Black hole mass estimate in OJ 287 based on the bulk-motion comptonization model

ABSTRACT

The multiwavelength outburst activity in the BL Lacertae source OJ 287 has sparked a lot of controversy about whether the source contains one or two black holes (BHs) and what characteristics of this BH binary would be. In this article, we present the results of analysis of the X-ray flaring activity of OJ 287 using the data of Swift/XRT observations. We discovered that the energy spectra in all spectral states can be adequately fit with the XSPEC bulk-motion Comptonization (BMC) model. As a result, we found that the X-ray photon index of the BMC model, |$\Gamma$| correlates with the mass accretion rate, |$\dot{M}$|⁠. We found the photon index |$\Gamma$| to increase monotonically with accretion rate |$\dot{M}$| from |$\Gamma \sim 2$| in the intermediate state (IS) to |$\Gamma \sim 2.5$| the high/soft state (HSS) with subsequent saturation at |$\Gamma \sim$| 2.6 level at higher luminosities. This type of behaviour of the spectral index is remarkably similar to the pattern observed in a number of established stellar-mass BH candidates. Assuming the universality of the observed pattern of the correlation between the photon index and mass accretion rate and using the well-studied stellar-mass binaries GX 339–4 and XTE J1859–226 to calibrate the model, we estimate a BH mass |$\sim 2\times 10^8$| solar masses, which likely pertains to the secondary component of the BH binary in OJ 287.

1 INTRODUCTION

The primary goal of our paper is to examine the value of the secondary black hole (BH) mass in the blazar OJ 287 applying the scaling method of BH mass determination (Shaposhnikov & Titarchuk 2009, hereafter ST09). OJ 287 demonstrated a noticeable 12 yr cycle (Valtonen et al. 2024, 2006) that can be explained by the presence of an accreting black hole binary system with systematic disturbance of the accretion disc (AD) around the primary by the secondary.

Valtonen, Ciprini & Pihajoki (2012, hereafter VCP12) presented results of the two X-ray observations of OJ 287 by XMM–Newton on 2005 April 12 and November 3–4. In Fig. 2, they plotted the observations of the 2005 campaigns. VCP12 claimed that for the 2005 April 12, the spectral energy distribution, the spectrum from radio to X-rays followed nicely a synchrotron self-Compton model. VCP12 further stated that the BH mass value of the secondary determined from the orbit solution |$M_{sec}\sim 1.4 \times 10^8$||${\rm M}_\odot$| agrees with the measured properties of the optical outburst. VCP12 also formulated a question regarding the primary BH mass necessary to guarantee the stability of the primary AD. They found that the minimum value of the primary mass |$1.8 \times 10^{10}\, {\rm M}_{\odot }$| is quite close to the BH mass determined from the orbit, |$1.84 \times 10^{10} \,{\rm M}_{\odot }$|⁠.

To find evidence for the emission of the secondary, VCP12 needed to look at the short time-scale variability in OJ 287. It has been found to be variable from 15 min time-scale upwards on many occasions (see e.g. Gupta et al. 2012) and on one occasion the light curve has shown sinusoidal variations with a period of 228 min (Sagar et al. 2004). If this variation is associated with the last stable orbit of a maximally rotating BH, the mass of the BH would be |$1.46\times 10^8 {\rm M}_{\odot }$| (Gupta et al. 2012), i.e. identical to the mass obtained from the orbit solution (Valtonen et al. 2010).

Komossa  et al. (2021, hereafter KOM21) made a detailed analysis of XMM–Newton spectra of OJ 287 spread over 15 yr. KOM21 also presented data from Swift UVOT and XRT observations of OJ 287, which began in 2015, along with all public Swift information after 2005. During this period, OJ 287 was found in the low/hard extreme state and outburst soft states. In addition, they established that the OJ 287 X-ray spectrum was highly variable, passing all states seen in blazars from the low/hard (flat) state to exceptionally soft steep state. KOM21 found that these spectra can consist of two parts: inverse-Compton (IC) radiation which is prevailing at the low-state, and very soft radiation component that becomes extremely powerful when OJ 287 becomes more luminous. KOM21 have concluded that their 2018 XMM–Newton spectra almost identical with the EHT examination of OJ 287, and were well characterized by a model with a hard IC component of the photon index |$\Gamma \sim 1.5$| and a soft component.

We reanalysed the data of the X-ray telescope (XRT) onboard of Swift Observatory for OJ 287 and applied the ST09 scaling method to this data in order to make a BH mass estimate. Using this method requires an accurate knowledge of the distance to the source OJ 287. The method was proposed back in 2007 by Shaposhnikov & Titarchuk (2007, hereafter ST07) and also by ST09. It is worth noting that there are two scaling methods: the first method based on the correlation between the photon index |$\Gamma$| and the quasi-periodic oscillation frequency (QPO) |$\nu _L$|⁠; and the second method is based on the correlation between |$\Gamma$| and normalization of the spectrum proportional to |$\dot{M}$|⁠. If the first method (⁠|$\Gamma -\nu _L$|⁠) is used to estimate the mass of the BH, the distance to the source is not required (ST07), but for the second method (⁠|$\Gamma -\dot{M}$|⁠) the source distance and the inclination of the AD relative to the Earth observer are needed (ST09).

For both methods, it is important that the source shows a change in spectral states during the outburst and a characteristic behaviour of |$\Gamma$|⁠, namely, a monotonic increase of |$\Gamma$| with |$\nu _L$| or |$\dot{M}$| in the LHS|$\rightarrow$|IS|$\rightarrow$|HSS transition and reaching a constant level (saturating) at high values of |$\nu _L$| or |$\dot{M}$|⁠, followed by a monotonic decrease in |$\Gamma$| during the HSS|$\rightarrow$|IS|$\rightarrow$|LHS transition during the outburst decay.

The saturation of |$\Gamma$| (so-called |$\Gamma$|-saturation phase) during the outburst is a specific signature that this particular object contains a BH (Titarchuk & Zannias 1998). Indeed, the |$\Gamma$|-saturation phase can be caused only by an accretion flow converging to the event horizon of a BH [see the Monte-Carlo simulation results in Laurent & Titarchuk (1999) and Laurent & Titarchuk (2011)]. Because of this, it makes sense to compare BH sources that have the same |$\Gamma$|-saturation levels. In the second method (⁠|$\Gamma -\dot{M}$|⁠), it is assumed that BH luminosity is directly proportional to |$\dot{M}$| (and, consequently, to the mass of the central BH), and inversely proportional to the squared distance to the source. Thus, we can determine the BH mass by comparing the corresponding track |$\Gamma {\!-\!}\dot{M}$| for a pair of sources with BHs, in which all parameters are known for one source, and for the other source parameters except a BH mass are known (for more details on the scaling method, see ST09).

The scaling method has a number of advantages in determination of a BH mass compared to other methods, namely, the calculation of the X-ray spectrum originating in the innermost part of disc based on first-principle (fundamental) physical models, taking into account the Comptonization of the soft disc photons by hot electrons of the internal disc part and in a converging flow to BH.

It is necessary to emphasize that our approach is only justifiable if the observed X-ray emission in OJ 287 is indeed produced by bulk-motion Comptonization (BMC) in the accretion flow. In reality, it may be dominated by emission produced in relativistic jets, which is a popular explanation of the multiwavelength emission properties of blazars in general. Nevertheless, we apply the scaling method to OJ 287 because, as will be shown below, it yields results (specifically, the spectral slope versus normalization dependence) that indicate that at least a significant fraction of the observed X-ray emission in this blazar is produced by the BMC mechanism.

Titarchuk et al. (2020) applied the scaling technique to measuring the masses of supermassive BHs (SMBHs) in active galactic nuclei (AGNs). Specifically, they applied it to the low-luminosity AGN M87 and the blazar 3C 454.3, using a mix of Galactic (X-ray binaries) and extragalactic (ultraluminous X-ray sources and AGN) with reliable BH mass estimates as reference sources. The BH mass they inferred for 3C 454.3 turned out to be in good agreement with the estimates based on more traditional methods, whereas for M87, the scaling method underestimated the BH mass by two orders of magnitude. Therefore, these results send a mixed message about the applicability of the scaling method to AGN, but it is certainly worthwhile to probe it on other representatives of this class of object.

In this paper, based on Swift data analysis, we estimate a BH mass in OJ 287 by applying the scaling technique. In Section 2, we provide details of our data analysis, while in Section 3, we present a description of the spectral models used for fitting of this data. In Section 4, we focus on observational results and their interpretation. In Section 5, we discuss the main results of the paper. In Section 6, we present our final conclusions.

2 OBSERVATION AND DATA REDUCTION

We analysed observational data of OJ 287 carried out by XRT instrument aboard Swift observatory from 2016 April to 2017 June (MJD 57501-57918). We processed |$\sim$|140 ks of pointed observations of the source. We retrieved the data from the UK Swift Science Data Centre Archive¹ and used XRT data both in Windowed Timing (WT) and Photon Counting (PC) modes.

The lowest source count rate was detected at the very beginning and at the end of this observational cycle (2016 April–June, 2017 May–June). It corresponds approximately to XRT observations in PC mode with the flux below |$\sim$|1 mCrab. This covers 31 PC observations of |$\sim$|34 ks in total. The rest of the observations were carried out during an epoch of strong flaring activity of OJ 287 in the middle of this period from 2016 October to 2017 April and they consisted of |$\sim$| 105 ks of 109 WT observations. We excluded only 3 very short observations from our analysis with accumulation time less than 100 s per ObsID and an additional 6 ones when the source position on the detector was at the edge of the field of view (FOV).

For our comprehensive analysis, we reprocessed original Level 1 XRT data using standard xrtpipeline screening settings from heasoft package v6.30 and calibration files version 20210915. We also checked PC data for the pile-up effect and found its possible presence in two observations with contamination radius of two detector pixels.

The source spectra were extracted from every individual PC and WT observations for our preliminary analysis. For the PC mode, we used a 30-pixel circular region for the source spectrum and a 60-pixel circular region taken from source-free area for background correction. Because of the lack of 2D image in WT mode, we used a rectangular 20 × 40 pixels region co-aligned to the axis of 1D image for both source and background spectra.

A typical pointed XRT observation of OJ 287 consists of |$\sim$|1 ks or less. As such, a short duration did not allow us to obtain statistically significant best-fitting spectral model parameters. At the same time, the estimation of the source flux by the applicable model to the spectrum can be a tool for the further averaging of individual source spectra over the flux. In order to implement this approach, we used the tbabs*bmc (Bulk motion Comptonization) model with fixed |$N_{H}=2.7\times 10^{20}$| and log|$(A)=2.0$|⁠. The applicable above absorption toward OJ 287 was adopted from Willingale et al. (2013)² and constant log|$(A)$| was used for simplification and reduction of free model parameters.

The preliminary spectral analysis demonstrated the 0.3 to 10 keV source flux variations in the following ranges: 0.5|$-2.6\times 10^{-11}$| and 0.5|$-4.1\times 10^{-11}$| erg s|$^{-1}$| cm|$^{-2}$| for PC and WT observations. Since our goal was the averaging of the source spectra with similar flux, we grouped 31 PC and 100 WT observations into 7 and 18 flux bins correspondingly.

The procedure of retrieving averaged spectrum is trivial for PC observations and includes the following steps: reading of re-processed event files, application of region filters for source and background spectra extraction with xselect; building the accumulated exposure map with ximage; and generation of ancillary response files (ARFs) with xrtmkarf. Similar to the preliminary spectral analysis described above per individual ObsID, we applied the same 30/60-pixel circular regions for the source extraction and background correction.

The retrieving of averaged source spectrum over WT observations is not trivial if the orientation of the detector does not match among all observations plus if the source positions on the detector were shifted. As a result, the averaged 2D image will be a combination of 1D images of the same length under different angles and with different shifts centred to the source position. The hardest task in this procedure is the proper background extraction and source/background area correction using event lists and constructed exposure maps.

In order to extract the source spectrum from the set of accumulated WT observations, we used a 20-pixel circular region as a filter with xselect. In this case, we extracted the source counts using the same 40-pixel width/length region as we did before for individual WT observations (see above). For background extraction we used the annulus centred to the source position with inner/outer radii of 80/120 pixels. Since the detector size is only 200 pixels in width, we are then getting the same 40 linear pixels of 1D image on the detector despite the individual 1D-images orientations and shifts. The last step in getting of WT averaged spectrum is the manual correction of the background scaling factor stored in BACKSCAL keyword of the spectral file. Since the obtained background effective surface is actually the length and it has the same width of 40-pixels as the source, we then manually matched this value of BACKSCAL keyword in the header of the background file to the source spectrum one.

3 ANALYSIS AND RESULTS

For our comprehensive spectral analysis we fitted 7 PC and 18 WT averaged over the flux spectra by tbabs*bmc model with fixed |$N_{H}=2.7\times 10^{20}$| (see above). The typical OJ 287 spectra with |$\Gamma =2.0$| and |$\Gamma =2.6$| are shown in Fig. 1.

For our further analysis, we plotted the spectral index |$\Gamma$| versus N in Fig. 2. The correlation between |$\Gamma$| and N is noticeable for N lower than |$\sim 2.5\times 10^{-4}$|⁠. Taking into account that |$\Gamma$| does not fluctuate significantly at higher N values, we separated our data points shown in Fig. 2 in two parts and fitted them by linear function and a constant at lower and higher N correspondingly. The result of this best-fitting approximation is shown in Fig. 2 by a solid line.

Additionally, we fitted the same data points using the analytic function

widely used as scalable pattern between reference and target sources in BH mass estimation (see ST09). The results of this approximation are shown in Table 1. GX 339-4 best-fitting parameters corresponding to observed LHS to IS source transition in 2007 were taken from ST09 [Fig. 3 and Table 2 (28 data points, online extended table)]. XTE J1859-226 data were adopted from ST09 (see fig. 9 there).

Taking into account |$F(N)$| tends asymptotically to a constant at infinity, we projected the saturation value of N we found for OJ 287 to |$F(N)$|⁠. In Fig. 2, it corresponds to the projection of the break point of the solid curve to the dotted curve. We then repeated the same approach in scaling |$F(N)$| for GX 339-4 and XTE J1859-226. For the reference sources N should be the same way equidistant from the upper limit of |$F(N)$| as N for the target source. In other words, the relative height of N position between the asymptotes should be the same.

The curves corresponding to analytical function |$F(N)$| of the reference and target sources from Table 1 and their |$N_{t}$| and |$N_{r}$| are shown in Fig. 3 in details.

3.1 X-ray spectra

To fit the energy spectra of this source, we used an XSPEC model consisting of the Comptonization (BMC) component (see Titarchuk & Zannias 1998; Laurent & Titarchuk 1999). We also used a multiplicative tbabs model (Wilms, Allen & McCray 2000) which takes into account absorption by neutral material. We assume that accretion on to a BH is described by two main zones (see e.g. fig. 1 in Titarchuk & Seifina 2021): a geometrically thin AD [e.g. the standard Shakura–Sunyaev disc, see Shakura & Sunyaev (1973) and a transition layer (TL), which is an intermediate link between the AD, and a converging (bulk) region (see Titarchuk & Fiorito 2004), which is assumed to exist, at least, below 3 Schwarzschild radii, |$3R_S = 6GM_{\rm BH}/c^2$|⁠. The spectral model parameters are the equivalent hydrogen absorption column density |$N_H$|⁠; the photon index |$\Gamma$|⁠; |$\log (A)$| is related to the Comptonized factor f [|$={A}/{(1+A)}$|]; the colour temperature and normalization of the seed photon blackbody component, |$kT_s$| and N, respectively.

Similarly to the ordinary bbody XSPEC model, normalization is a ratio of the source (disc) luminosity L to the square of the distance d (ST09, see equation 1 there):

This encompasses an important property of our model. Namely, using this model one can correctly evaluate normalization of the original ‘seed’ component, which is presumably a correct |$\dot{M}$| indicator (Seifina & Titarchuk 2011). In its turn

Here, |$R_{*} = r_{*} R_S$| is an effective radius where the main energy release takes place in the disc, |$R_S = 2GM/c^2$| is the Schwarzschild radius, |$\eta = 1/(2r_{*})$|⁠, |$\dot{m} = \dot{M}/\dot{M}_{\rm crit}$| is the dimensionless |$\dot{M}$| in units of the critical mass accretion rate |$\dot{M}_{\rm crit} = L_{\rm Ed}/c^2$|⁠, and |$L_{\rm Ed}$| is the Eddington luminosity.

For the formulation of the Comptonization problem, one can see Titarchuk, Mastichiadis & Kylafis (1997), Titarchuk & Zannias (1998), Laurent & Titarchuk (1999), Borozdin et al. (1999), and ST09.

Spectral analysis of the Swift/XRT data of OJ 287, in principle, provides a general picture of the spectral evolution. We can trace the change in the spectrum shape during the IS–HSS transition in Fig. 1, which demonstrates two representative |$E*F_E$| spectral diagrams for different states of OJ 287. The emergent spectra (see Fig. 1) can be described as a sum of the low energy blackbody and its fraction convolved with the Comptonization Green function (CGF; see equations 16 and B5 in Sunyaev & Titarchuk 1980). The HSS and IS spectra are characterized by a strong soft blackbody component (presumably, related to the AD) and a power law (as the hard tail of the CGF), while in the LHS the Comptonization component is dominant and the blackbody component is barely seen because the innermost part of the disc is fully covered by the scattering media which has a Thomson optical depth more than 2.

Analysis of the Swift/XRT data fits (see Fig. 1) showed that |$\Gamma$| monotonically increases from 2 to 2.6, when normalization of the spectral component (or |$\dot{M}$|⁠) increases by a factor of about 5 (see points, in Fig. 2) at the outburst rise phase (IS–HSS).

4 A BH MASS ESTIMATE

Now, we use the scaling method for a BH mass estimate (⁠|$M_{oj287}$|⁠) in OJ 287. The BH mass scaling method using the |$\Gamma {\text {--}}N$| correlation is described in detail in ST09. This method consists of (i) searching for such a pair of BHs for which the |$\Gamma$| correlates with increasing normalization N (which is proportional to mass accretion rate |$\dot{M}$| and a BH mass M, see ST09, equation 7 there) and the saturation level, |$\Gamma _{sat}$| are the same and (ii) calculating the scaling coefficient |$s_{N}$| which allows to determine a BH mass of the target object. It is worthwhile to emphasize that one needs a ratio of distances for the target and reference sources in order to estimate a BH mass using the following equation for the scaling coefficient

where |$N_r$| and |$N_t$| are normalizations of the spectra, |$m_t=M_t/{\rm M}_{\odot }$|⁠, |$m_r=M_r/{\rm M}_{\odot }$| are the dimensionless BH masses with respect to solar, |$d_t$| and |$d_r$| are distances to the target and reference sources, correspondingly. A geometry factor, |$f_G=\cos i_r/\cos i_t$| where |$i_r$| and |$i_r$| are the disc inclinations for the reference and target sources, respectively (see ST09, equation 7).

We found that XTE 1859–226 and GX 339-4 can be used as the reference sources because these sources met all aforementioned requirements to estimate a BH mass of the target source OJ 287 [see items (i) and (ii) above].

In Fig. 1, we show two types of the spectral states observed in OJ 287. The first one (in the bottom there) is a typical intermediate spectrum observed when the resulting luminosity is relatively low. We presented all emergent spectra of this source in terms of |$EF_(E)$| diagrams in order to estimate the resulting luminosity. In Fig. 2, we demonstrate the |$\Gamma$| versus N where N is presented in the units of |$L_{39}/d^2_{10}$| (⁠|$L_{39}$| is the source luminosity in units of |$10^{39}$| erg s⁻¹ and |$d_{10}$| is the distance to the source in units of 10 kpc). As one can see, the correlations of these sources are characterized by similar shapes and saturation levels |$\Gamma _{\rm sat}\gt 2.5$|⁠. In order to implement the scaling method we use an analytical approximation |$F(N)$| for the |$\Gamma {\!-\!}N$| correlation,

We estimated a BH mass for OJ 287 using Fig. 2 of this manuscript and Figs 3 and 9 in ST09, for GX 339-4 and XTE1859-226, respectively. Thus, we found that the |$\Gamma$| versus N correlations are self-similar, at least for |$\Gamma \gt 2$|⁠, see Fig. 3 and from these correlations we could estimate |$N_t$|⁠, |$N_r$| for OJ 287 and GX 339-4 and XTE1859-226, respectively. They are |$N_t=2.3\times 10^{-4}$| and |$N_{r, GX}= 0.27$|⁠, |$N_{r, 1859}= 0.24$|⁠. taken at the beginning of the |$\Gamma$|-saturation part (see solid points).

Thus, for GX 339-4 we obtained |$s_N=N_r/N_t \sim 0.1\times 10^{4}$| applying N-values: |$N_r=0.27$| and |$N_t=2.3\times 10^{-4}$| (see Fig. 3). On the other hand, a value of a factor |$f_G=\cos {i_r}/\cos {i_t} \sim 0.53$| for the target and reference sources can be obtained using inclinations |$i_t=50^{o}$| and |$i_r=70^{o}$| (see Table 2 and Hynes et al. 2003). As a result of the estimated target mass (OJ 287), |$m_t$| we find that

or

where we use values of |$d_t=1.073$| Gpc and |$d_r=5.75$| kpc (see Table 2).

Also using the reference source XTE J1859-226, we estimate

applying equation (6) if we substitute the values of |$f_G=\cos i_r/\cos i_t =0.53$|⁠, |$s_N=0.1\times 10^4$|⁠, |$d_r=4.2$| kpc, and |$m_r=5.4$| (see Table 2).

5 DISCUSSION

The most popular scenario for OJ 287 is of a very high mass (⁠|$\sim 1.8\times 10^{10}$| |${\rm M}_\odot$|⁠) primary BH and a much lighter (⁠|$\sim 1.5\times 10^{8}$| |${\rm M}_\odot$|⁠) secondary BH in an eccentric, inclined, and precessing orbit that crosses the primary’s AD twice per orbit (VCP12; Valtonen et al. 2024). However, Komossa et al. (2023), using new observational data, have presented strong arguments in favour of an alternative model where the primary is much smaller, |$\sim 10^{8}$| |${\rm M}_\odot$|⁠.

KOM21 found two X-ray spectral states in OJ 287, using a large volume of data (see fig. 4 there). Their ‘hard state’ is dominated by a power-law component and the ‘soft state’ is characterized by a soft component, which became very strong when the source was very bright. From our analysis of the Fall 2016–Spring 2017 Swift observations, we similarly identified two distinct spectral states of OJ 287: an intermediate and a soft one (see Fig. 1). These states correspond to the initial rise of the X-ray spectral index correlated to the increasing mass accretion rate (intermediate state), followed by saturation of the spectral index after the accretion rate reached a certain level (soft state). We used the results of the spectral analysis of the intermediate and soft states to estimate the mass accretion rate corresponding to the saturation of the spectral index and consequently to constrain the BH mass.

According to the standard model for OJ 287 (Valtonen et al. 2024), the X-ray observations discussed here presumably captured the BH binary in a post-impact state, with the secondary having punctured the AD of the primary a few years earlier. According to simulations, this should have caused a massive accretion flow from the disc on to the secondary, perhaps similar to accretion flows detected in stellar mass binary systems. In such a scenario, our X-ray analysis constraints the mass of the secondary, rather than of the primary BH.

6 CONCLUSIONS

The multiwavelength outburst activity in OJ 287 with XRT on the Swift call into question whether the source contains one or two BHs. It is very important to reveal the characteristics of this binary. In the presented work, we demonstrated that the OJ 287 X-ray spectra underwent the state transition from the intermediate state (IS) to the high/soft state (HSS) (see Fig. 1). We found that energy spectra in all spectral states can be modelled using a product of the tbabs and a Comptonization component, BMC (see XSPEC). Moreover, in OJ 287 we discovered the correlation of the photon index |$\Gamma$| with normalization, N (proportional to the disc mass accretion rate |$\dot{M}$|⁠, see Fig. 2) similar to those established in BH Galactic sources by ST09. We found that |$\Gamma$| increases monotonically with |$\dot{M}$| from the IS to the HSS, and then saturates at |$\Gamma \sim$| 2.6. This can be regarded as observational evidence of the presence of a BH in OJ 287. Based on this correlation, we apply the scaling method (ST09) to estimate a BH mass |$\sim 2\times 10^8$| solar masses, using the well-studied X-ray BH binaries, GX 339–4 and XTE J1859–226 as reference sources (see Fig. 3). Most likely, this mass estimate pertains to the secondary component of the BH binary.

ACKNOWLEDGEMENTS

This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. The authors are grateful to Dr. Kim Page of the UK Swift Science Data Centre for the help with Swift/XRT data processing and analysis.

The authors would like to thank Sergey Sazonov, Alexey Vikhlinin, and Sergey Trudolyubov for careful reading of the manuscript and valuable suggestions. We are especially grateful to Colm Elliott, Marla Kouri-Towe, and Michele Delmaire for the proof reading and useful suggestions about corrections to the text of the manuscript.

DATA AVAILABILITY

The Swift data are available to download through the UK Swift Data Science website https://www.swift.ac.uk/archive.

Footnotes

REFERENCES