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The early afterglow of a Gamma-ray burst (GRB) can provide critical information on the jet and progenitor of the GRB. The extreme brightness of GRB 221009A allows us to probe its early afterglow in unprecedented detail. In this letter, we report comprehensive observation results of the early afterglow of GRB 221009A (from $T_0$+660 s to $T_0$+1860 s, where $T_0$ is the \textit{Insight}-HXMT/HE trigger time) in X/$\gamma$-ray energy band (from 20 keV to 20 MeV) by \textit{Insight}-HXMT/HE, GECAM-C and \textit{Fermi}/GBM. We find that the spectrum of the early afterglow in 20 keV-20 MeV could be well described by a cutoff power-law with an extra power-law which dominates the low and high energy bands respectively. The cutoff power-law $E_{\rm peak}$ is $\sim$ 30 keV and the power-law photon index is $\sim$ 1.8 throughout the early afterglow phase. By fitting the light curves in different energy bands, we find that a significant achromatic break (from keV to TeV) is required at $T_0$ + 1246$^{+27}_{-26}$ s (i.e. 1021 s since the afterglow starting time $T_{\rm AG}$=$T_0$+225 s), providing compelling evidence of a jet break. Interestingly, both the pre-break and post-break decay slopes vary with energy, and these two slopes become closer in the lower energy band, making the break less identifiable. Intriguingly, the spectrum of the early afterglow experienced a slight hardening before the break and a softening after the break. These results provide new insights into the understanding of this remarkable GRB., Comment: Accepted for publication in ApJ Letters on 19-Jan-2024, 11 pages, 7 figures and 2 tables

We present an X-ray spectrum of the diffuse X-ray background (DXRB) between 1.5 and 120 keV, as measured with the Low-Energy Detector (LE) and the High-Energy Detector (HE) aboard the Insight-HXMT satellite, based on 'blank-sky' observations. LE covers a nominal energy range of 1-15 keV and HE 20-250 keV, but calibration issues and data quality narrowed the energy range for this work. The LE background was directly measured with `blind' detector modules, while the HE background was derived from Earth-occultation data. With the LE data alone, the measured DXRB spectrum can be well described by a power law; fitting the LE and HE data jointly, however, a spectral cut-off must be introduced in the model to account for the measurements above 30 keV. Modelling the combined spectrum with a cut-off power law, the best-fit photon index is 1.40, normalisation $9.57$~$\rm ph~cm^{-2}~s^{-1}~keV^{-1}~sr^{-1} $ (at 1 keV), and cut-off energy 55 keV, after correcting for the effects of the Earth albedo and atmospheric emission (which are significant in the HE band). Based on the best-fit cut-off power law, we derived the spectral energy distribution (SED) of the DXRB. The shape of the SED is in general agreement with the published measurements, but the overall normalization is lower by varying amounts, except for the HEAO-1 result, with which our result is in good agreement., Comment: 9 pages, 14 figures, published in MNRAS

We have performed a spectral-timing analysis on the black hole X-ray binary MAXI J1535--571 during its 2017 outburst, with the aim of exploring the evolution of the inner accretion flow geometry. X-ray reverberation lags are observed in the hard-intermediate state (HIMS) and soft-intermediate state (SIMS) of the outburst. During the HIMS, the characteristic frequency of the reverberation lags $\nu_0$ (the frequency at which the soft lag turns to zero in the lag-frequency spectra) increases when the spectrum softens. This reflects a reduction of the spatial distance between the corona and accretion disc, when assuming the measured time lags are associated with the light travel time. We also find a strong correlation between $\nu_0$ and type-C Quasi Periodic Oscillation (QPO) centroid frequency $\nu_{QPO}$, which can be well explained by the Lense-Thirring (L-T) precession model under a truncated disk geometry. Despite the degeneracy in the spectral modellings, our results suggest that the accretion disc is largely truncated in the low hard state (LHS), and moves inward as the spectrum softens. Combine the spectral modelling results with the $\nu_0$ - $\nu_{QPO}$ evolution, we are inclined to believe that this source probably have a truncated disk geometry in the hard state.

GRB 221009A is the brightest gamma-ray burst ever detected since the discovery of this kind of energetic explosions. However, an accurate measurement of the prompt emission properties of this burst is very challenging due to its exceptional brightness. With joint observations of \textit{Insight}-HXMT and GECAM-C, we made an unprecedentedly accurate measurement of the emission during the first $\sim$1800 s of GRB 221009A, including its precursor, main emission (ME, which dominates the burst in flux), flaring emission and early afterglow, in the hard X-ray to soft gamma-ray band from $\sim$ 10 keV to $\sim$ 6 MeV. Based on the GECAM-C unsaturated data of the ME, we measure a record-breaking isotropic equivalent energy ($E_{\rm iso}$) of $\bf \sim 1.5 \times 10^{55}$ erg, which is about eight times the total rest-mass energy of the Sun. The early afterglow data require a significant jet break between 650 s and 1100 s, most likely at $\sim950$ s from the afterglow starting time $T_{AG}$, which corresponds to a jet opening angle of $\sim {0.7^\circ} \ (\eta_\gamma n)^{1/8}$, where $n$ is the ambient medium density in units of $\rm cm^{-3}$ and $\eta_\gamma$ is the ratio between $\gamma$-ray energy and afterglow kinetic energy. The beaming-corrected total $\gamma$-ray energy $E_{\gamma}$ is $\sim 1.15 \times10^{51} \ (\eta_\gamma n)^{1/4}$ erg, which is typical for long GRBs. These results suggest that this GRB may have a special central engine, which could launch and collimate a very narrowly beamed jet with an ordinary energy budget, leading to exceptionally luminous gamma-ray radiation per unit solid angle. Alternatively, more GRBs might have such a narrow and bright beam, which are missed by an unfavorable viewing angle or have been detected without distance measurement., Comment: Submitted to National Science Review. This paper is under press embargo, contact the corresponding author for details

The first X-ray source catalog of Insight-HXMT Galactic Plane (|b|<10deg) Scanning Survey (GPSS) is presented based on the data accumulated from June 2017 to August 2021. The 4 yr limit sensitivities at main energy bands can reach 8.2x10^(-12) erg/s/cm^2} (2-6 keV), 4.21x10^(-11) erg/s/cm^2 (7-40 keV) and 2.78x10^(-11) erg/s/cm^2 (25-100 keV). More than 1300 sources have been monitored at a wide band (1$-$100\,keV), of which 223 sources have a signal-to-noise ratio greater than 5. We combined the GPSS data of Insight-HXMT and MAXI and found it is feasible to obtain more complete long-term light curves from their scanning results. The flux variabilities at different energy bands of the 223 bright sources are analyzed based on the excess variances. It is found that the fluxes of X-ray binaries are more active than those of supernova remnants and isolated pulsars. Different types of binaries, e.g., low-mass X-ray binaries (LMXBs), high-mass X-ray binaries (HMXBs), neutron star binaries, and black hole binaries, also distinctively show different regularities. In addition, the relations between the hardness ratio (HR) and excess variances, and HR and source types are analyzed. It is obvious that the HRs of HMXBs tend to be harder than those of LMXBs and HMXBs tend to be more active than those of LMXBs., Comment: 43 pages, 26 figures, accepted for publication in ApJS

Purpose: We present the five-year in-orbit background evolution of Insight-HXMT since the launch, as well as the effects of the background model in data analysis. Methods: The backgrounds of the three main payloads, i.e., Low-Energy Telescope, Medium-Energy Telescope and High-Energy Telescope, are described, respectively. The evolution of the background over time is obtained by simply comparing the background in every year during the in-orbit operation of Insight-HXMT. Results: The major observational characteristics of the Insight-HXMT in-orbit background are presented, including the light curve, spectrum, geographical distribution, and long-term evolution. The systematic error in background estimation is investigated for every year. Conclusion: The observational characteristics of the five-year in-orbit background are consistent with our knowledge of the satellite design and the space environment, and the background model is still valid for the latest observations of Insight-HXMT., Comment: 22 pages, 25 figures, accepted for publication in RDTM

Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM) is a pair of microsatellites (i.e. GECAM-A and GECAM-B) dedicated to monitoring gamma-ray transients including gravitational waves high-energy electromagnetic counterparts, Gamma-ray Bursts, Soft Gamma-ray Repeaters, Solar Flares and Terrestrial Gamma-ray Flashes. Since launch in December 2020, GECAM-B has detected hundreds of astronomical and terrestrial events. For these bursts, localization is the key for burst identification and classification as well as follow-up observations in multi-wavelength. Here, we propose a Bayesian localization method with Poisson data with Gaussian background profile likelihood to localize GECAM bursts based on the burst counts distribution in detectors with different orientations. We demonstrate that this method can work well for all kinds of bursts, especially for extremely short ones. In addition, we propose a new method to estimate the systematic error of localization based on a confidence level test, which can overcome some problems of the existing method in literature. We validate this method by Monte Carlo simulations, and then apply it to a burst sample with accurate location and find that the mean value of the systematic error of GECAM-B localization is $\sim 2.5^{\circ}$. By considering this systematic error, we can obtain a reliable localization probability map for GECAM bursts. Our methods can be applied to other gamma-ray monitors., Comment: The paper has been accepted by Astrophysical Journal Supplement Series

The detection of cyclotron resonance scattering features (CRSFs) is the only way to directly and reliably measure the magnetic field near the surface of a neutron star (NS). The broad energy coverage and large collection area of \emph{Insight}-HXMT in the hard X-ray band allowed us to detect the CRSF with the highest energy known to date, reaching about 146 keV during the 2017 outburst of the first galactic pulsing ultraluminous X-ray source (pULX) Swift J0243.6+6124. During this outburst, the CRSF was only prominent close to the peak luminosity $\sim 2\times10^{39}$ erg s$^{-1}$, the highest to date in any of the Galactic pulsars. The CRSF is most significant in the spin phase region corresponding to the main pulse of the pulse profile, and its centroid energy evolves with phase from 120 to 146 keV. We identify this feature as the fundamental CRSF, since no spectral feature exists at $60-70$ keV. This is the first unambiguous detection of an electron CRSF from an ULX. We also estimate a surface magnetic field $\sim1.6\times10^{13}$ G for Swift J0243.6+6124. Considering that the dipole magnetic field strengths, inferred from several independent estimates of magnetosphere radius, are at least an order of magnitude lower than our measurement, we argue that the detection of the highest energy CRSF reported here unambiguously proves the presence of multipole field components close to the surface of the neutron star. Such a scenario has previously been suggested for several pulsating ULXs, including Swift J0243.6+6124, and our result represents the first direct confirmation of this scenario., Comment: Accepted for publication in ApJL

The Hard X-ray Modulation Telescope (Insight-HXMT), is China's first X-ray astronomy satellite launched on June 15, 2017. The anti-coincidence CsI detectors of the High Energy X-ray telescope (HE) onboard Insight-HXMT could serve as an all-sky gamma-ray monitor in about 0.2-3 MeV. In its first four years of operation, Insight-HXMT has detected 322 Gamma-Ray Bursts (GRBs) by offline search pipeline including blind search and targeted search. For the GOLDEN sample of Insight-HXMT GRBs, joint analyses were performed with other GRB missions, including Fermi Gamma-ray Burst Monitor (Fermi/GBM), Swift Burst Alert Telescope (Swift/BAT) and Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM). It shows that Insight-HXMT can provide better constraint on GRB spectrum at higher energy band. The properties of Insight-HXMT GRBs are reported in detail, including their trigger time, duration, spectral parameters, peak fluxes of different time scales and fluence. This catalog is an official product of the Insight-HXMT GRB team., Comment: 46 pages, 22 figures, accepted by APJS

Realtime trigger and localization of bursts are the key functions of GECAM, which is an all-sky gamma-ray monitor launched in Dec 10, 2020. We developed a multifunctional trigger and localization software operating on the CPU of the GECAM electronic box (EBOX). This onboard software has the following features: high trigger efficiency for real celestial bursts with a suppression of false triggers caused by charged particle bursts and background fluctuation, dedicated localization algorithm optimized for short and long bursts respetively, short time latency of the trigger information which is downlinked throught the BeiDou satellite navigation System (BDS). This paper presents the detailed design and deveopment of this trigger and localization software system of GECAM, including the main functions, general design, workflow and algorithms, as well as the verification and demonstration of this software, including the on-ground trigger tests with simulated gamma-ray bursts made by a dedicated X-ray tube and the in-flight performance to real gamma-ray bursts and magnetar bursts., Comment: Draft, comments welcome

Low-frequency quasi-periodic 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 (Insight-HXMT) 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 ~0.9s in the 150-200 keV band. The detection at energies above 200 keV, the large soft lag and the energy-related behaviors of the LFQPO pose a great challenge for most currently existing models, but suggest that the LFQPO probably originates from the precession of a small-scale jet., Comment: 36 pages, 12 figures, 3 tables; published in Nature Astronomy

Accurate background estimation is essential for spectral and temporal analysis in astrophysics. In this work, we construct the in-orbit background model for the High-Energy Telescope (HE) of the Hard X-ray Modulation Telescope (dubbed as Insight-HXMT). Based on the two-year blank sky observations of Insight-HXMT/HE, we first investigate the basic properties of the background and find that both the background spectral shape and intensity have long-term evolution at different geographical sites. The entire earth globe is then divided into small grids, each with a typical area of 5x5 square degrees in geographical coordinate system. For each grid, an empirical function is used to describe the long-term evolution of each channel of the background spectrum; the intensity of the background can be variable and a modification factor is introduced to account for this variability by measuring the contemporary flux of the blind detector. For a given pointing observation, the background model is accomplished by integrating over the grids that are passed by the track of the satellite in each orbit. Such a background model is tested with both the blank sky observations and campaigns for observations of a series of celestial sources. The results show an average systematic error of 1.5% for the background energy spectrum (26-100 keV) under a typical exposure of 8 ks, and <3% for background light curve estimation (30-150 keV). Therefore, the background model introduced in this paper is included in the Insight-HXMT software as a standard part specialized for both spectral and temporal analyses., Comment: 27 pages, 16 figures, accepted by Journal of High Energy Astrophysics

The CsI detectors of the High Energy X-ray Telescope of the Hard X-ray Modulation Telescope (HXMT/CsI) can be used for gamma-ray all sky monitoring and searching for the electromagnetic counterpart of gravitational wave source. The instrumental responses are mainly obtained by Monte Carlo simulation with the Geant4 tool and the mass model of both the satellite and all the payloads, which is updated and tested with the Crab pulse emission in various incident directions. Both the Energy-Channel relationship and the energy resolution are calibrated in two working modes (Normal-Gain mode & Low-Gain Mode) with the different detection energy ranges. The simulative spectral analyses show that HXMT/CsI can constrain the spectral parameters much better in the high energy band than that in the low energy band. The joint spectral analyses are performed to ten bright GRBs observed simultaneously with HXMT/CsI and other instruments (Fermi/GBM, Swift/BAT, Konus-Wind), and the results show that the GRB flux given by HXMT/CsI is systematically higher by $7.0\pm8.8\%$ than those given by the other instruments. The HXMT/CsI-Fermi/GBM joint fittings also show that the high energy spectral parameter can be constrained much better as the HXMT/CsI data are used in the joint fittings., Comment: 22 pages, 17 figures, 4 tables, accepted by Journal of High Energy Astrophysics

With more than 150 blank sky observations at high Galactic latitude, we make a systematic study to the background of the Low Energy Telescope (LE) of the Hard X-ray Modulation Telescope (dubbed as Insight-HXMT). Both the on-ground simulation and the in-orbit observation indicate that the background spectrum mainly has two components. One is the particle background that dominates above 7 keV and its spectral shape is consistent in every geographical locations. Another is the diffuse X-ray background that dominates below 7 keV and has a stable spectrum less dependent of the sky region. The particle background spectral shape can be obtained from the blind detector data of all the blank sky observations, and the particle background intensity can be measured by the blind detector at 10-12.5 keV. The diffuse X-ray background in the high Galactic latitude can also be obtained from the blank sky spectra after subtracting the particle background. Based on these characteristics, we develop the background model for both the spectrum and the light curve. The systematic error for the background spectrum is investigated with different exposures (T_exp). For the spectrum with T_exp=1 ks, the average systematic errors in 1-7 keV and 1-10 keV are 4.2% and 3.7%, respectively. We also perform the systematic error analyses of the background light curves with different energy bands and time bins. The results show that the systematic errors for the light curves with different time bins are <8% in 1-10 keV., Comment: 24 pages, 17 figures, accepted by Journal of High Energy Astrophysics

The Medium Energy X-ray Telescope (ME) is one of the main payloads of the Hard X-ray Modulation Telescope (dubbed as Insight-HXMT). The background of Insight-HXMT/ME is mainly caused by the environmental charged particles and the background intensity is modulated remarkably by the geomagnetic field, as well as the geographical location. At the same geographical location, the background spectral shape is stable but the intensity varies with the level of the environmental charged particles. In this paper, we develop a model to estimate the ME background based on the ME database that is established with the two-year blank sky observations of the high Galactic latitude. In this model, the entire geographical area covered by Insight-HXMT is divided into grids of $5^{\circ}\times5^{\circ}$ in geographical coordinate system. For each grid, the background spectral shape can be obtained from the background database and the intensity can be corrected by the contemporary count rate of the blind FOV detectors. Thus the background spectrum can be obtained by accumulating the background of all the grids passed by Insight-HXMT during the effective observational time. The model test with the blank sky observations shows that the systematic error of the background estimation in $8.9-44.0$ keV is $\sim1.3\%$ for a pointing observation with an average exposure $\sim5.5$ ks. We also find that the systematic error is anti-correlated with the exposure, which indicates the systematic error is partly contributed by the statistical error of count rate measured by the blind FOV detectors., Comment: to be published in Journal of High Energy Astrophysics

We make the in-orbit calibration to the point-spread functions (PSFs) of the collimators of the Hard X-ray Modulation Telescope with the scanning observation of the Crab. We construct the empirical adjustments to the theoretically calculated geometrical PSFs. The adjustments contain two parts: a rotating matrix to adjust the directional deviation of the collimators and a paraboloidal function to correct the inhomogeneity of the real PSFs. The parameters of the adjusting matrices and paraboloidal functions are determined by fitting the scanning data with lower scanning speed and smaller intervals during the calibration observations. After the PSF calibration, the systematic errors in source localization in the Galactic plane scanning survey are 0.010 deg, 0.015 deg, 0.113 deg for the Low-Energy Telescope (LE), the Medium-Energy telescope (ME) and the High-Energy telescope (HE), respectively; meanwhile, the systematic errors in source flux estimation are 1.8%, 1.6%, 2.7% for LE, ME and HE, respectively., Comment: 15 pages, 27 figures, accepted for publication in JHEAP

The Hard X-ray Modulation Telescope (HXMT) named Insight is China's first X-ray astronomical satellite. The Low Energy X-ray Telescope (LE) is one of its main payloads onboard. The detectors of LE adopt swept charge device CCD236 with L-shaped transfer electrodes. Charges in detection area are read out continuously along specific paths, which leads to a time response distribution of photons readout time. We designed a long exposure readout mode to measure the time response distribution. In this mode, CCD236 firstly performs exposure without readout, then all charges generated in preceding exposure phase are read out completely. Through analysis of the photons readout time in this mode, we obtained the probability distribution of photons readout time.

Timing analysis provides information about the dynamics of matter accreting on to neutron stars and black holes, and hence is crucial for studying the physics of the accretion flow around these objects. It is difficult, however, to associate the different variability components with each of the spectral components of the accretion flow. We apply several new methods to two Rossi X-ray Timing Explorer observations of the black hole binary GRS 1915+105 during its heartbeat state to explore the origin of the X-ray variability and the interactions of the accretion-flow components. We offer a promising window into the disc--corona interaction through analysing the formation regions of the disc aperiodic variabilities with different time-scales via comparing the corresponding transition energies of the amplitude-ratio spectra. In a previous paper, we analysed the Fourier power density as a function of energy and frequency to study the origin of the aperiodic variability, and combined that analysis with the phase lag as a function of frequency to derive a picture of the disc--corona interaction in this source. We here, for the first time, investigate the phase lag as a function of energy and frequency, and display some interesting details of the disc--corona interaction. Besides, the results from the shape of amplitude-ratio spectrum and from several other aspects suggest that the quasi-periodic oscillation originates from the corona., Comment: 12 pages, 7 figures

We present a timing analysis of two Rossi X-ray Timing Explorer observations of the microquasar GRS 1915+105 during the heartbeat state. The phase-frequency-power maps show that the intermediate-frequency aperiodic X-ray variability weakens as the source softens in the slow rise phase, and when the quasi-periodic oscillation disappears in the rise phase of the pulse of the double-peaked class its sub-harmonic is still present with a hard phase lag. In the slow rise phase, the energy-frequency-power maps show that most of the aperiodic variability is produced in the corona, and may also induce the aperiodic variability observed at low energies from an accretion disk, which is further supported by the soft phase lag especially in the intermediate-frequency range (with a time delay up to 20 ms). In the rise phase of the pulse, the low-frequency aperiodic variability is enhanced significantly and there is a prominent hard lag (with a time delay up to 50 ms), indicating that the variability is induced by extension of the disk toward small radii as implied by the increase in flux and propagates into the corona. However, during the hard pulse of the double-peaked class, the variability shows no significant lag, which may be attributed to an optically thick corona. These timing results are generally consistent with the spectral results presented by Neilsen et al. (2011, 2012) which indicated that the slow rise phase corresponds to a local Eddington limit and the rise phase of the pulse corresponds to a radiation pressure instability in the disk., Comment: 8 pages, 7 figures; Accepted for publication in MNRAS

We measure primordial alignments for the red galaxies in the sample of eight massive galaxy clusters in the southern sky from the CLASH-VLT Large Programme, at a median redshift of 0.375. We find primordial alignment with about $3\sigma$ significance in the four dynamically young clusters, but null detection of primordial alignment in the four highly relaxed clusters. The observed primordial alignment is not dominated by any single one of the four dynamically young clusters, and is primarily due to a population of bright galaxies ($M_r<-20.5\ \rm{m}$) residing in the region 300 to 810 kpc from the cluster centers. For the first time, we point out that the combination of radial alignment and halo alignment can cause fake primordial alignment. Finally, we find that the detected alignment for the dynamically young clusters is real rather than fake primordial alignment., Comment: 10 pages, 8 figures, 1 table. Accepted for publication in MNRAS

We model the evolution of the spin frequency's second derivative $\ddot\nu$ and the braking index $n$ of radio pulsars with simulations within the phenomenological model of their surface magnetic field evolution, which contains a long-term power-law decay modulated by short-term oscillations. For the pulsar PSR B0329+54, a model with three oscillation components can reproduce its $\ddot\nu$ variation. We show that the "averaged" $n$ is different from the instantaneous $n$, and its oscillation magnitude decreases abruptly as the time span increases, due to the "averaging" effect. The simulated timing residuals agree with the main features of the reported data. Our model predicts that the averaged $\ddot\nu$ of PSR B0329+54 will start to decrease rapidly with newer data beyond those used in Hobbs et al.. We further perform Monte Carlo simulations for the distribution of the reported data in $|\ddot\nu|$ and $|n|$ versus characteristic age $\tau_{\rm c}$ diagrams. It is found that the magnetic field oscillation model with decay index $\alpha=0$ can reproduce the distributions quite well. Compared with magnetic field decay due to the ambipolar diffusion ($\alpha=0.5$) and the Hall cascade ($\alpha=1.0$), the model with no long term decay ($\alpha=0$) is clearly preferred for old pulsars by the p-values of the two-dimensional Kolmogorov-Smirnov test., Comment: 13 pages, 5 figures. Accepted for publication in RAA. arXiv admin note: substantial text overlap with arXiv:1307.6413

Accurate atomic transition data are important in many astronomical research areas especially in line spectroscopy study. Whereas transition data of He-like and H-like ions (i.e., ions at high-charge states) are accurately calculated, that of K transitions of neutral or low-ionized metal elements are still very uncertain. Spectroscopy of absorption lines produced in the interstellar medium (ISM) has been proven to be an effective way to measure the central wavelengths of these atomic transitions. In this work we analyze 36 Chandra High Energy Transmission Grating observations and search for and measure the ISM absorption lines along sight lines of 11 low-mass X-ray binaries. We correct the Galactic rotation velocity to the rest frame for every observation and then use two different methods to merge all the corrected spectra to a co-added spectrum. However the co-added spectra obtained by these methods exhibit biases, either to the observations of high counts or high signal-to-noise ratios of the lines. We make Bayesian analysis to several significantly detected lines to obtain the systematic uncertainty and the bias correction of other lines. Compared to previous studies (e.g., Yao et al. 2009), our results improve the accuracy of wavelengths by a factor from two to five and significantly reduce the systematic uncertainties and biases. Several weak transitions (e.g., 1s--2p of Mg IV and Mg V; 1s--3p of Mg III and Mg V) are also detected for the first time, albeit with low significance; future observations with improved accuracy are required to confirm these detections., Comment: 38 pages, 14 figures, 2 tables, 2 appendices. Accepted for publication in ApJ