# The accretion/ejection link in the neutron star X-ray binary 4U 1820-30 I:
A boundary layer-jet coupling?

A. Marino1,2,3, T. D. Russell3, M. Del Santo3, A. Beri4,5, A. Sanna6, F. Coti
Zelati1,2, N. Degenaar7 D. Altamirano5, E. Ambrosi3, A. Anitra8, F.
Carotenuto9, A. D’Aì3, T. Di Salvo8, A. Manca6, S. E. Motta10 C. Pinto3, F.
Pintore3, N. Rea1,2, J. van den Eijnden11
1Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans
s/n, E-08193 Barcelona, Spain
2Institut d’Estudis Espacials de Catalunya (IEEC), Carrer Gran Capità 2–4,
E-08034 Barcelona, Spain
3INAF/IASF Palermo, via Ugo La Malfa 153, I-90146 - Palermo, Italy
4Indian Institute of Science Education and Research (IISER) Mohali, Punjab
140306, India
5School of Physics and Astronomy, University of Southampton, Southampton, SO17
1BJ, UK
6Università degli Studi di Cagliari, Dipartimento di Fisica, SP Monserrato-
Sestu km 0.7, I-09042 Monserrato, Italy
7Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science
Park 904, 1098 XH, Amsterdam, the Netherlands
8Università degli Studi di Palermo, Dipartimento di Fisica e Chimica, via
Archirafi 36 - 90123 Palermo, Italy
9Astrophysics, Department of Physics, University of Oxford, Keble Road, Oxford
OX1 3RH, UK
10Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Brera, via E.
Bianchi 46, I-23807 Merate (LC), Italy
11Department of Physics, University of Warwick, Coventry CV4 7AL, UK
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The accretion flow / jet correlation in neutron star (NS) low-mass X-ray
binaries (LMXBs) is far less understood when compared to black hole (BH)
LMXBs. In this paper we will present the results of a dense multi-wavelength
observational campaign on the NS LMXB 4U 1820-30, including X-ray (NICER,
NuSTAR and AstroSat) and quasi-simultaneous radio (ATCA) observations in 2022.
4U 1820-30 shows a peculiar 170 day super-orbital accretion modulation, during
which the system evolves between "modes" of high and low X-ray flux. During
our monitoring, the source did not show any transition to a full hard state.
X-ray spectra were well described using a disc blackbody, a Comptonisation
spectrum along with a Fe K emission line at $\sim$6.6 keV. Our results show
that the observed X-ray flux modulation is almost entirely produced by changes
in the size of the region providing seed photons for the Comptonisation
spectrum. This region is large ($\sim$15 km) in the high mode and likely
coincides with the whole boundary layer, while it shrinks significantly
($\lesssim$10 km) in low mode. The electron temperature of the corona and the
observed RMS variability in the hard X-rays also exhibit a slight increase in
low mode. As the source moves from high to low mode, the radio emission due to
the jet becomes $\sim$5 fainter. These radio changes appear not to be strongly
connected to the hard-to-soft transitions as in BH systems, while they seem to
be connected mostly to variations observed in the boundary layer.

###### keywords:

accretion, accretion discs – stars:neutron – X-rays: binaries – X-rays,
individuals: 4U 1820-30 – ISM: jets and outflows

††pubyear: 2023††pagerange: The accretion/ejection link in the neutron star
X-ray binary 4U 1820-30 I:  A boundary layer-jet coupling?–The
accretion/ejection link in the neutron star X-ray binary 4U 1820-30 I:  A
boundary layer-jet coupling?

##  1 Introduction

Neutron Star (NS) low-mass X-ray Binaries (LMXBs) are binary systems composed
of a NS accreting matter from a companion low-mass, i.e., typically lower than
1 M⊙, star. The material accreted onto the compact object is responsible for
most of the electromagnetic emission of these sources from the optical to the
X-rays. These systems have been historically grouped in two main classes, Z-
and atoll sources, based on the particular tracks they draw in X-rays colour-
colour diagrams (Hasinger & van der Klis, 1989).
Z-sources are the brightest among the two classes, being persistently active
and always accreting around the Eddington limit, i.e., at a typically observed
X-ray luminosity range of L${}_{X}\sim 10^{37}-10^{38}$ erg/s (see, e.g. van
der Klis, 2006). Atolls are typically fainter, i.e., at L${}_{X}\sim
10^{36}-10^{37}$ erg/s (Muñoz-Darias et al., 2014) and thereby are considered
to be accreting at lower rates. They can be persistent or transients, i.e.
usually found in a dormant, faint X-ray regime called quiescence with only
episodic outbursts where the X-ray luminosity becomes comparable to the level
of the persistent NS LMXBs. However, the mere existence of several systems
showing both Z or atoll behaviours make the distinction between these regimes
somehow blurred. This is the case for XTE J1701-462 which transitioned from an
atoll to a Z-source regime in both its 2006/2007 (see, e.g., Homan et al.,
2010) and 2022 (Homan et al., 2022a, b) outbursts and the other two transient
Z-sources IGR J17480-2446 (e.g. Chakraborty et al., 2011) and MAXI J0556-332
(Homan et al., 2011).
The accretion flow consists typically of an optically thick accretion disc, an
optically thin cloud of hot electrons usually dubbed corona, and a boundary
layer (BL) connecting the inner edge of the disc with the NS surface. The
observed X-ray spectral continuum from these sources can be broken down in
several components, corresponding to these regions of the accretion flow: a
multi-colour disc black body in the soft X-rays and a Comptonisation spectrum,
which can extend up to hundreds of keV (Pintore et al., 2016; Ludlam et al.,
2016; Gambino et al., 2019). The contribution from a boundary layer between
the disc and the NS surface, or the surface itself, can also be visible
directly as an additional black body component or as source of the seed
photons for the Comptonisation spectrum at a blackbody temperature $kT_{\rm
bb}$ of about 1-2 keV (see, e.g., Mondal et al., 2020; Marino et al., 2022).
The X-ray spectral-timing properties of these objects evolve between two main
states: one dominated by the corona emission, typically referred to as the
hard state, and the other dominated by the accretion disc and/or the
NS/boundary layer, i.e., the soft state (for a review, Done et al., 2007).
In the radio–mid-IR region, the contribution of a compact jet, i.e., a
collimated ionised outflow of relativistic particles ejected by the system, is
instead dominant. The observed properties of the compact jet show a clear
correlation with the accretion flow. This connection is well-established for
black hole (BH) transients (see, e.g., Corbel et al., 2000; Coriat et al.,
2011), where as their X-ray spectral-timing properties display dazzling
variations between hard and soft states, similar to the states observed in NS
LMXBs, the jet evolves from being radio loud to a quenched state, respectively
(Fender & Belloni, 2004). These radio/X-ray changes occur usually over time-
scales of the order of one or few weeks in both BH and NS LMXBs (see, e.g.,
Russell et al., 2014; Marino et al., 2019; Marcel et al., 2019; De Marco et
al., 2021; Rhodes et al., 2022). However, this standard pattern is less clear
for NS systems. Despite being observed several times (e.g. Gusinskaia et al.,
2017), it is yet not established whether jet quenching in the soft state is
also the norm for all NS LMXBs, with some cases where the presence of compact
jets was reported even after the transition to the soft state (Migliari et
al., 2004). Interestingly, jet quenching in some accreting NSs has been
sometimes observed without a state transition but corresponding to an
evolution in the flux (Russell et al., 2021; Panurach et al., 2023),
suggesting a more complex accretion/ejection coupling with respect to BH X-ray
binaries (XRBs). When observed, jets in NS LMXBs are generally $\sim$20 times
radio-fainter than BH LMXBs (e.g., Gallo et al., 2018; van den Eijnden et al.,
2021), although several systems, often harbouring X-ray millisecond pulsars
(e.g., Russell et al., 2018; Gusinskaia et al., 2020; Coti Zelati et al.,
2021), have been observed at radio luminosity comparable to BH systems.
Different jet geometries and/or weaker couplings with the accretion flow in
accreting NSs with respect to BHs have been also proposed (Marino et al.,
2020). The emerging observational picture is yet not well understood and, in
particular, the role (if any) played by the NS magnetic field, its emitting
surface, its spin, or the presence of a boundary layer is unclear. Multi-
wavelength surveys of these systems that probe the behaviour of the jets and
the accretion flow over a variety of mass accretion rates/X-ray states are
crucial to self-consistently explore jet launching in NSs.

###  1.1 4U 1820-303

A particularly intriguing target to perform this kind of studies is the NS
LMXB 4U 1820-30. This source is composed by a NS accreting matter from a white
dwarf (WD) companion in a tight orbit. Indeed, with its orbital period of only
11.4 minutes (Stella et al., 1987), i.e., the shortest orbital period known
for any XRB, 4U 1820-30 is identified as an Ultra-Compact XRB (UCXB, for a
recent review Armas Padilla et al., 2023). Located at a distance of about 7.6
kpc (Kuulkers et al., 2003), the system resides within the globular cluster
NGC 6624. The source is classified as an atoll and it is persistently
accreting at a relatively high luminosity, displaying mostly soft X-ray
spectral states (the so-called "banana" state for atolls), with occasional
transitions to the hard state ("island" state) (Tarana et al., 2007). Its
behaviour is indeed similar to what observed in the so-called "bright atolls"
group (e.g., D’Aì et al., 2010; Egron et al., 2013; Iaria et al., 2020).
Perhaps the most peculiar aspect of the source is the $\sim$ 170 d, super-
orbital accretion cycle exhibited by the source. The luminosity modulation is
intrinsic, i.e., not due to absorption from occulting plasma (Zdziarski et
al., 2007) and it likely originates from the presence of a third object
orbiting the system from afar (Chou & Grindlay, 2001). According to this
theory, the tidal forces exerted by this third object on 4U 1820-30 trigger
fluctuations in the orbital eccentricity of the binary, which in turn
translate to periodic increases in the mass-accretion rate. As a consequence,
4U 1820-30 oscillates between a low mode, at $L_{\rm low}\sim 8\times 10^{36}$
erg s-1 and a high mode, at $L_{\rm high}\sim 6\times 10^{37}$ erg s-1 (in the
range 0.5-10 keV and assuming a distance D= 7.6 ${\rm kpc})$ over a time-scale
of about 170 d. These modes can be characterized by different spectral
properties, most likely connected to changes in the accretion flow. In the low
mode, the system can be found in soft ("banana") and sometimes in the hard
("island") X-ray spectral states (in’t Zand et al., 2012), during which it
exhibits frequent type-I X-ray bursts. On the other hand, in the high mode,
the system is only soft and bursts are typically absent (see, e.g., Titarchuk
et al., 2013).
The presence of the Fe K line in the X-ray spectrum is debated, with
detections reported only by a number of X-ray spectral studies (Cackett et
al., 2008; Titarchuk et al., 2013) and not by others (e.g., Costantini et al.,
2012; Mondal et al., 2016). Moreover, while 4U 1820-30 was initially
identified as a non-quenching jet NS (Migliari et al., 2004), it has been
recently suggested that compact jet quenching does occur (Russell et al.,
2021). Indeed, the change in spectral properties of the jet seem to occur only
when, in the transition from low to high mode, the X-ray flux exceeds a
certain threshold (see, Fig. 2, Russell et al., 2021). Such a result would
suggest a critical connection between jet and mass-accretion rate rather than
spectral hardness, in a way that was never observed for BH systems and that is
instead sometimes observed in accreting NSs, both in LMXBs (Panurach et al.,
2023) and in XRBs hosting high-mass companion stars (HMXBs, see van den
Eijnden et al., 2018). However, those results were obtained from observations
taken sporadically over the past $\sim$17 years. To properly understand the
accretion-ejection coupling in this system - and potentially in similar
objects - it is fundamental to measure the accretion flow/jet properties over
a single accretion cycle.
In this series of papers, we present the results of a comprehensive
radio–X-rays observational campaign performed throughout 2022, aimed at
following 4U 1820-30 in the X-rays and radio during a whole super-orbital
cycle. In this manuscript, we present the results of a broadband X-ray
spectral analysis and timing analysis using NICER , NuSTAR and AstroSat data
from the 2022 April-September cycle. We also used data from the Australia
Telescope Compact Array (ATCA) taken close to our broadband X-ray spectra to
show the jet evolution during this cycle. A following paper (Paper II of this
series, Russell et al., in preparation) will present the results of the
complete radio monitoring and how they compare with the X-rays data analysis
reported here.

Figure 1: (_Top_) 4U 1820-30 daily light curve as observed by MAXI from June
2020 to June 2023, displaying the super-orbital modulation typical of the
system. The time interval enclosing the times of the observations used in this
paper is drawn as a green rectangle. (_Bottom_) A zoom of the top light curve
displaying MAXI light curve from April to September 2022. The observation
dates for NICER, NuSTAR and AstroSat are highlighted as vertical lines in
green dashed, purple solid and red solid, respectively. Colored boxes with
numbers are displayed to identify the dates of the single NICER, NuSTAR and
AstroSat observations using the labels introduced in Table 1 and the same
colors chosen for the vertical lines.

##  2 Observations & Data reduction

A dense X-ray campaign has been performed between April 2 and July 26 2022,
with 17, 3 and 1 observations for NICER , NuSTAR and AstroSat , respectively.
A summary of these observations is reported in Table 1. All data were
reprocessed using the HEAsoft package v. 6.30. The latest available CALDB
version was used for all the instruments. More details on the data reduction
for each observatory are given in the following subsections.

###  2.1 NICER

A two-weeks cadence monitoring campaign was performed by NICER (see Table 1).
Data were reduced using nicerl2 task (NICERDAS 2019-05-21 v006). We set
recommended calibration processes, standard screening and we added the
niprefilter2$\\_$coltypes=base,3c50 parameter so that the 3C50 model can be
used to derive background spectra later. We extracted the cleaned event files,
checking that all detectors were active during observations and excluding data
from the "noisy" detectors (labelled 14 and 34), in order to reduce the
detector noise. We accumulated light curves from all the observations using
the xselect tool, with the aim to check for type-I X-ray bursts, finding only
one in observation 5604010304. In the following data analysis, the burst was
excluded. Then we selected the GTI using NIMAKETIME and applied them to the
data via NIEXTRACT-EVENTS, selecting events with PI channel between 25 and
1200 (0.25–12.0 keV). We used the nibackgen3C50 tool to extract both the
spectra of the source and the background from the cleaned event files,
selecting the 2020 gain calibration.
During the writing of this paper, the updated HEAsoft version 6.31 was
released, along with substantial changes to the NICER mission data analysis
pipeline. To check for consistency, we reanalysed three observations of the
2022 NICER campaign using a different background model, i.e. the SCORPEON
model. The spectra obtained with the different HEAsoft versions are basically
identical and the best-fit parameters obtained are not significantly affected
by the change of version and/or background model. We therefore did not
reanalyse the whole data set and kept working on the spectra obtained with the
previous HEAsoft version.

###  2.2 NuSTAR

NuSTAR observed the system three times during this campaign, for a total
exposure of about 58.6 ks. We reduced the data using standard tools within the
Nustardas package. A 100" radius circular region centered at the coordinates
of the source was selected as source region. In order to take into account any
background non-uniformity on the detector, we extracted the background spectra
using four circles of $\sim$50" radii placed on different areas which were
well far away from the source region. Finally, we used Nuproducts to extract
spectra and light curves. We systematically checked for the presence of type-I
X-ray bursts within the NuSTAR observations, but we did not find any.

Id.a | ObsID | Start Time | Exposure
---|---|---|---
|  | (UTC) | (MJD) | ks
|  NuSTAR
Nu01 | 30802009002 | 2022-04-14 | 59683 | 23.9
Nu02 | 30802009004 | 2022-05-31 | 59730 | 14.6
Nu03 | 30802009006 | 2022-07-10 | 59770 | 20.1
| AstroSat
As01 | 9000005070 | 2022-04-15 | 59684 | 22.8
| NICER
Ni01 | 5604010101 | 2022-04-02 | 59671 | 8.1
Ni02 | 5604010102 | 2022-04-14 | 59683 | 4.2
Ni03 | 5604010103 | 2022-04-16 | 59685 | 1.1
Ni04 | 5604010301 | 2022-04-30 | 59699 | 2.6
Ni05 | 5604010302 | 2022-05-01 | 59700 | 6.5
Ni06 | 5604010304 | 2022-05-31 | 59730 | 9.0
Ni07 | 5604010305 | 2022-06-01 | 59731 | 2.0
Ni08 | 5604010401 | 2022-06-12 | 59743 | 9.2
Ni09 | 5604010402 | 2022-06-13 | 59743 | 1.3
Ni10 | 5604010501 | 2022-06-26 | 59756 | 1.3
Ni11 | 5604010502 | 2022-06-27 | 59757 | 1.3
Ni12 | 5604010503 | 2022-06-27 | 59758 | 3.4
Ni13 | 5604010601 | 2022-07-08 | 59768 | 6.3
Ni14 | 5604010602 | 2022-07-09 | 59769 | 4.1
Ni15 | 5604010701 | 2022-07-24 | 59784 | 2.9
Ni16 | 5604010702 | 2022-07-25 | 59785 | 4.0
Ni17 | 5604010703 | 2022-07-26 | 59786 | 2.1
Table 1: List of the NuSTAR, AstroSat and NICER observations of 4U 1820-30
used in this work. aEach observation is marked with an identification code.

###  2.3 AstroSat

As part of the multi-wavelength campaign, AstroSat observed 4U 1820-30 on
April 15, 2022. We have analysed data from the Soft X-ray Telescope (SXT,
Singh et al., 2016) and the Large Area X-rays Proportional Counter (LAXPC
Yadav et al., 2016; Antia et al., 2017, 2021) on-board AstroSat (Agrawal,
2006; Singh et al., 2014). LAXPC, one of the primary instruments on-board and
consists of three co-aligned identical proportional counter detectors, viz.
LAXPC10, LAXPC20 and LAXPC30. Each of these works in the energy range of
3$-$80 keV (for details see, Yadav et al., 2016; Antia et al., 2017, 2021).
Due to the gain instability caused by the gas leakage, LAXPC10 data were not
used while LAXPC30 was switched off during these observations111LAXPC30 is
switched off since 8 March 2018, refer to http://astrosat-ssc.iucaa.in/.
Therefore, we have used data from LAXPC20 for our work. These data were
collected in the Event mode (EA) which contains the information about the
time, channel number and anodeID of each event. LaxpcSoft
v3.3222http://www.tifr.res.in/~astrosat_laxpc/LaxpcSoft.html software package
was used to extract spectra. Background files are generated using the blank
sky observations (see Antia et al., 2017, for details).

The SXT aboard AstroSat is a focusing instrument sensitive mainly in the 0.3–7
keV energy band (Singh et al., 2014, 2017) and its camera assembly uses an e2v
CCD, identical to that on _XMM-Newton_ /MOS and _Swift_ -XRT. The SXT
observations of 4U 1820-30 were carried out in the photon counting mode. We
have used Level-2 data provided by the SXT payload operation center (POC) in
Mumbai, India, reduced using the most recent pipeline and calibration database
(version 1.4b). Events from each orbit were merged using SXT Event Merger Tool
(Julia Code333http://www.tifr.res.in/~astrosat_sxt/dataanalysis.html). These
merged events were used to extract image and spectra using the ftool task
xselect. In SXT, pile up effects are notable at count rates higher than 40
$cs^{-1}$444https://web.iucaa.in/~astrosat/AstroSat_handbook.pdf. In our
observations, the source showed 80 $cs^{-1}$, suggesting a significant pile-
up. To minimise the effect of the pile-up, source spectrum is extracted from
an annulus between 5 $\arcmin$ and 15 $\arcmin$ from the centre of the image,
following the method described in (Chakraborty et al., 2020). We have used the
response (sxt_pc_mat_g0to12.rmf) and background
(SkyBkg_comb_EL3p5_Cl_Rd16p0_v01.pha) files provided by the SXT team. The
appropriate ARF file suitable for the specific source region is generated
using the command line auxiliary tool sxtARFModule.

Figure 2: Hardness Intensity Diagram of 4U 1820-30, produced by using all
available MAXI observations and all corresponding Swift/BAT count-rates. In
particular we used MAXI count-rates over the 2–20 keV energy range for the
intensity, while we estimate the hardness as the ratio between the BAT count-
rate (15–50 keV) and the MAXI count-rate in the soft band (2–4 keV) taken the
same day (as in Russell et al., 2021). Superimposed to the grey data points,
we highlight with green circles the position in the HID during the dates of
the single NICER observations, labeled with progressive numbers. For the NICER
observations used in broadband spectra A, B and C, we adopted purple diamonds
with those letters as labels. The labels "UB" and "LB" indicate the locations
of the "Upper" and "Lower" Banana branch.

##  3 Spectral analysis

We present the three-year light curve of 4U 1820-30 as observed by the Monitor
of All Sky X-ray Image (MAXI Matsuoka et al., 2009) in Figure 1 (top panel),
displaying its super-orbital modulation. On the bottom panel, we zoom in on
the period during which our campaign was carried out, with the dates of the
NICER , NuSTAR and AstroSat visits highlighted. It is apparent how our source
showed a slightly more irregular behaviour during our $\sim$150 days observing
window, with several highs and lows in rapid succession. In order to set the
evolution of the system during this cycle in the framework of its
observational history, we created a Hardness Intensity Diagram (HID) using
MAXI and Swift /BAT data (Krimm et al., 2013). In particular we collected all
the available MAXI count-rates (in the 2–4 keV and 2–20 keV energy ranges)
since October 2009 and the corresponding, i.e. taken the same day, BAT count-
rates (15–50 keV) from the respective websites555MAXI:
http://maxi.riken.jp/top/index.html, BAT:
https://swift.gsfc.nasa.gov/results/transients/. We then plotted MAXI total
count-rates versus the ratio between BAT and MAXI count-rates in the 2–4 keV
band to build the HID (see Fig. 2). In the Figure, we highlighted the position
of the source in the HID in the days of the NICER and/or NuSTAR observations,
showing that the source lingered in the soft ("banana") state during the whole
surveyed cycle.
In order to perform the spectral analysis, we grouped all NICER and NuSTAR
spectra through optimal binning (Kaastra & Bleeker, 2016), i.e. in order to
have a grouping consistent with the spectral resolution of the instrument (and
avoid oversampling) in a given energy range, but at the same time keeping at
least 20 counts per bin to ensure the use of the $\chi^{2}$ statistics. The
SXT and LAXPC spectra were grouped to have at least 25 counts/bin. The LAXPC
spectra showed a large calibration uncertainty, with background dominating
above 20 keV. Similar issues have also been observed in other observations
(see e.g., Beri et al., 2021; Sharma et al., 2023). Therefore, we have used
data only up to 20 keV for our spectral analysis.
We used Xspec v.12.12.1 for all the performed spectral fits. In all cases, we
used the tbabs model to take into account interstellar absorption, including
the photoelectric cross-sections and the element abundances to the values
provided by Verner et al. (1996) and Wilms et al. (2000), respectively. When
data from different instruments were used simultaneously, a constant component
was also included to account for inter-calibration uncertainties between
different instruments. We consistently checked that discrepancies between the
values for the constant term found for different instruments were not larger
than 20% . When fitting together NICER and NuSTAR, a small offset between the
slopes of those spectra could be appreciated, as often observed using data
from different instruments (see, e.g., Ludlam et al., 2020). To take into
account such an instrumental issue, we left the $\Gamma$ parameter in the
Xspec Comptonisation component untied between NICER and NuSTAR, in order to
allow some flexibility in between the two data sets. However, we checked
systematically that the difference in $\Gamma$ was never above 10%.

Among the seventeen NICER observations used, several have been performed in a
span of a few days within each other. In order to maximize the statistics in
each spectrum, we checked whether any difference in flux and/or hardness could
be appreciated between close-in-time observations. If the spectra were
compatible, we summed them by means of the FTOOL addspec. Otherwise, we
analysed them separately. This strategy leaves us with eleven final NICER
observations. The three NuSTAR observations caught the source during two high
modes and a low mode. In all three cases, at least one NICER observation was
performed within $\sim$days from the NuSTAR visit, giving us the opportunity
to investigate the broadband X-ray spectral behaviour of the source at the
extremes of its super-orbital oscillation. In particular we paired
observations Ni02 with Nu01, Ni06 with Nu02, Ni10 with Nu03. In the following,
these broadband spectra will be simply referred to as A, B and C respectively.

###  3.1 Broadband spectra: the continuum

An initial fit of spectra A, B and C with a simple absorbed powerlaw model
resulted in poor fits in all cases. We replaced the power-law with a more
physically motivated thermal Comptonisation model, using the convolution model
thcomp (Zdziarski et al., 2020) and a blackbody model bbodyrad as seed photons
spectrum. The involved parameters are the power-law photon index $\Gamma$, the
electron temperature of the Comptonising medium $kT_{e}$, the fraction of the
seed source covered by the scattering cloud $f_{\rm cov}$, the blackbody
temperature $kT_{\rm bb}$ and its normalisation $K_{\rm bb}$, the latter being
connected to the actual blackbody radius of the source through the formula:
$K_{\rm bb}=\left(R_{\rm bb}/D_{\rm 10\ kpc}\right)^{2}$, with $D_{\rm 10\
kpc}$ the distance of the source in units of 10 kpc. Using a model with a high
energy roll-over such as thcomp improved the fit, but apparent residuals at
low energies suggested the presence of an additional spectral component to be
included. We therefore added a diskbb component, characterised by a disc
blackbody temperature $kT_{\rm disc}$ and a normalisation $K_{\rm disc}$
which, similarly to the bbodyrad normalisation, can be translated into the
size of the black body emitting region by the formula $K_{\rm
disc}=\left(R_{\rm disc}/D_{\rm 10\ kpc}\right)^{2}\cos{i}$ with $i$ the
inclination of the system. In the disc case, the size of the emitting region
can be considered as the inner radius of the disc. Using diskbb, the fit to
the continuum becomes acceptable and the residuals are significantly
flattened. The model chosen is therefore:

${\rm Model\
0}:\texttt{tbabs}\times(\texttt{thcomp}\times\texttt{bbodyrad}+\texttt{diskbb})$
(1)

We tried to swap diskbb and bbodyrad, testing a scenario where the disc
photons serve as Comptonisation seed photons but we found that the resulting
estimates for $R_{\rm disc}$ are relatively small for all spectra, in
particular for spectrum C with an unphysical upper limit of 8 km. We also
tried to apply a second thcomp component to diskbb, driven by the expectation
that the corona should also Compton scatter at least a fraction of the disc
photons, but without any statistical improvement.
We used Model 0 also to describe the AstroSat observation (labelled As01),
obtaining a satisfactory fit and overall accordance between the best-fit
parameters found and A, B and C spectra.

Figure 3: Broadband NICER (green) and NuSTAR (blue) spectra with Model 1 and
residuals. Different line styles were adopted to distinguish between the
different components: dot for diskbb, dash for thcomp$\times$bbodyrad and
dash-dot for diskline.

###  3.2 Broadband spectra: discrete spectral features

Even with a satisfying description of the continuum, some localised residuals
could still be spotted at about 6.5-7 keV, clear sign of an unmodelled
feature. The presence of residuals in this region has been also reported by
other authors, and tackled with a combination of absorption edges (in
particular in Mondal et al., 2016) or as a reflection Fe line (e.g., Titarchuk
et al., 2013). In this work, we successfully modelled the feature with a
diskline component in all three spectra. We refer to the Appendix, section A,
for a comparison between different models to describe these residuals and to
justify our final choice for the diskline model.
The line was relatively weak in all observations (as typically observed in
UCXBs, e.g. Koliopanos et al., 2021), i.e., normalisation $K_{\rm line}$
ranging from 2$\times$10-3 for spectra A and B to 8$\times 10^{-4}$ for
spectrum C. The contribution to the total flux from the line was about
0.1%-0.2% in all cases, so that the lower normalisation in spectrum C can be
ascribed to a global fading of the X-ray output from the source. Due to the
weakness of the feature, not all line parameters could be well constrained. We
then left the line energy $E_{\rm line}$, the inner radius of the disc $R_{\rm
in}$ and $K_{\rm line}$ as the only free parameters, fixing the inclination to
45∘ (in accordance with the inclination range individuated by Anderson et al.,
1997), the emissivity index $\epsilon$ to -2 and the outer radius of the disc
$R_{\rm out}$ to 1000 RG. The feature is found at an energy $E_{\rm line}$ of
$\sim$6.6 keV in all three spectra. Only upper limits could be posed to
$R_{\rm in}$, in all cases suggesting a disc that extends relatively close to
the NS.

Residuals in the hard X-ray band were apparently flattened by the simple
addition of a diskline and did not show any trace of other reflection
features, such as the Compton hump beyond 10 keV. However, the presence of the
Iron line feature signals the existence of an underlying reflection component
in the spectrum, despite being probably very weak and contributing only
marginally to the continuum. A more detailed analysis of the reflection
component with self-consistent and more sophisticated models will be presented
in a forthcoming companion paper (Anitra et al., in preparation).
Clear absorption residuals were also present in the soft X-ray band, below 1
keV. Those features are consistent with O VIII (at $\sim$0.6 keV) and the Ne
IX complex (at $\sim$0.9 keV), respectively, which are known to be present in
the spectra of the source and have been ascribed to the interstellar medium
(ISM) (e.g. Costantini et al., 2012). We improved the fit by multiplying the
whole model by two gabs components, i.e., to account for absorption lines of
gaussian profiles.
With these additions, our final model, herafter Model 1, is the following:

$\texttt{tbabs}\times\texttt{gabs}\times\texttt{gabs}\times(\texttt{thcomp}\times\texttt{bbodyrad}+\texttt{diskbb}+\texttt{diskline})$
(2)

Furthermore, some absorption features were found in the NICER spectra at
energies of $\sim$1.8 keV, $\sim$2.2 keV as well as an emission feature at
$\sim$1.7 keV. The nature of such lines is most likely instrumental, e.g. due
to silicon and gold in the detector or the filters. We therefore introduced
some additional gaussian features to take them into account.
For the fit to the AstroSat As01 spectrum, we included the diskline component,
but left out instead the two absorption gaussian component. Indeed, AstroSat
known calibration issues makes evaluate the presence of such features more
challenging. The broadband spectra fitted with Model 1 and respective
residuals are shown in Figure 3, while we refer to Table 2 for the best-fit
parameters obtained.

Broadband spectral analysis
---
model:
tbabs$\times$gabs$\times$gabs$\times$(thComp$\times$bbodyrad+diskbb+diskline)
|  | A1 | A2 | B | C
Parameters |  | Ni02+Nu01 | As01 | (Ni06+Ni07)+Nu02 | (Ni13+Ni14)+Nu03
$N_{\rm H}$ | ($\times$1022 cm-2) | $0.161^{+0.003}_{-0.004}$ |  $0.237\pm$0.007 | 0.165$\pm$0.002 |  $0.165^{+0.002}_{-0.001}$
$\Gamma$ |  | $1.84\pm 0.03$ | 2.60$\pm$0.03 | $1.70^{+0.03}_{-0.02}$ |  $2.34^{+0.07}_{-0.06}$
$kT_{\rm e}$ | (keV) | $3.17\pm{0.04}$ | (4.80) | $2.97^{+0.03}_{-0.02}$ |  $4.85^{+0.15}_{-0.24}$
$kT_{\rm bb}$ | (keV) | $1.16^{+0.05}_{-0.03}$ |  $1.15\pm$0.04 | $1.04^{+0.05}_{-0.04}$ |  $1.46^{+0.04}_{-0.06}$
$R_{\rm bb}$ | (km) | 12.1$\pm$5.0 | 12.2$\pm$5.0 | 16.0$\pm{6.0}$ | 6.0$\pm$2.0
$kT_{\rm disc}$ | (keV) | $0.80^{+0.03}_{-0.03}$ |  $0.57\pm$0.02 | $0.73^{+0.03}_{-0.02}$ |  $0.811^{+0.010}_{-0.012}$
$R_{\rm disc}$ | (km) | 18${}^{+7}_{-6}$ | 35${}^{+14}_{-16}$ | 22${}^{+6}_{-7}$ | 16$\pm$3.0
$E_{\rm diskline}$ | (keV) | $6.62\pm 0.06$ | (6.6) | $6.53^{+0.16}_{-0.08}$ | 6.6$\pm$0.1
$R_{\rm in}$ | (km) | (20) | (20) |  $<$35 |  $<$18
$K_{\rm diskline}$ | ($\times 10^{-3}$) | 1.6$\pm$0.4 | (1.8) | 1.9${}^{+0.4}_{-0.6}$ | 0.8$\pm$0.2
$F_{\rm bol}$ | ($\times$10-8 erg cm-2 s-1) | 1.21$\pm$0.10 | 1.20$\pm$0.15 | 1.34$\pm$0.15 | 0.70$\pm$0.08
$\chi^{2}_{\nu}$ | (d.o.f.) | 1.02(377) | 1.13(489) | 0.75(390) | 0.93(374)
Table 2: Results of the spectral analysis of our 4 broadband spectra (3 NICER
+NuSTAR and 1 AstroSat). Quoted errors reflect 90% confidence level. The
parameters that were kept frozen during the fits are reported between round
parentheses. The reported flux values correspond to the 0.01–100 keV energy
range. The values of $R_{\rm disc}$ have been calculated assuming a distance
of 7.6 kpc (Kuulkers et al., 2003) and an inclination of 45∘ (Anderson et al.,
1997).

###  3.3 Results on the NICER monitoring

In order to reconstruct a more detailed physical evolution of the system
during this cycle, we then analysed individually each of the final 11 NICER
spectra (see above for the criteria followed in pairing some of the original
17 spectra to increase the statistics). We consistently used a modified
version of Model 1. Indeed, without the hard X-rays coverage provided by
NuSTAR and/or AstroSat, the degeneracies between $kT_{e}$, $\Gamma$ and the
blackbody parameters made the parameters of the fits with
thcomp$\times$bbodyrad completely unconstrained. We therefore decided to
replace this component with the simpler nthcomp, the main difference being the
lack of knowledge on the normalisation of the seed photons spectrum. For the
same reason, we had to fix the seed photons temperature in nthcomp $kT_{\rm
seed}$ to 1.0 keV, compatible with the values obtained for the broadband fits.
In addition, for the modelling of the discrete features, we had to fix some
parameters as the fit was unable to find meaningful constraints for them. In
particular, we fixed $R_{\rm in}$ in diskline to 20 RG and the energies of the
absorption features $E_{\rm line,1}$ and $E_{\rm line,2}$ to 0.68 keV and 0.87
keV respectively. The best-fit parameters obtained are shown in Tab. 5. In
Fig. 9 we display how the main best-fit parameters, the 0.5-10 keV flux and
the hardness ratio evolve over time during this cycle. From the Table and the
plot it is apparent how some parameters, e.g., $K_{\rm compt}$, seem to follow
the super-orbital modulation traced by the flux, while others, in particular
the disc temperatures $kT_{\rm disc}$ and radius $R_{\rm disc}$, appear
stable.

##  4 Timing analysis

In order to investigate the short-term X-ray variability of the source during
the mid-2022 accretion cycle, we extracted Leahy-normalised power density
spectra (PDS) from NuSTAR, NICER and AstroSat/LAXPC using as energy ranges
3-25 keV, 0.5-10 keV and 3-25 keV, respectively. We performed dead-time
correction on each NuSTAR PDS using the Fourier Amplitude Difference (FAD)
technique (Bachetti & Huppenkothen, 2018) and then extracted PDS averaging
over 150-s long segments with bin time of 1 ms. A representative sample of the
obtained PDS for NuSTAR is shown in Figure 4. For NICER we broke down the
observations in 26-s long segments and used a bin-time of 0.2 ms. We then
averaged the PDS created from each segment to produce one averaged PDS per
observation with a Nyquist frequency of $\approx$ 2.5 kHz. Finally, for LAXPC,
light curves created with a time resolution of 10 ms were used to create
Leahy-normalized PDS with 1/8192 s time bins. Also in this case, we average
the power spectra obtained from all the segments to obtain one resultant power
spectrum. Instead of subtracting the Poisson noise contribution, we rather
fitted it with a constant component.
We did not find any significant detection of discrete features like quasi-
periodic oscillations in those spectra. From each PDS, we estimated the
fractional root mean square (RMS) variability, listed in Tables3 (see Table 6
for a complete breakdown of the NICER sample). While the obtained values for
RMS in NICER show little-to-no evolution through the 17 considered snapshots,
the third NuSTAR observation (C) shows a stronger RMS variability compared to
the previous ones (A-B).

Fractional RMS variability (%)
---
NuSTAR (3-25 keV) |  |  NICER (0.5-10 keV) |  |  AstroSat/ LAXPC (3-25 keV)
Nu01 | 8.5$\pm$0.6 |  | Ni02 | 3.4$\pm$1.0 |  | As01 | 5.0$\pm$0.5
Nu02 | 5.0$\pm$0.9 |  | Ni06 | 2.8$\pm$1.7 |  |  |
Nu03 | 13.9$\pm$1.0 |  | Ni13 | 2.6$\pm$1.3 |  |  |
Table 3: Fractional RMS variability for the NICER, NuSTAR and ATCA
observations used in the broadband spectral analysis, computed for the
frequency range 0.1-100 Hz. All reported errors and upper limits correspond to
a confidence levels of 3$\sigma$. Figure 4: X-rays PDS for the NuSTAR (3-25
keV) observations used in the broadband spectral analysis. A cons model at
value 2.0 is displayed as an horizontal black line.

##  5 Radio observations

###  5.1 ATCA data reduction

4U 1820-30 was observed by the Australia Telescope Compact Array (ATCA) 13
times throughout 2022. In the present work, we will only use the observations
which were performed close to the NuSTAR observations, while an analysis of
the complete sample will be presented in a forthcoming paper (Russell et al.,
in preparation). The dates of the three observations presented here are: 2022
April 15, May 28 and July 10. During these observations, ATCA was in its more
extended 6D, 1.5B, and 6B
configurations666https://www.narrabri.atnf.csiro.au/operations/array_configurations/configurations.html,
respectively. In all cases, the fixed location antenna 6 (located 6 km from
the array core) was used during the analysis, providing angular resolutions of
$\sim$a few arcseconds for all observations. Observations were recorded
simultaneously at central frequencies of 5.5 and 9 GHz, with a bandwidth of 2
GHz at each central frequency comprised of 2048 1-MHz channels. We used PKS
B1934$-$638 for bandpass and flux density calibration, and B1817$-$254 for
phase calibration. Data were flagged, calibrated, and imaged following
standard procedures777https://casaguides.nrao.edu/index.php/ATCA_Tutorials in
the Common Astronomy Software Application (casa version 5.1.2; CASA Team et
al. 2022). Imaging used a Briggs weighting scheme with a robust parameter of
0, balancing sensitivity and resolution, providing angular resolutions of
$\sim$a few arcseconds.

###  5.2 Results

The flux density, $S_{\nu}$ at frequency $\nu$, of the point source was
measured by fitting an elliptical Gaussian with full width at half maximum
(FWHM) set by the synthesised beam shape. Errors on the absolute flux density
scale include conservative systematic uncertainties of 4% for the 5.5/9 GHz
ATCA data888https://www.atnf.csiro.au/observers/memos/d96783~1.pdf (e.g.,
Murphy et al., 2010), which were added in quadrature with the root mean square
(RMS) of the image noise. The radio luminosity, $L_{\rm R}$, was calculated as
$L_{\rm R}=4\pi S_{\nu}\nu D^{2}$, where $\nu$ is the observing frequency and
$D$ is the distance to the source.
According to our measurements, a significant radio enhancement can be
appreciated during the low X-ray mode (compared to the high-mode). In
particular, the radio flux density increases from 70-110 $\mu$Jy (in epochs A
and B) to $\sim$500 $\mu$Jy in epoch C. This is the brightest radio flux
density recorded for 4U 1820-30 at these frequencies (see, for records of
radio flux density of the source, Migliari et al., 2004; Díaz Trigo et al.,
2017; Russell et al., 2021).
We then estimated the radio spectral index $\alpha$, where
$S_{\nu}\propto\nu^{\alpha}$, in order to explore the properties of the
outflow in each of the three observations. A flat/inverted radio spectrum,
where $\alpha\gtrsim 0$, is associated with persistent synchrotron emission
from an optically-thick, self-absorbed compact jet, typically observed in XRBs
during their hard states. On the other hand, steep radio spectra, where
$\alpha\approx-0.7$, are observed from discrete, optically-thin knots of
synchrotron emitting plasma that are launched from the system, often referred
to as transient jets. Transient jets are detected as the source transitions
from the hard to soft state (e.g. Fender, 2001).
For 4U 1820-30 the radio spectral shape was found to be flat during epoch C
($\alpha\sim$-0.2), steep for epoch B ($\alpha\sim$-0.9), and unconstrained
for epoch A, being consistent with flat, inverted or steep. This implies a
dramatic evolution of the jet properties between high and low modes, as
already reported by Russell et al. (2021). We will compare this intriguing
trend with the accretion flow evolution tracked by the X-rays data analysis in
Section 6.2.

ATCA observations
---
Start date | End date | 5.5 GHz Flux density | 9 GHz Flux density |  $\alpha$
(UTC) | (UTC) | ($\mu$Jy) | ($\mu$Jy)  |
2022-04-15T18:18:40 | 2022-04-16T00:22:00 | 76$\pm$16 | 74$\pm$16 | -0.1$\pm$0.7
2022-05-28T13:52:50 | 2022-05-28T19:19:50 | 110$\pm$13 | 74$\pm$11 | -0.9$\pm$0.4
2022-07-10T12:43:30 | 2022-07-10T18:01:40 | 500$\pm$23 | 450$\pm$25 | -0.22$\pm$0.15
Table 4: Results from our ATCA radio observations. A bandwidth of 2 GHz is
associated to each frequency band. Flux density errors include systematic
uncertainties. Radio spectral indices, provided as $\alpha$, i.e., where
$S_{\rm\nu}\propto\nu^{\alpha}$, are also reported. Figure 5: Radio emission
from 4U 1820-30 during epochs A, B and C (see Tab. 4 for more details). Best-
fit models for the spectra of each epoch are shown. Radio spectral indices
$\alpha$ are reported on the plots as well. A dramatic change in radio flux
can be appreciated between epoch C (in low mode) and epochs A and B (high
mode). In addition, epoch B shows also a steeper spectrum.

##  6 Discussion

4U 1820-30 provides an almost unique opportunity to observe super-orbital
modulations of the accretion rate over relatively short time-scales in a X-ray
binary. The spectral evolution of the source during several accretion cycles
has been studied in detail by Titarchuk et al. (2013) using Rossi X-ray Timing
Explorer, at energies higher than 3 keV. In the work presented here, thanks to
the excellent effective area of NICER in the soft X-ray band, we are able to
investigate the system’s behaviour during one super-orbital modulation in the
soft X-ray band for the first time. In addition, we see how the radio
emission, and, therefore, the jet, evolved corresponding to these changes in
the X-ray spectra.

###  6.1 The origin of the fluctuation in the Comptonisation component and the
accretion flow geometry

In this paper we showed how the X-ray spectral-timing parameters evolve as the
systems bounces between high and low modes. According to the traditional
classification scheme based on the colour-colour diagram, 4U 1820-30 lingered
in the banana state for the whole considered period, moving back and forth
between the upper and the lower banana branch. Such a trend seems to reflect
more an evolution in the flux rather than in the hardness value, whose
relative stability is consistent with the lack of a spectral transition. We
found that a model composed of a disc blackbody, a Comptonisation component
and a Fe K line was sufficient to describe the continuum in all the considered
spectra. Moving along the super-orbital modulation, however, these two
components behave in a rather distinct way. The disc parameters stay more or
less constant, in terms of both temperature (about 0.7-0.8 keV), inner radius
(20-30 km) and normalisation. On the contrary, the Comptonisation component
displays a substantial evolution mostly in its normalisation, i.e., an almost
50% reduction in the 0.5-10 keV flux going from high to low mode, compared to
the less than 10% drop in the disc component. Such a trend has been already
spotted by Titarchuk et al. (2013) using RXTE data, although with a model
slightly different than ours. A closer inspection to the obtained best-fit
parameters reveals that such an evolution is driven mostly by the
normalisation, thereby the physical size, of the source of the seed photons.
Such a source has been described with a black body component and associated to
the innermost part of the accretion flow. In the high mode, seed photons seem
to be radiated by a bigger region with respect to the low modes, i.e., the
size going from about 15 km in spectra A-B to about a third of this value in
spectrum C. A change can be also observed in the electron temperature of the
corona, which seems slightly anti-correlated with the flux, i.e., going from 3
keV (high mode) to about 5 keV (low mode). While a clear trend is visible in
energy spectra, the PDS show less variability. In particular, the fractional
RMS is stable at about 2-3.5% in all NICER observations. On the other hand, an
increase in the power subtended by the PDS, and thereby in the RMS, can be
spotted in NuSTAR PDS going from A-B (RMS$\sim$5-8%) to C (RMS$\sim$14%), i.e.
with C being significantly more variable. Such a trend is compatible with the
increase in temperature of the corona in spectrum C, as hotter coronae are
expected to drive stronger X-rays fluctuations.

We can piece together all these observed spectral-timing properties into a
single interpretation scheme making the following points: (i) in high mode,
the mass-accretion rate increases as a consequence of the accretion cycle
characterising the system. (ii) The energy fuelled by accretion is dissipated
by a $\sim$15 km region in the BL, resulting in more photons and thereby a
stronger cooling of the corona. (iii) In low mode, while $\dot{M}$, and
therefore the energy supply to the innermost regions of the system, drops,
only a smaller, i.e. $\lesssim$10 km, region of the accretion flow remains hot
enough to cool the corona by charging it with photons; this region could be a
hot spot on the NS surface or a fraction of the BL. Alternatively, the
shrinking of the region that provides seed photons for Comptonisation could be
explained by invoking a spreading layer covering a larger fraction of the NS
surface in high modes than in low modes, once again in response to a changing
$\dot{m}$ in the two regimes. (iv) With less photons injected, the corona
cools down less and stays hotter, driving more power in the X-rays PDS.
Recently, the new X-ray spectro-polarimetry mission _Imaging X-ray Polarimetry
Explorer (IXPE)_ (Weisskopf et al., 2022) has opened a new avenue to study the
accretion flows in XRBs. An IXPE observational campaign has been performed
between 2022 and 2023 on 4U 1820-30 (Di Marco et al., 2023). The source was
found in high mode in all those observations. The model used by these authors
to analyse the broadband X-rays spectra, consisting of a disc blackbody, a
Comptonisation spectrum and a gaussian component for the Fe K line, is
consistent with ours. In addition, quasi-simultaneous radio observations (with
ATCA ) revealed a steep radio spectrum as in our epoch B. These results are
consistent with compact jet quenching or transient ejecta during the high
modes of 4U 1820-30. In addition, these authors measured a significant
($\sim$10%) polarisation degree beyond 7 keV along the direction perpendicular
to the disc and interpreted these results as possibly due to a mildy
relativistic outflow or to reflection. Further studies are necessary to
investigate whether such an outflow can be connected with the ejecta
responsible for the radio emission in the same state.

###  6.2 A boundary layer-jet (anti-)coupling?

In the radio band, which is dominated by the jet emission, the source shows
dramatic changes between our observations. In the low mode (epoch C), its
radio flux density is enhanced by a factor of 5 with respect to the high mode
(epochs A and B) and also its spectral shape seems to change. The mode
dependency of the jet in 4U 1820-30 has already been reported Russell et al.
(2021), using new and also archival radio data (i.e., from Díaz Trigo et al.,
2017; Panurach et al., 2021), and recently confirmed by Di Marco et al.
(2023).
In this work, for the first time, we can compare the jet evolution with the
simultaneous X-rays spectral-timing properties of the source. In Section 6.1
we have showed that the X-rays evolution during a super-orbital cycle in 4U
1820-30 is connected to fluctuations in the boundary layer emission, going
from bright to faint in the high to low mode transitions. Such a behaviour
produces oscillations in the X-ray light curves that however seem not to be
accompanied by transitions between hard and soft states. Indeed, during all of
our observations, the source never departs from the vertical "banana" track,
as displayed in Fig. 2. Despite slight increases in $kT_{\rm e}$ and the hard
X-rays RMS seem to indicate that in epoch C a "micro-transition" towards
harder states might be ongoing, the spectral and timing properties are not
compatible with a full hard state either. Indeed, when 4U 1820-30 has been
observed in hard / "island" state, it showed remarkably higher $kT_{\rm e}$
(up to 20-30 keV, e.g., Titarchuk et al., 2013) and hard X-rays RMS (up to 20%
and above, e.g., Muñoz-Darias et al., 2014). Since the observed jet evolution
is not occurring in tandem with a soft-to-hard tradition, the behaviour shown
by 4U 1820-30 seems markedly distinct from what is typically observed in BH
and several NS LMXBs (e.g., Migliari & Fender, 2006; Miller-Jones et al.,
2010; Rhodes et al., 2022; Fijma et al., 2023). What then determines the
evolution in the jet? A link with the boundary layer (which was also suggested
by Russell et al., 2021, for the same source) seems plausible, as it drives
the entire evolution of the accretion flow that we observe in our X-ray
observations of 4U 1820-30. According to several accretion/ejection models
(e.g. Blandford & Payne, 1982; Marcel et al., 2018), jet launching requires
the presence of a hot, thin and extended corona (however, see Méndez et al.,
2022, for observational evidences of an anti-correlation between radio bright
jets and hot coronae in the BH XRB GRS 1915+105). The temperature and the
geometrical thickness of the corona change as a consequence of the interaction
with the photons coming from the disc or, in NS systems, from the BL and the
NS surface itself. During the high modes, the boundary layer is bright and
extended and irradiates the corona more than during the low modes, making it
colder and thicker. On the other hand, during low modes, the corona is charged
with less photons and can therefore expand and heat up, an ideal condition to
support robust matter ejections. This is also witnessed by the increment in
$kT_{\rm e}$ and RMS variability (in NuSTAR) going from A/B to C (see Tab. 2
and 3). Furthermore, it is noteworthy that according to the Internal Shocks
Model (Malzac, 2013, 2014), an increase in X-rays variability would indeed
produce brighter jets. Indeed, with more X-rays power we expect larger
variability in the velocity with which ejecta in the jet are launched and
subsequently more energy dissipated in the shocks between shells moving at
different velocity.
The proposed scenario is sketched in Fig. 6. Ultimately in this source, the BL
seems to take the main role in regulating the jet properties, to such an
extent that we should talk about BL-jet coupling instead of disc-jet coupling,
a common term used in the context of LMXBs. An intriguing implication of this
scenario is that jet quenching can occur beyond a certain X-ray luminosity but
within the same spectral state. Disentangling jet suppression from spectral
state transition could be key to explain the proposed presence of compact jets
even after the transition to the soft state in a few NS LMXBs (Migliari et
al., 2004, 2011). It is also noteworthy that a BL-jet coupling has been
already proposed for a system very different from 4U 1820-30, i.e., in the
dwarf nova SS Cyg where jet launching was found to be possibly connected with
the formation of the boundary layer (Russell et al., 2016). Unfortunately, the
radio–X-ray observational campaign presented in this paper is one of the very
few available multi-wavelength data sets of a NS LMXB followed through
different regimes and/or spectral states. New radio–X-rays observational
campaigns, dense enough to investigate how accretion and ejection evolve over
time, have to be performed in the future in order to confirm the existence of
such BL-jet coupling in other NS LMXBs.
Based on the results presented in this paper, we can speculate that BLs, a
rather common ingredient in NS LMXBs, may play a role in regulating jet
launching in several different classes, e.g., in in Z-sources and/or in
bright, persistent atolls. All of these sources exhibit rather soft spectra,
with contribution from both the disc and the BL (see, e.g. D’Aì et al., 2010;
Mazzola et al., 2021; Saavedra et al., 2023). In addition, Z-sources
continuously traverse along three branches in their color-color diagrams,
showing drastic changes in both the radio emission and the X-rays variability,
but without traditional hard-to-soft transitions (Penninx et al., 1988;
Migliari & Fender, 2006; Soleri et al., 2009). A similar behaviour has been
exhibited also by the bright atoll GX 13+1 (Homan et al., 2004). Finally, jet-
related radio emission from the persistent atoll Ser X-1 has been reported
while the source was in a soft state (Migliari et al., 2004).
On the other hand, we do not expect BLs to form in other classes of NS LMXBs,
namely the sources where the disc is truncated very far away from the NS
surface. This could be the case for faint atolls typically found in rather
hard states, such as Accreting Millisecond X-ray Pulsars (AMXPs Di Salvo &
Sanna, 2020). In these sources, the magnetospheric pressure could disrupt the
accretion flow in proximity of the compact object, inhibiting the formation of
a BL (Degenaar et al., 2017; Bult et al., 2021; Marino et al., 2022). Of note
is that AMXPs can be remarkably radio bright (Russell et al., 2018), sometimes
as much as BH LMXBs at the same X-ray luminosity, where BLs can not form
either. As an extra ingredient that however may not be present in all NS
LMXBs, the role of the BL could then be crucial to explain e.g. why NS LMXBs
are typically radio fainter than BH LMXBs, why compact jets could still
survive in NS LMXBs during low luminosity soft states and what produces large
scatter in radio luminosity within the NS LMXB population (e.g., Tetarenko et
al., 2016).

Figure 6: A simplified scheme for our interpretation of the X-rays and radio
data. In particular, we show here how the accretion flow and the jet change
going from high to low modes.

##  7 Conclusions

In this paper, we have presented the results of the 2022 multi-wavelength
campaign on the ultra-compact X-ray binary 4U 1820-30, using X-rays (NICER,
NuSTAR and AstroSat) and radio (ATCA) observatories. Throughout this campaign,
we were able to follow how the spectral/timing behavior of the accretion flow
and the jet properties evolve in tandem, something rarely seen in NS XRBs.
During the surveyed period, the source went through its typical low and high
modes, showing a X-ray flux oscillation amplitude of about 40%. Despite such a
strong variability, the source lingered in the banana state and did not show
dramatic spectral changes throughout this cycle. A model including a
Comptonisation spectrum (with seed photons provided by a boundary layer), the
disc multi-colour blackbody emission and a Fe K line worked well in describing
the broadband NICER +NuSTAR and AstroSat spectra and the single NICER
observations as well. We showed that among these components, the
Comptonisation spectrum shows the most dramatic variability, while the disc
component is relatively stable. The results of our analysis suggest that
modulations in the amplitude of the Comptonisation spectral component are
indeed driving such variability, following the very same pattern observed in
the X-ray light curve. These modulations suggest an energy flow going from a
more extended region in high mode, i.e., the boundary layer, from a more
confined region in the low mode, i.e., the NS surface. Furthermore, the hot
corona also changes in response to this trend, becoming colder in the high
mode as more radiation is pumped into it by the innermost regions of the
accretion flow. A correlation between the corona temperature and the values
found for the NuSTAR RMS variability can also be noted. Meanwhile, the jet
evolved dramatically in the three observations presented here, brightening
considerably during the low mode, coupled with a change in the radio spectrum.
We propose that the jet is responding to the changes in the corona, becoming
respectively stronger (weaker) as the corona becomes hotter (colder).
Ultimately, we suggest that the jet evolution is then driven by the radiation
emitted from the BL in an anti-correlation pattern where the jet switches on
as the BL switches off. Such a BL-jet (anti-)coupling could be acting also in
other NS LMXBs and might in part explain the complex phenomenology of matter
ejection in accreting NSs. In order to confirm the above scenario and pinpoint
the exact moment where the jet properties evolve, a more detailed look at the
radio evolution during this cycle is required (Russell et al., in
preparation).

## Acknowledgements

We thank the anonymous referee for their helpful comments. AMarino, FCZ and NR
are supported by the H2020 ERC Consolidator Grant “MAGNESIA” under grant
agreement No. 817661 (PI: Rea) and National Spanish grant PGC2018-095512-BI00.
This work was also partially supported by the program Unidad de Excelencia
Maria de Maeztu CEX2020-001058-M, and by the PHAROS COST Action (No. CA16214).
MDS and TDR acknowledge support from the INAF grant "ACE-BANANA". AB is
grateful to the Royal Society, United Kingdom. She is supported by an INSPIRE
Faculty grant (DST/INSPIRE/04/2018/001265) by the Department of Science and
Technology, Govt. of India. A.B. also acknowledges the financial support of
ISRO under the AstroSat Archival Data Utilisation Programme
(No.DS-2B-13013(2)/4/2019-Sec. 2). TDS and AS acknowledge financial support
from PRIN-INAF 2019 with the project "Probing the geometry of accretion: from
theory to observations" (PI: Belloni). FCZ is supported by a Ramón y Cajal
fellowship (grant agreement RYC2021-030888-I). EA acknowledges funding from
the Italian Space Agency, contract ASI/INAF n. I/004/11/4. FC acknowledges
support from the Royal Society through the Newton International Fellowship
programme (NIF/R1/211296). JvdE acknowledges a Warwick Astrophysics prize
post-doctoral fellowship made possible thanks to a generous philanthropic
donation, and was supported by a Lee Hysan Junior Research Fellowship awarded
by St. Hilda’s College, Oxford, during part of this work. We thank Jamie
Stevens and ATCA staff for making the radio observations possible. ATCA is
part of the Australia Telescope National Facility (https://ror.org/05qajvd42)
which is funded by the Australian Government for operation as a National
Facility managed by CSIRO. We acknowledge the Wiradjuri people as the
Traditional Owners of the ATCA observatory site. NICER is a 0.2–12 keV X-ray
telescope operating on the International Space Station, funded by NASA. NuSTAR
is a project led by the California Institute of Technology, managed by the Jet
Propulsion Laboratory and funded by NASA. This publication uses the data from
the AstroSat mission of the Indian Space Research Organisation (ISRO),
archived at the Indian Space Science Data Centre (ISSDC).

## Data Availability

The X-rays data utilised in this article are publicly available at
https://heasarc.gsfc.nasa.gov/cgi-bin/W3Browse/w3browse.pl, while the analysis
products and the ATCA data will be shared on reasonable request to the
corresponding author.

## References

  * Agrawal (2006) Agrawal P. C., 2006, Advances in Space Research, 38, 2989
  * Anderson et al. (1997) Anderson S. F., Margon B., Deutsch E. W., Downes R. A., Allen R. G., 1997, ApJ, 482, L69
  * Antia et al. (2017) Antia H. M., et al., 2017, ApJS, 231, 10
  * Antia et al. (2021) Antia H. M., et al., 2021, arXiv e-prints, p. arXiv:2101.07514
  * Armas Padilla et al. (2023) Armas Padilla M., Corral-Santana J. M., Borghese A., Cúneo V. A., Muñoz-Darias T., Casares J., Torres M. A. P., 2023, arXiv e-prints, p. arXiv:2305.07691
  * Bachetti & Huppenkothen (2018) Bachetti M., Huppenkothen D., 2018, ApJ, 853, L21
  * Beri et al. (2021) Beri A., et al., 2021, MNRAS, 500, 565
  * Blandford & Payne (1982) Blandford R. D., Payne D. G., 1982, MNRAS, 199, 883
  * Bult et al. (2021) Bult P., Strohmayer T. E., Malacaria C., Ng M., Wadiasingh Z., 2021, ApJ, 912, 120
  * CASA Team et al. (2022) CASA Team et al., 2022, PASP, 134, 114501
  * Cackett et al. (2008) Cackett E. M., Wijnands R., Miller J. M., Brown E. F., Degenaar N., 2008, ApJ, 687, L87
  * Chakraborty et al. (2011) Chakraborty M., Bhattacharyya S., Mukherjee A., 2011, MNRAS, 418, 490
  * Chakraborty et al. (2020) Chakraborty S., Navale N., Ratheesh A., Bhattacharyya S., 2020, MNRAS, 498, 5873
  * Chou & Grindlay (2001) Chou Y., Grindlay J. E., 2001, ApJ, 563, 934
  * Corbel et al. (2000) Corbel S., Fender R. P., Tzioumis A. K., Nowak M., McIntyre V., Durouchoux P., Sood R., 2000, A&A, 359, 251
  * Coriat et al. (2011) Coriat M., et al., 2011, MNRAS, 414, 677
  * Costantini et al. (2012) Costantini E., et al., 2012, A&A, 539, A32
  * Coti Zelati et al. (2021) Coti Zelati F., et al., 2021, A&A, 655, A52
  * D’Aì et al. (2010) D’Aì A., et al., 2010, A&A, 516, A36
  * De Marco et al. (2021) De Marco B., Zdziarski A. A., Ponti G., Migliori G., Belloni T. M., Segovia Otero A., Dziełak M., Lai E. V., 2021, arXiv e-prints, p. arXiv:2102.07811
  * Degenaar et al. (2017) Degenaar N., Ootes L. S., Reynolds M. T., Wijnands R., Page D., 2017, MNRAS, 465, L10
  * Di Marco et al. (2023) Di Marco A., et al., 2023, arXiv e-prints, p. arXiv:2306.08476
  * Di Salvo & Sanna (2020) Di Salvo T., Sanna A., 2020, arXiv e-prints, p. arXiv:2010.09005
  * Díaz Trigo et al. (2017) Díaz Trigo M., Migliari S., Miller-Jones J. C. A., Rahoui F., Russell D. M., Tudor V., 2017, A&A, 600, A8
  * Done et al. (2007) Done C., Gierliński M., Kubota A., 2007, A&ARv, 15, 1
  * Egron et al. (2013) Egron E., et al., 2013, A&A, 550, A5
  * Fender (2001) Fender R. P., 2001, MNRAS, 322, 31
  * Fender & Belloni (2004) Fender R., Belloni T., 2004, ARA&A, 42, 317
  * Fijma et al. (2023) Fijma S., van den Eijnden J., Degenaar N., Russell T. D., Miller-Jones J. C. A., 2023, MNRAS, 521, 4490
  * Foreman-Mackey (2016) Foreman-Mackey D., 2016, Journal of Open Source Software, 1, 24
  * Gallo et al. (2018) Gallo E., Degenaar N., van den Eijnden J., 2018, MNRAS, 478, L132
  * Gambino et al. (2019) Gambino A. F., et al., 2019, A&A, 625, A92
  * Goodman & Weare (2010) Goodman J., Weare J., 2010, Communications in Applied Mathematics and Computational Science, Vol.~5, No.~1, p.~65-80, 2010, 5, 65
  * Gusinskaia et al. (2017) Gusinskaia N. V., et al., 2017, MNRAS, 470, 1871
  * Gusinskaia et al. (2020) Gusinskaia N. V., et al., 2020, MNRAS, 492, 1091
  * Hasinger & van der Klis (1989) Hasinger G., van der Klis M., 1989, A&A, 225, 79
  * Homan et al. (2004) Homan J., Wijnands R., Rupen M. P., Fender R., Hjellming R. M., di Salvo T., van der Klis M., 2004, A&A, 418, 255
  * Homan et al. (2010) Homan J., et al., 2010, ApJ, 719, 201
  * Homan et al. (2011) Homan J., Linares M., van den Berg M., Fridriksson J., 2011, The Astronomer’s Telegram, 3650, 1
  * Homan et al. (2022a) Homan J., et al., 2022a, The Astronomer’s Telegram, 15605, 1
  * Homan et al. (2022b) Homan J., et al., 2022b, The Astronomer’s Telegram, 15627, 1
  * Iaria et al. (2020) Iaria R., Mazzola S. M., Di Salvo T., Marino A., Gambino A. F., Sanna A., Riggio A., Burderi L., 2020, A&A, 635, A209
  * Kaastra & Bleeker (2016) Kaastra J. S., Bleeker J. A. M., 2016, A&A, 587, A151
  * Koliopanos et al. (2021) Koliopanos F., Péault M., Vasilopoulos G., Webb N., 2021, MNRAS, 501, 548
  * Krimm et al. (2013) Krimm H. A., et al., 2013, ApJS, 209, 14
  * Kuulkers et al. (2003) Kuulkers E., den Hartog P. R., in’t Zand J. J. M., Verbunt F. W. M., Harris W. E., Cocchi M., 2003, A&A, 399, 663
  * Ludlam et al. (2016) Ludlam R. M., et al., 2016, ApJ, 824, 37
  * Ludlam et al. (2020) Ludlam R. M., et al., 2020, ApJ, 895, 45
  * Malzac (2013) Malzac J., 2013, MNRAS, 429, L20
  * Malzac (2014) Malzac J., 2014, MNRAS, 443, 299
  * Marcel et al. (2018) Marcel G., et al., 2018, A&A, 615, A57
  * Marcel et al. (2019) Marcel G., et al., 2019, A&A, 626, A115
  * Marino et al. (2019) Marino A., et al., 2019, MNRAS, 490, 2300
  * Marino et al. (2020) Marino A., et al., 2020, MNRAS, 498, 3351
  * Marino et al. (2022) Marino A., et al., 2022, MNRAS, 515, 3838
  * Matsuoka et al. (2009) Matsuoka M., et al., 2009, PASJ, 61, 999
  * Mazzola et al. (2021) Mazzola S. M., et al., 2021, A&A, 654, A102
  * Méndez et al. (2022) Méndez M., Karpouzas K., García F., Zhang L., Zhang Y., Belloni T. M., Altamirano D., 2022, Nature Astronomy, 6, 577
  * Migliari & Fender (2006) Migliari S., Fender R. P., 2006, MNRAS, 366, 79
  * Migliari et al. (2004) Migliari S., Fender R. P., Rupen M., Wachter S., Jonker P. G., Homan J., van der Klis M., 2004, MNRAS, 351, 186
  * Migliari et al. (2011) Migliari S., Miller-Jones J. C. A., Russell D. M., 2011, MNRAS, 415, 2407
  * Miller-Jones et al. (2010) Miller-Jones J. C. A., et al., 2010, ApJ, 716, L109
  * Mondal et al. (2016) Mondal A. S., Dewangan G. C., Pahari M., Misra R., Kembhavi A. K., Raychaudhuri B., 2016, MNRAS, 461, 1917
  * Mondal et al. (2020) Mondal A. S., Dewangan G. C., Raychaudhuri B., 2020, MNRAS, 494, 3177
  * Muñoz-Darias et al. (2014) Muñoz-Darias T., Fender R. P., Motta S. E., Belloni T. M., 2014, MNRAS, 443, 3270
  * Murphy et al. (2010) Murphy T., et al., 2010, MNRAS, 402, 2403
  * Panurach et al. (2021) Panurach T., et al., 2021, ApJ, 923, 88
  * Panurach et al. (2023) Panurach T., et al., 2023, ApJ, 946, 88
  * Penninx et al. (1988) Penninx W., Lewin W. H. G., Zijlstra A. A., Mitsuda K., van Paradijs J., 1988, Nature, 336, 146
  * Pintore et al. (2016) Pintore F., et al., 2016, MNRAS, 457, 2988
  * Rhodes et al. (2022) Rhodes L., Fender R. P., Motta S., van den Eijnden J., Williams D. R. A., Bright J., Sivakoff G. R., 2022, MNRAS, 513, 2708
  * Russell et al. (2014) Russell T. D., Soria R., Miller-Jones J. C. A., Curran P. A., Markoff S., Russell D. M., Sivakoff G. R., 2014, MNRAS, 439, 1390
  * Russell et al. (2016) Russell T. D., et al., 2016, MNRAS, 460, 3720
  * Russell et al. (2018) Russell T. D., Degenaar N., Wijnands R., van den Eijnden J., Gusinskaia N. V., Hessels J. W. T., Miller-Jones J. C. A., 2018, ApJ, 869, L16
  * Russell et al. (2021) Russell T. D., et al., 2021, MNRAS, 508, L6
  * Saavedra et al. (2023) Saavedra E. A., García F., Fogantini F. A., Méndez M., Combi J. A., Luque-Escamilla P. L., Martí J., 2023, MNRAS, 522, 3367
  * Sharma et al. (2023) Sharma R., Sanna A., Beri A., 2023, MNRAS, 519, 3811
  * Singh et al. (2014) Singh K. P., et al., 2014, in Takahashi T., den Herder J.-W. A., Bautz M., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 9144, Space Telescopes and Instrumentation 2014: Ultraviolet to Gamma Ray. p. 91441S, doi:10.1117/12.2062667
  * Singh et al. (2016) Singh K. P., et al., 2016, in den Herder J.-W. A., Takahashi T., Bautz M., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 9905, Space Telescopes and Instrumentation 2016: Ultraviolet to Gamma Ray. p. 99051E, doi:10.1117/12.2235309
  * Singh et al. (2017) Singh K. P., et al., 2017, Journal of Astrophysics and Astronomy, 38, 29
  * Soleri et al. (2009) Soleri P., Tudose V., Fender R., van der Klis M., Jonker P. G., 2009, MNRAS, 399, 453
  * Stella et al. (1987) Stella L., Priedhorsky W., White N. E., 1987, ApJ, 312, L17
  * Tarana et al. (2007) Tarana A., Bazzano A., Ubertini P., Zdziarski A. A., 2007, ApJ, 654, 494
  * Tetarenko et al. (2016) Tetarenko A. J., et al., 2016, MNRAS, 460, 345
  * Titarchuk et al. (2013) Titarchuk L., Seifina E., Frontera F., 2013, ApJ, 767, 160
  * Verner et al. (1996) Verner D. A., Ferland G. J., Korista K. T., Yakovlev D. G., 1996, ApJ, 465, 487
  * Weisskopf et al. (2022) Weisskopf M. C., et al., 2022, Journal of Astronomical Telescopes, Instruments, and Systems, 8, 026002
  * Wilms et al. (2000) Wilms J., Allen A., McCray R., 2000, ApJ, 542, 914
  * Yadav et al. (2016) Yadav J. S., et al., 2016, in den Herder J.-W. A., Takahashi T., Bautz M., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 9905, Space Telescopes and Instrumentation 2016: Ultraviolet to Gamma Ray. p. 99051D, doi:10.1117/12.2231857
  * Zdziarski et al. (2007) Zdziarski A. A., Wen L., Gierliński M., 2007, MNRAS, 377, 1006
  * Zdziarski et al. (2020) Zdziarski A. A., Szanecki M., Poutanen J., Gierliński M., Biernacki P., 2020, MNRAS, 492, 5234
  * in’t Zand et al. (2012) in’t Zand J. J. M., Homan J., Keek L., Palmer D. M., 2012, A&A, 547, A47
  * van den Eijnden et al. (2018) van den Eijnden J., Degenaar N., Russell T. D., Wijnand s R., Miller-Jones J. C. A., Sivakoff G. R., Hernández Santisteban J. V., 2018, Nature, 562, 233
  * van den Eijnden et al. (2021) van den Eijnden J., et al., 2021, MNRAS, 507, 3899
  * van der Klis (2006) van der Klis M., 2006, Advances in Space Research, 38, 2675

##  Appendix A On the modelling of the Fe K line

The 6-7 keV region of all the spectra from 4U 1820-30 used in this paper
showed residuals, as evident in the top panel of Fig. 7, where we show
Spectrum B as a representative example. The presence of similar residuals in
this region has been also reported by other authors, and tackled with a
combination of absorption edges (in particular in Mondal et al., 2016) or as a
reflection Fe line (e.g., Titarchuk et al., 2013). Following the former
authors’ prescription, we included two absorption edges with the edge model in
Xspec. We limited the energies of the edges to the ranges 6.8-7.0 keV and
7.5-7.8 keV respectively, as done for the NuSTAR spectra in Mondal et al.
(2016). A slight improvement in the fit can be appreciated, but the structure
in the residuals is still present (Middle panel, Fig. 7). We therefore removed
the edges and added instead a diskline component to the three spectra.
Not only does the inclusion of the feature result in a better improvement of
the fit, but also in flat residuals. The feature is found significant999We
estimated the significance as the ratio between $K_{\rm line}$ and the error
to the normalisation at a confidence level of 1$\sigma$. in all spectra
(significance ranging from 6$\sigma$ to 4.5$\sigma$ confidence). In order to
further investigate the line profile, we applied the Goodman-Weare algorithm
of Monte Carlo Markov Chain (MCMC; Goodman & Weare, 2010) to produce contour
plots for $E_{\rm line}$ and $K_{\rm line}$. We used 20 walkers and a chain
length of 5$\times$105, to calculate the marginal posterior distributions of
the best-fit parameters. The results are presented in Figure 8, where we use
corner.py (Foreman-Mackey, 2016) to visualise the MCMC chains.

Figure 7: Comparison between the 4–10 keV residuals obtained in Spectrum B
with different models to fit the iron line complex region. Models tested:
(_Top_) Model 0; (_Middle_) Model 0 plus two absorption edges with energies
of$\sim$6.9 keV and $\sim$7.6 keV respectively (following the approach by
Mondal et al., 2016); (_Bottom_) Model 0 plus a diskline model. Data: NICER
(green) and NuSTAR (both FPMA and FPMB, blue). Figure 8: Posterior probability
distributions for $E_{\rm line}$ and $K_{\rm line}$ for spectra A (top), B
(middle) and C (bottom). Contours represent the 1$\sigma$ , 2$\sigma$ and
3$\sigma$ confidence levels. Marginal posterior distributions are shown as
histograms with the median and 1 $\sigma$ intervals of confidence highlighted
as dashed lines.

##  Appendix B A NICER look at 4U 1820-30

In the following, we present Tables for the spectral and timing analysis
performed on any single NICER observation of this observational campaign
(Tables 5-6). In order to visualise the changes of the main spectral and
timing parameters of the source during this period, we present a tower plot
with the time evolution of selected parameters in Fig. 9.

NICER spectral analysis
---
model: tbabs$\times$(nthComp+diskline+diskbb)
| 01 | 02 | 03 | 04 | 05 | 06
Parameters | (Ni01) | (Ni02) | (Ni03) | (Ni04) | (Ni05) | (Ni06+Ni07)
$N_{\rm H}$ ($\times$1022 cm-2) |  $0.170\pm$0.005 |  $0.167\pm$0.004 |  $0.167\pm$0.006 |  $0.169\pm$0.005 |  $0.168\pm$0.005 |  $0.168\pm$0.005
$\Gamma$ | 1.99$\pm$0.11 | 2.10${}^{+0.03}_{-0.06}$ | 1.71${}^{+0.13}_{-0.16}$ | 1.92$\pm$0.14 | 1.75${}^{+0.09}_{-0.08}$ |  $1.83\pm 0.07$
$kT_{\rm e}$ (keV) | 4.2${}^{+3.0}_{-0.8}$ |  $>$6.0 | 3.0${}^{+0.8}_{-0.4}$ | 3.3${}^{+1.2}_{-0.5}$ | 2.8${}^{+1.3}_{-0.2}$ | 3.3${}^{+0.5}_{-0.3}$
$K_{\rm compt}$ | 0.145$\pm$0.010 | 0.199${}^{+0.003}_{-0.009}$ | 0.187${}^{+0.030}_{-0.020}$ | 0.184${}^{+0.015}_{-0.017}$ | 0.197${}^{+0.015}_{-0.013}$ | 0.201${}^{+0.011}_{-0.010}$
$E_{\rm diskline}$ (keV) | 6.53${}^{+0.16}_{-0.13}$ | 6.68$\pm$0.10 |  $>$6.50 | 6.71$\pm$0.10 | 6.58${}^{+0.19}_{-0.12}$ | 6.69${}^{+0.15}_{-0.10}$
$K_{\rm diskline}$ ($\times$10-3) | 1.4$\pm$0.5 | 2.1$\pm$0.6 | 1.7${}^{+1.4}_{-1.2}$ | 2.2$\pm$0.9 | 1.8$\pm$0.8 | 2.4$\pm$0.7
$kT_{\rm disc}$ (keV) | 0.68$\pm$0.02 | 0.67${}^{+0.13}_{-0.10}$ | 0.72${}^{+0.06}_{-0.03}$ | 0.69$\pm$0.03 | 0.69$\pm$0.02 | 0.70$\pm$0.03
$R_{\rm disc}$ (km) | 13.0$\pm$4.0 | 15.0$\pm$4.0 | 13.0$\pm$6.0 | 14.0$\pm$6.0 | 14.0$\pm$5.0 | 15.0$\pm$4.0
$\tau_{\rm line,1}$ (keV) | 0.23$\pm$0.10 | 0.28$\pm$0.10 | 0.24$\pm$0.12 | 0.23$\pm$0.11 | 0.26$\pm$0.11 | 0.26$\pm$0.10
$\tau_{\rm line,2}$ (keV) | 0.08$\pm$0.06 | 0.07$\pm$0.06 |  $<$0.10 | 0.08$\pm$0.06 | 0.09$\pm$0.06 | 0.09$\pm$0.05
$F_{X}$ ($\times 10^{-9}$ erg cm-2 s-1) | 6.7$\pm$0.7 | 8.5$\pm$0.9 | 9.7$\pm$1.0 | 8.6$\pm$0.9 | 9.8$\pm$0.1 | 9.4$\pm$0.9
$\chi^{2}_{\nu}$ (d.o.f.) | 0.69(151) | 0.71(142) | 0.83(142) | 0.79(146) | 0.69(154) | 0.66(162)
| 07 | 08 | 09 | 10 | 11 |
| (Ni08+Ni09) | (Ni10) | (Ni11+Ni12) | (Ni13+Ni14) | (Ni15+Ni16+Ni17) |
$N_{\rm H}$ ($\times$1022 cm-2) |  $0.170\pm$0.005 | $0.168\pm 0.005$ |  $0.170\pm$0.005 |  $0.167\pm$0.005 |  $0.165\pm$0.004  |
$\Gamma$ | $1.84\pm 0.09$ | 1.99$\pm$0.05 | $1.79^{+0.10}_{-0.12}$ | $1.73^{+0.12}_{-0.11}$ |  $1.74\pm 0.09$ |
$kT_{\rm e}$ (keV) | 2.9${}^{+0.3}_{-0.2}$ |  $>$5.0 | 2.8${}^{+0.5}_{-0.3}$ | 3.0${}^{+0.5}_{-0.3}$ | 2.8$\pm$0.3  |
$K_{\rm compt}$ | 0.198${}^{+0.013}_{-0.012}$ | 0.143${}^{+0.012}_{-0.003}$ | 0.149${}^{+0.014}_{-0.016}$ | 0.085${}^{+0.009}_{-0.008}$ | 0.165${}^{+0.014}_{-0.01\textordmasculine}$ |
$E_{\rm line}$ (keV) | 6.60${}^{+0.15}_{-0.10}$ | 6.59$\pm$0.30 | 6.74${}^{+0.15}_{-0.13}$ |  $>$6.4 | 6.67$\pm$0.10 |
$K_{\rm line}$ ($\times$10-3) | 1.8$\pm$0.6 | 1.0$\pm$0.9 | 1.8$\pm$0.7 | 0.5$\pm$0.4 | 2.0$\pm$0.6  |
$kT_{\rm disc}$ (keV) | 0.70$\pm$0.02 | 0.69${}^{+0.02}_{-0.01}$ | 0.69$\pm$0.03 | 0.73$\pm$0.03 | 0.71${}^{+0.03}_{-0.02}$ |
$R_{\rm disc}$ (km) | 15.0$\pm$4.0 | 13.0$\pm$4.0 | 13.0$\pm$5.0 | 12.0$\pm$3.0 | 13.0$\pm$4.0  |
$F_{X}$ ($\times 10^{-9}$ erg cm-2 s-1) | 9.5$\pm$1.0 | 6.6$\pm$0.7 | 7.4$\pm$0.7 | 5.2$\pm$0.5 | 8.4$\pm$0.8  |
$\chi^{2}_{\nu}$ (d.o.f.) | 0.61(163) | 0.91(139) | 0.71(149) | 0.65(151) | 0.53(156)  |
Table 5: Results of the spectral analysis of the single NICER spectra. Quoted
errors reflect 90% confidence level. The values of $R_{\rm disc}$ have been
calculated assuming a distance of 7.6 kpc (Kuulkers et al., 2003) and an
inclination of 45∘ (Anderson et al., 1997). Figure 9: Evolution of the main
spectral-timing parameters from the 2022 NICER campaign. In panel (a) we
report the flux in the 0.5-10 keV range as estimated from spectral fitting
(see sec. 3 for details). Panel (b) shows the NICER Hardness ratio (2-10
keV/0.5-2 keV). In panel (c) we display the NICER fractional RMS amplitude in
each of the NICER pointings considered in this work. The evolution of the main
best-fit parameters used in the spectral analysis (Sec. 3) is plotted in
panels (d)–(i). NICER timing analysis
---
| Ni01 | Ni02 | Ni03 | Ni04 | Ni05 | Ni06 | Ni07 | Ni08 | Ni09
RMS (%) | 3.3$\pm$1.0 | 3.4$\pm$1.0 |  $<$4.0 | 3.4$\pm$1.2 |  $<$6.1 | 3.0$\pm$0.7 | 2.8$\pm$1.7 | 3.1$\pm$0.7 | 3.9$\pm$1.4
| Ni10 | Ni11 | Ni12 | Ni13 | Ni14 | Ni15 | Ni16 | Ni17 |
RMS (%) | 3.5$\pm$2.2 | 3.6$\pm$2.0 | 2.6$\pm$1.7 | 2.6$\pm$1.3 |  $<$4.0 | 2.8$\pm$1.5 | 3.1$\pm$1.2 | 3.4$\pm$1.6 |
Table 6: Fractional RMS for each of the NICER observations used in this work.
The values have been calculated for the 0.5-10 keV energy range and for
0.1-100 Hz as frequency range. All reported errors and upper limits correspond
to a confidence levels of 3$\sigma$.