11institutetext: Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique
Nucléaire et de Hautes Energies, LPNHE, 4 place Jussieu, 75005 Paris, France
11email<EMAIL_ADDRESS>22institutetext: Université Paris-Cité,
AstroPrticules et Cosmologie, APC, 10 rue Alice Domon et Léonie Duquet, 75013
Paris, France 33institutetext: Université Paris-Saclay, Université Paris-Cité,
CEA, CNRS, AIM, 91191, Gif-surYvette, France 44institutetext: INAF-
Osservatorio Astronomico di Brera, via E. Bianchi 46, I-23807, Merate, Italy
55institutetext: European Space Agency (ESA), European Space Research and
Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, the Netherlands
66institutetext: Institut de Planétologie et d’Astrophysique de Grenoble,
Université de Grenoble Alpes, 38000 Grenoble, France 77institutetext: Dr. Karl
Remeis-Sternwarte and Erlangen Centre for Astroparticle Physics, Friedrich-
Alexander Universität Erlangen-Nürnberg, Sternwartstr. 7, 96049 Bamberg,
Germany

#  INTEGRAL study of MAXI J1535$-$571, MAXI J1820+070 and MAXI J1348$-$630
outbursts

I. Detection and polarization properties of the high-energy emission

F. Cangemi 1122 J. Rodriguez 33 T. Belloni 44 C. Gouiffès 33 V. Grinberg 55 P.
Laurent 33 P.-O. Petrucci 66 J. Wilms 77

(Accepted;)

###### Abstract

Context. In black hole X-ray binaries, a non-thermal high-energy component is
sometimes detected at energies above 200 keV. The origin of this high-energy
component is debated and distinct spectral modelizations can lead to different
interpretations. High-energy polarimetry measurements with INTEGRAL allow new
diagnostics on the physics responsible for the MeV spectral component in black
hole X-ray binaries.

Aims. In this work, we aim to investigate the high-energy behavior of three
bright sources discovered by the Monitor of All-sky X-ray Image: MAXI
J1535$-$571, MAXI J1820+070 and MAXI J1348$-$630\. We take advantage of their
brightness to investigate their soft $\gamma$-ray (0.1–2 MeV) properties with
INTEGRAL. We use both spectral and polarimetric approaches to probe their
high-energy emission with the aim to bring new constraints on the $\sim$ MeV
emission in black hole X-ray binaries.

Methods. We first study the spectral characteristics of the sources in the
3–2000 keV using JEM-X, IBIS and SPI with a semi-phenomenological description
of the data. We then use IBIS as a Compton telescope in order to evaluate the
polarization properties of the sources above 300 keV.

Results. A high-energy component is detected during the Hard-InterMediate
State and Soft-Intermediate State of MAXI J1535$-$571, the Low-Hard State of
MAXI J1820+070 and the Low-Hard State of MAXI J1348$-$630\. The components
detected in MAXI J1820+070 and MAXI J1348$-$630 are polarized with a
polarization fraction of $26\pm 9$° and $>56$ % in the 300–1000 keV,
respectively. With no polarization information for MAXI J1535$-$571, the
component detected could either come from the jets rather than the corona. In
the case of MAXI J1820+070, the extrapolation of the synchrotron spectrum
measured in the infrared indicates that the component is likely due to a non-
thermal distribution of electrons from a hybrid corona. For MAXI J1348$-$630,
the high fraction of polarization points towards a jets origin, however, we
cannot formally conclude without any infrared data giving information on the
optically thin part of the synchrotron spectrum.

###### Key Words.:

Accretion, accretion disks — Physical data and processes — Black hole physics
— X-rays: binaries — Stars: black holes

††offprints<EMAIL_ADDRESS>
##  1 Introduction

Black hole X-ray binaries are transient systems that can transit through
various spectral states during their outburst. The two main states are denoted
the Low Hard State (LHS) and the High Soft State (HSS; see Remillard &
McClintock, 2006; Belloni, 2010, for a precise definition of spectral states).
The LHS corresponds to the rising phase of the outburst; its 1–200 keV
spectrum can be well described by a powerlaw with a photon index of
$\Gamma\sim$ 1.5 with an exponential cutoff usually around 100 keV. This
component is usually interpreted as the emission from Compton scattering of
disk photons by electrons from a hot plasma called the “corona”. These sources
are also sites of ejections of material at relativistic speeds, and sources of
strong disk winds. The discovery of jets (Mirabel et al., 1992) led to name
them microquasars. A small extension, steady “compact” jet is observed in the
LHS, and has been resolved in a few sources: Cygnus X–1, GRS 1915+105, and
more recently, MAXI J1348–630 (e.g., Stirling et al., 2001; Fuchs et al.,
2003; Carotenuto et al., 2021). Transitions from the harder to the softer
states are accompanied by transient, discrete, and large scale ejections
(e.g., Fender et al., 1999; Hannikainen et al., 1999; Mirabel et al., 1998;
Corbel et al., 2001; Rodriguez et al., 2008a) and no jet seems to persist in
the HSS (although see Rushton et al. (2012); Zdziarski et al. (2020) for the
case of Cygnus X-1). The X-ray flux in the HSS is dominated by the photon disk
emission peaking at $\sim$ 1 keV. This component is associated with a
continuum usually described with a powerlaw with a photon index $\Gamma>2.5$
and whose origin is still not yet understood.

In several sources, observations made at higher energies ($>200$ keV) have
revealed the presence of a high-energy non-thermal component extending up to 1
MeV (Grove et al., 1998; Cadolle Bel et al., 2006; Laurent et al., 2011;
Rodriguez et al., 2015; Cangemi et al., 2021a). The origin of this high-energy
emission is still not well understood and (at least) two scenarios have been
invoked to explain its origin. In the first scenario, this component is the
extension of the Synchrotron spectrum from the basis of the jets (Markoff et
al., 2005; Laurent et al., 2011; Jourdain et al., 2014; Rodriguez et al.,
2015; Kantzas et al., 2021). The alternative explanation suggests that this
component arises from a non-thermal distribution of electrons in a hybrid
thermal/non-thermal corona (e.g., Del Santo et al., 2013; Romero et al., 2014;
Cangemi et al., 2021b, a). In the case of the high mass BHB, Cygnus X-1,
Cangemi et al. (2021a) have suggested that the high-energy tails, seen both in
the HSS and LHS have different origins: in the HSS an hybrid corona is
favoured while the jet would be at the origin of the LHS high-energy tail.

Polarization measurements of the high-energy emission from BHBs is probably
the best way to disentangle between these different scenarios as we expect
distinct polarization properties between a Compton or synchrotron emission.
INTEGRAL has already brought important insights on polarization measurements
thanks to the design of the SPectrometer on board on INTEGRAL (SPI, Vedrenne
et al., 2003) and the Imager on Board on INTEGRAL Satellite (IBIS; Ubertini et
al., 2003) which can be used as a Compton telescope with its two layers plane
(ISGRI and PICsIT). Indeed the high polarization degree of the $>400$ keV
Cygnus X-1 high-energy tail detected both with IBIS and SPI (Laurent et al.,
2011; Jourdain et al., 2012) has be shown to be compatible with the emission
of the compact jet in the LHS of this source (Rodriguez et al., 2015). Cygnus
X-1 is currently the only source for which polarization measurements have been
able to constrain the origin of the high-energy component. It is therefore
important to look at other sources in order to probe the origin of this
component and try to obtain a more general understanding of the $\sim$ MeV
emission in microquasars.

MAXI J1535$-$571, MAXI J1820+070 and MAXI J1348$-$630 are X-ray transients
discovered by the Monitor of All-Sky X-ray Image (MAXI) on board on the
International Space Station (Matsuoka et al., 2009) during their outburst in
September 2017 (Negoro et al., 2017), March 2018 (Kawamuro et al., 2018) and
January 2019 (Yatabe et al., 2019) respectively. The three outbursts were then
followed by INTEGRAL (e.g., Lepingwell et al., 2018; Bozzo et al., 2018;
Cangemi et al., 2019b, a) and all three sources were particularly bright and
reached a maximum flux of a few Crabs. Not many other sources have reached
such a brightness previously, and therefore, polarization studies on short
accumulation (i.e. a few days) of data led to totally unconstrained results.
Even for Cygnus X-1 the detection of polarised emission required accumulation
of Ms of data over large intervals of time.

Although the mass of the compact object in MAXI J1535$-$571 has not been
established yet, bright radio emission associated with a flat radio spectrum
(Russell et al., 2017) and strong emission in the infrared band (Dinçer, 2017;
Vincentelli et al., 2021) led to identify the source as a BHB. The source
displays strong X-ray variability, including low-frequency Quasi-Periodic
Oscillations (QPOs, Stiele & Kong, 2018; Huang et al., 2018; Stevens et al.,
2018; Bhargava et al., 2019; Sreehari et al., 2019). MAXI J1820+070 is a X-ray
binary harbouring a black hole of mass $\sim 8.5$ M⊙ accreting from a
companion star of $\sim 0.4$ M⊙ (Torres et al., 2019, 2020). The intense
brightness of the system has triggered multiple multi-wavelength observing
campaigns (e.g., Bright et al., 2020; Trushkin et al., 2018; Tetarenko et al.,
2021; Hoang et al., 2019) and the source was the center of many studies. MAXI
J1348$-$630 is also a BHB with a black hole of mass $\sim 11$ M⊙ (Lamer et
al., 2020) and the source is located at $\sim 3.3$ kpc according to the
measurement of Lamer et al. (2020) with SRG/eROSITA and XMM-Newton
observations. The source shows also strong X-ray variability and QPOs were
observed during LHS to HSS transition (Belloni et al., 2020). The source shows
also a interesting behavior when looking at is radio/X-ray correlation which
infers the relation between the emission from the compact jets and the inner
accretion flow (Corbel et al., 2013). The correlation displays two different
tracks reffered as the standard and the outliers tracks. Usually, a source
follows one of the tracks during its outburst, but Carotenuto et al. (2021)
have shown that in the the case of MAXI J1348$-$630, the source follows the
outliers track during the first part of the outburst before joining the
standard track. Table LABEL:tab:source_characteristics summarises all the
known parameters for the three sources.

Table 1: Summary of the known parameters for the three studied sources. Source | MAXI J1535$-$571 | MAXI J1820+070 | MAXI J1348$-$630
---|---|---|---
Mass of the black hole [M⊙] | – | $8.5^{+0.8}_{-0.7}$ | $11^{+2}_{-2}$
| – | Torres et al. (2020) | Lamer et al. (2020)
Mass of the companion [M⊙] | – | $0.6^{+0.1}_{-0.1}$ | –
| – | Torres et al. (2020) | –
Distance [kpc] | $4.1^{+0.6}_{-0.5}$ | $3.0^{+0.3}_{-0.3}$ | $3.3^{+0.3}_{-0.3}$
| Chauhan et al. (2019) | Atri et al. (2020) | Lamer et al. (2020)
Inclination [°] | $67.4^{+0.8}_{-0.8}$ | $63^{+3}_{-3}$ | $28^{+3}_{-3}$
| Miller et al. (2018) | Torres et al. (2020) | Anczarski et al. (2020)

In this study, we present the evolution of the outbursts of those three
different sources as observed by INTEGRAL. We make use of its unique
capabilities in order to probe the main properties over the full 3–1000 keV
range covered by the observatory. We also present polarization measurements of
the high-energy component when significant emission is detected above 300 keV.
The description of the observations, and the data reduction methods are
reported in Sect. 2. Section 3 is dedicated to the phenomenological spectral
analysis. We then present the results from our polarization measurements with
the Compton mode above 300 keV for the three sources in Sect. 4. The results
are finally discussed in Sect 5.

##  2 Data reduction

###  2.1 Spectral extraction: INTEGRAL/JEM-X

We only use data from JEM-X unit 1. The data are reduced with the Off-Line
Scientific Analysis (osa) version 11.1 software. We follow the standard steps
described in the JEM-X user
manual111https://www.isdc.unige.ch/integral/download/osa/doc/11.1/osa_um_jemx/man.html..
Spectra are extracted for each SCience Windows222INTEGRAL individual pointings
of a duration of 1800–3600 s typical duration. (scw heareafter) where the
source is automatically detected by the software at the image creation and
fitting step. Spectra are then computed over 32 logarithmic spectral channels
from $\sim 3$ to $\sim 34$ keV using the standard binning definition.
Individual spectra for each period are then combined with the OSA spe_pick
tool according to the classification scheme described in Sect. 2.4. The
appropiate ancillary response files (arfs) are produced during the spectral
extraction and are combined with spe_pick, while the redistribution matrix
file (rmf) is rebinned from the instrument characteristic standard rmf with
j_rebin_rmf. We add 3 % systematic error on all spectral channels for each of
the stacked spectra, as recommended in the JEM-X user manual. For our spectral
analysis, we consider the spectra from 3 to 20 keV.

###  2.2 Spectral extraction: INTEGRAL/IBIS/ISGRI

Data from INTEGRAL/IBIS upper detector ISGRI are also reduced with the osa
11.1 software. We use the standard procedure described in the IBIS
manual333https://www.isdc.unige.ch/integral/download/osa/doc/11.1/osa_um_ibis/man.html..
For each scw, we create the sky model and reconstruct the sky image and the
source count rates by deconvolving the shadowgrams projected onto the detector
plane. For the three sources, spectra are extracted using 60 logarimically
spaced channels between 20 keV and 1000 keV. Response matrixes are
automatically generated running the osa 11.1 spectral extraction. We then use
the spe_pick tool to create stacked spectra for each different outburst
periods (see Sect. 2.4). 2 % of systematics are added to each stacked spectra
as indicated in the IBIS user manual.

###  2.3 Spectral extraction INTEGRAL/SPI

We followed a similar procedure already applied in the case of Cygnus X-3
(Cangemi et al., 2021b). To summarize, we use the Spi Data Analysis
Interface444https://sigma-2.cesr.fr/integral/spidai. (Spidai) to reduce SPI
data. During the outburst of MAXI J1348$-$630, SPI was in annealing from MJD
58501 to MJD 58522 (INTEGRAL revolutions 2047 to 2054), therefore we do not
have available SPI data during the LHS and the IMS but we extract the SPI
spectrum in the HSS. We respectively create a sky model containing MAXI
J1535$-$571, MAXI J1820+070 and MAXI J1348$-$630 and set their variability to
5 scws. We then create the background model by setting the variability
timescale of the normalization of the background pattern to 5 scws. Sometimes,
solar flares, radiation belt entries, and other non-thermal incidents can lead
to unreliable results. Therefore, we remove scws for which the reconstructed
count compared to the detector counts give a poor $\chi^{2}$
($\chi^{2}_{\mathrm{red}}$ ¿ 1.5) in order to avoid these effects. This
selection reduces the total number of scws by $\sim 10$ %. The shadowgrams are
then deconvolved to obtain the source flux, and spectra are extracted between
20 keV and 2000 keV using 27 logarithmically spaced channels. For each
spectrum, we apply a correcting factor of 1/0.85 above 400 keV in order to
take into account a change efficiency above this threshold (Roques & Jourdain,
2019).

###  2.4 Data selection and period definition

We consider scw between MJD 58004–58019 (09/08/2017–09/23/2017), 58193–58249
(03/16/2018–05/11/2018) and 58512–58541 (01/29/2019–02/27/2019) respectively
corresponding to the outburst of MAXI J1535$-$571, MAXI J1820+070, and MAXI
J1348$-$630 where the sources are less than 10° off axis. Figure 1 shows the
INTEGRAL/ISGRI lightcurves between 30 keV and 50 keV along with the MAXI/GSC
monitoring in order to show the INTEGRAL observations in the long-term context
of the whole outburst.

Figure 1: MAXI/GSC 2–20 keV (in black) and INTEGRAL/IBIS 30–50 keV (colored
dots) lightcurves of MAXI J1535$-$571 (top panel), MAXI J1820+070 (middle
panel), and MAXI J1348$-$630 (bottom panel). Left and right y axis indicate
the countrate for MAXI/GSC and INTEGRAL/IBIS respectively. Definitions of the
different periods and the corresponding colors are described in Sect. 2.4. The
counrates for 1 Crab is indicated with the pink and blue dotted lines for
MAXI/GSC and INTEGRAL/IBIS, respectively.

For the three sources, we perform purely phenomenological fit for each scw, in
the 3–300 keV energy range using JEM-X unit 1 and ISGRI in order to separate
the three datasets into different periods according to their spectral shapes
and properties. The fits are performed using Xspec (Arnaud, 1996); we use a
cutoff powerlaw model (cutoffpl) and added the emission from a disk (diskbb)
when needed.We also multiply the model with a constant (constant) allowing us
to take into account calibration issues between the instruments and the
differences in total exposure between the instruments555Given the INTEGRAL
observing pattern around the pointed source and since IBIS has a larger field
of view than JEM-X, sources can be outside the JEM-X field of view while still
in the IBIS one). Constants are let free whereas other parameters are tied
between instruments.

In summary, we use constant*cutoffpl or constant*(cutoffpl+diskbb) when high
residuals are observed at low energy. Because of the low exposure of the
individual spectra, we do not use absorption here, the aim being to roughly
describe the shape of the spectra in order to separate the different periods
of the outbursts. We then extract the values of the photon index, the
exponential cutoff and the disk temperature. The evolution of these different
parameters are shown in Fig. 2 for the three sources.

Figure 2: Temporal evolution of the different spectral parameters extracted
from our phenomenological spectral fitting for MAXI J1535$-$571 (left panel),
MAXI J1820+070 (middle panel), and MAXI J1348$-$630 (right panel). Definitions
of the different periods and their corresponding colors are described in Sect.
2.4

For MAXI J1535$-$571, based on the value of the photon index which transits
from $\sim 1.9$ to $\sim 2.3$ from MJD 58004 to MJD 58016, we divide our
datasets in two periods: the first one from 58004 to 58012 and the second one,
after MJD 58016. The two periods are shown in green and orange on Fig. 1. This
subdivision is consistent with the epochs defined in Russell et al. (2020)
where they find that the source was in a Hard InterMediate State (HIMS) state
from MJD 58008 to 58016 before its transition into a Soft Intermediate State
(SIMS) at MJD 58017. Therefore, we name our two periods according to this
classification.

Concerning MAXI J1820+070, the values of the photon index and the exponential
cutoff are consistent with typical values observed in a LHS during all the
INTEGRAL observations. We thus define a unique period for the characterization
of this outburst. The unique period is shown in blue in Fig. 1. This is
consistent with the different epochs defined in Buisson et al. (2019) where
they show that the source starts its transition into the HSS around MJD 58306,
after our observations.

The study of the MAXI J1348$-$630 spectral evolution shows two changes in the
spectral shape. The first change occurs around MJD 58517 where we observe an
increase of the photon index from $\sim$1.6 to 2.3 and an increase of the
cutoff energy from 50 keV to above detection threshold. We define these two
periods as the LHS (in blue of Fig. 1) and InterMediate State (IMS, in yellow
on Fig. 1) states. Here we are not able to identify the different flavors
(HIMS and SIMS) of the IMS. The observations from the last period, after MJD
58539, show a higher photon index value $\sim 2.3$ associated with a high-
energy exponential cutoff, not constrained in the majority of our observations
(see the lower limits on Fig 2). Belloni et al. (2020) find a similar state
classification when analysing data from NICER. Figure 1 shows the LHS, IMS and
HSS state periods in blue, yellow and pink, respectively.

The broadband INTEGRAL spectra are shown on Fig. 3. The different state
spectra are plotted with different colors using the same color code as in Fig.
1.

Figure 3: Stacked spectra extracted from JEM-X, ISGRI and SPI for MAXI
J1535$-$571 (left panel), MAXI J1820+070 (middle panel), and MAXI J1348$-$630
(right panel). The different color indicates the different epochs considered
using the same color code as in Fig. 1.

##  3 State dependent spectral analysis

###  3.1 Methodology

According to the state classification described in Sect. 2.4, we have
different stacked spectra for different periods of the three outbursts. In
order to assess the potential presence of a high-energy tail in a state-
resolved way, we follow the same methodology described in Cangemi et al.
(2021b, a). This methodology is divided in two steps: we first analyse the
data from 3 to 100 keV with a reflected (reflect, Magdziarz & Zdziarski, 1995)
thermal Comptonization continuum (nthcomp, Zdziarski et al., 1996). We also
add the iron line at 6.4 keV with a Gaussian (gaussian). Although, the
reflection is not needed in the individual spectra, it is needed in the
stacked spectra in order to obtain a statistically good fit. We choose this
Comptonization model rather than another because the MAXI J1820+070 spectrum
is better fitted with this model than with other thermal Comptonization models
we have tested (e.g., comptt). This model has also been used by Shidatsu et
al. (2019) to fit MAXI/GSC and Swift/BAT data of MAXI J1820+070. For the sake
of consistency, we also use nthcomp for MAXI J1535$-$571 and MAXI
J1348$-$630\. We also add the absorption by the interstellar medium (tbabs,
Wilms et al., 2000) using angr solar abundances (Anders & Ebihara, 1982). The
model is written constant*tbabs*(reflect(nthcomp) + gaussian) in Xspec. We add
the emission from a disk (diskbb, Mitsuda et al., 1984) when needed. In this
case, the model becomes constant*tbabs*(reflect(nthcomp) + diskbb + gaussian).
We let the energy of the iron line vary between 6.2 keV to 6.5 keV whereas its
width is allowed to vary between 0.2 keV to 0.5 keV. Once we obtain a
satisfactory fit, we add the data above 100 keV, let the parameters vary
freely and search for presence of residuals at high-energy. In case of large
residuals observed above 300 keV, we add a powerlaw component
(constant*tbabs*(reflect(nthcomp) + gaussian + powerlaw) or
constant*tbabs*(reflect(nthcomp) + diskbb + gaussian + powerlaw) to the model
and investigate the significance of this component by performing a F-test. We
use an inclination of $i=67$° (Miller et al., 2018), 63° (Torres et al.,
2019), and 28° (Anczarski et al., 2020) for the reflection component for MAXI
J1535$-$571, MAXI J1820+070 and MAXI J1348$-$630 respectively. The reflection
fraction is allowed to vary between 0 ¡ $\Omega/2\pi$ ¡ 2.

The best-fit parameters obtained in the 3–2000 keV band are reported in Tab. 2
and the corresponding spectral fits for each source in the different states
are shown in Fig. 4. If the addition of a disk is necessary to fit the data,
we indicate “yes” in the row called “Disk”. Rows “Flux” and “Fluxpo”
respectively refer to the flux given by the total model and the flux which
comes from an additional powerlaw component in the 300–1000 keV range.

Figure 4: Best-fit models obtained from our phenomenological fitting of the 3–2000 keV for MAXI J1535$-$571 (top panel), MAXI J1820+070 (middle panel), and MAXI J1348$-$630 (bottom panel). Different colors indicate different epochs using the same color code as in Fig. 1. JEM-X, ISGRI and SPI data are represented with blue, red and yellow respectively. Residuals for each period are plotted separately at the bottom of the corresponding spectrum. Different model components are shown with different line styles: Comptonized continnum,(dashed), disk (dotted-dashed), additional powerlaw (densely dotted), gaussian (dotted). Table 2: Parameters obtained for our phenomenological fitting for each source and each period. Parameters | MAXI J1535$-$571 | MAXI J1820+070 | MAXI J1348$-$630
---|---|---|---
| HIMS | SIMS | LHS | LHS | IMS | HSS
CISGRI | $0.93^{+0.04}_{-0.03}$ | $1.14^{+0.01}_{-0.02}$ | $0.91^{+0.03}_{-0.02}$ | $0.82^{+0.03}_{-0.02}$ | $0.8^{+0.2}_{-0.2}$ | $0.85^{+0.04}_{-0.04}$
CSPI | $0.90^{+0.04}_{-0.03}$ | $1.20^{+0.01}_{-0.02}$ | $0.91^{+0.03}_{-0.02}$ | – | – | $0.90^{+0.04}_{-0.04}$
$n_{\mathrm{H}}$ [$\times 10^{22}$ cm-2] | $3.3^{+0.6}_{-0.7}$ | $2.5^{+1}_{-1}$ | 0.14 F | 0.86 F | 0.86 F | 0.86 F
$k\mathrm{T}_{\mathrm{0}}$ [keV] | 0.3 F | $1.24^{+0.04}_{-0.03}$ | 0.2 F | 0.5 F | $1.21^{+0.09}_{-0.08}$ | $0.84^{+0.03}_{-0.03}$
$k\mathrm{T}$ [keV] | $52^{+43}_{-17}$ | $40^{+106}_{-26}$ | $57^{+4}_{-4}$ | $44^{+5}_{-4}$ | ¿ 193 | ¿ 471
$\Omega/2\pi$ | $1.1^{+0.8}_{-0.3}$ | ¿ 1.8 | ¿ 1 | $0.8^{+0.1}_{-0.1}$ | $1.0^{+0.2}_{-0.1}$ | $0.46^{+0.09}_{-0.08}$
$E_{\mathrm{Fe}}$ [keV] | $6.5^{+0.0}_{-0.1}$ | $6.2^{+0.3}_{-0.0}$ | $6.2^{+0.3}_{-0.0}$ | $6.20^{+0.02}_{-0.00}$ | $6.20^{+0.09}_{-0.00}$ | $6.2^{+0.3}_{-0.00}$
$\sigma_{\mathrm{Fe}}$ [keV] | $0.5^{+0.0}_{-0.2}$ | $0.2^{+0.3}_{-0.0}$ | $0.5^{+0.0}_{-0.3}$ | $0.5^{+0.0}_{-0.2}$ | 0.4 F | $0.5^{+0.0}_{-0.2}$
$\Gamma_{\mathrm{th}}$ | $2.38^{+0.05}_{-0.09}$ | $2.52^{+0.08}_{-0.09}$ | $1.61^{+0.01}_{-0.01}$ | $1.69^{+0.04}_{-0.03}$ | $2.06^{+0.03}_{-0.03}$ | $2.19^{+0.02}_{-0.02}$
$\Gamma_{\mathrm{po}}$ | $2.1^{+0.4}_{-0.5}$ | $2.0^{+0.4}_{-0.4}$ | $2.09^{+0.03}_{-0.03}$ | $2.0^{+0.3}_{-0.3}$ | – | –
Disk | no | yes | no | yes | yes | yes
Flux 300–1000 keV [$\times 10^{-9}$ ergs cm-2 s-1] | 1.6 | 1.6 | 5.6 | 5.6 | 0.9 | 0.2
Fluxpo 300–1000 keV [$\times 10^{-9}$ ergs cm-2 s-1] | 1.6 | 1.6 | 4.6 | 5.3 | – | –
$\chi^{2}$/dof | 112.45/91 | 133.88/92 | 88.68/75 | 62.56/68 | 110.18/72 | 135.67/95

###  3.2 Results

####  3.2.1 MAXI J1535$-$571

During the HIMS, the seed-photon energy is unconstrained, we thus fix its
value to 0.3 keV according to e.g., Sridhar et al. (2019), Tao et al. (2018).
The value for the density column $n_{\mathrm{H}}$ $\sim 3.3\times 10^{22}$
cm-2 is consistent with the value measured by Sridhar et al. (2019) (Astrosat)
but it is slighly lower compared to the value obtained by Xu et al. (2018)
(NuSTAR). This difference can arise by the use of slighly different epochs of
observations between the different analysis. Moreover, Xu et al. (2018)
attribute their high value ($n_{\mathrm{H}}$ $\sim 8\times 10^{22}$ cm-2) to
the inclusion of the thermal disk in their modelling. The electron temperature
of $k\mathrm{T}$ $\sim 52$ keV we obtain is consistent with results from
Sridhar et al. (2019) and Tao et al. (2018). We find a photon index of the
Comptonized continuum rather soft $\Gamma_{\mathrm{th}}$ $\sim 2.38$ slighly
higher that found in the different modelizations of Sridhar et al. (2019) and
a reflection fraction of $\Omega/2\pi$ $\sim 1.1$. During the SIMS, we observe
residuals below $\sim$10 keV and we add a disk to model the corresponding
spectra. The disk temperature is tied to the photon seed temperature of
nthcomp. We find $k\mathrm{T}_{\mathrm{0}}$ $\sim 1.24$ keV in agreement with
the value obtained by Tao et al. (2018). The other parameters are roughly the
same as in the SIMS except for $\Gamma_{\mathrm{th}}$ $\sim 2.52$ for which we
observe a slight increase. Our best fit gives a lower limit of $>1.8$ for the
reflection fraction. We have tested other reflection model like relxill which
also give a similarly large reflection fraction. In their study, Miller et al.
(2018) have tested different reflection models, and notably relxill and
relline and also obtain a large reflection fraction. Following these authors
such large value is compatible with an X-ray source very close to the black
hole, the large reflection then being due to the strong expected light
bending. Our results agree with their best fit parameters. We will not enter
in more details of the reflection component here since it is not the main
subject of this paper.

Interestingly, we need an addionnal powerlaw component for both states in
order to model the spectra above 300 keV. For the HIMS, inclusion of the
powerlaw improves $\chi^{2}_{\mathrm{red}}$ from $155.95/93$ dof to
$\chi^{2}_{\mathrm{red}}$ $=112.45/91$ dof; for the SIMS, it is improved from
$\chi^{2}_{\mathrm{red}}$ $=292.30/94$ dof to $\chi^{2}_{\mathrm{red}}$
$=133.88/92$ dof. The photon index $\Gamma_{\mathrm{po}}$ of this powerlaw is
consistent between the two periods, and we find $\Gamma_{\mathrm{po}}$
${}^{\mathrm{HIMS}}=2.1^{+0.4}_{-0.5}$ and $\Gamma_{\mathrm{po}}$
${}^{\mathrm{SIMS}}=2.0^{+0.4}_{-0.4}$. We observe that the flux ¿ 300 keV is
dominated by this additional component. In order to assess the existence of
this powerlaw component, we also try to fit the data using solely a powerlaw
instead of the thermal Comptonization model. In this case, the data is poorly
represented ($\chi^{2}_{\mathrm{red}}$ HIMS = 490.53/94 dof and
$\chi^{2}_{\mathrm{red}}$ SIMS = 210.15/95 dof), and we observe strong
residuals in the 30–50 keV range clearly indicating the presence of a cutoff
in this energy range.

####  3.2.2 MAXI J1820+070

In MAXI J1820+070, the value of the density column is unconstrained, thus, we
fix it according to the value $n_{\mathrm{H}}$ $=1.4\times 10^{21}$ obtained
by Kajava et al. (2019). We find a Comptonized continuum rather hard with a
photon index of $\Gamma_{\mathrm{th}}$ $\sim 1.61$ and an electron energy
$k\mathrm{T}$ $\sim 57$ keV. Our value for the electron energy is higher
compared to the value found by Zdziarski et al. (2021), $k\mathrm{T}$ $\sim
12$ keV, which use the data above 20 keV from ISGRI and SPI and the 3–80 keV
data from NuSTAR. However, they use a modified version of compps666They use a
sinusoïdal distribution of the seed photons in a sphere. as their thermal
description of the continuum and this could explain the difference compared to
our study. The value we find for the electron temperature is also roughly
consistent with the work of Chakraborty et al. (2020) and Buisson et al.
(2019) where they combine NuSTAR and Astrosat data. They both use a two
coronal component model and find $k\mathrm{T}$ $\sim$ 38 keV when tying the
two corona temperature components. We do not add a disk component to the model
and we fix the photon seed energy to $k\mathrm{T}_{\mathrm{0}}$ = 0.2 keV
(e.g., Wang et al., 2020; Dziełak et al., 2021). We find a reflection fraction
$\Omega/2\pi$ ¿ 1.

When adding the data above 300 keV, the addition of a powerlaw to the model
strongly improve the goodness of the fit (from $\chi^{2}_{\mathrm{red}}$
$=367.23/77$ dof to $\chi^{2}_{\mathrm{red}}$ $=88.68/75$ dof). We observe
that the ¿ 300 keV is largely dominated by the emission from this high-energy
component (82 % of the 300–1000 keV flux).

####  3.2.3 MAXI J1348$-$630

The parameter $n_{\mathrm{H}}$ is unconstrained and we fix its value to
$n_{\mathrm{H}}$ $=8.6\times 10^{21}$cm-2 (Tominaga et al., 2020). Parameters
found in LHS are very close to those found during the outburst of MAXI
J1820+070. We obtain a photon index $\Gamma_{\mathrm{th}}$ $\sim 1.69$ and an
electron energy $k\mathrm{T}$ $\sim 44$ keV. It is mentioned that a black body
component is present in the LHS (e.g., Tominaga et al., 2020; Chakraborty et
al., 2020; Zhang et al., 2021) with a temperature of $\sim 0.5$ keV. At such a
temperature, the flux of the disk could contribute $>3$ keV and therefore we
add a diskbb component in our model. The normalization of this component is
fixed to 12000, value found by Chakraborty et al. (2020). Strong residuals are
observed at high energy when fitting solely with const*(reflect(nthcomp) +
gauss). The addition of a powerlaw component improves
$\chi^{2}_{\mathrm{red}}$ from $112.42/70$ dof to $62.56/68$ dof. We find a
photon index of $\Gamma_{\mathrm{po}}$ = 2.0 and measure a reflection fraction
of $\sim$ 0.8.

We also use a disk to model the IMS and the HSS. As for the states of MAXI
J1535$-$571, the flux at low energy is dominated by the disk emission. The
photon disk energy is slighly higher during the IMS than during the HSS. Using
NICER and Astrosat, Zhang et al. (2021) and Jithesh et al. (2021) find a
consistent value analysing data from different observations made during the
HSS. However, Zhang et al. (2021) observe a higher value of
$\Gamma_{\mathrm{th}}$ ($\sim 3.3$) than observed during both periods
corresponding to our HIMS and SIMS. Note that we also model those two periods
with a simple reflected powerlaw and a disk (reflect(powerlaw) + diskbb +
gaussian). In this case, we do not find a satisfactory fit for the IMS
($\chi^{2}_{\mathrm{red}}$ Int = 248.13/75), but the HSS can be well described
by this purely phenomenological model and parameters are consistent with the
previous modelization.

##  4 Polarization with the Compton mode

###  4.1 Principle of the Compton Mode

Thanks to its two layer detectors; ISGRI at the top and the Pixellated Imaging
Caesium Iodide Telescope (PICsIT, Labanti et al., 2002) at the bottom, IBIS
can be used as a Compton polarimeter.

This concept relies on the cross section $d\sigma$ which represents the
probability for a polarized photon with an energy $E_{\mathrm{1}}$ to enter in
interaction with an electron from the detector (e.g., Evans & Beiser, 1956):

$\frac{d\sigma}{d\Omega}=\frac{r_{\mathrm{0}}^{2}}{2}\left(\frac{E_{\mathrm{2}}}{E_{\mathrm{1}}}\right)^{2}\left(\frac{E_{\mathrm{2}}}{E_{\mathrm{1}}}+\frac{E_{\mathrm{1}}}{E_{\mathrm{2}}}-2\sin^{2}\theta_{\mathrm{c}}\cos^{2}\phi\right)$
(1)

where $E_{\mathrm{2}}$ is the energy of the scattered photon in the solid
angle $d\Omega$, $\theta_{\mathrm{c}}$ is the scatter angle, $r_{\mathrm{0}}$
is the electron radius and $\phi$ is the azimuthal angle of the scattered
photon with respect to the polarization direction (see e.g., Fig. 1 of Forot
et al., 2007). Using the relation between $E_{\mathrm{1}}$ and
$E_{\mathrm{2}}$:

$\frac{E_{\mathrm{1}}}{E_{\mathrm{2}}}=\frac{1}{1+\frac{E_{\mathrm{2}}}{m_{e}c^{2}}(1-\cos\theta_{\mathrm{c}})}$
(2)

we note that for a fixed scattered angle, the cross section will be maximal
for $\phi=\pi/2+k\pi$ with $k\in\mathds{Z}$. This creates an asymmetry in the
number of detected photons by PICsIT. We can evaluate the detected photon
distribution on the PICsIT detector with respect to the azimuth $\phi$:

$N(\phi)=C[1+a_{\mathrm{0}}\cos(2(\phi-\phi_{\mathrm{0}}))]$ (3)

where $C$ is the mean count rate. Then we can deduce the polarization angle
$PA=\phi_{\mathrm{0}}-\pi/2$ and the polarization fraction $\Pi$:

$\Pi=\frac{a_{\mathrm{0}}}{a_{\mathrm{100}}}$ (4)

where $a_{\mathrm{100}}$ represents the amplitude of a 100 % polarized source
(Suffert et al., 1959). The value of $a_{\mathrm{100}}$ depends on several
factors as the detector dimension, the detection threshold, the level of noise
etc. In the case of IBIS, we simulate the emission from a monochromatic source
for which we apply the same treatment as for a real source. The resulting
modulation is used to deduce the value of $a_{\mathrm{100}}$ for this energy.
We then weight this value by the source spectrum and obtain the value of
$a_{\mathrm{100}}$ for the desired energy band. It is usually around 0.2–0.3
depending on the considered energy band (Laurent et al., 2011; Rodriguez et
al., 2015). Figure 10 shows the evolution of $a_{\mathrm{100}}$ as a function
of the energy.

In order to measure $N(\phi)$, we need to select the simple Compton events,
i.e, those for which photons interact only once in ISGRI and once in PICsIT. “
Spurious events ” are removed according to the method described in Forot et
al. (2007). Photons are accumulated in six different angle ranges of 30° each.
In order to improve the signal to noise ratio in each channel, we take
advantage of the $\pi$ symmetry of the differential cross section described by
equation (1) since e.g., the first channel contains photons with an azimuth 0°
$<\phi<$ 30° and photons with an azimuth 180° $<\phi<$ 210°. Shadowgrams are
formed for each channel angle chosen by the user, then deconvolved and count
rates are extracted.

The uncertainty on $N(\phi)$ is dominated by statistical fluctuations, since
our observations are background dominated. Therefore, confidence intervals for
$\phi_{0}$ and $a_{0}$ are not derived by a $N(\phi)$ fit to the data but
obtained with a Bayesian approach following the work of Forot et al. (2008)
and described in Vaillancourt (2006) and Weisskopf et al. (2006). In this
computation, we suppose that all real polarization angles and fractions have a
uniform probability distribution (non-informative prior densities, Quinn,
2012; Maier et al., 2014) and that the real polarization angle and fraction
are $\phi_{0}$ and $a_{0}$. We then need the probability density distribution
of measuring $a$ and $\phi$ from $N_{\mathrm{pt}}$ independent data points in
$N(\phi)$ during a period $\pi$, which is given by (Vaillancourt, 2006; Forot
et al., 2008; Maier et al., 2014) :

$\mathrm{d}P(a,\phi)=\frac{N_{\mathrm{pt}}C^{2}}{\pi\sigma_{\mathrm{C}}^{2}}\exp\Bigg{[}-\frac{N_{\mathrm{pt}}C^{2}}{2\sigma_{\mathrm{C}}^{2}}\Bigg{.}[a^{2}+a_{\mathrm{0}}^{2}-\\\
2aa_{\mathrm{0}}\cos(2\phi-2\phi_{\mathrm{0}})]\Bigg{.}\Bigg{]}\,a\,\mathrm{d}a\,\mathrm{d}\phi$
(5)

where $\sigma_{\mathrm{C}}$ is the uncertainty of $C$. Uncertainties of $a$
and $\phi$ can then be deduced by integrating $\mathrm{d}P(a,\phi)$ by respect
to the other dimension. We emphasize that this probability is a conditional
probability and is calculated by supposing that the emission is indeed
polarized.

There are also several systematics uncertainties that arise from measurements
of polarization with a Compton telescope using a coded mask. The non-
axisymmetric geometry of the detectors and the systematics due to the analysis
process have been studied in details in Forot et al. (2008). We also study the
modulation from the background by selecting events from detector pixels hidden
from the source by opaque mask elements, for scws of MAXI J1820+070. We find a
modulation of 5 % for the different energy bands used in the analysis. All
these systematics uncertainties are taken into account in the derivation of
the polarization constrains measured in this paper.

Table 3: Parameters obtained for our polarization analysis using the Compton mode. C and S is the value of the $\chi^{2}_{\mathrm{red}}$ obtained using a constant (C) or a sinusoïdal (S) function for our polarigram fit. Source | State period | Exposure time | Energy band | Signal | $a_{\mathrm{100}}$ |  $\chi^{2}$/dof | $p_{\mathrm{unpola}}$ | Polarization | Polarization | Polarization
---|---|---|---|---|---|---|---|---|---|---
|  | [Ms] |  | to noise ratio |  |  | [%] | Angle [°] | fraction [%] | detected
MAXI J1535$-$571 | HIMS | 0.22 | 300–400 keV | 4.9 | 0.278 | C = 2.35/5 | – | – | – | $\times$
|  |  |  |  |  | S = 1.52/4 |  |  |  |
|  |  | 400–1000 keV | 7.2 | 0.194 | C = 1.30/5 | – | – | – | $\times$
|  |  |  |  |  | S = 0.64/4 |  |  |  |
|  |  | 300–1000 keV | 8.7 | 0.224 | C = 1.35/5 | – | – | – | $\times$
|  |  |  |  |  | S = 0.92/4 |  |  |  |
| SIMS | 0.16 | 300–400 keV | 3.3 | 0.278 | C = 8.00/5 | – | – | – | $\times$
|  |  |  |  |  | S = 5.60/4 |  |  |  |
|  |  | 400–1000 keV | 3.7 | 0.194 | C = 2.00/5 | – | – | – | $\times$
|  |  |  |  |  | S = 2.72/4 |  |  |  |
|  |  | 300–1000 keV | 4.9 | 0.224 | C = 6.35/5 | – | – | – | $\times$
|  |  |  |  |  | S = 6.40/4 |  |  |  |
MAXI J1820+070 | LHS | 1.3 | 300–400 keV | 71 | 0.278 | C = 12.05/5 | 0.57 | $120\pm 14$ | $17\pm 8$ | ✓
|  |  |  |  |  | S = 6.44/4 |  |  |  |
|  |  | 400–1000 keV | 67 | 0.194 | C = 13.1/5 | 0.11 | $105\pm 11$ | $35\pm 12$ | ✓
|  |  |  |  |  | S = 4.48/4 |  |  |  |
|  |  | 300–1000 keV | 94 | 0.224 | C = 20.65/5 | 0.003 | $110\pm 11$ | $26\pm 9$ | ✓
|  |  |  |  |  | S = 7.44/4 |  |  |  |
MAXI J1348$-$630 | LHS | 0.32 | 300–400 keV | 22.9 | 0.278 | C = 12.30/5 | 0.02 | $160\pm 9$ | $75\pm 26$ | ✓
|  |  |  |  |  | S = 0.84/4 |  |  |  |
|  |  | 400–1000 keV | 22 | 0.194 | C = 9.40/5 | 0.06 | $180\pm 10$ | $>70$ | ✓
|  |  |  |  |  | S = 5.28/4 |  |  |  |
|  |  | 300–1000 keV | 30.7 | 0.224 | C = 15.45/5 | 0.008 | $180\pm 10$ | $79\pm 23$ | ✓
|  |  |  |  |  | S = 0.68/4 |  |  |  |
| IMS | 0.17 | 300–400 keV | 8.2 | 0.278 | C = 13.15/5 | – | – | – | $\times$
|  |  |  |  |  | S = 12.84/4 |  |  |  |
|  |  | 400–1000 keV | 7.2 | 0.194 | C = 4.95/5 | – | – | – | $\times$
|  |  |  |  |  | S = 3.88/4 |  |  |  |
|  |  | 300–1000 keV | 10.42 | 0.224 | C = 7.45/5 | – | – | – | $\times$
|  |  |  |  |  | S = 6.32/4 |  |  |  |
| HSS | 0.42 | 300–400 keV | 2.79 | 0.278 | C = 3.15/5 | – | – | – | $\times$
|  |  |  |  |  | S = 0.48/4 |  |  |  |
|  |  | 400–1000 keV | 3.01 | 0.194 | C = 11.01/5 | – | – | – | $\times$
|  |  |  |  |  | S = 4.08/4 |  |  |  |
|  |  | 300–1000 keV | 4.12 | 0.224 | C = 5.55/5 | – | – | – | $\times$
|  |  |  |  |  | S = 1.32/4 |  |  |  |
Figure 5: Polarigrams of the three sources obtained in the 300–1000 keV energy
band range.

###  4.2 Results

Figure 6: Probability density described by equation (5) in function of the
polarization angle and the polarization fraction calculated for MAXI J1820+070
(left) and MAXI J1348$-$630 in the LHS (right).

Figure 5 shows polarigrams in the 300–1000 keV band for the different periods
of the three sources, following the same color code as in Fig. 1. Figures 12
and 13 show polarigrams in the 300–1000 keV and 400–1000 keV bands
respectively. Polarigrams are fitted with a constant (dashed grey line) and
the sinusoid function described in equation (3) (colored line). During the LHS
periods of MAXI J1820+070 and MAXI J1348$-$630, we also show in Fig. 6 the
integrated probability function described by equation (5) in function of the
polarization angle $\phi$ and the polarization fraction $\Pi$. Other
probability density functions are shown on Fig. 11. Table 3 summarizes the
different parameters we measure for the three sources and for three different
energy bands: 300–400 keV, 400–1000 keV and 300–1000 keV. We indicate the
total effective exposure time, the signal to noise ratio, the
$a_{\mathrm{100}}$ value, the $\chi^{2}_{\mathrm{red}}$ obtained by fitting
$N(\phi)$ by a constant (C) or by the sinusoid function (S) described by
equation (3), the polarization angle $PA$ and the polarization fraction $\Pi$.
Note that we use a range of 0–180° for our fitting. Uncertainties represent an
interval confidence of 67 %. The last column indicates whether polarization is
detected (✓) or not ($\times$). We consider that polarization is detected by
validating two conditions: (1) we need a signal to noise ratio higher than 12
to obtain reliable results; this value is based on empirical results on the
Crab (Laurent et al., 2016), and (2) the probability $p_{\mathrm{unpola}}$ of
measuring modulation knowing that the source is unpolarized is $<1$ %. All
$p_{\mathrm{unpola}}$ are shown in Table 3 (only for polarigrams where the
signal to noise ration is higher than 12).

We do not detect polarization for MAXI J1535$-$571\. Indeed, for both states
and for the three energy bands, the signal to noise ratio is too poor and no
modulation is detected.

The diagnosis is different for MAXI J1820+070. Indeed, for the three
considered energy bands, polarigrams show clear deviation from a constant
which poorly represents the data We find a much better description of the data
with the sine function (eq. 3). In the three energy bands, we calculate the
probability given by equation (eq. 5) using the values of $a$ and $\phi$ we
find in our best fit. Figure 6 (left) shows the contour plot we obtain in the
300–1000 keV bands; polarization is detected with a interval confidence higher
than 99 %, and we find a polarization angle and a polarization fraction
consistent with $PA\sim 110$° and $\Pi\sim 25$ % in the three energy bands.

Concerning MAXI J1348$-$630, polarigrams extracted from the IMS and HSS
periods have poor signal to noise ratio. On the other hand, polarigrams from
the LHS period have sufficient signal to noise to probe the presence of a
modulation. We find that polarigrams are poorly described by a constant and
$p_{\mathrm{unpol}}<1$ % in the different energy bands. We then calculate the
probability (eq. 5) to measure the polarization angle $PA$ and a polarization
fraction $\Pi$. The contour plot is shown on Fig. 6 (right). We find lower
limits for the polarization fraction of 49 %, 70 %and 56 % with a polarization
angle of $\sim 160$ °, $\sim 180$ ° and $\sim 180$ ° for the 300–400 keV,
300–1000 keV and 300–1000 keV bands respectively.

##  5 Discussion and interpretation

###  5.1 Summary of the results

####  5.1.1 MAXI J1535$-$571

We separate the data in two intervals corresponding to a HIMS and SIMS, which
respectively match epochs defined in Russell et al. (2020). In both periods,
the source spectra are rather soft and characterized by a photon index
$\Gamma_{\mathrm{th}}^{\mathrm{HIMS}}=2.38^{+0.05}_{-0.09}$ and
$\Gamma_{\mathrm{th}}^{\mathrm{SIMS}}=2.52^{+0.08}_{-0.09}$. The low energy
emission starts to be dominated by the accretion disk during the SIMS period
and its energy temperature peaks at
$k\mathrm{T}_{\mathrm{0}}=1.24^{+0.04}_{-0.03}$ keV which is a typical value
usually observed in soft states of BHBs (e.g., Remillard & McClintock, 2006).
The energy from the corona electrons is not well defined in both states with a
value greater than 50 keV.

We detect an additional component above the Comptonization bump during both
states. This high-energy component is described by a powerlaw with a photon
index of $\Gamma_{\mathrm{po}}^{\mathrm{HIMS}}=2.1^{+0.4}_{-0.5}$ and
$\Gamma_{\mathrm{po}}^{\mathrm{SIMS}}=2.0^{+0.4}_{-0.4}$.

Using the Compton mode, we do not detect polarization in either both states.
We remark, however, that the source flux above 300 keV is quite low (see Table
2) resulting in a poor signal to noise ratio for our polarization
measurements. The non-detection is compatible with this empirical minimum
value to obtain a trustworthy detection of signal. Therefore, we cannot
conclude for MAXI J1535$-$571 if the lack of polarization detection at high
energy is an intrinsically characterictic of the source or an observationnal
issue.

####  5.1.2 MAXI J1820+070

MAXI J1820+070 is the brightest of the three sources observed in the ISGRI
30–50 keV range. The source is observed during its LHS (e.g., Buisson et al.,
2019). The spectrum is characterized by a hard photon index
$\Gamma_{\mathrm{th}}$ $=1.61^{+0.01}_{-0.01}$ and corona electron energy of
$57^{+4}_{-4}$ keV. An additional powerlaw component clearly improves the fit
and we find a photon index of $\Gamma_{\mathrm{po}}$ $=2.09^{+0.03}_{-0.03}$.
This component strongly dominates the spectrum above 300 keV with a flux of
$4.6\times 10^{-9}$ erg s-1 cm-2.

Polarigrams extracted in the 300–400 keV, 400–1000 keV and 300–1000 keV show a
strong modulation of the signal and we measure a 300–1000 keV polarization
fraction of $\Pi=26\pm 9$ and a polarization angle $PA=110\pm 11$° (see Tab. 3
for the energy dependent results), errors are given in a 67 % confidence
range.

####  5.1.3 MAXI J1348$-$630

We follow the evolution of the source during its outburst and identify three
different periods corresponding to three different states of the source, LHS,
IMS and HSS. During its LHS, we find a photon index of $\Gamma_{\mathrm{th}}$
= $1.69^{+0.04}_{-0.03}$ and an electron energy $k\mathrm{T}=44^{+5}_{-4}$
keV. We detect an additional powerlaw component with a photon index of
$\Gamma_{\mathrm{po}}=2.0^{+0.3}_{+0.3}$.

While a high-energy tail is clearly present in the LHS, no high-energy
component is detected in either of the softer states. Consistently
polarization can be probed only in the LHS, and we indeed detect the same
polarization angle $PA=180\pm 10$° for the 400–1000 keV and 300–1000 keV
bands. This value is not strictly consistent with the value of $PA=160\pm 9$°
we measure in the 300–400 keV band, but it is consistent at 90 % confidence
($PA=160\pm 30$°). This slight discrepancy could arise from some contribution
of the Comptonized continuum, as the 300–400 keV range is not purely described
by the additional powerlaw. We measure a high polarization fraction for the
three energy bands with a lower limit $>70$ % for the 400–1000 keV. The other
energy bands allows lower polarization fractions; $\Pi^{300-400keV}>49$ % and
$\Pi^{300-1000keV}>56$ %.

###  5.2 Origin of the high-energy emission

We detect a powerlaw tail in addition to the standard Comptonisation component
during the HIMS and SIMS of MAXI J1535$-$571, the LHS of MAXI J1820+070 and
during the LHS of MAXI J1348$-$630\. This component is strongly present at the
beginning of the outburst when the global spectral shape is hard and its
strenght decays as the outburst evolves to softer states. There are two
obvious possibilities for the “apparent” absence of high-energy tails in
softer states. Either 1) the emission genuinely vanishes; 2) the high-energy
emission falls below detection threshold.

Case 1) implies that the medium responsible for the high-energy component
disappears in the softer states. One obvious candidate is the compact jet,
which is known to be quenched in the HSS (e.g., Fender et al., 1999), and was
claimed to emit in the 400–2000 keV range in Cygnus X-1 (Laurent et al., 2011;
Jourdain et al., 2012; Rodriguez et al., 2015). Since ejections of coronae
state transitions have been proposed in other sources (e.g., Rodriguez et al.,
2008a, b), the corona would also be a good candidate. Case 2) implies an
evolution of the high-energy component parameters (at least its flux) which
also leads to at least two interpretations. 2a) Same medium with evolving
properties, e.g., in Cygnus X-3, the tails seems un-related to the jets
behavior, and well explained by an hybrid corona in all states (Cangemi et
al., 2021b). 2b) Different emitting media, as observed in Cygnus X-1 (Cangemi
et al., 2021a). In the case of Cygnus X-1, we note that the jets origin in
both states could also be a possibility (Zdziarski et al., 2020).

Polarization is an additional diagnostic to constrain the origin of the tail.
The synchrotron spectrum of a population of $N$ electrons with an energy
between $E$ and $E+dE$ and with an electron index $p$, $dN(E)\propto E^{-p}dE$
can be approximated by a powerlaw $P(E)\propto E^{-\alpha}$. The spectral
index $\alpha$ and the electron index $p$ are tied by the equation
$\alpha=(p-1)/2$ (Rybicki & Lightman, 1986) and $\alpha$ can also be related
to the photon index $\Gamma$ : $\alpha=\Gamma-1$. In a very ordered magnetic
field, the polarization fraction of a polarized emission expected in the
optically thin regime of the synchrotron spectrum, is (Rybicki & Lightman,
1986):

$\Pi=\frac{p+1}{p+\frac{7}{3}}$ (6)

In the case of MAXI J1348$-$630, the value of the photon index during the LHS
$\Gamma_{\mathrm{po}}=2.0^{+0.3}_{-0.3}$ leads to a polarization fraction of
$\Pi=75^{+11}_{-11}$ % which is consistent with the polarization fraction
observed in the three energy bands considered. Therefore, the observed
emission could arise from the synchrotron emission from the jets base in a
very ordered magnetic field. Besides, synchrotron emission from compact radio
jets has been observed during the LHS of MAXI J1348$-$630 (e.g., Russell et
al., 2020; Carotenuto et al., 2021).

While the upper limit (or non-detection) in the case of MAXI J1535$-$571 does
not allow to conclude, the case of MAXI J1820+070 is quite interesting. The
rather low level of polarization (compared to MAXI J1348$-$630 and Cygnus X-1)
may indicate various possibilities. Here the measured value of the photon
index $\Gamma_{\mathrm{po}}=2.09^{+0.03}_{-0.03}$ leads to a polarization
fraction of $75\pm 2$ % not consistent with the polarization fraction we
measure. This could indicates (1) the magnetic field is disrupted by some
mechanism and/or differents jet zones emits polarized radiation with different
angles; or (2) another origin than the jets for the polarized emission.

###  5.3 SEDs basic analysis

While a precise spectral modelisation with physical models is beyond the scope
of this paper, we can apply a simple approach using spectral energy
distribution to verify the jet hypothesis. Here, the goal is to investigate
whether the optically thin part of the synchrotron spectrum from the jets is
consistent with our measured high-energy component. Therefore, we need the
information on the synchrotron break frequency of the jets spectrum as well as
the spectral index of the optically thin part. Then, we can extrapolate the
synchrotron spectrum up to 1 MeV and check the consistency with the hard
X-rays.

####  5.3.1 MAXI J1535$-$571

Figure 7 shows different datasets from Russell et al. (2020) in the HIMS
(green) and in the SIMS (orange). The grey line indicates the energy of the
synchrotron break, whereas the green line is the optically thin part of the
synchrotron spectrum obtained by Russell et al. (2020) ($\alpha=0.83\pm 0.09$,
where $\alpha$ is the spectral index of the optically thin part of the
synchrotron spectrum), extrapolated up to 1000 keV. We also show the spectra
extracted in this work and their associated measured powerlaws. The box on the
top right corner of the figure is an enlarged view from 100 keV to 1000 keV.
We observe that the extrapolation of the optically thin spectrum is
consistent, within the errorbars, with the powerlaw in the HIMS. This could
point towards a jets origin of the high-energy component in this state.
However, the uncertainties are large at high energy, and without polarization
measurements, we cannot exclude a hybrid corona origin. Concerning the SIMS,
Russell et al. (2020) shows that the radio emission is quenched in this state.
Therefore, the non-thermal component $>200$ keV in this state could come from
another region from the jets that still radiates in the X-ray or has another
origin.

Figure 7: MAXI J1535$-$571 spectra using observational data from Russell et
al. (2020) and this work. HIMS and SIMS data are represented in green and
orange, respectively. The measured additional high-energy components are
indicated with dotted line. Their 90 % uncertainties interval range are
represented by the colored area. The purple dotted line is the extrapolation
of the optically thin synchrotron spectrum from Russell et al. (2020) with
$\alpha=0.83\pm 0.09$.

####  5.3.2 MAXI J1820+070

The dotted green line on Fig. 8 shows the extrapolation of the optically thin
synchrotron spectrum measured with simulatenous (12th of april 2018) X-Shooter
data (green dots Rodi et al., 2021). The X-ray spectrum from this work is
shown with blue dots whereas the dotted blue line shows our measured powerlaw.
Here, the IR optically thin spectrum is not consistent with the high-energy
component that we measure. This result clearly excludes a pure synchrotron
jets origin for the additional component and favours a hybrid corona origin as
proposed by Zdziarski et al. (2021). Regarding our polarization measurements,
a polarization fraction of $26\pm 9$ % is also consistent with a hybrid corona
origin (Beheshtipour et al., 2017).

Figure 8: MAXI J1820+070 spectrum using observational data from Rodi et al.
(2021) and this work. The measured additional high-energy component is
indicated with the blue dotted line. The green dotted line is the
extrapolation of the optically thin synchrotron spectrum from Rodi et al.
(2021).

####  5.3.3 MAXI J1348$-$630

No infrared data has been published on MAXI J1348$-$630 so far. Therefore, we
do not have informations on the synchrotron cutoff. However, we try to
investigate the consistency of the high-energy emission detected with
synchrotron emission from the jets assuming a spectral index
$-0.5<\alpha<0.8$, a flux $40<\mathrm{F}<300$ mJy at the synchrotron cutoff
energy $1.5\times 10^{15}$ Hz. Figure 9 shows the resulting broad band
spectrum. We also plot the optically thick part of the synchrotron spectrum as
measured by Carotenuto et al. (2021) with ATCA at MJD 58514.01.

Figure 9: Broad band spectrum of MAXI J1348$-$630\. The light blue line is the
spectrum as measured by Carotenuto et al. (2021). The green zone corresponds
to our synchrotron thin spectrum hypothesis (see the text). The insert plot
focus on the 1–1000 keV range. The different colors indicates the resulting
powerlaw for different normalization value of the diskbb.

As we add a disk to model the spectrum (see Sect. 3), we investigate the
impact of the black body disk normalization value on the powerlaw
normalization and photon index values. We let the normalization parameter of
diskbb vary from $1\times 10^{4}$ to $2\times 10^{4}$ which is the upper limit
obtained by Chakraborty et al. (2020). The resulting powerlaws from the fit
are shown in different colors on Fig. 9 and the insert is an enlarged view
from 1 keV to 1000 keV. The normalization of the black body disk has a strong
impact on the powerlaw properties and we note that for normalization higher
than $\sim 15000$, the powerlaw component is consistent with the purple zone
and therefore with the synchrotron scenario. However, although the high
polarization fraction is also consistent with synchrotron emission, our
synchrotron hypothesis also strongly depends on the energy of the synchrotron
break, and we cannot formally conclude for a synchrotron origin without any
precise measurement of the optically thin part of the synchrotron spectrum.

##  6 Summary and conclusion

In this work, we use the INTEGRAL unique capabilities to investigate the high-
energy properties of three sources, MAXI J1535$-$571, MAXI J1820+070, MAXI
J1348$-$630 during their outburst. For each outburst, we divide the data into
different state periods based on their spectral characteristics. Thanks to the
combination of JEM-X, ISGRI and SPI data, we create stacked spectra in the
3–2000 keV band range for each of these states. We then use a simple
phenomenological spectral approach in order to investigate the behavior of the
sources at high-energy and search for an additional high-energy component.

We use the Compton mode of INTEGRAL/IBIS to study polarization properties and
find that the 300–1000 keV emission from the LHS of MAXI J1820+070 and MAXI
J1348$-$630 are polarized.

We extrapolate the optically thin part observed in the IR of the synchrotron
spectrum to investigate the potential origin of the high-energy component
detected in these sources. In the HIMS of MAXI J1535$-$571, the synchrotron
spectrum is consistent with the detected high-energy component. However, we
could not measure polarization in this source and therefore cannot exclude a
hybrid corona origin. For MAXI J1820+070, the extrapolation of the synchrotron
spectrum is not consistent with the extension measured in the X-rays.
Therefore the non-thermal component could arise from a non-thermal
distribution of electron from the corona. The polarization fraction that we
measure is also consistent with this scenario. In the case of the high-energy
component detected in the LHS of MAXI J1348$-$630, the high polarization
fraction we measure is consistent with synchrotron emission in a very ordered
magnetic field. However, we prefer not to conclude on the origin of the high-
energy component without any clear information on the optically thin part of
the synchrotron spectrum.

###### Acknowledgements.

J.R., P.L. P.-O.P & C.G. acknowledge partial funding from the French Space
Agency (CNES). J.R. & P.-O.P acknowledge partial fundings from the French
Programme National des Hautes Energies (PNHE). T.M.B. acknowledges financial
contribution from the agreement ASI-INAF n. 2017-14-H.0 and from PRIN INAF
2019 n.15. Based on observations with INTEGRAL, an ESA project with
instruments and science data centre funded by ESA member states (especially
the PI countries: Denmark, France, Germany, Italy, Switzerland, Spain) and
with the participation of Russia and the USA.

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##  Appendix A Additional figures

Figure 10: Evolution of the modulation parameter $a_{\mathrm{100}}$ as a
function of the energy. Figure 11: Probability density described by equation
(5) in function of the polarization angle and the polarization fraction
calculated for MAXI J1820+070 (top) and MAXI J1348$-$630 (bottom) in the LHS
for different energy bands. Figure 12: Polarigrams of the three sources
obtained in the 300–400 keV energy band range. Figure 13: Polarigrams of the
three sources obtained in the 400–1000 keV energy band range.

¨


59535.06680 | 32.357 | 0.082 | $-75.868$ | 0.090 | UVES | 59911.04934 | $-61.462$ | 0.082 | 19.925 | 0.090 | UVES
59536.09456 | 35.192 | 0.082 | $-79.004$ | 0.090 | UVES | 59925.06899 | $-44.436$ | 0.082 | 2.704 | 0.090 | UVES
59537.11937 | $-14.930$ | 0.082 | $-27.758$ | 0.090 | UVES | 57362.18855 | 22.442 | 0.058 | $-65.573$ | 0.070 | HARPS
59538.16960 | $-65.775$ | 0.082 | 24.243 | 0.090 | UVES | 59199.02701 | $-62.502$ | 0.058 | 21.026 | 0.070 | HARPS
59541.11069 | $-48.431$ | 0.082 | 6.456 | 0.090 | UVES | 59202.01912 | $-16.083$ | 0.058 | $-26.735$ | 0.070 | HARPS
59546.07537 | 36.675 | 0.082 | $-80.250$ | 0.090 | UVES | 59208.03110 | $-70.055$ | 0.058 | 28.753 | 0.070 | HARPS
59554.15904 | $-8.518$ | 0.082 | $-33.955$ | 0.090 | UVES | 59209.06678 | $-69.171$ | 0.058 | 27.787 | 0.070 | HARPS
59556.15975 | 28.780 | 0.082 | $-72.135$ | 0.090 | UVES | 59235.01630 | 2.792 | 0.058 | $-45.526$ | 0.070 | HARPS
59563.10454 | $-37.906$ | 0.082 | $-4.236$ | 0.090 | UVES | 59374.40763 | 18.663 | 0.058 | $-61.711$ | 0.070 | HARPS
59575.12233 | $-14.953$ | 0.082 | $-27.599$ | 0.090 | UVES | 59375.41487 | 35.429 | 0.058 | $-78.820$ | 0.070 | HARPS
59578.07905 | 36.999 | 0.082 | $-80.400$ | 0.090 | UVES | 59438.35386 | 18.580 | 0.058 | $-61.634$ | 0.070 | HARPS
59579.08825 | 25.140 | 0.082 | $-68.225$ | 0.090 | UVES | 59439.30190 | 34.679 | 0.058 | $-78.020$ | 0.070 | HARPS
59865.16985 | 27.169 | 0.082 | $-70.958$ | 0.090 | UVES | 59440.20093 | 34.897 | 0.058 | $-78.208$ | 0.070 | HARPS
59870.16359 | $-66.655$ | 0.082 | 24.895 | 0.090 | UVES | 59511.18575 | $-14.741$ | 0.058 | $-27.894$ | 0.070 | HARPS
59885.03753 | $-0.016$ | 0.082 | $-42.971$ | 0.090 | UVES | 59512.18261 | 3.669 | 0.058 | $-46.422$ | 0.070 | HARPS
59891.05273 | $-70.426$ | 0.082 | 28.939 | 0.090 | UVES | 59513.19091 | 22.802 | 0.058 | $-66.019$ | 0.070 | HARPS
59893.18047 | $-43.082$ | 0.082 | 1.240 | 0.090 | UVES |  |  |  |  |  |
HD188088
59508.14059 | $-41.300$ | 0.112 | 31.766 | 0.103 | UVES | 55722.24620 | $-9.665$ | 0.032 | $-0.357$ | 0.042 | HARPS
59530.03570 | 11.775 | 0.112 | $-22.098$ | 0.103 | UVES | 55722.24832 | $-9.595$ | 0.032 | $-0.438$ | 0.042 | HARPS
59532.07695 | 9.127 | 0.112 | $-19.153$ | 0.103 | UVES | 55811.03862 | $-49.606$ | 0.032 | 40.378 | 0.042 | HARPS
59535.01529 | 5.161 | 0.112 | $-14.974$ | 0.103 | UVES | 55811.04000 | $-49.615$ | 0.032 | 40.386 | 0.042 | HARPS
59538.02463 | 0.635 | 0.112 | $-10.774$ | 0.103 | UVES | 55812.01082 | $-56.913$ | 0.032 | 47.788 | 0.042 | HARPS
59648.38497 | $-40.070$ | 0.112 | 30.769 | 0.103 | UVES | 55812.01226 | $-56.926$ | 0.032 | 47.802 | 0.042 | HARPS
59667.39384 | 16.039 | 0.112 | $-26.409$ | 0.103 | UVES | 55812.07947 | $-57.463$ | 0.032 | 48.347 | 0.042 | HARPS
59670.38139 | 11.879 | 0.112 | $-22.291$ | 0.103 | UVES | 55812.08088 | $-57.477$ | 0.032 | 48.374 | 0.042 | HARPS
59859.14120 | 9.702 | 0.112 | $-20.365$ | 0.103 | UVES | 55812.08227 | $-57.492$ | 0.032 | 48.373 | 0.042 | HARPS
59861.13277 | 7.025 | 0.112 | $-17.581$ | 0.103 | UVES | 55813.10141 | $-65.597$ | 0.032 | 56.613 | 0.042 | HARPS
59865.10971 | 1.451 | 0.112 | $-11.822$ | 0.103 | UVES | 55813.10266 | $-65.604$ | 0.032 | 56.615 | 0.042 | HARPS
59875.11233 | $-15.618$ | 0.112 | 6.102 | 0.103 | UVES | 55813.10391 | $-65.616$ | 0.032 | 56.632 | 0.042 | HARPS
59881.05136 | $-33.649$ | 0.112 | 23.973 | 0.103 | UVES | 56137.05270 | $-39.461$ | 0.032 | 30.105 | 0.042 | HARPS
59887.02527 | $-68.195$ | 0.112 | 59.308 | 0.103 | UVES | 56137.10775 | $-39.744$ | 0.032 | 30.390 | 0.042 | HARPS
59891.06231 | 24.551 | 0.112 | $-35.258$ | 0.103 | UVES | 56137.24634 | $-40.471$ | 0.032 | 31.115 | 0.042 | HARPS
59899.05115 | 19.541 | 0.112 | $-29.811$ | 0.103 | UVES | 56138.03680 | $-44.994$ | 0.032 | 35.624 | 0.042 | HARPS
53279.13535 | $-30.323$ | 0.032 | 20.626 | 0.042 | HARPS | 56138.09850 | $-45.370$ | 0.032 | 35.993 | 0.042 | HARPS
53280.03581 | $-33.872$ | 0.032 | 24.230 | 0.042 | HARPS | 56138.19538 | $-45.959$ | 0.032 | 36.610 | 0.042 | HARPS
53332.01740 | $-66.817$ | 0.032 | 57.744 | 0.042 | HARPS | 56178.15045 | $-19.343$ | 0.032 | 9.510 | 0.042 | HARPS
53891.33812 | $-48.004$ | 0.032 | 38.668 | 0.042 | HARPS | 56179.03994 | $-21.683$ | 0.032 | 11.878 | 0.042 | HARPS
55721.13777 | $-55.138$ | 0.032 | 46.060 | 0.042 | HARPS | 56179.14919 | $-21.992$ | 0.032 | 12.181 | 0.042 | HARPS
55721.26571 | $-50.750$ | 0.032 | 41.594 | 0.042 | HARPS | 56885.05123 | $-34.516$ | 0.032 | 24.963 | 0.042 | HARPS
55721.26725 | $-50.693$ | 0.032 | 41.538 | 0.042 | HARPS | 56887.07058 | $-44.843$ | 0.032 | 35.440 | 0.042 | HARPS
55721.34824 | $-47.606$ | 0.032 | 38.370 | 0.042 | HARPS | 57119.42519 | $-35.828$ | 0.032 | 26.336 | 0.042 | HARPS
55721.35006 | $-47.533$ | 0.032 | 38.295 | 0.042 | HARPS | 57119.42980 | $-35.842$ | 0.032 | 26.350 | 0.042 | HARPS
55721.43193 | $-44.265$ | 0.032 | 34.954 | 0.042 | HARPS | 57120.42356 | $-40.667$ | 0.032 | 31.326 | 0.042 | HARPS
55722.14422 | $-13.435$ | 0.032 | 3.658 | 0.042 | HARPS | 57281.11653 | 14.179 | 0.032 | $-24.550$ | 0.042 | HARPS
55722.14632 | $-13.350$ | 0.032 | 3.574 | 0.042 | HARPS |  |  |  |  |  |
$o$ Leo
59509.36177 | -28.463 | 0.085 | 88.090 | 0.085 | UVES | 59959.35809 | -27.395 | 0.085 | 86.393 | 0.085 | UVES
59533.34135 | 58.279 | 0.085 | -9.871 | 0.085 | UVES | 55259.95943 | -16.980 | 0.054 | 75.010 | 0.082 | SOPHIE
59536.33618 | -7.796 | 0.085 | 64.638 | 0.085 | UVES | 55261.95506 | -27.322 | 0.054 | 86.810 | 0.082 | SOPHIE
59547.33935 | 66.906 | 0.085 | -19.924 | 0.085 | UVES | 55266.99879 | 66.284 | 0.054 | -18.776 | 0.082 | SOPHIE
59566.28758 | -22.310 | 0.085 | 80.770 | 0.085 | UVES | 55268.02101 | 78.391 | 0.054 | -32.472 | 0.082 | SOPHIE
59589.32020 | 80.659 | 0.085 | -35.189 | 0.085 | UVES | 55270.95938 | 57.327 | 0.054 | -8.642 | 0.082 | SOPHIE
59592.12908 | 41.217 | 0.085 | 9.082 | 0.085 | UVES | 55271.96791 | 35.285 | 0.054 | 16.053 | 0.082 | SOPHIE
59595.12107 | -20.433 | 0.085 | 78.642 | 0.085 | UVES | 55281.86844 | 71.859 | 0.054 | -24.846 | 0.082 | SOPHIE
59596.12677 | -28.252 | 0.085 | 87.513 | 0.085 | UVES | 55283.91363 | 78.545 | 0.054 | -32.661 | 0.082 | SOPHIE
59903.33916 | -0.123 | 0.085 | 55.737 | 0.085 | UVES | 55285.87765 | 48.729 | 0.054 | 1.006 | 0.082 | SOPHIE
Table 10: continued.

##  Appendix D Parameters of the interferometric calibrators used for the
GRAVITY observations

Table 11: Interferometric calibrators used for our GRAVITY observations taken from the SearchCal software. # | HD | Sp. type | $V$ | $K$ | $\theta_{\mathrm{UD}}$
---|---|---|---|---|---
|  |  | (mag) | (mag) | (mas)
AK~For
1 | HD22575 | K0/1III | 7.54 | 6.93 | $0.198\pm 0.005$
2 | HD19873 | K0III/IVCNII/III | 9.17 | 6.84 | $0.203\pm 0.005$
3 | HD21967 | K1III | 7.37 | 6.77 | $0.212\pm 0.005$
HD9312
1 | HD8910 | K0III | 7.98 | 5.39 | $0.409\pm 0.010$
HD41255
1 | HD41648 | K0III | 9.15 | 6.90 | $0.196\pm 0.005$
2 | HD41917 | K1(III) | 9.47 | 6.94 | $0.195\pm 0.005$
HD70937
1 | HD69687 | K1III | 8.58 | 5.67 | $0.358\pm 0.008$
2 | HD71263 | K1III | 8.48 | 5.86 | $0.328\pm 0.008$
HD210763
1 | HD212458 | K0III | 8.48 | 5.80 | $0.332\pm 0.008$
2 | HD211650 | K2III | 9.03 | 5.98 | $0.322\pm 0.008$
HD224974
1 | HD318 | K0III | 8.55 | 6.09 | $0.288\pm 0.007$
HD188088
1 | HD187516 | K0III | 7.52 | 4.93 | $0.534\pm 0.013$
2 | HD188276 | K2/3III | 7.94 | 4.97 | $0.506\pm 0.011$
LL~Aqr
1 | HD214548 | K0 | 10.4 | 7.88 | $0.127\pm 0.004$
2 | HD213691 | G5V | 9.47 | 7.95 | $0.113\pm 0.003$
$o$~Leo
1 | HD83511 | M0 | 8.60 | 3.89 | $1.047\pm 0.074$
V963~Cen
1 | HD119887 | K1/2III | 10.2 | 7.51 | $0.154\pm 0.004$
2 | HD114082 | F3V | 8.20 | 7.16 | $0.146\pm 0.004$

##  Appendix E Isochrones fit

Figure 11: Fitted PARSEC, BaSTI, MIST, and DSEP isochrones for the HD9312
(left) and HD41255 (right) systems. Luminosities of both components and the
radius of the secondary are displayed but not fitted (see text). For HD9312,
the black colour is for isochrones with a chosen metallicity of $0.1$ dex,
while the grey colour is for the metallicity from Kiefer et al. (2018).

Figure 12: Fitted PARSEC, BaSTI, MIST, and DSEP isochrones for the HD70937
(left) and HD210763 (right) systems. The black colour is for isochrones with a
chosen metallicity of $0.1$ dex, while the grey colour is for our measured
metallicity.

Figure 13: Fitted PARSEC, BaSTI, MIST, and DSEP isochrones for the HD224974
(left) and HD188088 (right) systems.

Figure 14: Fitted PARSEC, BaSTI, MIST, and DSEP isochrones for the LL Aqr
(left) and $o$ Leo (right) systems. For LL Aqr, the black colour is for
isochrones with a chosen metallicity of $0.15$ dex. while the grey colour is
for the metallicity from Graczyk et al. (2022).

Figure 15: Fitted PARSEC, BaSTI, MIST, and DSEP isochrones for the V963 Cen
system. The black colour is for isochrones with a chosen metallicity of
$0.1\pm 0.1$ dex, while the grey colour is for the metallicity from Graczyk et
al. (2022).