Hard X-ray emission in Centaurus A

We investigated the X-ray flux and spectral variations of the source using data from the Neil Gehrels Swift Observatory/Burst Alert Telescope (Swift/BAT) 157-Month Hard X-ray Survey¹¹1https://swift.gsfc.nasa.gov/results/bs157mon/671. While in survey mode (not specifically targeting a GRB), BAT continuously scans the sky with a time resolution as fine as 64 s (Krimm et al., 2013). Monthly averaged light curves and spectra of sources in the hard X-ray (14-195 KeV) sky are publicly available at https://swift.gsfc.nasa.gov/results/bs157mon/671. In addition to the 8-band (14-20, 20-24, 24-35, 35-50, 50-75, 75-100, 100-150, and 150-195 KeV) monthly averaged data, the website also provides 8-band snapshot light curves, starting from 2005. The snapshot light curves are extremely useful for exploring the short-timescale variability. The snapshot data is binned to generate 10-day binned light curves in different energy bands, then a total count rate for the 14-100 KeV energy range. While binning, we flagged the low-exposure ($<$1 day) epochs to reduce systematic errors. Given the low single-to-noise (S/N) ratio in bands 7 and 8, we discarded the 100-195 KeV energy band data.

Figure 1 (a) shows the monthly averaged hard X-ray (14-195 KeV) light curve from Dec. 2004 until Dec. 2017 (blue circles). Prominent flux variations were detected in the source during this period. The red squares show the 10-days binned light curves in the 14-100 KeV energy range. The count rates are scaled by a factor of 15 for visualization only. Given the high single-to-noise (S/N) ratio in the monthly binned data, the intensity variations can be studied in different energy bands. Photon flux light curves in different energy bands, 14-20, 20-24, 24-35, 35-50, 50-75, 75-100, and 100-150 KeV, are plotted in panel (b). Band 8 (150-195 KeV) is not included in the plot because of low S/N ratio. Similar variations are seen across the multiple bands. Variability is less pronounced at higher energy bands ($>$75 KeV) because of the low S/N ratio.

Monthly (blue circles) and bimonthly (red squares) averaged hard X-ray photon index curve are illustrated in Fig. 1 (c). Despite significant flux variations in the X-ray bands, changes in the photon index were small but significant ($\Gamma$ $\sim$1.7 – 1.9) until the end of 2012. Spectral variations were more pronounced afterward. Steepening of the spectrum was observed until December 2013, reaching $\Gamma$ $\sim$2.0. Later, spectral hardening occurred until February 2015 ($\Gamma$ $\sim$1.7). The spectra soften back to the average value ($\Gamma$ $\sim$1.8) in recent years, with some mild variations. In short, the hard X-ray spectra follow a steeper-when-brighter trend. The trend is evident in index versus photon flux plot (Fig. 2 top). A linear Pearson correlation test is used to quantify the correlation; we obtained $r_{P}$ (correlation coefficient) = 0.43 at the 99.8$\%$ confidence level for the bimonthly binned data, and $r_{P}$ = 0.16 at the 90$\%$ confidence level for the monthly binned data.

We further investigate the spectral variability by analyzing hardness ratio (HR) time series. The monthly averaged data is used to calculate the time series in the following three energy bands: low or L-channel from 14-24 keV, medium or M-channel from 24-50 keV, and high or H-channel from 50-150 keV. We rebin the hard X-ray spectrum in this way in order to maximize the signal-to-noise. (We exclude the 150-195 keV data due to low S/N ratio.) We then calculate HR values using those three channels, and confirm through a chi-squared test that the HR time series show statistically significant variability (p-value $<$0.05). Ratios of the time-series in different channels (HM versus HL) are then plotted against each other to produce an “HR-plane” (Fig. 2 black circles), and are used to investigate the nature of the spectral variability in the source. A visual correlation can be seen between the HL and ML ratios. Linear Pearson correlation analysis confirms the correlation between the two. Formally we get, the Pearson correlation coefficient equals to 0.71 at $>$99.99$\%$ confidence level. We further tested the spectral variations using simulations. The spectral simulations, using different power law slopes, were performed using the ’fakeit’ command on Xspec (Arnaud, 1996). The simulations were based on the simple ”pegpwrlw” model, with $\Gamma$ in the range of 1 to 3 (typical photon indices of AGN in the Swift/BAT catalog). We then calculated the hardness ratios from the fake spectra (shown as colored stars in Fig. 2). The details of the simulations can be found in Mundo et al. 2022 (in preparation). The simulated points agree with the data, suggesting that the changing spectrum can be well described as a simple power-law with a varying photon index over monthly timescales, spanning the range  1.6–2.

The nature of hard X-ray variability in the source is explored using the power spectrum density (PSD Vaughan et al., 2003) analysis method. Both monthly averaged 14-195 KeV (data A) and 10-day binned 14-100 KeV (data B) light curves are used for the PSD analysis. As a first step, we calculated the raw PSDs, squared modulus of the discrete Fourier transform. The raw PSDs are then logarithmically binned to extract the slope of the underlying power spectrum, $P(f)\propto f^{\alpha}$ (details are referred to Chidiac et al., 2016). The Poisson noise level in the PSD is calculated following Vaughan et al. (2003). The PSD analysis results are shown in Fig. 3, where cyan and brown steps are the raw PSDs respectively for data A and data B, blue circles and red squares are their logarithmic binned values; errors mark the scatter of the raw PSD points. The best-fit power-law slope for data A is $-(1.36\pm 0.16)$, and for data B is $-(1.29\pm 0.11)$. A combined power-law fit gives, $\alpha$ = $-(1.27\pm 0.13)$ (black dashed line in Fig. 3). We do not find any evidence of a break in the PSD, as is sometimes seen in the 2-10 KeV PSD of Seyfert galaxies (Vaughan et al., 2005). A similar value of the PSD slope was reported by Shimizu & Mushotzky (2013) using 58 months of the Swift/BAT data, and comparable slopes have been seen in PSDs of beamed AGN (Chidiac et al., 2016; Algaba et al., 2018) as well. This implies that the hard X-ray variability of the source can be characterized simply as a red-noise process. Since there is no excess power at any frequency in the given time range, the PSD analysis rules out the presence of periodic variations in the source.

We used the 230 GHz data provided by the Submillimeter Array (SMA) Observer Center²²2http://sma1.sma.hawaii.edu/callist/callist.html database (Gurwell et al., 2007) to investigate the flux variations in the radio regime. Figure 4 (red squares) shows the flux density variations observed in the source since July 2005. The radio flux variations are superimposed on top of a constant flux level of about 6 Jy (dashed line), and this could be related to the extended jet emission (see Section 3.1 for details). Compared to X-rays (blue circles), the radio data is sparsely sampled, especially in the beginning (segment T1). Some similarities in the long-term decay trend can be seen in the two data sets over segment T2, and the flux variations are quite similar afterward (segment T3).

The apparent correlation among X-ray and radio data sets was quantified using the discrete correlation function (DCF Edelson & Krolik, 1988) method, and the significance of the correlation was tested via simulations as discussed in Rani et al. (Section A 2014). The DCF results are presented in Fig. 4 (right). Monthly binned DCF points are in blue, while the red curves shows the 95$\%$ confidence levels. The DCF analysis of the two data sets shows a peak above 95$\%$ confidence level at 0 days. This implies that the flux variations at X-ray and regimes are well correlated with no time lag. Since the X-ray data is monthly sampled, a time-delay shorter than 30 days cannot be tested. The correlation analysis therefore suggests that the hard X-rays and radio emission regions are co-spatial. This agrees with a tight correlation found among the parsec-scale radio luminosity and X-ray luminosity of BAT detected Seyfert galaxies (Baek et al., 2019). Radio and X-ray (especially soft X-rays) correlations have also been reported in several other Seyfert galaxies (Chatterjee et al., 2009, 2011; Marscher et al., 2018) and explicitly used to probe the disk-jet connection in AGN.

There have been many PSD studies of AGN, characterizing the PSD slopes, breaks, and their relation to the physical properties of the central engine. Breaks are a common feature in the PSDs of Seyfert galaxies (Papadakis, 2004; Done & Gierliński, 2005; Markowitz et al., 2003). These studies, however, are focused on the soft X-ray emission ($<$10 KeV), and the hard X-ray variability studies differ from this picture (Shimizu & Mushotzky, 2013). The hard X-ray PSD of Cen A is well-fitted using a slope of $-1.3$, with no evidence of a break. If we scale the breaks seen in the X-ray PSDs by the mass as in McHardy et al. (2004), the predicted break timescale is higher than 20 days (log10 (Frequency) $>-1.3$ day^-1) and thus is not sensed by the BAT data. It is important to note that, unlike Seyfert galaxies, Cen A is a low-luminosity radio-loud AGN, and as our study suggests, the PSD slope is comparable to that has been seen in PSDs of beamed AGN.

Except for the power-law slope ($\Gamma$ = 1.6–2.0), the X-ray spectrum of the source (no reflection and very high cutoff-Energy, Fürst et al., 2016) differs from that of Seyfert galaxies. Since the power-law slope from the jet and from the thermal Compotonization is very similar, the spectral slope cannot be used as a distinction between the two. However, the difference in source spectrum and temporal variations favor that the nature of X-ray emission in Cen A is similar to beamed AGN.

The radio variations comprise of two components, quiescent and variable. As shown in Fig. 4, even at 230 GHz, we have about 6 Jy contribution from the extended jet region. Earlier studies found a contribution of about 7 Jy from the extended jet emission in the total flux density of the source (Israel et al., 2008). Since Cen A has a complex extended jet structure, the location of the variable component remained unclear. Using continuum observations in the millimeter and sub-millimeter regime, Israel et al. (2008) investigated the flux and spectral variability of the source, and reported that most (if not all) variations are from the milli-arcsecond core. On micro-arcsecond scales, the Event Horizon Telescope (EHT) discovered a completely different picture of the core (Janssen et al., 2021). The core of the source is opaque at 230 GHz and the turnover frequency is at $\sim$THz frequencies. The source has a flux density of $\sim$2 Jy with an edge-brightened jet. It is quite probable that either the flux density of the core or of the two lanes is varying, but multiple observations are required to confirm that. The radio luminosity of the source, measured by the EHT, is 7.5$\times$10³⁹ erg s^-1. However, EHT observed the source not in its brightest phase (see Fig. 4). After subtracting the quiescent flux (6 Jy) from the total flux, the peak flux of the variable component is $\sim$7 Jy, which corresponds to 2.6$\times$10⁴⁰ erg s^-1.

In an ADAF model, the radio emission is because of cyclo-synchrotron radiation from hot electrons in the equipartition magnetic field; it should be isotropic. In the absence of a radio jet, the expected radio luminosity is roughly proportional to the mass of the central black hole and its accretion rate (Yi & Boughn, 1999; Mahadevan, 1997), and is given by

where $m_{7}$ is the black hole mass in units of 10⁷ M_⊙ and ${\dot{m}}_{-3}$ = ${\dot{m}}/10^{-3}$, ${\dot{m}}$ is accretion in units of Eddington rate. Using $m_{7}$ = 5 (Neumayer, 2010) and ${\dot{m}}_{-3}$ = 0.2 (Evans et al., 2004), the 230 GHz ADAF luminosity for Cen A is $\sim$5$\times$10³⁸ erg s^-1, which is significantly lower than the observed 230 GHz radio luminosity. This implies that the ADAF component has a negligible contribution to the observed radio luminosity of the source.

Jet luminosity, in case of mainly powered by black hole accretion, can be estimated using eq. 9 in Janssen et al. (2021),

where $0\leq a_{*}\leq 1$ is the normalized black hole spin, $1\leq\phi\leq 15$ is the normalized magnetic flux at the black hole event horizon, $f(a_{*})\approx a_{*}^{2}\left(1+\sqrt{(1-a_{*}^{2})}\right)^{-2}$ (for $a_{*}<0.95$), $\dot{M}=2\times 10^{-4}\dot{M}_{\rm edd}$, and $M=5\times 10^{7}M_{\odot}$. For $a_{*}\leq 0.2$ and $\phi\leq 1$, we have a marginally low jet power of $P_{\rm jet}\leq\times 10^{39}\rm erg\,s^{-1}$. Slightly larger values of $a_{*}=0.3$ and $\phi=2$ gives $P_{\rm jet}$ $\sim 1.5\times 10^{40}\rm erg\,s^{-1}$, which well explains the observed radio luminosity.

Both ADAF and jet models predict a strong correlation between radio and X-ray flux variations. However, the ADAF models predict a very characteristic spectrum of slope 1/3 in the radio regime (Mahadevan, 1997). The observed radio spectrum of the source has a slope of $\sim$ 0.7 below the turnover frequency (around 5 to 20 GHz). A slightly steeper spectrum, slope  0.8, is observed at higher frequencies (Israel et al., 2008). This implies that the observed radio spectrum of the source is not consistent with the ADAF model. Moreover, the shape of the hard X-ray spectrum in ADAF models is thermal bremsstrahlung not a power-law. For low luminosity AGN (accreting close to m_critical = 0.003 to 0.02, Mahadevan, 1997; Narayan, 1996), X-ray spectrum is very hard ($\Gamma$ $\sim$0.7). The power-law spectrum of Cen A, $\Gamma$ varying between 1.7 to 2, rules out the ADAF models. Another factor that argues in favor of the jet-based origin of the hard X-ray emission is the steeping of the X-ray spectrum as the source gets brighter. ADAF models predict harder-when-brighter behavior (Esin et al., 1997). As discussed in Section 2.1, the spectrum gets steeper while the source gets brighter.