GRS 1716249 is a stellarmass black hole in a lowmass Xray binary that underwent a giant outburst in 201617. In this paper we use simultaneous observations from the Hard Xray Modulation Telescope InsightHXMT and the Nuclear Spectroscopic Telescope Array NuSTAR to determine its basic parameters. The observations were performed during the softest part of the outburst and the spectra show clear thermal disk emission and reflection features. We fit the Xray energy spectra using the joint fitting method of the continuum and reflection components with the kerrbb2  relxill model. Since there is a possibility that the distance to this source was previously underestimated we used the latest distance parameter of 6.9 kpc in our study in contrast to previous works where the distance was set at 2.4 kpc. Through a spectral fitting of the black hole mass at 6.4 MSUBSUB we observe a strong dependence of the derived spin on the distance aSUBSUB  0.972SUB0.005SUBSUP0.004SUP at an assumed distance of 2.4 kpc and aSUBSUB  0.464SUB0.007SUBSUP0.016SUP at an assumed distance of 6.9 kpc at a confidence level of 90. When considering the uncertainties in the distance and black hole mass there will be a wider range of spin with aSUBSUBlt 0.78. The fitting results with the new distance indicate that GRS 1716249 harbors a moderate spin black hole with an inclined i  40  50 accretion disk around it. Additionally we have also found that solely using the method of reflection component fitting while ignoring the constraints on the spin from the accretion disk component will result in an extremely high spin.
['accretion', 'accretion disks', 'black hole physics', 'stars: individual: GRS 1716-249', 'X-rays: binaries', 'Astrophysics - High Energy Astrophysical Phenomena']
Revised spin for the black hole in GRS 1716249 given a new distance determination
{'A Revised Spin of the Black Hole in GRS 1716-249 with a New Distance': 'S. J. Zhao 1 , 2 , L. Tao 1 ⋆ , Q. Q. Yin 1 ⋆⋆ , S. N. Zhang 1 , 2 , R. C. Ma 1 , 2 , P. P. Li 1 , 2 , Q. C. Zhao 1 , 2 , M. Y. Ge 1 , L. Zhang 1 , J. L. Qu 1 , S. Zhang 1 , X. Ma 1 , Y. Huang 1 , J. Q. Peng 1 , 2 , and Y. X. Xiao 1 , 2  \n- 1\n- Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China\n- 2 University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, China  \nReceived ; accepted', 'ABSTRACT': 'GRS 1716-249 is a stellar-mass black hole in a low-mass X-ray binary that underwent a gaint outburst in 2016 / 17. In this paper we use simultaneous observations of Insight-HXMT and NuSTAR to determine its basic parameters. The observations were performed during the softest part of the outburst, and the spectra show clear thermal disk emission and reflection features. We have fitted the X-ray energy spectra using the joint fitting method of the continuum and reflection components with the kerrbb2 + relxill model. Since there is a possibility that the distance to this source was previously underestimated, we use the latest distance parameter of 6.9 kpc in our study, in contrast to previous work in which the distance was set at 2.4 kpc. Through spectral fitting of fixing black hole mass at 6.4 M ⊙ , we observe a strong dependence of the derived spin on the distance: a ∗ = 0 . 972 + 0 . 004 -0 . 005 at an assumed distance of 2.4 kpc and a ∗ = 0 . 464 + 0 . 016 -0 . 007 at an assumed distance of 6.9 kpc, at a confidence level of 90%. If considering the uncertainties in the distance and black hole mass, there will be a wider range of spin with a ∗ < 0.78. The fitting results with the new distance indicate that GRS 1716-249 harbors a moderate spin black hole with an inclined ( i ∼ 40 -50 · ) accretion disk around it. Additionally, we have also found that solely using the method of the reflection component fitting but ignoring the constraints on the spin from the accretion disk component will result in an extremely high spin.  \nKey words. X-ray binaries - black hole physics - accretion, accretion disk - stars: individual: (GRS 1716-249)', '1. Introduction': 'Spin is an important parameter of a black hole (BH), which, together with its mass, determines the spacetime around it and influences the accretion of matter and the formation of jets (for a review, see Reynolds 2021). Generally, the BH spin a ∗ is defined as a ∗ = Jc / GM 2 , where J represents the angular momentum of the black hole, G stands for the gravitational constant and c denotes the speed of light. The magnitude of the spin determines the radius of the innermost stable circular orbit (ISCO), R ISCO. A larger value of a ∗ corresponds to a smaller R ISCO. For example, when a ∗ = 0 (Schwarzschild black hole), R ISCO is equal to 6 R g (where R g = GM / c 2 is called the gravitational radius); when a ∗ = 1 (extreme Kerr black hole), R ISCO is equal to 1 R g. Currently, there are two main methods for measuring black hole spin through spectral fitting: continuum fitting (Zhang et al. 1997; McClintock et al. 2014) and reflection component fitting (Fabian et al. 1989; Reynolds & Fabian 2008; García et al. 2014, 2018b). Both methods require the common prerequisite that the inner edge of the accretion disk is located at the position of the ISCO ( R in = R ISCO).  \nAccording to the standard accretion disk theory (Shakura & Sunyaev 1973; Novikov & Thorne 1973), the spin of a black hole a ff ects the temperature of the inner disk, which in turn affects the thermal emission of the accretion disk. The method of continuum fitting is precisely used to constrain the spin of the black hole by fitting the spectrum of the disk. However, the use  \nof this method requires that the distance to the source ( D ), the inclination of the accretion disk ( i ), and the mass of the black hole ( M BH) are known (the reasons can be found in McClintock et al. 2011). Two commonly used models for fitting the disk component are kerrbb (Li et al. 2005) and kerrbb2 (McClintock et al. 2006), which consider the full relativistic e ff ects. The key fitting parameters of these models include the black hole spin and the mass accretion rate ( ˙ M ).  \nThe typical reflection features are the iron line (at ∼ 6-7 keV) and the Compton hump (at ∼ 20-30 keV). The iron line emitted from the inner disk close to the black hole is influenced by the Doppler e ff ect, relativistic beaming e ff ect, and gravitational redshift, resulting in a broadened and distorted profile (Reynolds & Nowak 2003; Miller 2007). The gravitational redshift mainly affects the red wing of the iron line. The larger the black hole spin, the further the red wing extends to lower energies. This is because a larger spin allows the inner disk to be closer to the black hole and experience a stronger gravitational potential well. The core of the reflection component fitting is to fit the profile of the iron line. This method does not depend on M BH and D and can also be used to constrain i .  \nIn theory, there are billions of stellar-mass black holes in the Milky Way galaxy (Brown & Bethe 1994). However, there are only around twenty X-ray binary systems containing a dynamically confirmed black hole (Remillard & McClintock 2006; Özel et al. 2010; Corral-Santana et al. 2016). GRS 1716-249 is one of them. This source was discovered in 1993 by the CGRO / BATSE and Granat / SIGMA telescopes (Harmon et al. 1993; Ballet et al. 1993). After about 23 years of quiescence, GRS 1716-249 had  \nanother outburst detected by MAXI on December 18, 2016 (Negoro et al. 2016). During this outburst, when the source was in the hard intermediate state, it is believed that the accretion disk was a standard disk with the inner edge located at the ISCO (Bassi et al. 2019). Additionally, the spectrum showed significant power-law (PL) components from the corona, as well as prominent reflection features (broad iron line and Compton hump) (Bassi et al. 2019; Tao et al. 2019). Therefore, this source presents an ideal case for measuring the black hole spin because both continuum fitting and reflection component fitting methods can be combined to simultaneously constrain the parameters of the black hole.  \nThe system parameters of this source, especially the distance, have not been well constrained. della Valle et al. (1994) estimated the distance to be 2.2-2.8 kpc. Masetti et al. (1996) provided a lower limit on the black hole mass of 4.9 M ⊙ , a companion star mass of ∼ 1.6 M ⊙ , an orbital period of ∼ 14.7 hr, and a distance of 2 . 4 ± 0 . 4 kpc. By fixing the distance at 2.4 kpc, Tao et al. (2019) found the black hole spin of a ∗ > 0 . 92, the accretion disk inclination of i ∼ 40 -50 · , and the black hole mass of M BH < 8 M ⊙ , and Chatterjee et al. (2021) used a two-component advective flow (TCAF) model to constrain the black hole mass to be between 4.5-5.9 M ⊙ . However, Saikia et al. (2022) argue that the distance of 2.4 kpc is an underestimate. They conservatively estimated the distance of GRS 1716-249 to be 4-17 kpc based on the global optical / X-ray correlation and suggested a most likely value of D ∼ 4-8 kpc based on the dynamics of the binary system. Casares et al. (2023) presented evidence for a 6.7 hr orbital period and used the empirical relationship between the quiescent r -band magnitude and the orbital period to constrain the distance to 6 . 9 ± 1 . 1 kpc, consistent with the results given by Saikia et al. (2022). Furthermore, Casares et al. (2023) also provided an orbital inclination of 61 ± 15 · and a BH mass of 6 . 4 + 3 . 2 -2 . 0 , M ⊙ at 68% confidence.  \nDue to the distance-dependent nature of continuum fitting methods, di ff erent distances may yield di ff erent spin measurement results. Therefore, in this paper, we used two di ff erent distance parameters, the previously used 2.4 kpc (Masetti et al. 1996) and the most recent 6.9 kpc provided by Casares et al. (2023), to highlight the impact of distance changes on spin measurements. We employed a joint fitting method using continuum and reflection spectra to constrain the spin, utilizing data from Insight-HXMT and NuSTAR simultaneous observations during the hard intermediate state in the 2016-2017 outbrst. In the following section (Sect. 2), we will describe the observations and data reduction. Sect. 3 will present the spectral fitting and results. The obtained results will be discussed in Sect. 4 and summarized in Sect. 5.', '2. Observations and data reduction': "In contrast to Tao et al. (2019), which utilized simultaneous Swift and NuSTAR data, in this study we use simultaneous Insight-HXMT and NuSTAR data. Insight-HXMT can provide high-statistics spectra up to 150 keV for this source, enabling effective constraint of the PL and reflection components, and the lower energy limit of 1 keV for Insight-HXMT ensures accurate modeling of the disk component. Moreover, unlike the Swift data used by Tao et al. (2019), the spectra are not prone to distortion due to pile-up e ff ects as Insight-HXMT does not su ff er from this issue.  \nInsight-HXMT observed GRS 1716-249 twice during the 2016-2017 outburst. According to the spectral classification of Bassi et al. (2019), both observations are in the hard intermedi-  \nFig. 1. MAXI / GSClight-curve (2-20 keV) of GRS 1716-249. The solid red vertical line represents the simultaneous Insight-HXMT and NuSTAR observations used in this work.  \n<!-- image -->  \nFig. 2. The light curves of Insight-HXMT / LE (top pannel) and NuSTAR / FPMA (bottom panel). The black dashed vertical line represents the division point for the two data sets.  \n<!-- image -->  \nate state. NuSTAR observed the source three times in the hard intermediate state. The second observation by Insight-HXMT (obsID P0114335002) is strictly simultaneous with the third NuSTAR observation (obsID 90301007002), which started on July 28, 2017, and ended on July 30, 2017. The simultaneous observations by Insight-HXMT and NuSTAR are indicated on the outburst light curve obtained from MAXI / GSC (see Fig. 1). The e ff ective exposure times for Insight-HXMT / LE and NuSTAR / FPMAare 26ks and 89 ks, respectively (see Table 1). Since the observation span exceeds two days and the source's luminosity, that is, accretion rate, changes drastically during this period, we split the observations of Insight-HXMT and NuSTAR into two data sets (see Fig. 2) to more accurately measure the spin. The information on the divided data is provided in Table 2.", '2.1. Insight-HXMT': 'Weperform data reduction using the Insight-HXMT Data Analysis Software ( HXMTDAS v2.05 1 ) and the calibration database files ( CALDB v2.06 ). To determine the good time intervals, we established the following criteria: (a) pointing o ff set angle should  \nTable 1. Observation information of Insight-HXMT and NuSTAR  \nNotes. For Insight-HXMT and NuSTAR, the observation logs of LE and FPMA are listed as a representation, respectively.  \nTable 2. Information of Data Set 1 and 2.  \nNotes. For Insight-HXMT and NuSTAR, the observation logs of LE and FPMA are listed as a representation, respectively.  \nbe less than 0.04 · ; (b) Earth elevation angle should be greater than 10 · ; (c) there should be a minimum time interval of 300 s from the crossing of the South Atlantic Anomaly region; (d) the geomagnetic cuto ff rigidity should exceed 8 GV. The background for the Low Energy (LE), Medium Energy (ME), and High Energy (HE) telescopes were generated using the scripts lebkgmap , mebkgmap , and hebkgmap , respectively, based on the Insight-HXMT background models (Liao et al. 2020b; Guo et al. 2020; Liao et al. 2020a). The response files for LE, ME, and HE were generated using lerspgen , merspgen , and herspgen , respectively. Following the recommendation of the Insight-HXMT calibration group, the combined spectra are rebinned as follows: The spectra of LE, ME and HE are respectively rebinned with 1000, 800 and 600 counts per bin at least. Additionally, systematic errors of 1%, 1%, and 2% are applied to the LE, ME, and HE spectra, respectively.', '2.2. NuSTAR': "The nupipeline routine of NuSTARDAS v1.9.7 in HEASoft v6.29 with CALDB v20211115 , is employed to process the cleaned event files. The nuproducts tool is then used to extract the source events, by adopting a circular region surrounding the source with a radius of 80 '' to optimize the signal-to-noise ratio of the spectra 2 . The corresponding background extraction region is a nearby source-free circle with a radius of 80 '' . The spectra are rebinned with 50 counts per bin at least.", '3. Analysis and results': "To obtain more reliable results, we performed a joint fit of the spectra from Data Sets 1 and 2. The energy bands used for Insight-HXMT data are 1-7 keV for LE, 10-35 keV for ME, and 35-150 keV for HE. For NuSTAR, we select the energy band of 3-79 keV. The spectral fitting is conducted using XSPEC v12.12.0 (Arnaud 1996). The abundances are set to WILM (Wilms et al. 2000), and the cross-sections are set to VERN (Verner et al. 1996). All errors are estimated via the Markov chain Monte Carlo algorithm (MCMC) with a length of 600000.  \nDue to the source being in the hard intermediate state (Bassi et al. 2019), where the spectra exhibit prominent disk emission and reflection features (Tao et al. 2019), we perform a joint fitting of the spectra using both a continuum and reflection spectral model. The model selected for the fitting is tbabs*(kerrbb+relxill) . Additionally, a multiplicative constant model ( constant ) is included to account for the normalization discrepancies between di ff erent telescopes. Therefore, our fitting model is M1 = constant*tbabs*(kerrbb+relxill) , as shown in Table A.1. The kerrbb model is a multi-temperature blackbody model that describes the spectrum emitted by a geometrically thin, steadystate accretion disk around a Kerr black hole, taking into account full relativistic e ff ects (Li et al. 2005). The relxill 3 model is a relativistic disk coronal reflection model that describes the reflection produced by the corona (with a cuto ff PL spectrum) illuminating the inner regions of the accretion disk (Dauser et al. 2014; García et al. 2014). In the kerrbb model, we fix the BH mass at 6.4 M ⊙ (Casares et al. 2023) and the normalization at 1,  \nTable 3. Joint fitting parameters of Insight-HXMT and NuSTAR with M1 ( constant*tbabs*(kerrbb+relxill)) .  \nNotes. All errors are quoted at the 90% confidence level. The probability distributions of parameters for M1B obtained from Data Set 1 through MCMC are presented in Fig. B.1; ⋆ indicates that the parameters between di ff erent data sets are linked; N H is the X-ray absorption column density in units of 10 22 atoms cm -2 ; ˙ M is the e ff ective mass accretion rate of the disk in units of 10 15 g s -1 ; f h is the spectral hardening factor; q in is the inner emissivity index; R b represents the transition radius between the inner and outer emissivity indices, measured in R ISCO units, and is capped at 100 R ISCO; a ∗ is the BH spin; i is the disk inclination angle in units of deg; Γ is the photon index of the incident cuto ff PL spectrum; ξ is the ionization parameter of the accretion disk in units of erg cm s -1 ; A Fe is the iron abundance of the accretion disk in units of solar abundance; E cut is the cuto ff energy in units of keV; R f is the reflection fraction; norm is the normalization of relxill in units of 10 -3 ; Flux is the 0.1-100 keV unabsorbed fluxes in units of 10 -8 erg cm -2 s -1 .  \nand link the BH spin ( a ∗ ) and the disk inclination ( i ) to that of relxill . In the relxill model, we fix the inner radius of the accretion disk ( R in) to -1 since the disk inner edge is at the ISCO (Bassi et al. 2019), and presume that within the range from R in to a specific break radius ( R b), the emissivity is defined by a single inner emissivity index ( q in), and beyond R b, it generally adopts the standard r -3 ( q out = 3) profile. For di ff erent data sets, some parameters are linked and allowed to vary freely, including the X-ray absorption column density ( N H), a ∗ , i , and iron abundance ( A Fe). Other parameters are independent between di ff erent data sets, such as the mass accretion rate ( ˙ M ) and the spectral hardening factor f h in kerrbb , and q in, R b, the photon index ( Γ ), ionization parameter (log ξ ), cuto ff energy of the incident spectrum ( E cut), reflection factor ( R f ), and normalization in relxill . To determine the BH spin under the most recent measured distance and investigate the influence of distance on spin measurement, we perform two sets of fits: fixing the distance D in the kerrbb at 2.4 kpc ( M1A ; See Table A.1) and 6.9 kpc ( M1B ), respectively.  \nThe two fittings at di ff erent distances yield similar goodness of fit, and their detailed fitting parameters are listed in Table 3. In both models M1A and M1B , the accretion rate shows a  \ngradual decrease from Data Set 1 to Data Set 2, which aligns with the light curve's variability; both models yield N H ∼ 0.7, i ∼ 44 · , Γ ∼ 1 . 9, log ξ ∼ 3 . 8, and E cut ≳ 900 keV, indicating that these parameters do not exhibit strong distance dependence. The spin fitting results exhibit noteworthy changes, where an increase in distance transitions high spin values to moderate ones. The relationship between a ∗ and f h shown in Fig. B.1 demonstrates an inverse correlation, in agreement with the findings of Salvesen & Miller (2021). This suggests that f h has a significant impact on spin fitting. To reduce this impact and achieve reliable spin measurements, we have substituted kerrbb in M1 with kerrbb2 (McClintock et al. 2006). Unlike Kerrbb , Kerrbb2 incorporates the spectral hardening e ff ect using two search tables for f h, each corresponding to di ff erent viscosity parameters: α = 0.01 and 0.1. These look-up tables are generated via bhspec (Davis et al. 2005), relying on non-LTE atmosphere models within an α -viscosity framework. Other features of Kerrbb2 , such as Doppler boosting, gravitational redshift, and returning radiation, remain consistent with kerrbb . The updated model is now M2 = constant*tbabs*(kerrbb2+relxill) , as shown in Table A.1. We chose α = 0.1 (Steiner et al. 2011) in M2 and  \nTable 4. Joint fitting parameters of Insight-HXMT and NuSTAR with M2 ( constant*tbabs*(kerrbb2+relxill)) .  \nNotes. All errors are quoted at the 90% confidence level. The probability distributions of parameters for M2A and M2B obtained from Data Set 1 through MCMC are presented in Figs. B.2 and B.3, respectively.  \nTable 5. Fitting results of partial parameters with M2 by assuming di ff erent distances.  \nNotes. All errors are quoted at the 90% confidence level. The joint fitting results of BH spin, disk inclination, accretion rate of Data Set 1, iron abundance, and goodness of fitting at di ff erent distances with M2 are listed in the table (values without parentheses). For distances of 2.4 and 3 kpc, besides the results with the iron abundance freely fitted, we also include the fitting parameters set to a fixed iron abundance of 5 (values in parentheses).  \nkept the other parameter settings the same as in M1 , such as keeping the black hole mass fixed at 6.4 M ⊙ . Additionally, similar to M1 , we fixed the distance parameter at two specific values: D = 2.4 kpc ( M2A ; See Table A.1) and D = 6.9 kpc ( M2B ), respectively.  \nThe fitting results with M2 are showed in Table 4 and Fig. 3. Compared to M1 , the fitting results of M2 did not exhibit notable di ff erences, with M2A leading to a high spin value of a ∗ ∼ 0.97, and M2B resulting in a lower spin value of a ∗ ∼ 0.46. These dis-  \nes in spin are attributed to the di ff erent distance assumptions. To investigate the influence of distance variations on spin measurements, by maintaining a constant BH mass, we conduct additional spectral fits using M2 with di ff erent distance parameters. The resulting spin values, inclination angles, accretion rate of Data Set 1, iron abundance, and goodness of fit are detailed in Table 5. The analysis revealed that the best-fit iron abundance exhibits two distinct sets of values: for distances of 2.4 and 3 kpc,  \nFig. 3. Spectra (black for Insight-HXMT / LE, red for InsightHXMT / ME, green for Insight-HXMT / HE, gray for NuSTAR / FPMA and blue for NuSTAR / FPMB), model components of M2B , and spectral residuals of M2A and M2B . The black solid line is the total model fitted to the data, and the yellow and purple dotted lines show the kerrbb2 and relxill spectral components, respectively. The models are plotted based on the best-fit parameters obtained from Insight-HXMT.  \n<!-- image -->  \nwe observe very high values of A Fe > 9 . 3; in contrast, for distances between 4 and 8 kpc, the iron abundance stabilizes around A Fe ∼ 5. The latter A Fe is similar to the values measured for other BH binaries, such as GX 339-4 with A Fe = 5 ± 1 (García et al. 2015), V404 Cyg with A Fe ∼ 5 (Walton et al. 2017), and Cyg X1 with A Fe = 4 . 7 ± 0 . 1 (Parker et al. 2015). To examine the e ff ect of di ff erent A Fe, we fixed A Fe at 5 for distances of 2.4 and 3 kpc during the fitting process. The corresponding results are shown in Table 5 in parentheses, where a ∗ shows a slight decrease and i becomes more consistent with the cases of larger distances. Our analysis demonstrates a significant decrease in the spin with increasing distance. This emphasizes the importance of accurate distance determination when using continuum spectrum fitting for BH spin measurements. Any inaccuracies in the distance estimation can lead to deviations in the measured spin values, even if the reflection component modeling is also employed.", '4. Discussion': 'In this paper, we perform a joint fitting of the simultaneous spectra of GRS 1716-249 observed by Insight-HXMT and NuSTAR. The data used are obtained during the softest phase of the out-  \nFig. 4. Comparison diagram of di ff erent models. Top panel: Di ff erent models and their disk components and reflection components. Bottom panel: The ratio of each model relative to M2B .  \n<!-- image -->  \nburst, where the disk component is most prominent and the inner edge of the disk is located at the ISCO (Bassi et al. 2019). Additionally, the presence of significant reflection features in the spectra allows us to measure the spin and inclination of the black hole using a combined fitting method of the continuum and reflection components.', '4.1. System Parameters with Updated Distance': 'The fitting of the continuum is intrinsically linked to the distance, as altering the distance will impact the determination of the inner disk radius, consequently influencing the constraint on the spin. By fitting the spectra using M2 with varying distance parameters, we obtain distinct spin results (refer to Table 5). Notably, assuming a distance of 2.4 kpc, we obtain a near-extreme spin, aligning with the findings in Tao et al. (2019). However, assuming a distance of 6.9 kpc based on the recent works of Saikia et al. (2022) and Casares et al. (2023), resulted in a moderate spin of a ∗ ∼ 0 . 46, implying that this source is not a rapidly rotating BH. This suggests that the spin was previously overestimated under the prior distance assumption. The disk inclination, even with varying distance assumptions, remains nearly constant  \nTable 6. Joint fitting parameters of Insight-HXMT and NuSTAR with Tbabs*(diskbb+relxill) .  \nNotes. All errors are quoted at the 90% confidence level. The definition of each parameter is the same as that in Table 3.  \naround 43 -47 · , which is within the error margin of the orbital inclination of 61 ± 15 · (with 68% confidence) as reported by Casares et al. (2023).  \nIn the joint fitting of the continuum and reflection spectra, the distance measurement primarily a ff ects the fitting of the continuum spectrum model ( kerrbb2 ). Therefore, to investigate the impact of distance changes on the model, we plotted the best-fit M2 with its disk component Kerrbb2 and reflection component relxill at di ff erent distances (shown as solid lines in Fig. 4). The variation in distance did not result in significant changes in the total models, with di ff erences of less than 2% in each energy band (see Fig. 4 bottom panel). Importantly, we found that the energy corresponding to the peak flux of the disk component ( E disk peak ) did not show significant changes. Since the observed flux is fixed, an increase in distance leads to an increase in the accretion rate, as indicated by the parameter ˙ M in Table 5. According to accretion disk theory (Shakura & Sunyaev 1973), when other parameters remain constant, an increase in the accretion rate causes E disk peak to shift towards higher energies, while a decrease in spin leads to an increase in R in ( = R ISCO), resulting in a decrease in E disk peak . Therefore, to maintain a constant E disk peak , the model compensates for the increase in accretion rate due to larger distances by reducing the spin. This corresponds to the inverse correlation between a ∗ and ˙ M shown in Figs. B.1-B.3.  \nFurthermore, when other parameters remain constant, an increase in BH mass will cause E disk peak to shift towards lower energies. In this case, the model compensates for the mass in-  \ncrease by increasing the spin. Therefore, within the constraints of distance and mass provided by Casares et al. (2023), setting the lower limit (upper limit) of distance and the upper limit (lower limit) of mass yields the upper (lower) limit of the spin. When fixing the distance at 5.8 kpc and the BH mass at 9 . 6 M ⊙ ( M3 ; See Table A.1), we obtain a moderately high spin value of a ∗ = 0 . 757 + 0 . 023 -0 . 011 , with a goodness of fit of χ 2 / dof = 6416.4 / 6358 (see Fig. B.4 for the parameter probability distribution of Data Set 1). When fixing the distance at 8 kpc and the BH mass at 4 . 4 M ⊙ ( M4 ; See Table A.1), we obtain a near non-rotating black hole with a ∗ = -0 . 008 + 0 . 011 -0 . 013 , with a goodness of fit of χ 2 / dof = 6499.9 / 6358. The red and green dashed lines in Fig. 4 represent M3 and M4 . Therefore, considering the upper and lower limits of distance and mass provided by Casares et al. (2023), there will be a wider range of spin with a ∗ < 0.78.  \nThe above discussion indicates that the variation in the measured spin values with changes in distance and mass is a result of the degeneracy in the model. A similar phenomenon was observed when measuring the spins of LMC X-1 and Cyg X-1 using continuum spectra (Zdziarski et al. 2024). Their analysis shows that the disk components dominate the spectra, so E disk peak derived from fitting matches the energy of the peak flux seen in the spectra ( E obs peak ). Increasing the hardening factor or convolving with Comptonization components outside the disk components will shift the E disk peak towards higher energies. To maintain E disk peak corresponding as closely as possible to E obs peak , the remaining free parameters in the continuum spectrum, spin, and accretion rate, will decrease accordingly to counteract the e ff ects of the hardening factor or Comptonization component.  \nFurthermore, the inconsistency in iron abundance at di ff erent distances as shown in Table 5 ( A Fe > 9.3 for D = 2.4 and 3 kpc; A Fe ∼ 5 for D = 4-8 kpc) primarily reflects not only the degeneracies among the parameters of the continuum model but also a certain level of competition between the continuum and reflection components, particularly in the low energy band of ≲ 2 keV (García et al. 2018a; Tomsick et al. 2018). For instance, M2 with D = 2.4 and 3 kpc, as depicted in Fig. 4, exhibits a relatively higher proportion of disk component and a diminished reflection component compared to other models. The shape of the reflection spectrum in the low energy is significantly influenced by the configuration of the incident spectrum and the parameters of the disk as the reflector, leading to intertwined dependencies among various parameters in the overall model and rendering the parameter space exceptionally complicated. Zdziarski et al. (2024) reported local minimum iron abundance of A Fe ≲ 1 and global minimum values of A Fe ∼ 8 at ∆ χ 2 ≈ -0 . 6 while fitting the spectra of LMC X-1 using continuum and reflection components ( kerrbb2+reflkerr ), thereby corroborating this point. Therefore, for obtaining more rational and precise parameters during spectral fitting, a comprehensive analysis of the entire parameter space is imperative to assess potential biases introduced.', '4.2. Further Insights into Spin Measurements': 'Given this, we attempted to replace kerrbb2 with diskbb , which only has two parameters, disk temperature T in in units of keV and Norm, without considering the impact of distance, and re-conduct the spectral fitting ( M5 = constant*tbabs*(diskbb+relxill) ; See Table A.1). The fitting results are shown in Table 6, which are very close to the fitting results of M1A . We obtain an extreme spin of a ∗ ≳ 0 . 99, which is similar to the results obtained by Draghis et al. (2023a) using the reflection component fitting method, that is, using the  \nmodel diskbb combined with a reflection model. Furthermore, utilizing diskbb Norm ≈ 5000-6000 and i ≈ 48 · of M5 , and assuming a distance of D = 5.8-8 kpc, a hardening factor of f h = 1 . 3 (from M1A ), and a boundary condition correction factor ζ = 0 . 412, we obtain the inner disk radius R in ≈ 35-53 km using the formula R in = √ Norm / cos i × ζ × f 2 h × D / 10kpc (Kubota et al. 1998). Assuming the source mass of 4.4-9.6 M ⊙ (Casares et al. 2023), the gravitational radius R g is about 6.5-14.3 km, thus M5 yields R in ≈ 2 . 4 -8 . 2 R g. By setting R in = R ISCO, the spin derived from the diskbb component is a ∗ ∼ -0 . 72 -0 . 88, which is inconsistent with the result of extreme spin obtained from the reflection model.  \nSimilar to GRS 1716-249, when constraining the spin of some other sources, such as LMC X-3 (Draghis et al. 2023a; Steiner et al. 2014), H 1743-322 (Draghis et al. 2023b; Steiner et al. 2012), and MAXI J1820 + 070 (Draghis et al. 2023b; Guan et al. 2021; Zhao et al. 2021), results obtained solely from the reflection component fitting method yield close to extreme spin values, while the continuum spectrum fitting method yields low spins of a ∗ ≲ 0 . 3. The examples above demonstrate that when fitting the spectrum, using either the continuum or the reflection component fitting method separately resulted in di ff erent inner radii of the accretion disk, leading to di ff erent spin values and hence physically inconsistent results. The joint fitting method of the continuum and reflection components may help to avoid this issue by considering the jointly optimal parameter space during the fitting process.', '5. Conclusion': 'In conclusion, we re-evaluated several key parameters of the black hole GRS 1716-249 utilizing simultaneous data from Insight-HXMT and NuSTAR. This paper, through the application of a combined fitting method for the continuum and reflection components and the integration of updated distance and black hole mass, found that the black hole has a moderate spin and a moderately inclined accretion disk. Given the source distance of 6.9 kpc and the black hole mass of 6.4 M ⊙ , a ∗ is 0 . 464 + 0 . 016 -0 . 007 and i is 43 . 8 + 0 . 5 -0 . 8 · with 90% confidence level. Taking into account the uncertainties in distance and black hole mass, the spin range extends with a ∗ < 0.78.  \nAcknowledgements. We thank the anonymous referee for useful comments that have allowed us to improved this manuscript. This work made use of data from the Insight-HXMT mission, a project funded by China National Space Administration (CNSA) and the Chinese Academy of Sciences (CAS). This work is supported by the National Key R&D Program of China (2021YFA0718500). 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Various models and the setting of the black hole mass ( M ) and distance ( D ) parameters in the disk components.  \n```\nM1 = constant*tbabs*(kerrbb+relxill) with M = 6 . 4 M ⊙ M1A = M1 with D = 2.4 kpc M1B = M1 with D = 6.9 kpc M2 = constant*tbabs*(kerrbb2+relxill) with M = 6 . 4 M ⊙ M2A = M2 with D = 2.4 kpc M2B = M2 with D = 6.9 kpc M3 = constant*tbabs*(kerrbb2+relxill) with M = 9 . 6 M ⊙ and D = 5.8 kpc M4 = constant*tbabs*(kerrbb2+relxill) with M = 4 . 4 M ⊙ and D = 8 kpc M5 = constant*tbabs*(diskbb+relxill)\n```  \nFig. B.1. Probability distributions of the parameters for M1B obtained from Data Set 1 through MCMC.  \n<!-- image -->  \nFig. B.2. Probability distributions of the parameters for M2A obtained from Data Set 1 through MCMC.  \n<!-- image -->  \nFig. B.3. Probability distributions of the parameters for M2B obtained from Data Set 1 through MCMC.  \n<!-- image -->  \nFig. B.4. Probability distributions of the parameters for M3 obtained from Data Set 1 through MCMC.  \n<!-- image -->'}