11institutetext: Institute of Astronomy, University of Cambridge, Madingley
Road, Cambridge, CB3 0HA, UK
11email<EMAIL_ADDRESS>22institutetext: European Southern Observatory,
3107, Alonso de Córdova, Vitacura, Santiago, Chile 33institutetext: European
Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching bei München,
Germany 44institutetext: Departamento de Física, Universidad de Santiago de
Chile, Av. Victor Jara 3659, Santiago, Chile 55institutetext: Millennium
Nucleus on Young Exoplanets and their Moons (YEMS), Chile 66institutetext:
Center for Interdisciplinary Research in Astrophysics and Space Exploration
(CIRAS), Universidad de Santiago de Chile, Estación Central, Chile
77institutetext: Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
88institutetext: Department of Physics and Astronomy, University of Victoria,
Victoria, BC, V8P 5C2, Canada 99institutetext: Instituto de Física y
Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Av. Gran Bretaña
1111, Valparaíso, Chile 1010institutetext: Núcleo Milenio de Formación
Planetaria - NPF, Valparaíso, Chile 1111institutetext: Instituto de
Astrofísica, Universidad Andres Bello, Fernandez Concha 700, Las Condes,
Santiago RM, Chile 1212institutetext: Joint ALMA Observatory, Avenida Alonso
de Córdova 3107, Vitacura, Santiago, Chile 1313institutetext: Astronomy
Department, University of California, Berkeley, CA 94720, USA
1414institutetext: Department of Astronomy and Institute for Astrophysical
Research, Boston University, 725 Commonwealth Avenue, Boston, MA 02215, USA
1515institutetext: Observatorio Astronómico Nacional (OAN, IGN), Calle Alfonso
XII, 3. 28014 Madrid, Spain 1616institutetext: Jet Propulsion Laboratory,
California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109,
USA

# The ALMA view of MP Mus (PDS 66): a protoplanetary disk with no visible gaps
down to 4 au scales

Á. Ribas 11 2 2 E. Macías 33 P. Weber 445566 S. Pérez 445566 N. Cuello 77 R.
Dong 88 A. Aguayo 99 10 10 C. Cáceres 11111010 J. Carpenter 1212 W. R. F. Dent
1212 I. de Gregorio-Monsalvo 22 G. Duchêne 131377 C. C. Espaillat 1414 P.
Riviere-Marichalar 1515 M. Villenave 1616

(Received 09 December 2022 / Accepted 17 February 2023)

###### Abstract

Aims. We aim to characterize the protoplanetary disk around the nearby
(d$\sim$100 pc), young solar analog MP Mus (PDS 66) and to reveal any signs of
planets or ongoing planet formation in the system.

Methods. We present new ALMA observations of MP Mus at 0.89 mm, 1.3 mm, and
2.2 mm with angular resolutions of $\sim$ 1″, 0.05″, and 0.25″, respectively.
These data probe the dust and gas in the disk with unprecedented detail and
sensitivity.

Results. The disk appears smooth down to the 4 au resolution of the 1.3 mm
observations, in contrast with most disks observed at comparable spatial
scales. The dust disk has a radius of 60$\pm$5 au, a dust mass of
$0.14_{-0.06}^{+0.11}$ $M_{\rm Jup}$, and a mm spectral index $<2$ in the
inner 30 au, suggesting optically thick emission from grains with high albedo
in this region. Several molecular gas lines are also detected extending up to
130$\pm$15 au, similar to small grains traced by scattered light observations.
Comparing the fluxes of different CO isotopologues with previous models yields
a gas mass of $0.1-1$ $M_{\rm Jup}$, implying a gas to dust ratio of 1-10. We
also measure a dynamical stellar mass of $M_{\rm dyn}$=1.30$\pm$0.08
$M_{\odot}$ and derive an age of 7-10 Myr.

Conclusions. The survival of large grains in an evolved disk without
gaps/rings is surprising, and it is possible that existing substructures
remain undetected due to optically thick emission at 1.3 mm. Alternatively,
small structures may still remain unresolved with the current observations.
Based on simple scaling relations for gap-opening planets and gap widths, this
lack of substructures places upper limits to the masses of planets in the disk
as low as 2 $M_{\oplus}$-0.06 $M_{\rm Jup}$ at $r>40$ au. The lack of mm
emission at radii $r>60$ au also suggests that the gap in scattered light
between 30-80 au is likely not a gap in the disk density, but a shadow cast by
a puffed-up inner disk.

###### Key Words.:

Accretion disks – Protoplanetary disks – Planets and satellites: formation –
Stars: individual: MP Mus – Stars: pre-main sequence – Techniques:
interferometric

##  1 Introduction

Our theories of planet formation are largely informed by observations of
protoplanetary disks in young, nearby star-forming regions. Both surveys and
studies of individual systems have built a general understanding of properties
such as the disk typical lifetimes, accretion rates, masses and sizes (e.g.,
see Manara et al., 2022; Miotello et al., 2022; Pascucci et al., 2022, and
other Protostars and Planets VII chapters for a recent review of the field),
all of which are crucial to characterize the timescales and environment in
which planets form. In recent years, SPHERE and ALMA observations have also
revealed gaps, rings and other substructures to be very common in
protoplanetary disks (e.g. Long et al., 2018; Andrews et al., 2018a; Avenhaus
et al., 2018), providing new clues about planet-disk interactions and the
underlying population of newborn planets.

Although a large portion of our knowledge of protoplanetary disk properties
comes from statistical analysis of large samples, there are a few individual
sources that have had a particularly high impact in our understanding of
planet formation. Perhaps the most iconic example of such a system is TW Hya,
which hosts what is arguably the most and best studied protoplanetary disk to
date. A combination of different factors make TW Hya a unique cornerstone in
the study of planet formation. At a distance of only 60 pc (Gaia Collaboration
et al., 2022), it is significantly closer than the nearest (140-400 pc) star-
forming regions such as Taurus, Ophiuchus, Lupus, Chamaeleon, Upper Scorpius
or the Orion Molecular Cloud. Its proximity and almost face-on orientation
allow for very detailed studies of the disk structure: high angular resolution
observations of the gas and dust components have revealed, among other
features, a concentric system of rings and gaps (including an inner gap as
small as 1 au, Andrews et al., 2016), a clump of dust at $\sim$50 au which may
be associated with circumplanetary material (Tsukagoshi et al., 2019), a
spiral structure in its gas component (Teague et al., 2019), and shadows in
scattered light moving azimuthally across the disk surface, probably cast by
the inner disk (Debes et al., 2017). It is also one of the few protoplanetary
disks for which a detection of hydrogen deuteride (HD) is available, allowing
for a CO-independent estimate of its mass (Bergin et al., 2013) and dust-to-
gas mass ratio (Macías et al., 2021), as well as the only disk in which line
polarization has been measured (Teague et al., 2021). Its 0.6 $M_{\odot}$
stellar mass also makes it a great target to better understand the early
stages of the Solar System. TW Hya greatly exemplifies the potential of nearby
protoplanetary disks for planet formation studies.

Within 100 pc, the only other gas-rich disk around a single star is MP Muscae
(MP Mus, PDS 66), a K1V star (Mamajek et al., 2002) located at 97.9$\pm$0.1 pc
(Gaia Collaboration et al., 2022). It was originally identified as a classical
T Tauri star by Gregorio-Hetem et al. (1992) and first believed to belong to
the $\sim$17 Myr old Lower Centaurus-Crux association (Mamajek et al., 2002),
but later studies of its kinematic properties and parallax showed it to be a
member of the younger, 3-5 Myr old $\epsilon$ Chamaeleon ($\epsilon$ Cha)
association (Torres et al., 2008; Murphy et al., 2013; Dickson-Vandervelde et
al., 2021). The source is still accreting weakly (Pascucci et al., 2007;
Ingleby et al., 2013) at its estimated age of 7-10 Myr, and hosts a gas-rich
disk extending up to 130 au (Kastner et al., 2010). The SED and mid-IR spectra
of the system have also been studied (Schütz et al., 2005; Bouwman et al.,
2008; Cortes et al., 2009), revealing signs of grain growth in the disk. More
recently, Wolff et al. (2016) and Avenhaus et al. (2018) presented scattered
light observations from the Gemini Planet Imager (GPI) and SPHERE/VLT, which
revealed a drop in the disk brightness between 60-80 au. If this drop
corresponds to a gap in the disk surface density, then it could be produced by
the gravitational influence of one or multiple planets, representing an
excellent source to study recently formed planets in a nearby system. With a
stellar mass of 1.3 $M_{\odot}$, MP Mus may be the nearest analog to the young
Solar System.

Despite the obvious interest of MP Mus and many of its aspects being already
well characterized, it still remains comparatively unexplored at millimeter
wavelengths. Here we present new observations of the system with the Atacama
Large Millimeter/submillimeter Array (ALMA), including 0.89 mm (Band 7), 1.3
mm (Band 6), and 2.2 mm (Band 4) continuum emission as well as several
molecular gas lines. These observations, with an angular resolution down to 4
au at 1.3 mm, provide a wealth of new information and an unprecedented view of
the system. We describe the ALMA observations as well as re-processing of
ancillary SPHERE data in Sect. 2. We then present the results and analysis in
Sect. 3, and discuss their implications in Sect. 4. Finally, the main findings
are summarized in Sect. 5.

##  2 Observations and data processing

###  2.1 ALMA observations

MP Mus was observed during ALMA Cycle 5 by three different programs at 0.89 mm
(Band 7), 1.3 mm (Band 6), and 2.2 mm (Band 4). Project 2017.1.01687.S (P.I.:
Álvaro Ribas) included observations in Bands 4 and 7, while both projects
2017.1.01167.S (P.I.: Sebastián Pérez, part of the Disks ARound TTauri Stars
with ALMA (DARTTS-A) programme) and 2017.1.01419.S (P.I.: Claudio Cáceres)
used Band 6. Observations with two antenna configurations exist in all cases
except for the Band 7 data, for which only observations with a compact
configuration are available. Also, two different executions of the Band 4
compact configuration were made. A summary of the different datasets used and
the corresponding correlator configurations is available in Tables 1 and 2. We
used the standard pipeline calibration provided by ALMA staff using CASA
(McMullin et al., 2007) version 5.1.1-5, including water vapor radiometer and
system temperature correction, as well as bandpass, amplitude, and phase
calibrations. Some additional flagging was applied to the Band 6 and Band 7
data.

Table 1: Summary of ALMA observations ALMA Project Code | Band | Conf. & Baselines | Date | Nant | Time On-Source | PWV | Flux Calibrator
---|---|---|---|---|---|---|---
|  | (m) |  |  | (min) | (mm) |
2017.1.01687.S | 4 | C43-3, 15–500 | 2018 Apr 09 | 45 | 8.1 | 3.0 | J1107-4449
(P.I: Álvaro Ribas) | 4 | C43-3, 15–500 | 2018 Apr 29 | 44 | 8.1 | 2.4 | J1427-4206
| 4 | C43-6, 15–2500 | 2017 Dec 30 | 45 | 19.1 | 2.2 | J1617-5848
| 7 | C43-1, 15–300 | 2018 Jul 10 | 45 | 8.8 | 0.2 | J1427-4206
2017.1.01167.S | 6 | C43-5, 15–2400 | 2018 Jan 15 | 46 | 5.6 | 1.6 | J1427-4206
(P.I: Sebastián Pérez) | 6 | C43-8, 90–8300 | 2017 Nov 16 | 44 | 11.4 | 1.1 | J1427-4206
2017.1.01419.S | 6 | C43-2, 15–300 | 2018 Jul 06 | 44 | 8.7 | 0.7 | J1427-4206
(P.I: Claudio Cáceres) | 6 | C43-5, 15–2500 | 2017 Dec 26 | 43 | 17.1 | 0.3 | J1427-4206
Table 2: Correlator configuration of the different ALMA projects used in this study ALMA Project Code | Band | Central Freq. | Bandwidth | Channels | Spectral lines
---|---|---|---|---|---
|  | (GHz) | (MHz) |  |
2017.1.01687.S | 4 | 130.884 | 1875 | 3840 | …
|  | 132.801 | 1875 | 3840 | …
|  | 144.874 | 1875 | 3840 | DCO+ (2-1), DCN (2-1), HC3N (16-15)
|  | 142.994 | 1875 | 3840 | …
| 7 | 330.575 | 469 | 3840 |  13CO (3-2)
|  | 331.709 | 1875 | 1920 | …
|  | 343.292 | 1875 | 3840 | CS (7-6), HC15N (4-3)
|  | 345.783 | 469 | 3840 |  12CO (3-2)
2017.1.01167.S | 6 | 230.525 | 1875 | 960 |  12CO (2-1)
|  | 232.483 | 1875 | 128 | …
|  | 244.983 | 1875 | 128 | …
|  | 246.983 | 1875 | 128 | …
2017.1.01419.S | 6 | 217.542 | 1875 | 128 | …
|  | 219.486 | 1875 | 3840 |  13CO (2-1), C18O (2-1)
|  | 230.611 | 234 | 1920 |  12CO (2-1)
|  | 231.196 | 234 | 1920 | …
|  | 232.791 | 1875 | 128 | …

Continuum emission from the disk was clearly detected with a high signal to
noise ratio (S/N) at the three wavelengths. Therefore, after pipeline
calibration, we performed phase only self-calibration on each individual
dataset using the mtmfs deconvolver, Briggs weighting, a robust value of 0.5,
and nterms=2. Channels with emission lines were excluded during this process.
We then re-scaled all the data in each band to a common flux value (as
reference, we chose the flux of the observation closest in time to
observations of the corresponding amplitude calibrator by the ALMA
observatory), set their phase centers to that of a Gaussian fit to the data
(i.e., centered on the peak of the disk emission), and then set them to a
common coordinate to correct for pointing deviations and proper motion. In the
case of the Band 6 observations, we also performed one final round of phase
only self-calibration to the combined data to ensure that they were properly
aligned. The self-calibration process improved the peak S/N by factors of
2-10, depending on the dataset.

###  2.2 SPHERE scattered light observations

MP Mus was observed in dual-beam polarimetric imaging mode (DPI, de Boer et
al., 2020; van Holstein et al., 2020) with the InfraRed Dual-band Imager and
Spectrograph (IRDIS) at SPHERE within the DARTTS-program. The data were taken
in $J$-band and $H$-band and presented in Avenhaus et al. (2018, see this
reference for details on the observational setup). We re-reduced the DARTTS
scattered light data with the reduction pipeline IRDAP111irdap.readthedocs.io
(IRDIS Data reduction for Accurate Polarimetry, version 1.3.3, van Holstein et
al., 2020), which uses a data-independent polarization model specific for the
optical instrument to correct for instrumental polarization and crosstalk. The
double-sum/double-difference technique provides the total intensity $I$ and
the linear polarization components $Q$ and $U$ (rotated by 45 °with respect to
each other) as data products. The total polarized intensity can be calculated
from those components:

$PI=\sqrt{Q^{2}+U^{2}}\,.$ (1)

However, in the case of a single central light source and single-scattering
events, it is convenient to transform the polarized components to polar
coordinates (Schmid et al., 2006; de Boer et al., 2020):

$\begin{cases}Q_{\phi}=-Q\cos{\left(2\phi\right)}-U\sin{\left(2\phi\right)}\\\
U_{\phi}=+Q\sin{\left(2\phi\right)}-U\cos{\left(2\phi\right)}\end{cases}$ (2)

Here, positive $Q_{\phi}$ is the polarization component perpendicular to the
direction of the star. Positive $Q_{\phi}$ is expected to capture all stellar
light that was polarized in single-scattering events with the additional
benefit of a lower noise level than $PI$ due to the lack of squared
operations. On the other hand, significant signal in $U_{\phi}$ or negative
$Q_{\phi}$ can indicate regions where light is scattered more than once
(Canovas et al., 2015) or where other, off-centered light sources contribute
significantly to the scattering (Weber et al., 2023).

The reprocessing of the SPHERE observations does not differ significantly from
the findings of Avenhaus et al. (2018), but it provides additional information
about the angle and degree of linear polarization of the stellar halo. These
results are discussed in Sec. 3.3.

##  3 Results

Figure 1: ALMA images of MP Mus at 1.3 mm. These are displayed using both
linear (left) and logarithmic (right) scales to emphasize details at different
brightness levels. The 0.06″x0.04″beam is shown at the bottom left corners as
white ellipses.

The new ALMA observations can be used to derive several parameters of the MP
Mus system, including dust, gas, and stellar masses, its age, the spectral
index of the millimeter continuum emission, and the overall morphology of the
disk. The SPHERE observations provide additional information about the
polarization level and the distribution of small grains in the system. The
corresponding analysis is described throughout this section, and we provide a
summary of the derived properties in Table 3.

Table 3: Summary of results derived for MP Mus.

Parameter | Value
---|---
$M_{*,\rm dyn}$ | $1.30\pm 0.08M_{\odot}$
$L_{*}$ | $1.2\pm 0.1L_{\odot}$
Age{\dagger}{\dagger}${\dagger}$Based on the derived luminosity and the MIST isochrones (Dotter, 2016; Choi et al., 2016). | 7 - 10 Myr
$V_{\rm LSR}$ |  $3.98\pm 0.04$ km/s
$M_{\rm dust}$ |  $0.14_{-0.06}^{+0.11}$ $M_{\rm Jup}$
$M_{\rm gas}$ | 0.1-1 $M_{\rm Jup}$
$R_{\rm dust}${\dagger}{\dagger}{\dagger}{\dagger}${\dagger}{\dagger}$The uncertainties correspond to beam size of the observations. |  $60\pm 5$ au
$R_{\rm gas\,(^{12}CO)}${\dagger}{\dagger}{\dagger}{\dagger}${\dagger}{\dagger}$The uncertainties correspond to beam size of the observations. |  $130\pm 15$ au
$i_{\rm dust}$ |  $32\pm 1$°
PAdust |  $10\pm 1$°
$DoLP$ |  $0.46\pm 0.08$%
$AoLP$ |  $98\pm 8$°
222

###  3.1 Dust continuum

####  3.1.1 Continuum images and fluxes

We synthesized continuum images at 0.89 mm, 1.3 mm, and 2.2 mm from the self-
calibrated data described in Sect. 2 using the tclean algorithm with the mtmfs
deconvolver and nterms=2. For each dataset at 1.3 and 2.2 mm, the extended and
compact configurations were combined to produce the continuum images (in the
particular case of the 1.3 mm data from project 2017.1.01419.S, the compact
configuration was excluded since it was noisier and did not improve the image
sensitivity). A robust value of 0.5 was used to synthesize the images to
measure fluxes, resulting in beam sizes of 1.0″$\times$0.82″,
0.12″$\times$0.10″, and 0.39″$\times$0.31″at 0.89 mm, 1.3 mm, and 2.2 mm,
respectively. The disk around MP Mus is clearly detected at all wavelengths
(peak S/N values of several hundreds/thousands) and is well resolved in both
the 1.3 mm and 2.2 mm observations. We used aperture photometry to estimate
continuum fluxes from these images, obtaining 370$\pm$40 mJy at 0.89 mm,
148$\pm$7 mJy at 1.3 mm, and 49$\pm$2 mJy at 2.2 mm (see Table 4). These
uncertainties are largely dominated by absolute calibration and not the noise
in the images. The emission at 1.3 mm and 2.2 mm extends up to 60 au (0.6″),
as determined from the 3-5 $\sigma$ contours. To ease the comparison with
other studies, we also list the radii enclosing 68 % and 90 % of the total
flux in Table 5. Based on the most compact antenna configuration in each band
(Table 1), the maximum recoverable scales are $\sim$10.8″, 2.9″, and 8.3″at
2.2 mm, 1.3 mm and 0.89 mm, respectively333See ALMA Technical Handbook, which
are significantly larger than the observed disk size. Therefore, the
observations are likely recovering all the emission from the disk. We also
produced images with a lower robust value of -0.5 to try to reveal small
substructures, reaching angular resolutions of 0.89$\times$0.66″,
0.06″$\times$0.04″, and 0.25″$\times$0.19″at 0.89 mm, 1.3 mm, and 2.2 mm
(corresponding to $\sim$75, 4, and 20 au at 98 pc). Interestingly, the disk
appears smooth even at such resolutions, with no clear rings, gaps, or
asymmetries. The continuum image at 1.3 mm is shown in Fig. 1, and the 0.89 mm
and 2.2 mm observations can be found in Appendix A.

Table 4: ALMA Continuum Fluxes

Wavelength | Frequency | Flux | RMS | Peak S/N | Beam
---|---|---|---|---|---
(mm) | (GHz) | (mJy) | ($\mu$Jy/beam) |  |
0.89 | 338.187 | 370$\pm$40 | 130 | 2230 | 1.00″$\times$0.82″, PA=46°
1.29 | 232.269 | 148$\pm$7 | 19 | 720 | 0.12″$\times$0.10″, PA=-5°
2.17 | 137.883 | 49$\pm$3 | 14 | 1660 | 0.39″$\times$0.31″, PA=-42°
444All fluxes estimated from images with a robust parameter of 0.5.
Uncertainties are dominated by the ALMA absolute flux calibration uncertainty
(10 % for Band 7 and 5 % for Bands 6 and 4).

Table 5: Disk radius encompassing 68 % and 90 % of the total flux.

Component |  $R_{\rm 68\,\%}$ (au) |  $R_{\rm 90\,\%}$ (au)
---|---|---
Continuum (1.3 mm) | 30$\pm$5 | 45$\pm$5
Continuum (2.2 mm) | 30$\pm$20 | 45$\pm$20
Gas (12CO (2-1)) | 80$\pm$15 | 110$\pm$15
555The uncertainties correspond to the beam size of each observation.

####  3.1.2 Disk dust mass

Assuming that the (sub)mm emission from the disk is optically thin and
isothermal, the measured flux is linearly related to the dust mass (e.g.
Beckwith et al., 1990):

$M_{\rm dust}=\frac{F_{\nu}\,d^{2}}{\kappa_{\nu}\,B_{\nu}(T_{\rm dust})},$ (3)

where $M_{\rm dust}$ is disk dust mass, $F_{\nu}$ is the flux at the observed
frequency $\nu$, $d$ is the distance to the source, $\kappa_{\nu}$ is the dust
opacity at the frequency $\nu$, and $B_{\nu}(T_{\rm dust})$ is the blackbody
emission at the corresponding frequency and dust temperature $T_{\rm dust}$.
Since we have observations at three different frequencies, we can compute
three dust mass values. We adopted standard values for the opacity and dust
temperatures of $\kappa_{\rm 230\,GHz}$=2.3 cm2/g and $T_{\rm dust}=20$ K
(e.g., Andrews & Williams, 2005), and a distance of $d$=98 pc (Gaia
Collaboration et al., 2022). For the observations at 0.89 mm and 2.2 mm, we
computed the corresponding $\kappa_{\nu}$ value using a power-law dependence
of the opacity with frequency, i.e. $\kappa_{\nu}$ = $\kappa_{\rm
230\,GHz}\times(\nu/{\rm 230\,GHz})^{\beta}$, where $\beta$ is between 0.0-0.6
for most protoplanetary disks (e.g., Tazzari et al., 2021, also in agreement
with the $\beta$ range of 0.1-0.4 derived for MP Mus in Sec. 4.2). We
bootstrapped the dust masses and their uncertainties by adopting uncertainties
of 5 K for $T_{\rm dust}$ and 20 % for $\kappa_{\rm 230\,GHz}$, and a uniform
distribution of $\beta$ values between 0 and 0.6. The derived disk dust masses
are 0.16${}_{-0.05}^{+0.1}$ $M_{\rm Jup}$, 0.13${}_{-0.04}^{+0.07}$ $M_{\rm
Jup}$, and 0.13${}_{-0.04}^{+0.07}$ $M_{\rm Jup}$ at 0.89 mm, 1.3 mm, and 2.2
mm (the reported values correspond to the median and the 16 %, and 84 %
percentiles). These values are all compatible with each other, and we adopt a
final dust mass value of $M_{\rm dust}=0.14_{-0.06}^{+0.11}$ $M_{\rm Jup}$ as
the average of the three measurements.

####  3.1.3 1.3 mm continuum radial profile

Figure 2: ALMA 1.3 mm observations and model of MP Mus. The observed continuum
emission (left) and the resulting image reconstructed from the frank radial
profile (middle) are shown. The residuals (right) are displayed in units of
the image RMS and are below the 5-$\sigma$ level.

To further investigate the presence (or lack) of substructures in the disk, we
focused on the 1.3 mm continuum data since they have the highest angular
resolution ($\sim$4 au in the case of the robust=-0.5 image). We first de-
projected this image adopting a disk inclination of 32° and a position angle
(PA) of 10° based on a Gaussian fit to the data, in full agreement with
previous estimates from scattered light observations (e.g., Schneider et al.,
2014; Wolff et al., 2016; Avenhaus et al., 2018). The averaged radial profile
was then calculated as the median intensity within concentric annuli centered
on the source. To reveal even smaller details in the disk, we also used the
frank software (Jennings et al., 2020) to reconstruct the radial profile
directly from the visibilities. frank calculates super-resolution radial
profiles of protoplanetary disks assuming azimuthal symmetry, a condition
which is met in the case of MP Mus. We tried different combinations of frank’s
$\alpha$ and $w_{\rm smooth}$ hyperparameters and found no major differences
in the resulting radial profile, so we adopted $\alpha$=1.3 and $w_{\rm
smooth}=10^{-3}$ for the analysis. A comparison of the observed visibilities
and the frank fit is shown in Fig. 12. The inclination and PA derived from
frank are in complete agreement with the values adopted earlier. Both the
profile extracted directly from the image and the one from frank reveal
radially decreasing emission extending up to $\sim$60 au, with changes in the
slope at $\sim$10 and 30 au as well as a plateau between 30-40 au, and bump in
the outermost region which may suggest the presence of a low-contrast gap and
small, barely resolved ring. However, no clear signatures of substructures are
found down to a 4 au scale. We also produced a residual map by extending the
radial profile from frank azimuthally, projecting the resulting image with the
corresponding disk inclination and orientation, and convolving it with the
observed beam before subtracting it from the observations. The residuals (Fig.
2) are all below the 5-$\sigma$ level and do not reveal any azimuthal
substructures. The resulting radial profiles are shown in Fig. 3.

Figure 3: Radial profiles of the 1.3 mm continuum and 12CO (2-1) emission of
MP Mus. The continuum profile derived from the synthesized ALMA image is shown
as a red line, and the orange line corresponds to the resulting profile from
frank (Jennings et al., 2020). The profile for the 12CO (2-1) line is also
shown as a blue line. The 1-$\sigma$ uncertainties for the continuum and 12CO
(2-1) are also plotted as red and blue shaded areas. In all cases, we adopted
a disk inclination and PA of 32°and 10°. For comparison, the FWHM of the
continuum and 12CO (2-1) beams are also shown as solid horizontal red and blue
lines, respectively.

####  3.1.4 (Sub)mm spectral indices

The spectral index ($\alpha_{\rm mm}$) of optically thin (sub)mm emission from
protoplanetary disks depends on the size of dust grains in them, and has been
used in the past to investigate grain growth in disks in several star-forming
regions (e.g. Ricci et al., 2010b, a; Ribas et al., 2017; Tazzari et al.,
2021). Using the derived continuum fluxes, we computed three spectral indices
in different wavelength ranges: $\alpha_{\rm 0.89-1.3\,mm}=2.4\pm 0.3$,
$\alpha_{\rm 1.3-2.2\,mm}=2.12\pm 0.11$, and $\alpha_{\rm
0.89-2.2\,mm}=2.25\pm 0.13$ (including the absolute calibration uncertainties
of ALMA). These values were computed from the integrated fluxes and they
reflect the average spectral index in the disk only, but the spectral index is
expected to vary spatially as a result of factors such as radial changes in
the optical depth and grains sizes. To investigate such spatial variations, we
combined the resolved 1.3 mm and 2.2 mm observations to produce a resolved map
of the spectral index. During this process, the most extended configuration of
the available Band 6 data was excluded to avoid problems with very different
coverage of the uv-plane at different bands. The 1.3 and 2.2 mm data were
jointly imaged with the tclean algorithm, the mtmfs deconvolver, and nterms=2,
and we then used the resulting alpha image as the spectral index map. After
various tests we adopted a robust parameter of 0.0 in this case, which yielded
a beam of 0.2″$\times$0.17″. The derived spectral index map and its radial
profile are shown in Fig. 4. As expected, the value of $\alpha_{\rm
1.3-2.2\,mm}$ is not constant throughout the disk and increases as a function
of radius, ranging from $\sim$1.7 in the inner regions to $\sim$3 in the outer
parts of the disk. These results are discussed in further detail in Sec. 4.2.

Figure 4: Derived millimeter spectral index for MP Mus between 1.3 and 2.2 mm.
Top: Spectral index map. Only pixels with S/N$>$5 are considered. The solid
and dashed contours correspond to $\alpha_{\rm 1.3-2.2\,mm}$ of 2 and 2.5,
respectively. The image beam is shown on the bottom left corner. Bottom:
Corresponding de-projected $\alpha_{\rm 1.3-2.2\,mm}$ radial profile and
uncertainties (solid red line and area). The beam FWHM is shown as a
horizontal red line. The dashed line marks the $\alpha=2$ transition.

###  3.2 Gas lines

####  3.2.1 Line cubes, fluxes, and morphology

The observations in this study cover multiple molecular gas emission lines,
which were imaged using tclean after applying the self-calibration solutions
and re-centering derived in Sec. 2 and subtracting the corresponding
continuum. We detected 12CO (3-2), 13CO (3-2), and CS (7-6) in Band 7, 12CO
(2-1), 13CO (2-1), and C18O (2-1) in Band 6, and DCO+ (2-1), DCN (2-1), and
HC3N (16-15) in Band 4. HC15N (4-3) was also tentatively detected in the Band
7 data. We used CASA to produce the zero-th and first moments for each line,
and applied Keplerian masking during the process to minimize noise from
signal-free areas (e.g., Salinas et al., 2017). The moments and spectra for
the12CO (2-1), 13CO (2-1), and C18O (2-1) are shown in Fig. 5, and similar
figures for the remaining lines are provided in Appendix C. The line fluxes
measured from the zero-th moments are listed in Table 6. Note that each
project used different antenna and correlator configurations, so the spectral
and spatial resolutions are different for each line (also listed in Table 6).
In the case of the Band 6 observations, we only used the observations from
project 2017.1.01419.S to generate the cubes (data from 2017.1.01167.S have a
significantly higher angular resolution which results in a much lower
sensitivity per channel, as well as a coarser spectral resolution). We also
used different weighting depending on the line as a compromise between angular
resolution and sensitivity: all lines in Band 4 as well as HC15N (4-3) in Band
7 were imaged with natural weighting to maximize the S/N, and the remaining
lines were imaged using a robust value of 0.5.

Table 6: Gas Line Detections and Properties

Line | Band | Rest. Frequency | Line Flux | Beam size | Spectral resolution
---|---|---|---|---|---
|  | (GHz) | (Jy km/s) | (″) | (km/s)
12CO (3-2) | 7 | 345.796 | 10 $\pm$ 1 | 1.06$\times$0.86 | 0.11
CS (7-6) | 7 | 342.883 | 0.43 $\pm$ 0.05 | 1.05$\times$0.87 | 0.43
HC15N (4-3) | 7 | 344.200 | 0.04 $\pm$ 0.02 | 1.14$\times$0.97 | 0.85
13CO (3-2) | 7 | 330.588 | 1.8 $\pm$ 0.2 | 1.10$\times$0.91 | 0.11
12CO (2-1) | 6 | 230.538 | 4.6 $\pm$ 0.2 | 0.23$\times$0.20 | 0.16
13CO (2-1) | 6 | 220.399 | 0.79 $\pm$ 0.05 | 0.24$\times$0.21 | 0.66
C18O (2-1) | 6 | 219.560 | 0.21 $\pm$ 0.02 | 0.24$\times$0.21 | 0.67
HC3N (16-15) | 4 | 145.561 | 0.34 $\pm$ 0.02 | 0.50$\times$0.40 | 1.01
DCN (2-1) | 4 | 144.828 | 0.08 $\pm$ 0.01 | 0.50$\times$0.40 | 1.01
DCO+ (2-1) | 4 | 144.078 | 0.11 $\pm$ 0.01 | 0.50$\times$0.40 | 1.02
666Uncertainties include the absolute ALMA flux calibration uncertainties.

The observations show gas emission at velocities from $\sim$-5 to 13 km/s, and
we measured a systematic velocity of 3.98 $\pm$ 0.04 km/s (local standard of
rest) using a Keplerian disk model (see Sec. 3.2.2), similar to previous
estimates (e.g., Kastner et al., 2010). As shown in Figs. 5, 13, and 14, the
emission shape of most lines is that of a full disk., i.e. no clear gaps or
rings are found. Exceptions are DCO+ (2-1), which shows a clear ring-like
morphology with a gap radius of $\sim$20 au (a morphology commonly observed
for this line, e.g., Huang et al., 2017), and DCN (2-1) and HC15N (4-3), where
the low S/N prevents any reliable estimate of their morphology. The gaseous
disk extends up to 130 au (1.3″) in 12CO (2-1) based on the 3-5 $\sigma$
contours, in agreement with previous studies using unresolved APEX
observations of the 12CO (3-2) line (when corrected from the updated Gaia
distance, Kastner et al., 2010). We also provide the radii encircling 68 % and
90 % of the total 12CO (2-1) emission in Table 5. The gas radius is
$\sim$twice that of the dust disk (60 au, Sec. 3.1) yielding a ratio of the
gas and dust radii similar to those found for disks in Lupus (Ansdell et al.,
2018; Sanchis et al., 2021). A comparison of the de-projected radial profiles
of the continuum and 12CO (2-1) emission is shown in Fig. 3. We note that none
of the ALMA projects used in this work aimed at studying the chemistry of MP
Mus and yet these observations detected various molecular emission lines of
multiple species, evidencing the large potential of this system for future
astrochemical studies of protoplanetary disks.

Figure 5: ALMA Band 6 observations of CO isotopologues from the protoplanetary
disk around MP Mus. The top, middle, and bottom rows correspond to 12CO (2-1),
13CO (2-1), and C18O (2-1), respectively. The zero-th (left column) and first
(middle column) moments are shown, together with the 5$\sigma$ contour of the
1.3 mm continuum as a black line. The corresponding spectra are displayed in
the right column.

####  3.2.2 Dynamical stellar mass and disk kinematics

Emission from gas lines experiences Doppler shifts due to the disk rotation,
and can thus be used to estimate stellar mass that independently of
theoretical isochrones and stellar evolution models. For this purpose, we used
the eddy software (Teague, 2019) to model the first moment map of the 12CO
(2-1) emission using a Keplerian rotation profile. This line was chosen as it
offers the best compromise between S/N and the available spatial resolution.
Only the extended configuration of 2017.1.01419.S was used for this purpose
since the compact one is significantly noisier, but tests including this
second observations yielded noisier but completely compatible results (as
mentioned in Sec. 3.2.1, the observations from 2017.1.01167.S have a coarser
spectral resolution and significantly less sensitivity per channel, so they
were not included in this analysis). Given the high S/N of the observations,
we imaged the line with a robust=0.0 weighting (0.17″x0.15″beam) to improve
the angular resolution. The first moment map and its corresponding
uncertainties were then calculated using the bettermoments software (Teague &
Foreman-Mackey, 2018). In Sec. 3.1.3 we derived a disk inclination and PA of
32°and 10°based on the dust continuum observations which have a significantly
higher angular resolution, so we kept those values fixed during the fitting
777eddy defines the PA with respect to the red-shifted semi-major axis, so the
adopted value was 190°.. We performed various tests during this process,
including the use of first moment maps computed with the CASA immoments task
instead, down-sampling the map to the beam size to ensure that only spatially-
independent pixels are fit, masking the inner 0.3″of the disk, and modifying
the disk inclination by $\pm$1°to account for this uncertainty in the final
results. In all cases, we obtain very similar stellar mass values for MP Mus,
and adopt a final value of $M_{*}$=1.30 $\pm$ 0.08 $M_{\odot}$. This value is
slightly higher than the 1.2 $M_{\odot}$ value in the literature based on pre-
MS evolutionary tracks (e.g. Mamajek et al., 2002), but in complete agreement
when updating the luminosity with the new Gaia distance. This process also
yields the aforementioned systemic velocity of 3.98$\pm$0.04 m/s (local
standard of rest) for MP Mus. The 12CO (2-1) map used, model, and residuals
are shown in Fig .6.

The 12CO (2-1) data and moment maps show no obvious flaring, and the disk back
surface is also not visible. This suggests a very flat morphology of the
gaseous disk, in agreement with the results from the scattered light
observations (Avenhaus et al., 2018). To further explore this, we also tested
the elevated surface emission prescription from a tapered disk in eddy, which
parametrizes the emission height as a function of radius following
$z(r)=z_{0}(r/1\arcsec)^{\psi}\exp{[-(r/r_{tapper})^{q_{tapper}}]}$ (where
$z_{0}$ is the disk aspect ratio at 1 ″, $\psi$ is the disk flaring, and
$r_{tapper}$ and $q_{tapper}$ account for the disk tappering). This resulted
in a stellar mass similar to that of the geometrically thin disk case, largely
unconstrained values for $\psi$, $r_{tapper}$ and $q_{tapper}$, and a $z_{0}$
value of 0.1$\pm$0.1, showing that the disk is indeed significantly flat.

Figure 6: Keplerian fit to the 12CO (2-1) line emission of MP Mus using eddy.
The observed first moment (left), model (middle), and corresponding residuals
(right) are shown. The 0.17″x 0.15″beam is shown on the bottom left corner.
The area inside the black ellipse shown in the residuals was masked during the
fit. The tentative localized residuals mentioned in the text are also marked
with a red line. Only the extended configuration from 2017.1.01419.S was used
for this analysis.

There are two interesting features worth noticing from the fitting of
Keplerian rotation profiles. Firstly, the 12CO (2-1) first moment shows a
tentative twist in the inner disk (i.e., change in the PA in the inner
regions), and the residuals are structured and quite high in this area (up to
$\sim$1 km/s). These residuals could indicate the presence of a warped,
twisted, or misaligned inner disk (e.g. Marino et al., 2015; Casassus et al.,
2015; Min et al., 2017; Benisty et al., 2018; Mayama et al., 2018; Bohn et
al., 2022). Such structures can cast azimuthal shadows on the disk that can be
detected in scattered light data, and Wolff et al. (2016) tentatively detected
such a shadow in GPI observations of MP Mus. Later observations with SPHERE
did not recover this feature, and Avenhaus et al. (2018) suggested that an
imperfect correction of instrumental or interstellar polarization may create a
similar effect. Alternatively, variability in the inner disk could also change
the appearance of a shadow considering the 2 year separation between both
observations. The angle of linear polarization of the unresolved stellar
signal derived from the SPHERE data (see Sec. 3.3) also suggests that the
inner and outer disks are aligned. Secondly, we also find some localized
residuals in the first moment at radii 50-100 au between PA 110-170 °(Fig. 6).
A detailed analysis of this structure is beyond the scope of this work, but
its localized nature is suggestive of the velocity perturbations attributed to
unseen planets in other systems (e.g., Pinte et al., 2018; Pérez et al., 2018;
Teague et al., 2018). The emission in some other channels also displays
tentative deviations from the expected Keplerian profile that are typically
interpreted as such kinks (e.g., see the 12CO (2-1) NE emission in Fig. 7),
but the sensitivity and resolution of our observations do not allow us to draw
any conclusion. Further observations of the 12CO (2-1) and optically thinner
tracers at higher spatial and spectral resolution are needed to better
characterize the inner regions and possible deviations from Keplerian rotation
in MP Mus.

####  3.2.3 Disk gas mass and gas-to-dust ratio

The bulk of mass in protoplanetary disks is in gaseous form. However, in
contrast with the dust mass which can be derived (or at least approximated)
from mm fluxes, such estimates are much more complex for the gas. A number of
methods can be used for this purpose, but reliable gas mass measurement
usually require detailed modeling using chemical networks, radiative transfer,
a good knowledge of the disk structure, and resolved observations of multiple
emission lines (together with a large number of assumptions regarding chemical
abundances). Such a study is outside the scope of this work, but we can obtain
some order-of-magnitude estimates by comparing the observed 13CO (2-1) and
C18O (2-1) line luminosities (9.5$\times$104 Jy km/s pc2 and 2.5$\times$104 Jy
km/s pc2, respectively) with model grids.

Williams & Best (2014) produced a suite of disk models with various properties
and derived the resulting line fluxes for different CO lines. Their modeling
did not include the selective photodissociation for the 13CO and C18O
isotopologues and, instead, they included this effect by calculating half of
their models with the usual CO abundances and the other half with a
[C18O]/[13CO] ratio three times lower. Comparing the observed luminosities of
13CO (2-1) and C18O (2-1) in MP Mus with their grid of models (focusing on the
M∗=1 M⊙ and inclination=10°models since they are the closest to this system)
results in gas masses between 3$\times$10-4 M⊙ and 1$\times$10-3 M⊙ for the
cases without and with C18O depletion, respectively. Similarly, Miotello et
al. (2016) investigated the dependence between disk masses and the
luminosities of various CO lines for different disk properties using a grid of
models including chemical modeling. Comparing the derived line luminosities
with their grid of models (see Fig.7 in Miotello et al., 2016) places the gas
mass of MP Mus between 10-4 and 10-3 M⊙, depending on whether isotope-
selective processes are considered or not.

Although these models are not specifically tailored to MP Mus, these general
comparisons suggest that its total gas mass is
Mdisk=1$\times$10${}^{-4}-10^{-3}$ M⊙ (0.1-1 MJup). Taken at face value and
combined with the dust mass estimate in Sec. 3.1.2, this implies a global gas-
to-dust ratio of 1-10, lower than the standard value of 100 in the ISM. We
note that these values are derived using the global dust and gas masses but,
since the dust disk is considerably smaller than the gas one, this implies an
even lower gas-to-dust ratio in the area where both gas and large dust grains
are present. MP Mus then joins the increasing number of sources with a gas-to-
dust ratio below 100, which recent ALMA surveys have shown to be common in
protoplanetary disks: as an example, Miotello et al. (2017) found that 23 out
of 34 disks surveyed in the Lupus star-forming region showed gas-to-dust
ratios below 10\. Traditionally, these values are interpreted as a signpost of
disk evolution, where this ratio decreases over time as gas dissipates in the
disk while dust grains remain. Such a scenario is reasonable for an evolved
and flat disk such as MP Mus. However, another possible explanation is that
the CO abundance in disks is lower than expected and results in fainter line
emission, as suggested by mass measurements based on HD for TW Hya, GM Aur and
DM Tau (Bergin et al., 2013; McClure et al., 2016) and in Lupus using N2H+
(Anderson et al., 2022). Unfortunately, testing this hypothesis requires
reliable gas mass estimates that are independent of the CO abundance, which
are extremely challenging and not yet available for MP Mus. The actual reason
for the low CO-based gas masses in disks is still an open question for planet
formation theories.

###  3.3 Scattered light results

Avenhaus et al. (2018) presented the DPI data taken in $J$\- and $H$-band
within the DARTSS program. These data were reduced by minimizing the non-
azimuthal component of the radiation field, as an accurate polarization model
for the IRDIS instrument was not available at the time. In contrast, we
employed the instrument-specific polarization model used within the IRDAP
pipeline, which allowed us to subtract instrumental polarization and
polarization crosstalk from the image without any assumption about the data.
Besides the scattered light of the disk, the image then still contains a
background level of polarization and some unresolved polarization carried
within the stellar halo. IRDAP measures the background polarization in regions
where the signal intensity is at noise level and subtracts this background
from the entire image. To estimate the stellar polarization, we measured $Q$
and $U$ from the stellar halo in image areas seemingly free of disk-scattered
light (in an annulus mask of 1.72″- 2.08″distant to the star). Then, we can
calculate the degree of polarization ($DoLP$) within the stellar halo and its
angle of linear polarization ($AoLP$):

$\displaystyle{DoLP}$ $\displaystyle=$ $\displaystyle PI/I\,,$ (4)
$\displaystyle{AoLP}$ $\displaystyle=$
$\displaystyle\frac{1}{2}{\arctan\left(U/Q\right)}\,.$ (5)

We found that the light carried in the stellar halo is polarized with a $DoLP$
of $0.46\pm 0.08\%$ and with an $AoLP$ of $98\pm 8\,$deg East of North.
Because direct stellar light is expected to be entirely unpolarized, a
measurement of polarization from the isolated stellar halo indicates that
there is an unresolved polarized signal within the star-centered point spread
function (PSF) of the observation. This is typically attributed to parts of
the observed light scattering off interstellar dust within the line-of-sight,
or due to an unresolved disk component close to the star (e.g. Keppler et al.,
2018; van Holstein et al., 2020). The measured $AoLP$ of the unresolved
polarization is perpendicular to the PA of the outer disk, consistent with a
co-planar inner disk component. This is further consistent with the continuous
disk around MP Mus, extending close to the central star as observed with ALMA
for gas and dust. We subtracted the respective measured unresolved
polarization from the $Q$\- and $U$-components before calculating $Q_{\phi}$.

Figure 7: Comparison of ALMA and SPHERE observations of MP Mus. _Top left_ :
$Q_{\phi}$-image in $H$-band ($\lambda_{\rm obs}=1.6\,\mu$m) taken with
SPHERE/IRDIS. The colormap is shown in logarithmic stretch. The central blue
circle masks the area covered by the coronagraph of the observation. _Top
right_ : Comparison of the 1.3 mm continuum emission (orange contour), the
SPHERE $Q_{\phi}$ $H$-band data (purple), and one of the 12CO (2-1) channels
(blue). The 1.3 mm contour corresponds to the 5 RMS level, while only data
above the corresponding 3 RMS levels are shown for the ${12}$CO (2-1) and
scattered light observations. _Bottom_ : Comparison of the radial profiles of
the SPHERE $Q_{\phi}\times r^{2}$ in $H$-band (purple line), the 1.3 mm
continuum (orange line), and the 12CO (2-1) emission (blue line). The SPHERE
coronagraph is also shown.

Figure 7 shows the resulting $Q_{\phi}$-image of MP Mus in $H$-band in
logarithmic stretch and the comparison with the continuum and 12CO (2-1) from
ALMA. We used the flux frames of the IRDIS observation to convert the observed
polarized flux from counts to Jy/arcsec2, assuming an $H$-band magnitude of
$7.64\pm 0.02$ (2MASS, Cutri et al., 2003). The final product is very similar
to the presented image in Avenhaus et al. (2018). Figure 7 also compares the
radial profile of $Q_{\phi}\times r^{2}$ in $H$-band with those of the ALMA
1.3 mm and the 12CO (2-1) zero-th moment. The SPHERE image show a bright inner
region (the inner $\sim$20 au are attenuated due to the SPHERE coronagraph)
and a decrease in intensity from 20 to 30 au. The emission then increases
slowly up to 60 au and then rises faster in an outer ring centered at $\sim$
80 au, dropping below the noise level at 130 au, similar to the extent of the
12CO (2-1). The slight asymmetry of this outer ring suggests that the near
side of the disk is to the east, the far side is west. This is consistent with
promoted forward-scattering (e.g. Stolker et al., 2016), as the near side of
the disk appears brighter than the far side (by a factor of $\sim 1.5$ on
average).

Avenhaus et al. (2018) mentioned an azimuthally-localized intensity decrease
in the western half of the disk (P.A.$\sim 270^{\circ}$). This feature is also
present in our image. Its location at the far side of the disk, where signal-
to-noise is lowest, makes it a very tentative detection. We further find that
the disk’s brightest part is to the northeast of the star.

##  4 Discussion

###  4.1 Comparison with stellar evolutionary models

The stellar mass $M_{*,\rm dyn}=1.30\pm 0.08\,M_{\odot}$ derived from the disk
rotation (Sec. 3.2.2) is independent of theoretical isochrones and
evolutionary models, and offers an interesting comparison with such models.

MP Mus is classified as a K1V star (Mamajek et al., 2002), corresponding to
$T_{\rm eff}$ values between 4900 and 5100 K in the spectral type
(SpT)-$T_{\rm eff}$ relations of Kenyon & Hartmann (1995) and Pecaut & Mamajek
(2013). This temperature is also in agreement with the 5110 K value derived in
the Gaia DR3 (Gaia Collaboration et al., 2022). Its interstellar extinction
$A_{V}$ has been measured in the range of 0.2-0.7 mag (Mamajek et al., 2002;
Cortes et al., 2009). More recently, Asensio-Torres et al. (2021) derived
values of 4600 K and 0.8 mag for this system from fitting the optical/near-IR
SED, although this $T_{\rm eff}$ value appears a bit too low for a K1 star
based on the formerly mentioned SpT-$T_{\rm eff}$ tables. We perform a similar
process and fit the Tycho and 2MASS photometry using the BT-Settl photospheres
(Allard et al., 2011, 2012) with $T_{\rm eff}$ values between 4500 to 5500 in
100 K steps, $A_{V}$ values from 0 to 1 mag in 0.1 mag steps, and stellar
luminosity values between 0.8-1.6 $L_{\odot}$ in steps of 0.1 $L_{\odot}$.
Adopting a distance of d=98 pc (Gaia Collaboration et al., 2022) we derive
values of $T_{\rm eff}$=4900 K, $A_{V}$=0.6 mag, and $L_{*}$=1.3 $L_{\odot}$.
Such a $T_{\rm eff}$ value is higher than the effective temperature in
Asensio-Torres et al. (2021) and more comparable to those adopted in earlier
studies. Alternatively, we also normalize 4900 and 5100 K photospheres to the
observed 2MASS photometry using $A_{V}$ values of 0.2 and 0.7 mag, which
yields stellar luminosities between 1.1-1.3 $L_{\odot}$ (compatible with
previous values when corrected for the updated distance from Gaia). We thus
adopt $T_{\rm eff}=5000\pm 100$ K and $L_{*}=1.2\pm 0.1$ $L_{\odot}$ for MP
Mus. Figure 8 shows its location in the corresponding HR diagram using the
MESA Isochrones and Stellar Tracks (MIST, Dotter, 2016; Choi et al., 2016).
This results in a stellar mass and age of $\sim$1.3 $M_{\odot}$ and 7-10 Myr
for the system. MP Mus is a confirmed member of the old $\epsilon$ Cha
association based on its kinematic properties (e.g., Murphy et al., 2013;
Dickson-Vandervelde et al., 2021). Murphy et al. (2013) assigned a 3-5 Myr age
to that region (younger than our estimate), but the re-analysis of $\epsilon$
Cha by Dickson-Vandervelde et al. (2021) including Gaia data yielded an age of
$5^{+3}_{-2}$ Myr that is compatible with our results. A lower $T_{\rm eff}$
such as the one proposed in Asensio-Torres et al. (2021) would result in a
younger (but still compatible) age for MP Mus, although the dynamical stellar
mass of $\sim$1.3 $M_{\odot}$ derived from the ALMA observations appears more
difficult to reconcile with this lower $T_{\rm eff}$ value.

The mass derived from the MIST tracks also appears fully compatible with the
dynamical mass estimate. Given the good agreement between various recent pre-
main sequence evolutionary models (Simon & Toraskar, 2017), this result is not
restricted to these tracks. Studies comparing dynamical stellar masses with
predictions from evolutionary models without magnetic fields typically find
the latter to underestimate masses by a significant amount, especially for
low-mass stars (by 30 %-80 % for stellar masses $<$1.4 $M_{\odot}$, e.g.,
Simon et al., 2019; Pegues et al., 2021). In contrast, evolutionary tracks
including stellar magnetic fields (e.g., Feiden, 2016) yield more compatible
results with dynamical mass estimates. This discrepancy is usually attributed
to starspots (e.g., Pegues et al., 2021; Flores et al., 2022a), which become
more relevant for late-type stars. Given the relatively high mass of MP Mus
compared to the samples in the aforementioned works, the agreement between the
dynamical mass estimate and the evolutionary tracks without magnetic fields
used in our study is likely an indication that the effect of starspots in this
system is moderate/negligible. We also notice that these works focused on
younger sources (mostly in Taurus and Ophiuchus, with estimated ages of 1-2
Myr). Similar comparisons for larger samples of stars covering a range of
masses and ages could help to further inform theoretical models of early
stellar evolution.

Figure 8: Location of MP Mus (black dot) in the HR diagram. MIST mass tracks
(1.2, 1.3, and 1.4 $M_{\odot}$) and isochrones (5, 7, 10, and 13 Myr) are also
shown (Dotter, 2016; Choi et al., 2016).

###  4.2 Grain growth and optically thick emission in MP Mus

Assuming optically thin emission and a sufficiently warm dust temperature for
the emission to be in the Rayleigh-Jeans regime, $\alpha_{\rm mm}$ relates to
the power law index of the dust opacity, $\kappa_{\nu}\propto\nu^{\beta}$, via
$\alpha_{\rm mm}=2+\beta$. $\beta$ is sensitive to the maximum grain size
($a_{\rm max}$) of the dust size distribution (e.g. Natta & Testi, 2004;
Draine, 2006; Testi et al., 2014): dust distributions with maximum grain sizes
around or larger than 1 mm have opacity power-law indices $\beta\lesssim 1$,
while smaller grains have higher $\beta$ values (ISM-like grains show
$\beta\sim 1.7$). The spectral indices measured in Sec. 3.1.4 then translate
to average $\beta$ values of $\sim$0.1-0.4 and suggest the presence of mm-
sized grains in MP Mus. Our results are very similar to those of Cortes et al.
(2009), who found the mm spectral index of MP Mus between 3 mm and 12 cm to be
$\alpha=2.4\pm 0.1$, and first indicated the presence of large grains in the
disk. Similar $\alpha_{\rm mm}$ values are found in disks in younger star-
forming regions such as Taurus, Ophiuchus, Lupus, and Chamaeleon I (Ricci et
al., 2010b, a; Ribas et al., 2017; Tazzari et al., 2021), but also in other
evolved disks such as TW Hya, HD 98800B or TWA 3 (Macías et al., 2021; Ribas
et al., 2018; Czekala et al., 2021). This implies that, despite grain drift
and evolution, protoplanetary disks can retain a population of large grains
during most of their lifetimes.

The spectral index map in Sec. 4 provides additional spatial information about
the disk, and two of its features are worth discussing. First, $\alpha_{\rm
1.3-2.2\,mm}$ increases with radius, similar to many other sources observed at
multiple (sub)mm wavelengths with enough angular resolution (e.g., Pérez et
al., 2015; Carrasco-González et al., 2016; Tazzari et al., 2016; Dent et al.,
2019; Macías et al., 2019, 2021). This is attributed to a combination of
higher optical depths in the inner regions and to the inward drift of large
grains due to gas drag (Weidenschilling, 1977). Thus, this can be interpreted
as additional evidence of grain growth and radial drift in the disk. It is
also worth noticing that the disk radii at 1.3 mm and 2.2 mm are similar
within the uncertainties. Although this interpretation is limited by the
moderate angular resolution of the 2.2 mm observations ($\sim$20 au), if both
radii are indeed similar this could suggest the presence of some mechanism
preventing strong dust radial drift in the disk, since it would otherwise
appear more compact at 2.2 mm than at 1.3 mm.

Maybe more interesting is the fact that MP Mus displays values $\alpha_{\rm
1.3-2.2\,mm}<2$ in its inner region ($r<$30 au). Such values are below the
spectral index of black body radiation, and they have been traditionally
interpreted as indicators of additional emission mechanisms such as free-free
radiation from ionized photoevaporative winds or stellar chromospheric
activity (e.g., MacGregor et al., 2015; Macías et al., 2016). However, these
processes usually become significant at wavelengths longer than those
considered here. Cortes et al. (2009) also observed MP Mus at cm wavelengths
and obtained only upper limits at 3 cm and 6 cm, suggesting a negligible
contribution from a possible stellar wind. Alternatively, $\alpha_{\rm mm}<2$
values can also arise from optically thick emission from dust grains with high
albedo (Miyake & Nakagawa, 1993; Liu, 2019; Zhu et al., 2019). Recently, ALMA
has shown that spectral indices below 2 in the inner regions of disks are not
unusual (e.g. Huang et al., 2018; Dent et al., 2019), and an integrated
$\alpha_{\rm mm}$ value below 2 was also found in the circumbinary disk of the
TWA 3 triple system (Czekala et al., 2021). The spectral index map of MP Mus
is one more example of these cases, adding observational support to the idea
that at least part of the emission from protoplanetary disks is optically
thick even at $\sim$2 mm, and that dust scattering needs to be considered at
these wavelengths. In turn, this is yet another indication that dust masses
derived from mm surveys may be underestimated, and explains why SED modeling
of disks accounting for the disk structure and dust scattering results in
systematically higher dust masses (Ballering & Eisner, 2019; Ribas et al.,
2020; Rilinger et al., 2023). The fact that these low $\alpha_{\rm mm}$ values
are also found on evolved disks such as TW Hya or MP Mus shows that this
effect could be significant throughout most of the disk lifetime.

###  4.3 Lack of mm substructures and comparison with TW Hya

The high angular resolution view of MP Mus presents a stark contrast with
respect to most protoplanetary disks imaged at similar spatial resolutions to
date: while the majority of disks display some substructures in high angular
resolution mm observations (i.e. gaps, rings, spiral arms, asymmetries), MP
Mus shows a smooth disk down to a 4 au resolution, with the possible exception
of a barely resolved outer ring at $\sim$50 au. There are also no signs of an
inner cavity, in agreement with the $AoLP$ derived from the SPHERE
observations (Sec. 3.3) as well as with previous modeling of its SED which
suggested that the disk extends down to the dust sublimation radius (Cortes et
al., 2009). The featureless appearance is even more puzzling when we consider
its age (7-10 Myr), which is quite older than typical disk lifetimes. Without
substructures acting as dust traps (e.g. Pinilla et al., 2012; Zhu et al.,
2014), the gas drag would quickly deplete the disk of large grains on
timescales much shorter than disk lifetimes (Weidenschilling, 1977), so one of
the following scenarios must be true for MP Mus: either its dust population
comprises small ($<100$ $\mu$m) dust grains only that are weakly affected by
radial drift, or there are undetected/unresolved substructures in the disk
that are stopping the inward migration of large grains.

In the first scenario, a population of smaller grains would have both a lower
opacity at mm wavelengths and a steeper opacity power law index (e.g. Natta &
Testi, 2004; Testi et al., 2014; Tazzari et al., 2016). A significantly higher
dust mass would be needed to both account for the observed fluxes and to
maintain a spectral index of 2-2.5 in most of the disk, which in this case
would be mostly due to optically thick emission. Although this explanation
cannot be ruled out with the current data, it seems unlikely that the actual
dust mass would be much higher than the measured value, as it would imply that
MP Mus was originally very massive (possibly above the disk instability
limit). Moreover, the disk size at mm wavelengths and those of the gas and
scattered light observations would be difficult to reconcile with a population
of small grains only. Additional high-resolution observations at other mm
wavelengths covering a broader wavelength range are needed to perform a
detailed modeling of the dust population in the disk (e.g., Macías et al.,
2021) and to further investigate this possibility.

The second explanation for the survival of large grains in an evolved disk
with apparently no substructures is that this conclusion is limited by the
optical depth and/or angular resolution of the observations, i.e., there are
structures in the disk but they remain undetected or unresolved with the
current observations. Structures narrower than 5 au have been found in some
nearby disks such as TW Hya, HD 169142 and V4046 Sgr (Andrews et al., 2016;
Pérez et al., 2019; Martinez-Brunner et al., 2022), although the last two also
displayed much broader gaps in the dust distribution (and V4046 Sgr is a
circumbinary disk). TW Hya probably provides the best comparison given its
similarities with MP Mus: high angular resolution observations revealed a
system of concentric rings and gaps with 1-5 au widths and varying amplitudes
(Andrews et al., 2016). These authors argued that such structures may be
common in disks, playing a fundamental role in their evolution and in the
planet formation process. Figure 9 compares the radial profiles of MP Mus and
TW Hya at 1.3 mm from Macías et al. (2021) after degrading the angular
resolution of the latter to match the $\sim$5 au of the MP Mus data. This
comparison demonstrates that both profiles are significantly different, and it
is still possible to identify several features in TW Hya at this resolution
such as a flat profile in the inner region (caused by the central cavity) and
two gaps at 25 and 40 au. On the other hand, a number of the known
substructures in TW Hya are no longer visible in the profile, as could be the
case for MP Mus. We note that gas rings with radial widths much smaller than
their vertical extent are unstable (Ono et al., 2016; Dullemond et al., 2018),
which limits how packed substructures can be. Given the flat appearance of MP
Mus, realistic values for $h/r$ are likely in the range of 0.03-0.07, which
could allow for the presence of rings in the outer regions that are
narrow/close enough to remain unresolved. This consideration is also relevant
for the comparison with TW Hya: the stellar mass of MP Mus is $\sim$twice that
of TW Hya (1.3 $M_{\odot}$ for MP Mus, and $\sim$0.6 $M_{\odot}$ in the case
of TW Hya Sokal et al., 2018), so its scale height is expected to be smaller
(by a factor of $\sim\sqrt{2}$ when ignoring the higher stellar luminosity of
MP Mus). As a result, MP Mus may host narrower rings than TW Hya. In addition,
Xu & Bai (2022a, b) showed that within one broad gas pressure bump, two radial
dust rings separated by a distance comparable or less than $h$ may form,
assisted by the dust back reaction to gas. This further promotes the
possibility of having packed dust rings currently unresolved. Finally, high
optical depths also limit our ability to identify gaps/rings in the system. As
suggested by the map of spectral index, the inner 30 au of the disk appear to
be optically thick, displaying $\alpha<2$ (Fig. 4). It is thus possible that
the observed 1.3 mm continuum emission in these regions is coming from an
elevated surface, preventing the detection of substructures in the midplane.

Figure 9: Comparison of the radial profiles of MP Mus (red) and TW Hya (black)
at 1.3 mm. The TW Hya data were taken from Macías et al. (2021), and convolved
with a 0.08″Gaussian to match the resolution and distance of the MP Mus
observations. The inner cavity and two of the known gaps gaps of TW Hya (at 25
and 45 au) are still visible in the case of TW Hya, in contrast with the
smooth profile of MP Mus.

Overall, despite the high angular resolution and structureless appearance of
MP Mus, the current data cannot discard small ($<$4 au) rings especially in
the inner regions, or even larger ones if the disk is sufficiently optically
thick. If undetected substructures are the explanation for the long-lived disk
around MP Mus, then this system lends further support to the idea that small
rings may be a common feature in disks. As proposed by Tripathi et al. (2017,
2018); Andrews et al. (2018b), if some of these rings are (partially)
optically thick, they could help to explain the observed relation between the
radii and mm luminosity of disks. Evolutionary disk models by Toci et al.
(2021) also showed that the gas-to-dust radii ratios ($R_{\rm CO}$/$R_{\rm
dust}$) become $>$5 in very short timescales ($<$1 Myr) in the absence of
mechanisms preventing radial drift, in clear conflict with the $R_{\rm
CO}$/$R_{\rm dust}\sim 2$ value found in MP Mus at 7-10 Myr. Given its
proximity, ALMA observations of MP Mus at even better angular resolutions and
longer wavelengths would aid in explaining the long lifetime of the system and
exploring the frequency and properties of small structures in disks.

###  4.4 Upper limits to the presence of planets

Planets with enough mass are expected to open gaps in the gas and dust
distribution (e.g., Crida et al., 2006; Zhu et al., 2011; Dong & Fung, 2017;
Dong et al., 2018), although the properties of these gaps are highly dependent
on the conditions in the disk. Deriving planetary masses from gap widths and
contrasts requires detailed hydrodynamic models including many (uncertain)
free parameters and is a quite degenerate process, but comparisons with
results from different models provide some constraints on the maximum mass of
planets in the MP Mus system based on the absence of visible substructures
larger than $>$4 au in dust distribution. Here, we use the scaling relation
between the planet Hill sphere ($R_{\rm H}$) and width of the gap
($\triangle$, defined as the separation between the minimum brightness in a
gap and the maximum brightness of the corresponding external ring) following
Lodato et al. (2019). For disks with viscosity values $\alpha\lesssim 0.01$,
these two quantities are related following:

$\triangle=kR_{\rm H}=k\biggl{(}\frac{M_{\rm p}}{3M_{*}}\biggr{)}^{1/3}r,$ (6)

where $M_{\rm p}$ is the mass of the planet, $M_{\rm*}$ is the mass of the
star, $r$ is the orbital radius of the planet, and $k$ is a proportionality
constant that depends on disk properties and ranges between $\sim$4-8 for gaps
observed in the mm (see Lodato et al., 2019, and references therein, where
they adopt a value of $k$=5.5). Assuming that we would have resolved widths
$\triangle\geq 4$ au and the derived 1.30 $M_{\odot}$ mass for MP Mus, Fig. 10
shows the corresponding upper limits for $M_{\rm p}$ at different radii for
$k$=4, 5.5, and 8. Based on this simple relation and further assuming that
each gap is carved by a single planet, the lack of resolved gaps in these
observations would imply that there are no planets more massive than 0.5-4
$M_{\rm Jup}$ at orbital radii $r>10$ au (depending on the adopted value of
$k$), and these constraints decrease to $0.05-0.5$ $M_{\rm Jup}$ and 2
$M_{\oplus}-$0.06 $M_{\rm Jup}$ for $r>20$ au and $r>40$ au, respectively. We
emphasize that this analysis assumes that any sufficiently large gap carved by
planets would be visible in the 1.3 mm observations, but the high optical
depth within the inner 30 au suggested by their $\alpha<2$ spectral index
could hide such gaps (see Sec. 4.3). Therefore, the derived limits are likely
underestimated, especially in the inner regions of the disk. Also, these
limits only apply for $r\leq 60$ au since that is the radial extent of the mm
dust continuum emission.

The 1.3 mm radial profile obtained with _frank_ shows a shallow plateau
between 30-40 au, which could be interpreted as a low-contrast gap. Although
it is not clear that this structure is an actual gap in the dust density
distribution of the disk, here we also use Eq. 6 to calculate the mass of a
hypothetical planet that could carve such a gap at that location. Assuming
that the planet is at the center of the plateau ($\sim$35 au) and given the
location of the outer bump ($\sim$45 au), the gap width would be
$\triangle$=10 au, and the corresponding planet mass is 0.2 $M_{\rm Jup}$, 0.6
$M_{\rm Jup}$, and 1.5 $M_{\rm Jup}$ for a value of $k$ of 8, 5.5, and 4,
respectively.

Figure 10: Upper limits to the presence of planets in the disk around MP Mus
as a function of radius. These upper limits are derived using equation 6
(Lodato et al., 2019) and the fact that no gaps with width $\triangle\geq 5$
au are detected in the disk. Three different values are used for the
proportionality constant ($k$) linking the planet Hill radius and the
corresponding gap width.

On the other hand, the drop in scattered light signal between 30-80 au seen in
the radial profile of the scattered light (see Sec. 4.5) may indicate the
presence of one or more massive planets outside the continuum emission, and
studies based on scattered light data have placed different upper limits to
their masses. Wolff et al. (2016) observed MP Mus with GPI and could reject
the presence of a 3 $M_{\rm Jup}$ planet outside of 40 au with a 90 %
confidence for a 7 Myr disk. Similarly, SPHERE observations of MP Mus allowed
Asensio-Torres et al. (2021) to place upper limits on the masses of possible
companions888The planetary mass upper limits in Asensio-Torres et al. (2021)
were derived assuming a 3 Myr age for MP Mus. If the system is older as
suggested by our analysis and other studies, then the upper limits would be
higher., now reaching a 5-$\sigma$ limit of $\sim$2.5-3 $M_{\rm Jup}$ at
$r\geq$50 au. Asensio-Torres et al. (2021) also proposed that a planet located
at 55 au may be the origin of this decrease in scattered light intensity.
However, the lack of a wide gap at this location in the ALMA continuum
observations suggests that the lower intensity of scattered light between
30-80 au is not due to an actual gap in the disk surface density (see Sec.
4.5). Recently, the GAPlanetS survey (Follette et al., 2022) targeted several
sources in Hα searching for accreting protoplanets in fourteen disks, but did
not identify any potential candidate in the disk around MP Mus. If the lack of
any clear rings/gaps in the 1.3 mm continuum is real and not due to the high
optical depth of the disk in the inner regions, then this work and previous
studies analyzing scattered light observations appear to rule out the presence
of planets more massive than $3\,M_{\rm Jup}$ at radii $r>10-15$ au. If that
is the case, the exoplanet population of a hypothetical planetary system
around MP Mus may not be very different from that of the Solar System, making
it an ideal laboratory for further planet formation studies given its
proximity and age.

Finally, the mm observations in this work also place some constraints on the
presence of circumplanetary disks outside of the dust disk ($r>$60 au). The
RMS of the 1.3 mm continuum image is 19 $\mu$Jy/beam, and thus we can reject
the presence of point-like sources with fluxes $\geq 90$ $\mu$Jy in the dust-
free region at a 5 $\sigma$ confidence. There are two $\sim 4$ $\sigma$ peaks
at angular separations 1.4” NE and 1.6” SE from the source center ($\sim$140
and 160 au projected orbital radii) which lie outside the scattered light
outer ring, but these are likely associated with noise. Converting these
limits to disk masses involves many unknown quantities (see Isella et al.,
2014, 2019), but we can compare the sensitivity limit of these data to the
flux of the circumplanetary disk recently detected around PDS 70c (Isella et
al., 2019; Benisty et al., 2021): considering its 86 $\mu$Jy flux at 855
$\mu$m, an spectral index of 2.3, and the closer distance of MP Mus, a similar
circumplanetary disk would have a flux of 42 $\mu$Jy at 1.3 mm and would
therefore remain undetected with our observations.

###  4.5 The panchromatic view of MP Mus

The ALMA observations of MP Mus reveal a smooth disk in the mm continuum with
a radius of 60 au, and a gaseous disk that extends further out to 130 au. In
contrast, the scattered light images probing small dust grains show a
different morphology, with a bright inner region and a significant drop in
flux between 30-80 au (Cortes et al., 2009; Schneider et al., 2014; Wolff et
al., 2016; Avenhaus et al., 2018). In particular, SPHERE observations of MP
Mus show that: (1) the strongest signal in scattered light arises from the
inner 25 au, (2) there is a discontinuity in the brightness at 60 au, (3)
there is an outer ring at 80 au, and (4) the disk extends up to 125 au. Many
of these coincide with features seen in the ALMA images (see Fig. 7 for a
comparison of the mm continuum, 12CO, and scattered light observations and
radial profiles). Regarding the inner regions, the 1.3 mm continuum emission
also arises mostly from the inner 25-30 au, the slopes of the radial profiles
of both continuum and 12CO emission changes at this radius (Fig. 3), and the
emission has a spectral index $\alpha_{\rm mm}<2$ within this radius (Fig. 4).
The discontinuity observed at 60 au in scattered light coincides with the
outer radius of the mm continuum emission, and the extent of the gaseous
component of the disk is in great agreement with the one inferred from the
scattered light data. Overall, this matches predictions from the radial drift
of dust grains: while small grains remain well coupled to the gas and are thus
co-located, larger grains migrate toward pressure maxima and accumulate in the
inner regions of the disk or localized pressure bumps (e.g., Weidenschilling,
1977; Pinilla et al., 2012).

The gap seen in scattered light between 30-80 au is quite prominent (it is the
largest of all the sources in Avenhaus et al., 2018), and two scenarios have
been proposed to explain it, namely that it is a real decrease in the disk
density carved by one or multiple planets, and that it is shadow cast by the
disk itself (Wolff et al., 2016). We can now revisit these explanations in the
light of the new ALMA observations.

Planets are one of the leading explanations for the plethora of rings and gaps
found in protoplanetary disks, and the properties of many of these structures
appear to support this explanation (e.g., Huang et al., 2018; Zhang et al.,
2018; Pérez et al., 2019). In these cases, the gravitational influence from
the planet decreases the local gas density and induces a pressure bump outside
of its orbit, which acts as a dust trap for large (mm/cm-sized) grains. For MP
Mus, however, the lack of any mm emission in the outer ring visible in
scattered light implies that the ring is mostly devoid of large dust grains,
suggesting that the gap in scattered light is not a gap in the surface density
opened by one or several planets. Although the available observations do not
reject planet masses below sub-Jovian values, the lack of companions discussed
in Sec. 4.3 also supports the interpretation that the drop in scattered light
at 30-80 au is due to a different process.

A shadow cast by the disk inner rim (e.g. Dullemond & Dominik, 2004) is also a
plausible explanation for the apparent gap in the scattered light
observations, especially considering that MP Mus shows a rather flat
structure. The possibility of a shadowed disk in the system was proposed by
Cortes et al. (2009) based on its low near/mid-IR excess (4-20 $\mu$m) with
respect to the median disk SED of Taurus, even before high-angular resolution
observations in scattered light were available. Dong (2015) found that a
puffed-up inner rim with a sharp edge in the vertical direction could produce
a pattern similar to that seen in MP Mus (i.e., a drop in scattered light
emission at intermediate radii), although rims with more physically-motivated
structures did not produce such results. It is interesting to note that a
steep increase in the SPHERE radial profile occurs at 60 au, matching the
outer radius of the mm emission. Based on this and the overall SPHERE radial
profile, we propose that MP Mus probably has a puffed-up inner disk that
shadows radii beyond 30 au. However, the lack of large grains in the disk
midplane at radii r$>$60 au could result in a less efficient cooling of the
disk (and hence a warmer midplane), increasing in the disk scale height and
allowing the disk surface to grow out of the shadow at longer radii. Direct
observational evidence for such an effect (i.e., higher temperatures in the
outer regions devoid of large grains) exist for the edge-on disk Oph 163131
based on tomographic reconstruction of its temperature structure (Flores et
al., 2022b; Villenave et al., 2022).

We explore this idea by calculating a simple disk model for MP Mus using the
MCFOST code (Pinte et al., 2006, 2009). We adopt the stellar and disk
parameters derived in this study and include two different dust populations:
one for small grains (0.01 $\mu$m - 10 $\mu$m) extending from 0.1 to 130 au,
and a more compact disk of larger grains (10 $\mu$m - 1 mm) from 0.1 to 60 au.
At 60 au, the inter-phase between the large and small grain disks results in
an increase of the midplane temperature from 10 to 15 K. For a vertically
isothermal disk with a scale height $H=c_{s}/\Omega$, this change in
temperature would imply a local increase of $\sim$20 % in the scale height,
which could expose the upper disk layers to stellar radiation again. We
emphasize that none of these numbers are to be considered as accurate
estimates for MP Mus given the oversimplified model used, but they show that
the change in the disk opacity at the end of the mm continuum radius could
lead to a local increase of the disk temperature at that location. We do not
find signs of a colder disk at $r=60-80$ au in the 12CO (2-1) radial profile,
which does not show any significant feature at these radii down to 3 K (the
brightness temperature uncertainty at 70 au). However, the 12CO (2-1) emission
arises from above the midplane and may not reflect the midplane temperature.
Unfortunately, the same analysis cannot be performed for optically thinner
isotopologues such as 13CO (2-1) or C18O (2-1), since their emission only
extends to $\lesssim$60 au. Detailed physico-chemical modeling of the gas and
dust components of MP Mus is needed to calculate a consistent temperature
structure for the disk and to determine the origin of the gap seen in the
scattered light observations.

##  5 Summary

We present new ALMA observations of the nearby, evolved protoplanetary disk
around MP Mus, including 0.89 mm, 1.3 mm, and 2.2 mm continuum emission, as
well as multiple gas emission lines. These data are the first spatially
resolved observations of the disk at these wavelengths and provide a wealth of
new information of this system. Our key results and findings are:

  * •

The continuum emission shows a disk with no detected inner cavity and a radius
of 60$\pm$5 au. Despite the high angular resolution of these data, the dust
disk appears smooth down to 4 au scales, making MP Mus an interesting
exception when compared with the plethora of substructures found in most disks
observed at comparable resolutions, and an great counterpart to TW Hya in
particular.

  * •

Based on the mm fluxes and using standard assumptions for the dust opacity and
disk temperature, we derive a dust disk mass of $M_{\rm
dust}=0.14_{-0.06}^{+0.11}$ $M_{\rm Jup}$.

  * •

The continuum spectral index between 1.3 and 2.2 mm has a value $<2$ for radii
$r<30$ au, indicative of optically thick emission from dust grains with a high
albedo in this region.

  * •

These observations yield detections of 12CO (3-2), CS (7-6), HC15N (4-3), and
13CO (3-2) in Band 7, 12CO (2-1), 13CO (2-1), and C18O (2-1) in Band 6, as
well as HC3N (16-15), DCN (2-1), and DCO+ (2-1) in Band 7.

  * •

The 12CO (2-1) observations reveal a gaseous disk extending up to 130$\pm$15
au, a factor of $\sim$2 larger than the dust disk. Similar to the dust, no
clear gaps are found.

  * •

By fitting a Keplerian profile to the first moment of the 12CO (2-1), we
derive a dynamical mass for MP Mus of $1.30\pm 0.08M_{\odot}$. This value is
consistent with predictions from theoretical stellar evolutionary models,
which date the system at an age of 7-10 Myr.

  * •

By comparing the 13CO (2-1) and C18O (2-1) fluxes with grids of disk models,
we estimate the gas mass in the system to be $10^{-4}-10^{-3}$ $M_{\odot}$,
resulting in a global gas to dust ratio of 1-10.

  * •

A comparison of these data with previous scattered light observations shows
that small grains and the gas are co-located while larger grains concentrate
in the inner regions, in line with expectations from dust radial drift.

  * •

From the scattered light observations, we derive an angle of linear
polarization that speaks for disk material inside the stellar PSF, co-planar
with the outer disk. This is in agreement with the expectations from a disk
extending inward to regions close to the star (within 0.05″).

  * •

The survival of large grains in a gas-rich disk is surprising for such an
evolved system, especially considering the lack of substructures in the
continuum emission. This suggests that structures preventing the radial drift
of large grains may be present in the disk but not visible due to a high
optical of the emission at 1.3 mm, or they may be smaller than the resolution
limit of these observations (4 au).

  * •

Based on scaling relations between the planet mass and the gap widths and
assuming that substructures are not hidden by high optical depths, we use the
lack of any clearly resolved gap to place upper limits to the mass of possible
planets in the disk. We find that no planets more massive than $\sim$0.5-4
$M_{\rm Jup}$, $0.05-0.5$ $M_{\rm Jup}$, and 2 $M_{\oplus}-$0.06 $M_{\rm Jup}$
exist at radii $r>$10, 20, and 40 au, respectively. Using a similar approach,
if the tentative plateau seen at 30 - 40 au is caused by a planet, it would
have a mass $\sim 0.2-1.5\,M_{\rm Jup}$.

  * •

The scattered light observations also revealed a drop in intensity between 30
and 80 au, and an outer ring from 80 to 130 au. The lack of mm emission from
this outer ring suggests this drop in scattered light emission is probably not
an actual gap in the disk surface density due to planets, since such a gap
would trap large grains in the ring. Instead, the data appear more consistent
with this feature being a shadow, cast between 30-80 au by a puffed-up inner
rim. The rapid increase of scattered light signal at radii $>$ 60 au may be
explained by the lack of large dust grains at these locations, which could
result in a warmer disk. This would increase the disk scale height and expose
the disk surface to stellar radiation at longer radii, explaining the outer
ring visible in scattered light.

Given its nearby location, age, and properties, MP Mus is an optimal target to
study many aspects of protoplanetary disks, a great laboratory to probe the
chemistry of planet formation, an interesting counterpart to the TW Hya system
and, possibly, the closest analog to the young Solar System. Because of all
these factors, MP Mus may be one of the most promising individual sources to
advance our understanding of planet formation.

###### Acknowledgements.

We thank the anonymous referee for their constructive comments, which helped
to improve the quality of the manuscript. We also thank Richard Teague and
Jeff Jennings for useful comments on using eddy and frank. This paper makes
use of the following ALMA data: ADS/JAO.ALMA#2017.1.01687.S,
ADS/JAO.ALMA#2017.1.01167.S, and ADS/JAO.ALMA#2017.1.01419.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. A.R. has been supported by
the UK Science and Technology research Council (STFC) via the consolidated
grant ST/S000623/1 and by the European Union’s Horizon 2020 research and
innovation programme under the Marie Sklodowska-Curie grant agreement No.
823823 (RISE DUSTBUSTERS project). P.W. acknowledges support from FONDECYT
grant 3220399. S.P. acknowledges support from FONDECYT grant 1191934\. This
work was funded by ANID – Millennium Science Initiative Program – Center Code
NCN2021_080. This project has received funding from the European Research
Council (ERC) under the European Union Horizon 2020 research and innovation
program (grant agreement No. 101042275, project Stellar-MADE). A.A.
acknowledges support through a Fellowship for National PhD students from ANID,
grant number 21212094 and funding by ANID, Millennium Science Initiative, via
the Núcleo Milenio de Formación Planetaria (NPF). P.R.M. thanks the Spanish
MINECO for funding support from PID2019-106235GB-I00. C.C. acknowledges
support by ANID BASAL project FB210003 and ANID, – Millennium Science
Initiative Program – NCN19_171. M.V. research was supported by an appointment
to the NASA Postdoctoral Program at the NASA Jet Propulsion Laboratory,
administered by Oak Ridge Associated Universities under contract with NASA.

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##  Appendix A Continuum images at 0.89 mm and 2.2 mm

The ALMA synthesized images at 0.89 mm and 2.2 mm are shown in Fig. 11.

Figure 11: ALMA continuum images of MP Mus at 0.89 mm (top, unresolved) and
2.2 mm (bottom, resolved) shown in logarithmic scales. The images were
synthesized with a robust value of -0.5. The corresponding beams
(0.89″$\times$0.66″and 0.25″$\times$0.19″at 0.89 mm and 2.2 mm, respectively)
are shown at the bottom left corners as white ellipses.

##  Appendix B frank visibility fit

Figure 12 shows a comparison of the observed continuum visibilities at 1.3 mm
and the corresponding fit derived with frank.

Figure 12: Comparison of the observed ALMA 1.3 mm continuum visibilities of MP
Mus (black dots) and the results from the frank fit (red line). The
visibilities are shown in 30-k$\lambda$ bins.

##  Appendix C Molecular gas emission line images

Figures 13, and 14, show the zero-th and first moments of the molecular
emission lines detected by ALMA in Bands 7 and 4, as well as their spectra.

Figure 13: Moments and spectra of the molecular lines detected by ALMA in the
MP Mus protoplanetary disk in Band 7. Figures and symbols are the same as in
Fig. 5.

Figure 14: Moments and spectra of the molecular lines detected by ALMA in the
MP Mus protoplanetary disk in Band 4. Symbols are the same as in Figs. 5 and
13.