID=P0114661006) with the best-fitting of
TBabs ∗ ( diskbb + relxillCp + xillverCp ) ∗ constant model(top) and the data/model ratio (bottom). The spectrum consists of the data from LE (green), ME (blue)and HE (red) spectrum. The black dashed line is the best-fit spectrum, which is decomposed into thediskbb (orange), the Comptonization (dashed line in purple) and the reflection (dashed line in cyan) fromthe relxillCp component, and the reflection (dot-dashed line in cyan) from the xillverCp component. Thesource of uncertainties in Supplementary Figure 1b arises from the statistical uncertainties. abcd Supplementary Figure 2.
Time-evolutions of the ionization parameter log ( ξ ) (in units of erg cm s − ),the iron abundance with respect to the solar value A Fe , the constant factor of ME instrument and theconstant factor of HE instrument, are plotted from top to bottom panel, respectively. The black pointscorrespond to the median of the values and the error bars correspond to 68% confidence interval, which iscalculated using the corner package to analyse the probability distributions derived from the MCMCchains. The uncertainties of the fitted parameters arise from both the statistical and systematicuncertainties. ab ce fd Supplementary Figure 3.
The correlations of the reflection fraction of the relxillCp , the iron abundance A Fe with respect to the solar abundance value, the constant factor of ME instrument and the constantfactor of HE instrument, with respect to each other, which are investigated with the Spearman’s rank test.The black points correspond to the median of the values and the error bars correspond to 68% confidenceinterval, which is calculated using the corner package to analyse the probability distributions derivedfrom the MCMC chains. The uncertainties of the fitted parameters arise from both the statistical andsystematic uncertainties. a b Energy(keV)
Time(MJD) E ⋅ F E ( k e V / c m / s ) R f Supplementary Figure 4. (a):
Relativistic reflection models in the HXMT bandpass using the relxillCp for the iron abundance A Fe = 1.0, 5.0 and 10.0, in the case of the incident photon index Γ = . ξ = . (b): The best-fitting values of the reflection fraction R f , with theidentical configuration of the fitting model in Fig. 3 of the main text, except fixing the iron abundance A Fe =
5. The black points correspond to the median of the values and the error bars correspond to 68%confidence interval, which is calculated using the corner package to analyse the probabilitydistributions derived from the MCMC chains. The uncertainties of the fitted parameters arise from boththe statistical and systematic uncertainties. abc E W ( k e V ) E W ( k e V ) N o r m Time(MJD)
Supplementary Figure 5. (a):
Time-evolutions of Equivalent width (in units of keV) of the broad Fe K α line which is measured from the total model spectrum ( relxillCp + xillverCp ) in 4-10 keV; (b): Time-evolutions of Equivalent width of the broad Fe K α line which is measured from the model spectrumof the relxillCp component; (c): Time-evolutions of the normalization of the xillverCp component. Theblack points correspond to the median of the values and the error bars correspond to 68% confidenceinterval, which is calculated using the corner package to analyse the probability distributions derivedfrom the MCMC chains. The uncertainties of the fitted parameters arise from both the statistical andsystematic uncertainties. abcd T i n ( k e V ) N o r m ( d i s k ) F l u x ( d i s k ) R i n ( R g ) Time(MJD)
Supplementary Figure 6.
Time-evolutions of the diskbb parameters, as plotted from top to bottom: thetemperature at inner disk radius T in in units of keV, the normalization, the diskbb flux in units of erg/cm /s,and the inner radius of the disk estimated from the diskbb photon flux. The black points in (a) and (b) ,correspond to the median of the values and the error bars correspond to 68% confidence interval, which iscalculated using the corner package to analyse the probability distributions derived from the MCMCchains. The uncertainties of the fitted parameters arise from both the statistical and systematicuncertainties. a b β [ v / c ] Γ Time(MJD) A β [ v / c ] Supplementary Figure 7. (a):
The outflowing velocities of the lamppost X-ray source in the best-fittingof
TBabs ∗ ( diskbb + relxilllpionCp + xillverCp ) ∗ constant model. The new model relxilllpionCp (attributing to the reflection with the broad iron line) includes a velocity of the lamppost X-ray sourcewhich is set to be free here, and the height of the lamppost X-ray source is fixed at H = R g . Assuming aninclination angle θ = ◦ , the inner/outer radius of the reflection disk R in = R ISCO ( R ISCO is innermoststable circular orbit) and R out = R g , the black hole spin a = . corner package to analyse the probability distributions derived from the MCMC chains. Theuncertainties of the fitted parameters arise from both the statistical and systematic uncertainties. (b): Thegeometrical factors µ s -dependent Compton amplification factor A and the photon index Γ , as a function ofoutflowing velocity β = v / c , are plotted in red and blue line, respectively. Time(MJD) R f Time(MJD) R f θ a Supplementary Figure 8. (a):
The reflection fraction for six epochs in the best-fitting of
TBabs ∗ ( diskbb + relxillCp + xillverCp ) ∗ constant model, but the black hole spin a = .
5. Assuming aninclination angle θ = ◦ . The reflection fraction (b) and the inclination angle (c) for six epochs in thebest-fitting of TBabs ∗ ( diskbb + relxillCp + xillverCp ) ∗ constant model, where the inclination angle(degree) is a free parameter, but the spin is fixed at a = . R in = R ISCO ( R ISCO is innermost stable circular orbit) and R out = R g . The black pointscorrespond to the median of the values and the error bars correspond to 68% confidence interval, which iscalculated using the corner package to analyse the probability distributions derived from the MCMCchains. The uncertainties of the fitted parameters arise from both the statistical and systematicuncertainties. The observation ID of six epochs are listed as follows: ObsID = P0114661006,P0114661017, P0114661024, P0114661032, P0114661043, P0114661055. .0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9[ v / c ]345678910 H [ R g ] EW = 0.2 keV (keV)0.010.10.20.30.40.50.60.70.80.91.0
Supplementary Figure 9.
Equivalent width (EW), in units of keV, as a function of the outflowing velocty( β = v / c ) and the height, of the lower lamppost, while fixing the photon index Γ = .
55. The EW iscalculated with Equation (1), intergrating the reflection model spectrum by relxilllpionCp in 4-10 keV.The dashed line corresponds to the constant EW = 0.2 keV. The color bar represents the values of EW inunits of keV, with the minimum and maximum being 0.01 and 1.0, respectively. R f Supplementary Figure 10.
The evolution of the reflection fractions of the relativistic reflection model relxillCp , which are estimated from the fits of NuSTAR spectrum. The numbers at lower right cornercorrespond to the obsID in Table 1 of ref. . Note that, the first point (i.e., obsID = 02) is at the rise ofMAXI 1820+070. For completeness, we still add it together with the rest points which roughlycorrespond to the decay of the outburst (see Fig. 1 of ref ). The data points correspond to the median ofthe values and the error bars correspond to 68% confidence interval, which is calculated using the corner package to analyse the probability distributions derived from the MCMC chains. Theuncertainties of the fitted parameters arise from both the statistical and systematic uncertainties. .06 +0.520.65 . . . . . (a1) +0.010.01 . . . . l o g (a2) (b1) +0.040.05 . . . . . A F e (a3) (b2) (c1) +0.220.25 k T e (a4) (b3) (c2) (d1) +2.021.47 . . . . . R f (a5) (b4) (c3) (d2) (e1) +0.030.02 . . . . N r e l x ill C p (a6) (b5) (c4) (d3) (e2) (f1) +0.000.00 . . . . C o n s t a n t ( M E ) (a7) (b6) (c5) (d4) (e3) (f2) (g1) +0.010.01 . . . . q . . . . . C o n s t a n t ( H E ) (a8) .
552 1 .
560 1 .
568 1 .
576 1 . (b7) .
85 3 .
90 3 .
95 4 . log (c6) . . . . . A Fe (d5)
51 54 57 60 63 kT e (e4) .
24 0 .
28 0 .
32 0 .
36 0 . R f (f3) .
084 0 .
090 0 .
096 0 . N relxillCp (g2) .
020 1 .
035 1 .
050 1 . Constant(ME) (h1) .
04 1 .
06 1 .
08 1 .
10 1 . Constant(HE)1.08 +0.010.01
Supplementary Figure 11.
An illustration of one and two dimensional projections of the posteriorprobability distributions derived from the MCMC analysis for the parameters in relxillCp , i.e., theemissivity profile q , the photon index Γ , the ionization parameter log ξ (in units of erg cm s − ), theabundance A Fe with respect to the solar value, the electron temeperature kT e (in units of keV), thereflection fraction R f , the normalization, the constant for ME and the constant for HE. The contours in thetwo dimensional projections (the second to the bottom panel of each column) for each two parameterscorrespond to 1-, 2- and 3- σ confidence interval. The top nine panels (a1-i1) in each column are their onedimensional projections on the corresponding x axis. The values above each one dimensional projectionindicate the median value of each parameter, as well as the upper and lower limits of the 68% confidenceintervals. The vertical lines in the one dimensional projections correspond to the lower, median and uppervalue of each parameters. The MCMC analysis and the resultant figures above are produced using thecorner package . This illustration corresponds to the spectral fitting (see Fig. 1) of MJD 58204 (ObsID =P0114661006). omponent Model Parameter OBSID02 04 06 08Soft flux DISKBB
Norm
FPMA . + . − . . + . − . . + . − . . + . − . kT FPMA /keV 1 . + . − . . + . − . . + . − . . + . − . DISKBB
Norm
FPMB . + . − . . + . − . . + . − . . + . − . kT FPMB /keV 1 . + . − . . + . − . . + . − . . + . − . Comptoncontinuum
NTHCOMP Γ FPMA , B . + . − . . + . − . . + . − . . + . − . kT FPMA , B /keV 55 + − + − + − + − Disc
RELXILL C P R in / r ISCO . ∗ . ∗ . ∗ . ∗ θ / ◦ ∗ ∗ ∗ ∗ A Fe / A Fe , (cid:12) . + . − . . + . − . . + . − . . + . − . Reflection
RELXILL C P R f . + . − . . + . − . . + . − . . + . − . log ( ξ / erg cm s − ) . + . − . . + . − . . + . − . . + . − . XILLVER C P R f − ∗ − ∗ − ∗ − ∗ log ( ξ / erg cm s − ) . ∗ . ∗ . ∗ . ∗ RELXILL C P Norm
FPMA , B . + . − . . + . − . . + . − . . + . − . XILLVER C P Norm
FPMA , B . + . − . . + . − . . + . − . . + . − . χ / d . o . f . .
11 1 .
13 1 .
09 1 . Supplementary Table 1.
Best-fitting values to the NuSTAR spectra of MAXI J1820+070 in the hardstate. The obsIDs: 904013090NN, correspond to the ones in Table. 1 of ref . The model is TBabs ∗ (diskbb+relxillCp+xillverCp) ∗ constant . The asterisk indicates the parameters are fixed. Theindex of emissivity profile q are pegged at zero, which are consistent with the spectral fits of HXMT.Errors represent 68% confidence intervals. omponent Model Parameter OBSID10 12 13 14Soft flux DISKBB
Norm
FPMA . + . − . . + . − . . + . − . . + . − . kT FPMA /keV 0 . + . − . . + . − . . + . − . . + . − . DISKBB
Norm
FPMB . + . − . . + . − . . + . − . . + . − . kT FPMB /keV 0 . + . − . . + . − . . + . − . . + . − . Comptoncontinuum
NTHCOMP Γ FPMA , B . + . − . . + . − . . + . − . . + . − . kT FPMA , B /keV 60 + − + − + − + − Disc
RELXILL C P R in / r ISCO . ∗ . ∗ . ∗ . ∗ θ / ◦ ∗ ∗ ∗ ∗ A Fe / A Fe , (cid:12) . + . − . . + . − . . + . − . . + . − . Reflection
RELXILL C P R f . + . − . . + . − . . + . − . . + . − . log ( ξ / erg cm s − ) . + . − . . + . − . . + . − . . + . − . XILLVER C P R f − ∗ − ∗ − ∗ − ∗ log ( ξ / erg cm s − ) . ∗ . ∗ . ∗ . ∗ RELXILL C P Norm
FPMA , B . + . − . . + . − . . + . − . . + . − . XILLVER C P Norm
FPMA , B . + . − . . + . − . . + . − . . + . − . χ / d . o . f . .
12 1 .
36 1 .
12 1 . Supplementary Table 2.
Best-fitting values to the NuSTAR spectra of MAXI J1820+070 in the hardstate. The obsIDs: 904013090NN, correspond to the ones in Table. 1 of ref . The model is TBabs ∗ (diskbb+relxillCp+xillverCp) ∗ constant . The asterisk indicates the parameters are fixed. Theindex of emissivity profile q are pegged at zero, which are consistent with the spectral fits of HXMT.Errors represent 68% confidence intervals. omponent Model Parameter OBSID16 18 19Soft flux DISKBB
Norm
FPMA . + . − . . + . − . . + . − . kT FPMA /keV 0 . + . − . . + . − . . + . − . DISKBB
Norm
FPMB . + . − . . + . − . . + . − . kT FPMB /keV 0 . + . − . . + . − . . + . − . Comptoncontinuum
NTHCOMP Γ FPMA , B . + . − . . + . − . . + . − . kT FPMA , B /keV 151 + − + − + − Disc
RELXILL C P R in / r ISCO . ∗ . ∗ . ∗ θ / ◦ ∗ ∗ ∗ A Fe / A Fe , (cid:12) . + . − . . + . − . . + . − . Reflection
RELXILL C P R f . + . − . . + . − . . + . − . log ( ξ / erg cm s − ) . + . − . . + . − . . + . − . XILLVER C P R f − ∗ − ∗ − ∗ log ( ξ / erg cm s − ) . ∗ . ∗ . ∗ RELXILL C P Norm
FPMA , B . + . − . . + . − . . + . − . XILLVER C P Norm
FPMA , B . + . − . . + . − . . + . − . χ / d . o . f . .
17 1 .
17 1 . Supplementary Table 3.
Best-fitting values to the NuSTAR spectra of MAXI J1820+070 in the hardstate. The obsIDs: 904013090NN, correspond to the ones in Table. 1 of ref . The model is TBabs ∗ (diskbb+relxillCp+xillverCp) ∗ constant . The asterisk indicates the parameters are fixed. Theindex of emissivity profile q are pegged at zero, which are consistent with the spectral fits of HXMT.Errors represent 68% confidence intervals.are pegged at zero, which are consistent with the spectral fits of HXMT.Errors represent 68% confidence intervals.