The Spin of New Black Hole Candidate: MAXI J1803-298 Observed by NuSTAR and NICER

MAXI J1803-298 was observed by NuSTAR on May 23, 2021 (ObsID: 90702318002). According to standard procedures³³3https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/nustar_swguide.pdf, we process the NuSTAR data using HEAsoft v6.28 based on the calibration files v20210315. We use a circle centered on the position of the source with a radius of $80^{\prime\prime}$ to extract the source spectra. The background spectra are extracted with the same radius. In addition, we also make the dead-time correction. FPMA and FPMB are fitted jointly over 3.0-79.0 keV.

Considering that NICER has three observations on the same day with NuSTAR, we select the observation (OBsID: 4202130110) with more overlapping time with NuSTAR observation. We process the NICER data following the standard steps⁴⁴4https://heasarc.gsfc.nasa.gov/docs/nicer/analysis_threads/ based on the latest calibration files⁵⁵5https://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/caldb_supported_missions.html v202107220315. We use tools nicerl2⁶⁶6https://heasarc.gsfc.nasa.gov/docs/nicer/analysis_threads/nicerl2/ and nibackgen3C50⁷⁷7https://heasarc.gsfc.nasa.gov/docs/nicer/tools/nicer_bkg_est_tools.html to extract the source and background spectra, respectively. The response matrix 20170601v003 and ancillary file 20170601v005⁸⁸8https://heasarc.gsfc.nasa.gov/docs/nicer/analysis_threads/arf-rmf/ are used. Dead-time correction is applied. Considering the impact of low energy noise (< 0.5 keV), in this work, the spectrum of NICER is fitted over the energy band of 0.7-10.0 keV, ignoring the energy range of 1.7-2.1 keV (calibration residuals remain found in Si band) and 2.2-2.3 keV (calibration residuals remain in Au edges), respectively. Details of NICER calibration are described in LaMarr et al. (2016). Furthermore, following Jaisawal et al. (2019), we also add the systematic error of 1.5% with command fparkey⁹⁹9https://heasarc.gsfc.nasa.gov/lheasoft/ftools/fhelp/fparkey.html.

We first fit the NuSTAR and NICER/XTI data with our preliminary model: crabcor*constant*TBabs*(diskbb+powerlaw). Model crabcor is described in Section 2. Model constant coordinates the calibration differences in different instruments in the process of joint fit. As to the model constant, we mainly fix the constant of NICER $C_{\mathrm{NICER}}$ to 1 and allow the constant of FPMA $C_{\mathrm{FPMA}}$ and FPMB $C_{\mathrm{FPMB}}$ to vary. The subsequent usage of constant is the same. TBabs is the Galactic interstellar medium absorption model, and we set the abundance in Wilms et al. (2000) and put the cross-section in Verner et al. (1996). Finally, we find a broadened iron line at 6.0-7.0 keV, and a Compton hump at 20.0-30.0 keV with a reduced chi-square $\chi_{v}^{2}=1.64$ (4244.66/2592), by ignoring the 6.0-8.0 keV and 20.0-40.0 keV energy range (Figure 2).

To study the reflection features of MAXI J1803-298, we firstly focus on the basic properties of the broadened iron line with model: crabcor*constant*TBabs*(diskbb+powerlaw+gauss). After setting the central energy of the Gaussian line profile to 6.4-6.97 keV, we obtain that the equivalent width of the broadened iron line is 618 eV for NICER data and 418 eV for NuSTAR data, respectively, and the line peak is pegged at $E=6.97$ keV, with $\chi_{v}^{2}=1.42$ (3670.21/2589).

In order to analyze the reflection composition better, we use a physical model which utilizes a Comptonization continuum as an incident spectrum, i.e., crabcor*constant*TBabs*(diskbb+relxillCp). To ensure the inner radius of the accretion disk has extended to the innermost stable circular orbit (ISCO), during the fitting process, we set the disk inner radius ($R_{\text{in}}$) fitted freely, while we fix the dimensionless spin of black hole ($a_{*}$) to its maximum value ($a_{*}=0.998$). We also bound the emissivity index of inner region ($q_{\mathrm{in}}$) in 3-10, the emissivity index of outer region ($q_{\mathrm{out}}$) in the range of 0-3, and the break radius ($R_{\mathrm{br}}$) in $2R_{\mathrm{g}}-6R_{\mathrm{g}}$, where $R_{\mathrm{g}}=\mathrm{GM}/c^{2}$ is the gravitational radius (see Miller et al. 2018 for details), then allow them to fit freely within the range above. Owing to the limited fitting energy range, we also fix the electron temperature of corona ($kT_{\text{e}}$) at 1/3 default value of the power-law cut-off energy ($E_{\text{cut}}=300\mathrm{~{}keV}$), i.e., $kT_{\text{e}}=100\mathrm{~{}keV}$. The outer radius of disk ($R_{\text{out}}$) is fixed at its default value (400 $R_{\text{g}}$), iron abundance ($A_{\mathrm{Fe}}$) is fixed at a solar iron abundance, and redshift (z) is fixed at zero. We set other parameters (hydrogen column density ($N_{\mathrm{H}}$), inclination angle ($i$), photon index of the X-ray spectrum ($\Gamma$), ionization state of accretion disk ($\log\xi$), reflection fraction ($R_{\text{ref}}$) and normalization ($N_{\text{relxillCp}}$) ) to vary freely. We name the model above as Model A. We also define our baseline model, Model B, which differs only from Model A in freeing the spin and fixing the $R_{\text{in}}$ to an ISCO. We list the detailed fitting results for both Model A and B in Table 2, and the spectral fit of Model B is shown in Figure 3. We also use command steppar in XSPEC, to search for the best fit for the spin from 0.99 to 0.998 for our baseline model, as shown in Figure 4. The three dashed lines represent 99%, 90%, and 68% confidence levels from top to bottom.

From Model B, we can easily find a steep broken power-law emissivity profile, of which the upper limit of the inner emissivity index is pegged at 10 (taking $q_{\text{in}}$ as an example, the contour plot of $a_{*}$ and $q_{\text{in}}$ as shown in Figure 5), the outer emissivity index is pegged at 3, and a small break radius is pegged at 6 $R_{\mathrm{g}}$. This phenomenon is common among BHXRBs, which can be explained by a compact corona close to the black hole (e.g., Wilkins & Fabian 2012). This is because, if the corona is far away from the black hole, the light-bending will be weak, and the reflection fraction will be less than 1. Conversely, our results show that the reflection fraction of relxillCp in Model B is $R_{\text{ref}}$=$2.87\pm 0.84$, which confirms our inference.

In Model B, we fix iron abundance to a standard solar iron abundance, but the reality may be more complex. To test the quantity effect on fitting results caused by variation of iron abundance, we change the iron abundance to its typical value ($A_{\mathrm{Fe}}=5A_{\mathrm{Fe},\odot}$) of most sources (García et al. 2018), and name it as Model C. For the convenience of comparison, we also list the result of Model C in Table 2. The spin only changes 0.5% from Model B ($\chi_{\nu}^{2}$=1.063) to Model C ($\chi_{\nu}^{2}$=1.007), while the inclination angle varies 3.7%. Therefore, for MAXI J1803-298, we conclude that the iron abundance has a negligible effect on our results.

Another parameter that may affect the result is the electron temperature of the corona. For Model D, we fix $kT_{\text{e}}$ to its default maximum value (400 keV) and other parameters are the same as Model B. We still list the relevant result in Table 2. We can easily find that the best-fitting parameters did not change significantly, like spin $a_{*}=0.995^{+0.001}_{-0.002}$ ($a_{*}=0.991$$\pm$0.001) and inclination $i=73.4\pm 1.3$ degree (70.8 $\pm$ 1.1 degree) in Model D (Model B). Similarly, we can see that the electron temperature of the corona has no significant effect on the spin.

Though we can not find additional narrow iron line composition from in Figure 3. To test the contribution of the cold plasma faraway to the spectra, we still add a second non-relativistic reflection Model xillverCp over Model B. The full expression is crabcor*constant*TBabs*(diskbb+relxillCp+xillverCp) (Model E). Except for the ionization state ($\log\xi$), the reflection fraction ($R_{\text{ref}}$), and the normalization of xillverCp ($N_{\text{xillverCp}}$), we link the parameters of model xillverCp with that of model relxillCp. Since the materials are neutral owing to the farther distance from the central black hole, we fix the $\log\xi=0$ in xillvercp. Moreover, we fix the reflection fraction of xillverCp to -1 and let $N_{\text{xillverCp}}$ be free. To simplify the fitting parameters, we also fix $q_{\text{in }}$, $q_{\text{in}}$ and $R_{\mathrm{br}}$ to the same value in Model B. We list the result in Table 2. Comparing the results between Model E and Model B, it can be seen that the addition of the non-relativistic reflection component does not improve the results, so we prefer not to add the second reflection component that xillverCp for MAXI J1803-298.