Decomposing X-ray Variability in Seyfert I AGN with Principal Component Analysis

Decomposing X-ray Variability in Seyfert I AGN with Principal Component Analysis Ashkbiz ‘Ash’ Danehkar Eureka Scientific, 2452 Delmer St Suite 100, Oakland, CA 94602, USA Summary | We use principal component analysis (PCA) to investigate the X-ray variability in some Seyfert I AGN (NGC 3783 presented here). Our PCA results indicate that changes in the normalization of power-law source are mainly responsible for the hardness transition. Higher-order PCA components include small variations in ionizing absorbers, which may be caused by time delays between different layers in outflows, in addition to a tiny contribution from relativistic blurred reflection caused by light-bending near the event horizon, which is consistent with the fact that the supermassive black hole spin remains stable over the course of observations. Brenneman, Reynolds, Nowak, et al. 2011, ApJ, 736, 103 Danehkar & Brandt 2024, ApJ, submitted Danehkar, Drake & Luna, 2024a, ApJ, accepted, arXiv:2406.17161 Danehkar, Silich, Herenz & Östlin, 2024b, A&A, accepted, arXiv:2407.01604 Danehkar, et al. 2024c, in preparation References CONCLUDING REMARKS TIMING AND HARDNESS ANALYSES To assess the X-ray variability, we generate light curves within specific energy bands: Soft (S: 0.4–1.1 keV), Medium (M: 1.1–2.6 keV), Hard (H: 2.6–10 keV). The hardness ratios are computed using the light curves in the following manner: FIG 1. Light curves (left) and hardness diagrams (right) of NGC 3783 in the bands S+M and M+H along with the hardness ratios binned at 600 sec made with the XMM-Newton, from Danehkar et al. (2024c). PCA COMPONENTS E-mail: [email protected] INTRODUCTION Some active galactic nuclei (AGN) in Seyfert I galaxies show stochastic variability in addition to hardness transitions similar to those seen in X-ray binaries, according to X-ray surveys. This type of transient obscuration has been identified in NGC 3783 (Mehdipour et al. 2017; Kriss et al. 2019), NGC 3227 (Turner et al. 2018), Mrk 335 (Longinotti et al. 2019), and a few other AGNs. We do not fully understand the origin of such transition X-ray variability, but we attribute some to transient obscuration events caused by eclipsing outflow and others to X-ray coronal flares. Because the spin of a supermassive black hole (SMBH) stays constant over human timescales, this kind of X-ray variability should have no impact on relativistic reflection. To check the variations of relativistic reflection, we can decompose X-ray variability via PCA into principal components that mainly cause the X-ray fluctuations (see e.g., Danehkar et al. 2024a,b). FIG 4. The PCA components fi(E) (left) and the corresponding time series Ai(t) (right) obtained with the XMM-Newton (pn) and Suzaku (XIS1) time-sliced data of NGC 3783 (Danehkar et al. 2024c). We conduct spectral analysis with two sets of XMM-Newton data of NGC 3783 taken in the high/soft (2000–2001) and low/hard states (2016), which are simultaneously fitted together with NuSTAR data (Fig. 2). Despite hardness changes due to transient obscuration events, the black-hole spin remains the same at a = 0.994. This is in agreement with a ⩾ 0.89 found by Brenneman et al. (2011) and Reynolds et al. (2012), as well as analysis of Chandra data (Danehkar & Brandt 2024). Singular Value Decomposition (SVD): M=U⋅Σ⋅V M: matrix (m ⨯ n), spectra of n time-segmented data binned with m energies, U: unitary matrix (m ⨯ m), PCA components, energy-binned spectra fi(E), Σ: diagonal matrix (m ⨯ n), PCA eigenvalues, variability fractions λi, V: square matrix (n ⨯ n), PCA eigenvectors, time-binned light curves Ai(t). PRINCIPAL COMPONENT ANALYSIS SPECTRAL ANALYSIS Figure 1 shows the light curves and hardness diagrams of NGC 3783. The uncertainties were computed using the program BEHR (Park et al. 2006). Observations indicate that the source was harder in 2016 is compared to those between 2000 and 2001, while the bands S+M and M+H were lower than the previous observations. Figure 4 displays the PCA spectra fk(E) and light curves Ak(t) (eigenvectors) derived from time-segmented data from the XMM (pn) and Suzaku (XIS1) datasets of NGC 3783. Following Parker et al. (2018)'s approach, we consider these PCA components to be statistically significant because they deviate from the linear correlations depicted in the log-eigenvalue diagrams (see Figure 3). We employ a customized version of the Python code developed by Parker et al. (2015) to conduct principal components analysis (PCA). PCA is a method used to break down temporal variable data into its various components. This code uses the singular value decomposition (SVD) function to separate a collection of timesegmented spectra into the PCA components (spectra), eigenvalues, and eigenvectors (time series) in the following manner: FIG 3. log-eigenvalue diagrams of PCA components derived from the XMM-Newton and Suzaku data of NGC 3783. The correlation among eigenvalues with the orders of > 3 is plotted (Danehkar et al. 2024c). The line in the log-eigenvalue diagrams in Fig. 3 represents a linear correlation between logarithmic eigenvalues with orders higher than 3. These eigenvalues were obtained from XMM (pn) and Suzaku (XIS1) data. This correlation may be associated with background noise. Our findings are summarized as follows: X-ray variability mainly (>90%) corresponds to the variations in the continuum of a power-law emitting source of the corona above the inner accretion disk. Tiny variability (<2%) in relativistic reflection is likely made by light-bending near the event horizon. variability has no effect on the spin derived from all multi-epoch observations. In conclusion, PCA decomposition could help us make X-ray variability in AGN less complicated, leading to simpler data that could be used for more accurate spectral analysis with complex algorithms such as machine learning. AD acknowledges NASA grant 80NSSC22K0626. Kriss, Mehdipour, Kaastra, et al. 2019, A&A, 621, A12 Longinotti, Kriss, Krongold, et al. 2019, ApJ, 875, 150 Mehdipour, Kaastra, Kriss, et al. 2017, A&A, 607, A28 Parker, Reeves, Matzeu, et al. 2018, MNRAS, 474, 108 Parker, Fabian, Matt, et al. 2015, MNRAS, 447, 72 Reynolds, Brenneman, Lohfink, et al. 2012, ApJ, 755, 88 Turner, Reeves, Braito, et al. 2018, MNRAS, 481, 2470 FIG 2. The XMM-Newton/EPIC-pn data of NGC 3783 in the high/soft (2000–2001; left) and low/hard states (2016; right) simultaneously fitted together with the NuSTAR data (Danehkar et al. 2024c). Powerlaw Norm Powerlaw Index Reflection Likely noise Powerlaw Norm Powerlaw Index Reflection Likely noise Powerlaw Norm Powerlaw Index Reflection Powerlaw Norm Powerlaw Index Reflection FIG 5. The spectra of the third PCA components reconstructed from the XMM-Newton/EPIC-pn data of NGC 3783 (Danehkar et al. 2024c). To evaluate the third PCA component associated with relativistic reflection in NGC 3783, we created an XSPECcompatible spectrum with the FTOOL program ftflx2xsp. We fitted the reconstructed spectrum to a relativistic reflection line model (relline), as shown in Figure 5. This feature aligns with the spin rate of 0.97, in line with the spectral analysis value (see Fig. 2). The variations in relativistic reflection could be due to light bending near the event horizon.