11institutetext: Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
22institutetext: Departamento de física, Universidade Federal de Minas Gerais,
Belo Horizonte, MG, 31270-901, Brazil 33institutetext: University of Tartu,
Faculty of Science and Technology, Tartu Observatory, Estonia 44institutetext:
Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120
Uppsala, Sweden 55institutetext: Science Division, Directorate of Science,
European Space Research and Technology Centre (ESA/ESTEC), Keplerlaan 1,
NL-2201AZ Noordwijk, the Netherlands

# Star-disk interactions in the strongly accreting T Tauri Star S CrA
N††thanks: PI (Perraut) Program 18AF12. Based on observations obtained at the
Canada-France-Hawaii Telescope (CFHT) which is operated by the National
Research Council of Canada, the Institut National des Sciences de l’Univers of
the Centre National de la Recherche Scientifique of France, and the University
of Hawaii.

H. Nowacki , 11<EMAIL_ADDRESS>E. Alecian 11 K. Perraut
11 B. Zaire 22 C.P. Folsom 33 K. Pouilly 44 J. Bouvier 11 R. Manick 11 G.
Pantolmos 11 A.P. Sousa 11 C. Dougados 11 G.A.J Hussain 55 S.H.P. Alencar 22
J.B. Le Bouquin 11

(Received June 9${}^{\text{th}}$, 2023; accepted August 3${}^{\text{rd}}$,
2023)

###### Abstract

Context. Classical T Tauri Stars are thought to accrete material from their
surrounding protoplanetary disks through funnel flows along their magnetic
field lines. Among them, those with high accretion rates ($\sim 10^{-7}$M⊙
yr-1) are ideal targets to test this magnetospheric accretion scenario in a
sustained regime.

Aims. We aimed at constraining the accretion-ejection phenomena around the
strongly-accreting Northern component of the S CrA young binary system (S CrA
N) by deriving its magnetic field topology and its magnetospheric properties,
and by detecting ejection signatures, if any.

Methods. We led a two-week observing campaign on S CrA N with the ESPaDOnS
optical spectropolarimeter at the Canada-France-Hawaii Telescope. We recorded
12 Stokes $I$ and $V$ spectra over 14 nights. We computed the corresponding
Least-Square Deconvolution (LSD) profiles of the photospheric lines and
performed Zeeman-Doppler Imaging (ZDI). We analysed the kinematics of
noticeable emission lines, namely He I $\lambda 5876$ and the four first lines
of the Balmer series, known to trace the accretion process.

Results.  We found that S CrA N is a low-mass (0.8 M⊙), young ($\sim$ 1 Myr),
and fully convective object exhibiting a strong and variable veiling (with a
mean value of 7 $\pm$ 2), which suggests that the star is in a strong
accretion regime. These findings could indicate a stellar evolutionary stage
between Class I and Class II for S CrA N. We reconstructed an axisymmetric
large-scale magnetic field ($\sim$ 70% of the total energy), primarily located
in the dipolar component but with significant higher poloidal orders. From the
He I $\lambda 5876$ narrow emission component radial velocity curve, we
derived a stellar rotation period of $P_{*}=7.3\pm 0.2$ days. We found a
magnetic truncation radius of $\sim$ 2 R∗ which is significantly closer to the
star than the corotation radius of $\sim$ 6 R∗, suggesting that S CrA N is in
an unstable accretion regime. The truncation radius being quite smaller than
the size of the Br$\gamma$ line emitting region, as measured with the GRAVITY
interferometer ($\sim$ 8 R∗), supports the presence of outflows, which is
nicely corroborated by the line profiles presented in this work.

Conclusions. The findings from spectropolarimetry are complementary to those
provided by optical long-baseline interferometry, allowing us to construct a
coherent view of the innermost regions of a young, strongly accreting star.
Yet, the strong and complex magnetic field reconstructed for S CrA N is
inconsistent with the observed magnetic signatures of the emission lines
associated to the post-shock region. We recommend a multi-technique,
synchronized campaign of several days to put more constrains on a system that
varies on a $\sim$ 1 day timescale.

###### Key Words.:

Stars: variables: T Tauri – Stars: individual: S CrA N – Stars: magnetic field
– Techniques: spectroscopic, polarimetric – Accretion, accretion disk

##  1 Introduction

Protoplanetary disks are gas- and dust-rich regions, mostly constituted of
hydrogen and helium gas, with a small fraction of their content in dust
grains. As the reservoir from which matter is accreted onto the star and
planets are built, they set the initial conditions for planet formation. In
the innermost regions of these disks, accretion flows, winds, and outflows are
essential to control angular momentum, alter the gas content, and drive the
dynamics of the gas (Alexander et al. 2014). While they are key elements for
understanding locally and globally the disk dynamics and its evolution, the
physical structure, the exact nature of the processes acting in these inner
regions, as well as their interplay, are still poorly constrained and not well
understood.

Classical T Tauri stars (CTTS) are young suns (¡ 2 M⊙) that still accrete from
their surrounding disk. The most accepted scenario is that accretion is
funneled by the stellar magnetic field (Hartmann et al. 2016; Bouvier et al.
2007) that is strong enough to truncate the circumstellar disk at a few
stellar radii from the central star. This magnetic field drives the ionized
gas of the inner disk that falls onto the central object, and forms shocks and
hot spots at high latitudes on the stellar surface (Camenzind 1990; Koenigl
1991; Espaillat 2022). These phenomena shape many properties of the accreting
objects and can be investigated by spectroscopy, spectropolarimetry, and
photometry as their host stars exhibit excess continuum emission in the
optical and near-infrared ranges, hot and cold spots, as well as broad,
intense, and variable emission lines in the visible and near-infrared ranges
(e.g., Alencar et al. 2012, 2018; Sousa et al. 2021, 2023).

The accretion regime depends on the large-scale magnetic field strength (i.e.,
usually a dipole), the angle between the dipolar magnetic-field and stellar
rotation axes, and the mass accretion rate (Kulkarni & Romanova 2008; Blinova
et al. 2016). It can be either stable when occurring through two funnels, one
per hemisphere, or unstable when several equatorial tongues penetrate the
stellar magnetosphere. These tongues are transient on timescales of the
stellar rotation period and can coexist with stable accretion funnels
(Kulkarni & Romanova 2008; Pantolmos et al. 2022). The transition between
these regimes strongly depends on the mass accretion rate: unstable accretion
is expected to be observed mostly in strong accretors rather than in low
accretors (Blinova et al. 2016). Strong accretors allow us to probe a
different accretion regime, through which all low-mass stars should go during
their early pre-main sequence (PMS) evolution as they move away from the
protostellar phase (Baraffe et al. 2017). Yet, they have been poorly explored
until now, because their variability in the optical domain complicates their
spectral analysis.

Until recently, the structure of the magnetosphere has been mostly probed
through indirect observations thanks to the measurements of magnetic field
strength and topology (Donati et al. 1997), and mass accretion rate estimates
(Manara et al. 2021; Alcalá et al. 2021). The drastic improvement of
sensitivity of optical long-baseline interferometers has opened a new
promising way to probe the interaction between the young stars and their inner
disks. The K-band interferometric beam-combiner GRAVITY at the VLTI (GRAVITY
Collaboration et al. 2017a) makes it possible to spatially resolve the Br
$\gamma$ line emitting region for a few T Tauri stars (Gravity Collaboration
et al. 2023). Combined with spectropolarimetry, this appears very promising as
it allows comparing the size of the Br $\gamma$ line emitting region with that
of the magnetosphere derived by spectropolarimetry, and thus to investigate
the accretion-ejection processes at (sub-)astronomical unit scale (Bouvier et
al. 2020; Gravity Collaboration et al. 2020, 2023).

With the aim of studying the peculiar accretion regime of a strong accretor
through complementary observing techniques, we focus our work on the North
component of the young binary system S Coronae Australis (S CrA N) as it is
one of the strongest accretors of the GRAVITY T Tauri sample ($\dot{M}\sim$
10-7 M⊙ yr-1; Gahm et al. 2018 ; Sullivan et al. 2019). To complete the
GRAVITY data set and better understand the accretion-ejection phenomena at
play, we have conducted an observing campaign with the optical
spectropolarimeter ESPaDOnS.

S CrA is a T Tauri binary system whose components are coeval (Gahm et al. 2018
and references therein) and separated by about 1.4” (Reipurth & Zinnecker
1993). Due to the inverse P Cygni profiles of its hydrogen H$\gamma$ and
H$\delta$ lines, Rydgren (1977) classified this system as a YY Ori object, a
sub-class of PMS stars characterized by their excess in the Ultra-Violet (UV)
and the inverse P Cygni structure in the high orders of the Balmer series
(Walker 1972). Many spectroscopic studies in the optical and near-infrared
ranges of S CrA have been reported in the literature and focused on
characterizing its veiling (Prato et al. 2003), its variability (Edwards 1979;
Sullivan et al. 2019), and more generally on the accretion-ejection processes
at play (Gahm et al. 2018). From these spectral analyses, S CrA N appears to
be highly obscured by a variable veiling and to exhibit a high mass accretion
rate onto the star, suggesting that this star might be transitioning between
the Class I and Class II stages of stellar evolution.

S CrA has been part of the ALMA survey of protoplanetary disks in the Corona
Australis region (Cazzoletti et al. 2019); a continuum emission at 1.3 mm with
a half-width of half-maximum of about 0.22” is detected around S CrA N; it
exhibits neither clear substructures nor an inner cavity with radii larger
than 25 au. S CrA N has also been observed in the mid-infrared range with the
MIDI instrument of the VLTI (Schegerer et al. 2009; Varga et al. 2018): a
half-flux radius of the continuum emitting region of about 1.4 au was derived,
but the observations did not allow to accurately constrain the disk
properties. More recently, the near-infrared continuum emission of S CrA N has
been partially resolved in the H-band with PIONIER (Anthonioz et al. 2015) and
in the K-band with GRAVITY (GRAVITY Collaboration et al. 2017b, 2021), and a
half-flux radius of about 0.1 au has been derived for this continuum emission.
Moreover, by fitting the continuum K-band interferometric data obtained with
GRAVITY, GRAVITY Collaboration et al. (2021) derived an inclination of the
inner disk of 27 ${}^{\circ}\pm$ 3∘. Thanks to the spectrometric capabilities
of GRAVITY, the Br$\gamma$ emitting region close to the star has also been
partially resolved (0.06-0.07 au), appearing more compact than the continuum
(GRAVITY Collaboration et al. 2017b; Gravity Collaboration et al. 2023).

In this paper, we report on the spectropolarimetric campaign we led on S CrA N
in the optical range to complete the GRAVITY near-infrared interferometric
study of Gravity Collaboration et al. (2023). The observations and the data
processing are described in Section 2. We present our results in Section 3 and
discuss them in Section 4.

##  2 Data

###  2.1 Observations

Table 1: Log of the ESPaDOnS observations of S CrA N including the Date of observation, Heliocentric Julian Date (HJD), total exposure time ($t_{\rm exp}$), Signal to Noise Ratios (SNR) as the average value computed in the order centered on 581 nm, and seeing as measured by the Mauna Kea Atmospheric Monitor (MKAM) at the time of observation. Date | HJD | $t_{\rm exp}$ | SNR(I) | SNR(V) | Seeing
---|---|---|---|---|---
(2018) | (-2458000) | (s) |  |  | (arcsec)
June 21 | 290.96670 | 3562 | 159 | 121 | 0.43
June 22 | 291.97893 | 3600 | 90 | 68 | 0.81
June 23 | 292.95395 | 3600 | 118 | 93 | 0.58
June 24 | 293.99200 | 3600 | 117 | 88 | 0.63
June 25 | 294.93505 | 3600 | 124 | 94 | 0.52
June 26 | 295.97417 | 3448 | 156 | 116 | 1.30
June 27 | 296.94506 | 3600 | 114 | 84 | 1.35
June 28 | 297.91663 | 3600 | 121 | 88 | 1.05
June 29 | 298.94801 | 3600 | 115 | 86 | 0.50
June 30 | 299.95373 | 3600 | 117 | 86 | 0.60
July 01 | 300.90393 | 3600 | 114 | 80 | 0.62
July 04 | 303.93473 | 3600 | 100 | 67 | 0.57

S CrA N was observed with ESPaDOnS (Donati 2003), the spectropolarimeter at
Canada France Hawaii Telescope (CFHT), for 11 consecutive nights from the
21${}^{\text{st}}$ of June to the 2${}^{\text{nd}}$ of July 2018, plus one
last observation on the 4${}^{\text{th}}$ of July. Altogether, they represent
a set of 12 observations over a spectral range from 367 nm to 1048 nm, with a
spectral resolution $R\sim 65\,000$. The log of the observations is given in
Table 1. Each observation consists of Stokes $I$, $V$, and null ($N$) spectra
per Heliocentric Julian Date (HJD). The Stokes $I$ parameter represents the
total intensity of the light and allows for a classical spectroscopic analysis
at a very high resolution. The Stokes $V$ parameter is the difference between
left and right circularly polarized light, which provides the observer with
information on the line-of-sight component of the magnetic field in the region
where the light comes from. The $N$ signal is computed in a way that cancels
the polarization of the incoming light. It is used to check for spurious
polarization signals in the Stokes $V$ data: any detection in Stokes $V$
tallying with a $N$ signal significantly above its Root Mean Square (RMS)
noise should be considered spurious.

Since the separation between S CrA N and S Cra S is 1.4” while the average
seeing at CFHT was 750 mas during our observations, we made sure that the
contribution of S CrA S to the total observed flux was negligible (see
Appendix A for the complete treatment). In the end, the average contribution
of S CrA S is as low as 1.7%, with 3 observations exceeding a contribution of
5% : June 26, 27 and 28 with 9.0%, 9.3% and 5.3%, respectively. We considered
these contributions negligible for the rest of the study but stayed vigilant
to any unexpected behaviour that would come out from any of these three
observations.

###  2.2 Data reduction

The data were reduced automatically through the Libre ESpRIT procedure (see
Donati et al. 1997). This reduction also includes the normalization of the
Stokes $I$ continuum, which was imperfect in the case of S CrA N due to the
high activity of the object. The numerous intense emission lines led to a
biased estimation of the continuum level in some spectral windows. We used the
SpeNT code developed by Martin et al. (2018) to refine the normalization of
our spectra until the continuum level varied by no more than the RMS signal
outside any line in Stokes $I$. The code fits a third order spline to the
continuum considering a $\sigma$-clipping procedure to automatically reject
absorption/emission lines. Nevertheless, this procedure can be manually
adjusted by visually rejecting any fixed point of the spline should the
considered portion of the spectrum be highly variable. For S CrA N, we
performed the fit on the average spectrum of all the Stokes $I$ spectra in our
sample. Then, the resulting normalization was applied to all the spectra. This
procedure proved to be essential to obtain good normalized spectra for S CrA
N.

We recovered 12 good-quality spectra (one per night) displaying the usual
telluric lines, photospheric lines, and classical emission lines for CTTS, as
previously reported for this object (Gahm et al. 2018). We present a portion
of the spectra in Fig. 1 where all these different features are visible at the
same time. Photospheric lines are present but appear very weak on average
(about 5% of the continuum level) due to veiling over the whole range of
observation. The emission lines are particularly intense on average, with
variable shapes (e.g. the iron lines on the left of Fig. 1). Many of the
observed emission lines sensitive to the magnetic field exhibit significant
Stokes $V$ counterparts, suggesting a strong magnetic field (these lines are
presented in Appendix B). Finally, the telluric lines were not removed since
no line of interest was located inside a telluric region.

###  2.3 Least Square Deconvolution

Figure 1: Portion of all the normalised spectra. Each color stands for one
observation. The same color code will be used for the rest of the study.

One convenient way to look at these data is to compute their Least Square
Deconvolution (LSD) profiles in both Stokes $I$ and Stokes $V$ spectra (Donati
et al. 1997): the photospheric absorption lines and their Stokes $V$
counterpart are weighted by their central wavelength, depth and Landé factor;
then these weighted lines are averaged altogether over one observation. We
built a mask that identifies the lines to include in this computation using
the VALD database111VALD database : http://vald.astro.uu.se/(Piskunov et al.
1995; Ryabchikova et al. 2015): by scanning the average spectrum over-plotted
to a synthetic spectrum produced with the MARCS stellar atmosphere model
(Gustafsson et al. 2008), we searched for undisturbed photospheric lines to be
included. We paid particular attention not to include absorption lines
contaminated by emission or telluric lines. Usually, the LSD $I$ profiles
obtained exhibit distortions that are attributable to spots located at the
photosphere level. In the case of LSD $V$, these profiles are shaped by the
magnetic field along the line of sight at the surface of the star. The weak
field approximation assumes that the broadening of the photospheric profiles
due to the Zeeman effect (proportional to the local magnetic intensity along
with the Landé factor and the central wavelength of a line) is negligible
compared to all the other sources of broadening (instrumental broadening,
thermal Doppler broadening, non-thermal Doppler broadening, microturbulent and
macroturbulent velocities dispersions). Combined in quadratic sum, these
effects correspond to a broadening of $\Delta
v_{\text{tot}}\leavevmode\nobreak\ =\leavevmode\nobreak\ 16.58$ km/s. For the
specific case of S CrA N observed with ESPaDOnS, this $\Delta v_{\text{tot}}$
translates into $B\ll 10\leavevmode\nobreak\ \text{kG}$. In other words, the
use of the LSD profiles is justified under the condition that the surface
averaged magnetic field does not reach 10 kG or more.

After applying the LSD computation with a Landé factor of 1.2 and a central
wavelength of 500 nm to the complete Stokes $I$ and $V$ spectra, we obtain 12
set of LSD $I$, LSD $V$ and LSD $N$ profiles (Fig. 2): one profile represents
one observation date, which will be mentioned as (HJD - 2458000) hereafter
(see Table 1), for convenience. We report that the LSD $N$ profiles show no
spurious signal at any velocity for any observation.

Figure 2:  LSD $I$ and $V$ profiles of S CrA N sorted by HJD (HJD - 2458000
mentioned on the right of each plot) normalized by the maximum EW, observed at
date 303.93. The color coding is the same as in Fig. 1. The spacing between
two profiles stands for the time span between the observations. Each profile
is represented with a solid colored line and is surrounded by its
uncertainties in faded color. Black dotted lines represent the reference Voigt
profile for the $I$ profiles and the continuum for the $V$ profiles. Dashed
vertical lines represent the radial velocity of the star. $V$ profiles are
magnified by a factor 5 for clarity.

##  3 Results

Table 2: Stellar parameters of S CrA N.

Parameter | This work | Literature | Method in the literature | Our method (if different)
---|---|---|---|---
$T_{\text{eff}}\leavevmode\nobreak\ [K]$ | $4300\pm 100$ | 4250 | Fit of photospheric linesaa$a$Gahm et al. (2018); | Fit of photospheric lines
$4800\pm 400$ | Comparison to spectral type standard starbb$b$Prato et al. (2003);
$v\sin{i}\leavevmode\nobreak\ [km/s]$ | $10\pm 2$ | 12 | Fit of photospheric linesaa$a$Gahm et al. (2018); |
$r$ | $[4-11]$ | 8.3 | Fit of photospheric linesaa$a$Gahm et al. (2018); |
$v_{r}\leavevmode\nobreak\ [km/s]$ | $0\pm 1$ | $0.9\pm 2.5$ | Fit of photospheric linesaa$a$Gahm et al. (2018); |
$d\leavevmode\nobreak\ [\text{pc}]$ | $152.4\pm 0.4$ | 129 |  $uvby,\beta$ photometrycc$c$Marraco & Rydgren (1981); | ”On-cloud” sub-region distanceee$e$Galli et al. (2020);
$138\pm 16$ | Light echoes analysisdd$d$Ortiz et al. (2010);
$L_{*}\leavevmode\nobreak\ [L_{\sun}]$ | $1.67\pm 0.8$ | $2.29^{+0.76}_{-0.65}$ | Fit of SEDbb$b$Prato et al. (2003); | Distance-corrected valuebb$b$Prato et al. (2003);.
$M_{*}\leavevmode\nobreak\ [M_{\sun}]$ | $0.8\pm 0.1$ | 0.7ff$f$Sullivan et al. (2019) | From $T_{\text{eff}}$ assuming an age of 2 Myr | Position in HR diagram
$R_{*}\leavevmode\nobreak\ [R_{\sun}]$ | $2.3\pm 0.6$ |  |  | Position in HR diagram
$P_{*}$ [days] | $7.3\pm 0.2$ | $4.2\pm 1$ | Periodicity in the He I narrow componentaa$a$Gahm et al. (2018); |
$\log g\leavevmode\nobreak\ [\text{dex}]$ | $3.6\pm 0.2$ |  |  | Direct computation

222 References for the values and method in the literature.

In this section, we present the methods used for the analysis of the set of
data introduced above, and present our results.

###  3.1 Fit of the Stokes $I$ spectra

We used the ZEEMAN code (Landstreet 1988; Wade et al. 2001; Folsom et al.
2018) to derive the stellar parameters of S CrA N from the fitting of
photospheric lines in our spectra. The ZEEMAN code solves the radiative
transfer assuming Local Thermodynamic Equilibrium (LTE) in a 1D stellar
atmosphere. We used the MARCS stellar atmosphere model and the theoretical
properties of the photospheric lines are extracted from the VALD database as
mentioned in Sect. 2.3. Then, the procedure for ZEEMAN is to adjust a
synthetic spectrum to an observed one by minimizing a $\chi^{2}$ function
taking into account its seven free parameters, which are the effective
temperature $T_{\text{eff}}$, the equatorial rotation velocity of the star
projected on the line of sight $v\sin{i}$, the radial velocity $v_{r}$, the
local veiling $r$ taken to be an excess continuum flux as a fraction of
continuum, the surface gravity $\log g$, the micro-turbulent velocity
$v_{\text{mic}}$, and the macro-turbulent velocity $v_{\text{mac}}$. A 7D
$\chi^{2}$ map being likely to display several local minima, we adjusted the
parameters by pairs: $T_{\text{eff}}$ along with $r$, then $v\sin{i}$ along
with $v_{r}$, then $v_{\text{mic}}$ along with $v_{\text{mac}}$, $\log g$
being adjusted on its own. At first, all constant parameters were set to an
arbitrary value until a minimum $\chi^{2}$ was reached for a considered pair
of parameters. Then, the two previously fitted quantities were set constant to
their new value, before fitting two new parameters until reaching a new
minimum $\chi^{2}$, which gives two different constant values to the new
couple of parameters, and so on until we fitted all parameters. Then, the
procedure is repeated until a whole cycle of fitting produces no variation in
any of the parameters. We tested the sensitivity to initial conditions by
setting different starting values for each parameter, but the procedure always
converged to the same set of values, except for $\log g$ and $v_{\text{mic}}$.
Their values did not change, regardless of the number of cycles performed,
which shows little sensitivity of our fit to these parameters. For the
procedure to run, we fixed $\log g$ = 4.0, which is common for CTTS, and
derived the mass and radius as described in Sect. 4. Concerning
$v_{\text{mic}}$, we retained a value of 1 km/s minimizing the $\chi^{2}$
function for the procedure to run, but did not derive any uncertainties based
on the $\chi^{2}$ function. This fitting is done over 15 spectral windows (the
central wavelength of which are mentioned in Fig. 3) that display clear
photospheric lines (i.e., deeper than 10% of the continuum level).

All our results are gathered on the first four rows of Table 2. Each value
corresponds to the average of the values over the 15 spectral windows, and the
uncertainty corresponds to their standard deviation. We obtained an effective
temperature of ($T_{\text{eff}}=4300\pm\leavevmode\nobreak\ 100$ K). We
retrieved a rotational velocity of $v\sin{i}$ = 10$\leavevmode\nobreak\ \pm$ 2
km/s, where $i\leavevmode\nobreak\ =\leavevmode\nobreak\ 0^{\circ}$
corresponds to a face-on object. We obtained a radial velocity of $v_{r}$ = 0
$\pm$ 1 km/s, and a macroscopic turbulence velocity $v_{\text{mac}}$ = 11
$\pm$ 3 km/s. When plotting the veiling values against the spectral windows in
which it is measured, no clear trend is observed unlike in most CTTS where
veiling decreases with wavelength in the optical domain (see e.g. Fischer et
al. 2011). When plotting the veiling as a function of time for different
spectral windows (Fig. 3), no clear periodicity can be identified, suggesting
that an additional source must be at play, on top of the continuum emission
from an accretion spot (e.g. accretion-powered emission lines). The mean
veiling $r$ over the 15 spectral windows and over time is as high as 7 on
average, and ranges between 4 and 11.

Figure 3: Evolution of the average optical veiling with time. For each date,
each color point stands for the mean veiling over one spectral window whose
center value is indicated in the caption. The error bars are centered on the
average of the values computed over the 15 spectral windows and spread over
their standard deviation.

###  3.2 Variability in LSD profiles

The LSD $I$ profiles presented in Fig. 2 show strong variability in intensity,
which is unsurprising due to changes in veiling intensity. Indeed, we found a
negative correlation between the mean veiling and the equivalent width (EW) of
the LSD $I$ profile at each date. Thus, both LSD $I$ and $V$ profiles were
scaled to the greatest EW (occurring at the Julian date 2,458,303.93) so they
all had the same EW. By doing so, one retains only their intrinsic shape
variability presumably due to spots.

The shape of the LSD $I$ profiles changes entirely from one date to the
following (Fig. 2). From date 291.98 to 292.95, for instance, the minimum
intensity switches from the red to the blue side of the profile, and the small
excess observed in the blue wing at first becomes reddened at 292.95. Then at
date 303.93, the profile looks just like the one at 291.98 again, with only
minor changes in intensity. To try and constrain the origin of this
variability, we checked whether the LSD $I$ profiles were deformed
differently, depending on the intrinsic depth of the lines included in the LSD
mask (see Appendix B for the detailed procedure). It results that no matter
the depth limit of the lines taken into account for the LSD computation, the
shapes of the profiles remain the same, with just a loss in signal-to-noise
ratio (SNR) when removing more lines. We could not find a way to compute LSD
$I$ profiles with attenuated perturbations, and therefore adopted the LSD mask
that gives the best SNR in the line profiles.

The source of these distortions must break the spherical symmetry of the
surface of the star, and considering the high variability of our LSD $I$
profiles, we cannot interpret them as deviations from a rest profile. Hence,
we compared the LSD $I$ profiles to a synthetic Voigt profile. We adjusted
this profile by fitting it to the median LSD $I$ observed within a velocity
range of [-25 km/s; +25 km/s]. This reference profile is shown as a dotted
line over the LSD $I$ profiles in Fig. 2.

When looking at the $V$ profiles, they also exhibit a variety of shapes, from
flat (date 303.93) to typically anti-symmetric (e.g. at date 292.95). We also
note that similar $I$ profiles can display very different $V$ profiles. That
is the case for profiles at dates 293.99 and 303.93, where the $I$ profiles
are very similar, but the $V$ profiles are respectively strong and flat.
Conversely, at dates 291.98, 292.95, and 293.99, the $V$ profiles remain
constant in intensity over those 3 observations, with just a smooth drift of
the centroid from negative to positive velocities. In contrast, the $I$
profiles are drastically different. There is no evident correlation between
the $I$ and $V$ variations, suggesting that brightness inhomogeneities at the
surface of S CrA N might have additional sources besides brightness spots
induced by the magnetic activity.

To recover the stellar rotation period, we computed 2D periodograms for the
LSD $I$ and $V$ profiles (Fig. 4). We ran a Lomb-Scargle periodogram routine
over each velocity channel (i.e., wavelength) to build the periodograms, where
a time series of 12 unevenly sampled observations were considered. We
restrained the search for periods larger than 2 days (Shannon theorem applied
to a 1 day sampling, which is the smallest sampling of our data) and smaller
than 14 days. Any periodicity above -or near- 14 days cannot be considered
reliable since that was the total span of our observations. False Alarm
Probability (FAP) contours of $3\%$ are drawn in Fig. 4. All the FAPs of this
study were computed assuming white noise in the continuum, i.e. independent
measurements, following the method described in Zechmeister & Kürster (2009).
The 2D periodograms reveal no apparent periodicity in the LSD $I$ profiles.
While these profiles might be influenced by stochastic activity in the post-
shock region (see, e.g. Petrov et al. 2011; Dodin & Lamzin 2012; Rei et al.
2018), which could explain the deformations observed and hide periodic
features from hot/cool surface spots, the LSD $V$ profiles are more robust to
such a contamination since the intensity of the magnetic field decreases
rapidly with distance to the stellar surface ($\propto r^{-3}$ at least, for a
pure dipole). While the LSD $I$ profiles display no clear periodicity, we can
compute, for each line of the LSD $V$ periodogram, the 2D periodogram’s powers
weighted by a 1-FAP factor over a range of velocity narrowed to the region of
variability of the profiles (i.e., [-20 km/s; +20 km/s]). We are left with a
1D weighted periodogram whose peak’s maximum is the stellar rotation period
and whose standard deviation is the uncertainty. That yields a period of
$7.6\pm 1.3$ days located at the extrema of the $V$ profile, where the
amplitude variation is the most important, strengthening the reliability of
this signal detection.

Figure 4: 2D periodograms for the LSD $I$ (left) and $V$ (right) profiles. The
dashed lines correspond to a period of 7.6 days (red) and FAP = 3% contours
(black). Below the periodograms are shown the average profiles (black line)
surrounded by their 1$\sigma$ deviations (light blue).

###  3.3 Variability in emission lines

CTTS are known to show strong and broad Balmer emission lines, as well as a
narrow emission in He I lines. They are all often associated with red-shifted
absorption features, indicating infall of material (Edwards et al. 1994;
Beristain et al. 2001). It is now well accepted that a good part of these
lines are formed through magnetospheric accretion (Hartmann et al. 1994,
2016). In our spectra, the Balmer and He I lines show various features, both
in emission and absorption, as well as strong variability. We therefore report
below our analysis on this variability to understand the origin of formation
of these lines, and how they can constrain the magnetospheric accretion
processes in a strongly accreting T Tauri star as S CrA N.

Figure 5: He I $\lambda$5876 line for all observations. Stokes $I$ (top) is
normalised in intensity with respect to the continuum. Stokes $V$ (bottom) is
magnified by a factor 5 to make it more visible. The color code is the same as
Figure 2. Solid black lines are the average spectra. Dashed black lines
represent the continuum level for each component. The dotted black line is the
radial velocity of the star. The inset plot is a zoom on the absorption
component.

#### Helium I $\boldsymbol{\lambda 5876}$.

This line can be composite with up to 3 distinct components, which are
particularly discernible in the case of S CrA N (Fig. 5-top):

  * •

A narrow component (NC) which is asymmetric and goes from -30 km/s to 50 km/s
and peaks around 0 km/s. Due to its very high excitation potential, this
emission line is believed to trace accretion footprints at the surface of the
star.

  * •

A broad component (BC), as wide as $\pm$ 250 km/s and well reproduced by a
Gaussian fit. Its origin is still poorly constrained, but might itself be
composite.

  * •

An absorption component (AC) in the red wing of the broad component (between
$\sim 200$ and $\sim 350$ km/s).

Strong Zeeman signatures are present in Stokes V spectra (Fig. 5-bottom). The
S-shaped signature spreads from -30 km/s to +50 km/s on average and is as
strong as 20% of the continuum intensity. Due to its broadening and asymmetric
shape, this $V$ signal is attributed to the NC and thus traces the magnetic
field at the footprint of the accretion columns. In order to study all the
components separately, a fit with 3 independent Gaussian profiles was applied
to each observed I profile. Each component is extracted by removing the models
of the two other components from the profiles: the BC and AC Gaussian models
were subtracted to the whole line as they did match the shape and intensity of
the observed BC and AC at all phases. On the contrary, due to the intrinsic
asymmetry of the NC, removing its Gaussian model left significant NC residuals
in the extracted BC and AC profiles. Instead, a smoothed NC was subtracted
from the original total profile, along with the AC/BC Gaussian model. This
smoothed NC was obtained using a three-point moving average of the extracted
NC.

We performed radial velocity, equivalent width and longitudinal field
measurements in the NC. The longitudinal field is obtained thanks to the first
moment method (Donati et al. 1997; Wade et al. 2000) The equivalent width is
computed between -30 km/s and +50 km/s. Finally, we measured the radial
velocity of the NC’s centroid by computing the first moment of the profile at
each date. All three quantities are presented in Table 3 and Fig. 6. The
radial velocity modulation was used to estimate the stellar period thanks to a
point-like accretion spot model described in further detail in Pouilly et al.
(2021). We obtained a period $P=7.3\pm 0.2$ days.

The 2D periodograms were computed for $V$ profiles and all three Stokes $I$
components (Fig. 7). Each emitting component displays its own periodicity. The
center of the NC shows a 7.4 $\pm$ 1.4 days period with strong significance
(FAP ¡ $3\%$). However, this period drifts down to 6.6 $\pm$ 1.3 days in the
red wing (above +30 km/s). The BC shows a 3.2 $\pm$ 0.3 days period with a
much lower significance (FAP $\sim 15\%$), whereas there is no signal at 7.4
days. The high power signal at long periods cannot be considered significant
since it could not be observed for a full cycle, and the white noise
assumption in the FAP computations tends to overestimate its significance
level. The AC displays a 6.6 $\pm$ 1.3 days period from 0 to +200 km/s, and a
3.4 $\pm$ 0.4 days period beyond +200 km/s. Both periods are detected with a
high significance level (FAP ¡ $3\%$). All the derived periods are gathered
and compared in Fig. 8, and will be discussed in Sec. 4.

Table 3: Radial velocities, equivalent width and longitudinal field derived for each phase in the He I NC. Phase | Radial vel. | Equ. width | Long. field
---|---|---|---
($\pm$ 0.03) | (km.s-1) | (km.s-1) | (kG)
0.00 | 1.373 $\pm$ 0.003 | 41 $\pm$ 1 | 1.17 $\pm$ 0.03
0.14 | 2.35 $\pm$ 0.04 | 54 $\pm$ 2 | 1.30 $\pm$ 0.05
0.27 | 2.54 $\pm$ 0.03 | 74 $\pm$ 2 | 1.68 $\pm$ 0.04
0.41 | 2.37 $\pm$ 0.03 | 66 $\pm$ 2 | 1.31 $\pm$ 0.03
0.54 | 2.40 $\pm$ 0.03 | 63 $\pm$ 2 | 1.12 $\pm$ 0.03
0.69 | 1.80 $\pm$ 0.02 | 42 $\pm$ 1 | 1.08 $\pm$ 0.03
0.82 | 0.99 $\pm$ 0.01 | 44 $\pm$ 2 | 0.84 $\pm$ 0.03
0.95 | 0.88 $\pm$ 0.01 | 46 $\pm$ 2 | 1.37 $\pm$ 0.05
1.09 | 1.96 $\pm$ 0.04 | 50 $\pm$ 2 | 1.33 $\pm$ 0.04
1.23 | 2.27 $\pm$ 0.04 | 48 $\pm$ 2 | 1.32 $\pm$ 0.04
1.36 | 2.80 $\pm$ 0.02 | 93 $\pm$ 2 | 1.08 $\pm$ 0.02
1.78 | 1.91 $\pm$ 0.03 | 43 $\pm$ 2 | 1.01 $\pm$ 0.05
Figure 6: Radial velocities (top), equivalent width (middle), and longitudinal
magnetic field (bottom) of the He I NC as a function of the stellar phase,
when considering a stellar rotation period of $7.3\pm 0.2$ days and
considering the first date of observation as $\phi=0$. When not visible,
uncertainties are smaller than the symbol. Dotted black lines illustrate the
best fits obtained, with a simple sine (middle and bottom) and the model of
Pouilly et al. (2021) (top). The color code is the same as in Fig. 1.

Figure 7: 2D Periodograms of the Stokes $I$ NC (upper-left), BC (lower-left),
AC (lower-right), and Stokes $V$ (upper-right) in He I $\lambda$5876\. The red
dashed lines mark a period of 7.4 days (NC and Stokes $V$), 3.2 days (BC and
AC), and 6.6 days (AC). The black dashed contours denote a constant FAP of 3%
(except 15% for the BC). Below the periodograms are shown the average profiles
(black line) surrounded by their 1-$\sigma$ deviations (light blue). Figure 8:
Comparison of all the periods derived in this study, gathered according to
what profile gave them. Red dashed vertical lines illustrate the stellar
rotation period ($P_{*}$) and half its value, surrounded by their uncertainty
(light blue shade). All values are estimated from 2D periodograms except for
(a), which is derived from radial velocities, and is chosen as $P_{*}$.

#### Balmer series.

The detectable Balmer lines in the ESPaDOnS spectral range are displayed in
Fig. 9. The corresponding periodograms exhibit signals at periods similar to
those found in the LSD and Helium profiles (see Appendix B). Still, the
regions of the lines concerned with these periods are not the same for all the
lines, making it hard to interpret which physical process causes their
variability. General behaviours can be retrieved nonetheless. The emission
lines are broad and asymmetric, ranging from -400 km/s to +400 km/s (even more
for H$\alpha$). Albeit variable in intensity and shape, a persistent blue-
shifted absorption is present at all phases (peaking at about -100 km/s). On
top of this absorption, a narrow emission can be observed in H$\delta$ and
H$\gamma$, along with a red-shifted absorption spreading from +50 to +300
km/s. A similar red-shifted absorption is barely detected in H$\beta$ and
cannot be seen in H$\alpha$, although its underlying presence could explain
the asymmetry of the far wings in the latter. The exact span of this
absorption is not the same for all the lines though. The complexity of the
Balmer lines can be interpreted as a multi-component origin of the hydrogen
emission, coming from different phenomena and/or different locations in the
inner disk and magnetospheric regions, which will be discussed in Section 4.

Figure 9: Balmer series in S CrA N. The color code is the same as Fig. 2. The
vertical dotted line shows the stellar radial velocity, while the horizontal
dotted lines show the continuum level for each line. The y-scale of H$\alpha$
has been changed, for clarity.

Figure 10: Correlation matrices in He I (top row): auto-correlation of the
full Helium line at 587.6 nm (left), correlation between the He I NC and the
$V$ profile (middle), and correlation between the He I BC and the $V$ profile
(right). Correlations matrices in H$\alpha$ (bottom row): auto-correlation of
the full H$\alpha$ line (left), correlation between the H$\alpha$ line and the
full He I line (middle), and correlation between the H$\alpha$ line and the He
I $V$ profile (right). The dashed black contours show the $2\sigma$
significance level. The average profiles are represented on the bottom and
left side of each panel (solid black line) and are surrounded by their
standard deviation (light blue shade), with the continuum level shown with
dashed black lines.

###  3.4 Correlations in spectral lines

We computed correlation matrices based on the Pearson coefficients to
highlight different behaviours within a line profile and/or to link different
lines between them (see e.g. : Kurosawa et al. 2005; Pouilly et al. 2020).
More explicitly, for two given lines, one can compute the correlation between
each pixel (i.e., velocity channel or wavelength) of the first line and each
pixel of the second line, thanks to the time series of these lines. Given a
pixel $i$ in the first line and a pixel $j$ in the second line, the
correlation coefficient $R_{ij}$ between these pixels is given by:

$R_{ij}=\frac{C_{ij}}{\sqrt{C_{ii}C_{jj}}}$ (1)

with $C_{ij}$ the covariance between $i$ and $j$ :

$C_{ij}=\frac{1}{N-1}\sum_{k=1}^{N}\left(F_{i,k}-\overline{F_{i}}\right)\left(F_{j,k}-\overline{F_{j}}\right)$
(2)

where $N$ is the number of observations (12 here), $F_{i,k}$ is the flux in
pixel $i$ for observation $k$, and $\overline{F_{i}}$ is the mean flux in
pixel $i$ over the $N$ observations.
The coefficients of $R_{ij}$ hence range from -1 (perfect anti-correlation) to
+1 (perfect correlation), with a null value meaning no correlation. To define
some value above which we would consider a correlation level as significant,
we computed 1 billion samples where two random variables were taken 12 times
(one for each observation) in a white noise equivalent to our Stokes $I$ RMS =
0.05. This gives a Gaussian distribution of $R_{ij}$ centered on 0 and with
$\sigma=0.38$. We chose to take a 2$\sigma$ level of significance,
corresponding to $\lvert R_{ij}\rvert\geq 0.76$ for significant correlation,
while $0.38\leq\lvert R_{ij}\rvert\leq 0.76$ will correspond to a moderate
correlation, and $\lvert R_{ij}\rvert\leq 0.38$ to low correlation.

#### Correlations in He I.

The decomposition of the Helium line into BC and NC components is well
justified by the auto-correlation matrix of the whole line (Fig. 10-top-left).
These components are neither correlated nor anti-correlated. Hence, their
origin is linked to different processes. When checking for the correlations
between each component and the Stokes $V$ signature, the NC is well correlated
with the positive peak of the $V$ profile, while anti-correlated with the
negative peak. The BC displays no clear correlation with any part of the $V$
profile, confirming that the $V$ signal is produced by the magnetic field in
the region of formation of the NC, and is unrelated with the BC formation.

#### Correlations in $\boldsymbol{H\alpha}$.

Fig. 10-bottom-left shows the auto-correlation matrix of the H$\alpha$ line.
Two main components can be identified: a main broad symmetric emission (from
-400 to 400 km/s), truncated by a strong absorption from -200 to 0 km/s. It
should be noted that this blue-shifted absorption is actually twofold: a
saturated part spreads between -200 and -100 km/s, and a variable one between
-100 and 0 km/s. This variable component is moderately anti-correlated
($R_{ij}<-0.38$) with the broad emission.

#### Cross-correlations between He I and $\boldsymbol{H\alpha}$.

All the correlations found between the H$\alpha$ and the He I lines are
moderate compared to the ones found for the previously mentioned auto-
correlations matrices. Still, hints for possible correlation are visible and
presented here. Fig. 10-bottom-middle shows that the He I NC seems correlated
with the saturated part of the blue-shifted absorption in the H$\alpha$ line,
even though the correlation coefficient does not reach the 2$\sigma$
significance level. This partial correlation is confirmed when inspecting Fig.
10-bottom-right. Indeed, the $V$ profile exhibits the same correlation pattern
with both the variable part in the blue-shifted absorption of H$\alpha$ and
the He I NC (see Fig. 10-top-middle). A moderate anti-correlation
($R_{ij}\sim-0.38$) is found between the variable blue-shifted absorption of
H$\alpha$ and the He I BC. However, considering the previous results, a
negative correlation between the He I V profile and the He I BC should be
found (Fig. 10-top-right), which is not the case. Either there is no
correlation between these components, or the underlying correlation is being
quenched due to a potential cross-talk. Such a moderate correlation can also
be found between the whole blue-shifted absorption of H$\alpha$ and the He I
AC, with $R_{ij}\sim 0.38$ (green light area at the top of Fig. 10-bottom-
middle). Only this time, we do not have other diagnoses to confirm this
correlation.

###  3.5 Magnetic field reconstruction

Figure 11: Polar projection of the magnetic maps (right) reconstructed from
the LSD $V$ observations (left, coloured lines). Black crosses overplotted to
the LSD profiles show the reconstructed $V$, on the right of which the cycle
number and phase are mentioned. The red ticks surrounding each map show the
observed phases, going increasingly clock-wise, starting from the South
direction. Dashed black circles show colatitudes of $27^{\circ}$ (i),
$63^{\circ}$ (90-i) and $117^{\circ}$ (90+i). The solid black line shows the
equator.

The Zeeman Doppler Imaging (ZDI) technique uses the rotational modulation of
Stokes $V$ profiles to infer the large-scale magnetic configuration. We use
the ZDIpy code which assumes a decomposition of the field in spherical
harmonics and adopts a weak-field approximation to reconstruct it’s topology,
as described in full details in Folsom et al. (2018). ZDIpy applies a
regularized fitting algorithm that simultaneously maximizes the entropy of the
reconstructed topology while keeping the corresponding $\chi^{2}$ below some
target value (Skilling & Bryan 1984). The obtained map is therefore
interpreted as the minimal information map fitting the observed LSD $V$ data
with a goodness determined by the target $\chi^{2}$.

The ZDI procedure described above usually also fits Stokes $I$ profiles to
reconstruct the brightness distribution of the star. However, for S CrA N, we
never reached a satisfying fit for the LSD $I$. That is why a uniform
brightness was assumed. This uniform brightness was obtained with a Voigt
model fitting the observed median shape of LSD $I$ (see Fig. 2). In order to
reconstruct the magnetic maps, one needs to know the stellar rotation period
and inclination with respect to the line of sight. From the variability
analysis of the He I line, we adopt a stellar period $P_{*}=7.3\pm 0.2$ days
(see Table 2). Combining this stellar period with $v\sin{i}$, and a radius
estimate presented in Section 4, we derive the star’s inclination
$i=39^{\circ}\pm 16^{\circ}$, which is in agreement at a 1-$\sigma$ level with
the inclination of the inner disk as determined by GRAVITY Collaboration et
al. (2021) (27 ${}^{\circ}\pm$ 3∘). Considering the propagation of
uncertainties in the computation of our stellar inclination, we adopt
hereafter the value from GRAVITY Collaboration et al. (2021) as the
inclination of the star: $i=27^{\circ}\pm 3^{\circ}$. The ZDI procedure ran
over 16 iterations to maximize entropy reaching the target reduced $\chi^{2}$
of 1.5. This value represents the smallest target we could reach without
fitting the noise of the data. The spherical harmonics expansion was truncated
to consider only the modes where $l\leq 10$ and reproduced the LSD $V$
profiles between -25 km/s and +25 km/s.

The reconstructed $V$ profiles are over-plotted to the observed LSD $V$
profiles along with the derived magnetic maps in Fig. 11. The three maps
represent the projection of the magnetic vector on the spherical basis, which
translates into a radial field (positive polarity meaning a vector going out
of the surface), azimuthal field (positive polarity meaning a vector oriented
clock-wise), and meridional field (positive polarity meaning a vector oriented
toward the South direction). We represent on each map the rotation phases at
which each observation is obtained, with the initial phase $\phi=0$
corresponding to the first date of observation. The large-scale magnetic field
best reproducing our Stokes V profiles is as strong as 5.4 kG (which is within
the weak-field approximation validity domain), with a mean intensity of 950 G,
and a global axisymmetry of 68%. The poloidal component of this field (82% of
the total energy) is primarily located in the dipolar component, which
represents 27% of the total magnetic energy, even though higher order poloidal
modes are significantly present (up to 25% and 16% of the total magnetic
energy for the quadrupole and the octupole, respectively). This dipole’s
maximum intensity (816 G) is reached at intermediate latitude ($56^{\circ}$),
at phase 0.29. The main magnetic properties of the system are listed in Table
3.

Table 4: Main magnetic field properties from ZDI.

Property | Value
---|---
Maximum intensity | 5.4 kG
Mean intensity | 950 G
Axisymmetryaa$a$expressed in % of the total magnetic energy | 68 %
Toroidal fieldaa$a$expressed in % of the total magnetic energy | 18%
Axisymmetrybb$b$expressed in % of the toroidal field’s magnetic energy | 41 %
Poloidal fieldaa$a$expressed in % of the total magnetic energy | 82%
Axisymmetrycc$c$expressed in % of the poloidal field’s magnetic energy | 73 %
Dipolecc$c$expressed in % of the poloidal field’s magnetic energy | 33 %
Maximum intensity | 816 G
Pole’s locationdd$d$Visible pole, negative polarity. [lat; phase] | [56∘; 0.29]
Quadrupolecc$c$expressed in % of the poloidal field’s magnetic energy | 30 %
Octupolecc$c$expressed in % of the poloidal field’s magnetic energy | 19 %
333 ; ; ;

##  4 Discussion

###  4.1 S CrA N: a strong accretor ?

Typical CTTS have effective temperatures between 3000 and 5000 K, (spectral
type G or later), masses most generally between 0.3 and 1 M⊙, with an upper
limit of about 2 M⊙, and mass accretion rates of the order of
$10^{-7}$-$10^{-10}$ M⊙ yr-1. They probe the end of the fully convective
Hayashi phase of the pre-main sequence evolution, around ages of 1 to 2 Myr
(e.g. Herczeg & Hillenbrand 2014; Villebrun et al. 2019; Nicholson et al.
2021).

When fitting our ESPaDOnS spectra, we found an effective temperature for S CrA
N of 4300 $\pm$ 100 K, in agreement with the previous determinations (Table
2). We used the Gaia DR3 data and applied the method of Galli et al. (2020) to
derive the distance to S CrA N (see Appendix C). We adopted a value of d =
$152.4\pm 0.4$ pc. We used the luminosity $L_{*}=1.67\pm
0.8\leavevmode\nobreak\ L_{\sun}$ from Prato et al. (2003), corrected with our
new distance to place S CrA N in the Hertzsprung-Russell diagram. Using the
CESAM evolutionary model (Morel & Lebreton 2008; Marques et al. 2013), we
estimated a mass $M_{*}=0.8\pm 0.1$ M⊙ and stellar radius $R_{*}=2.3\pm
0.6\leavevmode\nobreak\ R_{\sun}$, which gives $\log g=3.6\pm 0.2$. The star
is placed at an age of about 1 Myr, i.e. younger than typical CTTS. As most of
the CTTS, S CrA N is then fully convective.

The photospheric lines of CTTS generally appear shallower than those of non-
accreting stars, suggesting an excess of continuum emission. This so-called
veiling can be observed in different regions of the spectrum of CTTS, with
different interpretations: in the near-infrared range, this excess might be
attributed to the dust emission of the protoplanetary disk (Sousa et al.
2023); in the ultraviolet-visible range, this excess is attributed to an
accretion shock that behaves like a $\sim$ 8 000 K blackbody continuum
emission that superimposes to the photospheric continuum. In very active
stars, emission lines spectra may also blend the photospheric lines as early
discussed in, e.g., Bertout (1984) and shown in, e.g., Petrov et al. (2011);
Dodin & Lamzin (2012); Rei et al. (2018). This veiling of optical spectral
lines is typically lower than 2 around 5500 Å (Basri & Batalha 1990; Hartigan
et al. 1991). In S CrA N, we found no trend between wavelength and the
veiling, which happens to be strongly variable around 5500 Å with values
ranging from 2 to 11. This finding is consistent with that of Sullivan et al.
(2019), who also detected a strong variability and a large amplitude (between
2-6) of veiling in the near-infrared range. Combined with its young age, this
evidence of very strong accretion could indicate an evolutionary stage between
Class I and Class II for S CrA N. This is further confirmed by the place of
the S CrA system in the color-color diagram proposed by Koenig & Leisawitz
(2014). With All-WISE measurements $W1=5.1\pm 0.1$, $W2=4.0\pm 0.1$ and
$W3=2.08\pm 0.01$, the binary system lands at the frontier between protostars
and T Tauri stars444With All-WISE, S CrA N is observed together with S CrA S,
due to the angular resolution of the observations ($\sim 6"$). Since the two
components are coeval (Gahm et al. 2018), this does not affect the
interpretation regarding their young age..

###  4.2 The magnetosphere

From its fundamental parameters, S CrA N can be pictured as a young, fully
convective T Tauri star. Should the surface magnetic field of CTTS be
controlled by their internal structure only, we might expect a strong ($\sim$1
kG) axisymmetric large-scale field, mostly poloidal, with a strong dipole
relative to higher poloidal modes (Gregory et al. 2012). This expectation is
only partially met by the magnetic maps obtained in Section 3: the total field
is mostly (82%) a poloidal field that is axisymmetric (73%), with a strong
(816 G) dipole. However, the dipole and the quadrupole represent a similar
portion of the poloidal field (33% and 30%, respectively), while the
octupole’s contribution is smaller, but still significant (19%). Our
uncertainties on the luminosity may be the reason for this difference between
the prediction and the reconstructed maps, but it should be noted that this
region of the H-R diagram is observationally found to be populated with a
variety of magnetic topologies (Donati et al. 2020; Nicholson et al. 2021). It
is also worth reminding that S CrA N is a strong accretor, and that the
possible impact of accretion on the inner structure of stars is still to be
explored.

We estimate the truncation radius (i.e. radius at which the magnetic pressure
equals the ram gas pressure) from this magnetic reconstruction, using the
formula from Bessolaz et al. (2008):

$\frac{R_{t}}{R_{*}}\simeq
2\,B_{*}^{4/7}\dot{M}^{-2/7}M_{*}^{-1/7}R_{*}^{5/7},$ (3)

where the stellar field in the equatorial plane $B_{*}$ (i.e., half the
dipole’s maximum intensity) has been normalised to 140 G, the accretion rate
$\dot{M}$ to $10^{-8}$ M⊙ yr-1, the stellar mass to 0.8 M⊙, and the stellar
radius to 2 R⊙, and where a Mach number of $\sim 1$ has been assumed. Since
the ESPaDOnS data are not flux-calibrated, we estimated the accretion rate
thanks to the width of H$\alpha$ at 10% peak intensity using the relationship
from Natta et al. (2004):

$\log{\dot{M}_{\text{acc}}}=-12.89(\pm 0.3)+9.7(\pm 0.7)\times
10^{-3}\;\text{H}\alpha 10\%,$ (4)

where $\text{H}\alpha 10\%$ is the considered width in km/s, and
$\dot{M}_{\text{acc}}$ is in M⊙ yr-1. With widths ranging from 579 km/s to 693
km/s, we obtained accretion rate logarithms between -7.3 and -6.2 with a
median value $\log{\dot{M}_{\text{acc}}}\leavevmode\nobreak\
=\leavevmode\nobreak\ -6.9\pm 0.7$, which is consistent with the value of
$(1.0\pm 0.1)\times 10^{-7}\leavevmode\nobreak\ $ M⊙ yr-1 from Sullivan et al.
(2019), when correcting the distance. Because they use the Br$\gamma$ line to
derive this accretion rate, we considered this value as more reliable than our
own (see Alcalá et al. 2014) to compute the truncation radius. Combined with
the stellar radius and mass, and the magnetic topology from the present work,
we obtained:

$R_{t}=2.1\pm 0.4\leavevmode\nobreak\ R_{*},$ (5)

where the uncertainty is derived from the propagation of errors on the
involved parameters through Eq. 3. This value is likely a lower boundary for
the truncation radius since the ZDI technique is blind to the magnetic field
in the region of formation of the emission lines, leading to inconsistency
between our reconstructed maps and the direct diagnoses of accretion, as shown
below.

The derived truncation radius implies a colatitude of the accretion spot of
44∘ $\pm$ 5∘ in a purely dipolar accretion model, which is consistent with the
derived obliquity of the dipole from ZDI (56∘). However, both values seem to
contradict the very high apparent latitude of the post shock region as traced
by the He I NC radial velocity curve (Fig. 6-top). The single spot model from
Pouilly et al. (2021) applied to these data gives a latitude of 86∘ $\pm$ 1∘.
The asymmetry of the NC attributed to a velocity gradient in the post-shock
region does not vary with phase, which is also supportive of a spot located at
high latitude.

The magnetic field projected along the line of sight (or longitudinal magnetic
field $B_{l}$) associated with the NC of He I is positive at all phases (see
Fig.6-bottom, Table 3). If one assumes that the NC is arising from the post-
shock region, this means at least part of the total magnetic field should be
positive near the pole of the star, as shown earlier. However, the magnetic
maps reconstructed from ZDI (Fig. 11) show that regions with a positive
magnetic field (i.e. coming towards the observer) at virtually every phase are
only present in colatitudes larger than $\sim 60^{\circ}$, which corresponds
to a portion of the star occasionally visible only (outside the second dashed
black ring). This discrepancy leads us to consider the tomographic
reconstructions presented in this work as not definite. Additional
developments considering this emission line or any other line constraining a
different region than the LSD profiles (e.g., Ca II infrared triplet (IRT), Fe
II 42 multiplet) are required to combine the different constraints in a single
tomographic reconstruction (such as in Donati et al. 2020), which is beyond
the scope of this paper.

Finally, from this truncation radius, one can also deduce the expected
accretion velocity $v_{\text{acc}}$ (i.e. the velocity of the gas free-falling
from the truncation radius onto the stellar surface) thanks to energy
conservation. This gas is producing the AC observed in He I (Fig. 5), the
higher members of the Balmer series (Fig. 9) and FeII (Fig. 12). Thanks to our
estimate of stellar mass and radius, we obtain $v_{\text{acc}}$ = 267
km.s${}^{\text{-1}}$. This velocity is included in the range of velocities of
the AC, which makes the value of $R_{t}$ derived from ZDI consistent with our
values of $M_{*}$ and $R_{*}$. However, the maximum velocity of the AC is
larger than the free-fall velocity from infinity ($v_{\infty}$ = 370
km.s${}^{\text{-1}}$), which points out either a wrong estimate of $M_{*}$ and
$R_{*}$, or a significant broadening of these absorptions, the source of which
remaining unknown.

###  4.3 An unstable accretion regime ?

The observed intensity and variability of various emission lines (He I, Fe II,
Ca II, for instance; see Appendix B), combined with the highly veiled
photospheric lines, suggest that intense accretion processes occur in the
vicinity of S CrA N.

One way to better constrain the accretion process is to compare the corotation
radius and the truncation radius. Indeed, when the truncation to corotation
radii ratio becomes small enough, Rayleigh-Taylor instability can be triggered
at the magnetosphere-disk boundary (Kulkarni & Romanova 2008). Then,
magnetospheric accretion enters the so-called unstable accretion regime, where
classical accretion funnels are observed, but also accretion tongues. This
phenomenon and its observable signatures have been extensively modeled
(Kurosawa & Romanova 2013; Blinova et al. 2016) and has recently been
reproduced in laboratory experiments that scale to the expected YSOs’
accretion tongues (Burdonov et al. 2022). Blinova et al. (2016) observed
unstable accretion for simulations where $R_{t}/R_{\text{co}}<0.71$, for
obliquities lower than $20^{\circ}$.
With the set of stellar parameters we derived (see Table 2) we computed a
corotation radius of $R_{\text{co}}=6.4\pm 1.7$ R∗, which yields a truncation
to corotation radii ratio $R_{t}/R_{\text{co}}=0.33\leavevmode\nobreak\
\pm\leavevmode\nobreak\ 0.11$, and places S CrA N in the unstable accretion
scenario. The simulations from Kurosawa & Romanova (2013) showed that a proxy
to the accretion regime lies in the profiles of the higher members of the
Balmer series ($H\gamma$ and $H\delta$): in the stable case, a red-shifted
absorption appears for about half the rotation cycle, before it disappears,
coming and going with stellar periodicity. This absorption is due to the
visible accretion funnel which is absorbing the star’s continuum while it
remains in the line of sight. In the unstable case, this red-shifted
absorption is expected to be present at virtually every phase of the rotation
cycle, since there is at least one accretion tongue in the line of sight at
all time. The profiles of $H\gamma$ and $H\delta$ we observe in S CrA N
display this absorption at all phases as seen in Fig. 9, in agreement with
unstable accretion.

###  4.4 Accreting structures

This unstable accretion regime sets a new context for the interpretation of
the features observed in the emission lines presented earlier.

The He I $\lambda 5876$ NC likely arises from a post-shock region in a single
accretion spot located at high latitudes ($\sim 86^{\circ}$). The origin in a
post-shock region is suggested by the small radial velocity of the flow
producing the NC ($\sim 2$ km/s, see Sec.4.2). The single-spot model is
corroborated by the consistency between the periodicity of the Stokes V
signatures (both in the LSD profiles and the He I line) and the periodicity of
the He I NC profiles. The longitudinal field’s curve in the He I line displays
a complex modulation, with a substantial departure from the sine model near
the extreme radial velocities, around phases 0.3 and 0.9 (see Fig. 6). That
could be explained if the star has a complex magnetic field, significantly
differing from a simple dipole as suggested by ZDI from the present work.
Finally, the asymmetry of the NC in Stokes $I$ (steep blue wing and mild red
wing; see Fig. 5) and the departure from anti-symmetry in Stokes $V$ (blue
lobe stronger than red lobe) would come from the velocity gradient in the
region of emission. This asymmetry is observed at all phases with no
noticeable modulation, suggesting a high latitude for the accretion spot.

We speculate that the red-shifted AC seen in He I $\lambda 5876$, $H\gamma$,
and $H\delta$ is formed in two distinct structures: first, in an accretion
funnel located around phase 0.2 (called the ”main” column hereafter), which
produces the NC at its footprint, when forming an accretion shock; then, in
another accretion column located around phase 0.7 (called the ”secondary”
column hereafter, opposed to the main one), which does not have any NC
counterpart, because its density is much smaller than in the main column,
where accretion is favoured, due to the magnetic misalignment. An AC is
nonetheless produced by the free-falling material of the secondary column
which absorbs the light emerging from the photosphere. These opposite
structures then produce an artificial periodicity of half the stellar period
($P_{*}/2=3.65\simeq 3.4\pm 0.4$ days, see Fig. 8), the actual stellar period
being detected for the lowest velocities of the AC ($P_{*}=7.3\simeq 6.6\pm
1.3$ days), because only the main accretion column is dense enough at small
velocities (i.e., in the upper part of the column) to produce an absorption.

Finally, the He I $\lambda 5876$ BC is most likely formed by the in-falling
gas in both the main and the secondary funnels, since the same artificial
periodicity as the AC is observed, and its centroid is mostly red-shifted. As
discussed in Beristain et al. (2001), this tendency in the central velocity of
the line can be obtained with material following a purely dipolar field at
polar angles lower than 54.7∘ which corresponds to accreting gas.

###  4.5 Outflows

Lima et al. (2010) modeled the H$\alpha$ line in the case of a CTTS undergoing
both magnetospheric accretion and a disk wind. When comparing the H$\alpha$
lines we observed (Fig. 9) with their grids of models, the deep blue-shifted
absorption of our profiles appears to be well reproduced with their models
combining a high accretion rate ($10^{-7}$ M⊙ yr-1), and a hot ($\sim$
8000-10000 K) disk wind with a density of a few $10^{-11}$ g/cm3 and an outer
radius of a few tens of stellar radii (see their Figs. 4 and 6). It should be
noted that their model reproduces the bulk of the absorption, but not the
variable features seen at small velocities. We guess that these features are
coming from disk outflows because of their moderate correlation with accretion
signatures (namely, the He I NC and He I AC) as seen in Fig. 10. Numerical
simulations (Romanova et al. 2009; Zanni & Ferreira 2013; Pantolmos et al.
2020) have shown that the stellar magnetic field lines threading the disk
outside the accretion columns are open, further producing transient ejections
(i.e., magnetospheric ejections/conical winds) and/or disk winds. These
outflows are also suspected when comparing the truncation radius we computed
with the size of the region emitting the hydrogen $Br\gamma$ line in S CrA N.
This region can be spatially constrained to
$R_{Br\gamma}=7.7\leavevmode\nobreak\ \pm 2.2\leavevmode\nobreak\ R_{*}$
thanks to interferometric observations (GRAVITY Collaboration et al. 2017b;
Gravity Collaboration et al. 2023). The given value is an update from Gravity
Collaboration et al. (2023) with our new values for distance and $R_{*}$.
Since $R_{Br\gamma}$ extends well beyond $R_{t}$ = 2.1 $\pm$ 0.4 $R_{*}$, disk
outflows must account for part of the emission observed in this line.
Finally, the Herbig-Haro object HH729 has been attributed to S CrA N (Peterson
et al. 2011). The forbidden lines of $[OI]$ at 6300.2 Å and 6363.8 Å and
$[SII]$ at 6730 Å are usually interpreted as tracers of outflows at different
scales (see e.g. Alexander et al. 2014; Pascucci et al. 2020; Gangi et al.
2023). These lines are present in the spectra of S CrA N with a strong blue-
shifted peak ($\sim$ -120 km/s) and asymmetry (see Appendix B for the
profiles), strengthening the idea of a large-scale outflow arising from the
inner regions.

##  5 Conclusions

Thanks to spectropolarimetric observations in the optical range with ESPaDOnS
at CFHT, we have probed the star-disk interaction in the innermost regions of
the North component of the young binary system S CrA. With its confirmed high
accretion rate ($10^{-7}$ M⊙ yr-1), this object is an ideal target for
studying the magnetospheric accretion scenario in a stronger regime than in
CTTS. Our major findings are summarized below:

  * •

When fitting the ESPaDOnS spectra and using CESAM evolutionary models, S CrA N
appears to have a mass of 0.8 M⊙, to be fully convective, and about 1 Myr old.
As in previous determinations in the near-infrared range, the veiling we
derive around 5500 $\AA$ is strongly variable and high (i.e., ranging from 2
to 11), which suggests that the star experiences a strong accretion regime.
Combined with the young age, this could indicate an evolutionary stage between
Class I and Class II.

  * •

This evolutionary stage is also in line with the large-scale magnetic field we
have reconstructed through ZDI. We obtained a total field as strong as 5.4 kG
and not strongly axi-symmetric, whose dipolar contribution represents about a
third of the total field. Higher poloidal orders being significant ($\sim$
50%), the large-scale topology of the magnetic field appears rather complex,
when compared with CTTSs.

  * •

Additional developments are needed to paint a complete and coherent view of
the magnetic topology of S CrA N by including the constraints from the
emission lines (such as He I, the Ca II IRT or the Fe II 42 multiplet) and
developing more complex models to reproduce the emitting regions of these
lines and their properties.

  * •

We derive a magnetic truncation radius of $\sim$ 2 $R_{*}$, and a corotation
radius of $\sim$ 6 $R_{*}$, suggesting that S CrA N is in an unstable
accretion regime. Looking at the Helium and Hydrogen line profiles and
periodicities, we suggest that this accretion occurs in an unstable scenario,
along two distinct accretion structures: one main accretion column associated
with the accretion shock, and a secondary accretion column with much less
density in it as to produce no detectable accretion shock.

  * •

The emission lines of the hydrogen Balmer series are highly variable and
display multi-component profiles. The observed H$\alpha$ line profiles exhibit
clear signatures of an outflow and are in good agreement with simulations of a
hot and dense disk wind. This finding is compatible with the size of the
$Br\gamma$ emitting region measured with GRAVITY ($\sim$ 8 $R_{*}$) which is
substantially larger than the truncation radius.

Our spectropolarimetric campaign in the optical allows us to characterize the
star-disk interactions at play in the innermost regions of S CrA N and, when
combined with near-infrared interferometry, to provide a consistent view of
these complex and variable regions. Given the strong and unstable accretion
regime, probing the accretion-ejection processes would benefit from a temporal
follow-up of these phenomena through simultaneous observations combining
photometry, spectroscopy, and interferometry in various spectral ranges.

###### Acknowledgements.

This work is supported by the French National Research Agency in the framework
of the ”investissements d’avenir” program (ANR-15-IDEX-02).
This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.
This work has made use of the VALD database, operated at Uppsala University,
the Institute of Astronomy RAS in Moscow, and the University of Vienna.
Finally, we address our greatest thanks to the referee of this article for
their fruitful suggestions and comments.

## References

  * Alcalá et al. (2021) Alcalá, J. M., Gangi, M., Biazzo, K., et al. 2021, A&A, 652, A72
  * Alcalá et al. (2014) Alcalá, J. M., Natta, A., Manara, C. F., et al. 2014, A&A, 561, A2
  * Alencar et al. (2018) Alencar, S. H. P., Bouvier, J., Donati, J. F., et al. 2018, A&A, 620, A195
  * Alencar et al. (2012) Alencar, S. H. P., Bouvier, J., Walter, F. M., et al. 2012, A&A, 541, A116
  * Alexander et al. (2014) Alexander, R., Pascucci, I., Andrews, S., Armitage, P., & Cieza, L. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen, C. P. Dullemond, & T. Henning, 475–496
  * Anthonioz et al. (2015) Anthonioz, F., Ménard, F., Pinte, C., et al. 2015, A&A, 574, A41
  * Baraffe et al. (2017) Baraffe, I., Elbakyan, V. G., Vorobyov, E. I., & Chabrier, G. 2017, A&A, 597, A19
  * Basri & Batalha (1990) Basri, G. & Batalha, C. 1990, ApJ, 363, 654
  * Beristain et al. (2001) Beristain, G., Edwards, S., & Kwan, J. 2001, ApJ, 551, 1037
  * Bertout (1984) Bertout, C. 1984, Reports on Progress in Physics, 47, 111
  * Bessolaz et al. (2008) Bessolaz, N., Zanni, C., Ferreira, J., Keppens, R., & Bouvier, J. 2008, A&A, 478, 155
  * Blinova et al. (2016) Blinova, A. A., Romanova, M. M., & Lovelace, R. V. E. 2016, MNRAS, 459, 2354
  * Bouvier et al. (2007) Bouvier, J., Alencar, S. H. P., Harries, T. J., Johns-Krull, C. M., & Romanova, M. M. 2007, in Protostars and Planets V, ed. B. Reipurth, D. Jewitt, & K. Keil, 479
  * Bouvier et al. (2020) Bouvier, J., Perraut, K., Le Bouquin, J. B., et al. 2020, A&A, 636, A108
  * Burdonov et al. (2022) Burdonov, K., Yao, W., Sladkov, A., et al. 2022, A&A, 657, A112
  * Camenzind (1990) Camenzind, M. 1990, Reviews in Modern Astronomy, 3, 234
  * Cazzoletti et al. (2019) Cazzoletti, P., Manara, C. F., Liu, H. B., et al. 2019, A&A, 626, A11
  * Dodin & Lamzin (2012) Dodin, A. V. & Lamzin, S. A. 2012, Astronomy Letters, 38, 649
  * Donati (2003) Donati, J. F. 2003, in Astronomical Society of the Pacific Conference Series, Vol. 307, Solar Polarization, ed. J. Trujillo-Bueno & J. Sanchez Almeida, 41
  * Donati et al. (2020) Donati, J. F., Bouvier, J., Alencar, S. H., et al. 2020, MNRAS, 491, 5660
  * Donati et al. (1997) Donati, J. F., Semel, M., Carter, B. D., Rees, D. E., & Collier Cameron, A. 1997, MNRAS, 291, 658
  * Edwards (1979) Edwards, S. 1979, PASP, 91, 329
  * Edwards et al. (1994) Edwards, S., Hartigan, P., Ghandour, L., & Andrulis, C. 1994, AJ, 108, 1056
  * Espaillat (2022) Espaillat, C. 2022, in American Astronomical Society Meeting Abstracts, Vol. 54, American Astronomical Society Meeting Abstracts, 413.01
  * Fischer et al. (2011) Fischer, W., Edwards, S., Hillenbrand, L., & Kwan, J. 2011, ApJ, 730, 73
  * Folsom et al. (2018) Folsom, C. P., Bouvier, J., Petit, P., et al. 2018, MNRAS, 474, 4956
  * Gahm et al. (2018) Gahm, G. F., Petrov, P. P., Tambovsteva, L. V., et al. 2018, A&A, 614, A117
  * Gaia Collaboration et al. (2023) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1
  * Galli et al. (2020) Galli, P. A. B., Bouy, H., Olivares, J., et al. 2020, A&A, 634, A98
  * Gangi et al. (2023) Gangi, M., Nisini, B., Manara, C. F., et al. 2023, A&A, 675, A153
  * GRAVITY Collaboration et al. (2017a) GRAVITY Collaboration, Abuter, R., Accardo, M., et al. 2017a, A&A, 602, A94
  * Gravity Collaboration et al. (2020) Gravity Collaboration, Garcia Lopez, R., Natta, A., et al. 2020, Nature, 584, 547
  * GRAVITY Collaboration et al. (2017b) GRAVITY Collaboration, Garcia Lopez, R., Perraut, K., et al. 2017b, A&A, 608, A78
  * GRAVITY Collaboration et al. (2021) GRAVITY Collaboration, Perraut, K., Labadie, L., et al. 2021, A&A, 655, A73
  * Gravity Collaboration et al. (2023) Gravity Collaboration, Wojtczak, J. A., Labadie, L., et al. 2023, A&A, 669, A59
  * Gregory et al. (2012) Gregory, S. G., Donati, J. F., Morin, J., et al. 2012, ApJ, 755, 97
  * Gustafsson et al. (2008) Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951
  * Hartigan et al. (1991) Hartigan, P., Kenyon, S. J., Hartmann, L., et al. 1991, ApJ, 382, 617
  * Hartmann et al. (2016) Hartmann, L., Herczeg, G., & Calvet, N. 2016, ARA&A, 54, 135
  * Hartmann et al. (1994) Hartmann, L., Hewett, R., & Calvet, N. 1994, ApJ, 426, 669
  * Herczeg & Hillenbrand (2014) Herczeg, G. J. & Hillenbrand, L. A. 2014, ApJ, 786, 97
  * Koenig & Leisawitz (2014) Koenig, X. P. & Leisawitz, D. T. 2014, ApJ, 791, 131
  * Koenigl (1991) Koenigl, A. 1991, ApJ, 370, L39
  * Kulkarni & Romanova (2008) Kulkarni, A. K. & Romanova, M. M. 2008, MNRAS, 386, 673
  * Kurosawa et al. (2005) Kurosawa, R., Harries, T. J., & Symington, N. H. 2005, MNRAS, 358, 671
  * Kurosawa & Romanova (2013) Kurosawa, R. & Romanova, M. M. 2013, MNRAS, 431, 2673
  * Landstreet (1988) Landstreet, J. D. 1988, ApJ, 326, 967
  * Lima et al. (2010) Lima, G. H. R. A., Alencar, S. H. P., Calvet, N., Hartmann, L., & Muzerolle, J. 2010, A&A, 522, A104
  * Manara et al. (2021) Manara, C. F., Frasca, A., Venuti, L., et al. 2021, A&A, 650, A196
  * Marques et al. (2013) Marques, J. P., Goupil, M. J., Lebreton, Y., et al. 2013, A&A, 549, A74
  * Marraco & Rydgren (1981) Marraco, H. G. & Rydgren, A. E. 1981, AJ, 86, 62
  * Martin et al. (2018) Martin, A. J., Neiner, C., Oksala, M. E., et al. 2018, MNRAS, 475, 1521
  * Morel & Lebreton (2008) Morel, P. & Lebreton, Y. 2008, Ap&SS, 316, 61
  * Natta et al. (2004) Natta, A., Testi, L., Muzerolle, J., et al. 2004, A&A, 424, 603
  * Nicholson et al. (2021) Nicholson, B. A., Hussain, G., Donati, J. F., et al. 2021, MNRAS, 504, 2461
  * Ortiz et al. (2010) Ortiz, J. L., Sugerman, B. E. K., de La Cueva, I., et al. 2010, A&A, 519, A7
  * Pantolmos et al. (2020) Pantolmos, G., Zanni, C., & Bouvier, J. 2020, A&A, 643, A129
  * Pantolmos et al. (2022) Pantolmos, G., Zanni, C., & Bouvier, J. 2022, in Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, 48
  * Pascucci et al. (2020) Pascucci, I., Banzatti, A., Gorti, U., et al. 2020, ApJ, 903, 78
  * Peterson et al. (2011) Peterson, D. E., Caratti o Garatti, A., Bourke, T. L., et al. 2011, ApJS, 194, 43
  * Petrov et al. (2011) Petrov, P. P., Gahm, G. F., Stempels, H. C., Walter, F. M., & Artemenko, S. A. 2011, A&A, 535, A6
  * Piskunov et al. (1995) Piskunov, N. E., Kupka, F., Ryabchikova, T. A., Weiss, W. W., & Jeffery, C. S. 1995, A&AS, 112, 525
  * Pouilly et al. (2020) Pouilly, K., Bouvier, J., Alecian, E., et al. 2020, A&A, 642, A99
  * Pouilly et al. (2021) Pouilly, K., Bouvier, J., Alecian, E., et al. 2021, A&A, 656, A50
  * Prato et al. (2003) Prato, L., Greene, T. P., & Simon, M. 2003, ApJ, 584, 853
  * Rei et al. (2018) Rei, A. C. S., Petrov, P. P., & Gameiro, J. F. 2018, A&A, 610, A40
  * Reipurth & Zinnecker (1993) Reipurth, B. & Zinnecker, H. 1993, A&A, 278, 81
  * Romanova et al. (2009) Romanova, M. M., Ustyugova, G. V., Koldoba, A. V., & Lovelace, R. V. E. 2009, MNRAS, 399, 1802
  * Ryabchikova et al. (2015) Ryabchikova, T., Piskunov, N., Kurucz, R. L., et al. 2015, Phys. Scr, 90, 054005
  * Rydgren (1977) Rydgren, A. E. 1977, PASP, 89, 557
  * Schegerer et al. (2009) Schegerer, A. A., Wolf, S., Hummel, C. A., Quanz, S. P., & Richichi, A. 2009, A&A, 502, 367
  * Skilling & Bryan (1984) Skilling, J. & Bryan, R. K. 1984, MNRAS, 211, 111
  * Sousa et al. (2021) Sousa, A. P., Bouvier, J., Alencar, S. H. P., et al. 2021, A&A, 649, A68
  * Sousa et al. (2023) Sousa, A. P., Bouvier, J., Alencar, S. H. P., et al. 2023, A&A, 670, A142
  * Sullivan et al. (2019) Sullivan, K., Prato, L., Edwards, S., Avilez, I., & Schaefer, G. H. 2019, ApJ, 884, 28
  * Varga et al. (2018) Varga, J., Ábrahám, P., Chen, L., et al. 2018, A&A, 617, A83
  * Villebrun et al. (2019) Villebrun, F., Alecian, E., Hussain, G., et al. 2019, A&A, 622, A72
  * Wade et al. (2001) Wade, G. A., Bagnulo, S., Kochukhov, O., et al. 2001, A&A, 374, 265
  * Wade et al. (2000) Wade, G. A., Donati, J. F., Landstreet, J. D., & Shorlin, S. L. S. 2000, MNRAS, 313, 851
  * Walker (1972) Walker, M. F. 1972, ApJ, 175, 89
  * Zanni & Ferreira (2013) Zanni, C. & Ferreira, J. 2013, A&A, 550, A99
  * Zechmeister & Kürster (2009) Zechmeister, M. & Kürster, M. 2009, A&A, 496, 577

##  Appendix A Influence of the South component

In order to address the possible contamination of our observations by S CrA S,
we simulated the observed Field of View (FoV) of ESPaDOnS. We placed S CrA S
to a distance of 1.4” from S CrA N (astrometry from Gaia Collaboration et al.
2023), and accounted for a circular FoV of 1.6” (from the official ESPaDOnS
website555http://www.ast.obs-mip.fr/projets/espadons/espadons.html) centered
on S CrA N. We attributed a normalised flux of 1 for S CrA N, hence a flux of
0.63 for S CrA S based on a difference in magnitude of 0.5 in the I band (Gahm
et al. 2018). Finally, we applied a seeing as a 2D Gaussian distribution
centered on each star, with its full width at half maximum equal to the seeing
of our observations (see Table 1). This description represents the actual
observation and we computed the total flux observed as the sum of the flux in
each pixel within the FoV. We also computed the sole contribution of S CrA S
by modifying the model as such: the FoV is untouched in size and position, but
we only take into account the Gaussian model of S CrA S (hence not fully
included inside the FoV). The contribution of S CrA S is then the sum of the
flux in each pixel within the FoV. The ratio between these fluxes gives the
contribution of S CrA S to the total flux observed. This method yields a
contribution of $8.96\%$ at worse (seeing of 1350 mas), with a minimum of
$0.03\%$ (seeing of 430 mas) and an average of $1.58\%$ (seeing=750 mas).
Three observations exceeded a contribution of 5% : June 26, 27 and 28 with
9.0%, 9.3% and 5.3%, respectively. All the results obtained in this work have
been checked excluding these three observations. No significant difference
were found, except for a decrease in SNR.

##  Appendix B Spectra of S CrA N

###  B.1 Classical emission lines in Classical T Tauri Stars

Figure 12: Emission lines in S CrA N. All $V$ profiles have been magnified by
a factor 5, for clarity. Rainbow shading has the same meaning as in Figure 1,
solid black line is the median profile.

Some lines classically tracing the accretion-ejection processes in CTTS are
displayed in Figure 12. We provide a short comment on the aspect and behaviour
for each of these lines.

#### Iron triplet

This triplet thought to originate from the chromospheric activity of the star
is presented in the top row of Fig. 12. They show great variability and strong
intensity. They all exhibit two common features : A broad and a narrow
emission, both centered near the radial velocity of the star. The lines at
$\lambda 4924$ and $\lambda 5018$ also have an additional red-shifted
absorption at high velocities, likely to be interpreted just like the ones
observed in He I $\lambda 5876$, $H\gamma$ and $H\delta$. Their Stokes $V$
profiles show anti-symmetric signatures associated to the narrow emissions
which are exceptionally strong and symmetric. Combined with the simple
decomposition of their Stokes $I$ counterparts, this makes them good
candidates for a future tomographic reconstruction taking emission lines as
constraints.

#### Calcium infrared triplet (IRT)

Commonly used to study the activity of CTTS, this triplet is presented in the
middle row of Fig. 12. Its intensities are comparable to those of H$\alpha$,
which put these lines amongst the most dominant ones in the spectrum of S CrA
N. Their shape is complex and no simple decomposition (based on the sum of up
to 4 Gaussians) was successful in reproducing them. It should be noted that
the Stokes V signatures are strong and define a narrow component emitted near
the surface of the star, unlike the rest of the lines.

#### He I $\boldsymbol{\lambda 6678}$

Likely originating from the same processes as He I $\lambda 5876$. Its
different excitation potential is used to compute line ratios and infer the
electron density and temperature encountered in the region producing these
lines. No attempt to derive these parameters was tried in this work. The
decomposition of this line appears similar to that of He I $\lambda 5876$,
albeit the noticeable absence of the red-shifted AC.

#### Oxygen

This forbidden line of oxygen is usually threefold (see e.g. Pascucci et al.
2020) : A narrow low velocity component (NLVC) traces a wind arising in the
outermost part of the inner disk ($\sim$ 1 au). A broad low velocity component
(BLVC) traces a wind arising in the innermost part of the inner disk ($\leq$
0.1 au). A high velocity blue-shifted component (HVC) traces a jet. The HVC is
observed peaking around -120 km/s and confirmed by a Herbig Haro object
(HH729) associated to S CrA N. Regarding the low velocity components, S CrA N
seems to display a BLVC with no NLVC, which is unexpected since disk
evaporation models predict an evolution going from BLVC + NLVC (when the inner
wind is dense enough to shield the outer disk from high energy stellar
photons) to NLVC as the inner wind’s density decreases and the disk starts
evaporating (Alexander et al. 2014). Since the disk is not expected to
evaporate before the late class II stage, another model should be invoked to
explain the profiles observed in S CrA N (class I - class II transition
stage). No Stokes V signal is detected, as expected from a line formed away
from the star, in a region where the magnetic field is weak.

#### Sulfur

Just like for the forbidden oxygen line, this line is tracing a jet, with a
peak at similar velocities as the HVC of OI : $\sim$ -120 km/s.

###  B.2 Variability Of the Balmer series

Figure 13: 2D periodograms of the lower Balmer series. Red dashed lines show
periods of 7.3 days ($P_{*}$) and 3.65 days ($P_{*}/2$). Black dashed contour
show a 3% FAP level.

The Balmer series are composite lines, as discussed in this work. Their 2D
periodograms are shown in Fig. 13. Multiple signals can be seen, but as
discussed in the core of this work, the higher periods will not be commented,
because of the white noise assumption made in the computation of the
periodograms, and because of the total span of observation, which does not
allow to observe these periodicities for more than a full cycle. The blue side
of the broad emission (near -180 km/s) has a periodicty of the order of
stellar rotation period ($7.3\leavevmode\nobreak\ \pm\leavevmode\nobreak\ 0.2$
days) in all the lines but $H\delta$. The red side of this broad absorption
(near +100 km/s) has no clear periodicity for $H\alpha$ and $H\beta$, while a
somewhat significant signal near 4 days can be seen for $H\gamma$ and
$H\delta$. This periodicity is found nowhere in any other feature we studied
in this work, and its origin remains unknown. The red-shifted absorption seen
in $H\beta$, $H\gamma$ and $H\delta$, which has been extensively discussed in
previous sections is found to be periodic with a period similar to the one in
the red-shifted absorption met in the He I $\lambda 5876$ line. That is,
slightly lower than half the rotation period (3.2 days instead of 3.65 days)

###  B.3 LSD profiles dependence on the lines depth

In order to test the potential influence of the depth of the lines taken into
account during the LSD procedure, we performed a test where we excluded the
deepest lines, which should be the most affected by veiling (Rei et al. 2018),
and the ones located within their $\pm$ 15 km/s vicinity, which could be
affected by them. We applied different depths thresholds to obtain a mask, and
computed the resulting LSD $I$ and $V$ profiles. We illustrate this with 3
different masks on Fig.14. The first mask is the one we cleansed naturally,
i.e. without any depth threshold (green curves). It includes 10 263 lines out
of the 27,502 coming from the raw synthetic spectrum. Then, with a threshold
of 0.8, only 7,301 lines were left in the mask (blue curve). And finally, with
a threshold of 0.4, 4,279 lines remained (red curve). At this stage, the
profiles’ SNR becomes so low that any further cut would significantly impact
the the LSD signal. It is visible from Fig. 14 that no matter the depth limit
applied to a mask, the qualitative shape of the LSD profiles remain constant.
We can then exclude the continuum veiling as the source of the quick and
intense variations observed in our LSD profiles, and favour an origin in the
chromospheric emission lines.

Figure 14: Illustration of the lines depth test. Top : Number of lines
included in each mask, as a function of their intrinsic depth. Bottom-left :
LSD $I$ profiles associated to each mask. Bottom-right : LSD $V$ profiles
(magnified by a factor 5, for clarity) associated to each mask. Black curve
stands for the raw synthetic spectrum. Green curve corresponds to the mask
used in this study. Blue curve corresponds to a depth limit of 0.8. Red curve
corresponds to a depth limit of 0.4.

##  Appendix C Distance estimate of the S CrA system

The distance found for S CrA N in the most recent literature comes from Prato
et al. (2003) with $130\pm 20$ pc. This value is taken from an even earlier
estimate of the distance of the whole R CrA T region by Marraco & Rydgren
(1981), while the associated uncertainty is simply assumed a priori, and does
not derive from the observations. The latest Gaia-DR3 data (Gaia Collaboration
et al. 2023) provides a distance of $160\pm 2$ pc for S CrA N from its
parallax measurements666S CrA N Gaia ID : 6731210253964165632, while S CrA S
is found to be at $147\pm 2$ pc with the same data release777S CrA S Gaia ID :
6731210258265107584, which is inconsistent with the assumption of S CrA being
a close binary. This discrepancy alone is not enough to question the binarity
of the S CrA system though. The nebulosity in its surroundings, coupled with
its binary nature, can explain such a discrepancy in the Gaia parallax
measurements. Galli et al. (2020) used the Gaia-DR2 data on a sample of 313
stars associated with the Corona Australis region to draw a line between the
so-called ”on-cloud” and ”off-cloud” sub-regions. In their study, this
distinction is based on a Bayesian distance estimate and tangential velocities
measurements. Using the Gaia-DR3 data, we placed S CrA S and S CrA N in the
diagram in Figure 15 (proper motion in right ascension against proper motion
in declination for both Gaia DR2 and DR3 data) adapted from Galli et al.
(2020) and non-ambiguously assigned S CrA N to the ”on-cloud” region with a
proper motion of $7.05\pm 0.06$ mas/yr in right ascension and $-26.51\pm 0.06$
mas/yr in declination. We thus adopted the distance of the ”on-cloud” region,
that is $152.4\pm 0.4$ pc for S CrA N.

Figure 15: Proper motions for the two subgroups of the Corona Australis region
in Gaia DR2, S CrA N and S CrA S in Gaia DR2 and Gaia DR3. Adapted from Galli
et al. (2020).