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# Discovery of oscillations above 200 keV in a black hole X-ray binary with Insight-HXMT

## Abstract

Low-frequency quasiperiodic oscillations (LFQPOs) are commonly found in black hole X-ray binaries, and their origin is still under debate. The properties of LFQPOs at high energies (above 30 keV) are closely related to the nature of the accretion flow in the innermost regions, and thus play a crucial role in critically testing various theoretical models. The Hard X-ray Modulation Telescope is capable of detecting emissions above 30 keV, and is therefore an ideal instrument to do so. Here we report the discovery of LFQPOs above 200 keV in the new black hole MAXI J1820+070 in the X-ray hard state, which allows us to understand the behaviours of LFQPOs at hundreds of kiloelectronvolts. The phase lag of the LFQPO is constant around zero below 30 keV, and becomes a soft lag (that is, the high-energy photons arrive first) above 30 keV. The soft lag gradually increases with energy and reaches ~0.9 s in the 150–200 keV band. The detection at energies above 200 keV, the large soft lag and the energy-related behaviours of the LFQPO pose a great challenge for most existing models, but suggest that the LFQPO probably originates from the precession of a small-scale jet.

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## Data availability

The data that support the plots within this paper and other findings of this study are publicly available for download from the Insight-HXMT website (http://www.hxmt.cn/ or http://hxmt.org/).

## Code availability

The Insight-HXMT data reduction was performed using software available from the Insight-HXMT website (http://www.hxmt.cn/ or http://hxmt.org/). The model fitting of power spectra was completed with XSPEC, which is available from the HEASARC website (https://heasarc.gsfc.nasa.gov/xanadu/xspec/). The phase lag was performed with Stingray (see https://stingray.readthedocs.io/en/latest/index.html).

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## Acknowledgements

We thank A. Ingram, K. Karpouzas and M. Mendez for useful suggestions. This work made use of the data from the Insight-HXMT mission, a project funded by the China National Space Administration (CNSA) and the Chinese Academy of Sciences (CAS). The Insight-HXMT team acknowledges support from the National Program on Key Research and Development Project (grant no. 2016YFA0400800) from the Ministry of Science and Technology of China (MOST) and the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB23040400). The authors thank the National Natural Science Foundation of China for support under grant nos. U1838111, U1838115, U1838201, U1838202, 11473027, 11633006, 11673023 and 11733009, the National Key Research and Development Program of China (grant no. 2016YFA0400704) and the Royal Society Newton Funds.

## Author information

Authors

### Contributions

X.M., L.T., S.-N.Z., L.Z., Q.-C.B., M.-Y.G. and J.-L.Q. were involved in the analysis. S.-N.Z., L.T., J.-L.Q., F.Y. and F.-G.X. contributed to the theoretical discussions. The manuscript was produced by L.T., S.-N.Z., X.M., L.Z., Q.-C.B., J.-L.Q., M.-Y.G., S.Z., F.-J.L., L.-M.S. and Y.-J.Y. The PI of the Insight-HXMT mission is S.-N.Z. All other authors contributed to the development of the mission concept and/or construction and testing of Insight-HXMT.

### Corresponding authors

Correspondence to Lian Tao or Shuang-Nan Zhang.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Light curve, hardness ratio, LFQPO’s frequency, Q factor and fractional rms of MAXI J1820+070 in the X-ray hard state.

a, Insight-HXMT/HE light curve (35–200 keV) of MAXI J1820+070 in the hard state from MJD 58190 to MJD 58301. b, is the evolution of the hardness ratio (defined as the ratio of the net count rate in the 3.0–10.0 keV to 1.0–3.0 keV bands). Panels c-e, show the evolution of the LFQPO’s frequency, Q factor and fractional rms. Phases A to D are marked in the top panel. The red dashed lines indicate the three typical observations in Extended Data Fig. 3.

### Extended Data Fig. 2 LFQPO centroid frequency (left) and fractional rms amplitude (right) as a function of energy for a typical observation (ObsID P0114661003).

The LFQPO rms is calculated in the full frequency range of the PDS. The fractional rms-squared normalization depends on the PDS, and the Lorentzian functions are used to fit the PDS. The green, red and blue points represent LE, ME and HE data, respectively. The gray points indicate the LFQPO rms values from the jet precession model with p = 1.

### Extended Data Fig. 3 Frequency-dependent phase-lag spectra and LFQPO phase lags for three typical observations.

The observations are marked with red vertical dashed lines in Extended Data Fig. 1, and their general properties are listed in Supplementary Table 3. The spectra of the three observations continue to soften. a, Frequency-dependent phase-lag spectra in the 67–100 keV band. The vertical dashed lines mark the LFQPO frequency, and the cyan points show the narrow dip-like feature. b, The ‘original’ LFQPO phase lags relative to the 1–2.6 keV band. By averaging the phase lags over the LFQPO frequency range ν ± FWHM/2 in different energy bands, we obtain the ‘original’ LFQPO phase lags as a function of photon energy. c, The ‘intrinsic’ LFQPO phase lags, which are determined using the ‘original’ LFQPO phase lags minus the phase-lag continuum. The average value of data points below the LFQPO frequency (purple points in panel (a)) is used as the phase-lag continuum.

### Extended Data Fig. 4 Simulated light curves at four energies for p = 1: 10 keV, 50 keV, 100 keV, 200 keV.

From Eqs. (3) and (4), we simulate the light curves by changing the phase angle φflow, assuming θflow, v, α, θobs and φobs to be constant. Using the light curves, we can calculate the jet speed based on the observed LFQPO fractional rms (see Extended Data Fig. 8).

### Extended Data Fig. 5 The PDS of MAXI J1820+070 in the 150–200 and 200–250 keV bands with different detectors: NaI and CsI, for ObsID P0114661004.

The power is multiplied by a different factor for plotting clarity.

### Extended Data Fig. 6 Insight-HXMT hardness-intensity diagram (HID) (upper) and hardness-rms diagram (HRD) (lower) of MAXI J1820+070.

Each point represents a single Insight-HXMT exposure. Data points during the six phases (A to F) are shown in different symbols. The intensity is the LE count rate in the 1.0–10.0 keV band. The hardness ratio is defined as the ratio of the net count rate in the 3.0–10.0 keV to 1.0–3.0 keV bands. The total fractional rms is calculated in the 0.01–32 Hz frequency range. Arrows show the evolutionary track of the outburst. The black points show the three typical observations used to calculate the LFQPO phase lag (Extended Data Fig. 3).

### Extended Data Fig. 7 One frequency-dependent time-lag spectrum of Insight-HXMT.

To test the consistency between Insight-HXMT and NICER, we make the Frequency-dependent time-lag spectrum between 0.7–1 keV and 1–10 keV for ObsID P0114661003 (MJD 58199.5–58200.9). The spectrum is consistent with the result from a quasi-simultaneous NICER observation taken within one day (ObsID 1200120106, see the red spectrum of Fig. 2 in Kara et al.31).

### Extended Data Fig. 8 The relations between β and the LFQPO rms for p = 1, 2 and 3, respectively.

As discussed above, the rms is determined by the amplitude of the light curves, which is a function of v. We change v in the range of (0.01-0.99)c with a step length of 0.01c, and simulate light curve for each v. The rms are calculated from these light curves, so we can obtain the relation between v and the rms. Using the observed rms (~ 10%), the jet speed can be inferred.

## Supplementary information

### Supplementary Information

Supplementary Tables 1–3.

### Supplementary Video 1

The LFQPO and its phase lag between different energy bands in MAXI J1820+070. As the relativistic jet precesses around the spin axis of the black hole, the observed light curves are modulated due to Doppler boosting of the jet, and the LFQPOs are generated in this process. The closer to the black hole, X-ray photons with higher energies are emitted from the jet. As the jet precesses, we see higher energy photons earlier than lower energy photons, resulting in the observed longer "soft lag" at higher energies.

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Ma, X., Tao, L., Zhang, SN. et al. Discovery of oscillations above 200 keV in a black hole X-ray binary with Insight-HXMT. Nat Astron 5, 94–102 (2021). https://doi.org/10.1038/s41550-020-1192-2

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• ### Insight-HXMT observations of jet-like corona in a black hole X-ray binary MAXI J1820+070

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Nature Communications (2021)