# NICER, NuSTAR, and Swift follow-up observations of the $\gamma$-ray flaring
blazar BL Lacertae in 2020 August–October

F. D’Ammando1
1INAF - Istituto di Radioastronomia, Via Gobetti 101, I-40129 Bologna, Italy
E-mail<EMAIL_ADDRESS>
(Accepted. Received; in original form)

###### Abstract

During a period of strong $\gamma$-ray flaring activity from BL Lacertae, we
organized Swift, Neutron star Interior Composition Explorer (NICER), and
Nuclear Spectroscopic Telescope Array (NuSTAR) follow-up observations. The
source has been monitored by Swift-XRT (X-ray Telescope) between 2020 August
11 and October 16, showing a variability amplitude of 65, with a flux varying
between 1.0$\times$10-11 and 65.3$\times$10-11 erg cm-2 s-1. On 2020 October
6, Swift-XRT has observed the source during its historical maximum X-ray flux.
A softer-when-brighter behaviour has been observed by XRT, suggesting an
increasing importance of the synchrotron emission in the X-ray part of the
spectrum covered by XRT during this bright state. Rapid variability in soft
X-rays has been observed with both the Swift-XRT and NICER observations with a
minimum variability time-scale of 60 and 240 s, and a doubling time-scale of
274 and 1008 s, respectively, suggesting very compact emitting regions
(1.1$\times$1014 and 4.0$\times$1014 cm). At hard X-rays, a minimum
variability time-scale of $\sim$5.5 ks has been observed by NuSTAR. We report
the first simultaneous NICER and NuSTAR observations of BL Lacertae during
2020 October 11–12. The joint NICER and NuSTAR spectra are well fitted by a
broken power law with a significant difference of the photon index below
(2.10) and above (1.60) an energy break at $\sim$2.7 keV, indicating the
presence of two different emission components (i.e. synchrotron and inverse
Compton) in the broad band X-ray spectrum. Leaving the total hydrogen column
density towards BL Lacertae free to vary, a value of N${}_{\rm\,H,tot}$ =
(2.58 $\pm$ 0.09) $\times$1021 cm-2 has been estimated.

###### keywords:

radiation mechanisms: non-thermal; galaxies: active; galaxies: jets; X-rays:
galaxies

##  1 Introduction

The extragalactic $\gamma$-ray sky is dominated by blazars, a class of radio-
loud active galactic nuclei (AGN) in which one of the two relativistic jets
points in the direction of the Earth. The spectral energy distribution (SED)
of blazars shows a non-thermal continuum from radio to $\gamma$-rays,
characterized by two distinct components: one peaking in infrared-to-X-rays
and associated with synchrotron emission by e±, and one peaking in the
$\gamma$-ray energy range and associated, in leptonic models, with inverse
Compton (IC) scattering between the e± and a soft photon field (which can be
their own synchrotron radiation, or an external photon field such as the
emission from the broad-line region, the torus, or the disc). A common feature
of all blazars is to show strong flux and spectral variability at all
wavelengths and on a variety of time-scales, from minutes to years (e.g.,
Wagner et al., 1995; Ulrich et al., 1997). The variability time-scale of the
emission can give constraints on the size of the emitting region (e.g.,
Tavecchio et al., 1998, 2010).

Blazars are classified into BL Lac objects and flat-spectrum radio quasars
(FSRQ) according to the presence or absence of broad emission lines
(equivalent width EW $>$ 5 Å; e.g., Stickel et al., 1991) in their optical
spectrum, respectively. A further classification is based on the synchrotron
peak frequency: While FSRQ show generally a low peak frequency (in infrared),
in BL Lac objects the peak frequency ranges from radio to X-rays and are
further classified as low/intermediate/high-frequency-peaked BL Lacs (LBL,
IBL, and HBL; with peak frequency lower than 1014 Hz, between 1014 and 1015
Hz, and above 1015 Hz, respectively; see e.g. Padovani et al., 1995)111A
similar classification (low/intermediate/high-synchrotron-peaked blazar) has
been introduced in Abdo et al. (2010) not distinguishing BL Lac and FSRQ and
making an explicit reference to the synchrotron origin of the ﬁrst bump of the
SED.. Therefore, observations in the X-ray energy range can cover different
parts of the SED depending on the type of objects: the peak of the synchrotron
component in HBL, the valley between synchrotron and IC components in IBL, the
rising part of the IC component in LBL and FSRQ.

BL Lacertae, a blazar at redshift $z$ = 0.069 (Miller & Hawley, 1997), has
been historically defined as the prototype of the BL Lac objects. According to
its synchrotron peak frequency, it has been classified as an LBL (Nilsson et
al., 2018) or IBL (Ajello et al., 2020). Optical spectra of BL Lacertae have
shown broad H$\alpha$ and H$\beta$ lines (Vermeulen et al., 1995) that vary in
flux (Capetti et al., 2010). The discovery of broad emission lines, although
weak, in BL Lac seems to indicate that BL Lac itself can be more similar to
FSRQ than to less luminous BL Lac objects. BL Lacertae has been studied
intensively since its discovery in $\gamma$-rays by the Energetic Gamma Ray
Experiment Telescope (EGRET) onboard the Compton Gamma Ray Observatory
satellite (Catanese et al., 1997) and has been the target of several
observational campaigns in the last two decades from radio to very high
energies (e.g., Villata et al., 2002, 2009; Bach et al., 2006; Raiteri et al.,
2010, 2013; Wierzcholska et al., 2015; Wehrle et al., 2016; Abeyesekara et
al., 2018; Acciari et al., 2019, and the references therein).

After a strong $\gamma$-ray flaring activity detected by the Large Area
Telescope (LAT) onboard the Fermi Gamma-Ray Space telescope (Ojha et al.,
2020) and the MAGIC telescopes (Blanch, 2020) on 2020 August 19, BL Lacertae
remains in a high activity in the following weeks and Swift observations
performed on 2020 October 5 and 6 found the source at the historical maximum
level in X-rays and in one of the brightest states observed in optical and
ultraviolet (UV D’Ammando, 2020a, b). On 2020 October 6, the source reached
the second highest daily averaged $\gamma$-ray flux observed from Fermi-LAT so
far (Mereu, 2020). Following the historical maximum flux observed from optical
to $\gamma$-rays, simultaneous NICER and NuSTAR follow-up observations have
been requested. Preliminary results are presented in D’Ammando (2020c).
Results about the multi-frequency campaign over the entire electromagnetic
spectrum will be presented in a separate publication. In this paper, we focus
on the Swift, Neutron star Interior Composition Explorer (NICER) and Nuclear
Spectroscopic Telescope Array (NuSTAR) data of BL Lacertae collected during
2020 August–October. We present the observations and data reduction in Section
2. The results of analysis of the data collected by the three satellites
separately and the joint fit of the NICER and NuSTAR X-ray data are shown in
Sections 3 and 4, respectively. In Section 5, we discuss and summarize our
results.

Unless stated otherwise, uncertainties correspond to 90 per cent confidence
limits on one parameter of interest ($\Delta\chi^{2}$ = 2.7). The photon
indices are parameterized as $N(E)\propto E^{-\Gamma}$ with $\Gamma=\alpha+1$
($\alpha$ is the spectral index). Throughout this paper, we assume the
following cosmology: $H_{0}=71\;{\rm km\;s^{-1}\;Mpc^{-1}}$, $\Omega_{\rm
M}=0.27$, and $\Omega_{\rm\Lambda}=0.73$ in a flat Universe (Ade et al.,
2016). At the redshift of the source the luminosity distance DL is 307 Mpc.

Figure 1: Swift-XRT light curve of BL Lacertae in terms of flux (top panel)
and photon index (bottom panel). The arrow indicates the time of the NICER and
NuSTAR observations.

##  2 Observations and data reduction

###  2.1 Swift observations

The Neil Gehrels Swift observatory satellite (Gehrels et al., 2004) carried
out 33 observations of BL Lacertae between 2020 August 11 (MJD 59072) and
October 16 (MJD 59138). The observations were performed with all three
instruments onboard: the X-ray Telescope (XRT; Burrows et al., 2005, 0.2–10.0
keV), the Ultraviolet/Optical Telescope (UVOT; Roming et al., 2005, 170–600
nm), and the Burst Alert Telescope (BAT; Barthelmy et al., 2005, 15–150 keV).

XRT observations were performed in photon counting mode, except for the first
observation performed on 2020 October 6 for which observations in windowed
timing (WT) mode were carried out (for a description of XRT read-out modes,
see Hill et al., 2004). The XRT spectra were generated with the Swift-XRT data
product generator tool at the UK Swift Science Data
Centre222http://www.swift.ac.uk/user_objects (for details, see Evans et al.,
2009). Spectra having count rates higher than 0.5 counts s-1 may be affected
by pile-up. To correct for this effect, the central region of the image has
been excluded, and the source image has been extracted with an annular
extraction region with an inner radius that depends on the level of pile-up
(see e.g., Moretti et al., 2005).

The hard X-ray flux of this source is usually below the sensitivity of the BAT
instrument for daily short exposures. Based on the Swift-BAT Hard X-ray
Transient Monitor (Krimm et al.,
2013)333https://swift.gsfc.nasa.gov/results/transients/weak/QSOB2200p420,
considering daily light curves, only in three cases a detection with a
significance $>$ 3 $\sigma$ has been observed in the studied period, on 2020
August 28 (MJD 59089), September 1 (MJD 59093), and September 13 (MJD 59105),
with a corresponding count rate of (3.97 $\pm$ 1.11) $\times$10-3, (4.54 $\pm$
1.27) $\times$10-3, and (3.35 $\pm$ 1.05) $\times$10-3 counts cm-2 s-1,
respectively. BL Lacertae is also included in the Swift-BAT 105-month hard
X-ray catalogue (Oh et al., 2018), for observations carried out between 2004
December and 2013 August, with a photon index of $\Gamma$ = 1.76
${}^{+0.18}_{-0.17}$.

During the Swift pointings, the UVOT instrument observed the sources in its
optical ($v$, $b$, and $u$) and UV ($w1$, $m2$, and $w2$) photometric bands
(Poole et al., 2008; Breeveld et al., 2010). The UVOT data in all filters were
analysed with the uvotimsum and uvotmaghist tasks and the 20201215 CALDB-UVOTA
release. Source counts were extracted from a circular region of 5 arcsec
radius centred on the source, while background counts were derived from a
circular region with a 20 arcsec radius in a nearby source-free region. All
UVOT exposures were checked for possible small-scale sensitivity problems,
which occur when the source falls on small detector regions where the
sensitivity is
lower444https://swift.gsfc.nasa.gov/analysis/uvot_digest/sss_check.html.

###  2.2 NICER observations

The NICER (Gendreau et al., 2012) on the International Space Station observed
BL Lacertae for a Discretionary Data Time (DDT) request (PI: D’Ammando;
ObsIds: 3201820101 and 3201820102) between 2020 October 11 17:35:04 UTC and
October 12 23:13:04 UTC (MJD 59133.73268519–59134.96740741) for an effective
time of 14.7 ks. The NICER observations were reduced using NICERDAS v7a and
the calibration files available in the CALDB release 20200727. Good time
intervals (GTI) were generated using nimaketime to select events that occurred
when the particle background was low (KP555KP is the space weather index
Kennziffer Planetary (Bartels et al., 1939). KP is derived from a worldwide
network of magnetometers: https://www.swpc.noaa.gov/products/planetary-k-index
$<$ 5 and COR_SAX666The COR_SAX parameter estimates the magnetic cut-off
rigidity. $>1.5$), and avoiding times of high optical loading. Moreover, the
NICER focal plane modules 34, 14, 43, and 54 show episodes of increased
detector noise. Data from these detectors have been excluded from the final
events file.

The background was estimated using the tool nibackgen3C50_v6 (Remillard et
al.,
2021)777https://heasarc.gsfc.nasa.gov/docs/nicer/tools/nicer_bkg_est_tools.html.
Comparing the results to the background obtained using the tool
nicer_bkg_estimator_v6 (Gendreau et al., in preparation), we did no find
significant differences. The event file filtered using the GTI is loaded into
XSELECT to extract the source spectrum and a 240 s light curve. The source
spectrum is rebinned with a minimum of 20 counts per energy bin with grppha to
allow for $\chi^{2}$ spectrum fitting.

###  2.3 NuSTAR observations

The NuSTAR (NuSTAR; Harrison et al., 2013) observed BL Lacertae for a DDT
proposal (PI: D’Ammando; ObsId: 90601630002) between 2020 October 11 14:06:09
UTC and October 12 07:16:09 UTC (MJD 59133.58760417–59134.30288194) with its
two coaligned X-ray telescopes with corresponding focal planes, focal plane
module A (FPMA) and B (FPMB), for 30.7 and 30.4 ks, respectively. The level 1
data products were processed with the NuSTAR Data Analysis Software
(nustardas) package (v1.9.2). Cleaned event files (level 2 data products) were
produced and calibrated using standard filtering criteria with the nupipeline
software module, and the OPTIMIZED parameter for the exclusion of the South
Atlantic Anomaly (SAA) passages. We used the calibration files available in
the NuSTAR CALDB version 20210202.

Spectra of the source were extracted for the whole observation from the
cleaned event files using a circle of 30 pixel ($\sim$70 arcsec) radius, while
the background was extracted from a nearby circular region of 30 pixel radius
on the same chip of the source. The choice of the extraction region size
optimizes the signal-to-noise, but alternative choices do not affect the
results. The ancillary response files were generated with the numkarf task,
applying corrections for the point spread function losses, exposure maps, and
vignetting. The spectra were rebinned with a minimum of 20 counts per energy
bin to allow for $\chi^{2}$ spectrum fitting. The net count rate for the
entire observation is 0.193 $\pm$ 0.003 and 0.182 $\pm$ 0.003 counts s-1 for
FPMA and FPMB, respectively. The target is detected above the background in
both the focal plan modules up to $\sim$75 keV.

The observation is also divided by orbits, identified by the satellite’s
emergence from the SAA, as reported in the GTI file. The same procedure
applied to the entire observation has been used for producing a spectrum for
each satellite orbit.

##  3 Analysis results

Figure 2: Left: Swift-XRT photon index as a function of the 0.3–10 keV
unabsorbed flux of BL Lacertae. Right: Swift-XRT light curve of BL Lacertae
collected on 2020 October 6 is shown in terms of count rate using 60 s time
bins.

###  3.1 Swift-XRT

The X-ray spectra collected by XRT in the 0.3–10 keV energy range are fitted
by an absorbed power-law model using the photoelectric absorption model tbabs
and set abundances according to Wilms et al. (2000) and vern cross-sections
(Verner et al., 1996). The same abundances and cross-sections are also used
for fitting the NICER and NuSTAR spectra later. The Galactic column density in
the direction of the source has been initially fixed to $N_{H}$ =
2.70$\times$1021 cm-2, in agreement with the value used in Madejski et al.
(1999) and Weaver et al. (2020) (but see Section 5 for a discussion about the
total hydrogen column density towards BL Lacertae). We used the spectral
redistribution matrices in the Calibration data base maintained by HEASARC.
The X-ray spectral analysis was performed using the XSPEC 12.9.1 software
package (Arnaud et al., 1996). Data were grouped by single photons with grppha
and the Cash statistics (Cash, 1979) is used. The results of the fits are
reported in Table 3.

We plotted in Fig. 1 the X-ray flux (top panel) and photon index (bottom
panel) estimated in the 0.3–10 keV energy range with XRT observations. The
X-ray flux corrected for Galactic extinction varies between 1.01$\times$10-11
and 65.28$\times$10-11 erg cm-2 s-1, with a median value of 2.42$\times$10-11
erg cm-2 s-1. The corresponding variability amplitude, $V_{\mathrm{amp}}$,
calculated as the ratio of maximum to minimum flux, is 64.6. As a comparison,
the $V_{\mathrm{amp}}$ estimated between 2012 October 27 and 2013 November 5,
at the time of the 2012 December flare, was 6.7 (Wehrle et al., 2016). A
similar variability amplitude ($V_{\mathrm{amp}}$ $\sim$7) has been observed
in X-rays considering the period 2008 August 4–2012 October 31 (Raiteri et
al., 2013).

In addition, we estimated the fractional variability parameter,
$F_{\mathrm{var}}$, for taking into account also the uncertainties on the
flux. We followed the prescription given by Vaughan et al. (2003):

$F_{\mathrm{var}}=\sqrt{\frac{S^{2}-<\sigma_{\mathrm{err}}^{2}>}{<F_{\rm\,X}>^{2}}}$

where $<F_{\rm\,X}>$ denotes the average X-ray flux, $S$ denotes the standard
deviation of the $N$ flux measurements and $<\sigma_{\mathrm{err}}^{2}>$ the
mean squared error. The uncertainty of $F_{\mathrm{var}}$ is estimated
following Poutanen et al. (2008):

$\Delta
F_{\mathrm{var}}=\sqrt{F^{2}_{\mathrm{var}}+err(\sigma^{2}_{\mathrm{NXS}})}-F_{\mathrm{var}}$

where $err(\sigma^{2}_{\mathrm{NXS}})$ is given by equation 11 in Vaughan et
al. (2003):

$err(\sigma^{2}_{\mathrm{NXS}})=\sqrt{\left(\sqrt{\frac{2}{N}}\frac{<\sigma^{2}_{\mathrm{err}}>}{<F_{\rm\,X}>^{2}}\right)^{2}+\left(\sqrt{\frac{<\sigma^{2}_{\mathrm{err}}>}{N}}\frac{2F_{\mathrm{var}}}{<F_{\rm\,X}>}\right)^{2}}$

We obtained $F_{\mathrm{var}}$ = 0.44 $\pm$ 0.02, confirming the very high
variability of the source in X-rays during 2020 August–October and showing
that such variability is not dominated by the uncertainties on the flux.

The photon index varies between 1.35 and 2.63, with a median value of
$\langle\Gamma_{\rm\,X}\rangle$ = 1.95 $\pm$ 0.12. A softer-when-brighter
behaviour has been observed by XRT during 2020 August–October (see Fig. 2,
left-hand panel). To statistically investigate whether X-ray data follow this
trend, a correlation study between flux and photon index is performed, using
the Spearman rank test. We obtain a Spearman rank order correlation
coefficient rs = 0.71, indicating a strong correlation. For N = 33
observations, there is a 0.1 per cent probability that the null hypothesis is
correct (p = 0.001), corresponding to a 99.9 per cent statistical
significance.

The flux observed on 2020 October 6 is the historical maximum reached by the
source in X-rays888See also
https://www.swift.psu.edu/monitoring/source.php?source
=BLLacertae. As a comparison, the maximum 0.3–10 keV flux observed during the
2012 flaring activity was 8.02$\times$10-11 erg cm-2 s-1 (Wehrle et al.,
2016). That value is not corrected for Galactic absorption, so for a direct
comparison the peak flux observed on 2020 October 6 not corrected for Galactic
absorption is (36.89 $\pm$ 0.47) $\times$10-11 erg cm-2 s-1, a factor of 4.5
higher than the 2012 peak flux.

Correcting for instrumental artefacts (i.e. hot pixels and bad columns on the
CCD), pile-up, and after the background has been subtracted, we produced a
light curve with time bins of 60 s for the XRT observation performed on
October 6, i.e. at the peak of the activity (see Fig. 2, right-hand panel). A
significant change of the count rate ($>$ 3 $\sigma$)999The significance is
calculated as
$\Delta$CR/$\sqrt{(\sigma_{\rm\,CR1}^{2}+\sigma_{\rm\,CR2}^{2})}$, where
$\Delta$CR = $|$count rate 1–count rate 2$|$, and $\sigma_{\rm\,CR1}$ and
$\sigma_{\rm\,CR2}$ are the corresponding uncertainties. has been observed in
consecutive bins on a time-scale of 60 s. Following Saito et al. (2013), to
calculate the minimum doubling/halving time-scale between two consecutive
points we used $\tau$ = $\Delta$t $\times$ ln2 / ln(CR(t2)/CR(t1)), where
CR(t1) and CR(t2) are the count rate at time t1 and t2, respectively. We found
$\tau$ = 274 s (256 s in the source rest frame)101010The corresponding
exponential growth time-scale is $\tau$/ln2 = 396 s.. This value should be
considered an upper limit limited by the number of photons collected in light
curves produced with shorter time bins. In case of the XRT light curve
produced with time bins of 15 s (see Fig. 9), the minimum doubling/halving
time is $\tau$ = 50 s (47 s in the source rest frame). However, episodes of
change of the count rate between consecutive bins are detected only at a
significance level of 2 $<$ $\sigma$ $<$3.

On 2020 October 6, using an absorbed power law with $N_{H}$ fixed to
2.70$\times$1021 cm-2, we obtained a photon index of $\Gamma$ = 2.58 $\pm$
0.03 ($\chi^{2}$/dof = 404.34/254), while leaving the $N_{H}$ free to vary a
photon index of $\Gamma$ = 2.77 $\pm$ 0.06 and $N_{H}$ = (3.8 $\pm$ 0.4)
$\times$1021 cm-2 are obtained with a significant improvement of the fit
($\chi^{2}$/dof = 264.46/253). Fixing the photon index to 2.58 and leaving the
Galactic absorption free to vary, we obtained $N_{H}$ = (3.3 $\pm$ 0.1)
$\times$1021 cm-2 with an intermediate quality of fit with respect to the
previous two fits ($\chi^{2}$/dof = 312.21/253).

We also summed the XRT observations carried out in two periods: (i) before the
peak of the activity, i.e. 2020 September 6–25, for a total exposure of 6603
s; (ii) after the peak of the activity, i.e. 2020 October 11–16, for a total
exposure of 8574 s. Fitting the spectra with an absorbed power law with
$N_{H}$ fixed to 2.70$\times$1021 cm-2, we obtained a photon index of $\Gamma$
= 2.08 $\pm$ 0.06 ($\chi^{2}$/dof = 101.40/90) and 1.71 $\pm$ 0.07
($\chi^{2}$/dof = 73.32/72) for period (i) and (ii), respectively. Leaving the
Galactic absorption value free to vary, we obtained $\Gamma$ = 1.94 $\pm$ 0.10
and $N_{H}$ = (2.1 $\pm$ 0.3) $\times$1021 cm-2 ($\chi^{2}$/dof = 94.63/89),
and $\Gamma$ = 1.65 $\pm$ 0.11 and $N_{H}$ = (2.4 $\pm$ 0.5) $\times$1021 cm-2
($\chi^{2}$/dof = 71.73/71) for period (i) and (ii), respectively. Fitting
simultaneously the XRT spectra collected during the peak activity, periods (i)
and (ii), fixing the photon index to 2.58, 2.08, and 1.71, respectively, and
leaving the $N_{H}$ value free to vary, we obtained a value of (3.1 $\pm$ 0.1)
$\times$1021 cm-2.

Figure 3: Comparison of the light curve of BL Lacertae in X-ray (top panel;
0.3–10 keV), UV (middle panel; $w2$: black filled circles, $m2$: red filled
triangles, $w1$: green open squares), and optical bands (bottom panel; $u$:
black filled circles, $b$: red filled triangles, $v$: green open squares)
collected by Swift during 2020 August 11–October 16. All values are corrected
for Galactic extinction. The contribution of the host galaxy has been
subtracted in the optical and UV bands. Errors are smaller than symbols;
therefore, they are not shown in the plot. Figure 4: SED of BL Lacertae from
optical to X-rays collected by Swift-XRT and Swift-UVOT in five different
epochs. The UVOT data are corrected for Galactic extinction and the
contribution from the host galaxies has been subtracted. In X-rays the best-
fitting model of the spectra collected has been shown. Different symbols and
colours refer to different observational epochs.

###  3.2 Swift-UVOT

Optical and UV observations obtained with the UVOT telescope simultaneously to
XRT are useful to investigate variability properties, to build optical-to-X-
ray SED at different epochs and to study the connection with the X-ray
activity. The observed magnitudes of the source are reported in Table 4.
Following Raiteri et al. (2013), we assumed a flux density of 2.89, 1.30,
0.36, 0.026, 0.020, and 0.017 mJy for the host galaxy in the $v$, $b$, $u$,
$w1$, $m2$, and $w2$ bands. By considering the source extraction radius used,
the host galaxy contribution contaminating the UVOT photometry is about 50 per
cent of the total galaxy flux, and it is removed from the magnitude values for
calculating the flux densities. UVOT flux densities are also corrected for
dust extinction using the E(B–V) value of 0.291 from Schlafly & Finkbeiner
(2011) and the extinction laws from Cardelli et al. (1989).

The variability amplitude estimated with the UVOT data is 3.32, 3.47, 3.60,
3.85, 4.39, 4.40 in the $v$, $b$, $u$, $w1$, $m2$, $w2$ bands, respectively,
with an increasing variability going from the $v$ to the $uvw2$ band. This
behaviour has been already observed in this source (see e.g. Raiteri et al.,
2010, 2013), confirming a dominant contribution of the beamed synchrotron
emission from the jet with respect to the thermal emission from the accretion
disc also in the UV band, differently from what is observed in some FSRQ
(e.g., Raiteri et al., 2012; Orienti et al., 2020).

The unabsorbed flux densities corrected for the host galaxy contribution are
plotted in Fig. 3 for a comparison with the unabsorbed X-ray fluxes observed
during 2020 August–October. The source is less variable in optical and UV
bands with respect to X-rays, showing a similar variability pattern in the
three bands. It is interesting to notice that, although the flux density in
optical and UV is high at the time of the peak of the X-ray activity (i.e., on
August 6), the optical and UV activity peaked on August 5. This is in
agreement with a significant shift of the synchrotron peak to higher
frequencies, thus an increase of the contribution of the synchrotron component
in the X-ray band passing from August 5 to 6, corresponding to a larger
increase of the X-ray flux on August 6. Comparing the optical-to-X-ray SED of
the source collected at different epochs (see Fig. 4), such a shift of the
synchrotron peak is evident not only from August 5 to 6 but also between
different activity states. With respect to the periods of relatively low
activity, before (i.e. 2020 August 11; MJD 59072) and after (i.e. 2020 October
11; MJD 59133) the peak, at the time of the peak of the activity (i.e. 2020
October 5 and 6; MJD 59127 and MJD 59128) the optical–UV part of the SED is
flatter, while the X-ray spectrum is softer ($\Gamma_{\rm\,X}$ $>$ 2).

Figure 5: NICER light curve of BL Lacertae shown in terms of count rate using
240 s time bins starting from T0 = MJD 59133.58760417 (2020 October 11
17:35:04 UTC). Red triangles refer to periods of significant change of
activity in consecutive bins.

###  3.3 NICER

Figure 6: NICER spectrum of BL Lacertae collected on 2020 October 11–12 in the
0.4–5 keV energy range fitted with a log-parabola model and the Galactic
absorption fixed to 2.70$\times$1021 cm-2.

The source is detected above the background across the energy interval 0.4–5.0
keV, with an average count rate of 4.10 counts s-1. We produced a light curve
using 240 s time bins (Fig. 5). The 0.4–5 keV light curve shows variability by
factors of up to 2 across the observation, with the count rate varying between
3.15 and 7.30 counts s-1 and episodes of variability on time-scales of a few
thousand seconds. In particular, there are three episodes of significant
change of activity ($>$ 3 $\sigma$; see footnote 9) in consecutive bins of the
light curve, with changes from 3.54 $\pm$ 0.18 to 5.10 $\pm$ 0.41 counts s-1
in 9120 s, from 6.13 $\pm$ 0.16 to 7.23 $\pm$ 0.17 counts s-1 in 240 s, and
from 5.29 $\pm$ 0.21 to 6.83 $\pm$ 0.21 counts s-1 in 8840 s. It is
particularly remarkable the increase of count rate observed in only 240 s
considering that, differently from the other two cases, there are no
observational gaps between the values estimated in consecutive bins. Assuming
a redshift of $z$ = 0.069, the observed variability time-scale corresponds to
8531, 225, and 8269 s, respectively, in the source rest frame. The minimum
doubling/halving time-scale for the NICER observations is $\tau$ = 1008 s (943
s in the source rest frame).

Figure 7: Left-hand panel: NuSTAR light curve of BL Lacertae orbit-by-orbit as
seen by the FPMA module with flux (upper panel) and photon index (bottom
panel) in the 3.0–79 keV energy range. Right-hand panel: NuSTAR spectrum
collected on 2020 October 11–12 in the 3–79 keV energy range fitted with a
power-law model and the Galactic absorption fixed to 2.70$\times$1021 cm-2.

The NICER spectrum can be fitted in the 0.4–5.0 keV energy range with an
absorbed power law with a photon index of $\Gamma$ = 2.06 $\pm$ 0.01 and the
Galactic absorption corresponding to a hydrogen column density fixed to
$N_{H}$ = 2.70$\times$1021 cm-2 ($\chi^{2}$/dof = 527.11/457). A better fit
can be obtained by using an absorbed log-parabola model with a slope $\alpha$
= 2.10 $\pm$ 0.02 and a negative curvature parameter of $\beta$ = $-$0.19
$\pm$ 0.05, suggesting a concave X-ray spectrum ($\chi^{2}$/dof = 490.80/456;
see Fig. 6). Applying an F-test to compare the power-law and log-parabola
models, we obtained a probability that the null hypothesis is true of 1.19-8.
The corresponding flux (corrected for Galactic absorption) in the 0.3–10
keV/0.4–5.0 keV energy range is (1.62 $\pm$ 0.01) $\times$10-11 / (1.13 $\pm$
0.01) $\times$10-11 erg cm-2 s-1. Compared to the XRT observations, the NICER
observations have been carried out during an intermediate flux level (see Fig.
1, upper panel). Leaving the Galactic absorption value free to vary, in case
of a log-parabola model, we found a slight improvement of the fit
($\chi^{2}$/dof = 481.13/455) with larger uncertainties on the spectral
parameters, $\alpha$ = 2.32 $\pm$ 0.12 and $\beta$ = $-$0.48 $\pm$ 0.16, and
$N_{H}$ = (3.1 $\pm$ 0.3)$\times$1021 cm-2.

###  3.4 NuSTAR

The NuSTAR observations extended over 11 satellite orbits. First, we
investigated the behaviour orbit-by-orbit in the NuSTAR bandpass. A similar
variability amplitude and behaviour have been observed by considering the
count rate orbit-by-orbit in the 3.0–79, 3.0–10.0, and 10–79 keV energy range
(see Fig. 10). For clarity, only the count rate from FPMA is shown. Data from
FPMB showed a similar situation.

By fitting the spectra obtained for each orbit with a simple power law and
$N_{H}$ fixed to 2.70$\times$1021 cm-2, the photon index ranges between 1.44
and 1.63, with an average value of 1.54 and no significant variability
observed within the uncertainties. The corresponding 3–79 keV fluxes range
between 2.55$\times$10-11 and 3.85$\times$10-11 erg cm-2 s-1, with an average
value of 3.04$\times$10-11 erg cm-2 s-1 and an increase up to 50 per cent of
the flux over the observation (see Table 1 and Fig. 7, left-hand panel). A
significant ($>$3 $\sigma$) change of flux has been observed between the last
two orbits, in particular on a time-scale of 5844 s (5468 s in the source rest
frame). The minimum doubling/halving time-scale considering the orbit-by orbit
NuSTAR observations is $\tau$ = 17650 s (16510 s in the source rest frame).

Previous NuSTAR observations of the source have been carried out in 2012 and
2019. During 2012 December 11–12, the orbit-by-orbit photon index varied
between 1.81 and 1.93 with an average value of 1.86, and flux changes of up to
30 per cent (Wehrle et al., 2016). The 3–7 keV flux varied between 1.1 and
1.3$\times$10-11 erg cm-2 s-1. As a comparison, in our observation, the 3–7
keV flux varies between 3.6 and 5.5$\times$10-12 erg cm-2 s-1, a factor of 2–3
lower than the 2012 fluxes. On the contrary, during 2019 September 14–19, the
3–79 flux of the source estimated orbit-by-orbit has been lower than that in
2020 with values between 0.86 and 1.97$\times$10-11 erg cm-2 s-1, and the
photon index ranged between 1.56 and 2.15 with an average value of 1.87
(Weaver et al., 2020). Therefore, compared to previous NuSTAR observations,
the 2020 observations showed an intermediate hard X-ray flux between 2019 and
2012 observations and a harder photon index with respect to both of them.

We fitted the overall NuSTAR spectrum by using a simple power law and a log-
parabola model, assuming $N_{H}$ = 2.70$\times$1021 cm-2. We also included a
cross-normalization factor for FPMB with respect to FPMA that resulted in all
cases $<$ 5 per cent, consistent with the expectations from calibration
observations (Madsen et al., 2015). The simple power-law model gives
acceptable results with a $\chi^{2}$/dof of 452.85/458 and a photon index of
$\Gamma$ = 1.59 $\pm$ 0.03 (see Fig. 7, right-hand panel). The corresponding
3–79 keV flux is (2.97 ${}^{+0.05}_{-0.06}$)$\times$10-11 erg cm-2 s-1. A
comparable quality of fit has been obtained by using a log-parabola model
($\chi^{2}$/dof = 452.84/457) with a slope $\alpha$ = 1.59 $\pm$ 0.04 and a
negligible curvature parameter of $\beta$ = 0.003 $\pm$ 0.010. Fitting the
spectrum with a broken power-law model does not improve the fit in this case
either. No obvious spectral break is determined within the NuSTAR bandpass.

Table 1: Log and fitting results of NuSTAR orbit-by-orbit observations of BL Lacertae using a power-law model with $N_{\rm H}$ fixed to 2.70$\times$1021 cm-2. The fit refers to FPMA only. Orbit | Net exposure time | Count rate | Photon index | Flux${}_{\rm\,3-79\,keV}$
---|---|---|---|---
| (s) | (counts s-1) | ($\Gamma_{\rm\,X}$) | (10-11 erg cm-2 s-1)
1 | 3196 | 0.169 $\pm$ 0.007 | 1.44 $\pm$ 0.14 | 3.19 $\pm$ 0.30
2 | 3205 | 0.159 $\pm$ 0.007 | 1.57 $\pm$ 0.13 | 2.55 $\pm$ 0.23
3 | 3168 | 0.183 $\pm$ 0.008 | 1.57 $\pm$ 0.13 | 2.71 $\pm$ 0.25
4 | 3193 | 0.183 $\pm$ 0.008 | 1.60 $\pm$ 0.12 | 2.80 $\pm$ 0.24
5 | 3151 | 0.180 $\pm$ 0.008 | 1.53 $\pm$ 0.14 | 2.86 $\pm$ 0.24
6 | 2770 | 0.183 $\pm$ 0.008 | 1.47 $\pm$ 0.17 | 3.10 $\pm$ 0.36
7 | 2558 | 0.186 $\pm$ 0.009 | 1.57 $\pm$ 0.14 | 2.99 $\pm$ 0.30
8 | 2422 | 0.214 $\pm$ 0.010 | 1.53 $\pm$ 0.16 | 3.47 $\pm$ 0.30
9 | 2298 | 0.248 $\pm$ 0.011 | 1.57 $\pm$ 0.13 | 3.85 $\pm$ 0.42
10 | 2235 | 0.227 $\pm$ 0.010 | 1.50 $\pm$ 0.15 | 3.77 $\pm$ 0.37
11 | 2521 | 0.221 $\pm$ 0.010 | 1.63 $\pm$ 0.15 | 2.16 $\pm$ 0.30

##  4 Joint NICER and NuSTAR fit

Figure 8: NICER and NuSTAR spectra (upper panel) and residuals (bottom panel) of BL Lacertae collected on 2020 October 11–12 fitted in the 0.4–79 keV energy range with a broken power-law model with $N_{\rm H,tot}$ fixed to 2.70$\times$1021 cm-2. Black, red, and green points represent NuSTAR FPMA, NuSTAR FPMB, and NICER data, respectively. Table 2: Summary of fits to the 0.4–79 keV NICER and NuSTAR joint spectrum of BL Lacertae. Asterisk refers to a fixed parameter. Model | Parameter | Value
---|---|---
Power-law | $\Gamma$ | 1.98 $\pm$ 0.01
|  $N_{\rm H,tot}$ (cm-2) ∗ | 2.70$\times$1021 *
| Cross-normalization FPMA/FPMB | 1.06 $\pm$ 0.03
| Cross-normalization FPMA/NICER | 0.76 $\pm$ 0.02
|  $\chi^{2}$/dof | 1453.19/916
Log-parabola | $\alpha$ | $2.11\pm 0.02$
| $\beta$ |  $-$0.25 $\pm$ 0.02
|  $N_{\rm H,tot}$ (cm-2) ∗ | 2.70$\times$1021 *
| Cross-normalization FPMA/FPMB | 1.05 $\pm$ 0.03
| Cross-normalization FPMA/NICER | 0.89 $\pm$ 0.03
|  $\chi^{2}$/dof | 972.44/915
Two power-laws | $\Gamma_{1}$ | $2.09\pm 0.02$
| $\Gamma_{2}$ | $0.87\pm 0.06$
|  $N_{\rm H,tot}$ (cm-2) ∗ | 2.70$\times$1021 *
| Cross-normalization FPMA/FPMB | 1.09 $\pm$ 0.05
| Cross-normalization FPMA/NICER | 0.84 $\pm$ 0.04
|  $\chi^{2}$/dof | 1011.70/914
Broken power-law | $\Gamma_{1}$ | 2.10 $\pm$ 0.02
|  $E_{\rm\,break}$ (keV) | 2.67 ${}^{+0.29}_{-0.17}$
| $\Gamma_{2}$ | 1.60 ${}^{+0.03}_{-0.03}$
|  $N_{\rm H,tot}$ (cm-2) ∗ | 2.70$\times$1021 *
| Cross-normalization FPMA/FPMB | 1.05 $\pm$ 0.03
| Cross-normalization FPMA/NICER | 0.97 $\pm$ 0.04
|  $\chi^{2}$/dof | 954.69/914
Broken power-law | $\Gamma_{1}$ | 2.04 ${}^{+0.07}_{-0.04}$
|  $E_{\rm\,break}$ (keV) | 3.01 ${}^{+0.41}_{-0.45}$
| $\Gamma_{2}$ | 1.60 ${}^{+0.03}_{-0.03}$
|  $N_{\rm H,tot}$ (cm-2) | 2.59 ${}^{+0.14}_{-0.09}$$\times$1021
| Cross-normalization FPMA/FPMB | 1.05 $\pm$ 0.03
| Cross-normalization FPMA/NICER | 0.96 $\pm$ 0.04
|  $\chi^{2}$/dof | 953.17/913

To investigate in detail the broad band X-ray spectrum of BL Lacertae, a joint
fit to the lower energy NICER and higher energy NuSTAR data is performed. The
combination of NICER and NuSTAR observations is important for characterizing
the broad band spectrum and estimating the value of total hydrogen column
density towards the source, not well determined so far. The NICER spectrum has
a much better statistics than the Swift-XRT spectra collected on October 11
and 12 (74319 counts vs. 538 counts and 157 counts); for this reason, the XRT
data are not used. The Galactic column density has been initially set to
2.70$\times$1021 cm-2. A cross-normalization factor between the NICER and
NuSTAR instruments has been added for taking into account differences in the
absolute flux calibration and the slight offset of the observing times. A
comparable median count rate is observed in the NICER light curve for the
period simultaneous to the NuSTAR observation (4.94 counts s-1) and just after
that (5.01 counts s-1; see Fig. 11), justifying the use of the entire NICER
observation for the fitting. A simple power-law, a log-parabola, two power-
laws, and a broken power-law model has been applied for the joint fitting of
the NICER and NuSTAR data. The fitting results are summarized in Table 2.

The joint spectrum cannot be well represented from 0.4 to 79 keV by a simple
power law with a photon index $\Gamma$ = 1.98 $\pm$ 0.01 ($\chi^{2}$/dof =
1453.19/916). A log-parabola model has been also tested, with the pivot energy
fixed at 1 keV, and the fit significantly improves ($\chi^{2}$/dof =
972.44/915) with a slope $\alpha$ = 2.11 $\pm$ 0.02 and a negative curvature
$\beta$ = $-$0.25 $\pm$ 0.02, suggesting a concave spectrum as in the case of
the fit of the NICER spectrum alone. By applying an F-test, we obtain a
probability of 7.0$\times$10-82 that the null hypothesis is true. Using two
power-law models, the quality of the fit is worse than the case of the log-
parabola model ($\chi^{2}$/dof = 1011.70/914), with the photon index of the
second power law very hard ($\Gamma_{2}$ = 0.87).

A further improvement of the fit is obtained by using a broken power-law model
($\chi^{2}$/dof = 954.69/914). By applying an F-test, the improvement of the
fit using a broken power law with respect to a power law is even more
significant than a log-parabola model, with a probability that the null
hypothesis is true of 4.1$\times$10-84. We obtained photon indices of
$\Gamma_{1}$ = 2.10 $\pm$ 0.02 and $\Gamma_{2}$ = 1.60 $\pm$ 0.03 below and
above an energy break $E_{\rm\,break}$ = 2.67 ${}^{+0.29}_{-0.17}$,
respectively. The exposure of NICER and NuSTAR significantly overlapped, in
agreement also with the cross-normalization obtained (0.97 $\pm$ 0.04 between
FPMA and NICER). Fig. 8 shows the joint fit to the NICER and NuSTAR data for
the simultaneous observations performed on 2020 October 11–12.

Previous NuSTAR observations of the source in 2012 and 2019 have been carried
out contemporaneously to Swift-XRT observations, and the $N_{\rm H,tot}$ value
has not been left free to vary during the fitting procedure, probably due to
the small number of counts collected by XRT in the low-energy part of the
X-ray spectrum. Thanks to the NICER observations, we are able to test the
total hydrogen column density for BL Lacertae combining the NICER and NuSTAR
observations over a broad band energy range. Leaving the Galactic total
absorption free to vary, the fit marginally improved ($\chi^{2}$/dof =
953.17/913), with $N_{\rm H,tot}$ = (2.59 ${}^{+0.14}_{-0.09}$)$\times$1021
cm-2 (see Table 2). Fixing the spectral parameters of the broken power-law
model ($\Gamma_{1}$, $\Gamma_{2}$, $E_{\rm\,break}$) and leaving the Galactic
total absorption free to vary, we obtained $N_{\rm H,tot}$ = (2.69
${}^{+0.04}_{-0.04}$)$\times$1021 cm-2 with a comparable quality of the fit
($\chi^{2}$/dof = 954.54/916).

##  5 Discussion and conclusions

Considering the large flaring activity of BL Lacertae observed from optical to
$\gamma$-rays during 2020 August–October, that is an important possibility to
study in detail the spectrum of the source at different frequencies. In this
paper, we have analysed the X-ray data collected by Swift-XRT, NICER, and
NuSTAR. These data allowed us to investigate the spectral and flux variability
on different time-scales and to characterize in detail the broad band energy
range of the source from 0.4 to 79 keV. We have reported the results of the
first NICER observation of the source and, more generally, the first NICER and
NuSTAR simultaneous follow-up observations of a $\gamma$-ray flaring blazar.

Swift-XRT monitored BL Lacertae between 2020 August 11 and October 16,
observing on October 6 the historical maximum activity from this source in
X-rays, with an unabsorbed flux of 6.53$\times$10-10 erg cm-2 s-1 and a
corresponding luminosity of (7.86 $\pm$ 0.08) $\times$1045 erg s-1 in the
0.3–10 keV energy range. The $V_{\rm\,amp}$ estimated over the period 2020
August–October is 64.6, a factor of 10 higher than the value observed at the
time of the 2012 flaring activity, clearly indicating how exceptional is the
X-ray flaring activity observed in 2020 October.

Moreover, considering the Swift-XRT monitoring of other 10 bright $\gamma$-ray
BL Lacs during 2004 December–2012 August, only Mrk 421 has shown a variability
amplitude ($V_{\mathrm{amp}}$ = 81.5; Stroh et al., 2013) larger than the
value estimated in 2020 for BL Lacertae. However, Mrk 421 is an HBL with a
peak of the synchrotron emission usually in the soft X-ray energy range;
therefore, even assuming the same level of activity, a larger variability
amplitude is expected in that energy range for Mrk 421 with respect to IBL/LBL
sources, like BL Lacertae. A similar variability pattern has been observed
with XRT and UVOT in optical, UV, and X-rays with less variability in optical
and UV bands with respect to the X-ray one.

During the XRT monitoring of BL Lacertae, we observed a softer-when-brighter
behaviour in X-rays, with the photon index ranges between 1.35 and 2.63. This
behavior can be related to an increasing importance of the synchrotron
emission in the X-ray part of the spectrum covered by XRT during bright
states, likely due to a shift of the synchrotron and IC peaks to higher
frequencies (see Fig. 4). In this context, we noticed that an X-ray photon
index higher than 2.2 (see Table A1) has been estimated in the two XRT
observations close to the VHE detection of the source reported by the MAGIC
telescopes on 2020 August 19 (Blanch, 2020) and September 19 (Blanch, 2020, ;
see the SED collected on 2020 September 21, MJD 59113, in Fig. 4), in
agreement with a shift of both the SED peaks to higher frequencies in these
periods. A similar softer-when-brighter behaviour has been reported in Weaver
et al. (2020), when 40 XRT observations of BL Lacertae have been carried out
between 2019 September 14 and 19. In that period, the fluxes were lower than
the values observed in 2020 August–October [i.e. (3.1$\times$10-12) –
(1.8$\times$10-11) erg cm-2 s-1] with the photon index ranges from 1.79 to
2.72. A strong softer-when-brighter spectral variability pattern has been
observed in OJ 287 (Komossa et al., 2017, 2021), a BL Lac object classified as
LSP or ISP, similarly to BL Lacertae. On the contrary, a harder-when-brighter
behaviour for BL Lacertae has been reported by Wehrle et al. (2016) during the
2012 flaring activity. This can be an indication that different emission
mechanisms and/or changes of distinct jet parameters are at work in the source
during different flaring activities. The combination of the data analysed here
with other multi-wavelength data collected during this period, in particular
by Fermi-LAT and MAGIC, will be important to study in detail this behaviour.

Rapid variability in soft X-rays has been observed with both Swift-XRT and
NICER in 2020 October. In particular, at the peak of the activity (October 6)
a minimum variability time-scale of 60 s and a doubling time-scale of 274 s
(256 s in the source rest frame) have been observed by XRT. Based on causality
argument, it is possible to constrain the intrinsic size of the emitting
region to be R $<$ $c$ $\delta$ $\tau$ /(1+$z$), where $\tau$ is the minimum
doubling time-scale observed and $\delta$ is the Doppler factor. Assuming a
typical Doppler factor of $\delta$ = 15 (see e.g. Raiteri et al., 2013), we
obtain R $<$ 1.1$\times$1014 cm. NICER observations performed during an
intermediate X-ray flux level, a few days after the peak of activity, observed
a minimum variability time-scale of 240 s and a doubling time-scale of 1008 s
(943 s in the source rest frame). This corresponds to an emitting region R $<$
4.0$\times$1014 cm.

The light-crossing time for a Kerr black hole is tlc = 2G MBH /$c^{3}$ =
2$\times$103 (MBH/108 M⊙) s. Assuming a black hole mass of MBH =
1.7$\times$108 M⊙ for BL Lacertae (Woo et al., 2002), we have tlc = 3400 s.
After considering the relativistic Doppler effect, we have tlc/$\delta$, and
thus for $\delta$ = 15 we obtain 227 s, comparable to the minimum doubling
time-scale observed by Swift-XRT on October 6 for the light curve produced
with time bins of 60 s. However, a hint of shorter doubling time-scale (i.e.
50 s) has been observed inspecting the light curve produced with 15 s time
bins. A Doppler factor significantly higher, i.e. 70, is needed to reconcile
the light-crossing times of the black hole with such a short variability time-
scale. We are in a similar situation if we assume a black hole mass of MBH
$\sim$ 5$\times$108 M⊙, as obtained by Ghisellini et al. (2010) and Falomo et
al. (2003). The rapid increase of the X-ray activity observed by XRT can
indicate that in case of short time-scale variability the size of the black
hole is not a hard lower limit on the physical size of the emitting region. In
fact, the time-scales observed by XRT suggest that the emission is not
produced by the entire jet but by compact regions within the jet. Different
scenarios can explain such a small compact region: ‘jet-in-a-jet models’
including ultra-relativistic outﬂow of material from magnetic reconnection
sites (e.g., Giannios et al., 2009) or relativistic turbulence in the jet
(e.g., Narayan et al., 2012), or turbulent extreme multi-zone models (e.g.,
Marscher et al., 2014). In 1999 June, BeppoSAX observed that the soft X-ray
flux of the source doubled on a time-scale of $\sim$20 m (Ravasio et al.,
2002). Therefore, the minimum variability time-scales observed in 2020 October
by Swift-XRT and NICER in the soft X-ray band are the most extreme observed
from this source so far. More generally, fast X-ray variability has not been
revealed in a large number of blazars (e.g., Pryal et al., 2015). This can be
related to the fact that follow-up X-ray observations with different
satellites are usually carried out from 1 d to a few days after the peak of
the $\gamma$-ray flaring activity. In this way, we are usually observing the
source in a high state but not at the peak of the activity when the
variability would be extreme.

At hard X-rays, NuSTAR observed a significant variability between two
satellite’s orbits ($\sim$5.8 ks), with a doubling time-scale of 17650 s
(16510 s in the source rest frame). Previous NuSTAR observations in 2019 have
shown a variability time-scale significantly longer of 14.5 h (Weaver et al.,
2020).

The joint NICER and NuSTAR spectrum is well described by a broken power-law
model with photon indices $\Gamma_{1}$ = 2.10 $\pm$ 0.02 and $\Gamma_{2}$ =
1.60 $\pm$ 0.03 below and above an energy break $E_{\rm\,break}$ = 2.67
${}^{+0.29}_{-0.17}$, respectively. There is a significant difference of the
photon index estimated in the NICER and NuSTAR observations alone, in
agreement with the results obtained for the joint spectrum applying a broken
power-law model. This should be related to the presence of the high-frequency
end of the synchrotron emission below a few keV, and the IC component
dominating the emission at higher energies. The contemporaneous NuSTAR and
Swift-XRT spectra of BL Lacertae collected on 2012 December 11–12, during
another flaring activity, are well described by a broken power-law model with
a photon index of 3.3${}^{+1.3}_{-0.7}$ and 1.88 $\pm$ 0.01 below and above an
energy break of 1.0 $\pm$ 0.2 keV (Wehrle et al., 2016). On the contrary,
during the 2019 low-activity state no statistically significant improvement
has been obtained for a broken power-law model over a single power-law model
(Weaver et al., 2020).

This source has been observed with several X-ray satellites in the past.
Previous observations with ASCA (Sambruna et al., 1999) and BeppoSAX (Ravasio
et al., 2003) have shown that a broken power law is statistically preferred
over a single power-law model (Sambruna et al., 1999). In case of three XMM-
Newton observations carried out in 2007–2008, a double power-law model
represents better the 0.3–10 keV spectra with respect to a single power-law
model (Raiteri et al., 2009). In that case, the photon indices of the two
power-laws are $\Gamma_{1}$ = 2.48–2.58 and $\Gamma_{2}$ = 1.51–1.72, in
agreement with the two photon indices obtained below and above the energy
break of the joint fitting of the NICER and NuSTAR spectra with a broken
power-law model presented here.

The shape of the X-ray spectrum of BL Lacertae also depends on the Galactic
absorption assumed. The amount of absorption due to molecular hydrogen is not
directly measurable, making the estimation of the total absorption along our
line of sight uncertain. The Galactic atomic hydrogen column density towards
BL Lacertae is $N_{HI}$ = 1.75$\times$1021 cm-2, as obtained by the HI4PI
survey (Ben Bekhti et al., 2016). Approximately the same amount of Galactic
atomic hydrogen column density has been previously estimated with the
Leiden/Argentine/Bonn (LAB) survey (1.73$\times$1021 cm-2; Kalberla et al.,
2005). However, observations of local interstellar CO have shown the presence
of a Galactic molecular cloud towards the source (e.g., Bania et al., 1991;
Liszt et al., 1998). The total hydrogen column density towards BL Lacertae
($N_{H,tot}$) is thus composed by the atomic hydrogen column density,
$N_{HI}$, and the molecular column density, $N_{H_{2}}$. The estimation of the
amount of $N_{H_{2}}$ reported in literature changes significantly depending
on the X-ray satellites used, from 0.5$\times$1021 cm-2 using the ASCA data
(Madejski et al., 1999) to 1.7$\times$1021 cm-2 (Raiteri et al., 2009) using
the XMM-Newton data.

According to Liszt et al. (1998), the $\rm{}^{13}CO$ column density of the
molecular cloud is (8.48 $\pm$ 0.78) $\times$1014 cm-2. Assuming that the
molecular hydrogen column density $N_{\rm H_{2}}$ is usually (1–2)
$\times$$10^{6}$ times the $\rm{}^{13}CO$ one (see e.g., Liszt, 2007), the
estimation of hydrogen column density due to the molecular cloud varies
between 7.7$\times$1020 and 18.6$\times 10^{21}$ cm-2. This results in a total
hydrogen column density towards BL Lacertae of (2.52–3.61)$\times$1021 cm-2.
However, the CO component can provide only very approximately about the
molecular component of the gas. Moreover, the value also depends on the ratio
$N_{H_{2}}/N_{\rm{}^{13}CO}$ and therefore to the corresponding uncertainties.
Finally, a change of 14 per cent of the equivalent width of the H2CO
absorption lines along the line of sight of BL Lacertae in 2 yr has been
reported by Moore et al. (1995), suggesting possible variability of the
molecular column density. The best way to estimate the value of $N_{H,tot}$ in
BL Lacertae is to have an observation with a large number of counts, and
covering a broad energy range. For this reason, the joint NICER and NuSTAR
spectrum collected on 2020 October 11–12 is ideal for such a kind of study.
Leaving the total Galactic absorption free to vary and using a broken power-
law model, we obtain an $N_{H,tot}$ = (2.59 ${}^{+0.14}_{-0.09}$) $\times$1021
cm-2.

By applying the relationship between dust-emission-derived reddening E(B-V)
and hydrogen column density, $N_{H_{I}}$ = 8.3 $\times$1021
cm-2$\times$E(B-V), and using E(B-V) = 0.316 mag, we obtain 2.62$\times$1021
cm-2, comparable to the value obtained by the NICER and NuSTAR joint fit.

Further X-ray observations of blazars in high-activity periods for long
exposures and over a broad band energy range, as assured by the combination of
NICER and NuSTAR observations, are fundamental to better characterize the
X-ray spectrum of these sources and to perform searches for rapid X-ray
variability. In this context, this study has shown that NICER can be also
important for blazar science, even more if combined with the NuSTAR data at
hard X-rays.

## Acknowledgements

We thank the NuSTAR PI, Fiona Harrison, for approving the DDT request, and the
NuSTAR SOC for carrying out the observation and the excellent support.

We thank the NICER PI, Keith Gendreau, and the operation team for the rapid
approval and execution of the DDT request. We thank the Swift team for making
these observations possible, the PI, Brad Cenko, the duty scientists, and
science planners.

This research has made use of the XRT Data Analysis Software (XRTDAS). This
work made use of data supplied by the UK Swift Science Data Centre at the
University of Leicester. This research has made use of data obtained through
the High Energy Astrophysics Science Archive Research Center Online Service,
provided by the NASA/Goddard Space Flight Center. This research has made use
of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration. We thank the second
referee, Dirk Grupe, for constructive comments and suggestions.

## Data Availability

The data underlying this article are available in Swift Archive Download
Portal at the UK Swift Science Data Centre
(https://www.swift.ac.uk/swift_portal/) and the HEASARC database
(https://heasarc.gsfc.nasa.gov/docs/archive.html).

## References

  * Abeyesekara et al. (2018) Abeysekara, A. U., et al. 2018, ApJ, 856, 95
  * Abdo et al. (2010) Abdo, A. A., et al. 2010, ApJ, 716, 30
  * Acciari et al. (2019) Acciari, V. A., et al. 2019, A&A, 623, A175
  * Ade et al. (2016) Ade, P. A. R., et al. 2016, A&A, 594, A13
  * Ajello et al. (2020) Ajello, M., et al. 2020, ApJ, 892, 105
  * Arnaud et al. (1996) Arnaud, K. A. 1996, in Jacoby G. H., Barnes J., eds, ASP Conf. Ser. Vol. 101, Astronomical Data Analysis Software and Systems V. Astron. Soc. Pac., San Francisco, p. 17
  * Bach et al. (2006) Bach, U., et al. 2006, A&A, 456, 105
  * Bania et al. (1991) Bania, T. M., Marscher, A. P., Barvainis, R. 1991, AJ, 101, 2147
  * Bartels et al. (1939) Bartels, J., Heck, N. H., Johnston, H. F. 1939, J. Geophys. Res., 44, 411
  * Barthelmy et al. (2005) Barthelmy, S. D., et al. 2005, Space Sci. Rev., 120, 143
  * Ben Bekhti et al. (2016) Ben Bekhti, N., et al., 2016, A&A, 594, A116
  * Blanch (2020) Blanch, O. 2020a, The Astronomer’s Telegram, 13963
  * Blanch (2020) Blanch, O. 2020b, The Astronomer’s Telegram, 14032
  * Breeveld et al. (2010) Breeveld, A. A., et al. 2010, MNRAS, 406, 1687
  * Burrows et al. (2005) Burrows, D. N., et al. 2005, Space Sci. Rev., 120, 165
  * Capetti et al. (2010) Capetti, A., Raiteri, C. M., Buttiglione, S. 2010, A&A, 516, A59
  * Cardelli et al. (1989) Cardelli, J. A., Clayton, G. C., Mathis, J. S. 1989, ApJ, 345, 245
  * Cash (1979) Cash, W. 1979, ApJ, 228, 939
  * Catanese et al. (1997) Catanese, M., et al. 1997, ApJ, 480, 562
  * D’Ammando (2020a) D’Ammando, F. 2020a, The Astronomer’s Telegram, 14065
  * D’Ammando (2020b) D’Ammando, F. 2020b, The Astronomer’s Telegram, 14069
  * D’Ammando (2020c) D’Ammando, F. 2020c, The Astronomer’s Telegram, 14096
  * Evans et al. (2009) Evans, P. A., et al. 2009, MNRAS, 397, 1177
  * Falomo et al. (2003) Falomo, R., Carangelo, N., Treves, A. 2003, MNRAS, 343, 505
  * Gehrels et al. (2004) Gehrels, N., et al. 2004, ApJ, 611, 1005
  * Gendreau et al. (2012) Gendreau, K. C., Arzoumanian, Z., Okajima, T. 2012, in Takahashi T., Murray S. S., Herder J.-W. A. d., eds, Proc. SPIE Conf. Ser. Vol. 8443, Space Telescopes and Instrumentation 2012: Ultraviolet to Gamma Ray. SPIE, Bellingham, p. 13
  * Ghisellini et al. (2010) Ghisellini, G., et al. 2010, MNRAS, 402, 497
  * Giannios et al. (2009) Giannios, D., Uzdensky, D. A., Begelman, M. C. 2009, MNRAS, 395, L29
  * Harrison et al. (2013) Harrison, F. A., et al. 2013, ApJ, 770, 103
  * Hill et al. (2004) Hill, J. E., et al. 2004, in Flanagan K. A., Siegmund O. H. W., eds, Proc. SPIE Conf. Ser. Vol. 5165, X-ray and Gamma-Ray Instrumentation for Astronomy XIII. SPIE, Bellingham, p. 217
  * Kalberla et al. (2005) Kalberla, P. M. W., Burton, W. B., Hartmann, D., Arnal, E. M., Bajaja, E., Morras, R., Pöppel, W. G. L. 2005, A$\&$A, 440, 775
  * Komossa et al. (2017) Komossa, S., et al. 2017, Proc. IAU Symp. 324, New Frontiers in Black Hole Astrophysics. Kluwer, Dordrecht, p. 168
  * Komossa et al. (2021) Komossa, S., et al. 2021, MNRAS, 504, 5575
  * Krimm et al. (2013) Krimm, H., et al. 2013, ApJS, 209, 14
  * Liszt et al. (1998) Liszt, H. S., & Lucas, R. 1998, A&A, 339, 561
  * Liszt (2007) Liszt, H. S. 2007, A&A, 476, 291
  * Madsen et al. (2015) Madsen, K. K., et al. 2015, ApJS, 220, 8
  * Madejski et al. (1999) Madejski, G. M., Sikora, M., Jaffe, T., Blazejowski, M., Jahoda, K., Moderski, R. 1999, ApJ, 521, 145
  * Marscher et al. (2014) Marscher, A. P. 2014, ApJ, 780, 87
  * Mereu (2020) Mereu, I. 2020, The Astronomer’s Telegram, 14072
  * Miller & Hawley (1997) Miller, J. S., & Hawley, S. A. 1997, ApJ, 212, 47
  * Moore et al. (1995) Moore, E. M., & Marscher, A. P. 1995, 452, 671
  * Moretti et al. (2005) Moretti, A., et al. 2005, in Siegmund O. H. W., ed., Proc. SPIE Conf. Ser. Vol. 5898, UV, X-ray, and Gamma-Ray Space Instrumentation for Astronomy XIV. SPIE, Bellingham, p. 360
  * Narayan et al. (2012) Narayan, R., & Piran, T. 2012, MNRAS, 420, 604
  * Nilsson et al. (2018) Nilsson, K., et al. 2018, A&A, 620, A185
  * Ojha et al. (2020) Ojha, R., & Valverde, J. 2020, The Astronomer’s Telegram, 13964
  * Oh et al. (2018) Oh, K., et al. 2018, ApJS, 235, 4
  * Orienti et al. (2020) Orienti, M., D’Ammando, F., Giroletti, M., Dallacasa, D., Giovannini, G., Ciprini, S. 2020, MNRAS, 491, 858
  * Padovani et al. (1995) Padovani, P., & Giommi, P. 1995, ApJ, 444, 567
  * Poutanen et al. (2008) Poutanen, J., Zdziarski, A. A., Ibragimov, A. 2008, MNRAS, 389, 1427
  * Poole et al. (2008) Poole, T. S., et al. 2008, MNRAS, 383, 627
  * Pryal et al. (2015) Pryal, M., Falcone, A., Stroh, M. 2015, ApJ, 802, 33
  * Raiteri et al. (2009) Raiteri, C. M., et al. 2009, A&A, 507, 769
  * Raiteri et al. (2010) Raiteri, C. M., et al. 2010, A&A, 524, A43
  * Raiteri et al. (2012) Raiteri, C. M., et al. 2012, A&A, 545, A48
  * Raiteri et al. (2013) Raiteri, C. M., et al. 2013, MNRAS, 436, 1530
  * Ravasio et al. (2002) Ravasio, M. et al. 2002, A&A, 383, 763
  * Ravasio et al. (2003) Ravasio, M., Tagliaferri, G., Ghisellini, G., Tavecchio, F., Bottcher, M., Sikora, M. 2003, A&A, 408, 479
  * Remillard et al. (2021) Remillard, R. A., et al. 2021, AJ submitted [arXiv: 210509901]
  * Roming et al. (2005) Roming, P. W. A., et al. 2005, Space Sci. Rev., 120, 95
  * Saito et al. (2013) Saito, S., Stawarz, L., Tanaka, Y. T., Takahashi, T., Madejski, G., D’Ammando, F. 2013, ApJ, 766, L11
  * Sambruna et al. (1999) Sambruna, R. M., Ghisellini, G., Hooper, E., Kollgaard, R. I., Pesce, J. E., Urry, C. M. 1999, ApJ, 515, 140
  * Schlafly & Finkbeiner (2011) Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103
  * Stickel et al. (1991) Stickel, M., Padovani, P., Urry, C. M., Fried, J. W., Kuehr, H. 1991, ApJ, 374, 431
  * Stroh et al. (2013) Stroh, M. C, Falcone, A. D. 2013, ApJS, 207, 28
  * Tavecchio et al. (1998) Tavecchio, F., Maraschi, L., Ghisellini, G. 1998 ApJ, 509, 608
  * Tavecchio et al. (2010) Tavecchio, F., Ghisellini, G., Bonnoli, G., Ghirlanda, G. 2010, MNRAS, 405, L94
  * Ulrich et al. (1997) Ulrich, M.-H., Maraschi, L., Urry, C. M. 1997, ARA&A, 35, 445
  * Vaughan et al. (2003) Vaughan, S., et al. 2003, MNRAS, 345, 1271
  * Vermeulen et al. (1995) Vermeulen, R. C., Ogle, P. M., Tran, H. D., Browne, I. W. A., Cohen, M. H., Readhead, A. C. S., Taylor, G. B., Goodrich, R. W. 1995, ApJ, 452, L5
  * Verner et al. (1996) Verner, D. A., Ferland, G. J., Korista, K. T., Yakovlev, D. G. 1996, ApJ, 465, 487
  * Villata et al. (2002) Villata, M., et al. 2002, A&A, 390, 407
  * Villata et al. (2009) Villata, M., et al. 2009, A&A, 501, 455
  * Wagner et al. (1995) Wagner, S., & Witzel, A. 1995, ARA&A, 33, 163
  * Weaver et al. (2020) Weaver, Z. R., et al. 2020, ApJ, 900, 137
  * Wehrle et al. (2016) Wehrle, A., et al. 2016, ApJ, 816, 53
  * Wierzcholska et al. (2015) Wierzcholska, A., Ostrowski, M., Stawarz, L., Wagner, S., Hauser, M. 2015, A&A, 573, A69
  * Wilms et al. (2000) Wilms, J., Allen, A., McCray, R. 2000, ApJ, 542, 914
  * Woo et al. (2002) Woo, J.-H., & Urry, C. M. 2002, ApJ, 579, 530

##  Appendix A Swift results

###  A.1 Swift-XRT

Table 3: Log and fitting results of Swift-XRT observations of BL Lacertae using a power-law model with $N_{\rm H}$ fixed to 2.70$\times$1021 cm-2. Fluxes are corrected for the Galactic absorption. MJD refers to the start time of the Swift observation. MJD | Date | Net exposure time | Photon index | Flux${}_{\rm\,0.3-10\,keV}$
---|---|---|---|---
(UT) |  | (s) | ($\Gamma_{\rm\,X}$) | (10-11 erg cm-2 s-1)
59072.013301 | 2020-08-11 | 1144 | 1.95 $\pm$ 0.15 | 2.36 $\pm$ 0.26
59072.979057 | 2020-08-11 | 2460 | 1.73 $\pm$ 0.12 | 1.67 $\pm$ 0.16
59074.007524 | 2020-08-13 | 1089 | 1.78 $\pm$ 0.18 | 1.49 $\pm$ 0.21
59080.300875 | 2020-08-19 | 986 | 2.19 $\pm$ 0.13 | 3.16 $\pm$ 0.29
59081.600112 | 2020-08-20 | 974 | 1.76 $\pm$ 0.16 | 2.20 $\pm$ 0.29
59082.265103 | 2020-08-21 | 979 | 1.87 $\pm$ 0.15 | 2.74 $\pm$ 0.30
59083.054394 | 2020-08-22 | 979 | 1.87 $\pm$ 0.14 | 3.40 $\pm$ 0.37
59084.018388 | 2020-08-23 | 652 | 1.82 $\pm$ 0.18 | 2.70 $\pm$ 0.37
59085.319328 | 2020-08-24 | 1199 | 1.95 $\pm$ 0.15 | 2.45 $\pm$ 0.27
59086.086696 | 2020-08-25 | 854 | 2.08 $\pm$ 0.17 | 2.32 $\pm$ 0.27
59087.077198 | 2020-08-26 | 814 | 1.90 $\pm$ 0.17 | 2.41 $\pm$ 0.30
59088.073026 | 2020-08-27 | 697 | 1.88 $\pm$ 0.19 | 2.18 $\pm$ 0.32
59098.704090 | 2020-09-06 | 609 | 1.60 $\pm$ 0.18 | 2.92 $\pm$ 0.44
59104.806412 | 2020-09-12 | 922 | 1.74 $\pm$ 0.18 | 1.96 $\pm$ 0.31
59113.191735 | 2020-09-21 | 1983 | 2.20 $\pm$ 0.10 | 3.27 $\pm$ 0.22
59114.367874 | 2020-09-22 | 864 | 2.22 $\pm$ 0.18 | 2.42 $\pm$ 0.15
59116.151464 | 2020-09-24 | 817 | 2.25 $\pm$ 0.15 | 3.14 $\pm$ 0.16
59117.420004 | 2020-09-25 | 1408 | 1.95 $\pm$ 0.16 | 1.74 $\pm$ 0.20
59124.730783 | 2020-10-02 | 984 | 2.48 $\pm$ 0.11 | 9.99 $\pm$ 0.70
59125.655695 | 2020-10-03 | 989 | 1.93 $\pm$ 0.18 | 1.76 $\pm$ 0.23
59126.597595 | 2020-10-04 | 135 | 2.59 $\pm$ 0.50 | 1.90 $\pm$ 0.74
59127.638321 | 2020-10-05 | 989 | 2.37 $\pm$ 0.12 | 16.90 $\pm$ 1.26
59128.182674 | 2020-10-06 | 953 | 2.58 $\pm$ 0.02 | 65.28 $\pm$ 1.16
59128.942192 | 2020-10-06 | 1426 | 2.63 $\pm$ 0.08 | 17.14 $\pm$ 0.87
59129.906850 | 2020-10-07 | 237 | 2.53 $\pm$ 0.28 | 3.38 $\pm$ 0.56
59130.907624 | 2020-10-08 | 1558 | 2.32 $\pm$ 0.10 | 3.60 $\pm$ 0.25
59131.900956 | 2020-10-09 | 1483 | 2.43 $\pm$ 0.12 | 6.83 $\pm$ 0.53
59132.891488 | 2020-10-10 | 1463 | 2.60 $\pm$ 0.10 | 5.35 $\pm$ 0.31
59133.850977 | 2020-10-11 | 2934 | 1.64 $\pm$ 0.12 | 1.19 $\pm$ 0.12
59134.891522 | 2020-10-12 | 654 | 2.19 $\pm$ 0.23 | 1.70 $\pm$ 0.26
59135.835244 | 2020-10-13 | 2307 | 1.77 $\pm$ 0.12 | 1.72 $\pm$ 0.15
59137.660548 | 2020-10-14 | 1051 | 1.50 $\pm$ 0.25 | 1.01 $\pm$ 0.19
59138.269685 | 2020-10-15 | 1628 | 1.35 $\pm$ 0.17 | 1.21 $\pm$ 0.18
Figure 9: Swift-XRT light curve of BL Lacertae collected on 2020 October 6
shown in terms of count rate using 15 s time bins.

###  A.2 Swift-UVOT

Table 4: Observed magnitude (i.e. not corrected for Galactic extinction and the contribution of the host galaxy) of BL Lacertae obtained by Swift-UVOT. MJD refers to the start time of the Swift observation. MJD | Date (UT) | $v$ | $b$ | $u$ | $w1$ | $m2$ | $w2$
---|---|---|---|---|---|---|---
59072.013301 | 2020-08-11 | 12.75 $\pm$ 0.04 | 13.56 $\pm$ 0.05 | 13.08 $\pm$ 0.05 | 13.59 $\pm$ 0.06 | 14.23 $\pm$ 0.06 | 14.27 $\pm$ 0.06
59072.979057 | 2020-08-11 | 13.21 $\pm$ 0.03 | 14.01 $\pm$ 0.04 | 13.54 $\pm$ 0.05 | 14.10 $\pm$ 0.06 | 14.82 $\pm$ 0.06 | 14.82 $\pm$ 0.06
59074.007524 | 2020-08-13 | 13.02 $\pm$ 0.04 | 13.82 $\pm$ 0.05 | 13.38 $\pm$ 0.05 | 13.96 $\pm$ 0.06 | 14.61 $\pm$ 0.07 | 14.63 $\pm$ 0.06
59080.300875 | 2020-08-19 | 12.78 $\pm$ 0.03 | 13.53 $\pm$ 0.05 | 13.05 $\pm$ 0.05 | 13.61 $\pm$ 0.06 | 14.24 $\pm$ 0.06 | 14.24 $\pm$ 0.06
59081.600112 | 2020-08-20 | 12.58 $\pm$ 0.04 | 13.34 $\pm$ 0.05 | 12.86 $\pm$ 0.05 | 13.46 $\pm$ 0.05 | 14.15 $\pm$ 0.15 | 14.12 $\pm$ 0.06
59082.265103 | 2020-08-21 | - | 13.43 $\pm$ 0.04 | 12.95 $\pm$ 0.05 | 13.53 $\pm$ 0.05 | - | 14.17 $\pm$ 0.06
59083.054394 | 2020-08-22 | - | 13.34 $\pm$ 0.04 | 12.87 $\pm$ 0.05 | 13.42 $\pm$ 0.05 | - | 14.10 $\pm$ 0.06
59084.018388 | 2020-08-23 | 12.54 $\pm$ 0.04 | 13.31 $\pm$ 0.05 | 12.83 $\pm$ 0.05 | 13.36 $\pm$ 0.06 | 14.06 $\pm$ 0.06 | 14.08 $\pm$ 0.06
59085.319328 | 2020-08-24 | 12.70 $\pm$ 0.04 | 13.49 $\pm$ 0.04 | 13.01 $\pm$ 0.05 | 13.56 $\pm$ 0.06 | 14.23 $\pm$ 0.06 | 14.23 $\pm$ 0.06
59086.086696 | 2020-08-25 | 12.75 $\pm$ 0.04 | 13.54 $\pm$ 0.05 | 13.01 $\pm$ 0.05 | 13.59 $\pm$ 0.06 | 14.25 $\pm$ 0.06 | 14.21 $\pm$ 0.06
59087.077198 | 2020-08-26 | 12.89 $\pm$ 0.04 | 13.68 $\pm$ 0.05 | 13.16 $\pm$ 0.05 | 13.74 $\pm$ 0.06 | 14.31 $\pm$ 0.07 | 14.33 $\pm$ 0.06
59088.073026 | 2020-08-27 | 13.42 $\pm$ 0.04 | 14.23 $\pm$ 0.05 | 13.84 $\pm$ 0.05 | 14.42 $\pm$ 0.07 | 15.07 $\pm$ 0.07 | 15.14 $\pm$ 0.07
59098.704090 | 2020-09-06 | 13.04 $\pm$ 0.05 | 13.85 $\pm$ 0.05 | 13.42 $\pm$ 0.05 | 14.05 $\pm$ 0.05 | - | 14.71 $\pm$ 0.06
59104.806412 | 2020-09-12 | 13.45 $\pm$ 0.05 | 14.23 $\pm$ 0.05 | 13.83 $\pm$ 0.05 | 14.49 $\pm$ 0.05 | 15.16 $\pm$ 0.07 | 15.22 $\pm$ 0.07
59113.191735 | 2020-09-21 | 13.14 $\pm$ 0.05 | 13.89 $\pm$ 0.04 | 13.41 $\pm$ 0.05 | 13.95 $\pm$ 0.06 | 14.62 $\pm$ 0.06 | 14.61 $\pm$ 0.06
59114.367874 | 2020-09-22 | 13.00 $\pm$ 0.04 | 13.71 $\pm$ 0.05 | 13.23 $\pm$ 0.05 | 13.78 $\pm$ 0.06 | 14.43 $\pm$ 0.07 | 14.48 $\pm$ 0.06
59116.151464 | 2020-09-24 | 13.02 $\pm$ 0.04 | 13.72 $\pm$ 0.05 | 13.22 $\pm$ 0.05 | 13.78 $\pm$ 0.06 | 14.31 $\pm$ 0.07 | 14.39 $\pm$ 0.06
59117.420004 | 2020-09-25 | 13.05 $\pm$ 0.04 | 13.84 $\pm$ 0.04 | 13.34 $\pm$ 0.05 | 13.96 $\pm$ 0.06 | 14.60 $\pm$ 0.06 | 14.68 $\pm$ 0.06
59124.730783 | 2020-10-02 | 12.72 $\pm$ 0.04 | 13.46 $\pm$ 0.04 | 12.97 $\pm$ 0.05 | 13.51 $\pm$ 0.06 | 14.19 $\pm$ 0.11 | 14.19 $\pm$ 0.06
59125.655695 | 2020-10-03 | - | 13.87 $\pm$ 0.04 | 13.42 $\pm$ 0.05 | 14.01 $\pm$ 0.06 | - | 14.68 $\pm$ 0.06
59126.597595 | 2020-10-04 | 13.23 $\pm$ 0.07 | 13.99 $\pm$ 0.07 | 13.53 $\pm$ 0.07 | 14.07 $\pm$ 0.09 | 14.93 $\pm$ 0.15 | 14.79 $\pm$ 0.09
59127.638321 | 2020-10-05 | 12.40 $\pm$ 0.04 | 13.14 $\pm$ 0.05 | 12.56 $\pm$ 0.05 | 13.08 $\pm$ 0.06 | 13.70 $\pm$ 0.06 | 13.67 $\pm$ 0.06
59128.182674 | 2020-10-06 | 12.62 $\pm$ 0.04 | 13.30 $\pm$ 0.05 | 12.72 $\pm$ 0.05 | 13.19 $\pm$ 0.06 | 13.73 $\pm$ 0.06 | 13.76 $\pm$ 0.06
59128.942192 | 2020-10-06 | 12.85 $\pm$ 0.04 | 13.62 $\pm$ 0.05 | 13.10 $\pm$ 0.05 | 13.68 $\pm$ 0.05 | 14.21 $\pm$ 0.06 | 14.20 $\pm$ 0.06
59129.906850 | 2020-10-07 | - | - | 13.32 $\pm$ 0.06 | 13.89 $\pm$ 0.06 | - | -
59130.907624 | 2020-10-08 | 13.22 $\pm$ 0.04 | 13.99 $\pm$ 0.04 | 13.47 $\pm$ 0.05 | 14.03 $\pm$ 0.06 | 14.65 $\pm$ 0.07 | 14.66 $\pm$ 0.06
59131.900956 | 2020-10-09 | 12.91 $\pm$ 0.04 | 13.61 $\pm$ 0.04 | 13.14 $\pm$ 0.05 | 13.67 $\pm$ 0.06 | 14.38 $\pm$ 0.07 | 14.31 $\pm$ 0.06
59132.891488 | 2020-10-10 | 13.00 $\pm$ 0.04 | 13.74 $\pm$ 0.04 | 13.19 $\pm$ 0.05 | 13.74 $\pm$ 0.05 | 14.34 $\pm$ 0.06 | 14.36 $\pm$ 0.06
59133.850977 | 2020-10-11 | 13.32 $\pm$ 0.04 | 14.10 $\pm$ 0.04 | 13.63 $\pm$ 0.05 | 14.22 $\pm$ 0.06 | 14.89 $\pm$ 0.06 | 14.92 $\pm$ 0.06
59134.891522 | 2020-10-12 | - | 14.01 $\pm$ 0.06 | 13.54 $\pm$ 0.05 | 14.11 $\pm$ 0.06 | - | 14.75 $\pm$ 0.06
59135.835244 | 2020-10-13 | 13.12 $\pm$ 0.04 | 13.95 $\pm$ 0.04 | 13.46 $\pm$ 0.05 | 14.06 $\pm$ 0.06 | 14.69 $\pm$ 0.06 | 14.77 $\pm$ 0.06
59137.660548 | 2020-10-14 | 13.48 $\pm$ 0.04 | 14.32 $\pm$ 0.05 | 13.87 $\pm$ 0.05 | 14.50 $\pm$ 0.06 | 15.13 $\pm$ 0.07 | 15.16 $\pm$ 0.06
59138.269685 | 2020-10-15 | 13.61 $\pm$ 0.04 | 14.42 $\pm$ 0.05 | 13.92 $\pm$ 0.05 | 14.55 $\pm$ 0.06 | 15.30 $\pm$ 0.06 | 15.27 $\pm$ 0.07

##  Appendix B NuSTAR and NICER results

Figure 10: Count rate per orbit for NuSTAR as seen by the FPMA module in the
3–79 keV (black dots), 3–10 keV (red triangles), and 10–79 keV (blue squares)
energy range, respectively. Figure 11: Comparison of the count rate obtained
for NICER in the 0.4–5.0 keV energy range (black open circles) and NuSTAR (red
filled triangles) in the 3–79 keV energy range (black dots) during 2020
October 11–12.