11institutetext:  European Southern Observatory, Karl-Schwarzschild-Strasse 2,
85748 Garching bei München, Germany
11email<EMAIL_ADDRESS>22institutetext: NASA Headquarters, 300 E Street SW,
Washington, DC 20546, USA 33institutetext: Dipartimento di Fisica, Universitá
degli Studi di Milano, Via Giovanni Celoria 16, 20133 Milano, Italy
44institutetext: Max-Planck Institute for Extraterrestrial Physics,
Gießenbachstraße 1, 85748 Garching, Germany 55institutetext: INAF –
Osservatorio Astronomico di Capodimonte, via Moiariello 16, 80131 Napoli,
Italy 66institutetext: Astronomy Unit, School of Physics and Astronomy, Queen
Mary University of London, London E1 4NS, UK 77institutetext: Institute for
Astronomy, University of Hawai‘i at Mānoa, Honolulu, HI, USA

# Testing external photoevaporation in the $\sigma$-Orionis cluster
with spectroscopy and disk mass measurements

K. Maucó Based on observations collected at the European Southern Observatory
under ESO programmes 0104.C-0454(A) and 108.22CB.001.Testing external
photoevaporation in the $\sigma$-Orionis cluster  with spectroscopy and disk
mass measurementsTesting external photoevaporation in the $\sigma$-Orionis
cluster  with spectroscopy and disk mass measurements C. F. Manara Testing
external photoevaporation in the $\sigma$-Orionis cluster  with spectroscopy
and disk mass measurementsTesting external photoevaporation in the
$\sigma$-Orionis cluster  with spectroscopy and disk mass measurements M.
Ansdell Testing external photoevaporation in the $\sigma$-Orionis cluster
with spectroscopy and disk mass measurementsTesting external photoevaporation
in the $\sigma$-Orionis cluster  with spectroscopy and disk mass measurements
G. Bettoni Testing external photoevaporation in the $\sigma$-Orionis cluster
with spectroscopy and disk mass measurementsTesting external photoevaporation
in the $\sigma$-Orionis cluster  with spectroscopy and disk mass
measurementsTesting external photoevaporation in the $\sigma$-Orionis cluster
with spectroscopy and disk mass measurementsTesting external photoevaporation
in the $\sigma$-Orionis cluster  with spectroscopy and disk mass measurements
R. Claes Testing external photoevaporation in the $\sigma$-Orionis cluster
with spectroscopy and disk mass measurementsTesting external photoevaporation
in the $\sigma$-Orionis cluster  with spectroscopy and disk mass measurements
J. Alcala Testing external photoevaporation in the $\sigma$-Orionis cluster
with spectroscopy and disk mass measurementsTesting external photoevaporation
in the $\sigma$-Orionis cluster  with spectroscopy and disk mass measurements
A. Miotello Testing external photoevaporation in the $\sigma$-Orionis cluster
with spectroscopy and disk mass measurementsTesting external photoevaporation
in the $\sigma$-Orionis cluster  with spectroscopy and disk mass measurements
S. Facchini Testing external photoevaporation in the $\sigma$-Orionis cluster
with spectroscopy and disk mass measurementsTesting external photoevaporation
in the $\sigma$-Orionis cluster  with spectroscopy and disk mass measurements
T. J. Haworth Testing external photoevaporation in the $\sigma$-Orionis
cluster  with spectroscopy and disk mass measurementsTesting external
photoevaporation in the $\sigma$-Orionis cluster  with spectroscopy and disk
mass measurements G. Lodato Testing external photoevaporation in the
$\sigma$-Orionis cluster  with spectroscopy and disk mass measurementsTesting
external photoevaporation in the $\sigma$-Orionis cluster  with spectroscopy
and disk mass measurements J. P. Williams Testing external photoevaporation in
the $\sigma$-Orionis cluster  with spectroscopy and disk mass
measurementsTesting external photoevaporation in the $\sigma$-Orionis cluster
with spectroscopy and disk mass measurements

###### Abstract

Context. The evolution of protoplanetary disks is regulated by an interplay of
several processes, either internal to the system or related to the
environment. As most of the stars and planets, including our own Solar System,
have formed in massive stellar clusters that contain OB-type stars, studying
the effects of UV radiation on disk evolution is of paramount importance.

Aims. Here we test the impact of external photoevaporation on the evolution of
disks in the mid-age ($\sim$3–5 Myr) $\sigma$-Orionis cluster by conducting
the first combined large-scale UV to IR spectroscopic and mm-continuum survey
of this region.

Methods. We study a sample of 50 targets located at increasing distances from
the central, massive OB system $\sigma$-Ori. We combine new spectra obtained
with VLT/X-Shooter, used to measure mass accretion rates and stellar masses,
with new and previously published ALMA measurements of disk dust and gas
fluxes and masses.

Results. We confirm the previously found decrease of $M_{\rm dust}$ in the
inner $\sim$0.5 pc of the cluster. This is particularly evident when
considering the disks around the more massive stars ($\geq$ 0.4 $M_{\odot}$),
where those located in the inner part ($<$ 0.5 pc) of the cluster have $M_{\rm
dust}$ about an order of magnitude lower than the more distant ones. About
half of the sample is located in the region of the $\dot{M}_{\rm acc}$ vs
$M_{\rm disk}$ expected by models of external photoevaporation, namely showing
shorter disk lifetimes than expected for their ages. The shorter disk
lifetimes is observed for all targets with projected separation from
$\sigma$-Ori $<$ 0.5 pc, proving that the presence of a massive stellar system
affects disk evolution.

Conclusions. External photoevaporation is a viable mechanism to explain the
observed shorter disk lifetimes and lower $M_{\rm dust}$ in the inner
$\sim$0.5 pc of the $\sigma$-Orionis cluster, where the effects of this
process are more pronounced. Follow-up observations of the low stellar mass
targets are crucial to constrain disk dispersion time scales in the cluster
and to confirm the dependence of the external photoevaporation process with
stellar host mass. This work confirms that the effects of external
photoevaporation are significant down to at least impinging radiation as low
as $\sim 10^{4}$ G0.

###### Key Words.:

accretion,accretion disks – protoplanetary disks – stars:pre-main sequence –
stars:variables:TTauri, HerbigAe/Be

##  1 Introduction

Protoplanetary disks, made of gas and dust, are the byproduct of the star
formation process and are the places where planets form. Their evolution is
mediated by the interplay of several physical processes most likely acting
simultaneously, which makes understanding disk evolution challenging (Manara
et al. 2023, for a review). The standard theory is framed in the steady-state
viscous paradigm, where the transfer of angular momentum in the disk drives
its evolution, and results in accretion onto the central star (e.g., Hartmann
et al. 2016). Dispersal mechanisms, such as winds and outflows, also
contribute to the evolution through the depletion of disk material (e.g.,
Frank et al. 2014; Ercolano & Pascucci 2017; Winter & Haworth 2022; Pascucci
et al. 2022). Mass loss processes can have an internal origin, such as inside-
out clearing produced by the ionizing radiation of the host star, or come from
an external source, for example, the local environment. Dynamical interactions
between stars and external photoevaporation, driven by high-energy radiation
fields from OB massive stars, are among the most commonly discussed processes
affecting disk evolution in clustered environments (e.g., Winter et al. 2018;
Reiter & Parker 2022; Cuello et al. 2023).

Given the variety of properties found in planetary systems in our Galaxy, the
way forward for understanding disk evolution must include the analysis of
general disk and host star properties measured in a large statistical sample
of systems at different evolutionary stages and environments. This makes it
possible to identify correlations between the parameters (e.g., disk mass,
disk radii, mass accretion rates) and their possible connection with the age
of the region or its environment. Thanks to the availability of sensitive,
wide-band optical spectrographs, such as the X-Shooter instrument on the Very
Large Telescope (VLT), and radio interferometers, like the Atacama Large
Millimeter and sub-millimeter Array (ALMA), it is now possible to measure some
of these general properties (Miotello et al. 2023, for a review). In
particular, the mass accreted onto the central star per unit time
($\dot{M}_{\rm acc}$), drawn from UV-optical spectra, and the disk mass
($M_{\rm disk}$), from ALMA observations, have proven to be very useful for
this task (Manara et al. 2023). For instance, surveys of young stars in
different star-forming regions (SFRs) have found a tentative trend of
decreasing $\dot{M}_{\rm acc}$ with age (e.g., Sicilia-Aguilar et al. 2010;
Antoniucci et al. 2014; Briceño et al. 2019; Manzo-Martínez et al. 2020),
predicted by viscous evolution models (e.g., Lynden-Bell & Pringle 1974;
Hartmann et al. 1998). This observational trend, however, has large
uncertainties, mainly due to unreliable age estimates for individual stars
(e.g., Soderblom et al. 2014) and correlated uncertainties between stellar
properties and estimated individual ages (Da Rio et al. 2014). Finally, an
unexpectedly large fraction of high accretors are found in old ($>$5Myr)
regions (Ingleby et al. 2014; Manara et al. 2020, 2021; Testi et al. 2022).

Furthermore, measurements of $M_{\rm disk}$ (estimated from dust emission and
assuming a gas-to-dust ratio of 100) are now available for large samples of
disks (e.g., Ansdell et al. 2017, 2016; Pascucci et al. 2016; Barenfeld et al.
2016; Grant et al. 2021; van Terwisga & Hacar 2023), which in combination with
$\dot{M}_{\rm acc}$, has allowed us to connect what is happening in the
innermost regions ($\lesssim$1 au) with outer disk properties and thus test
disk evolution models. According to viscous evolution, $\dot{M}_{\rm acc}$
should positively correlate with $M_{\rm disk}$ (predicted from the gas mass)
in such a way as to expect a tighter correlation at older ages (Rosotti et al.
2017; Lodato et al. 2017; Somigliana et al. 2022). The $M_{\rm disk}$
–$\dot{M}_{\rm acc}$ relation has now been empirically established for nearby
SFRs, although with a (puzzling) large spread regardless of the age of the
region (e.g., Manara et al. 2016b, 2020; Mulders et al. 2017), pointing to a
deviation from the purely viscous evolution theory, possibly toward a further
importance of MHD winds in driving accretion in the disk (Manara et al. 2023;
Tabone et al. 2022, Somigliana et al. subm.).

However, these studies have mainly focused on nearby ($<$ 300 pc) low-mass
SFRs that distinctly lack OB stars (e.g., Taurus, Andrews et al. 2013), and do
not represent the environment where most planets have formed or the birth
environment of our Solar System (e.g., Lada & Lada 2003; Fatuzzo & Adams 2008;
Adams 2010; Winter et al. 2020). Given the increasing relevance attributed to
environmental factors in modulating disk evolution and planet formation,
several authors have now included the effects of external photoevaporation by
massive stars in models of viscous disk evolution (e.g., Clarke 2007; Anderson
et al. 2013; Facchini et al. 2016; Haworth et al. 2018; Sellek et al. 2020a;
Coleman & Haworth 2022). The ratio $M_{\rm disk}$/$\dot{M}_{\rm acc}$ has
gained particular attention as a proxy of disk evolution, and as a possible
discriminant between external effects and other internal disk evolution
mechanisms. Rosotti et al. (2017) showed that externally irradiated disks show
a $M_{\rm disk}$/$\dot{M}_{\rm acc}$ significantly lower than the expected
value for a given system age, due to the radical disk mass depletion
characteristic of this scenario. Similarly, external truncation in multiple
stellar systems leads to a similar decrease of $M_{\rm disk}$/$\dot{M}_{\rm
acc}$ (Zagaria et al. 2022).

An ideal region to test these aforementioned predictions is the
$\sigma$-Orionis cluster. Its intermediate age ($\sim$3-5 Myr, Oliveira et al.
2004; Hernández et al. 2014), makes it young enough to remain bound, yet old
enough for its central OB system ($\sigma$-Ori, Caballero 2007) to have left
its imprint. In contrast to the more extreme examples of externally irradiated
disks we have, the Orion proplyds (O’dell et al. 1993), where EUV photons
drive mass loss and shape the proplyds in close proximity ($<$0.03 pc) to
$\theta^{1}$ Ori C (Johnstone et al. 1998), the dispersal of disks in
$\sigma$-Orionis is controlled by far-UV (FUV) radiation (e.g., Adams et al.
2004; Facchini et al. 2016; Haworth et al. 2018) as a result of the lower mass
of its OB system (compared to $\theta^{1}$ Ori C) and the larger separation of
the stars to the center, depleting the disks close to $\sigma$-Ori. This was
shown in the ALMA survey of $\sigma$-Orionis (Ansdell et al. 2017), which
found a dearth of massive ($M_{\rm dust}$$>3M_{\oplus}$) disks close ($<$ 0.5
pc) to the central OB stars, and a smooth distance-dependent trend in the disk
dust mass distribution, in line with previous results in the NGC2024 and the
Orion Nebula Clusters (Mann et al. 2014, 2015), and in other less massive
regions in Orion (van Terwisga & Hacar 2023). This observed depletion of disk
masses in $\sigma$-Orionis was later reproduced using external
photoevaporative models (Winter et al. 2020). However, several other effects
are at play, including dynamics in the clusters, and this trend could be
coincidental (Parker et al. 2021).

Just measuring disk dust masses is not enough to firmly assess the effects of
external photoevaporation on disk evolution in massive star-forming regions.
Two additional observational probes can be used. The ratio of forbidden
emission lines is also a way to detect signs of externally photoevaporated
disks. Rigliaco et al. (2009) used this probe to claim that the SO587 disk in
$\sigma$-Orionis is currently being externally photoevaporated, and has also
been supported by photoevaporative models recently (Ballabio et al. 2023).
Additional forbidden emission line data analyzed by Gangi et al. (2023) for 3
targets in the $\sigma$-Orionis cluster are however still not conclusive tell-
tale tests of external photoevaporation, due both to the strong nebular
contamination and the small sample. The other observational proxy of external
photoevaporation, the correlation between $M_{\rm disk}$ and $\dot{M}_{\rm
acc}$, has not yet been well established due to the lack of accurate mass
accretion rates for sources with detected sub-mm fluxes. Previous estimates of
accretion rates for $\sigma$-Orionis members were obtained either for a small
sub-sample of very low-mass stars (Rigliaco et al. 2012) or using indirect
tracers such as U-band photometry (Rigliaco et al. 2011) or the H$\alpha$ line
from low-resolution spectroscopy (Maucó et al. 2016). Therefore, this latter
proxy is for the first time used in this work for the $\sigma$-Orionis
cluster.

Here we present the results of the first large-scale spectroscopic survey of
disk-bearing stars in the $\sigma$-Orionis cluster in which mass accretion
rates are analyzed together with - new and previously published - disk masses.
Our main objective is to study, for the first time, the relationship between
$\dot{M}_{\rm acc}$ and $M_{\rm disk}$, and to further constrain the
dependence of $M_{\rm disk}$ with the distance from the massive system
$\sigma$-Ori. After describing the sample in Sect. 2 and the observations and
data reduction in Sect.3, we present our results on stellar parameters, and
disk mass estimates in Sect. 4. We discussed the implications of our findings
in the context of external photoevaporation in Sect. 5. Finally, we summarize
our conclusions in Sect. 6.

##  2 Sample

The $\sigma$-Orionis cluster is located in the Orion OB1 association, which is
one of the largest and nearest OB associations spanning over 200 deg2 on the
sky (see the review in Reipurth 2008). Their OB stars were first recognized by
Garrison (1967) as a group of 15 B-type stars around the massive hierarchical
triple system $\sigma$-Ori, whose most massive component is an O9.5V star
(Caballero 2007; Simón-Díaz et al. 2015), shaping the photodisociation region
known as the Horsehead Nebula (e.g., Abergel et al. 2003; Pety et al. 2005)
and setting the UV field strength in the cluster (see Fig. 8). In the last
decades, several hundred low-mass stars and brown dwarfs have been already
identified as part of the cluster (e.g., Reipurth 2008). The disks around the
low-mass stars were first identified using Spitzer photometry (Hernández et
al. 2007; Luhman et al. 2008) and then followed with Herschel (Maucó et al.
2016) and, more recently, imaged with ALMA at 1.3 mm (Ansdell et al. 2017) and
followed down to the brown dwarf limit (Damian et al. 2023a, b). The low
reddening toward its center (E(B-V) $\lesssim$ 0.1 mag, e.g., Brown et al.
1994; Béjar et al. 1999; Sherry et al. 2008) makes it an excellent natural
laboratory to study protoplanetary disk evolution in the entire range of
stellar masses and in the context of externally irradiated disks in moderate-
to-high UV environments.

Our X-Shooter sample consists of 50 disk-bearing stars in the $\sigma$-Orionis
cluster with ALMA observations (Ansdell et al. 2017) and located at different
projected distances from $\sigma$-Ori (see Fig. 1). Of the 50 stars observed
with X-Shooter, 43 have been detected by ALMA. The sample includes the objects
studied in Rigliaco et al. (2012, 2009), and mainly consists of late-K and M
spectral type (SpT) stars at different evolutionary stages based on the
classification of their spectral energy distribution (SED, Luhman et al.
2003), as reported by Hernández et al. (2007); Rigliaco et al. (2011); Maucó
et al. (2016). Our sample includes five disks with central cavities or
transition disks (TD), one class I star (SO1153), which in the Luhman et al.
(2003) classification points to a strong IR excess rather than to an embedded
object (this source is visible at UV-optical wavelengths), and the rest are
class II stars. The list of the observed targets is reported in Table 1.

Figure 1: Spatial distribution of $\sigma$-Orionis sources (points), and
massive O-B stars (star symbols) in the cluster. The massive, multiple system
$\sigma$-Ori is indicated in cyan while the rest of the B-type stars in gray.
The color bar shows the incident FUV field strength (in terms of the
dimensionless parameter $G_{o}$) due to the massive stars. Black circles show
projected distances of 0.5, 1.2, and 2.0 pc.

The Gaia EDR3 astrometric solutions for the sample are generally good, with
low renormalized unit weight errors (RUWE). Only 8 targets (SO397, SO490,
SO563, SO583, SO587, SO736, SO823, SO897) have RUWE values $>$ 1.4, considered
an appropriate nominal limit for Gaia EDR3 (Gaia Collaboration et al. 2021).
For all targets, we assumed the individual distances inverting the parallaxes
from Gaia EDR3 (arithmetic distances, Gaia Collaboration et al. 2021). We then
estimated the average distance to the cluster, considering only sources with
RUWE $<$ 1.4, and found a median distance of 401 pc. This is compatible with
the values reported by Damian et al. (2023b). Therefore, for all our targets
we assumed their arithmetic distances unless the values were unreliable – RUWE
$>$ 1.4 and/or distance differing more than 60 pc from the mean distance to
the region (target SO936) – or not available (targets SO435, SO562, and
SO1155), in which case we assumed the median distance to the members of the
region. Distances for the sample are also listed in Table 1.

Through this analysis, we found four targets, namely SO73, SO299, SO411, and
SO848, whose distances are lower than the median by $\sim$40 pc and yet have
RUWE values $<$1.4. These can be possible members of the more sparse Orion
OB1a sub-association in front of $\sigma$-Orionis (Briceño et al. 2019). For
SO411 this seems to be the case based on its proper motions (Pérez-Blanco et
al. 2018), however, for the rest of these stars we cannot know for certain.
Therefore, we have included them in the analysis assuming their arithmetic
distances from Gaia, and we have pointed them out whenever they appear as
outliers from the main population. Similarly, the star SO828 with a distance
of 449.5 pc (i.e., $\sim$50 pc away from the median distance to the members of
the region) is treated in the same way.

##  3 Observations, and data reduction

###  3.1 Spectroscopy with VLT/X-Shooter

Observations were carried out between October 2019 and February 2020 (Pr.Id.
0104.C-0454(A), PI Ansdell) and between November 2021 and January 2022 (Pr.Id.
108.22CB.001, PI Ansdell) in Service Mode at the ESO Very Large Telescope
(VLT). The X-Shooter instrument (Vernet et al. 2011) was used for all
observations. This instrument acquires spectra simultaneously in three arms:
UVB ($\lambda\sim 300-550$ nm), VIS ($\lambda\sim 500-1050$ nm), and NIR
($\lambda\sim 1000-2500$ nm). All the stars were observed with a nodding
pattern using a set of narrow slits (1.0”–0.4”–0.4” in the UVB–VIS–NIR arms,
respectively), yielding the highest spectral resolution ($\sim$ 5400, 18400,
11600, respectively). For flux calibrating the spectra, a short ($\sim$1 min
to 10 min depending on target brightness) exposure in stare with a set of wide
slits (5.0”) prior to the science exposure was taken.

Data reduction was done using the X-Shooter pipeline v.3.2.0 (P104 data) and
v.3.5.0 (P108 data) (Modigliani et al. 2010) run within the ESO Reflex
environment (Freudling et al. 2013) using the same procedure as in previous
similar analyzes (e.g., Alcalá et al. 2017; Manara et al. 2020; Venuti et al.
2019). The pipeline runs the classical reduction steps, including bias
subtraction, flat-fielding, wavelength calibration, flexure and atmospheric
dispersion correction, background removal (in stare mode) or combination of
spectra obtained in a nodding cycle, and the extraction of the 1D spectrum.
Telluric correction was then performed on the high-resolution spectra with the
molecfit tool (Smette et al. 2015), which models the telluric absorption lines
on the observed spectra using information on the atmospheric conditions in the
night. Finally, the high-resolution spectra were rescaled to those obtained
with the wider slit in order to account for slit losses and obtain absolute
flux calibration. This methodology leads to accurate flux calibration of the
spectra (e.g., Manara et al. 2021).

Particular care was taken in the case of the resolved binary system SO1267,
where the two traces of the two targets, separated by 1.4”, were manually
extracted using the IRAF software. Throughout this paper, the source indicated
as SO1267 refers to SO1267A. For the targets observed on nights with humidity
higher than $\sim$40% or with PWV$\sim$9.5 mm, we did use the flux standard
observed in the closest night with optimal conditions, to avoid introducing
incorrect shapes in the NIR arm of the spectra. Finally, for SO844 and SO1154
we did rescale the narrow slit spectra to non-simultaneous photometric data,
since the wide slit spectra had non-reliable fluxes lower than the narrow slit
ones, possibly due to the presence of thin cirrus at the time of the
observations.

###  3.2 ALMA cycle 4 data

In this paper we use new, higher sensitivity Band 6 Cycle 4 ALMA observations
obtained with eight Execution Blocks (EBs) on 29, 30 October 2016, 2, 3
November 2016, 14 May 2017, 2, and 4 July 2017 (Project ID: 2016.1.00447.S;
PI: Williams). The array configuration used between 40 and 44 12m antennas,
with baselines of $\sim$20–2650 m in July 2017, leading to a spatial
resolution of $\sim$0.18”, and shorter baselines of $\sim$15 - 1125 m in May
2017 and in 2016, with corresponding spatial resolution $\sim$0.26”. The
correlator setup included two broadband continuum windows centered on 234.3
and 216.5 GHz with bandwidths of 1.875 GHz and channel widths of 31.25 and
1.129 MHz, respectively. The bandwidth-weighted mean continuum frequency was
225.77 GHz (1.33 mm). The spectral windows covered the 12CO (230.538 GHz),
13CO (220.399 GHz), and C18O (219.560 GHz) $J=2-1$ transitions at velocity
resolutions of 0.079 - 0.096 km/s. These spectral windows had bandwidths of
58.59 MHz and channel widths of 60.6 kHz - 0.071 MHz.

The raw data were pipeline calibrated at NRAO using the CASA package (version
4.7.2). The pipeline calibration included: absolute flux calibration with
observations of J0522-3627 or J0423-0120; bandpass calibration with
observations of J0510+1800 or J0522-3627; and gain calibration with
observations of J0532-0307. We estimate an absolute flux calibration error of
$\sim$10% based on the amplitude variations of gain calibrators over time. The
imaging of the continuum and line data was performed similarly to what was
done by Ansdell et al. (2017), cleaning with a Briggs robust weighting
parameter of 0.5. We find a median 1.33 mm continuum RMS of 50 $\mu$Jy and the
median 12CO RMS is 11 mJy in 0.5 km s-1 channels. The achieved RMS for the
Representative Window centered on 13CO $(J=2-1)$ (220.399 GHz) is of 9.5 mJy
Beam-1 with a bandwidth of 0.096km/s and a 0.30$\times$0.22 arcsec beam, while
the requested sensitivity was of 3.3 mJy -1over 1.0 km s-1 and a beam size of
0.22 arcsec. The achieved continuum RMS is of 4.5 $10^{-2}$ mJy Beam-1 with a
bandwidth of 3.4 GHz and a 0.27$\times$0.19 arcsec beam. Continuum and 12CO
images are shown in Fig. 10, and 11, respectively, in Appendix C.1.

Figure 2: Hertzsprung-Russell diagram for $\sigma$-Orionis disks (orange
circles) including those from R12. Sources from other SFRs are shown by gray
symbols. Isochrones for 1, 3, 5, 10, 30, and 100 Myr from Siess et al. (2000)
are overplotted. Evolutionary tracks are from Baraffe et al. (2015).  Figure
3: Ratio between the accretion and stellar luminosities vs effective
temperature. $\sigma$-Orionis sources are indicated by orange circles while
stars in other young SFRs by gray symbols. The dotted and dashed lines
represent the locus of the chromospheric emission defined by Manara et al.
(2013b, 2017a). Downward triangles indicate the non-accretors identified in
this work.

##  4 Results

###  4.1 Stellar and accretion properties

X-Shooter provides absolute flux calibrated spectra with sufficient spectral
resolution and wavelength coverage to simultaneously characterize stellar,
accretion, wind, jet, and ionization properties of young stellar objects (e.g,
Bacciotti et al. 2011; Rigliaco et al. 2012; Alcalá et al. 2014; Frasca et al.
2017; Manara et al. 2016a, 2021). The continuum regions needed to determine
stellar and accretion parameters range from $\lambda\,\sim$ 300-364 nm (the
Balmer continuum) to $\lambda\,\sim$ 700 nm (where several molecular bands are
present). Various absorption lines along the spectrum are required to
constrain stellar spectral type and photospheric parameters (e.g., Manara et
al. 2013a).

In order to derive the stellar and accretion properties of the targets, we
follow the same fitting procedure as Manara et al. (2013a). In short, we model
the spectra by adding a photospheric template spectrum plus a slab model to
match the observed, dereddened spectrum. The grid of Class III photospheric
templates includes targets with SpT from G- to late M taken from Manara et al.
(2013b, 2017a), different slab models, and extinction values ($A_{V}$),
assuming the Cardelli et al. (1989) reddening law ($R_{V}$ = 3.1). The output
from the models is the excess luminosity due to accretion ($L_{\rm acc}$),
given by the integrated flux of the best-fit slab models, and the stellar
luminosity ($L_{\star}$), which is estimated by measuring the normalization of
the Class III templates that best match the observations. Distances were
estimated as described in Sect. 2. In Fig. 16 in the appendix, we show the
best-fit spectrum of each of our targets. We note that, as expected, $A_{V}$
is typically low, reaching values above or equal to 1.0 mag only in 7 targets.

For the sake of comparison with other star-forming regions, we considered the
same assumptions as Manara et al. (2023) and derived all the stellar and
accretion parameters in a similar way. Therefore, we measure all luminosities
($L_{\star}$, $L_{\rm acc}$) using the new Gaia distances and obtain $T_{\rm
eff}$ from SpT using the calibration by Herczeg & Hillenbrand (2014). In Table
2 we list the stellar and accretion parameters estimated for our sample,
including those from the Rigliaco et al. (2012) sample, which are recalculated
with the same assumptions that we just stated, including rescaling the
distance from 360 pc to the Gaia-based ones.

Using the $T_{\mathrm{eff}}$ and $L_{\star}$ from the best-fit we were able to
locate each target on the Hertzsprung-Russell diagram (HRD), as shown in Fig.
2. The targets in the $\sigma$-Orionis cluster are located in the region of
the HRD consistent with their expected age (3-5 Myrs). Three targets are
located at lower $L_{\star}$ with respect to the bulk of the population at the
same $T_{\rm eff}$, namely SO500, SO848, and, SO1154. SO500 is a known brown
dwarf (Rigliaco et al. 2011) and its location on the HRD is in line with other
sub-stellar objects. For SO1154, partial obscuration of the star by a highly
inclined disk could explain their positions on the HRD. A highly inclined disk
can add gray extinction and make the star under-luminous, resulting in more
uncertain estimates of $L_{\star}$ and of the mass accretion rate (Alcalá et
al. 2014). This target is the one with the highest measured $A_{V}$=1.8 mag,
supporting the hypothesis of (partial) obscuration by a disk. Finally, SO848
could either be also a highly inclined disk, or a foreground object, as
discussed in Sect. 2.

In order to check the estimates from the fit, we compared the values of
$L_{\rm acc}$ obtained with the fitting procedure described above, with those
derived from the luminosity of 10 emission lines, namely CaK, H$\delta$,
H$\gamma$, H$\beta$, $\mathrm{HeI}587$ nm, H$\alpha$, $\mathrm{HeI}667$ nm,
Pa$\gamma$, Pa$\beta$, Br$\gamma$, using the relations between line and
accretion luminosity by Alcalá et al. (2017). The mean value of $L_{\rm acc}$
derived from the emission lines is generally in agreement with the one
obtained by fitting the continuum in the X-Shooter spectrum with no dependence
on the wavelengths of the lines, pointing toward correctly estimated $A_{V}$.

Figure 3 shows the ratio between accretion and stellar luminosities as a
function of the effective temperature, which is a diagram used to check
whether the measured accretion luminosity is larger than typical chromospheric
emission (Manara et al. 2013a). Assuming the locus of chromospheric emission
defined by Manara et al. (2017a), we found 6 non-accreting targets in our
sample (downward triangles). As shown in Fig. 16 these sources exhibit
negligible UV excess, in line with their non-accreting nature. The rest of
accreting targets have similar $L_{\rm acc}$/$L_{\star}$ values at any given
$T_{\rm eff}$ as those found in other star-forming regions, in line with
previous results.

After locating the targets in the HRD, we derive $M_{\star}$ using the non-
magnetic models of Baraffe et al. (2015) for colder stars ($T_{\rm
eff}\leq$3900 K), and of Feiden (2016) for hotter stars ($T_{\rm eff}>$3900
K). For targets having stellar properties outside of the range of values
sampled by these models, we used the Siess et al. (2000) models instead.
Finally, the $\dot{M}_{\rm acc}$ is obtained from the classic relation
$\dot{M}_{\rm acc}=1.25\times L_{\rm acc}R_{\star}/(GM_{\star})$ from Hartmann
et al. (1998), using $L_{\rm acc}$ from the fit. The stellar and accretion
parameters of the sample are found in Table 2.

The relation between $\dot{M}_{\rm acc}$ and $M_{\star}$ is shown in Fig. 4
(top panel). Given the expected uncertainties on both quantities (error bar),
the $\sigma$-Orionis disks seem to populate the same parameter space as the
one covered by other young SFRs like Lupus, and Chameleon I, and even by the
older (5-10 Myr; Pecaut & Mamajek 2016) Upper-Scorpius (USco). This will be
further discussed in Sect. 5.2.

Figure 4: Top: Mass accretion rates vs stellar mass. The expected uncertainties are indicated by the error bars at the top left. Bottom: Disk masses vs stellar mass. All the targets from our sample and from Rigliaco et al. (2012) are plotted. Downward triangles indicate upper limits. The vertical dashed line indicates a $M_{\star}$= 0.4 $M_{\odot}$.  Table 1:  $\sigma$-Orionis Disk Sample Name | RA2000 | Dec2000 | Distance | $d_{\rm p}$ | Log $G_{o}$ | Disk type
---|---|---|---|---|---|---
| hh:mm:ss.s | dd:mm:ss.s | [pc] | [pc] |  |
SO73 | 05:37:30.95 | -02:23:42.8 | $359.2_{+4.2}^{-4.4}$ | 2.32 | 2.34 | –
SO299 | 05:38:00.97 | -02:26:07.9 | $355.5_{+4.3}^{-4.4}$ | 1.52 | 2.70 | TD
SO341 | 05:38:06.74 | -02:30:22.8 | $409.0_{+4.3}^{-4.4}$ | 1.31 | 2.83 | II
SO362 | 05:38:08.27 | -02:35:56.3 | $402.3_{+4.6}^{-4.8}$ | 1.07 | 3.01 | II
SO397 | 05:38:13.20 | -02:26:08.8 | $401.0$ | 1.47 | 2.73 | II
SO411 | 05:38:14.12 | -02:15:59.8 | $365.5_{+2.2}^{-2.2}$ | 2.28 | 2.35 | TD
SO467 | 05:38:21.19 | -02:54:11.1 | $383.3_{+8.6}^{-9.0}$ | 2.13 | 2.41 | –
SO490 | 05:38:23.58 | -02:20:47.6 | $401.0$ | 1.88 | 2.52 | II
SO500 | 05:38:25.44 | -02:42:41.3 | $409.2_{+37.2}^{-45.4}$ | 0.98 | 3.09 | II
SO518 | 05:38:27.26 | -02:45:09.7 | $399.0_{+3.9}^{-4.0}$ | 1.18 | 2.93 | II
SO520 | 05:38:27.51 | -02:35:04.2 | $402.6_{+6.3}^{-6.5}$ | 0.52 | 3.64 | II
SO540 | 05:38:29.16 | -02:16:15.7 | $406.0_{+3.5}^{-3.6}$ | 2.38 | 2.32 | II
SO562 | 05:38:31.41 | -02:36:33.8 | $401.0$ | 0.39 | 3.88 | II
SO563 | 05:38:31.58 | -02:35:14.9 | $401.0$ | 0.39 | 3.88 | II
SO583 | 05:38:33.68 | -02:44:14.2 | $401.0$ | 1.01 | 3.06 | II
SO587 | 05:38:34.06 | -02:36:37.5 | $401.0$ | 0.32 | 4.06 | II
SO646 | 05:38:39.03 | -02:45:32.2 | $404.6_{+6.6}^{-6.8}$ | 1.13 | 2.96 | II
SO662 | 05:38:40.27 | -02:30:18.5 | $401.2_{+3.3}^{-3.4}$ | 0.68 | 3.41 | II
SO682 | 05:38:42.28 | -02:37:14.8 | $409.8_{+4.7}^{-4.8}$ | 0.17 | 4.63 | II
SO687 | 05:38:43.02 | -02:36:14.6 | $412.8_{+4.2}^{-4.3}$ | 0.06 | 5.52 | II
SO694 | 05:38:43.87 | -02:37:06.8 | $392.3_{+9.2}^{-9.6}$ | 0.13 | 4.85 | –
SO697 | 05:38:44.23 | -02:40:19.7 | $404.5_{+2.4}^{-2.4}$ | 0.51 | 3.66 | II
SO726 | 05:38:47.46 | -02:35:25.2 | $403.9_{+6.8}^{-7.0}$ | 0.10 | 5.03 | II
SO736 | 05:38:48.04 | -02:27:14.2 | $401.0$ | 1.03 | 3.05 | II
SO739 | 05:38:48.19 | -02:44:00.8 | $433.3_{+20.3}^{-22.3}$ | 1.02 | 3.06 | II
SO774 | 05:38:52.01 | -02:46:43.7 | $403.3_{+3.3}^{-3.4}$ | 1.28 | 2.86 | II
SO818 | 05:38:58.32 | -02:16:10.1 | $405.4_{+4.1}^{-4.2}$ | 2.37 | 2.32 | TD
SO823 | 05:38:59.11 | -02:47:13.3 | $401.0$ | 1.37 | 2.79 | II
SO844 | 05:39:01.37 | -02:18:27.5 | $415.5_{+3.7}^{-3.8}$ | 2.18 | 2.39 | II
SO848 | 05:39:01.94 | -02:35:02.9 | $356.3_{+16.3}^{-18.0}$ | 0.46 | 3.75 | II
SO859 | 05:39:02.98 | -02:41:27.2 | $407.9_{+6.4}^{-6.6}$ | 0.84 | 3.22 | II
SO897 | 05:39:07.61 | -02:32:39.1 | $401.0$ | 0.77 | 3.29 | TD
SO927 | 05:39:11.51 | -02:31:06.5 | $413.6_{+4.7}^{-4.8}$ | 1.0 | 3.07 | II
SO984 | 05:39:18.83 | -02:30:53.1 | $409.6_{+3.1}^{-3.2}$ | 1.18 | 2.92 | II
SO1036 | 05:39:25.20 | -02:38:22.0 | $395.0_{+3.4}^{-3.5}$ | 1.19 | 2.92 | II
SO1075 | 05:39:29.35 | -02:27:21.0 | $390.0_{+8.2}^{-8.6}$ | 1.60 | 2.66 | II
SO1152 | 05:39:39.38 | -02:17:04.5 | $398.6_{+3.8}^{-3.9}$ | 2.71 | 2.21 | –
SO1153 | 05:39:39.82 | -02:31:21.8 | $396.6_{+4.2}^{-4.3}$ | 1.68 | 2.62 | I
SO1154 | 05:39:39.83 | -02:33:16.0 | $401.0$ | 1.64 | 2.64 | –
SO1155 | 05:39:39.90 | -02:43:09.0 | $401.0$ | 1.81 | 2.55 | –
SO1156 | 05:39:40.17 | -02:20:48.0 | $403.8_{+2.6}^{-2.6}$ | 2.42 | 2.30 | II
SO1248 | 05:39:51.73 | -02:22:47.2 | $398.4_{+7.6}^{-7.9}$ | 2.47 | 2.28 | –
SO1260 | 05:39:53.63 | -02:33:42.7 | $386.3_{+6.2}^{-6.4}$ | 1.95 | 2.49 | II
SO1266 | 05:39:54.21 | -02:27:32.6 | $399.1_{+10.4}^{-11.0}$ | 2.24 | 2.37 | II
SO1267 | 05:39:54.29 | -02:24:38.6 | $400.5_{+5.2}^{-5.3}$ | 2.42 | 2.30 | –
SO1274 | 05:39:54.60 | -02:46:34.0 | $407.3_{+2.7}^{-2.7}$ | 2.42 | 2.30 | II
SO1327 | 05:40:01.96 | -02:21:32.6 | $397.7_{+5.7}^{-5.8}$ | 2.79 | 2.18 | II
SO1361 | 05:40:08.89 | -02:33:33.7 | $406.0_{+3.9}^{-4.0}$ | 2.50 | 2.27 | II
SO1362 | 05:40:09.33 | -02:25:06.7 | $399.4_{+10.2}^{-10.7}$ | 2.76 | 2.19 | II
SO1369 | 05:40:12.87 | -02:22:02.0 | $402.5_{+2.5}^{-2.5}$ | 3.05 | 2.10 | –
Table 2:  Stellar and accretion properties and disk masses Name | SpT | $T_{\rm eff}$ | $A_{V}$ | $L_{\star}$ | $\log L_{\rm acc}$ | $M_{\star}$ | $\log\dot{M}_{\rm acc}$ | Fmm | $M_{\mathrm{dust}}$ | F${}_{{}^{12}\rm CO}$
---|---|---|---|---|---|---|---|---|---|---
|  | [K] | [mag] | [$L_{\odot}$] | [$L_{\odot}$] | [$M_{\odot}$] | [$M_{\odot}$/yr] | [mJy] | $[\,\mathrm{M}_{\oplus}]$ | [mJy]
SO73 | M3 | 3410 | 1.0 | 0.2 | -1.13 | 0.29 | -7.89 | 0.53 $\pm$ 0.13 | 1.6 $\pm$ 0.4 |  $<$ 66.0
SO299 | M3.5 | 3300 | 0.2 | 0.22 | -2.62 | 0.24 | -9.26 | 1.01 $\pm$ 0.14 | 3.0 $\pm$ 0.4 |  $<$ 66.0
SO341 | M0 | 3900 | 0.8 | 0.55 | -1.18 | 0.59 | -8.14 | 1.19 $\pm$ 0.13 | 3.5 $\pm$ 0.1 |  $<$34.35
SO362 | M3 | 3410 | 1.4 | 0.6 | -0.7 | 0.3 | -7.23 | 0.56 $\pm$ 0.13 | 1.6 $\pm$ 0.1 |  $<$34.02
SO397 | M4.5 | 3085 | 0.0 | 0.24 | -2.62 | 0.19 | -9.06 |  $<$ 0.4 |  $<$ 1.6 |  $<$ 69.0
SO411 | G4 | 5516 | 0.6 | 11.67 | -0.4 | 2.65 | -7.66 | 5.16 $\pm$ 0.13 | 17.1 $\pm$ 0.1 | 130.35 $\pm$ 18.02
SO467 | M5.5 | 2920 | 0.3 | 0.07 | -3.18 | 0.1 | -9.57 | 0.61 $\pm$ 0.13 | 2.1 $\pm$ 0.5 |  $<$ 66.0
SO490 | M5.5 | 2920 | 0.0 | 0.1 | -3.01 | 0.13 | -9.41 |  $<$ 0.4 |  $<$ 1.6 |  $<$ 72.0
SO500 | M6 | 2860 | 0.0 | 0.02 | -3.84 | 0.06 | -10.22 |  $<$ 0.4 |  $<$ 1.6 |  $<$ 63.0
SO518 | K6 | 4115 | 1.6 | 0.48 | -0.69 | 0.8 | -7.86 | 0.52 $\pm$ 0.13 | 2.1 $\pm$ 0.1 | 96.61 $\pm$ 18.57
SO520 | M4.5 | 3085 | 0.1 | 0.23 | -2.01 | 0.18 | -8.45 | 0.52 $\pm$ 0.14 | 2.0 $\pm$ 0.5 |  $<$ 69.0
SO540 | K6 | 4115 | 0.5 | 0.57 | -1.84 | 0.77 | -8.96 | 10.69 $\pm$ 0.29 | 46.4 $\pm$ 0.3 | 1306.92 $\pm$ 45.33
SO562 | M5.5 | 2920 | 0.3 | 0.26 | -1.44 | 0.15 | -7.7 | 0.71 $\pm$ 0.13 | 2.9 $\pm$ 0.1 |  $<$33.66
SO563 | M0 | 3900 | 0.6 | 0.36 | -1.27 | 0.64 | -8.36 | 0.18 $\pm$ 0.04 | 0.7 $\pm$ 0.1 |  $<$ 33.0
SO583 | K4 | 4375 | 1.0 | 4.06 | -0.69 | 1.18 | -7.62 | 1.9 $\pm$ 0.13 | 7.1 $\pm$ 0.1 | 68.95 $\pm$ 12.52
SO587 | M4.5 | 3085 | 0.0 | 0.35 | -3.91 | 0.21 | -10.31 |  $<$ 0.1 |  $<$ 0.4 |  $<$ 33.6
SO646 | M3.5 | 3300 | 0.0 | 0.12 | -2.9 | 0.25 | -9.66 |  $<$ 0.4 |  $<$ 1.6 |  $<$ 69.0
SO662 | K7 | 4020 | 0.3 | 0.68 | -3.79 | 0.64 | -10.77 | 1.54 $\pm$ 0.14 | 8.8 $\pm$ 0.2 |  $<$33.99
SO682 | M0 | 3900 | 0.7 | 0.76 | -2.02 | 0.57 | -8.89 | 0.41 $\pm$ 0.14 | 1.0 $\pm$ 0.1 |  $<$30.78
SO687 | M1 | 3720 | 0.8 | 0.73 | -1.21 | 0.44 | -7.94 | 0.28 $\pm$ 0.04 | 1.1 $\pm$ 0.1 |  $<$ 32.1
SO694 | M5.5 | 2920 | 0.1 | 0.16 | -2.51 | 0.12 | -8.82 | 0.61 $\pm$ 0.14 | 2.2 $\pm$ 0.5 |  $<$ 69.0
SO697 | K6 | 4115 | 0.2 | 0.97 | -3.11 | 0.67 | -10.05 | 0.16 $\pm$ 0.04 | 0.6 $\pm$ 0.1 |  $<$ 33.9
SO726 | M0 | 3900 | 0.6 | 0.56 | -2.19 | 0.59 | -9.15 | 0.18 $\pm$ 0.04 | 0.7 $\pm$ 0.1 |  $<$ 33.4
SO736 | K7 | 4020 | 0.1 | 1.49 | -1.48 | 0.55 | -8.23 | 0.45 $\pm$ 0.14 | 2.8 $\pm$ 0.1 |  $<$35.88
SO739 | M6.5 | 2815 | 0.1 | 0.1 | -3.06 | 0.1 | -9.35 | 0.52 $\pm$ 0.14 | 2.3 $\pm$ 0.6 |  $<$ 69.0
SO774 | K7 | 4020 | 0.0 | 0.49 | -2.75 | 0.7 | -9.84 | 0.76 $\pm$ 0.14 | 3.4 $\pm$ 0.1 | 104.2 $\pm$ 15.91
SO818 | K7 | 4020 | 0.4 | 0.29 | -2.11 | 0.78 | -9.36 | 1.97 $\pm$ 0.15 | 7.5 $\pm$ 0.6 | 514.0 $\pm$ 58.0
SO823 | K7 | 4020 | 1.5 | 0.32 | -2.43 | 0.77 | -9.66 | 0.17 $\pm$ 0.04 | 0.6 $\pm$ 0.1 |  $<$ 32.2
SO844 | M1 | 3720 | 0.7 | 0.62 | -1.37 | 0.44 | -8.14 | 2.85 $\pm$ 0.14 | 15.3 $\pm$ 0.1 | 172.14 $\pm$ 16.73
SO848 | M4 | 3190 | 0.0 | 0.02 | -3.51 | 0.17 | -10.47 | 0.52 $\pm$ 0.14 | 1.5 $\pm$ 0.4 |  $<$ 66.0
SO859 | M3 | 3410 | 0.6 | 0.41 | -1.72 | 0.29 | -8.31 | 2.49 $\pm$ 0.14 | 9.7 $\pm$ 0.6 |  $<$ 69.0
SO897 | K6 | 4115 | 0.6 | 0.85 | -1.34 | 0.7 | -8.33 | 1.71 $\pm$ 0.14 | 6.8 $\pm$ 0.1 | 78.54 $\pm$ 15.28
SO927 | M0 | 3900 | 0.6 | 0.33 | -1.92 | 0.65 | -9.03 | 1.41 $\pm$ 0.15 | 8.0 $\pm$ 0.1 | 75.95 $\pm$ 10.77
SO984 | K7 | 4020 | 0.1 | 0.72 | -3.5 | 0.64 | -10.46 | 6.07 $\pm$ 0.15 | 28.4 $\pm$ 0.1 | 276.62 $\pm$ 30.32
SO1036 | M0 | 3900 | 0.7 | 0.53 | -0.89 | 0.59 | -7.86 | 5.94 $\pm$ 0.25 | 23.6 $\pm$ 0.2 | 233.88 $\pm$ 31.42
SO1075 | M3 | 3410 | 0.6 | 0.14 | -1.38 | 0.3 | -8.22 | 1.48 $\pm$ 0.15 | 5.2 $\pm$ 0.5 | 165.0 $\pm$ 33.0
SO1152 | M0 | 3900 | 0.8 | 0.61 | -1.26 | 0.58 | -8.19 | 8.57 $\pm$ 0.29 | 37.5 $\pm$ 0.3 | 748.6 $\pm$ 35.8
SO1153 | K5 | 4210 | 1.5 | 0.33 | 0.02 | 0.9 | -7.3 | 13.62 $\pm$ 0.27 | 62.5 $\pm$ 0.2 | 746.87 $\pm$ 37.91
SO1154 | K7 | 4020 | 1.8 | 0.08 | -0.78 | 0.62 | -8.19 | 1.44 $\pm$ 0.15 | 7.0 $\pm$ 0.1 |  $<$33.96
SO1155 | K4 | 4375 | 0.6 | 1.45 | -0.92 | 0.86 | -7.94 | 0.41 $\pm$ 0.04 | 0.7 $\pm$ 0.1 |  $<$ 34.4
SO1156 | K6 | 4115 | 0.4 | 0.66 | -1.26 | 0.74 | -8.33 | 5.66 $\pm$ 0.15 | 23.4 $\pm$ 0.2 | 263.26 $\pm$ 22.57
SO1248 | M5.5 | 2920 | 0.0 | 0.18 | -3.3 | 0.13 | -9.6 | 0.79 $\pm$ 0.15 | 2.9 $\pm$ 0.6 |  $<$ 72.0
SO1260 | M4 | 3190 | 0.0 | 0.15 | -1.94 | 0.19 | -8.53 |  $<$ 0.4 |  $<$ 1.5 |  $<$ 69.0
SO1266 | M4.5 | 3085 | 0.0 | 0.07 | -4.76 | 0.15 | -11.36 |  $<$ 0.5 |  $<$ 1.7 |  $<$ 72.0
SO1267 | M1 | 3720 | 0.6 | 0.76 | -1.85 | 0.43 | -8.57 | 2.27 $\pm$ 0.15 | 9.0 $\pm$ 0.1 | 170.01 $\pm$ 18.73
SO1274 | K7 | 4020 | 0.0 | 0.68 | -0.98 | 0.64 | -7.95 | 15.38 $\pm$ 0.42 | 67.9 $\pm$ 0.4 | 1018.3 $\pm$ 38.63
SO1327 | M4.5 | 3085 | 0.1 | 0.33 | -1.91 | 0.21 | -8.32 | 1.63 $\pm$ 0.16 | 6.0 $\pm$ 0.6 |  $<$ 75.0
SO1361 | M1 | 3720 | 0.5 | 0.47 | -0.61 | 0.46 | -7.46 | 5.34 $\pm$ 0.15 | 21.2 $\pm$ 0.1 | 208.19 $\pm$ 25.69
SO1362 | M5.5 | 2920 | 0.0 | 0.1 | -2.96 | 0.13 | -9.37 | 1.02 $\pm$ 0.15 | 3.8 $\pm$ 0.6 |  $<$ 72.0
SO1369 | K7 | 4020 | 0.0 | 1.26 | -1.45 | 0.57 | -8.24 | 1.4 $\pm$ 0.15 | 6.8 $\pm$ 0.1 | 55.79 $\pm$ 14.13

###  4.2 Disk masses

The disk masses are estimated through their submm ALMA flux at 1.3 mm (band 6)
from cycle 3 (C3, Ansdell et al. 2017) and, when available, from our new,
deeper ALMA observations taken in cycle 4 (C4) and reported here (Sect. 3.2).
ALMA continuum fluxes are estimated as in Ansdell et al. (2017), that is by
fitting point-source models to the visibility data using the uvmodelfit
routine in CASA. More information on the ALMA data is reported in Appendix
C.1, which includes the comparison between ALMA fluxes from C3 and C4
observations in Fig. 9. The measured fluxes are reported in Table 2. In total,
we have 6 new continuum detections from the C4 observations. These continuum
fluxes were converted to dust masses taking into account the same assumptions
as Manara et al. (2023) namely, following Ansdell et al. (2016), we used a
prescription for the opacity, $\kappa_{\nu}=2.3(\nu/230\rm GHz)cm^{2}/g$,
taken from Beckwith et al. (1990). We used a single dust temperature, $T_{\rm
dust}$ = 20 K, which has been empirically demonstrated to be a good disk-
average value (Tazzari et al. 2021). The total disk mass is then obtained by
multiplying the $M_{\rm dust}$ by a gas-to-dust ratio of 100. We rescaled the
dust masses of Ansdell et al. (2017), which were estimated assuming $d=385$
pc. The rescaled dust masses and their errors are reported in Table 2.

The dependence of $M_{\rm dust}$ with the stellar mass is reported in Fig. 4,
and shows a similar trend of increasing dust mass with stellar mass as in
other star-forming regions, although with a large spread at $M_{\star}$$>$0.4
$M_{\odot}$ (vertical dashed line). We do not attempt a fit of the relation as
in Ansdell et al. (2017), as we will describe in Sect. 5.2 how we think that,
in $\sigma$-Orionis, the spread is possibly a consequence of external
photoevaporation.

We do not attempt to derive disk gas masses from the new detections of 12CO in
the C4 data. However, we will use the fluxes of 12CO, measured as in Ansdell
et al. (2017) using a curve-of-growth method on the moment 0 maps for the
detected targets. In total, the C4 data lead to 13 new 12CO detections. More
information is provided in Appendix C.1.

Figure 5: Disk dust mass ($M_{\rm dust}$) as a function of projected
separation from $\sigma$-Ori. Left: Considering the whole sample of disks with
ALMA observations. Middle: Considering the more massive ($M_{\star}$$\geq$ 0.4
$M_{\odot}$) stars in our $\sigma$ Orionis sample. Right: Considering the less
massive ones ($M_{\star}$$<$ 0.4 $M_{\odot}$). Dashed lines show the $M_{\rm
dust}$ median inside and outside 0.5 pc for our X-Shooter sample (orange) and
also including upper limits with reported SpT in Hernández et al. (2014)
(gray). Orange points are continuum detections, downward triangles are
3$\sigma$ upper limits and, 12CO detections (3$\sigma$) are indicated by an
additional blue circle. The 12CO fluxes are listed in Table 2.

##  5 Discussion

###  5.1 Dependence of disk mass with projected separation (and UV flux) from
$\sigma$-Ori

As discussed in Ansdell et al. (2017), a dearth of massive
($M\rm_{dust}>3M_{\oplus}$) disks close ($<$ 0.5 pc) in projected distance to
the central O9 star $\sigma$-Ori was found in the $\sigma$-Orionis region,
together with a shallow distance-dependent trend in disk dust mass. This
result, similarly found in Mann et al. (2014, 2015) for other clusters in
Orion, suggested that external photoevaporation may be a viable mechanism for
disk depletion. In this work, we have included deeper ALMA data with 6 new
detections (see Sect. 3.2). The updated $M_{\rm dust}$ distribution as a
function of the projected separation from $\sigma$-Ori is shown in Fig. 5. We
confirm the lack of any disk more massive than $\sim 3M_{\oplus}$ in the inner
$\sim$0.5 pc of the cluster, and again a shallow distance-dependent trend of
$M_{\rm dust}$. The new detections further reinforce the limit in the inner
part of the cluster, with detections of disks as low mass as less than
$1M_{\oplus}$, and even more stringent upper limits. This strengthens the
claim that many disks close to the ionizing star $\sigma$-Ori have extremely
low masses due to its irradiation.

To further quantify the level at which $\sigma$-Ori affects the stars, we
calculate the FUV radiation field strength due to the central OB system (see
Appendix A for details). This is dominated by the radiation of $\sigma$-Ori
alone. The top axis of Fig. 5 reports this FUV radiation strength expressed in
terms of the Habing unit $G_{0}$ ($G_{0}=\rm 1.6\times
10^{-3}\,erg\,cm^{-2}\,s^{-1}$, Habing 1968). The range of FUV values for this
region is between $10^{2}$ and $10^{5}$ $G_{0}$, lower than what is usually
observed in the Orion Nebula Cluster (e.g., Winter & Haworth 2022), but still
significant. Indeed, previous findings suggested that even moderate FUV fields
($\geq$ 2$\times 10^{3}G_{0}$) can drive significant disk mass loss (Facchini
et al. 2016; Kim et al. 2016; Haworth et al. 2018), consistent with the
observed trend. In particular, the radiation received by a disk at a projected
separation of $\sim$0.5 pc from $\sigma$-Ori is $\sim 10^{4}G_{0}$, and in
this range, the disks are found to have severely lower disk masses than at
larger distances. However, the most massive disks ($M_{\rm dust}$$\gtrsim
10M_{\oplus}$) are found only at projected distances larger than $\sim$1 pc,
corresponding to FUV fields of $\sim 10^{3}G_{0}$. Moreover, the CO
detections, reported in Fig. 5 as blue circles, are found only at projected
distances larger than 0.5 pc, although in a much higher fraction than that
reported by Ansdell et al. (2017), mainly thanks to the deeper observations of
C4 that were focused on the disks around higher-mass stars ($M_{\star}$
$\geq\,0.5\,\rm M_{\odot}$) as they tend to have brighter millimeter emission.

At this lower FUV field strength than the Orion Nebula Cluster or other
massive regions, $\sigma$-Orionis is thus offering us the unique possibility
to study external photoevaporation even at $\sim$3-5 Myr, where the effects
are clearly detectable but the disks are not yet (all) dispersed. We note that
the observed distance-dependent depletion of disks has been reproduced using
external photoevaporative models (Winter et al. 2020), although with
overestimated (by a factor of 2) disk dust masses. Although, according to
Parker et al. (2021), this could be coincidental, it is interesting to report
on this new observational result to further constrain the models. Additional
information to further support the external photoevaporation hypothesis is
then discussed in the next sections.

###  5.2 Relations with stellar host mass

Thanks to large surveys of young stars performed in various SFRs, global
stellar and disk properties have been estimated revealing different relations
between the various parameters. Among the well-established ones is that of the
$\dot{M}_{\rm acc}$ vs $M_{\star}$, with a steeper-than-linear relation
roughly as a power law with exponent $\sim$2 (e.g., Hillenbrand et al. 1992;
Muzerolle et al. 2003; Natta et al. 2006), and reported spreads in
$\dot{M}_{\rm acc}$ values of about 1-2 dex (e.g., Alcalá et al. 2014; Manara
et al. 2016a, 2017b, 2023; Venuti et al. 2014, 2019; Hartmann et al. 2016).
Recently, evidence of a double power-law fit of this relation has also been
seen (Alcalá et al. 2017; Manara et al. 2017a), with a very steep relation for
the lowest-mass stars ($M_{\star}$$<0.2-0.3$ $M_{\odot}$) with slope $\sim$4.5
followed by a flatter relation (slope$\sim$1) at higher $M_{\star}$. The
distribution of the measured $\dot{M}_{\rm acc}$ as a function of the
$M_{\star}$ for $\sigma$-Orionis sources are shown in the top panel of Fig. 4.
These values reveal a great similarity with those found in other SFRs, like
Lupus (Alcalá et al. 2017), Chamaeleon I (Manara et al. 2017b), and even the
older USco SFR (Manara et al. 2020). A flatter dependence of $\dot{M}_{\rm
acc}$ on $M_{\star}$ seems to be present at the highest $M_{\star}$ even in
our sample, suggesting that the broken power-law could be a better fit to the
data, in line with previous studies.

The similar range of $\dot{M}_{\rm acc}$ as in other typically younger SFRs is
at odds with the usually assumed decline of $\dot{M}_{\rm acc}$ with age, a
prediction of viscous evolution (e.g., Hartmann et al. 1998). This is however
nowadays observed in several regions, from Orion OB1 (Ingleby et al. 2014;
Manara et al. 2021; Pittman et al. 2022), to TWA (Venuti et al. 2019),
$\eta$-Cha (Rugel et al. 2018), or even in the 30 Dor region (De Marchi et al.
2017). The reason why disks can have such a high accretion rate for a time not
compatible with the amount of mass accreted over their lifetime and the total
available mass in the disk, is still the subject of discussion (e.g., Hartmann
et al. 2006) and, it is possibly related with episodic accretion or other
mechanisms (Manara et al. 2020) but, in our specific case, it could be a
selection effect due to a combination of enhanced accretion due to the effects
of external photoevaporation (Rosotti et al. 2017), and the focus on just the
disks that are not fully dispersed yet. Similarly to other star-forming
regions, a large scatter of $\dot{M}_{\rm acc}$ at any $M_{\star}$ is observed
for the $\sigma$-Orionis sources. Such a spread has been demonstrated not to
be due to accretion variability or other sources of uncertainty (e.g., Manara
et al. 2023, for a review) and its origin remains an open question. As also
shown in Rigliaco et al. (2012); Winter et al. (2020), we find a positive
correlation between $\dot{M}_{\rm acc}$ and $M_{\star}$ and no correlation of
$\dot{M}_{\rm acc}$ with proximity to $\sigma$-Ori.

The bottom panel of Fig. 4 shows another correlation also well established
empirically for individual regions, the $M_{\rm dust}$ vs $M_{\star}$
relation. Several works surveying different SFRs have shown that $M_{\rm
dust}$ directly depends on $M_{\star}$ with a slope around 1.8-2.7 with the
larger values describing the older Upper Scorpius region (Ansdell et al. 2016,
2017; Barenfeld et al. 2016; Pascucci et al. 2016; Manara et al. 2023), and
holds down to the brown dwarf regime (e.g., Testi et al. 2016; Sanchis et al.
2021; Rilinger & Espaillat 2021). The steepening with age has been interpreted
as faster evolution of dust around low-mass stars, whether as a result of more
efficient conversion of millimeter grains into larger centimeter grains or
more efficient radial drift. Interestingly, the dispersion around the relation
is very similar in all the regions ($\sim$0.8 dex). In the case of the
$\sigma$-Orionis cluster, we find similar results as Ansdell et al. (2017)
with sources populating a similar locus on this plane as in other SFRs. We
also find a large scatter in $M_{\rm dust}$ for a given stellar mass,
particularly large around the more massive stars ($M_{\star}$ $\geq$ 0.4
$M_{\odot}$) in our sample. Since the dispersion is present for all regions,
regardless of age and environment, it has been acknowledged as an inherent
property of disk populations resulting from the range of disk initial
conditions and has been explained theoretically, by invoking a mixture of both
the initial conditions and the evolutionary process (Pascucci et al. 2016;
Pinilla et al. 2020). However, we think that the origin of this dispersion at
high stellar masses ($M_{\star}$ $\geq$ 0.4 $M_{\odot}$) is possibly related
to the effects of the massive star $\sigma$-Ori on the surrounding disks, as
we discuss in the next subsection.

####  5.2.1 The effect of stellar mass on the disk mass depletion

In the middle and right panels of Fig. 5, we show the distribution of $M_{\rm
dust}$ as a function of projected separation from $\sigma$-Ori for stars with
$M_{\star}\geq 0.4\,M_{\odot}$ and $M_{\star}<0.4\,M_{\odot}$, respectively.
Dashed lines indicate the median values of $M_{\rm dust}$ for sources inside
and outside a projected distance of 0.5 pc from the position of $\sigma$-Ori.
Since SpT estimates are available from Hernández et al. (2014) for a sub-
sample of stars with $M_{\rm dust}$ upper limits (gray triangles on the left
panel) and without X-Shooter spectra (i.e., without stellar mass estimates),
we have added them as white downward triangles on these panels. Our SpT
estimates are in good agreement within the uncertainties with those reported
in Hernández et al. (2014). The only three targets that deviate more than
expected are two strong accretors (SO562, SO1075) and one highly extincted
star (SO823). We assigned the objects with SpT earlier than M2 in the higher
mass panel, and for later SpT to the lower mass panel. The choice is motivated
by the correspondence between SpT and $M_{\star}$ found in the X-Shooter
sample. The $M_{\rm dust}$ medians taking into account these additional values
are shown with a gray dashed line, while those estimated from the X-Shooter
sample alone are shown with an orange dashed line.

Looking at Fig. 5 we note that, within the inner 0.5 pc from $\sigma$-Ori, the
more massive ($M_{\star}$ $\geq$ 0.4 $M_{\odot}$) stars in $\sigma$-Orionis
(middle panel), show $M_{\rm dust}$ about an order of magnitude lower than the
more distant ones considering only the targets with measured $M_{\star}$
(orange dashed lines), or about 4 times lower when including those where only
the SpT is measured (gray dashed lines), although, in this case, the median
inside 0.5 pc is more uncertain given the less stringent upper limits. By
contrast, low-mass stars ($M_{\star}$ $<$ 0.4 $M_{\odot}$) have an apparent
constant distribution of $M_{\rm dust}$, regardless of their distance from the
ionizing stars (right panel). Even though this trend will still hold including
the additional ($\sim$19) upper limits shown in the left panel for which no
SpT nor $M_{\star}$ estimate exists (as these upper limits are of the same
order as our detections), this apparent flatness in the $M_{\rm dust}$
distribution for the low-mass stars in our sample is surely affected by the
low numbers statistics in this stellar mass range, mainly due to the distance
of the cluster (d = 401 pc) which makes it harder to survey low-mass stars
with respect to closer star-forming regions. It could be, therefore, that
there are more low-mass stars inside 0.5 pc that were not targeted in the ALMA
surveys because they were not part of the initial Spitzer catalogs. If these
are fainter at mm-wavelengths than our targets, the few low-mass objects that
are detected in close proximity to $\sigma$-Ori could represent the high upper
tail of the low-mass distribution. Deeper ALMA observations on these
additional targets along with spectroscopic follow-up are needed in order to
probe the apparent flatness of the $M_{\rm dust}$ distribution of the low-mass
stars in $\sigma$-Orionis. At the same time, the lower median $M_{\rm dust}$
for the low-mass stars compared to the more massive ones in the outer part of
the cluster (beyond 0.5 pc), is due to the known steep dependence of $M_{\rm
dust}$ with $M_{\star}$ just discussed. It is possible, therefore, to ascribe
the differences in the outer part of the cluster to other (internal) effects
related to the evolution of disks as well (Pascucci et al. 2016; Pinilla et
al. 2020).

The large difference between the median $M_{\rm dust}$ for the more massive
stars inside and outside projected distances of 0.5 pc from $\sigma$-Ori
points, instead, to environmental factors, like external photoevaporation,
affecting the closest disks to $\sigma$-Ori, decreasing significantly their
$M_{\rm dust}$, as discussed in Sect. 5.1. We note that this discrepancy holds
even considering the additional upper limits for targets without $M_{\star}$
estimates from the spectroscopy presented in this work (gray dashed lines).
Note as well that this discrepancy can be even larger if the two outliers
(SO823 and SO1155, see Sect. 2) are not taken into account. Although the disks
in the low-mass sample are in general less massive, as expected due to their
faster dust evolution, the median $M_{\rm dust}$ within the innermost region
of the cluster is still lower for the high-mass star sample than for the low-
mass star regime (see Fig. 5). It is worth discussing, therefore, why such an
effect is observed.

A possible solution to this puzzling result could be that the effects of
external photoevaporation depend on the stellar mass of the host star in a
more complex fashion than what is typically assumed. Indeed, for the fact that
the gravitational potential is stronger for higher-mass stars, it is usually
assumed that photoevaporation is more effective around lower-mass stars. This
however is a very simplistic assumption, since it is known that the disk radii
depend on the stellar mass as well, albeit indirectly through the already
mentioned dependence of the continuum flux with the disk radii, and the fact
that the disk masses are measured from the continuum flux. If the relation
between the disk radii and the stellar mass is not linear, then external
photoevaporation should affect the disks in a different way depending on the
(unperturbed) disk radius.

External photoevaporation would result in a lower disk mass obtained as a
result of eroding the disk in the outer regions, at disk radii ($R_{\rm
disk}$) larger than the gravitational radius, defined as $R_{\rm
grav}=(GM_{\star})/c_{s}^{2}$ in an isothermal system, where $c_{s}$ is the
sound speed (Winter & Haworth 2022), or even down to 0.15
$\cdot\leavevmode\nobreak\ R_{\rm grav}$ (Adams et al. 2004), although with
lower mass-loss rates. If disks are eroded by this process, we expect the disk
radii to be typically smaller than $R_{\rm grav}$. Unfortunately, the spatial
resolution of our observations ($\sim$0.2”$\sim$80 au, see Sect. 3.2) is not
sufficient to properly resolve the disks. However, we obtain indirect
estimates of the disk radii using the measured continuum flux, known to
correlate with the disk dust radii (Tripathi et al. 2017; Andrews et al. 2018;
Long et al. 2022), and the measured 12CO fluxes, which can be related to the
disk gas sizes under the assumption that the emission is optically thick
(e.g., Zagaria et al. 2023; Toci et al. 2023; Trapman et al. 2023). In the
cases where the 12CO is not detected, it is possible to extrapolate the gas
radii from the dust radii assuming a ratio of 3, found here for the targets
with both continuum and 12CO detections, and typically found in other star-
forming regions (e.g., Ansdell et al. 2018). We note that this procedure is
based on several assumptions, and, in particular, the latter is most probably
not valid in the case of external photoevaporation, which mainly affects the
gaseous component of the disk, where we expect a lower gas-to-dust radii
ratio.

Assuming $c_{s}=1$ km/s (which gives $\sim$120 K in 1000 $G_{0}$ environment)
as representative for our sample, we can compare the inferred disk radii with
the inferred gravitational radii ($R_{\rm disk}$/$R_{\rm grav}$) for each
target. Although with many caveats, this analysis results in disk radii that
are always smaller than the gravitational radii for all the stars in the
cluster, with the lowest ratios ($R_{\rm disk}$/$R_{\rm grav}$ $<$ 0.1) for
disks around stars $M_{\star}$$>$0.4 $M_{\odot}$ and with projected separation
from $\sigma$-Ori smaller than 0.5 pc, whereas they are larger in the outer
part of the cluster. This is in line with the expectations of the imprint of
external photoevaporation, with a stronger effect on the inner regions of the
cluster. As shown in Adams et al. (2004), the mass-loss rate due to externally
irradiated disks can still be significant even for disk radii much smaller
than the gravitational radius, in particular for $R_{\rm disk}$/$R_{\rm
grav}>$ 0.15, as we found in the outer part of the cluster. This reinforces
the claim that even at intermediate FUV radiation fields (1-1000 $G_{0}$) the
effects of this process can have a significant impact on the evolution of
protoplanetary disks (van Terwisga & Hacar 2023). However, we note that the
dependence of $M_{\rm disk}$ with the distance from $\sigma$-Ori is not as
steep as it would be expected from the results of van Terwisga & Hacar (2023).
The disks around the lowest mass stars, however, seem to have a constant ratio
$R_{\rm disk}$/$R_{\rm grav}\sim$0.4 regardless of the distance to
$\sigma$-Ori, which is a consequence of the flat distribution of fluxes (and
disk dust masses) with projected distance from $\sigma$-Ori shown in Fig. 5.

With all the several assumptions of our approach, namely the dependence of
continuum and gas emission with the disk radii, the ratio between gas and dust
disk radii, and the sensitivity of the $R_{\rm disk}$/$R_{\rm grav}$ ratio to
the value assumed for $c_{s}$, our approach points to a different dependence
of the effect of external photoevaporation with stellar host mass. This is
particularly evident in the dependence of $M_{\rm disk}$ with the projected
distance from $\sigma$-Ori (Fig. 5).

Our findings suggest that the large spread in the $M_{\rm disk}$-$M_{\star}$
relation observed for disks around stars with $M_{\star}$$>0.4M_{\odot}$ is an
effect of the environment in the $\sigma$-Orionis cluster. If confirmed, this
would shed new light on the evolution of the $M_{\rm disk}$-$M_{\star}$
relation with age, which is mainly driven by the large scatter (e.g., Manara
et al. 2023), leading to an interpretation where, at least for the mid-aged
$\sigma$-Orionis region, the steepening of the relation is an effect of
external photoevaporation. Work should be done in trying to properly measure
disk radii in these systems, particularly around low-mass stars, to confirm
whether they are less affected by external photoevaporation, or whether the
different behavior with respect to the disks around higher-mass stars is due
to other processes.

Figure 6: Distribution of the $\dot{M}_{\rm acc}$–$M_{\rm disk}$ in
$\sigma$-Orionis. The triangles indicate the upper limit on $M_{\rm disk}$,
while the vertical arrows correspond to the upper limits on the $\dot{M}_{\rm
acc}$. The dotted and dashed lines are the isochrones at some relevant ages.
The ones in bold are related to the estimated age of the cluster, i.e. 3-5 Myr
(Oliveira et al. 2004). Values for other star-forming regions (Manara et al.
2023) are shown as gray symbols for comparison. Figure 7: Distribution of
$t_{\rm disk}$ as a function of projected separation from $\sigma$-Ori. The
triangles indicate the upper/lower limits on $\dot{M}_{\rm acc}$ and $M_{\rm
disk}$. The vertical dotted line is located at 0.5 pc from $\sigma$-Ori.
Targets within 0.5 pc are highlighted with an additional red outline. The
dashed lines are related to the estimated age of the cluster, i.e. 3-5 Myr
(Oliveira et al. 2004).

###  5.3 $\dot{M}_{\rm acc}$–$M_{\rm disk}$ plane as a proxy of Disk Evolution

According to the disk viscous evolution framework, $\dot{M}_{\rm acc}$ should
directly correlate with $M_{\rm disk}$ (e.g., Hartmann et al. 1998; Rosotti et
al. 2017; Lodato et al. 2017; Mulders et al. 2017; Manara et al. 2023). The
viscous quasi-steady state is characterized by the condition $M_{\rm
disk}$$\sim$ $\dot{M}_{\rm acc}$$\tau$, with $\tau$ as the viscous time-scale
at the outer radius of the disk (Rosotti et al. 2017). One property of this
paradigm is that $\tau$ is of the order of the system age independent of the
initial conditions and the assumptions on disk viscosity (Jones et al. 2012;
Lodato et al. 2017). Therefore, the ratio $M_{\rm disk}$/$\dot{M}_{\rm acc}$,
the so-called ”disk lifetime” ($t_{\rm disk}$) can be used as a proxy of disk
evolution (Manara et al. 2016b, 2023; Rosotti et al. 2017). The dependence
between $M_{\rm disk}$ and $\dot{M}_{\rm acc}$ has been explored extensively
in the literature and found to be almost linear, albeit with a very large
scatter (e.g., Manara et al. 2016b, 2020, 2023; Mulders et al. 2017).

The origin of the observed scatter at all ages is still unclear, although it
points toward particular conditions in the viscous framework (Lodato et al.
2017), or to the necessity to include other mechanisms to explain the
observations. Both Rosotti et al. (2017) and Zagaria et al. (2022) suggest
that external disturbances, such as external photoevaporation or multiplicity,
lead to shorter disk lifetimes, that is higher $\dot{M}_{\rm acc}$ than the
value expected by viscous evolution corresponding to the measured disk mass.
Zagaria et al. (2022) found that multiplicity can explain the high accretors
found in the Upper Scorpius region (Manara et al. 2020).

The data presented in this work allows us, for the first time, to test whether
the $\dot{M}_{\rm acc}$-$M_{\rm disk}$ relation can be used to confirm the
effect of external photoevaporation on disks close to a massive star. Fig. 6
shows the $\dot{M}_{\rm acc}$–$M_{\rm disk}$ plane for our $\sigma$-Orionis
disk sample. We highlight the $t_{\rm disk}$ = 3 Myr and, 5 Myr (dashed
lines), representative of the age of the cluster (Oliveira et al. 2004;
Hernández et al. 2014), for reference. We observe that the majority of the
targets are located at shorter disk lifetimes than the age of the region, in
line with the expectations from external photoevaporation models (Rosotti et
al. 2017). In particular, 28 targets ($\sim 54\%$) lay above the 1 Myr line,
17 targets ($\sim 34\%$) are between the 1 Myr and 10 Myr lines, while the
remaining five targets ($\sim 10\%$) are below the 10 Myr line, and they are
mainly non-accreting objects. This points toward confirming the effect of
external photoevaporation on the evolution of these disks.

We note, however, that the distribution of data on the $\dot{M}_{\rm
acc}$-$M_{\rm disk}$ plane is similar to what is observed in other SFRs.
According to Zagaria et al. (2022), most of the stars in Lupus, Chameleon I,
and USCo SFRs that have higher $\dot{M}_{\rm acc}$ given their $M_{\rm disk}$
can be explained by multiplicity (tidally truncated disks), with the bulk of
the binary population being clustered around $M_{\rm disk}$/$\dot{M}_{\rm
acc}$ = 0.1 Myr. Unfortunately, we do not have multiplicity information for
our $\sigma$-Orionis sample to further test this scenario, but we have
indicated in the plots the stars with RUWE values greater than 1.4, which may
point to possible binaries in the cluster. Interestingly, most of the targets
with high RUWE have also short disk lifetimes, suggesting that binarity might
play a role also in the $\sigma$-Orionis cluster in the observed spread in the
$\dot{M}_{\rm acc}$-$M_{\rm disk}$ relation.

To further check whether the short disk lifetimes could be instead related to
the presence of the massive $\sigma$-Ori star, we show in Fig. 7 how $t_{\rm
disk}$ depends on the projected distance to the massive $\sigma$-Ori system.
As shown, all objects within 0.5 pc from $\sigma$-Ori (red circles) have
$t_{\rm disk}<$ 0.5 Myr, while disks further out can reach higher values.
Outliers, having $t_{\rm disk}<$ 0.05 Myr at 1 pc or beyond, correspond to
objects whose distances deviate in more than $\sim$40 pc to the median (SO73,
SO848), strong accretors (SO1155, SO362) and/or edge-on disks candidates
(SO518). The low disk lifetimes of the disks closest to the OB stars along
with the distance-dependent trend in disk dust mass shown in Fig. 5, robustly
evidence the fact that, at least within 0.5 pc from the center, the disks are
actively being externally photoevaporated.

The dependence of the disk lifetime with the projected separation from
$\sigma$-Ori further suggests that, despite the similar distribution on the
$\dot{M}_{\rm acc}$-$M_{\rm disk}$ plane as in other regions, the large spread
observed in our $\sigma$-Orionis sample also supports the outside-in depletion
of these disks. As stated in Lodato et al. (2017), from disk population
synthesis models, a tighter $M_{\rm disk}$-$\dot{M}_{\rm acc}$ correlation is
expected at longer ages, so the fact that these sources show a similar spread,
even at these intermediate ages, to other younger SFRs implies a more
significant deviation of these stars from purely viscous evolution. Enlarging
the sample on the low disk mass side, by adding additional disk detections to
the available spectroscopic data, would constrain quantitatively how many
disks are consistent with the effects of external photoevaporation, or whether
other effects must be considered in order to explain the observations, such as
the effects of dust evolution (e.g., Sellek et al. 2020b) or binarity (e.g.,
Zagaria et al. 2022).

##  6 Conclusions

We conducted the first large-scale survey with both, UV-to-NIR spectroscopy
with X-Shooter, and mm-interferometry with ALMA, for disk-bearing stars in the
mid-age $\sigma$-Orionis cluster. We have derived the stellar and accretion
properties of 50 targets, and shown new ALMA detections to complement the data
presented by Ansdell et al. (2017). This has allowed us to test the effect of
external photoevaporation from the massive star $\sigma$-Ori on the
surrounding population of disks.

Our main conclusions are:

  * •

The disks in the $\sigma$-Orionis cluster show similar values and spread in
the $\dot{M}_{\rm acc}$ –$M_{\star}$ and $M_{\rm disk}$ –$M_{\star}$ relations
as those in surveys of protoplanetary disks in other young SFRs. No
correlation of $\dot{M}_{\rm acc}$ with proximity to $\sigma$-Ori was found,
in agreement with previous works.

  * •

We confirm the trend of decreasing $M_{\rm dust}$ at shorter distances from
the massive star $\sigma$-Ori, as expected from external photoevaporation.
Disks around more massive stars show a more pronounced reduction in their
masses if they are located in the inner 0.5 pc of the cluster than disks in
the outer regions. They were also found to have the smallest $R_{\rm
disk}$/$R_{\rm grav}$ at these separations, which corresponds to a value of
FUV radiation of $\sim 10^{4}G_{0}$. This effect is less pronounced in the
lowest mass stars, either due to a stellar mass-dependent effect of external
photoevaporation or to observational biases. Due to the low number statistics,
the conclusions for the low-mass regime are still to be firmly established.
Our results stress the need to develop a deeper understanding of disk
evolution around very low-mass stars in clustered environments.

  * •

Half of the sample lies in the expected region for externally irradiated disks
on the $\dot{M}_{\rm acc}$ vs $M_{\rm disk}$ plane, showing disk lifetime
($t_{\rm disk}$) lower than expected given the age of the system. This implies
that external photoevaporation may be a viable mechanism for disk depletion in
the cluster.

  * •

We found a tentative increasing trend of $t_{\rm disk}$ with projected
separation from the massive OB stars. Within the first 0.5 pc, sources have
very low $t_{\rm disk}$ ($\leq 0.5$ Myrs). This strengthens the claim that
outside-in depletion plays an important role in the evolution of disks,
particularly those that are in close proximity ($<$ 0.5 pc) to the central OB
system $\sigma$-Ori.

While this work has shown the power of combining information on disk
properties with measurements of stellar and accretion parameters as a function
of projected separation from the massive OB-system $\sigma$-Ori, the final
tell-tale test of external photoevaporation in this region is to detect the
photoevaporating winds in these targets. A detailed study on wind tracers and
mass-loss diagnostic (e.g., optical forbidden emission lines) of these sources
using X-Shooter and high-resolution spectra can potentially confirm the above
result and put better constraints on disk dispersal mechanisms in clustered
environments (e.g., Hasegawa et al. 2022). This has been attempted in a
limited number of targets (Rigliaco et al. 2009; Gangi et al. 2023), and it
will be assessed in a future paper (Maucó et al., in prep).

###### Acknowledgements.

We thank the anonymous referee for the critical review of our work that
improved the presented study. Funded by the European Union (ERC, WANDA,
101039452). Views and opinions expressed are however those of the author(s)
only and do not necessarily reflect those of the European Union or the
European Research Council Executive Agency. Neither the European Union nor the
granting authority can be held responsible for them. This work benefited from
discussions with the ODYSSEUS team (HST AR-16129),
https://sites.bu.edu/odysseus/. This research received financial support from
the project PRIN-INAF 2019 ”Spectroscopically Tracing the Disk Dispersal
Evolution” (STRADE) and from the Large Grant INAF 2022 YODA (YSOs Outflows,
Disks and Accretion: towards a global framework for the evolution of planet-
forming systems). TJH is funded by a Royal Society Dorothy Hodgkin Fellowship.
S.F. is funded by the European Union under the European Union’s Horizon Europe
Research & Innovation Programme 101076613 (UNVEIL). Views and opinions
expressed are however those of the author(s) only and do not necessarily
reflect those of the European Union or the European Research Council. Neither
the European Union nor the granting authority can be held responsible for
them. This paper makes use of the following ALMA data:
ADS/JAO.ALMA#2016.1.00447.S. ALMA is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ. This project has received funding from the European Union’s Horizon 2020
research and innovation program under the Marie Sklodowska-Curie grant
agreement No 823823 (DUSTBUSTERS). This work was partly supported by the
Deutsche Forschungs-Gemeinschaft (DFG, German Research Foundation) - Ref no.
FOR 2634/1 TE 1024/1-1. 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.

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##  Appendix A UV radiation field strength

We estimated the FUV radiation field strength due to the central OB system
$\sigma$-Ori. For this, we followed the same approach as Winter & Haworth
(2022). We considered the three most massive stars in the hierarchical system
$\sigma$-Ori: $\sigma$ Ori Aa ($M_{\star}$= 20 $M_{\odot}$), $\sigma$ Ori Ab
($M_{\star}$= 14.6 $M_{\odot}$), and $\sigma$ Ori B ($M_{\star}$= 13.6
$M_{\odot}$) from Simón-Díaz et al. (2015), and using Fig. 14 of Winter &
Haworth (2022) we estimated the FUV luminosity (LFUV) of the system. The FUV
field strength due to the massive OB stars was then obtained in terms of the
dimensionless parameter $G_{0}$ as:

$G_{0}=\frac{1}{F_{0}}\frac{L_{\rm FUV}}{4\pi d_{p}^{2}},$ (1)

where $F_{0}$ is the typical interstellar flux level of $1.6\times
10^{-3}\,\rm erg\,cm^{-2}\,s^{-1}$ (Habing 1968), and $d_{\rm p}$ represents
the distance from the photoevaporative source $\sigma$-Ori in parsecs (the
projected distance).

We found values of FUV flux between $10^{2}$ and $10^{5}$ $G_{0}$ (see Fig. 5,
top axis). We also estimated the FUV field strength produced by the other
B-stars in the cluster and found that the FUV field is completely dominated by
the multiple system $\sigma$-Ori. In Fig. 1 we showed the spatial distribution
of disks in the cluster (circles) along with the massive O and B stars (gray
stars). The color bar indicates the total $G_{0}$ values ($\sigma$-Ori +
B-stars) which as shown in Fig. 8 mainly corresponds to the FUV field produced
by $\sigma$-Ori.

Figure 8: G0 of O and B stars in the $\sigma$ Orionis cluster. The FUV
radiation is dominated by the central system $\sigma$-Ori.

##  Appendix B Stellar and accretion parameters from previous works

We show on Table 3 the stellar and accretion parameters of $\sigma$-Orionis
sources from Manara et al. (2021). Overall, we found a good agreement (given
our uncertainties) between our best-fit model and the results from Manara et
al. (2021). SO518 and SO1153 are peculiar sources. SO518 seems to be an almost
edge-on disk and, therefore, the estimate of its stellar parameters,
particularly $\dot{M}_{\rm acc}$, is more uncertain (Alcalá et al. 2014).
SO1153, on the other hand, is a strong accretor where the best-fit slab
spectrum is much brighter than the photospheric template. Such strong
accretors are problematic to fit, since the photospheric emission is veiled by
the accretion emission, leading to large uncertainties in the best fit SpT
(e.g., Calvet & Gullbring 1998), and many photospheric absorption lines are
seen in emission. To obtain the final results for this source and for SO518 we
had to constrain $A_{V}$ to low values. Considering these caveats, we were
able to obtain best-fit results compatible with the ones found by Manara et
al. (2021).

Table 3:  Comparison between our best fit results and the ones of Manara et al. (2021) for the targets SO518, SO583, and SO1153.  Name | SpT | $A_{V}$ | $L_{\star}$ | $\log L_{\mathrm{acc}}$ | $M_{\star}$ | $\log\dot{M}_{\mathrm{acc}}$
---|---|---|---|---|---|---
SO518 | K6 | 1.6 | 0.48 | -0.69 | 0.80 | -7.86
SO518 Manara et al. (2021) | K7 | 1.0 | 0.24 | -1.22 | 0.81 | -8.53
SO583 | K4 | 1.0 | 4.06 | -0.69 | 1.18 | -7.62
SO583 Manara et al. (2021) | K5 | 0.4 | 3.61 | -0.30 | 1.09 | -7.21
SO1153 | K5 | 1.5 | 0.33 | 0.02 | 0.90 | -7.30
SO1153 Manara et al. (2021) | K7 | 0.1 | 0.17 | -0.88 | 0.76 | -8.24

##  Appendix C Additional information on targets

###  C.1 ALMA observations

We obtained deeper ALMA Cycle 4 (C4) observations for disks in
$\sigma$-Orionis. Fig. 9 shows the comparison between ALMA observations from
Ansdell et al. (2017, C3) and our new C4 observations. ALMA observations for
our X-Shooter sample are reported in Table 2. The list of ALMA non-detections
is reported here (Table 4). The data between both cycles agree very well. In
general, the C4 fluxes are higher than in C3 by a factor $\sim$1.13 and the
new detections have fluxes just at the level of the C3 upper limits
(3$\sigma$). The C4 observations allow the detection of 6 new sources in the
continuum. Furthermore, in an effort to establish more robust population
statistics, especially for the gas, the higher sensitivity C4 data resulted in
13 new detections in 12CO. The 12CO fluxes are also reported in Table 2.
Continuum and 12CO images are shown in Fig. 10, and 11, respectively.

Figure 9: Comparison between ALMA fluxes from C3 and C4 for $\sigma$-Orionis sources. The arrows show 3$\sigma$ upper limits.  Figure 10: Continuum images at 1.33 mm of the 34 disks sampled by ALMA in Cycle 4, ordered by source name. Figure 11: 12CO Moment 0 maps of the 34 disks sampled by ALMA in Cycle 4, ordered by source name. Table 4:  ALMA non-detections Name | RA2000 | Dec2000 | Distance | $d_{\rm p}$ | Log $G_{o}$ | Disk type | $M_{\mathrm{dust}}$
---|---|---|---|---|---|---|---
| hh:mm:ss.s | dd:mm:ss.s | [pc] | [pc] |  |  | $[\,\mathrm{M}_{\oplus}]$
SO247 | 05:37:54.86 | -02:41:09.2 | $392.2_{-9.5}^{+10.0}$ | 1.54 | 2.69 | II | ¡1.42
SO254 | 05:37:55.60 | -02:33:05.3 | $373.4_{-33.8}^{+41.3}$ | 1.37 | 2.79 | II | ¡1.28
SO271 | 05:37:57.46 | -02:38:44.4 | $396.0_{-18.4}^{+20.2}$ | 1.4 | 2.78 | II | ¡1.43
SO300 | 05:38:01.07 | -02:45:38.0 | $401.0_{-15.0}^{+16.7}$ | 1.7 | 2.61 | – | ¡1.5
SO327 | 05:38:05.52 | -02:35:57.1 | $392.3_{-45.6}^{+59.3}$ | 1.12 | 2.97 | II | ¡1.44
SO396 | 05:38:13.16 | -02:45:51.0 | $404.6_{-3.8}^{+3.9}$ | 1.49 | 2.73 | II | ¡0.41
SO435 | 05:38:17.78 | -02:40:50.1 | $401.0$ | 0.97 | 3.1 | II | ¡1.48
SO451 | 05:38:18.86 | -02:51:38.8 | $409.2_{-5.9}^{+6.1}$ | 2.02 | 2.46 | – | ¡1.55
SO462 | 05:38:20.50 | -02:34:09.0 | $379.7_{-11.0}^{+11.7}$ | 0.7 | 3.38 | II | ¡1.34
SO482 | 05:38:23.08 | -02:36:49.4 | $403.3_{-20.1}^{+22.3}$ | 0.64 | 3.45 | – | ¡1.57
SO485 | 05:38:23.33 | -02:25:34.6 | $360.7_{-9.6}^{+10.2}$ | 1.23 | 2.89 | II | ¡1.23
SO514 | 05:38:26.84 | -02:38:46.1 | $351.5_{-14.6}^{+15.9}$ | 0.54 | 3.61 | II | ¡1.15
SO537 | 05:38:28.97 | -02:48:47.3 | $416.7_{-32.4}^{+38.3}$ | 1.62 | 2.65 | – | ¡1.62
SO598 | 05:38:34.60 | -02:41:08.8 | $400.4_{-7.3}^{+7.6}$ | 0.67 | 3.42 | II | ¡1.51
SO657 | 05:38:39.76 | -02:32:20.3 | $402.8_{-57.8}^{+81.1}$ | 0.45 | 3.76 | – | ¡1.57
SO663 | 05:38:40.54 | -02:33:27.6 | $405.5_{-8.7}^{+9.0}$ | 0.32 | 4.05 | – | ¡1.57
SO674 | 05:38:41.60 | -02:30:28.9 | $383.8_{-6.4}^{+6.6}$ | 0.62 | 3.48 | – | ¡1.47
SO707 | 05:38:45.28 | -02:37:29.3 | $405.5_{-16.7}^{+18.2}$ | 0.18 | 4.58 | – | ¡1.62
SO710 | 05:38:45.38 | -02:41:59.4 | $401.0_{-16.8}^{+19.4}$ | 0.7 | 3.38 | II | ¡0.4
SO723 | 05:38:47.19 | -02:34:36.8 | $392.0_{-8.8}^{+9.2}$ | 0.17 | 4.59 | II | ¡1.58
SO733 | 05:38:47.92 | -02:37:19.2 | $411.4_{-6.5}^{+6.7}$ | 0.18 | 4.54 | II | ¡0.43
SO738 | 05:38:48.10 | -02:28:53.6 | $377.2_{-21.3}^{+24.0}$ | 0.79 | 3.28 | – | ¡1.4
SO750 | 05:38:49.29 | -02:23:57.6 | $425.0_{-27.0}^{+31.0}$ | 1.5 | 2.72 | – | ¡1.85
SO754 | 05:38:49.70 | -02:34:52.6 | $392.6_{-11.8}^{+12.6}$ | 0.19 | 4.51 | – | ¡1.52
SO762 | 05:38:50.61 | -02:42:42.9 | $394.0_{-14.4}^{+15.5}$ | 0.79 | 3.28 | – | ¡1.53
SO827 | 05:38:59.23 | -02:33:51.4 | $410.7_{-8.0}^{+8.4}$ | 0.5 | 3.67 | II | ¡1.67
SO865 | 05:39:03.57 | -02:46:27.0 | $399.5_{-7.1}^{+7.3}$ | 1.33 | 2.82 | II | ¡1.61
SO866 | 05:39:03.87 | -02:20:08.2 | $379.7_{-12.8}^{+13.7}$ | 1.83 | 2.54 | II | ¡1.48
SO871 | 05:39:04.59 | -02:41:49.4 | $429.4_{-12.1}^{+12.8}$ | 0.95 | 3.11 | II | ¡1.84
SO908 | 05:39:08.78 | -02:31:11.5 | $383.6_{-7.8}^{+8.1}$ | 0.86 | 3.2 | II | ¡1.51
SO936 | 05:39:13.08 | -02:37:50.9 | $401.0_{-63.3}^{+85.4}$ | 0.85 | 3.21 | – | ¡1.64
SO967 | 05:39:15.83 | -02:36:50.7 | $396.0_{-8.3}^{+8.6}$ | 0.9 | 3.16 | II | ¡1.58
SO1050 | 05:39:26.33 | -02:28:37.7 | $389.5_{-10.8}^{+11.5}$ | 1.44 | 2.75 | – | ¡1.58
SO1182 | 05:39:43.19 | -02:32:43.3 | $390.0_{-9.1}^{+9.5}$ | 1.7 | 2.61 | – | ¡1.57
SO1193 | 05:39:44.51 | -02:24:43.2 | $439.8_{-21.2}^{+23.5}$ | 2.4 | 2.31 | – | ¡2.01
SO1230 | 05:39:49.45 | -02:23:45.9 | $413.6_{-10.3}^{+10.8}$ | 2.44 | 2.29 | – | ¡1.77
SO1268 | 05:39:54.33 | -02:37:18.9 | $441.6_{-37.7}^{+45.4}$ | 2.24 | 2.37 | TD | ¡2.03
SO1338 | 05:40:04.54 | -02:36:42.1 | $419.7_{-56.6}^{+77.5}$ | 2.44 | 2.3 | – | ¡1.84
SO1344 | 05:40:05.26 | -02:30:52.3 | $394.3_{-16.6}^{+18.1}$ | 2.38 | 2.32 | – | ¡1.62

###  C.2 Gaia observations

Gaia information for our X-Shooter sample is listed on Table 5. Information on
parallaxes ($\varpi$), proper motions ($\mu_{\alpha}$, $\mu_{\beta}$), and
RUWE values are provided for each source.

Table 5: Information on distances from Gaia for our X-Shooter sample Name |  $\varpi$ [mas] |  $\sigma_{\varpi}$ [mas] |  $\mu_{\alpha}$ [mas/yr] |  $\mu_{\delta}$ [mas/yr] | RUWE
---|---|---|---|---|---
SO73 | 2.7843 | 0.0333 |  1.757 $\pm$ 0.034 |  -1.313 $\pm$ 0.027 | 1.14
SO299 | 2.8126 | 0.0344 |  1.749 $\pm$ 0.036 |  -1.41 $\pm$ 0.028 | 0.99
SO341 | 2.4451 | 0.0259 |  1.334 $\pm$ 0.028 |  -0.529 $\pm$ 0.021 | 1.1
SO362 | 2.4859 | 0.0291 |  1.057 $\pm$ 0.034 |  -0.615 $\pm$ 0.026 | 1.08
SO397 | 2.4075 | 0.2217 |  0.816 $\pm$ 0.193 |  0.846 $\pm$ 0.161 | 2.45
SO411 | 2.736 | 0.0164 |  1.923 $\pm$ 0.014 |  -1.37 $\pm$ 0.013 | 0.83
SO467 | 2.6087 | 0.0601 |  1.237 $\pm$ 0.055 |  -1.306 $\pm$ 0.049 | 1.03
SO490 | 3.8006 | 0.6852 |  -0.999 $\pm$ 0.671 |  -3.064 $\pm$ 0.571 | 7.94
SO500 | 2.4437 | 0.2443 |  0.977 $\pm$ 0.293 |  -0.944 $\pm$ 0.229 | 1.1
SO518 | 2.5064 | 0.025 |  1.191 $\pm$ 0.027 |  -0.895 $\pm$ 0.022 | 1.2
SO520 | 2.4839 | 0.0397 |  1.409 $\pm$ 0.039 |  -0.571 $\pm$ 0.032 | 1.0
SO540 | 2.4629 | 0.0216 |  0.316 $\pm$ 0.019 |  0.709 $\pm$ 0.017 | 1.16
SO563 | 7.7206 | 0.8106 |  3.868 $\pm$ 0.767 |  5.7 $\pm$ 0.633 | 35.66
SO583 | 2.4699 | 0.223 |  1.07 $\pm$ 0.238 |  -0.485 $\pm$ 0.191 | 19.86
SO587 | 2.1903 | 0.2054 |  0.298 $\pm$ 0.202 |  0.855 $\pm$ 0.165 | 6.77
SO646 | 2.4714 | 0.0409 |  1.243 $\pm$ 0.044 |  -0.72 $\pm$ 0.037 | 1.04
SO662 | 2.4925 | 0.0208 |  0.871 $\pm$ 0.018 |  -0.61 $\pm$ 0.017 | 1.12
SO682 | 2.4402 | 0.0284 |  1.072 $\pm$ 0.027 |  -0.349 $\pm$ 0.022 | 1.22
SO687 | 2.4226 | 0.0251 |  1.566 $\pm$ 0.026 |  0.132 $\pm$ 0.022 | 1.13
SO694 | 2.5492 | 0.0612 |  1.733 $\pm$ 0.06 |  -1.114 $\pm$ 0.05 | 1.12
SO697 | 2.4723 | 0.0148 |  1.459 $\pm$ 0.014 |  -1.009 $\pm$ 0.012 | 1.03
SO726 | 2.4761 | 0.0425 |  2.21 $\pm$ 0.045 |  0.097 $\pm$ 0.04 | 1.14
SO736 | 2.5267 | 0.0608 |  1.456 $\pm$ 0.054 |  0.147 $\pm$ 0.05 | 3.32
SO739 | 2.3081 | 0.1132 |  1.368 $\pm$ 0.125 |  -0.946 $\pm$ 0.095 | 0.98
SO774 | 2.4796 | 0.0205 |  1.63 $\pm$ 0.021 |  -1.074 $\pm$ 0.016 | 1.11
SO818 | 2.4665 | 0.0253 |  0.746 $\pm$ 0.024 |  0.4 $\pm$ 0.021 | 1.1
SO823 | 2.2249 | 0.058 |  0.845 $\pm$ 0.062 |  0.104 $\pm$ 0.053 | 1.46
SO844 | 2.4067 | 0.0216 |  1.704 $\pm$ 0.023 |  -0.052 $\pm$ 0.02 | 1.1
SO848 | 2.8064 | 0.1347 |  1.689 $\pm$ 0.128 |  -0.225 $\pm$ 0.119 | 1.08
SO859 | 2.4517 | 0.0389 |  1.561 $\pm$ 0.037 |  -0.715 $\pm$ 0.033 | 1.04
SO897 | 2.6239 | 0.0517 |  1.588 $\pm$ 0.049 |  -0.922 $\pm$ 0.044 | 3.28
SO927 | 2.4178 | 0.0276 |  1.832 $\pm$ 0.026 |  -0.316 $\pm$ 0.024 | 1.27
SO984 | 2.4412 | 0.0188 |  1.808 $\pm$ 0.021 |  -0.654 $\pm$ 0.017 | 1.09
SO1036 | 2.5318 | 0.0221 |  1.843 $\pm$ 0.018 |  -0.349 $\pm$ 0.018 | 1.19
SO1075 | 2.5638 | 0.0554 |  1.701 $\pm$ 0.053 |  -0.122 $\pm$ 0.047 | 1.18
SO1152 | 2.5091 | 0.0245 |  2.105 $\pm$ 0.024 |  -0.033 $\pm$ 0.02 | 1.3
SO1153 | 2.5212 | 0.0268 |  1.798 $\pm$ 0.023 |  -0.094 $\pm$ 0.02 | 1.23
SO1154 | 2.4985 | 0.0797 |  2.113 $\pm$ 0.075 |  -0.824 $\pm$ 0.068 | 1.4
SO1156 | 2.4765 | 0.0159 |  2.44 $\pm$ 0.017 |  -0.255 $\pm$ 0.014 | 1.08
SO1248 | 2.51 | 0.0486 |  2.221 $\pm$ 0.049 |  -0.183 $\pm$ 0.042 | 1.09
SO1260 | 2.5888 | 0.0419 |  2.259 $\pm$ 0.039 |  -0.318 $\pm$ 0.032 | 1.03
SO1266 | 2.5055 | 0.0673 |  2.004 $\pm$ 0.062 |  -0.496 $\pm$ 0.053 | 0.98
SO1267 | 2.4967 | 0.0325 |  2.149 $\pm$ 0.03 |  -0.193 $\pm$ 0.026 | 1.29
SO1274 | 2.455 | 0.0164 |  2.166 $\pm$ 0.017 |  -0.781 $\pm$ 0.014 | 1.01
SO1327 | 2.5147 | 0.0363 |  2.336 $\pm$ 0.037 |  0.018 $\pm$ 0.03 | 1.01
SO1361 | 2.4632 | 0.0239 |  2.253 $\pm$ 0.019 |  -0.254 $\pm$ 0.018 | 1.16
SO1362 | 2.5041 | 0.0656 |  2.228 $\pm$ 0.058 |  -0.39 $\pm$ 0.052 | 1.08
SO1369 | 2.4843 | 0.0153 |  -2.476 $\pm$ 0.014 |  -4.16 $\pm$ 0.012 | 0.97

##  Appendix D Plots of the Balmer jump fits

Here, we present the best fit of the X-Shooter spectra of our sample obtained
following Manara et al. (2013a) and described in Sect. 4.1. We show the Balmer
jump region of the spectra for each target.

Figure 12: Best fit for the Balmer continuum region for targets in the
$\sigma$-Orionis cluster, ordered by source name. Figure 13: Best fit for the
Balmer continuum region for targets in the $\sigma$-Orionis cluster, ordered
by source name. - continued Figure 14: Best fit for the Balmer continuum
region for targets in the $\sigma$-Orionis cluster, ordered by source name. -
continued Figure 15: Best fit for the Balmer continuum region for targets in
the $\sigma$-Orionis cluster, ordered by source name. - continued Figure 16:
Best fit for the Balmer continuum region for targets in the $\sigma$-Orionis
cluster, ordered by source name. - continued