# The $\dot{M}$–$M_{\rm{disk}}$ relationship for Herbig Ae/Be stars: a
lifetime problem for disks with low masses?

Sierra L. Grant Max-Planck Institut für Extraterrestrische Physik (MPE),
Giessenbachstr. 1, 85748, Garching, Germany  Lucas M. Stapper Leiden
Observatory, Leiden University, 2300 RA Leiden, the Netherlands  Michiel R.
Hogerheijde Leiden Observatory, Leiden University, 2300 RA Leiden, the
Netherlands  Anton Pannekoek Institute for Astronomy, University of Amsterdam,
the Netherlands  Ewine F. van Dishoeck Leiden Observatory, Leiden University,
2300 RA Leiden, the Netherlands  Max-Planck Institut für Extraterrestrische
Physik (MPE), Giessenbachstr. 1, 85748, Garching, Germany  Sean Brittain
Clemson University, 118 Kinard Laboratory, Clemson, SC 29631, USA  Miguel
Vioque Joint ALMA Observatory, Alonso de Córdova 3107, Vitacura, Santiago
763-0355, Chile  National Radio Astronomy Observatory, 520 Edgemont Road,
Charlottesville, VA 22903, USA

###### Abstract

The accretion of material from protoplanetary disks onto their central stars
is a fundamental process in the evolution of these systems and a key
diagnostic in constraining the disk lifetime. We analyze the relationship
between the stellar accretion rate and the disk mass in 32 intermediate-mass
Herbig Ae/Be systems and compare them to their lower-mass counterparts, T
Tauri stars. We find that the $\dot{M}$–$M_{\rm{disk}}$ relationship for
Herbig Ae/Be stars is largely flat at $\sim$10-7 M⊙ yr-1 across over three
orders of magnitude in dust mass. While most of the sample follows the T Tauri
trend, a subset of objects with high accretion rates and low dust masses are
identified. These outliers (12 out of 32 sources) have an inferred disk
lifetime of less than 0.01 Myr and are dominated by objects with low infrared
excess. This outlier sample is likely identified in part by the bias in
classifying Herbig Ae/Be stars, which requires evidence of accretion that can
only be reliably measured above a rate of $\sim$10-9 M⊙ yr-1 for these
spectral types. If the disk masses are not underestimated and the accretion
rates are not overestimated, this implies that these disks may be on the verge
of dispersal, which may be due to efficient radial drift of material or outer
disk depletion by photoevaporation and/or truncation by companions. This
outlier sample likely represents a small subset of the larger young,
intermediate-mass stellar population, the majority of which would have already
stopped accreting and cleared their disks.

protoplanetary disks – stars: pre-main sequence – stars: variables: T Tauri,
Herbig Ae/Be – planets and satellites: formation

##  1 Introduction

Circumstellar disks are the birthplaces of planets and those planets must form
in the first several million years of the disk lifetime before the disk
dissipates. It is then important to understand how disks evolve and to
characterize how that evolution impacts planet formation and vice versa. The
rate at which material is being accreted onto the star from the disk and the
disk mass are two key parameters in assessing the evolutionary state of a
system. These two diagnostics probe different regions in the disk: the
accretion rate traces the innermost star-disk connection and the disk mass
traces the mass reservoir at tens to hundreds of au.

Despite the contrasting scales that the accretion rate ($\dot{M}$) and disk
mass (${M_{\rm{disk}}}$) probe, it has been predicted that the two quantities
should be related and can give an estimate of the disk lifetime,
$t_{\rm{disk}}=M_{\rm{disk}}/\dot{M}$ (e.g. Hartmann et al. 1998; Jones et al.
2012; Lodato et al. 2017; Rosotti et al. 2017; Sellek et al. 2020; Manara et
al. 2022). The transfer of material inward from the outer disk can be affected
by a variety of factors, including the formation of pressure traps, stellar
irradiation and photoevaporation, MHD disk winds, and the presence of giant
planets and companions (e.g., Jones et al. 2012; Rosotti et al. 2017; Tabone
et al. 2022; Zagaria et al. 2022). Deviations from the nominal
$\dot{M}$–$M_{\rm{disk}}$ relationship can then indicate the presence of one
or more of these processes.

Recent observational efforts conducted at optical and near-infrared
wavelengths paired with the numerous outer disk surveys, particularly with
ALMA, have led to large populations of disks with both $\dot{M}$ and
${M_{\rm{dust}}}$ measurements (Mendigutía et al., 2012; Manara et al., 2016,
2020; Ansdell et al., 2017; Mulders et al., 2017; Grant et al., 2021; Testi et
al., 2022; Fiorellino et al., 2022). However, these surveys have greatly
favored low-mass T Tauri stars, with the exception of Mendigutía et al. (2012)
which was carried out before ALMA was operational. The more massive Herbig
Ae/Be stars, by comparison, lack homogeneous (sub-)millimeter observations
(Stapper et al., 2022), while they are well-covered in surveys focusing on
accretion signatures (e.g., Donehew & Brittain 2011; Fairlamb et al. 2015,
2017; Grant et al. 2022; Vioque et al. 2022). The disks around these
intermediate-mass stars are thought to form giant exoplanets more efficiently
than low-mass stars (Johnson et al., 2010; Reffert et al., 2015). Indeed, van
der Marel & Mulders (2021) use disk properties to tentatively point to a
connection between stellar mass and giant planet formation. Therefore, it is
essential to understand disk evolution and planet formation in the disks
around intermediate-mass stars. In this work, we take these two key disk
diagnostics, $\dot{M}$ and ${M_{\rm{disk}}}$, to study the
$\dot{M}$–$M_{\rm{disk}}$ relationship in a sample of 32 Herbig Ae/Be objects.

Figure 1: Left: The $\dot{M}$–$M_{\rm{disk}}$ relationship for our sample of
Herbig Ae/Be stars (black points) and the T Tauri stars from Testi et al.
(2022) (blue points). We have excluded the few sources in the Testi et al.
(2022) sample that have $M_{*}$$>$1.5 $M_{\odot}$. The black line is the best
fit for the Herbig Ae/Be sample and the blue line is the best fit for the T
Tauri sample. The thin black lines and thin blue lines are 200 samples of the
posterior for the fits to the Herbig Ae/Be and T Tauri points, respectively.
Upper limits on the dust mass are shown as leftward facing triangles and upper
limits on the accretion rate are shown as downward facing triangles. If both
the accretion rate and dust mass measurements are upper limits, the triangle
points to the lower left. The dotted gray lines show different disk lifetimes.
The Herbig Ae/Be disks are outliers above the already large scatter seen for
the lower mass stars. Right: The relationship between the accretion luminosity
and the millimeter flux (normalized by the distance).

##  2 Sample, mass accretion rates, and dust masses

###  2.1 Sample

Our sample is compiled from the ALMA-observed sample of Stapper et al. (2022),
which provides the dust masses used in this work. Their sample consists of the
Herbig Ae/Be systems in Vioque et al. (2018) that are within 450 pc and had
available ALMA observations (see Stapper et al. 2022 for more details and
notes on some excluded objects).

The stellar properties for our sample are listed in Table 1 and are largely
from Vioque et al. (2018). Thirty-one of our 32 sources have high quality Gaia
DR2 parallaxes that were used in Vioque et al. (2018), which are largely
consistent with Gaia (E)DR3 (Guzmán-Díaz et al., 2021). One source, HD 53367,
was in the low quality sample, and the Gaia DR3 parallax is very different
from that of DR2 (parallax of 0.8199$\pm$0.2114 milliarcseconds in DR3 and
7.7682$\pm$0.7854 milliarcseconds in DR2). We keep this source in our sample,
using the stellar parameters based on the Gaia DR2 data, but we urge caution
in interpreting the results for this source and we do not include it in fits
to the $\dot{M}$–$M_{\rm{disk}}$ relationship that we present in Section 3.
The stellar masses range from 1.3 to 16.9 $M_{\odot}$, but 29 of our 32
sources have stellar masses less than 3 $M_{\odot}$. Our sample represents a
slightly older population, with 27 of our sources having ages greater than 3
Myr. The Meeus et al. (2001) Group determinations, that are determined from
the spectral energy distributions (SEDs) and are thought to reflect the dust
disk structure (e.g., Meeus et al. 2001; van Boekel et al. 2005; Maaskant et
al. 2013; Garufi et al. 2017; Stapper et al. 2022), are largely from the SED
analysis of Grant et al. (2022) and Guzmán-Díaz et al. (2021). Our sample is
nearly evenly split between Group I (17) and Group II (15) disks.

###  2.2 Mass accretion rates

The accretion rates for our sample come from the works of Grant et al. (2022),
Wichittanakom et al. (2020), and Garcia Lopez et al. (2006). Grant et al.
(2022) use Br$\gamma$ observations to derive $L_{\rm{Br\gamma}}$ which is then
converted to an accretion luminosity using the relationship from Fairlamb et
al. (2017). Similarly, Wichittanakom et al. (2020) do the same, except using
H$\alpha$ instead of Br$\gamma$. H$\alpha$ and Br$\gamma$ have a similar
spread in the empirical relationship between $L_{\rm{line}}$ and
$L_{\rm{acc}}$ and are both robust tracers of accretion, even if the line is
not generated in the accretion columns (e.g., Mendigutía et al. 2015). For one
object, TY CrA, we use the accretion rate from Garcia Lopez et al. (2006). For
this target, the Br$\gamma$ line is in absorption that is mostly consistent
with the photosphere, therefore there is only an upper limit on the accretion
rate and we do not include it in the $\dot{M}$–$M_{\rm{disk}}$ fits that we
discuss in the rest of the paper.

The median accretion rate in our sample is log${}_{10}(\dot{M})=-7.09$
($\rm{M_{\sun}\,yr^{-1}}$), not including upper limits, with a median log
error of 0.37. Both sources of the accretion rate measurements rely on the
assumption that magnetospheric accretion is the dominant mechanism in these
sources. However, the Herbig Ae/Be stellar mass/effective temperature range is
thought to be the regime where magnetospheric accretion may break down to
boundary layer accretion due to the weak stellar magnetic fields (e.g., Vink
et al. 2002; Donehew & Brittain 2011; Mendigutía et al. 2011; Cauley & Johns-
Krull 2014; Wichittanakom et al. 2020; Grant et al. 2022). Based on the
findings of Wichittanakom et al. (2020), Grant et al. (2022), and Vioque et
al. (2022), the accretion mechanism change may occur at the $\sim$4
$M_{\odot}$ boundary and only two stars in our sample above this boundary, HD
53367 and MWC 297.

We have no targets with an accretion rate detection below 10-9
$\rm{M_{\sun}\,yr^{-1}}$. One of the criteria needed for Herbig Ae/Be
classification is the presence of an accretion tracer, frequently H i lines in
emission (e.g., Herbig 1960; The et al. 1994). The use of these lines in
identifying Herbig Ae/Be stars is complicated by the fact that these stars
have photospheric absorption at those lines and that the depths of the
photospheric absorption depends on the stellar effective temperature (Joner &
Hintz, 2015; Fairlamb et al., 2017). The lower limit on the detectable
accretion rate varies with spectral type, the ability to characterize the
photosphere, and the measurement method. For example, the lower limit on the
measurement of the accretion rate from the veiling of the Balmer jump in the
near ultraviolet (NUV) ranges from a few times 10-9 $\rm{M_{\sun}\,yr^{-1}}$
for 2 $M_{\odot}$ Herbig stars to about 10-6 $\rm{M_{\sun}\,yr^{-1}}$ for 7
$M_{\odot}$ Herbig stars (see Figure 5 in Sicilia-Aguilar et al. 2016). If one
assumes that the calibration of line luminosity and accretion luminosity
inferred from the NUV excess is valid for lower accretion rates, then it is
possible to infer lower levels of accretion from spectroscopy of those lines.
Fairlamb et al. (2015) also highlight the changing lower accretion limits
based on stellar effective temperature (see their Figure 9). From Sicilia-
Aguilar et al. (2016) and Fairlamb et al. (2015), an accretion rate of
$\sim$10-9 $\rm{M_{\sun}\,yr^{-1}}$ is generally the lower limit for the
lowest stellar mass objects in the Herbig Ae/Be classification. The accretion
rate values in this work are all above this level, including the outlier
objects that are discussed in Section 3. We discuss the lack of low accretion
rate objects in more detail in Section 4.2.

###  2.3 Dust masses

The dust masses in this work were determined in Stapper et al. (2022) using
archival ALMA observations. The spatial resolution in these observations
ranges from 0.02″ to 1.84″. Our sample is evenly split between resolved and
unresolved disks, although more Group I disks are resolved (11/17) than Group
II (5/15). The average spatial resolution for the Group I disks is 0.″37,
while the average is 0.″88 for the Group II disks. The disk integrated
millimeter fluxes were converted to dust masses using a dust temperature that
is scaled by the stellar luminosity (Andrews et al., 2013). The adopted dust
opacities, $\kappa_{\nu}$ were determined by a power-law such that
$\kappa_{\nu}$=10 cm2g-1 at 1000 GHz (Beckwith et al., 1990) and scales with
an index of 1. In this work we assume that the disk mass is 100 times the dust
mass, however, we discuss the implications of this assumption in Section 4.1.

Figure 2: Left: The $t_{\rm{disk}}$ distribution for T Tauri disks from Testi
et al. (2022) (blue) and our Herbig Ae/Be sample (black). We have removed any
targets from the Testi et al. (2022) sample that have $M_{*}$$>$1.5
$M_{\odot}$. Objects with upper limits on $\dot{M}$ or ${M_{\rm{disk}}}$ are
not included. A two-sample Kolmogorov-Smirnov test returns a p-value of
2.7$\times$10-7, indicating that the distributions are drawn from different
populations. Right: The $t_{\rm{disk}}$ distribution for Group I disks (red)
and Group II disks (blue). A two-sample Kolmogorov-Smirnov test returns a
p-value of 0.02, indicating that the distributions may be drawn from different
populations.

##  3 Results

The $\dot{M}$–$M_{\rm{disk}}$ relationship for our Herbig Ae/Be sample is
presented in Figure 1. We fit the Herbig Ae/Be $\dot{M}$–$M_{\rm{disk}}$
relationship using the method from Kelly
(2007)111https://linmix.readthedocs.io, taking errors on $\dot{M}$ and
${M_{\rm{disk}}}$ and upper limits into account (Testi et al., 2022;
Fiorellino et al., 2022). We find that the $\dot{M}$–$M_{\rm{disk}}$
relationship in our Herbig Ae/Be sample is log10($\dot{M}$)=(-0.03 $\pm$
0.21)log10(${M_{\rm{disk}}}$)+(-6.99 $\pm$ 0.52), a mostly flat relationship
over three orders of magnitude in dust mass. This $\dot{M}$–$M_{\rm{disk}}$
relationship is drastically different from that of low-mass systems, in
particular the large sample compiled and analyzed by Testi et al. (2022)
(Figure 1). At the highest disk masses, the Herbig Ae/Be sample largely
overlaps with the T Tauri population, although at the higher end of the
accretion rate range. However, at the low disk mass end, the Herbig Ae/Be
objects lie at and well above the upper end of the T Tauri star accretion rate
distribution. The flat relationship that we find for our sample is likely
influenced by the fact that Herbig Ae/Be stars require accretion signatures to
be classified as such and generally accretion cannot be measured below
$\sim$10-9 $\rm{M_{\sun}\,yr^{-1}}$ in intermediate-mass stars. Therefore we
lack objects with low accretion rates that may steepen the relationship for
intermediate-mass stars in general. While this lower limit is important to
keep in mind when interpreting the Herbig Ae/Be $\dot{M}$–$M_{\rm{disk}}$
relationship, the flatness of the observed relationship highlights the objects
with high accretion rates and low dust masses as clear outliers.

Also shown in Figure 1 is the relationship between the accretion luminosity
and the millimeter flux (normalized by the distance) and the same flat trend
is present for the Herbig Ae/Be stars, while the T Tauri stars again show a
steeper relationship. The fact that these more “direct” quantities show the
same relationship indicates that any assumptions going into the determination
of the accretion rate and the disk mass (e.g., the dust temperature,
magnetospheric accretion being the only source of emission used in determining
the accretion rates, etc.) are not the root cause of the flat
$\dot{M}$–$M_{\rm{disk}}$ relationship for the Herbig Ae/Be sample.

The inferred disk lifetime, $t_{\rm{disk}}=M_{\rm{disk}}/\dot{M}$, is a good
measure of how much a given disk deviates from the relationship seen for the T
Tauri disks, which cluster around the $t_{\rm{disk}}$$\sim$1 Myr line. The low
disk mass objects in our sample have accretion rates that indicate that the
disk will be depleted on much shorter timescales, with 12 of our 32 disks
having inferred disk lifetimes of less than 10,000 years (0.01 Myr). We show
the distribution of $t_{\rm{disk}}$ in Figure 2, comparing the T Tauri sample
of Testi et al. (2022) to our sample of Herbig Ae/Be sources. A two-sample
Kolmogorov-Smirnoff test (Virtanen et al., 2020) returns a p-value of
2.7$\times$10-7, indicating that the T Tauri and Herbig Ae/Be samples are
drawn from different populations. Figure 2 also shows the Herbig Ae/Be
distribution when broken into Group I and Group II sources, showing that the
Group II sources are clearly bimodal, while the Group I distribution is
unimodal. A two-sample Kolmogorov-Smirnoff test (Virtanen et al., 2020)
returns a p-value of 0.02, indicating that the distributions may be drawn from
different populations. We show the $\dot{M}$–$M_{\rm{disk}}$ relationship
broken up into Group I and Group II objects in Figure 3.

In the Appendix we discuss each of the 12 low disk mass sources that stand out
in the $\dot{M}$–$M_{\rm{disk}}$ relationship. In particular, we compare our
$\dot{M}$ and ${M_{\rm{disk}}}$ values to previous values in the literature.
We find that our accretion rate values are consistent with those in the
literature, subject to differences in accretion determination and variability.
In contrast, our disk masses tend to be lower, due to a combination of higher
resolution observations, which reduce the amount of contamination from nearby
sources/cloud emission, and higher dust temperatures. For instance, this
population of high accretion rate, low disk mass objects was not seen in the
$\dot{M}$–$M_{\rm{disk}}$ analysis of Mendigutía et al. (2012), which found
that the $\dot{M}$–$M_{\rm{disk}}$ relationship for Herbig Ae/Be stars was in
line with that of the T Tauri stars. Nine of our objects overlap with their
sample and we have compared the accretion rates and dust masses used in each
work. Their accretion rates are within an order of magnitude of ours and are
evenly split between being higher and lower than our values. The Stapper et
al. (2022) disk mass values are lower than those in Mendigutía et al. (2012)
in 6 sources (one has a higher value in our work, one is an upper limit in
Mendigutía et al. 2012, and one has no disk mass determination in Mendigutía
et al. 2012 due to a lack of millimeter flux). This is due to two differences:
1) the millimeter fluxes from ALMA used by Stapper et al. (2022) are lower in
6 out of 7 targets, likely due to higher angular resolution observations which
suffer less from contamination, and 2) higher dust temperatures used by
Stapper et al. (2022). The dust temperatures in Stapper et al. (2022) were
determined by scaling by the stellar luminosity while the temperatures in
Mendigutía et al. (2012) were determined from graybody fits to photometry at
wavelengths longer than 350 $\mu$m. We note that if we adopt a uniform dust
temperature of 20 K, as is commonly done for lower-mass stars, the disk
lifetimes increase, but not enough to remove the low-inferred disk lifetimes,
with all 12 low disk mass sources having disk lifetimes still less than 0.1
Myr. See the Appendix for further comparison of various disk mass
determinations in the literature for these 12 targets.

Figure 3: The $\dot{M}$–$M_{\rm{disk}}$ relationship for the Herbig Ae/Be
stars broken up by group classification (Group I sources in red and Group II
sources in blue). Upper limits are the same as in Figure 1. ALMA continuum
images from Stapper et al. (2022) are shown for each object with a 100 au
scale bar and the beam at the bottom of each image. If the disk is unresolved
in the ALMA observations, the beam is shown in red.

##  4 Discussion

In this sample of Herbig Ae/Be objects, we find that the
$\dot{M}$–$M_{\rm{disk}}$ relationship is relatively flat. While the majority
of objects fall along the nominal, steep $\dot{M}$–$M_{\rm{disk}}$
relationship of the T Tauri stars, the relationship in our sample is being
affected by a subset of objects appearing to have accretion rates inconsistent
with their disk masses, such that the disks have a very short inferred
lifetime. This outlier sample is likely present due to the biases in Herbig
Ae/Be classification, which are limited to objects with accretion rates above
$\sim$10-9 $\rm{M_{\sun}\,yr^{-1}}$. Here we focus on these short lifetime
“outlier” objects, first to discuss factors that would move these targets into
the nominal $\dot{M}$–$M_{\rm{disk}}$ regime, and second how to explain these
targets if their disk masses and accretion rates are not under- and
overestimated, respectively.

###  4.1 Factors that would move the outliers into the general spread

Here, we consider the possibility that either the accretion rates or the dust
masses for the low-lifetime objects may be over and under estimated,
respectively.

  * •

Optical depth: In the scenario where Group II disks are undergoing efficient
radial drift, the dust disks will be compact and may be optically thick at
millimeter wavelengths which would then lead us to underestimate the dust, and
therefore disk, masses (Stapper et al., 2022; Liu et al., 2022). Modeling
efforts, paired with observations at centimeter wavelengths which may be
optically thin if the millimeter wavelengths are not, are needed to establish
if optically thick emission is the cause of the low disk mass determinations.
However, based on the gas masses available for some of these objects (next
point), it is unlikely that this is the case for all of these sources.

  * •

Gas mass: We are inferring a disk mass based on a gas-to-dust mass ratio of
100. If the true gas-to-dust mass ratio is higher, then our “low-mass” disks
may be high enough to move the objects to the right enough in the
$\dot{M}$–$M_{\rm{disk}}$ plane to make the relationship more consistent with
what is seen for lower mass stars (e.g., Sellek et al. 2020). Note that the
same problem may exist for low-mass stars, even when taking into account the
freeze-out of common gas tracers (e.g., Miotello et al. 2022). We find gas
mass or gas-to-dust mass ratios available in the literature for 11 of our 32
objects (van der Marel et al., 2016; Boehler et al., 2017; Miley et al., 2018;
Yen et al., 2018; Kama et al., 2020; Rivière-Marichalar et al., 2022). Of
these, 5 are upper limits which are above, and therefore consistent with, the
disk masses that we use here. There are 4 objects for which the gas mass, or
gas-to-dust mass ratios, are below the values inferred from the dust
continuum. Finally, two objects have gas masses that are above what we assume
here, neither of which changes the disk lifetime substantially. Further
discussion of gas masses for the low dust mass, high accretion rate objects is
given in the Appendix (Additionally, Stapper et al. in prep will provide a
detailed analysis of the gas tracers for this sample). Further careful
analysis of gas observations of the disks around Herbig Ae/Be stars is needed
to determine the true disk mass, in particular, using gas tracers that are
themselves optically thin (Booth et al., 2019). With these gas masses, we
would then be able to determine whether the “low-mass” disks are really on the
verge of dissipation or whether there is still a large gas reservoir.

  * •

Disk winds: There is evidence that disk winds contribute to the Br$\gamma$
line that is largely used to derive the accretion rates in this work (e.g.,
Kraus et al. 2008; Kurosawa et al. 2016; Hone et al. 2019; Wojtczak et al.
2022). If this is the case, then a given accretion rate used here may be
artificially inflated. If we instead take accretion rates determined using
ultraviolet observations from Donehew & Brittain (2011), Mendigutía et al.
(2011), and Fairlamb et al. (2015), which are unaffected by any contribution
from a disk wind, the mismatch in slope between T Tauri stars and the Herbig
Ae/Be objects is even larger. For example, Mendigutía et al. (2011) use the
Balmer discontinuity and find an accretion rate of 1.45$\times$10-5
$\rm{M_{\sun}\,yr^{-1}}$ for HD 58647, a factor of 10 higher than the value we
use that was determined from Br$\gamma$. On the other hand, Brittain et al.
(2007) found an accretion rate of 3.5$\times$10-7 $\rm{M_{\sun}\,yr^{-1}}$
using Br$\gamma$. Despite the discrepancies in the accretion rate, none of
these values solve the short lifetime implied for this disk which has a dust
mass of 1$\pm$0.1 $M_{\oplus}$. With the Brittain et al. (2007) accretion rate
the disk lifetime is 860 years, with the Grant et al. (2022) accretion rate
adopted here it is 206 years, and with the Balmer discontinuity accretion rate
from Mendigutía et al. (2011) it is only 21 years.

To summarize, if all of the outlier Group II disks are extremely optically
thick, have gas-to-dust ratios that are much larger than the standard
interstellar medium value of 100, or have disk winds that contribute
significantly to the accretion tracers used to determine the accretion rate,
these objects could really be in the nominal disk lifetime regime. While this
needs to be investigated further, literature values of the gas mass and
accretion rates determined from ultraviolet observations, which do not suffer
from contributions from disk winds, indicate that the trends we are seeing are
robust.

###  4.2 Making sense of the outliers

If the mass accretion rates, dust masses, and gas-to-dust ratios are not
wildly off due to the factors discussed above, how might we explain this low-
lifetime population of disks? Either these sources are rapidly depleting their
disks and we are observing them just as they are about to dissipate, or we are
witnessing these sources undergoing variable accretion and happen to be
catching them at a point of high accretion that will then decrease before the
disk is fully dissipated. We explore these options here.

The low disk lifetime objects are predominantly Group II disks. Our
understanding of what these group classifications means has evolved
significantly with additional observations and analysis since the
classification by Meeus et al. (2001). Maaskant et al. (2013), Garufi et al.
(2017), and Stapper et al. (2022) all find evidence for large cavities in the
disks of Group I objects. Additionally, Stapper et al. (2022) find that the
Group I disks have higher dust masses than Group II disks, with Group II disks
potentially unable to form giant planets at large radii, resulting in
efficient radial drift and compact disks. This agrees with the interpretation
of Kama et al. (2015) and Guzmán-Díaz et al. (2023), who found that refractory
elements were depleted in the photospheres of Group I objects relative to
Group II disks, suggesting dust trapping in Group I disks by giant planets.
The dust mass difference is the source of the difference in the
$\dot{M}$–$M_{\rm{disk}}$ relationship, as the accretion rates have been found
to be consistent between Group I and II systems (Mendigutía et al., 2012;
Banzatti et al., 2018; Grant et al., 2022).

If we apply the interpretations of Group I and Group II disks as being gapped
and potentially hosting giant planets at large radii vs. being unable to form
giant planets at large radii and thus having radially compact disks, then the
difference in the $\dot{M}$–$M_{\rm{disk}}$ relationship becomes more clear
(Figure 3). In this scenario Group I disks form giant planets, clearing large
gaps in the gas and dust and are surrounded by dust rings at large radii (see
the ALMA continuum images in Figure 3). If Group II disks are not able to form
giant planets, then they are unable to trap gas or dust in the outer disk,
resulting in a rapid inflow of material to the inner disk which maintains a
high accretion rate. It is unclear when these systems will then begin to
decrease in accretion rate and how rapid that decrease is. This would result
in radially compact dust disks for the Group II sources, but higher resolution
observations are needed to confirm, as none of the low disk lifetime ($<$0.01
Myr) Group II disks are currently resolved (Figure 3). The Group II disks have
an average spatial resolution in the ALMA observations of 0.″88, compared to
0.″37 for the Group I disks. Additionally, comparing the gas and dust radii
will be crucial for determining if efficient radial drift can explain these
systems (e.g., Trapman et al. 2019; Toci et al. 2021).

Other factors that can result in the low disk masses for these objects could
come from outer disk depletion from photoevaporation and/or due to
multiplicity. If these objects are close to nearby massive stars, the extreme
irradiation environments can strip away material, leaving the outer disk
depleted (e.g., Mann et al. 2014; Ansdell et al. 2017; Eisner et al. 2018;
Winter et al. 2018). Multiplicity has also been shown to impact outer disk
evolution, resulting in truncation of the disk (Manara et al., 2019; Panić et
al., 2021; Zagaria et al., 2022). If any companions are massive stars
themselves, then these disks may doubly suffer from truncation and
photoevaporation.

Twenty of the 32 objects in our sample are known binaries, however, the
fraction could be higher given the limited surveys that have searched for
multiple systems. To identify the binaries in this sample, we use the binary
information from Vioque et al. (2018), largely collected from Leinert et al.
(1997), Baines et al. (2006), and Wheelwright et al. (2010). There are two
interesting examples in our sample to study of the effects of multiplicity and
photoevaporation: the TY CrA/HD 176386 and HR 5999/HR 6000 systems. TY CrA is
in a close triple, if not quadruple, system (e.g., Vaňko et al. 2013), and is
close to HD 176386, another target in our sample which has a low inferred disk
lifetime, and is also a binary. The second example comes from HR 5999, which
is itself a binary and is 45″ ($\sim$7000 au at a distance of 158 pc) to HR
6000, an early A-type star with no evidence for a disk (Stelzer et al., 2009).
The low disk masses of these systems may be due to photoevaporation and/or
truncation from their companions. High spatial resolution observations, in
both the gas and dust, paired with photoevaporation and dynamic truncation
models (e.g., Rosotti & Clarke 2018) will help to distinguish the effects of
binarity and photoevaporation in these multiple systems.

If these disks are on the verge of dissipation, why do we see them at all?
Either these disks are going through an accretion outburst such that despite
their low disk masses, we are still able to classify them as Herbig Ae/Be
stars, or these high accretion rate, low disk mass objects make up only a
small portion of the young, intermediate-mass young stellar object population.

The fact that low $\dot{M}$ targets are not in our sample is not surprising:
Herbig Ae/Be stars are, in part, identified due to the presence of accretion-
tracing lines, namely H i lines in emission (e.g., Herbig 1960; The et al.
1994). In practice, only a handful of Herbig Ae/Be stars have rates lower than
1$\times$10-8 $\rm{M_{\sun}\,yr^{-1}}$ (7/267 in the sample of Vioque et al.
2022, 10/102 in the sample of Grant et al. 2022). Mooley et al. (2013)
searched for such objects in the Taurus star forming region. These authors
identify three B-type stars and two A-type stars that are probable members.
They identify two other stars that are plausible members. Thus, half of the A
and B stars in this star-forming region do not show obvious signatures of
accretion. Iglesias et al. (2023) use a volume-limited sample (out to 300 pc)
and find that only six out of 134 targets in their sample of young,
intermediate-mass stars (1.5 $\leq$ M∗ $\leq$ 3.5 $M_{\odot}$) show the
accretion signatures needed to designate them as Herbig Ae/Be stars. These
results suggest that there is a significant population of A and B stars in our
volume (out to 450 pc) that are analogous to the weak lined T Tauri stars.
Therefore, the sample of Herbig Ae/Be objects studied in this work may not be
representative of the intermediate-mass young stellar object population as a
whole, with most of these objects already having dissipated their disks, and
thus not meeting the criteria for Herbig Ae/Be objects. Despite this bias, HD
9672 (49 Cet) in our sample is potentially at an intermediate stage, as it has
been characterized in different works as a debris disk (Zuckerman & Song,
2012), albeit one with a large CO gas content (e.g., Moór et al. 2019; Higuchi
et al. 2020), and as a Herbig Ae system (Vioque et al., 2018). Similarly, HD
141569 in our sample, has been considered a “hybrid” disk in the transition
phase between a protoplanetary disk and a debris disk (Augereau & Papaloizou,
2004; Miley et al., 2018; Di Folco et al., 2020; Gravity Collaboration et al.,
2021; Iglesias et al., 2023). These targets may represent the bridge between
protoplanetary and debris disks.

The short disk lifetimes inferred in this work have relied on the assumption
that the accretion rate is constant in time. However, young stars are known to
be variable, with wide-ranging timescales for variability (see the recent
review by Fischer et al. 2022). If these low-lifetime targets are undergoing a
period of high accretion that will not last, then the disks may not deplete on
the short timescales inferred. This has been seen to impact T Tauri stars
(Claes et al., 2022), however this variability may not be enough to explain
the spread in the accretion rates measured for T Tauri stars (Manara et al.,
2022). How this variability might be different for higher mass objects, if it
is different at all, is unclear (see the discussion on this topic for Herbig
Ae/Be objects in Brittain et al. 2023). Characterizing variability in Herbig
Ae/Be objects, and putting them into context with young, diskless A and B
stars will be crucial for determining whether the low-lifetime population seen
here are simply a subset of the larger population that are undergoing periods
of strong accretion and thus are included in Herbig Ae/Be samples.

##  5 Summary and conclusions

We analyze a sample of 32 Herbig Ae/Be objects (1.3 to 16.9 $M_{\odot}$) to
determine the relationship between the accretion rate and the dust disk
masses. We find the following:

  1. 1.

The mass accretion rate is roughly constant with disk mass, as probed by the
dust mass, for Herbig Ae/Be stars ($\dot{M}$$\sim$10-7
$\rm{M_{\sun}\,yr^{-1}}$). This is significantly different from the steeper
relationship found for T Tauri stars, likely due in part to the biases in
classifying stars as Herbig Ae/Bes. While $\sim$two-thirds of the sample
follows the $\dot{M}$–$M_{\rm{disk}}$ relationship of the T Tauri stars, one-
third has high accretion rates relative to their dust masses.

  2. 2.

T Tauri stars and Herbig Ae/Be systems show very different disk lifetime
($t_{\rm{disk}}=M_{\rm{disk}}/\dot{M}$) distributions, with $\sim$30-40% of
the Herbig Ae/Be sample having disk lifetimes shorter than 0.01 Myr, with this
population being dominated by Group II disks (identified by low infrared
excesses).

  3. 3.

If the disk masses are underestimated (due to optical depth effects or a
higher-than-expected gas-to-dust mass ratio) or the accretion rates are
overestimated (due to contributions to the accretion tracers by winds), the
outlier objects may actually reside in the nominal $\dot{M}$–$M_{\rm{disk}}$
relationship. However, based on values of the disk gas mass measurements and
accretion tracers that cannot be contaminated by winds from the literature, it
is unlikely this is the cause of all of the low lifetime disks we are
observing.

  4. 4.

Unless these objects have extreme variability, the outlier disks are on the
verge of dissipation. This may be due to efficient radial drift for Group II
objects that may not be able to trap material in the outer disk like Group I
disks, photoevaporation, and/or truncation of the outer disk due to
multiplicity, all of which can result in low disk masses.

  5. 5.

We have no low disk mass, low accretion rate objects in our Herbig Ae/Be
sample, highlighting the bias in identifying these objects, which require
accretion signatures and infrared excesses to be considered as such. In
particular, the inability to measure accretion rates below $\sim$10-9
$\rm{M_{\sun}\,yr^{-1}}$ in these spectral types limits our ability to
characterize the $\dot{M}$–$M_{\rm{disk}}$ relationship during the last stages
of disk evolution in young, intermediate-mass systems.

Further work is needed to characterize the high accretion rate, low dust mass
sample. Future high-resolution ALMA observations of these disks are needed to
determine whether these disks are compact. Additionally, the sample of Herbig
Ae/Be systems with ALMA observations should be expanded, which would allow us
to determine whether the low inferred disk lifetime objects constitute only a
small fraction of Herbig Ae/Be systems or whether this population is
substantial. Finally, to better understand disk evolution around intermediate-
mass stars we should also characterize the precursors of Herbig Ae/Be stars,
intermediate-mass T Tauri stars, and their descendants, debris disks, to
understand how disks move through this plane from formation to dissipation.

We thank the referee for constructive comments that improved the manuscript.
We thank Rens Waters, Benoît Tabone, and Giovanni Rosotti for useful
discussions that contributed to this work. We thank Allegro, the ALMA Regional
Center node in the Netherlands, and Aida Ahmadi in particular, for assistance
with processing the ALMA data. Astrochemistry in Leiden is supported by the
Netherlands Research School for Astronomy (NOVA), by funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (grant agreement No. 101019751 MOLDISK), and by the Dutch
Research Council (NWO) grants 648.000.022 and 618.000.001. Support by the
Danish National Research Foundation through the Center of Excellence
“InterCat” (Grant agreement no.: DNRF150) is also acknowledged.

Table 1: Properties of our sample. Accretion rates with a come from Wichittanakom et al. (2020), d from Garcia Lopez et al. (2006), and the rest are from Grant et al. (2022). Groups marked with b are from Guzmán-Díaz et al. (2021), c from Boersma et al. (2009), and the rest are from Grant et al. (2022). Dust masses are from Stapper et al. (2022). Binary information is from the compilation in Vioque et al. (2018).  Source | RA | Dec | $M_{*}$ | log${}_{10}(L_{*})$ | Age | log${}_{10}(\dot{M})$ | $M_{\rm{dust}}$ | Group | Binary
---|---|---|---|---|---|---|---|---|---
|  |  | [$M_{\odot}$] | [$L_{\odot}$] | [Myr] | [$M_{\odot}/yr$] | [$M_{\oplus}$] |  |
AB Aur | 04:55:45.9 | +30:33:04 | 2.152 ${}_{-0.214}^{+0.359}$ | 1.61 ${}_{-0.21}^{+0.19}$ | 4.05 ${}_{-1.49}^{+1.43}$ | -6.13 $\pm$ 0.27 a | 11.8 $\pm$ 1.2 | I | Yes
AK Sco | 16:54:44.8 | -36:53:19 | 1.401 ${}_{-0.070}^{+0.070}$ | 0.62 ${}_{-0.01}^{+0.03}$ | 8.382 ${}_{-0.42}^{+1.72}$ |  $<$-8.06 | 6.1 $\pm$ 0.6 | II | Yes
BF Ori | 05:37:13.3 | -06:35:01 | 1.807 ${}_{-0.090}^{+0.090}$ | 1.29 ${}_{-0.05}^{+0.06}$ | 6.38 ${}_{-0.46}^{+0.32}$ | -7.28 $\pm$ 0.39 | 1.1 $\pm$ 0.1 | II |
CQ Tau | 05:35:58.5 | +24:44:54 | 1.468 ${}_{-0.109}^{+0.189}$ | 0.87 ${}_{-0.12}^{+0.18}$ | 8.898 ${}_{-2.52}^{+2.80}$ |  $<$-8.33 | 44.2 $\pm$ 4.8 | I | Yes
HD 100453 | 11:33:05.5 | -54:19:29 | 1.251 ${}_{-0.063}^{+0.063}$ | 0.79 ${}_{-0.00}^{+0.02}$ | 6.528 ${}_{-0.49}^{+0.45}$ | -8.32 $\pm$ 0.51 | 17.5 $\pm$ 1.8 | I | Yes
HD 100546 | 11:33:25.3 | -70:11:41 | 2.055 ${}_{-0.123}^{+0.103}$ | 1.37 ${}_{-0.05}^{+0.07}$ | 5.48 ${}_{-0.77}^{+1.41}$ | -6.95 $\pm$ 0.36 | 38 $\pm$ 3.9 | I |
HD 104237 | 12:00:04.9 | -78:11:35 | 1.849 ${}_{-0.092}^{+0.092}$ | 1.33 ${}_{-0.01}^{+0.04}$ | 5.48 ${}_{-0.4}^{+0.27}$ | -6.43 $\pm$ 0.34 | 10.5 $\pm$ 1.1 | II | Yes
HD 135344B | 15:15:48.4 | -37:09:16 | 1.432 ${}_{-0.072}^{+0.072}$ | 0.79 ${}_{-0.04}^{+0.03}$ | 8.927 ${}_{-0.91}^{+0.45}$ |  $<$-8.15 | 35.2 $\pm$ 3.8 | I | Yes
HD 139614 | 15:40:46.4 | -42:29:54 | 1.481 ${}_{-0.074}^{+0.074}$ | 0.77 ${}_{-0.01}^{+0.03}$ | 14.49 ${}_{-3.60}^{+1.41}$ | -8.14 $\pm$ 1.03 | 41.7 $\pm$ 4.3 | I |
HD 141569 | 15:49:57.7 | -03:55:17 | 1.860 ${}_{-0.093}^{+0.093}$ | 1.22 ${}_{-0.03}^{+0.03}$ | 8.616 ${}_{-1.19}^{+11.38}$ | -7.76 $\pm$ 0.65 | 0.36 $\pm$ 0.04 | II | Yes
HD 142527 | 15:56:41.9 | -42:19:24 | 1.613 ${}_{-0.081}^{+0.124}$ | 0.96 ${}_{-0.00}^{+0.03}$ | 6.627 ${}_{-1.55}^{+0.33}$ |  $<$-7.29 | 214.9 $\pm$ 22.1 | I | Yes
HD 142666 | 15:56:40.0 | -22:01:40 | 1.493 ${}_{-0.075}^{+0.075}$ | 0.94 ${}_{-0.05}^{+0.04}$ | 9.33 ${}_{-0.47}^{+0.77}$ | -7.63 $\pm$ 1.26 | 25.1 $\pm$ 2.6 | II |
HD 163296 | 17:56:21.3 | -21:57:22 | 1.833 ${}_{-0.092}^{+0.092}$ | 1.20 ${}_{-0.03}^{+0.06}$ | 7.598 ${}_{-1.22}^{+1.05}$ | -7.27 $\pm$ 0.75 | 46.7 $\pm$ 5 | II |
HD 169142 | 18:24:29.8 | -29:46:50 | 2.000 ${}_{-0.128}^{+0.131}$ | 1.31 ${}_{-0.22}^{+0.12}$ | 8.984 ${}_{-3.90}^{+11.02}$ | -7.09 $\pm$ 0.21 a | 22.9 $\pm$ 2.4 | I b |
HD 176386 | 19:01:38.9 | -36:53:27 | 2.299 ${}_{-0.299}^{+0.143}$ | 1.58 ${}_{-0.22}^{+0.12}$ | 4.05 ${}_{-0.57}^{+15.95}$ | -7.08 $\pm$ 0.2 a |  $<$0.06 | II c | Yes
HD 245185 | 05:35:09.6 | +10:01:51 | 1.923 ${}_{-0.096}^{+0.177}$ | 1.29 ${}_{-0.10}^{+0.13}$ | 7.643 ${}_{-2.56}^{+12.36}$ | -6.85 $\pm$ 0.36 | 41.5 $\pm$ 7.6 | I | Yes
HD 290764 | 05:38:05.3 | -01:15:22 | 1.691 ${}_{-0.085}^{+0.128}$ | 1.18 ${}_{-0.09}^{+0.09}$ | 6.89 ${}_{-1.41}^{+0.54}$ | -7.0 $\pm$ 0.39 | 90.3 $\pm$ 11.8 | I |
HD 31648 | 04:58:46.3 | +29:50:37 | 1.779 ${}_{-0.089}^{+0.131}$ | 1.27 ${}_{-0.05}^{+0.14}$ | 6.201 ${}_{-1.12}^{+0.31}$ | -6.57 $\pm$ 0.17 a | 70.9 $\pm$ 7.7 | II b |
HD 34282 | 05:16:00.5 | -09:48:35 | 1.450 ${}_{-0.072}^{+0.072}$ | 0.98 ${}_{-0.04}^{+0.05}$ | 6.54 ${}_{-0.63}^{+2.41}$ | -7.5 $\pm$ 0.73 | 86.8 $\pm$ 9.7 | I | Yes
HD 36112 | 05:30:27.5 | +19:25:57 | 1.564 ${}_{-0.078}^{+0.108}$ | 1.04 ${}_{-0.08}^{+0.12}$ | 8.289 ${}_{-1.40}^{+0.41}$ | -7.32 $\pm$ 0.4 | 18.8 $\pm$ 2 | I | Yes
HD 37258 | 05:36:59.3 | -06:09:16 | 1.881 ${}_{-0.108}^{+0.136}$ | 1.24 ${}_{-0.10}^{+0.12}$ | 7.929 ${}_{-2.45}^{+12.07}$ | -6.98 $\pm$ 0.37 | 2.4 $\pm$ 0.4 | II | Yes
HD 53367 | 07:04:25.5 | -10:27:16 | 12 ${}_{4-}^{+4}$ | 3.13 ${}_{-0.17}^{+0.23}$ | 0.08 ${}_{-0.08}^{+0.08}$ | -6.97 $\pm$ 0.45 |  $<$0.05 | I | Yes
HD 58647 | 07:25:56.1 | -14:10:44 | 3.867 ${}_{-0.193}^{+0.333}$ | 2.44 ${}_{-0.09}^{+0.11}$ | 0.8372 ${}_{-0.18}^{+0.12}$ | -5.84 $\pm$ 0.31 | 1 $\pm$ 0.1 | II | Yes
HD 9672 | 01:34:37.9 | -15:40:35 | 1.810 ${}_{-0.090}^{+0.090}$ | 1.17 ${}_{-0.02}^{+0.09}$ | 6.89 ${}_{-0.51}^{+0.34}$ | -7.8 $\pm$ 1.0 a | 0.13 $\pm$ 0.01 | II b |
HD 97048 | 11:08:03.2 | -77:39:17 | 2.252 ${}_{-0.135}^{+0.113}$ | 1.54 ${}_{-0.06}^{+0.07}$ | 4.37 ${}_{-0.32}^{+1.11}$ | -6.49 $\pm$ 0.34 | 155.9 $\pm$ 16 | I | Yes
HR 5999 | 16:08:34.3 | -39:06:19 | 2.432 ${}_{-0.122}^{+0.122}$ | 1.72 ${}_{-0.04}^{+0.05}$ | 2.729 ${}_{-0.35}^{+0.26}$ | -6.0 $\pm$ 0.11 a | 4 $\pm$ 0.4 | II b | Yes
MWC 297 | 18:27:39.5 | -03:49:52 | 16.901 ${}_{-1.215}^{+1.868}$ | 4.59 ${}_{-0.12}^{+0.12}$ | 0.02754 ${}_{-0.006}^{+0.006}$ |  $<$-5.89 | 65.7 $\pm$ 9.6 | I | Yes
TY CrA | 19:01:40.8 | -36:52:34 | 2.063 ${}_{-0.190}^{+0.223}$ | 1.41 ${}_{-0.23}^{+0.14}$ | 6.38 ${}_{-2.01}^{+13.62}$ |  $<$-8.31 d | 0.10 $\pm$ 0.01 | I b | Yes
V1787 Ori | 05:38:09.3 | -06:49:17 | 1.659 ${}_{-0.083}^{+0.094}$ | 1.15 ${}_{-0.09}^{+0.11}$ | 7.43 ${}_{-1.05}^{+0.59}$ | -7.17 $\pm$ 0.38 | 24.2 $\pm$ 2.9 | II |
V599 Ori | 05:38:58.6 | -07:16:46 | 2.029 ${}_{-0.101}^{+0.101}$ | 1.44 ${}_{-0.06}^{+0.06}$ | 4.289 ${}_{-0.54}^{+0.42}$ | -6.71 $\pm$ 0.37 | 75 $\pm$ 8.6 | I |
V718 Sco | 16:13:11.6 | -22:29:07 | 1.605 ${}_{-0.080}^{+0.080}$ | 0.90 ${}_{-0.04}^{+0.05}$ | 9.804 ${}_{-0.49}^{+2.80}$ | -7.49 $\pm$ 0.23 a | 11.9 $\pm$ 1.3 | II b | Yes
VV Ser | 18:28:47.9 | +00:08:40 | 2.892 ${}_{-0.145}^{+0.145}$ | 1.95 ${}_{-0.08}^{+0.10}$ | 2.77 ${}_{-0.21}^{+8.13}$ |  $<$-6.14 | 2.3 $\pm$ 0.3 | II |

## References

  * Alonso-Albi et al. (2008) Alonso-Albi, T., Fuente, A., Bachiller, R., et al. 2008, ApJ, 680, 1289
  * Andrews et al. (2013) Andrews, S. M., Rosenfeld, K. A., Kraus, A. L., & Wilner, D. J. 2013, ApJ, 771, 129
  * Ansdell et al. (2017) Ansdell, M., Williams, J. P., Manara, C. F., et al. 2017, AJ, 153, 240
  * Augereau & Papaloizou (2004) Augereau, J. C., & Papaloizou, J. C. B. 2004, A&A, 414, 1153
  * Baines et al. (2006) Baines, D., Oudmaijer, R. D., Porter, J. M., & Pozzo, M. 2006, MNRAS, 367, 737
  * Banzatti et al. (2018) Banzatti, A., Garufi, A., Kama, M., et al. 2018, A&A, 609, L2
  * Beckwith et al. (1990) Beckwith, S. V. W., Sargent, A. I., Chini, R. S., & Guesten, R. 1990, AJ, 99, 924
  * Boehler et al. (2017) Boehler, Y., Weaver, E., Isella, A., et al. 2017, ApJ, 840, 60
  * Boersma et al. (2009) Boersma, C., Peeters, E., Martín-Hernández, N. L., et al. 2009, A&A, 502, 175
  * Boissier et al. (2011) Boissier, J., Alonso-Albi, T., Fuente, A., et al. 2011, A&A, 531, A50
  * Booth et al. (2019) Booth, A. S., Walsh, C., Ilee, J. D., et al. 2019, ApJ, 882, L31
  * Brittain et al. (2023) Brittain, S. D., Kamp, I., Meeus, G., Oudmaijer, R. D., & Waters, L. B. F. M. 2023, arXiv e-prints, arXiv:2301.01165
  * Brittain et al. (2007) Brittain, S. D., Simon, T., Najita, J. R., & Rettig, T. W. 2007, ApJ, 659, 685
  * Cauley & Johns-Krull (2014) Cauley, P. W., & Johns-Krull, C. M. 2014, ApJ, 797, 112
  * Cazzoletti et al. (2019) Cazzoletti, P., Manara, C. F., Baobab Liu, H., et al. 2019, A&A, 626, A11
  * Claes et al. (2022) Claes, R. A. B., Manara, C. F., Garcia-Lopez, R., et al. 2022, A&A, 664, L7
  * Di Folco et al. (2020) Di Folco, E., Péricaud, J., Dutrey, A., et al. 2020, A&A, 635, A94
  * Di Francesco et al. (2008) Di Francesco, J., Johnstone, D., Kirk, H., MacKenzie, T., & Ledwosinska, E. 2008, ApJS, 175, 277
  * Donehew & Brittain (2011) Donehew, B., & Brittain, S. 2011, AJ, 141, 46
  * Eisner et al. (2018) Eisner, J. A., Arce, H. G., Ballering, N. P., et al. 2018, ApJ, 860, 77
  * Fairlamb et al. (2015) Fairlamb, J. R., Oudmaijer, R. D., Mendigutía, I., Ilee, J. D., & van den Ancker, M. E. 2015, MNRAS, 453, 976
  * Fairlamb et al. (2017) Fairlamb, J. R., Oudmaijer, R. D., Mendigutia, I., Ilee, J. D., & van den Ancker, M. E. 2017, MNRAS, 464, 4721
  * Fiorellino et al. (2022) Fiorellino, E., Tychoniec, Ł., Manara, C. F., et al. 2022, ApJ, 937, L9
  * Fischer et al. (2022) Fischer, W. J., Hillenbrand, L. A., Herczeg, G. J., et al. 2022, arXiv e-prints, arXiv:2203.11257
  * Garcia et al. (2013) Garcia, P. J. V., Benisty, M., Dougados, C., et al. 2013, MNRAS, 430, 1839
  * Garcia Lopez et al. (2016) Garcia Lopez, R., Kurosawa, R., Caratti o Garatti, A., et al. 2016, MNRAS, 456, 156
  * Garcia Lopez et al. (2006) Garcia Lopez, R., Natta, A., Testi, L., & Habart, E. 2006, A&A, 459, 837
  * Garufi et al. (2017) Garufi, A., Meeus, G., Benisty, M., et al. 2017, A&A, 603, A21
  * Grant et al. (2022) Grant, S. L., Espaillat, C. C., Brittain, S., Scott-Joseph, C., & Calvet, N. 2022, ApJ, 926, 229
  * Grant et al. (2021) Grant, S. L., Espaillat, C. C., Wendeborn, J., et al. 2021, ApJ, 913, 123
  * Gravity Collaboration et al. (2021) Gravity Collaboration, Ganci, V., Labadie, L., et al. 2021, A&A, 655, A112
  * Guzmán-Díaz et al. (2023) Guzmán-Díaz, J., Montesinos, B., Mendigutía, I., et al. 2023, A&A, 671, A140
  * Guzmán-Díaz et al. (2021) Guzmán-Díaz, J., Mendigutía, I., Montesinos, B., et al. 2021, A&A, 650, A182
  * Hartmann et al. (1998) Hartmann, L., Calvet, N., Gullbring, E., & D’Alessio, P. 1998, ApJ, 495, 385
  * Henning et al. (1994) Henning, T., Launhardt, R., Steinacker, J., & Thamm, E. 1994, A&A, 291, 546
  * Herbig (1960) Herbig, G. H. 1960, ApJS, 4, 337
  * Higuchi et al. (2020) Higuchi, A. E., Kóspál, Á., Moór, A., Nomura, H., & Yamamoto, S. 2020, ApJ, 905, 122
  * Hone et al. (2019) Hone, E., Kraus, S., Davies, C. L., et al. 2019, A&A, 623, A38
  * Iglesias et al. (2023) Iglesias, D. P., Panić, O., van den Ancker, M., et al. 2023, MNRAS, 519, 3958
  * Ilee et al. (2014) Ilee, J. D., Fairlamb, J., Oudmaijer, R. D., et al. 2014, MNRAS, 445, 3723
  * Johnson et al. (2010) Johnson, J. A., Aller, K. M., Howard, A. W., & Crepp, J. R. 2010, PASP, 122, 905
  * Joner & Hintz (2015) Joner, M. D., & Hintz, E. G. 2015, AJ, 150, 204
  * Jones et al. (2012) Jones, M. G., Pringle, J. E., & Alexander, R. D. 2012, MNRAS, 419, 925
  * Kama et al. (2015) Kama, M., Folsom, C. P., & Pinilla, P. 2015, A&A, 582, L10
  * Kama et al. (2020) Kama, M., Trapman, L., Fedele, D., et al. 2020, A&A, 634, A88
  * Kaufer et al. (1999) Kaufer, A., Stahl, O., Tubbesing, S., et al. 1999, The Messenger, 95, 8
  * Kelly (2007) Kelly, B. C. 2007, ApJ, 665, 1489
  * Kraus et al. (2008) Kraus, S., Hofmann, K. H., Benisty, M., et al. 2008, A&A, 489, 1157
  * Kurosawa et al. (2016) Kurosawa, R., Kreplin, A., Weigelt, G., et al. 2016, MNRAS, 457, 2236
  * Leinert et al. (1997) Leinert, C., Richichi, A., & Haas, M. 1997, A&A, 318, 472
  * Liu et al. (2022) Liu, Y., Linz, H., Fang, M., et al. 2022, arXiv e-prints, arXiv:2210.07478
  * Lodato et al. (2017) Lodato, G., Scardoni, C. E., Manara, C. F., & Testi, L. 2017, MNRAS, 472, 4700
  * Maaskant et al. (2013) Maaskant, K. M., Honda, M., Waters, L. B. F. M., et al. 2013, A&A, 555, A64
  * Manara et al. (2022) Manara, C. F., Ansdell, M., Rosotti, G. P., et al. 2022, arXiv e-prints, arXiv:2203.09930
  * Manara et al. (2016) Manara, C. F., Rosotti, G., Testi, L., et al. 2016, A&A, 591, L3
  * Manara et al. (2019) Manara, C. F., Tazzari, M., Long, F., et al. 2019, A&A, 628, A95
  * Manara et al. (2020) Manara, C. F., Natta, A., Rosotti, G. P., et al. 2020, A&A, 639, A58
  * Mann et al. (2014) Mann, R. K., Di Francesco, J., Johnstone, D., et al. 2014, ApJ, 784, 82
  * Meeus et al. (2001) Meeus, G., Waters, L. B. F. M., Bouwman, J., et al. 2001, A&A, 365, 476
  * Meeus et al. (2012) Meeus, G., Montesinos, B., Mendigutía, I., et al. 2012, A&A, 544, A78
  * Mendigutía et al. (2011) Mendigutía, I., Calvet, N., Montesinos, B., et al. 2011, A&A, 535, A99
  * Mendigutía et al. (2012) Mendigutía, I., Mora, A., Montesinos, B., et al. 2012, A&A, 543, A59
  * Mendigutía et al. (2015) Mendigutía, I., Oudmaijer, R. D., Rigliaco, E., et al. 2015, MNRAS, 452, 2837
  * Miley et al. (2018) Miley, J. M., Panić, O., Wyatt, M., & Kennedy, G. M. 2018, A&A, 615, L10
  * Miotello et al. (2022) Miotello, A., Kamp, I., Birnstiel, T., Cleeves, L. I., & Kataoka, A. 2022, arXiv e-prints, arXiv:2203.09818
  * Miotello et al. (2016) Miotello, A., van Dishoeck, E. F., Kama, M., & Bruderer, S. 2016, A&A, 594, A85
  * Mooley et al. (2013) Mooley, K., Hillenbrand, L., Rebull, L., Padgett, D., & Knapp, G. 2013, ApJ, 771, 110
  * Moór et al. (2019) Moór, A., Kral, Q., Ábrahám, P., et al. 2019, ApJ, 884, 108
  * Mulders et al. (2017) Mulders, G. D., Pascucci, I., Manara, C. F., et al. 2017, ApJ, 847, 31
  * Natta et al. (1997) Natta, A., Grinin, V. P., Mannings, V., & Ungerechts, H. 1997, ApJ, 491, 885
  * Panić et al. (2021) Panić, O., Haworth, T. J., Petr-Gotzens, M. G., et al. 2021, MNRAS, 501, 4317
  * Pezzuto et al. (1997) Pezzuto, S., Strafella, F., & Lorenzetti, D. 1997, ApJ, 485, 290
  * Pogodin et al. (2012) Pogodin, M. A., Hubrig, S., Yudin, R. V., et al. 2012, Astronomische Nachrichten, 333, 594
  * Pontoppidan et al. (2007) Pontoppidan, K. M., Dullemond, C. P., Blake, G. A., et al. 2007, ApJ, 656, 980
  * Reffert et al. (2015) Reffert, S., Bergmann, C., Quirrenbach, A., Trifonov, T., & Künstler, A. 2015, A&A, 574, A116
  * Rivière-Marichalar et al. (2022) Rivière-Marichalar, P., Fuente, A., Esplugues, G., et al. 2022, arXiv e-prints, arXiv:2207.06716
  * Rosotti & Clarke (2018) Rosotti, G. P., & Clarke, C. J. 2018, MNRAS, 473, 5630
  * Rosotti et al. (2017) Rosotti, G. P., Clarke, C. J., Manara, C. F., & Facchini, S. 2017, MNRAS, 468, 1631
  * Salyk et al. (2013) Salyk, C., Herczeg, G. J., Brown, J. M., et al. 2013, ApJ, 769, 21
  * Sandell et al. (2011) Sandell, G., Weintraub, D. A., & Hamidouche, M. 2011, ApJ, 727, 26
  * Sellek et al. (2020) Sellek, A. D., Booth, R. A., & Clarke, C. J. 2020, MNRAS, 498, 2845
  * Shenavrin et al. (2012) Shenavrin, V. I., Grinin, V. P., Rostopchina-Shakhovskaja, A. N., Demidova, T. V., & Shakhovskoi, D. N. 2012, Astronomy Reports, 56, 379
  * Sicilia-Aguilar et al. (2016) Sicilia-Aguilar, A., Banzatti, A., Carmona, A., et al. 2016, PASA, 33, e059
  * Stapper et al. (2022) Stapper, L. M., Hogerheijde, M. R., van Dishoeck, E. F., & Mentel, R. 2022, A&A, 658, A112
  * Stelzer et al. (2009) Stelzer, B., Robrade, J., Schmitt, J. H. M. M., & Bouvier, J. 2009, A&A, 493, 1109
  * Tabone et al. (2022) Tabone, B., Rosotti, G. P., Lodato, G., et al. 2022, MNRAS, 512, L74
  * Testi et al. (2022) Testi, L., Natta, A., Manara, C. F., et al. 2022, arXiv e-prints, arXiv:2201.04079
  * The et al. (1994) The, P. S., de Winter, D., & Perez, M. R. 1994, A&AS, 104, 315
  * Toci et al. (2021) Toci, C., Rosotti, G., Lodato, G., Testi, L., & Trapman, L. 2021, MNRAS, 507, 818
  * Trapman et al. (2019) Trapman, L., Facchini, S., Hogerheijde, M. R., van Dishoeck, E. F., & Bruderer, S. 2019, A&A, 629, A79
  * van Boekel et al. (2005) van Boekel, R., Min, M., Waters, L. B. F. M., et al. 2005, A&A, 437, 189
  * van der Marel et al. (2016) van der Marel, N., Cazzoletti, P., Pinilla, P., & Garufi, A. 2016, ApJ, 832, 178
  * van der Marel & Mulders (2021) van der Marel, N., & Mulders, G. D. 2021, AJ, 162, 28
  * van Terwisga et al. (2022) van Terwisga, S. E., Hacar, A., van Dishoeck, E. F., Oonk, R., & Portegies Zwart, S. 2022, A&A, 661, A53
  * Vaňko et al. (2013) Vaňko, M., Eiff, M. A.-v., Pribulla, T., et al. 2013, MNRAS, 431, 2230
  * Vink et al. (2002) Vink, J. S., Drew, J. E., Harries, T. J., & Oudmaijer, R. D. 2002, MNRAS, 337, 356
  * Vioque et al. (2018) Vioque, M., D. Oudmaijer, R., Baines, D., Mendigutía, I., & Pérez-Martínez, R. 2018, Astronomy & Astrophysics, 620, doi:10.1051/0004-6361/201832870
  * Vioque et al. (2022) Vioque, M., Oudmaijer, R. D., Wichittanakom, C., et al. 2022, ApJ, 930, 39
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261
  * Wheelwright et al. (2010) Wheelwright, H. E., Oudmaijer, R. D., & Goodwin, S. P. 2010, MNRAS, 401, 1199
  * Wichittanakom et al. (2020) Wichittanakom, C., Oudmaijer, R. D., Fairlamb, J. R., et al. 2020, MNRAS, 493, 234
  * Wilking et al. (1997) Wilking, B. A., McCaughrean, M. J., Burton, M. G., et al. 1997, AJ, 114, 2029
  * Winter et al. (2018) Winter, A. J., Clarke, C. J., Rosotti, G., et al. 2018, MNRAS, 478, 2700
  * Wojtczak et al. (2022) Wojtczak, J. A., Labadie, L., Perraut, K., et al. 2022, arXiv e-prints, arXiv:2210.13095
  * Yen et al. (2018) Yen, H.-W., Koch, P. M., Manara, C. F., Miotello, A., & Testi, L. 2018, A&A, 616, A100
  * Zagaria et al. (2022) Zagaria, F., Clarke, C. J., Rosotti, G. P., & Manara, C. F. 2022, MNRAS, 512, 3538
  * Zuckerman & Song (2012) Zuckerman, B., & Song, I. 2012, ApJ, 758, 77

In this section, we compare the $\dot{M}$ and ${M_{\rm{disk}}}$ values that we
use in this work to previous values in the literature for all of the objects
with an inferred disk lifetime less than 0.01 Myr. In general, we find that
high spatial resolution (sub-)millimeter observations are needed to properly
determine the disk dust masses, especially for targets with nearby companions
which may contaminate low-resolution observations.

  * •

AB Aur
Guzmán-Díaz et al. (2021) find that AB Aur has a disk mass of 0.009$\pm$0.002
$M_{\odot}$, assuming a gas-to-dust ratio of 100, using a variety of
(sub-)millimeter observations. This is within a factor of three of our value
of 0.0035 $M_{\odot}$(${M_{\rm{dust}}}$=11.8 $M_{\oplus}$). Rivière-Marichalar
et al. (2022) find that the gas-to-dust mass ratio varies in the disk of AB
Aur, from $\sim$10-40. Therefore, the disk mass is likely to be lower than
what we use here, resulting in an even lower disk lifetime than we infer.

There are several values of the accretion rate for AB Aur in the literature:
log10($\dot{M}$)=–6.85 ($\rm{M_{\sun}\,yr^{-1}}$) (Garcia Lopez et al., 2006),
log10($\dot{M}$)=-7.74 ($\rm{M_{\sun}\,yr^{-1}}$) (Donehew & Brittain, 2011),
log10($\dot{M}$)=-6.90 ($\rm{M_{\sun}\,yr^{-1}}$) (Salyk et al., 2013), and
log10($\dot{M}$)=-6.13 ($\rm{M_{\sun}\,yr^{-1}}$) (Wichittanakom et al.,
2020). We adopt the value from Wichittanakom et al. (2020).

  * •

HD 104237
Guzmán-Díaz et al. (2021) find a disk mass of 0.008$\pm$0.002 $M_{\odot}$ for
HD 104237, a factor of less than three larger than our value of 0.003
$M_{\odot}$ (${M_{\rm{dust}}}$=10.5 $M_{\oplus}$). The Guzmán-Díaz et al.
(2021) disk mass is based on 1.27 mm observations from Henning et al. (1994)
using the 15 m SEST telescope with a resolution of 23″, which would contain
several additional sources in the beam. The ALMA observations are not high
enough resolution to resolve the disk, but a companion is observed in the
continuum, indicating that we are resolving out some, if not all, sources of
additional contamination. Kama et al. (2020) using HD observations from
Herschel/PACS observations find a gas-to-dust mass ratio of $\leq$300.

HD 104237 hosts a binary pair at the center of the circumbinary disk. This has
resulted in interesting work on the nature of the inner disk in this system.
Garcia et al. (2013) find that Br$\gamma$ is variable, with the line
equivalent width changing by a factor of 2 depending on the binary
interaction, however Garcia Lopez et al. (2006) find an accretion rate of
log10($\dot{M}$)=–7.45 ($\rm{M_{\sun}\,yr^{-1}}$), one order of magnitude
lower than the value we use here.

  * •

HD 37258
van Terwisga et al. (2022) find a dust mass of 8.9$\pm$0.41 $M_{\oplus}$ for
HD 37258, relative to the one derived by Stapper et al. (2022) of 2.4$\pm$0.4
$M_{\oplus}$. These measurements are from the same ALMA observations
(2019.1.01813.S, PI: S. van Terwisga), but the fluxes derived are slightly
different and the dust temperatures are different, with van Terwisga et al.
(2022) assuming Tdust=20 K and Stapper et al. (2022) using Tdust=51 K, derived
from the stellar luminosity.

Fairlamb et al. (2015) find an accretion rate of log10($\dot{M}$)=-6.98
($\rm{M_{\sun}\,yr^{-1}}$), the same value as found by Grant et al. (2022).

  * •

BF Ori
Guzmán-Díaz et al. (2021) report a disk mass of 0.005$\pm$0.002 $M_{\odot}$
for BF Ori using observations from the IRAM 30 m telescope presented in Natta
et al. (1997). This is 15 times higher than our adopted value from ALMA
observations of 3.3$\times$10-4 $M_{\odot}$ (${M_{\rm{dust}}}$=1.1
$M_{\oplus}$). This is due to two reasons, the first is that the IRAM
observations have a main beam width of 11″, which likely suffer from
contamination compared to the ALMA observations which have a beam of
1.″49$\times$1.″03. The ALMA observations are still not high enough resolution
to resolve the disk, but are high enough to minimize contamination from nearby
objects and cloud contamination. The second contributing factor is the choice
of dust temperature, with Guzmán-Díaz et al. (2021) using a temperature of 25
K and Stapper et al. (2022) using a value of 58 K.

Several works have reported accretion rates for BF Ori: log10($\dot{M}$)=-7.06
($\rm{M_{\sun}\,yr^{-1}}$) (Donehew & Brittain, 2011), log10($\dot{M}$)$<$-8.0
($\rm{M_{\sun}\,yr^{-1}}$) (Mendigutía et al., 2011), log10($\dot{M}$)=-6.65
($\rm{M_{\sun}\,yr^{-1}}$) (Fairlamb et al., 2015), and log10($\dot{M}$)=-7.28
(Grant et al. 2022; adopted here). The Donehew & Brittain (2011), Mendigutía
et al. (2011), and Fairlamb et al. (2015) values are all determined using the
Balmer excess, which are 0.22, 0.0, and 0.15 mag, for each of those works,
respectively. BF Ori is known to exhibit UX Ori-type behavior (e.g., Shenavrin
et al. 2012), with photometric variability in the visual and infrared,
therefore we adopt the most recent measurement for the accretion rate, which
is within the spread of the previous measurements.

  * •

HR 5999
Guzmán-Díaz et al. (2021) find a disk mass of 0.008$\pm$2.19$\times$10-4
$M_{\odot}$, using observations from SCUBA (Sandell et al., 2011) and SMA
(Meeus et al., 2012), in comparison to the disk mass we adopt here of 0.0012
$M_{\odot}$. The derived fluxes are quite similar with Meeus et al. (2012)
deriving a 1.3 mm flux of 34.3$\pm$0.9 mJy and Stapper et al. (2022) deriving
a flux of 26.5 mJy. A companion is seen in the ALMA continuum observations
which is well-resolved from HR 5999. Yen et al. (2018) used 13CO and C18O ALMA
observations, paired with models from Miotello et al. (2016), to determine a
gas mass of 6${}_{-3.2}^{+7.2}\times$10-5 $M_{\odot}$ for HR 5999, which is 20
times lower than our estimate from the dust mass. This gas mass value, when
taken with an accretion rate of log10($\dot{M}$)=-6.0
($\rm{M_{\sun}\,yr^{-1}}$), results in an inferred disk lifetime of only 60
years.

Wichittanakom et al. (2020) re-derived the accretion rate for HR 5999 from the
observations of Fairlamb et al. (2015, 2017) with updated stellar parameters,
finding an accretion rate of log10($\dot{M}$)=-6.0 ($\rm{M_{\sun}\,yr^{-1}}$),
compared to the accretion rate by Fairlamb et al. (2015) of
log10($\dot{M}$)=-6.25 ($\rm{M_{\sun}\,yr^{-1}}$). We adopt the accretion rate
from Wichittanakom et al. (2020).

  * •

VV Ser
Guzmán-Díaz et al. (2021) determine a disk mass of
9.54$\times$10${}^{-4}\pm$2.730$\times$10-4 $M_{\odot}$ for VV Ser using
observations from the Plateau de Bure Interferometer (Alonso-Albi et al.,
2008; Boissier et al., 2011) with a beam of 1.″7$\times$0.″8 at 1.3 mm. This
matches well with our derived disk mass of 6.9$\times$10-4 $M_{\odot}$ (2.3
$M_{\oplus}$ in dust mass). Pontoppidan et al. (2007) found that the mass of
the small dust grains is only $\sim$0.03 $M_{\oplus}$.

Mendigutía et al. (2011) find a Balmer jump (0.54 mag) that is inconsistent
with magnetospheric accretion models, however Donehew & Brittain (2011) find a
Balmer jump of 0.16 mag, which is within the range of magnetospheric models
run by Mendigutía et al. (2011). Garcia Lopez et al. (2016) find that several
H i lines, including Br$\gamma$, are variable, with Br$\gamma$ likely to
originate in a disk wind. The models used in that work assume an accretion
rate of 3.3$\times$10-7 $\rm{M_{\sun}\,yr^{-1}}$. With these discrepant
measurements, it is unclear whether the accretion mechanism is variable, if
magnetospheric accretion is taking place in this object, and if so, how much
of the Br$\gamma$ line is generated from magnetospheric accretion. However,
while the accretion mechanism may be unclear, the accretion rate is likely to
be high, given the high Balmer jump observed in both Mendigutía et al. (2011)
and Donehew & Brittain (2011). We note that Donehew & Brittain (2011) find an
accretion rate of log10($\dot{M}$)=-7.49 ($\rm{M_{\sun}\,yr^{-1}}$), but with
a pre-Gaia distance and stellar properties. We adopt an upper limit to the
accretion rate of log10($\dot{M}$)$<$-6.14 ($\rm{M_{\sun}\,yr^{-1}}$) from
Grant et al. (2022) and do not include it in the $\dot{M}$–$M_{\rm{disk}}$
fits.

  * •

HD 58647
Few (sub-)millimeter observations of HD 58647 are available in the literature.
We consider the ALMA observations (from Program 2018.1.00814.S), with an RMS
of 0.14 mJy beam-1 and a beam of 0.″47$\times$0.″39, and the dust mass
determination of 1$\pm$0.1 $M_{\oplus}$ from Stapper et al. (2022) to be
robust.

In comparison to the lack of (sub-)millimeter observations, HD 58647 has
several U-band and near-infrared observations. Mendigutía et al. (2011) use
the Balmer discontinuity and find an accretion rate of log10($\dot{M}$)=–4.84
($\rm{M_{\sun}\,yr^{-1}}$) for HD 58647. Using Br$\gamma$ observations,
Brittain et al. (2007) find an accretion rate of log10($\dot{M}$)=-6.45
($\rm{M_{\sun}\,yr^{-1}}$), Ilee et al. (2014) find an accretion rate of
log10($\dot{M}$)=-6.32 ($\rm{M_{\sun}\,yr^{-1}}$), and Grant et al. (2022)
find an accretion rate of log10($\dot{M}$)=-5.84 ($\rm{M_{\sun}\,yr^{-1}}$).
We adopt the latter in this work.

  * •

HD 141569
Miley et al. (2018) find a gas mass of 6$\times$10-4 $M_{\odot}$ for HD 141569
using ALMA 13CO (2-1) observations, a factor of 6 above our inferred disk mass
of 1$\times$10-4 $M_{\odot}$. This higher disk mass is still low enough that
the inferred disk lifetime is only 0.03 Myr. Guzmán-Díaz et al. (2021) find a
disk mass of 1.46$\times$10-4 $M_{\odot}$ for HD 141569 from millimeter
observations, in good agreement with the value that we adopt from Stapper et
al. (2022).

For HD 141569 several accretion rates have been determined in the literature:
Garcia Lopez et al. (2006) find an accretion rate of log10($\dot{M}$)=-8.37
($\rm{M_{\sun}\,yr^{-1}}$), Mendigutía et al. (2012) find a value of
log10($\dot{M}$)=-6.89 ($\rm{M_{\sun}\,yr^{-1}}$), and Fairlamb et al. (2015)
find a value of log10($\dot{M}$)=-7.65 ($\rm{M_{\sun}\,yr^{-1}}$). Grant et
al. (2022) and Wichittanakom et al. (2020) update the value from Fairlamb et
al. (2015) to log10($\dot{M}$)=-7.76 ($\rm{M_{\sun}\,yr^{-1}}$) and
log10($\dot{M}$)=-7.23 ($\rm{M_{\sun}\,yr^{-1}}$), respectively. We adopt the
value from Grant et al. (2022).

  * •

HD 9672
Moór et al. (2019) find a CO gas mass of 1.11$\times$10-2 $M_{\oplus}$
(3.33$\times$10-8 $M_{\odot}$) for HD 9672/49 Cet, however, CO may not be a
good tracer of the total disk mass, in particular depending on the gas origin
(e.g., Moór et al. 2019). Using the dust continuum and assuming a gas-to-dust
mass ration of 100, Guzmán-Díaz et al. (2021) find a disk mass of
2.92$\times$10-4 $M_{\odot}$ from infrared photometry from Herschel/PACS, a
factor of seven higher than our value of 3.9$\times$10-5 $M_{\odot}$. The ALMA
observations analyzed in Stapper et al. (2022) should provide a more accurate
estimate of the dust mass due to the longer wavelength observations.

The accretion rate of log10($\dot{M}$)=-7.80 ($\rm{M_{\sun}\,yr^{-1}}$) for HD
9672 comes from Wichittanakom et al. (2020), derived from the Fiber-fed
Extended Range Optical Spectrograph (FEROS, Kaufer et al. 1999) spectra from
ESO Program 082.A-9011(A).

  * •

TY CrA
Cazzoletti et al. (2019) find a dust mass for TY CrA of 0.66 $M_{\oplus}$
(disk mass of 2$\times$10-4 $M_{\odot}$, assuming a gas-to-dust mass ratio of
100), compared to that derived by Stapper et al. (2022) of 0.1 $M_{\oplus}$
(disk mass of 3$\times$10-5 $M_{\odot}$, assuming a gas-to-dust mass ratio of
100), from the same dataset, largely due to the difference in dust temperature
assumed. Guzmán-Díaz et al. (2021) find a disk mass of less than 0.017
$M_{\odot}$, from the upper limits on the millimeter flux from Henning et al.
(1994) and Pezzuto et al. (1997).

The only accretion rate in the literature that we found is that of Garcia
Lopez et al. (2006), who found an accretion rate of log10($\dot{M}$)$<$–8.31
($\rm{M_{\sun}\,yr^{-1}}$), based on the depth of the Br$\gamma$ line, which
indicated little or no accretion taking place in this object.

  * •

HD 176386
HD 176386 is undetected in the ALMA observation, with the continuum only
present at the 1.6$\sigma$ level (Stapper et al., 2022). That observation had
an RMS of 0.20 mJy/beam, meaning that the upper limit for the flux of 0.32
mJy, corresponding to a dust mass of 0.06 $M_{\oplus}$ (1.8$\times$10-5
$M_{\odot}$ in total disk mass assuming a gas-to-dust ratio of 100). Guzmán-
Díaz et al. (2021) used sub-millimeter observations from SCUBA (Di Francesco
et al., 2008) to determine a disk mass of 0.121$\pm$0.01 $M_{\odot}$. This
nearly 4 orders of magnitude difference is due to contamination in the SCUBA
maps, which have a 14″ full width at half maximum in the 850 $\mu$m map used.
HD 176386B is a binary companion to HD 176386 with a separation of 3.″7
(Wilking et al., 1997), and would have contributed to the flux observed in the
low resolution SCUBA observations. The high resolution ALMA observations, with
a beam of 0.″43$\times$0.″32, is able to spatially distinguish the sources.

HD 176386 has several accretion rates in the literature. Garcia Lopez et al.
(2006) find an accretion rate of log10($\dot{M}$)=-8.11
($\rm{M_{\sun}\,yr^{-1}}$), Wichittanakom et al. (2020) find a value of
log10($\dot{M}$)=-7.08 ($\rm{M_{\sun}\,yr^{-1}}$), and Guzmán-Díaz et al.
(2021) find a value of log10($\dot{M}$)=-6.49 ($\rm{M_{\sun}\,yr^{-1}}$).
Pogodin et al. (2012), whose X-Shooter data is the source of the H$\alpha$
equivalent width used in Wichittanakom et al. (2020), conclude that
magnetospheric accretion cannot be applied to this object, given that the disk
may be dispersed. Given that we have stringent upper limits on the disk mass
for this object, we agree that the disk may be dispersed and the accretion
rate should be considered with caution. However, the Pogodin et al. (2012)
absorption H$\alpha$ profile for HD 176386 does show shallowing relative to a
photospheric model, which may be due to accretion. We take the adapted value
from Wichittanakom et al. (2020), however this value should be used with
caution.

  * •

HD 53367
The ALMA observations analyzed in Stapper et al. (2022) (from Program
2018.1.00814.S) show that HD 53367 is only present in the continuum at the
2.4$\sigma$ level with an RMS of 0.14 mJy beam-1. We are not aware of other
(sub-)millimeter observations of this target.

Donehew & Brittain (2011) find an accretion rate of log10($\dot{M}$)$<$-7.92
($\rm{M_{\sun}\,yr^{-1}}$) from a Balmer discontinuity of $<$0.09 mag.
Fairlamb et al. (2015) find a similar Balmer discontinuity of 0.10 mag and
they are unable to determine an accretion rate for this source given the very
high stellar effective temperature of 29500$\pm$1000 K. The $\dot{M}$ value
that we adopt here of log10($\dot{M}$)=-6.97 ($\rm{M_{\sun}\,yr^{-1}}$) is
from Grant et al. (2022), based on strong Br$\gamma$ line emission. However,
given the high stellar mass and effective temperature of this object, this
accretion rate should be viewed with caution. Given the low dust mass of this
object, if any accretion is taking place, the disk would likely be depleted
very quickly.