11institutetext:  Department of Physics and Astronomy ”Galileo Galilei” -
University of Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
11email<EMAIL_ADDRESS>22institutetext: INAF – Osservatorio
Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
33institutetext: Dept. of Physics - University of Rome Tor Vergata, Via della
Ricerca Scientifica 1, 00133 Rome, Italy 44institutetext: School of Natural
Sciences, Center for Astronomy, University of Galway, Galway, H91 CF50,
Ireland 55institutetext: ETH Zürich - Institute for Particle Physics and
Astrophysics, Wolfgang-Pauli Str. 27, 8093 Zürich, Switzerland
66institutetext: Institute for Astronomy, University of Hawaii at Manoa,
Honolulu, HI 96822, USA 77institutetext: Department of Astronomy, University
of Florida, Gainesville, FL 32611, USA 88institutetext: Univ. Grenoble Alpes,
CNRS, IPAG, F-38000 Grenoble, France 99institutetext: Université Côte d’Azur,
Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, France
1010institutetext: University Observatory, Faculty of Physics, Ludwig-
Maximilians-Universität München, Scheinerstr. 1, 81679 Munich, Germany
1111institutetext: Exzellenzcluster ORIGINS, Boltzmannstr. 2, D-85748
Garching, Germany 1212institutetext: Anton Pannekoek Institute for Astronomy,
University of Amsterdam, Science Park 904, 1098XH Amsterdam, The Netherlands
1313institutetext: Dipartimento di Fisica, Università degli Studi di Milano,
Via Celoria, 16, Milano, I-20133, Italy 1414institutetext: Mullard Space
Science Laboratory, University College London, Holmbury St Mary, Dorking, UK
1515institutetext: Max-Planck-Institut für extraterrestrische Physik,
Giessenbachstrasse 1, 85748 Garching, German 1616institutetext: Institute of
Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
1717institutetext: LESIA, Observatoire de Paris, Université PSL, CNRS, 5 Place
Jules Janssen, 92190 Meudon, France 1818institutetext: European Southern
Observatory, Alonso de Córdova 3107, Casilla 19001, Vitacura, Santiago, Chile
1919institutetext: Instituto de Estudios Astrofísicos, Facultad de Ingeniería
y Ciencias, Universidad Diego Portales, Av. Ejército Libertador 441, Santiago,
Chile 2020institutetext: Escuela de Ingeniería Industrial, Facultad de
Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejercito 441, Santiago,
Chile 2121institutetext: Millennium Nucleus on Young Exoplanets and their
Moons (YEMS)

#  Disk Evolution Study Through Imaging of Nearby Young Stars (DESTINYS): HD
34700 A unveils an inner ring ††thanks:  Based on observations collected at
the European Southern Observatory under ESO programme(s) 1104.C-0415(A),
0108.C-0583(A) and 0108.C-0583(B).

G. Columba 1122 E. Rigliaco 22 R. Gratton 22 D. Mesa 22 V. D’Orazi 22 3 3 C.
Ginski 44 N. Engler 55 J. P. Williams 66 J. Bae 77 M. Benisty 8899 T.
Birnstiel 10101111 P. Delorme 88 C. Dominik 1212 S. Facchini 1313 F. Menard 88
P. Pinilla 1414 C. Rab 10101515 Á. Ribas 1616 V. Squicciarini 221717 R. G. van
Holstein 1818 A. Zurlo 191920202121

###### Abstract

Context.  The study of protoplanetary disks is fundamental to understand their
evolution and interaction with the surrounding environment, and to constrain
planet formation mechanisms.

Aims.  We aim at characterising the young binary system HD 34700 A, which
shows a wealth of structures.

Methods.  Taking advantage of the high-contrast imaging instruments SPHERE at
the VLT, LMIRCam at the LBT, and of ALMA observations, we analyse this system
at multiple wavelengths. We study the rings and spiral arms morphology and the
scattering properties of the dust. We discuss the possible causes of all the
observed features.

Results.  We detect for the first time, in the $H\alpha$ band, a ring
extending from $\sim 65\text{\,}$ to $\sim 120\text{\,}$, inside the ring
already known from recent studies. These two have different physical and
geometrical properties. Based on the scattering properties, the outer ring may
consist of grains of typical size $a_{\mathrm{out}}\geq$4\text{\,}$$, while
the inner ring of smaller grains ($a_{\mathrm{in}}\leq$ $0.4\text{\,}$). Two
extended logarithmic spiral arms stem from opposite sides of the disk. The
outer ring appears as a spiral arm itself, with a variable radial distance
from the centre and extended substructures. ALMA data confirm the presence of
a millimetric dust substructure centred just outside the outer ring, and
detect misaligned gas rotation patterns for HD 34700 A and B.

Conclusions.  The complexity of HD 34700 A, revealed by the variety of
observed features, suggests the existence of one or more disk-shaping physical
mechanisms. Possible scenarios, compatible with our findings, involve the
presence inside the disk of a yet undetected planet of several Jupiter masses
and the system interaction with the surroundings by means of gas cloudlet
capture or flybys. Further observations with JWST/MIRI or ALMA (gas
kinematics) could shed more light on these.

###### Key Words.:

protoplanetary disks – intermediate-mass stars – planet formation – multiple
systems – direct imaging

##  1 Introduction

Recent years have seen an exponential growth in the number of discovered
exoplanets and we are now beyond the five thousands milestone111 See the NASA
Exoplanet Archive: https://exoplanetarchive.ipac.caltech.edu/index.html .
However, detecting substellar companions within infant systems disks has
proven to be a much harder task. In fact, the presence of dust and gas left
from stellar formation can hide the already faint light from planets and brown
dwarfs (Szulágyi et al., 2019; Sanchis et al., 2020; Szulágyi & Garufi, 2021).
Therefore, it is not surprising that to date only in one system giant planets
were clearly detected within its transition disk, PDS 70 (Keppler et al.,
2018; Mesa et al., 2019; Haffert et al., 2019). Recently, evidence for
strongly embedded protoplanets was presented (Boccaletti et al. 2020 and
Currie et al. 2022 for AB Aur, Hammond et al. 2023 for HD 169142),
demonstrating the efforts required to detect these very young objects at near-
infrared and optical wavelengths. The extensive study of protoplanetary disks
is crucial to understand the earliest phases of planet formation, drawing an
evolutionary path from the raw materials of the disk to the final features of
a fully formed system.

In this context, we have studied in depth the young system HD 34700 A (HIP
24855), which shows complex substructures. The stellar and disk parameters
available in the literature are summarised in Table 1. This system started to
receive attention since the early 2000s: Arellano Ferro & Giridhar (2003)
first determined that HD 34700 A was a double-lined spectroscopic binary of
G0IVe type (Mora et al., 2001). Torres (2004) confirmed the binarity of the
system and calculated for it an orbit with eccentricity $e=0.25$ and a period
of $\sim 23.5$ days. They found that the two stars have almost equal mass and
estimated their orbit to be seen at an inclination of $\sim$$$. They also
detected youth indicators: a weak $H\alpha$ emission, a strong Li I
absorption, a strong X-ray emission and high rotational velocities, all
supporting the hypothesis of a pre-main sequence system, of few tens of Myr.
Sterzik et al. (2005) discovered that HD 34700 is actually a multiple system
of at least 4 stars: the central binary (A) and two low-mass companions of the
M stellar type, projected at distances of $None$ (B) and $None$ (C). They also
found the radial velocities of B and C to be consistent with the A component,
and detected in all their spectra youth indicators such as Li I and $H\alpha$
emission.

More recently, HD 34700 A disk was resolved for the first time by Monnier et
al. (2019), through polarised $H$-band observations with the Gemini Planet
Imager (GPI; Macintosh et al. 2014), showing its wide ring, a cavity, several
spiral arms and an inner faint arc. They carried out a thorough analysis of HD
34700 A disk, comparing the data to radiative transfer models, to reproduce
the observed ring-like structure. They obtained for the ring an average radius
of $175\text{\,}$ at an inclination of $None$ to the line of sight (LoS). They
noticed that the ring projected semi-major axis and the peak polarisation axis
are misaligned, corresponding to position angles (PAs) respectively of $None$
and $None$ East of North (EoN). Moreover, Monnier et al. (2019) provided
updated estimates of the system parameters, based on the new accurate parallax
value: they confirmed HD 34700 A to be a $\sim
5\text{\,}\mathrm{M}\mathrm{y}\mathrm{r}$-old binary star with a total mass
around $4\text{\,}\mathrm{M}_{\odot}$ and a transition disk. Uyama et al.
(2020) imaged again the outer ring of HD 34700 A with Subaru/CHARIS in JHK
bands and focused on the characterisation of its morphology, spiral arms
included, employing angular differential imaging (ADI; Marois et al., 2006)
reduction techniques. They found the ring to have a PA of $None$ and an
inclination of $None$, by ellipse-fitting, and its centre to be offset from
the star of $52.7\text{\,}\mathrm{m}\mathrm{a}\mathrm{s}$ towards $None$.
While no substellar companion was found, they assessed upper limits for any
such object of around $5\text{\,}\mathrm{M_{J}}$ outside the ring and
$12\text{\,}\mathrm{M_{J}}$ in the cavity. At longer wavelengths, Benac et al.
(2020) presented Submillimeter Array (SMA) observations of HD 34700 A and B.
Their observations of the $\@element[12]{\mathrm{CO}}$ J=2–1 transition line
detected a counterclockwise Keplerian rotation of A’s disk, while the
$1.3\text{\,}$ continuum resolved a prominent azimuthally asymmetric emission,
they suggest could be evidence for a dust trap. This substructure appears to
peak right outside the scattered light ring, at around $155\text{\,}$ from the
central star, based on their deprojection. They resolved continuum emission
around the B component too, caused by its own circumstellar disk. Thanks to
the improved parallaxes obtained as part of the _Gaia Data Release 3_ (Gaia
Collaboration et al., 2022), the latest estimate place HD 34700 A at distance
of $350.5\text{\,}\mathrm{p}\mathrm{c}$.

In this work we present new observations of HD 34700 A and analyse its various
features, discussing the implications of a new ring within the large cavity,
not fully resolved in previous observations of Monnier et al. (2019) and Uyama
et al. (2020). Figure 1 illustrates the main features that are analysed and
discussed: the inner ring (detected for the first time), the outer ring, and
its discontinuity. We describe the new observational data that we have
obtained in Sec. 2 and dive into the analysis of the disk components in Sec.
3, highlighting what insight we can gain from the new data. Then, in Sec. 4 we
discuss the interpretation of our results, also in comparison to previous
studies on this object. Finally, we summarise and conclude in Sec. 5.

Table 1: Summary of known parameters of HD 34700 A. The ”bin” subscript
indicates the A binary parameters.

Parameter | Value | Reference
---|---|---
R.A. (J2000) | 05:19:41.41 | 1
DEC. (J2000) | +05:38:42.80 | 1
Distance |  $350.5\ (\pm 2.5)$ $\mathrm{p}\mathrm{c}$ | 1
$P_{\mathrm{bin}}$ | 23.4877 days | 2
$e_{\mathrm{bin}}$ | 0.25 | 2
$i_{\mathrm{bin}}$ | $None$ | 2
$T_{\mathrm{eff}}$ | 5900 K + 5800 K | 2
$q\equiv M_{1}/M_{2}$ | $0.987\pm 0.014$ | 2
$v\sin{i}$ (Aa, Ab) |  $26.3,\ 21.7\ (\pm 0.6)$ | 3
Spectral type | G0 IVe + G0 IVe | 4
Age | $\sim 5\text{\,}\mathrm{M}\mathrm{y}\mathrm{r}$ | 5
$M_{\mathrm{bin}}$ | $4\text{\,}\mathrm{M}_{\sun}$ | 5
$M_{\mathrm{dust}}$ | 1.2 $(\pm 0.2)\times 10^{-4}$ M☉ | 5
$i_{\mathrm{outring}}$ | $None$ | 5

(1) Gaia Collaboration et al. (2021); (2) Torres (2004); (3) Sterzik et al.
(2005); (4) Mora et al. (2001); (5) Monnier et al. (2019);

##  2 Observations and data reduction

HD 34700 A system has been the target of several observations in recent years.
In the following we present all the new observations acquired, and the data
reduction process. A short summary of all the observations and the relative
setups is reported in Table 2.

Figure 1:  ZIMPOL $Q_{\phi}$ image of HD 34700 A with annotations. The field of view is 2.16${}^{\prime\prime}\times 2.16^{\prime\prime}$. The blue circle represents the coronagraph. North is up and East is left. The colour bar is linear and has arbitrary units.  Table 2: Observation setup and observing conditions. Date | Instrument | Mode | Filter | Coronagraph | DIT [s] | # Frames | Seeing [arcsec] |  $\tau_{0}$ [ms]
---|---|---|---|---|---|---|---|---
27-10-2019 | SPHERE | IRDIS-DPI | BB_H | YJH_ALC | 64.0 | 68 | 0.71 | 4.6
14-11-2021 | SPHERE | IRDIS-DBI | K1/K2 | YJH_ALC | 16.0 | 66 | 0.76 | 5.9
14-11-2021 | SPHERE | IFS | YJH | YJH_ALC | 32.0 | 15 | 0.74 | 4.2
26-11-2021 | SPHERE | IRDIS-DBI | K1/K2 | YJH_ALC | 32.0 | 104 | 0.76 | 7.7
26-11-2021 | SPHERE | IFS | YJH | YJH_ALC | 32.0 | 14 | 0.75 | 7.3
08-12-2021 | SPHERE | ZIMPOL (slow pol) | B_$H\alpha$ | CLC | 100 | 20 | 0.46 | 10.7
14-02-2022 | LBT | LMIRCam | L′ | none | 0.81 | 14284 | 0.92 | –
21-08-2022 | ALMA | – | Band 6 | none | – | – | – | –

###  2.1 SPHERE observations

HD 34700 A was observed with SPHERE, the Spectro-Polarimetric High-contrast
Exoplanet REsearch facility (Beuzit et al., 2019), mounted at the UT3’s
Nasmyth focus of ESO Very Large Telescope (VLT), with all its scientific
systems: IRDIS (the Infra-Red Dual-beam Imager and Spectrograph, Dohlen et al.
2008; Vigan et al. 2010), IFS (the Integral Field Spectrograph, Claudi et al.
2008; Mesa et al. 2015) and ZIMPOL (the Zurich Imaging Polarimeter, Schmid et
al. 2018). The SPHERE data were acquired within the program _Disk Evolution
Study Through Imaging of Nearby Young Stars_ (DESTINYS; Ginski et al., 2020,
2021), aimed at studying young planet-forming disks in scattered light. To
determine the star position behind the coronagraph in the science frames,
additional ”centre frames” were taken for all instruments, using the satellite
spots obtained in the deformable mirror waffle mode.

####  2.1.1 IRDIS polarised data

SPHERE/IRDIS data was acquired on 27 October 2019 in broadband $H$ (BB_H,
$\lambda_{c}$=$1.625\text{\,}$, $\Delta\lambda$=$0.290\text{\,}$, and pixel
scale $12.251\text{\,}\mathrm{m}\mathrm{a}\mathrm{s}\
\mathrm{p}\mathrm{i}\mathrm{x}^{-1}$, Maire et al. 2016). The observations
were carried out in dual beam polarimetric imaging mode (DPI; de Boer et al.,
2020; van Holstein et al., 2020), with a coronagraphic mask of radius
$92.5\text{\,}\mathrm{m}\mathrm{a}\mathrm{s}$ (Carbillet et al., 2011; Guerri
et al., 2011), centred on the photocentre of the binary star. The observations
consisted of 14 polarimetric cycles, each containing four exposures taken at
half-wave plate (HWP) switch angles 0∘, 45∘, 22.5∘, and 67.5∘. The individual
frame exposure time was set to 64 s, resulting in a total integration time of
74 min. The data were reduced with the IRDAP tool222 The default settings were
adopted for this reduction. See the software documentation at:
https://irdap.readthedocs.io/en/latest/ (van Holstein et al., 2020), which
applied polarimetric differential imaging (PDI, Kuhn et al. 2001), producing
the images corresponding to the Stokes parameters $Q$ and $U$, $Q_{\phi}$ and
$U_{\phi}$, shown all together for completeness in Figure 10. The $Q_{\phi}$
image, particularly useful to our goals, is shown alongside the other data in
Figure 2 (third panel). The azimuthal Stokes parameters $Q_{\phi}$ and
$U_{\phi}$ were obtained according to the definitions of de Boer et al.
(2020):

$\begin{array}[]{@{}l@{}}Q_{\phi}=-Q\cos(2\phi)-U\sin(2\phi)\\\
U_{\phi}=Q\sin(2\phi)-U\cos(2\phi)\\\ \end{array}$ (1)

where $\phi$ is the EoN polar angle in the coordinate system centred on the
star.

Polarimetry is well suited for the study of circumstellar disks, allowing us
to isolate their signal from the excessive stellar brightness. The central
stars mostly emit non-polarised light, which can be easily distinguished from
the polarised light scattered by the dust in the disk. The observing strategy
was pupil tracking (van Holstein et al., 2017), which allows the rotation of
the field of view (FoV) in time with respect to the detector. Figure 3 shows
the $H$-band $Q_{\phi}$ $r^{2}$-scaled image of HD 34700 A, that accounts for
the $r^{-2}$ dependency of the stellar flux, after considering the inclination
of the disk.

####  2.1.2 IRDIS+IFS data

New data in _IRDIFS_EXT_ mode were acquired on 14 and 26 November 2021. This
mode uses simultaneously IRDIS and IFS, to join the advantages of simultaneous
imaging and spectroscopy. With our setup IFS covered the wavelength range
0.95-$1.65\text{\,}$ at a spectral resolution of R$\sim$30 (FoV 1.77 arcsec2),
and IRDIS covered the $K1$ and $K2$ bands (dual-band imaging mode, or DBI, see
Vigan et al., 2010, FoV of $\sim$10 arcsec2) at $2.09\text{\,}$ and
$2.22\text{\,}$, respectively. We used the N_ALC_YJH_S apodized Lyot
coronagraph (Boccaletti et al., 2008) with a field mask having a radius of
$92.5\text{\,}\mathrm{m}\mathrm{a}\mathrm{s}$. The observing strategy for this
set of data was star-hopping in pupil-stabilised mode (see e.g. Wahhaj et al.,
2021). The total field rotation angle was $None$ and $None$ for the two
epochs. Star-hopping consists of the acquisition of a template Point Spread
Function (PSF) from a chosen nearby reference star, in between the exposure of
the scientific target. Subtracting the reference PSF from the science target
has two main benefits. Firstly, at small separation one actually gains
sensitivity thanks to the lack of signal self-suppression (as there is in
ADI). Secondly, ADI distorts disk morphology due to self-subtraction and can
sometimes lead to false positive detections (see, e.g., Rameau et al., 2017).

We applied two techniques for the suppression of the stellar speckle field in
the IRDIFS_EXT data. The IRDIS K-band imaging data utilised the iterative
reference star differential imaging (iRDI) approach briefly outlined in Ginski
et al. (2021). In this case the reference star data observed during star
hopping is used as the library of PSF standards. To fit the reference star
data to the science data we use the KLIP (Soummer et al. 2012) principal
component analysis (PCA) code. Since the disk is bright relative to the
stellar speckle field, we need to prevent overfitting of the reference star
data. This is done iteratively by feeding the positive disk signal above a
specified threshold back into the routine and subtracting it from the science
data before the reference star images are fitted. For the reduction of HD
34700 data we used a threshold of 100 counts, which includes bright disk
signal but excludes remaining speckle noise. In each step we removed 15 KLIP-
modes and we ran a total of 100 iterations. We note that this technique is
basically identical to the iterative ADI approach presented in Stapper &
Ginski (2022), with the exception that a reference star is used for speckle
suppression instead of the science data itself.

For the IFS data we use a combination of classical angular and spectral
differential imaging (cASDI). The idea of cASDI is to overcome the self-
subtraction inherent to classical ADI and SDI individually by combining the
spectral and temporal dimensions of the IFS data. We compute the median PSF to
subtract from all images simultaneously in the temporal and the spectral
dimension. We first re-scale all wavelength channels so that the speckle
fields coincide. We then flatten this array across all parallactic angles and
compute the median. By including both the parallactic angle rotation as well
as the wavelength scaling, we increase the diversity within the data set such
that less disk signal remains in the median image used for subtraction
compared to classical ADI or SDI. The total intensity K-band iRDI and YJH-
bands cASDI images are shown in the fourth and second panel of Figure 2.

####  2.1.3 ZIMPOL data

ZIMPOL observations were acquired with excellent sky conditions (see Table 2)
on 7-8 December 2021, in the B_Ha
($\lambda_{c}$=$655.6\text{\,}\mathrm{n}\mathrm{m}$) and Cnt_Ha
($\lambda_{c}$=$644.9\text{\,}\mathrm{n}\mathrm{m}$) $H\alpha$ filters. ZIMPOL
achieves diffraction-limited performance in these bands, on a FoV of
$3.5^{\prime\prime}\times 3.5^{\prime\prime}$. These observations were
performed in the slow polarimetry P1 mode of the instrument. In five
polarimetric $QU$ cycles the consecutive measurements of the Stokes parameters
$Q^{+}$, $Q^{-}$, $U^{+}$, and $U^{-}$ were conducted with different HWP
switch angles of $0^{\circ}$, $45^{\circ}$, $22.5^{\circ}$, and
$67.5^{\circ}$, respectively. At the beginning of the science observation the
flux measurement was performed with the star offset from the coronagraphic
mask, using the neutral density filter ND_1.0 and DIT = $10\text{\,}$.

The ZIMPOL data were reduced with the ETH data reduction pipeline (described
in, e.g., Schmid et al. 2018; Hunziker et al. 2020). Pre-processing and
calibration of raw frames included subtraction of bias frames, flat-fielding,
and correction for the modulation and demodulation efficiency. The
instrumental polarisation was corrected through forced normalisation of the
fluxes in the frames of two opposite polarisation states. All frames were
centred at the position provided by the centre frames. The final format of the
reduced $Q$ and $U$ images is $1024\times 1024$ pixels with a pixel size of
approximately $3.6\times 3.6$ mas on sky. The final $Q_{\phi}$ image of the
ZIMPOL $H\alpha$ data, shown in Figure 1, is the mean of the independent
$Q_{\phi}$ frames from the two ZIMPOL cameras, for the B_Ha filter.

Figure 2:  Images of HD 34700 A showing the observational data used in this
paper, in order of increasing wavelength. North is up and East is to the left.
The FoV shown in all panels is 2.16${}^{\prime\prime}\times
2.16^{\prime\prime}$. The blue circles represent the coronagraphs, except for
LMIRCam observations in L′ band (without coronagraph), where the blue area
masks all the spurious signals within $\lambda/D$, and ALMA data. In the ALMA
continuum image the red line represents the outer ring, while the blue ellipse
the inner ring; the continuum beam size is
$0\aas@@fstack{\prime\prime}41\times 0\aas@@fstack{\prime\prime}28$ at a PA of
$None$. The dashed contours denote levels of [0.4, 2, 4, 6] mJy/beam. The
colour bars have arbitrary units except for ALMA; they all have linear scale,
except for IRDIS $H$-band, which is logarithmic.

###  2.2 LBT observations

New data were also acquired with LBT/LMIRCam (the Large Binocular Telescope
Mid-InfraRed interferometric Camera, Skrutskie et al. 2010) on 14 February
2022 as part of the program IT-2021B-AO-3 (P.I. Gratton). The observations log
is reported in Table 2. LMIRCam’s field of view of $11.0^{\prime\prime}\times
11.0^{\prime\prime}$, similar to IRDIS, was wide enough to include both the
system’s A and B components in the frames. The observation was performed in
pupil stabilised mode, with the $L^{\prime}$ band filter (effective wavelength
$3.7\text{\,}$, Skrutskie et al. 2010), with a final scientific exposure time
of $3.22\text{\,}$ ($0.81\text{\,}$ each frame), obtaining a final rotation of
the FoV of $None$ that is enough to effectively perform the ADI reduction. The
high thermal background was removed from the data by subtracting a median of
the two nodding positions adopted in the observing strategy. Then, the disk
was detected applying the PCA (see e.g. Soummer et al. 2012) algorithm, using
a custom-made code appositely prepared to reduce these data. To this aim, only
one principal component was used to create the image to be subtracted from the
science images. The final image is shown in the second to last panel of Figure
2.

###  2.3 ALMA observations

The ALMA observations were taken in ALMA Band 6 (240 GHz, 1.25 mm) on 21
August 2022 as part of the DESTINYS snapshot program 2021.1.01705.S (PI C.
Ginski). The integration time on source was only 1.5 minutes in moderate
weather conditions with precipitable water vapor levels of 0.35 mm. The
baseline lengths ranged from 15 m to 1200 m. The data were calibrated using
the Common Astronomy Software Applications package (CASA, McMullin et al.
2007), version 6.2.1, to first remove atmospheric and instrumental effects
using the quasar calibrators. We then self-calibrated the data to increase the
signal-to-noise ratio.

The correlator was configured with broad wavelength coverage for best
continuum sensitivity but included one spectral window centred on the 230.538
GHz lines of $\@element[12]{\mathrm{CO}}$ $J=2-1$ in the lower sideband. The
continuum image was produced using the _tclean_ task on all spectral channels
other than the CO window. The image shown in the last panel of Figure 2 was
produced with Briggs robust weighting parameter $-0.5$ and corrected for
primary beam attenuation. The beam size is
$0\aas@@fstack{\prime\prime}41\times 0\aas@@fstack{\prime\prime}28$ at a PA of
$None$ and the rms is 0.13 mJy beam-1. The $\@element[12]{\mathrm{CO}}$
spectral window was imaged channel by channel (0.65 km s-1) with a Briggs
robust equal to $+0.5$ and a resulting beam size
$0\aas@@fstack{\prime\prime}52\times 0\aas@@fstack{\prime\prime}48$ at a PA of
$None$ with an rms of 4.3 mJy beam-1.

##  3 Analysis

In the following, we analyse the disk structures seen in the new observations,
compare them to the previous ones and highlight the new insights on the
system’s morphology. In Figure 2 we illustrate all the new multi-band data
presented in this study. From a comparison of these images, it becomes clear
that we can divide the disk around HD 34700 A in two main features: the outer
disk, already detected and analysed in recent years, which is very bright in
all wavelengths; and an inner disk, whose first detection was possible thanks
to the $H\alpha$ -band polarimetry.

###  3.1 Rings fit

Outer ring. The scattered light from the outer dust ring is clearly visible in
all datasets of Figure 2, except for the ALMA continuum. Multiple spiral arms
structures outside a large cavity, characterised by a strong discontinuity
near $None$ EoN, were already detected in $J$\- and $H$-band images, obtained
with GPI and SCExAO by Monnier et al. (2019) and Uyama et al. (2020),
respectively. IRDIS images (Figure 3 and Figure 10) confirm the presence of
these structures. Our ALMA data (last panel of Figure 2) confirmed that the
ring discontinuity is near the asymmetric mm-dust structure first discovered
by Benac et al. (2020). The nearest side of the disk to the observer is
expected to be the Northern side, based on Monnier et al. (2019) and confirmed
by our observations. In this work we do not provide new estimates for the
outer ring PA and inclination, as it was already done by previous works;
instead, we attempt different interpretations, based on the new perspectives
offered by the inner ring discovery. Nevertheless, we do provide an analysis
of its scattering phase function (see Sec. 3.6) and of the spiral structures
tied to the outer ring (see Sec. 3.3).

Figure 3:  Face-on deprojection of IRDIS H-band $Q_{\phi}$ data, corrected by
$r^{2}$ light dilution, and with special logarithmic colour scale to highlight
the faint outer spirals. The two opposite arms at East and West (C1 and S1)
stand out from the disk. HD 34700 B component is also visible in the FoV, in
the upper-left corner. The inner ring plane ($i\sim$$$, see Table 3) was
considered for deprojecting to face-on.  Figure 4:  Overlay of the ellipse
axes (_orange_) and the inner ring (_white_) as fitted in this work. The
yellow cross marks the position of the central binary star. For reference we
included the ellipse axes obtained by Uyama et al. (2020) based on the outer
ring alone (_dotted green_). The underlying image is a two-band $Q_{\phi}$
composite of the IRDIS H-band (_green layer_) and the ZIMPOL $H\alpha$ (_blue
layer_).

Inner ring. Polarimetric observation from ZIMPOL in the $H\alpha$ band (Figure
1), revealed the clear presence of another ring structure located inside the
outer ring cavity. This inner ring extends radially from $\sim$65 au to
$\sim$120 au (or $186-$335\text{\,}\mathrm{m}\mathrm{a}\mathrm{s}$$) from its
centre. It appears to have an offset with respect to the nominal position of
the central star (more on the offsets in Sec. 3.2). It is intriguing to notice
the presence of a faint ”arc” inside the outer ring, towards N-E, already
detected by Monnier et al. (2019), that we found again in the IRDIS $Q_{\phi}$
image (see Figure 10). Based on the new ZIMPOL data, we can link this arc
structure to the inner ring as they are found to overlap well and trace the
same elliptical shape. Furthermore, the inner ring seems to partially merge
with the outer ring structure on the N-W side, especially near the step-like
discontinuity around $None$. Depending on the disk 3D geometry, however, this
intersection may be more a perspective effect than a physical contact.

We characterised the geometry of the inner ring by assuming a circular dust
ring and fitting two separate ellipses to its internal and external boundaries
(see Figure 4). We selected the ring boundaries by subtracting, from a
slightly smoothed (14-17.6 mas) version of the original image, a strongly
smoothed image (42.2-45.7 mas). The result of this subtraction yields positive
values for the pixels of the bright ring core and negative values on the
surrounding background. Then, we chose as the boundaries the set of
coordinates corresponding to a sign change in this subtraction image. This
method proved to be the most suitable for this system, since the brightness
fluctuates over scales of many pixels, creating fuzzy boundaries. Also, we
excluded from the fit the North-West quadrant points, as the two rings overlap
significantly there. The selected boundary points were successively fed to the
”least-squares ellipse fitting” algorithm developed by Hammel & Sullivan-
Molina (2020)333https://github.com/bdhammel/least-squares-ellipse-
fitting/tree/v2.0.0 in Python. The whole procedure was repeated by varying the
angle of the inner ring mask and the smoothing parameters. Finally, we
computed the best-fit values as the mean of the two independent boundaries,
taking the median for each parameter and having the standard deviations as the
uncertainty. These single-ellipse parameters are the ones employed in our
subsequent deprojections. We have summarised the resulting parameters and
errors in Table 3. We obtained an inner ring with a semi-major axis PA of
$None$ from the North direction, seen at an inclination of $None$. The PA
value differs by 15-$None$ from the outer ring values obtained by Monnier et
al. (2019) and Uyama et al. (2020). However, Monnier et al. (2019) already
noticed that the peak polarisation axis of the outer structure was found at
$None$, which is very close to the value we have obtained from the inner ring.
The LoS inclination we found is also compatible with previous estimates.

Table 3: Geometrical parameters of HD 34700 A inner ring.

Parameter | Value
---|---
Inner radius |  $65\pm 0.6$ (au)
Outer radius |  $117\pm 0.2$ (au)
Mean width |  $52\pm 0.7$ (au)
Mean PA |  $87.1\pm 1.22$ (°)
LoS inclination |  $39.7\pm 2.0$ (°)
Centre offsetaa$a$with respect to the nominal position of HD 34700 A. |  $9.8\pm 5.7$ (mas)
Centre PAaa$a$with respect to the nominal position of HD 34700 A. |  $-52.3\pm 15.4$ (°)
444
The reader can find in the Introduction the parameters fit by Uyama et al.
(2020) for the outer ring.

The two rings appear different. The external one has spiral arms of various
shapes and sizes, and it shows a sharp discontinuity. On the contrary, the
internal ring has a sharper boundary and appears as a highly regular
elliptical annulus. The differences between these two rings, however, are not
limited to their shape: while the inner ring is prominent in the $H\alpha$
band, it is almost undetected in the $H$-band. There is only a faint arc in
the N-E direction that can be seen in the IRDIS $H$-band $Q_{\phi}$ (bottom
left panel of Figure 10), overlapping with the inner ring edge. This faint
feature was already detected by Monnier et al. (2019), who noticed that the
cavity inside the outer ring was not completely devoid of dust scattering
light.

The fact that the inner ring was fully revealed at shorter wavelengths implies
an underlying segregation between the dust grain sizes, highlighting a deeper
physical distinction. We discuss the possible formation mechanisms of such
structures in Sec. 4.2.

###  3.2 Geometrical offsets

In the following, we analyse the geometrical offsets observed for the centres
of the inner and the outer ring.

####  3.2.1 Inner ring offset

HD 34700 A shows offsets of the inner/outer rings centres with respect to the
central star. The centre of the elliptical annulus traced by the inner ring,
as described in Sec. 3.1, shows a shift from the star of around $3\text{\,}$
towards the West and $2\text{\,}$ towards the North. Precisely, we find this
geometrical centre to be found at a PA of $None$ and distance of $9.8\pm
5.7\text{\,}\mathrm{m}\mathrm{a}\mathrm{s}$ ($3.4\pm 2.0\text{\,}$) from HD
34700 A nominal position, as reported also in Table 3. The uncertainties
provided originate from the $1\sigma$ errors on the inner ring geometrical
fit, plus the half-pixel star-centring error, causing a relatively large but
realistic uncertainty. The direction of these offsets was rather unexpected.
Offsets are common for flaring disks along the minor axis, due to the disk
height and image projection (see, e.g., Ginski et al., 2016; de Boer et al.,
2016). The offsets we retrieved for the inner ring are opposite of what would
be expected based on that: surface flaring should have shifted the centre
towards the South, whereas we find a vertical shift towards the North. There
is also a significant component along the major axis direction. These features
suggest that other mechanisms could be responsible for the observed offsets:
the inner ring is likely to be rather flat and eccentric. We notice in this
context that the PA of the inner ring centre has a value very close to the PA
of the supposed mm-dust trap. From the ALMA continuum, in fact, we find a
$PA_{\mathrm{mm}}\sim$$$ measuring the angle of the 95% peak intensity seen
from the central star. This $PA_{\mathrm{mm}}$ is only $None$ away from the
inner ring centre PA ($None$). We speculate on a correlation between these two
angles, but a reliable answer would require detailed theoretical simulations
beyond the scope of this work.

####  3.2.2 Outer ring offset

For the outer ring, assuming that the observed structure is a projection from
a circular ring, Uyama et al. (2020) reported a shift of the outer ellipse
centre of around $-17.3\text{\,}$ in the West direction and $-6.6\text{\,}$ in
the North direction from the central star. This is exactly opposite to what we
find from the inner ring (but in the direction which can be justified by
height projection). We did not fit the outer ring as a regular ellipse, thus
we do not provide updated estimates on its offsets and parameters. Given the
compatible position angles and inclinations between inner and outer ring, the
different parts of the outer ring may not be equidistant from the central star
(see the spiral fit in Sec. 3.3). Also, because of possible azimuthal and
radial variations in scale height, the light scattered by the outer dust may
not belong to a unique geometrical plane. Thus, the circular approximation
might not be particularly suited for the outer ring.

####  3.2.3 Unseen stellar companions

Having ruled out the inner disk flaring as a plausible cause of the observed
offsets, we investigated both the potential presence of an additional stellar
companion and a non-null eccentricity of the inner ring. We have searched for
other stellar companions in the vicinity of the central binary, massive enough
to bring the barycentre away from the photocentre. We used the calibration
frames saved during the observing runs to reveal potential close point-source
companions hidden behind the coronagraph. We processed the ”no-coro”
calibration frames from IFS, performing a simple ADI-like reduction by
subtracting the median PSF of the central binary and adding the de-rotated
frames, as in Bonavita et al. (2022). The maximum field rotation (42.7∘, see
also Sec. 2.1.2), obtained for the 26-11-2021 calibration frames, allows the
revelation of potential companions beyond
$1\text{rad}/$$\times\lambda/D=42\,$mas to be free from self-subtraction. The
post-processed IFS data provides a J magnitude contrast of $\sim 7\,$mag at
$50\text{\,}\mathrm{m}\mathrm{a}\mathrm{s}$, which corresponds to a limit in
mass of $50\text{\,}\mathrm{M_{J}}$, using the BHAC15 models (Baraffe et al.,
2015). The full contrast limits plot and the processed SNR map are shown in
the Appendix, in Figure 11 and Figure 12 respectively. We do not detect any
reliable point-source in the processed image, hence, we can definitely exclude
the presence of unseen stellar companions. Indeed, everything more massive
than 30-$50\text{\,}\mathrm{M_{J}}$ behind the coronagraph would have been
detected with this reduction.

We can reinforce and expand this argument with other considerations. Firstly,
the SED of HD 34700 A shows an infrared excess, which must be caused by an
innermost circumbinary dust ring, not visible due to its proximity to the
central star and heated up to high temperatures. Seok & Li (2015) fit results
suggested a disk starting around $0.3\text{\,}$ with a $T$\sim 1500\text{\,}$$
(they had an imprecise system parallax, however). Thus, any stellar companion
close to the central binary would irremediably perturb the inner disk edge,
causing issues to the infrared excess. Secondly, if a stellar companion were
further out of the central binary, we would have detected it easily, being
outside of the coronagraph. There are also astrometric arguments against this
stellar companion. The Gaia RUWE555”Renormalized Unit Weight Error”, it
indicates the quality of the astrometric fit. A RUWE ¿ 1.4 could indicate that
the source is non-single (or otherwise problematic) and it is commonly used as
a possible hint of unresolved companions. parameter for HD 34700 A of 1.04 is
fully consistent with a single object (and the central binary is tight enough
to have no effect on the RUWE parameter). Moreover, the proper motion anomaly
(PMa) measured by Kervella et al. (2022) is low and compatible with substellar
masses, thus not significant for a star. In fact, this excludes the presence
of a stellar companion with a mass above $0.2\text{\,}\mathrm{M}_{\odot}$ in
the separation range $3\text{\,}30\text{\,}$, the latter being approximately
the size of the coronagraph used in our SPHERE observations. All these points
suggest that there is no third stellar companion in the range
$2\text{\,}30\text{\,}$ that could have shifted the barycentre of this system.

####  3.2.4 Ring eccentricity

Lastly, we assume the inner ring is eccentric and estimate its eccentricity
from its offset. The binary star would be the centre of mass of the ring,
positioned in one of the two foci, which means that the offset between the
ellipse centre and the star is a function of the eccentricity and can be used
backwards to infer $e$. To estimate the eccentricity, we approximated the
semi-major axis as the same obtained from the geometrical fit described above.
For the centre of the ellipse we considered the displacements in both
directions, after deprojecting to the inner ring plane. We find for the focal
distance $c=3.2\pm 1.0\,$pix and for the semi-major axis $a=$74.0\pm
0.6\text{\,}\mathrm{p}\mathrm{i}\mathrm{x}$$, corresponding to a modest ring
eccentricity of $e=c/a=0.043\pm 0.014$. Taking into account this eccentricity
in the projection effects along the LoS, it would result in a smaller
inclination angle $i$ than for the circular scenario. The difference, however,
is below one degree less than what found in Table 3 and within the error bars.

Hydrodynamical simulations of protoplanetary disks demonstrate that objects
heavier than $\sim$$3\text{\,}\mathrm{M_{J}}$ lead to significantly eccentric
cavities in the dust (see, e.g., Kley & Dirksen, 2006; Pinilla et al., 2012;
Zhang et al., 2018). Specifically, Kley & Dirksen (2006) provide disk
eccentricity values as a function of radius, for different companion masses
(or, better, mass ratios). They report a peak eccentricity of $\sim 0.05$ for
$q=0.001$ ($4\text{\,}\mathrm{M_{J}}$ in HD 34700 A) for orbits both inside
and outside the planet. Heavier companions excite much higher eccentricities
in the disk outside their orbit (up to $0.22$), but again around $\gtrsim
0.05$ for inner orbits. Comparing these theoretical results with our
eccentricity estimate, we find a good agreement. A $\sim
4\text{\,}\mathrm{M_{J}}$ companion may be present either inside or outside HD
34700 A inner disk. Heavier planets are unlikely to reside inside the inner
ring cavity, as they would excite much higher eccentricities; they could be
present anyway in the gap between the inner and the outer rings. In addition,
Zhang et al. (2018) show that disk eccentricity is enhanced by low viscosity
and small aspect ratios. We know that the aspect ratio of HD 34700 A cannot be
too high, since the offsets along the projected minor axis are limited. A low-
viscosity coefficient, moreover, appears to be preferred among protoplanetary
disks, as reported by the DSHARP collaboration (Dullemond et al., 2018), but
also Pinte et al. (2022); Rosotti (2023).

In conclusion, the presence of a giant planet of several Jupiter masses, which
cannot be ruled out by our observations, would naturally explain the offset
issue by the excitation of disk eccentricity. Further discussion on a
potential substellar object and its impact on dust segregation is reported in
Sec. 4.2.

###  3.3 Spiral arms fit

Figure 5:  Polar-coordinate visualisation of the disk of HD 34700 A, from
IRDIS $Q_{\phi}$ frame, multiplied for a $r^{2}$ correction factor for the
flux dilution and lightly smoothed. Note: the disk is duplicated horizontally
to avoid cuts at the image boundaries (notice the $x$ axis). The colour scale
is logarithmic to highlight the faint spiral arms. In dashes, the fitted
logarithmic (_lime green_) and archimedean (_blue_) spiral arms. The cyan
circle around $None$ represents the approximate centre of the mm-dust
emission.

The outer spiral arms of HD 34700 A have some of the highest pitch angles and
radial extents analysed to date (see e.g. Fig. 4e and 4f of Bae et al., 2022).
To compare the geometrical properties of the spiral structures, we have
produced an extended polar-coordinates visualisation of the disk, shown in
Figure 5 and we performed spiral fits to compute the pitch angles. To obtain
the $(r,\phi)$ polar visualisation, we deprojected the IRDIS $Q_{\phi}$ based
on the inner ring geometry parameters (see Table 3), using the scikit-image
module in a custom-made Python code. We did not assume any disk flaring, to
avoid imposing a height profile for these outer regions of the disk, where the
spiral arms are found, and to be consistent with the scenario outlined in Sec.
3.6.

For the analytical spiral fit we opted to focus on the arms that we were able
to distinguish from the rest of the disk. The wealth of substructures in the
$$$<\phi<$$$ region, in fact, although interesting, mixes up together in a way
that would make any spiral fit partly arbitrary. Qualitatively, however, they
appear to have a steep and almost constant slope, as illustrated in Figure 5.
Closely inspecting the deprojected image, we noticed that the bright ridge of
the outer ring shows a varying radial distance along the azimuthal dimension,
culminating with the discontinuity at $None$, where there is a sharp jump. In
this context, it seemed interesting to calculate the pitch angle of the outer
ring, assuming that it was a spiral arm itself as a whole. Then, we decided to
fit analytically only the following large-scale features: the outer ring
(labelled ”outring” for short) and the two long arms extending furthest away
from the disk. We retained the name ”S1”666 To be precise, they referred to
this arm as ”S1b” in their paper, as the continuation of a ”S1a” after a
shadow. With our polar deprojection these two structures seemed independent of
each other; thus, we decided to label S1 the evident log-spiral at
$r>$300\text{\,}\mathrm{a}\mathrm{u}$$ and neglect the other fuzzy structure.
for the arm already labelled by Uyama et al. (2020), and we called ”C1” the
other arm (as for _Columba_), not to overlap with the previous authors’
labels. We sampled the two outer arms picking by hand the coordinates of the
brightest parts from Figure 5. For the outer ring we selected its bright ridge
using intensity contours and limiting the azimuthal angles range between
$$$<\phi<$$$, to leave a small margin around the discontinuity at $None$.
Then, we used the scipy.curve_fit algorithm to fit the collected data points
and find the best spiral parameters. We performed the regression with two
commonly used types of spiral:

$r(\phi)=\begin{cases}a\cdot e^{b\phi}&\mathrm{logarithmic}\\\
a+b\phi&\mathrm{archimedean}\\\ \end{cases}$ (2)

where $(\phi,r)$ are the polar coordinates on the disk plane. We fit the
logarithmic shape for the two outer arms and the archimedean for the outer
ring, based on their qualitative appearance. Indeed, a logarithmic growth
implies a steepening curve in polar coordinates, similarly to the S1 arm; that
archimedean spiral, instead, has a constant slope in polar coordinates, more
similar to the ridge of the outer ring. Real spiral wakes can take much more
complex shapes, however, it is still informative to use these simple shapes to
obtain quantitative insights on the disk morphology.

We report the pitch angles obtained for our spirals in Table 4, along with the
standard deviation errors. Since the pitch angle of an archimedean spiral is
not constant (as is the case for the logarithmic spiral), we chose to report
in the table the pitch angle value computed at the smallest radial distance
reached by the outer ring ($\sim 120\text{\,}$). To inspect in greater detail
the outer ring pitch angle behaviour, we repeated the analysis with a
piecewise fit of archimedean arms. We computed the arm fit parameter on a
window of $\Delta\phi=$$$, running along the outer ring at steps of $None$, to
see how its pitch angle evolved with the azimuthal angle. This piecewise
computation returns for the outer ring pitch angles within the range between
$None$ and $None$, with the highest values near $\phi\sim$$$. This could be
informative of possible perturbations along a spiral arm. Under appropriate
circumstances, and with sufficient resolution, a wake-launching planet can be
located where the pitch angle has a cusp, peaking theoretically near $None$
values (Zhu et al., 2015). No similar feature could be retrieved from our data
analysis.

Table 4:  Pitch angles of the spiral arms plotted in Figure 5. The uncertainty for the pitch angles corresponds to 1$\sigma$. The archimedean pitch angle is evaluated at $\sim 120\text{\,}$.  Spiral ID | Type | Pitch angle (°)
---|---|---
C1 | log | $31.1\pm 8.0$
S1 | log | $34.5\pm 1.9$
outring | arch | $4.4\pm 0.1$

We remark the similarities between C1 and S1, starting from the large pitch
angles $\gtrsim$$$, compatible within uncertainties. The two arms are
visualised and plotted on the disk plane in Figure 3, for context. They are
found on opposite sides of the disk, close to being $None$ apart. They are
both structures with the largest radial extensions and similar logarithmic
shape. S1 is detected up to $\sim 600\text{\,}$, while C1 extends to the
impressive $\sim 1000\text{\,}$ from the central stars. The fit of arm C1 has
large uncertainties, due to its intrinsic thickness and faintness; also, the
presence of the other substructures closer to the outer ring does not allow to
constrain its shape at shorter radii. We recall that the existence of these
two arms on a single orbital plane is not guaranteed. However, based on our
deprojection and the similarities between these spirals, it seems reasonable
to assume a connection between them. We discuss in further detail the
implications of the spiral shapes and pitch angles in Sec. 4.3 and Sec. 4.4.

###  3.4 Millimetre-dust asymmetry

HD 34700 A was observed in the mm wavelengths with ALMA (Figure 2 and Figure
16). The continuum thermal emission, tracing larger millimetre-dust, appears
to be significantly displaced from the centre of the system, where they have
been depleted. Similar results were obtained by Benac et al. (2020) using the
SMA (Ho et al., 2004). They argue this could be the manifestation of a dust
trap with an asymmetric, crescent-like morphology, where most of the remaining
mm grains accumulate. Such asymmetric traps are often (but not exclusively)
associated with vortices in the disk (e.g. Birnstiel et al., 2013; Lyra & Lin,
2013).

We traced the contours of the mm emission in the last panel of Figure 2 and
compared it to the disk structures observed in scattered light. The outer
parts of the outer ring in the North-West quadrant, the closest to the mm-
asymmetry, appear fainter and sparser, perhaps because of a locally lower
scale height of the disk (see panels 3 and 6 of Figure 2 and Figure 5).
Moreover, the mm-dust emission peak is near the point where the outer ring
seems to intersect the inner ring, hinting at a perturbed area. It is not
centred on the $None$ discontinuity. The inner ring, instead, does not appear
to be significantly warped in the proximity of the mm emission, but the ring’s
centre PA is interestingly close to the mm emission PA (see Sec. 3.2). The
simultaneous presence in the disk of HD 34700 A of an asymmetric dust
structure, in the ALMA continuum, and of spiral arms, seen in visible-IR
scattered light, points to a potential connection between these features (see,
e.g., Cazzoletti et al., 2018; van der Marel et al., 2021). We measured the
mm-continuum integrated fluxes for HD 34700 A and B to be of 9.1 mJy and 4.0
mJy respectively, with a rms uncertainty of 0.13 mJy. The continuum emission
around the B component is centred on the star and elliptical, contrary to
component A (see Figure 16).

###  3.5 Gas velocity

We determined the velocity of emission peak for the
$\@element[12]{\mathrm{CO}}$ line from the ALMA band 6 spectral datacube,
using the bettermoments package (Teague & Foreman-Mackey, 2018) to study the
gas kinematics. We detect gas rotation patterns for HD 34700 A and B, whereas
we did not detect the C component in either the gas or mm continuum. No gas
streamers connecting the A and B components are detected in our data.

The velocity map for the A component, shown in Figure 6, displays a rotating
gas that extends to the innermost regions of the disk, inside both the outer
and inner ring. The rotation is counterclockwise on the sky plane, in
agreement with the winding of the spiral arms. The source is well centred in
between the two lobes of the rotation pattern, confirming the host star as the
barycentre of the system. There is no significant velocity perturbation at the
location of the mm-dust peak, near the break in the scattered light outer
ring, at least at the moderate resolution of these data. Figure 6 data is
masked at $5\sigma$ to avoid including noisy background signal. We estimate
for the gas disk a position angle of $PA_{\mathrm{gas}}=$$$, from a straight
line fit of the peak velocity coordinates with scipy.curve_fit.

The companion HD 34700 B was also detected in the ALMA velocity map. The
smaller angular size of B, with an equal beam size, implies a worse gas
velocity resolution than for A. Nonetheless, we detect a velocity gradient
typical of rotating gas in the $\@element[12]{\mathrm{CO}}$ line (Figure 15).
The gas and dust emissions are both centred on the source, for B.

Interestingly, the disk around B rotates clockwise, opposite to the disk
around A, and with a very different semi-major axis PA. This misalignment
between the two components of HD 34700 suggests that A and B did not originate
from the same coherently-rotating gas disk. Instead, they may have collapsed
in different parts of a turbulent fragmented cloud (see e.g. Williams et al.,
2014; yi Luo et al., 2022).

Figure 6:  ALMA data velocity contours for HD 34700 A, obtained from the
$\@element[12]{\mathrm{CO}}$ molecular lines. For reference, we put as
background the IRDIS $H-$band $Q_{\phi}$ and marked the source position with a
yellow cross. The gas shows a well defined rotation pattern, extending to the
innermost regions of the disk. The beam is $$$\times$$$ at a PA of $None$. The
gas speed values refer to the Local Standard of Rest.

###  3.6 Scattering phase functions

####  3.6.1 Models

To better characterise the nature of HD 34700 A’s rings, we extracted their
azimuthal brightness profiles and fitted a theoretical scattering phase
function. In particular, following a standard approach (e.g., Engler et al.,
2017) we adopted the Henyey-Greenstein phase function (Henyey & Greenstein,
1941):

$F_{\mathrm{HG}}(\theta,g)\propto\frac{1}{4\pi}\frac{1-g^{2}}{(1+g^{2}-2g\cos\theta)^{\nicefrac{{3}}{{2}}}},$
(3)

which depends on the scattering angle $\theta$ and the asymmetry parameter
$g$. The latter can take any value in the interval $[-1,1]$ and parameterises
the balance of scattered power between forward $(g>0)$ and backward scattering
$(g<0)$. In case of polarised observations (as $Q_{\phi}$ data) we accounted
for the linear polarisation (LP) of light multiplying Eq. 3 by the single
scattering Rayleigh factor:

$LP(\theta)\approx\frac{1-\cos^{2}\theta}{1+\cos^{2}\theta}.$

A critical uncertainty for the fitting procedure was due to the unconstrained
3D structure of the disk itself, since to provide a scattering angle $\theta$
for each point of a ring requires assuming a particular geometry, in terms of
inclination, PA and flaring. In fact, considering an axially symmetric ring
around the central star, observed at an inclination $i$ and with a locally
constant flaring angle $\gamma$, we can infer the scattering angles following
the formulation of Quanz et al. (2011) and Stolker et al. (2016):

$\theta=\begin{cases}$$+(i+\gamma)\cdot\cos{\phi}&\quad$$<\phi<$$\\\
$$+(i-\gamma)\cdot\cos{\phi}&\quad$$<\phi<$$\end{cases},$ (4)

with $\phi$ being the azimuthal coordinate on the disk plane, starting from
zero at the closest point to the observer. We knew from the literature
(Monnier et al., 2019; Uyama et al., 2020; Benac et al., 2020) that the
closest side of HD 34700 A’s disk was in the northern half, so we imposed as
zero-point the angle of the semi-minor axis counterclockwise from the North.
Then, for a guess of $\left\\{i,\gamma,\mathrm{PA}\right\\}$ as disk geometry,
we can map each azimuthal angle of the deprojected ring - and the
corresponding median brightness $I(\phi)$ \- to a scattering angle,
$\theta(\phi)$ and thus obtain $I(\theta)$, in the approximation of single
scattering of photons from the star. In other words, $I(\theta)$ is a measure
of the dust brightness seen from the accessible scattering angles. The flaring
angle influences also the inferred brightness, when correcting for the
dilution of radiation flux (i.e. multiplying for a $r^{2}$ mask from the
source position).

####  3.6.2 Procedure

Based on the previous remarks, the less biased procedure we could use to fit
the scattering phase function, was to extract a reasonable
$\left\\{i,\gamma,\mathrm{PA}\right\\}_{k}$ deprojection triplet, via random-
sampling, and then run a MCMC regression on the theoretical phase function, to
find the best $g$ parameter. The first step fixed the mapping to the median
$I(\theta)$, while the second step found the model parameters minimising the
residual to the given data. The best final solution was eventually chosen
based on a maximum likelihood estimator, evaluating the overall goodness of
fit resulting from the given deprojection geometry and the fitted model
parameters.

The deprojections were performed with the same method as for the spiral
fitting analysis (see Sec. 3.3). The polar representations of the rings are
shown in the bottom panels of Figure 7 and Figure 8. The top panels show the
normalised brightness of each ring plotted as a function of the disk-plane
angles from the North ($\Phi$) in azimuthal slices of $None$. The normalised
brightness is measured as the median along the radial dimension. In detail,
the inner ring brightness was computed considering intensity contours (on the
smoothed data) to find the middle radial distance and taking the median within
$30\text{\,}\mathrm{a}\mathrm{u}$ of thickness around each core point. The
outer ring profile, instead, was computed taking the radial median of every
pixel within intensity contours chosen to encompass the entire structure, due
to its lower regularity; the radial distance was determined based on the
maxima for each angle.

The deprojection parameters were sampled from normal distributions centred on
the best fit values from the inner ring geometrical fit (see Table 3). Once
the image had been deprojected, fixing the $I(\theta)$, a MCMC computation was
launched to find the best model parameters for that brightness profile:
$\left\\{g,A,\sigma_{\mathrm{j}}\right\\}_{k}$, respectively the asymmetry
parameter, an amplitude proportionality factor, and a jitter term to
accommodate the spread of our data points. We used the emcee module (Foreman-
Mackey et al., 2013) to perform our MCMC runs, adopting flat priors on the
$g,A,\sigma_{\mathrm{j}}$ parameters and a standard log-likelihood for a
Gaussian distribution of the residues. After a few attempts, we noticed that
the flaring angle parameter was giving nonphysical results, warping the rings
artificially and pumping the forward scattering part by means of the $r^{2}$
correction. Moreover, estimating the expected flaring based on the offset
along the projected semi-minor axis of the disk, we obtained almost negligible
angles, in contrast to the MCMC-preferred values (¿$None$). This suggested
that the scattered light we see does not come from a regular, optically thick
surface but could originate from dust at different heights in a thin disk.
Motivated by this, we neglected the flaring angle for both rings and launched
our MC extractions of $\left\\{i,\gamma,\mathrm{PA}\right\\}_{k}$ always
imposing $\gamma=0$.

Figure 7:  Analysis of the polarised scattering brightness of the inner ring.
_Top:_ median radial brightness of the ring (green), as a function of the
azimuth angle on the disk plane ($None$ is North), normalised to the maximum.
_Middle:_ residues of the data to the best-fit function, with grey arrows
pointing towards the candidate shadow features. _Bottom:_ ZIMPOL $Q_{\phi}$
data transformed to polar-coordinates and corrected for the $r^{2}$ flux
dilution, from which the median brightness of the top panel was extracted. The
best-fit asymmetry parameter was $g=0.41\pm 0.01$. Figure 8:  Analysis of the
polarised scattering brightness of the outer ring. _Top:_ median radial
brightness of the ring (yellow), as a function of the azimuth angle on the
disk plane ($None$ is North), normalised to the maximum. _Middle:_ residues of
the data to the best-fit function, with grey arrows pointing towards the
candidate shadow features. _Bottom:_ IRDIS $Q_{\phi}$ data transformed to
polar-coordinates and corrected for the $r^{2}$ flux dilution, from which the
median brightness of the top panel was extracted. The best-fit asymmetry
parameter was $g=-0.16\pm 0.01$.

####  3.6.3 Results

The procedure described above was applied on three independent datasets: the
total-intensity iRDI reduction of the IRDIS K-band observation, the IRDIS
H-band $Q_{\phi}$ (bottom left panel of Figure 10) and the ZIMPOL $H\alpha$
$Q_{\phi}$ (Figure 1) data. The latter, in particular, was masked in two
variants, to isolate the inner and outer ring from one another. All of these
images allowed an estimate of the outer ring parameters, while only the ZIMPOL
$Q_{\phi}$ could be exploited for the inner ring. We randomly extracted 100
deprojection triplets for each dataset, to sample the ${i,PA}$ parameter
space, and run the MCMC regression on each one. From these runs we selected
the best solution as the one yielding the highest likelihood estimator, which
assessed the overall quality of the fit. The uncertainties were computed as
the $1\sigma$ spread of values on the best fit solution, for $g$. We remark
here that the main goal of our phase fitting was to provide an estimate of the
asymmetry parameter $g$ and assess the differences between the two rings. A
summary of all best-fit results is reported in Table 5.

The resulting brightness profiles show very different scattering properties
between the inner and outer ring. The inner ring, illustrated in Figure 7, is
characterised by a broad forward scattering peak (North is close to the
nearest point to the observer) and a weaker back-scattering valley, which
translates to a positive asymmetry parameter of $g_{\mathrm{in}}=0.41\pm
0.01$.

The outer ring was analysed in three bands, $H\alpha$ , $H$ and $K$. Detailed
values for the three bands are reported in Table 5. The resulting asymmetry
parameter values were consistently much smaller for the outer ring than for
the inner ring, oscillating around $g\sim 0$. This reflects an apparently
isotropic scattering of this dust, but it is likely to be an observational
effect, as we argue in the Discussion. As shown in the polarimetric
observation of Figure 8 there are two brightness peaks, around $None$ away
from the closest disk point, and two valleys in between. Additional figures
illustrating the phase fits on the outer ring for the total intensity data and
the $H\alpha$ data can be found in the Appendix, in Figure 13 and Figure 14
respectively. It is particularly striking how, focusing on the North direction
($None$ of both rings), the inner ring is close to its maximum brightness,
whereas the outer one is in the middle of a valley. This is the cause of a
major tension in the value of the asymmetry parameter between the two rings,
which we discuss in depth in Sec. 4.1.

Table 5:  Best-fit scattering asymmetry parameter $g$ and relative deprojection angles, obtained from the MCMC regression.  | $\mathbf{g}$ | $\mathbf{i}\ (^{\circ})$ | $\mathbf{PA}\ (^{\circ})$
---|---|---|---
Inner ring ($H\alpha$ , $Q_{\phi}$ ) | $+0.41\pm 0.01$ | $34.09$ | $87.72$
Outer ring ($H\alpha$ , $Q_{\phi}$ ) | $-0.03\pm 0.01$ | $33.06$ | $82.27$
Outer ring ( H, $Q_{\phi}$ ) | $-0.16\pm 0.01$ | $32.63$ | $84.21$
Outer ring (K, $I_{tot}$ ) | $+0.04\pm 0.01$ | $39.29$ | $79.00$

###  3.7 Shadowing effects

In this section we analyse the polar-coordinates images of the inner and outer
disk, looking for effects of shadowing. Similar effects on the outer ring were
already detected by Monnier et al. (2019) and Uyama et al. (2020).

Inner ring: the brightness profile of the inner ring is rather noisy, showing
strong fluctuations over angles of few degrees. In this condition, a thin
shadow might be buried under this noise or a random fluctuation could be
mislabelled as a shadow. When visually inspecting the bottom panel of Figure 7
it is not obvious to identify evidence of shadowing. In the middle panel,
where the residuals are reported, we identified only one main dip around
$None$, marked by the vertical grey arrow.

Outer ring: the outer ring data is less noisy than the inner ring, as
fluctuations from one angle to the next are smaller. However, considering its
wealth of substructures, it is not trivial to assess the nature of the
brightness dips, as real shadows or shapes on the illuminated dust surface.
Referring to Figure 8 and starting from the most visually-prominent features,
we identified a clear dip near $None$, one at $None$, and one near the
discontinuity, starting around $None$. Smaller dips can be found at $None$,
$None$, $None$ and $None$. Then, inspecting also the total intensity data of
Figure 13, we report another dip at $None$. The brightness profile of the
outer ring has so many features that the best fit line itself is heavily
influenced by the dips and thus it does not offer an ideal unbiased reference
to assess the supposed shadows analytically.

The alignment of two important dips in the outer ring along the North-South
axis, the one at $None$ near the discontinuity and the shadow at $None$,
constitutes an element of interest. Shadowing effects are not rare in
protoplanetary disks, and there are several examples of symmetrical shadows at
opposite sides of a disk, cast by inner misaligned rings (Benisty et al.,
2022, e.g. for a review). In this case, the shadows have converging angles, as
the ones of HD 100453 (Benisty et al., 2017), GG Tau A (Keppler et al., 2020),
or other disks in Fig.1 of Benisty et al. (2022). Instead, in HD 34700 A we
observe a discontinuity which, if anything, is rather parallel to the shadow
at $None$ and, maybe not coincidentally, is also parallel to most spiral
substructures. Neglecting for a moment the shadow angles, we can wonder which
disk structure is projecting its shadow onto the outer ring. The inner ring
resolved by ZIMPOL, based on our analysis, appears sufficiently aligned with
the outer ring that it would be difficult to create a thin shadow such as the
one at $None$. Most importantly, this shadow is near the disk minor axis,
whereas from geometrical considerations it should be projected along the major
axis (except for extreme disk warps, not supported by our data). Another
hypothesis could be an unresolved and misaligned ring close to the central
binary, launching its shadow on both the inner and the outer rings. However,
we report no detection of a $None$ shadow in the ZIMPOL’s inner ring (Figure
7) and in general no correlation with any other brightness dip found on the
outer ring. As a consequence, we suggest that the dip at $None$ may be linked
to the shapes of the disk and spiral arms, instead of being a projected
shadow. It could be similar to the dip at $None$, with the main difference
that the first one is better resolved, thanks to a lucky geometrical
alignment.

###  3.8 Mass constraints on potential detectable companions

Figure 9:  Limits on the mass of a planetary companion in the disk of HD 34700
A, based on the reduced observations from IFS (_green line_), LMIRCam (_red
dotted line_) and the AMES-COND models for a young gas giant
$5\text{\,}\mathrm{M}\mathrm{y}\mathrm{r}$ old. Shaded areas represent the
rough radial extension of the inner ring (_blue_) and the outer ring (_red_).

The new SPHERE/IFS and LBT/LMIRCam images allowed us to put constraints on the
mass limit of a possible candidate companion. We calculate these limits using
the method described in Mesa et al. (2015) and show them in Figure 9. The
luminosity contrasts are converted into mass detection limits based on the
”AMES-COND” theoretical models for the atmospheres of non-irradiated young
gaseous planets/brown dwarfs with no dust opacity (Allard et al., 2001), and
assuming a system age of $5\text{\,}\mathrm{M}\mathrm{y}\mathrm{r}$.

The presence of the bright outer ring worsens the detectability of substellar
objects in its proximity (light red shaded area in Figure 9), whereas the
inner ring has a negligible impact at the observed wavelengths. The L’ band
LMIRCam data improve the IFS detection limit in the outer ring region, pushing
it down to 10-$15\text{\,}\mathrm{M_{J}}$, and for small separations
($<60\text{\,}$), where only massive BDs are detectable anyway. From IFS, we
have a small window around $100\text{\,}\mathrm{a}\mathrm{u}$ from the star,
where we should be able to spot giant candidate companions of
$10\text{\,}\mathrm{M_{J}}$ and then outward
$200\text{\,}\mathrm{a}\mathrm{u}$ again. Further than
$280\text{\,}\mathrm{a}\mathrm{u}$ we should be able to detect gas giants of
the order of $5\text{\,}\mathrm{M_{J}}$, but we did not find any. The mass
limits we obtain are compatible with those of Uyama et al. (2020) for the
$JHK$ bands.

##  4 Discussion

HD 34700 A circumbinary disk mainly consists of two very different ring-like
substructures, whose morphology we have analysed in detail in Sec. 3. The
inner ring centre is offset with respect to the star, which suggests that it
could have a non-null eccentricity. The outer ring-like dust structure is tied
to wide spiral arms with similar logarithmic shape. The two ring structures do
not show equal scattering brightness in all passbands: the inner dust appears
qualitatively bluer than the outer one, as it is not detected in the longer-
wavelength near-infrared data. In addition, their scattering phase functions
are fit to significantly different effective asymmetry parameters. Almost all
mm-continuum emission in HD 34700 A is asymmetric and centred away from the
host star. We detect CO gas rotation in components A and B, but no gas
streamer in between, as reported in Sec. 3.5.

In the following, we discuss plausible physical causes of this diversity in
the disk of HD 34700 A. Based on our results and on previous literature, we
attempt to match the various pieces together, to create a globally coherent
model of this system and assess its limits.

###  4.1  Scattering asymmetry parameter tension

The scattering phase functions of the inner and outer ring around HD 34700 A
reveal evidence of the diversity in the dust populations of the two rings.
Their asymmetry parameters $g$, defined and calculated in Sec. 3.6, are
radically different. On the one hand, the $g\approx 0$ value fit for the outer
ring would suggest that its dust is scattering isotropically. This generally
happens in the Rayleigh regime, when the grains are much smaller than the
wavelength. On the other hand, the inner ring fit returned $g\sim 0.4$, which
would reflect more forward scattering, typical of grains with size comparable
to the scattered wavelength. However, the scattering cross section of dust
aggregates drops rapidly for wavelengths longer than their size (see e.g.
Tazaki & Tanaka, 2018; Min et al., 2016). This implies that, for a given
filter wavelength $\lambda$, we expect to see particles of size
$a\gtrsim\lambda$, where $a$ is the characteristic radius. The outer ring is
perfectly detected up to the $K2$ band. Assuming that the detection limits for
ZIMPOL in $H\alpha$ are not better than for IFS and IRDIS bands, the inner
ring is properly detected only in $H\alpha$ , suggesting a qualitatively
smaller grain size. Then, our results appear in contradiction: the outer ring
should not display isotropic scattering and at the same time consist of
particles larger than those in the inner ring. This tension can be solved
taking into account the difference between the theoretical scattering pattern
and the one actually measured from observations.

Min et al. (2016) derived the optical properties of dust aggregates with
detailed numerical computations using the discrete dipole approximation,
providing values of the asymmetry parameter as a function of wavelength and
for various grain sizes. They find that the _effective_ asymmetry parameter,
which is obtained by fitting observations of a limited range of scattering
angles, can have very different values than the _formal_ asymmetry parameter,
resulting from the complete theoretical computation of the aggregate
properties. Comparing their Fig. 5 (Min et al., 2016) with our results, we
find that for the $H\alpha$ band ($\lambda\sim 0.65\,\mu$m) and for particles
with size $a=$0.4\text{\,}$$ ($r_{\mathrm{V}}$ in their paper), their
effective $g$ parameter is very close to our fit value. To find an effective
$g\sim 0$ value in their results, the particle size increases to
$a=$4\text{\,}$$. And for these particles, the effective $g$ is close to zero
for wavelengths going from $H\alpha$ to $K2$, which is perfectly in line with
our results for the outer ring, across the different datasets we analysed.
Interestingly, for $4\text{\,}$ grains the corresponding formal asymmetry
parameter is around 0.8: the scattering is not at all isotropic, it is
strongly forward scattering. The effective parameter is much lower exactly
because a great amount of light is scattered to small angles that are not
accessible by our observation (same as Min et al., 2016 for a disk inclined of
$None$). The difference between effective and formal asymmetry parameter
should be taken into account when fitting from observations. Min et al. (2016)
conclude that the $g$ parameter is almost only influenced by the size of the
aggregate as a whole, making it a good size indicator. This allows us to
reconcile the results of the phase function fitting with the qualitative
expectations based on the ring detection wavelengths. Thus, we assume that the
outer ring is mainly composed of grains with
$a_{\mathrm{out}}\gtrsim$4\text{\,}$$, while the inner ring consists of grains
with $a_{\mathrm{in}}\lesssim$0.4\text{\,}$$.

A possible caveat to the inner ring $g$ value is that an azimuthally uniform
dust distribution was assumed. A similar brightness variation could in theory
be reproduced by a non-axisymmetric dust ring: the brighter North side could
have a higher particles density, which can be misinterpreted with a stronger
forward scattering component. Finally, we remark again that the ultimate goal
of the phase function fitting was not to constrain the parameter $g$ itself,
but to find a proxy for the grain size differences between inner and outer
ring. Constraining the real value of the asymmetry parameter $g$ is a tricky
task, based on single-angle observations, and depends on the adopted
scattering phase function, together with the assumptions on grain size
distribution.

###  4.2 A challenging dust segregation

The grain size difference, inferred from the scattering phase functions and
discussed in Sec. 4.1, requires a physical mechanism responsible for the
observed segregation. Dust segregation might be caused by a giant planet
creating a pressure bump outside its orbit and the gap between the two rings.
A pressure bump acts as a filter for larger grains, preventing their inward
migration, while allowing smaller dust particles to filter through and
populate the inner regions (Rice et al., 2006; Zhu et al., 2012; Pinilla et
al., 2012, 2016). However, this filtering is more efficient for particles
close to millimetre size and above, since smaller dust has a stronger
diffusion and is more coupled to the gas component. The depth of the gap
increases with the mass of the planet, filtering out progressively smaller
dust grains (Zhu et al., 2012). The dust size deduced from our observations of
HD 34700 A is approximately two orders of magnitude smaller than the
thresholds of Zhu et al. (2012) for effective filtering, as a general
reference. Due to turbulent diffusion, in fact, they found that even a
$6\text{\,}\mathrm{M}_{J}$ planet can only segregate dust bigger than
$100\text{\,}$.

The presence of more massive planets between the system’s rings would be
discouraged by the contrast estimates of both this work (Sec. 3.8) and Uyama
et al. (2020), but cannot be excluded. The limiting contrast, as a matter of
fact, provides the minimum planetary mass that can be seen in front of the
local background (actually averaged on circular annuli). If, for any reason, a
compact object is embedded into a dust structure, the contrast limits may be
misleading, as the emitted radiation is extincted within the dust cloud, with
sufficient optical depth. In this regard, then we must admit the difficulty of
ruling out the presence of planets with masses $\gtrsim 6\,\mathrm{M_{J}}$ in
a complex system as HD 34700 A. For example, the mm-dust structure seen from
the mm-data might be hiding a compact object, whose light could be completely
absorbed by the dust around it. This object would be more massive than our
limiting contrasts foresee. Having said that, the possibility that the mm-dust
substructure consists of a vortex with no compact object inside is also valid
(e.g., Zhu & Stone, 2014). Longer-wavelength observations, using e.g. the JWST
Mid-Infrared Instrument (MIRI), might help reduce the extinction from the dust
around a hypothetical compact object and better constraining its mass. Anyway,
in terms of dust segregation, consistently with the studies of Zhu et al.
(2012), Pinilla et al. (2012), the observed mm-dust structure retains much
larger grains than those revealed by IRDIS images in the outer ring. The
latter, in fact, does not seem dramatically altered by the trap.

Lastly, if dust filtration is not effective for micrometre-sized grains, the
difference in composition between the two rings could be regulated by
growth/fragmentation and radial drift dynamics at the two sides of the gap. In
particular, starting from an ideally homogeneous grain size distribution in
both rings, we can argue that the presence of the gap, although it does not
prevent the filtration of -dust from outer to inner ring, enhances the
efficiency of grain growth near the pressure bump (Pinilla et al., 2012). This
would result in an increased size of the dust observed in the outer ring
($\geq 4\text{\,}$) compared to the inner ($\leq 0.4\text{\,}$). In the inner
ring, higher particle speed could lead to increased fragmentation rates. In
addition, the inner ring may also be depleted of ”larger” grains
($\gtrsim$1\text{\,}$$), because of the radial drift. The drift speed, for a
given grain size, depends on the local gas density, which sets the Stokes
number (see e.g. Birnstiel & Andrews, 2014; Andrews, 2015). For HD 34700 A,
then, the grains $\gtrsim$1\text{\,}$$ may be depleted from the inner ring
much faster than those $<$1\text{\,}$$ and also faster than their growth
timescales. Eventually, the inner ring would be left only with the smallest
grains, $\leq$0.4\text{\,}$$. Detailed theoretical simulations of this disk
are required to settle this argument quantitatively, taking into account also
the effects of vertical dust distribution. We save a similar approach for
future studies.

###  4.3 Spiral arms excitation

In Sec. 3.3 we analysed the spiral structures observed in the disk of HD 34700
A. The literature on spiral arms is solid on the theoretical side, where
simulations are able to produce spiral perturbations as a result of several
different physical causes, such as planets (Zhu et al., 2015; Zhu & Zhang,
2022), flybys (Smallwood et al., 2023; Cuello et al., 2023), binarity (Calcino
et al., 2023), gravitational instability (Forgan et al., 2018) and vortices
(Paardekooper et al., 2010; Huang et al., 2019). Observationally, however, it
is difficult to determine the cause of a given spiral wake, as the spiral
morphology can be degenerate (see, e.g., Forgan et al., 2018; Bae et al.,
2022). In general, the presence of a compact object in a disk is manifested
through inner and outer spiral wakes. The outer wakes have a vanishing pitch
angle with increasing radius. With enough spatial resolution, the pitch angle
is expected to peak near the position of the perturber, theoretically reaching
values near $None$, with heavier objects yielding larger angles (Zhu et al.,
2015). Real spiral wakes most often do not adhere to a simple analytical
shape. The spiral fitting is relevant in the context of describing a
qualitative overall morphology and providing the pitch angle’s behaviour.
Addressing first the outer ring itself: the pitch angle is higher at smaller
radii, in the $$$<\phi<$$$ quadrant, but is limited to moderate values
($None$). The substructures above the outer ring (not fitted), assuming they
are spiral arms, show a much higher pitch angle. Zhu & Zhang (2022)
demonstrated how eccentric massive planets can have a strong impact on the
shape of spiral wakes, creating complex overlapping patterns. They themselves
mention that HD 34700 A’s spirals would be naturally produced by an eccentric
perturber.

Concerning arms C1 and S1, they stand out from the rest of the disk for their
extension and their large pitch angles $\gtrsim$$$. Based on the similarities
we found between C1 and S1, it seems reasonable to assume a physical
connection between them. Overall, their growing slope with increasing radius
would point to a perturber outside the observed disk, such as a bound compact
object or a flyby event. Uyama et al. (2020) already suggested a flyby between
HD 34700 A and B components, which should have been closer in the past 8000
years, as they infer from proper motion calculations. On the one hand,
simulations of Cuello et al. (2020) and Cuello et al. (2023) show that flybys
indeed produce large scale regular spiral patterns with large pitch angles. On
the other hand, they found that these induced spiral arms lasted only for a
few dynamical times after the flyby (which happens only once), translating to
a typical dissipation time of a few thousand years.
$8000\text{\,}\mathrm{y}\mathrm{r}$ could then push the upper limit on
survival time, although not ruling it out. On a side note, if the flyby is
close enough, the perturber can steal some dust and create a disk of its own
(Cuello et al., 2023). If HD 34700 B was the flyby perturber and has the same
age as the C component (as expected), this could explain why we do see a mm-
dust disk around B and not around C, in the ALMA continuum data. One last
hypothesis for the creation of C1 and S1 spirals involves the possibility of
accreting new interstellar matter from cold gas clouds, which we illustrate
separately in the next section.

###  4.4 Cloudlet capture and late infall

At a crossroad between dust segregation and ring morphology, we mention the
possibility of a late accretion event (see e.g. Ginski et al., 2021; Mesa et
al., 2022). It is possible for a young star moving through a heterogeneous
formation environment (giant molecular clouds) to encounter condensations of
cold insterstellar gas, or _cloudlets_ (Dullemond et al., 2019). Whether the
primordial disk is already depleted or is still present, the freshly captured
gas will evolve to form a new disk around the central star. Referring to the
work of Kuffmeier et al. (2020), we can find similarities between the
appearance of the newly formed disk and HD 34700 A. In particular, the
simulations illustrated in Fig.6 of Kuffmeier et al. (2020), display a wealth
of spiral arms due to the infall of the cloudlet gas, creating a ”flocculent”
new disk that qualitatively resembles the outer ring of HD 34700 A. Moreover,
peculiar to cloud capture is the creation of a widely extended and sparse
spiral arm, connecting the original gas cloud to the material condensing
around the star (as shown in the different simulations of Kuffmeier et al.
2020). The spiral arm C1 analysed in Sec. 3.3, may result from a similar
cloudlet capture event. We might also interpret the HD 34700 A inner ring as
the remains of a primordial disk (ALMA data point to a high depletion of mm-
sized grains in the disk) and the outer ring and spirals as the results of a
late infall event. This hypothesis might provide a reasonable justification
for the wildly different morphology of the two rings and the properties of
their dust grains. Some caveats of this argument concern the intrinsic
properties of the interstellar dust captured, which should be more pristine
than the processed material of the original disk, and the interaction between
a pre-existing disk and the captured gas. Considering statistically random
orientations for the star-cloudlet encounter and for their angular momenta,
the creation of a new ring lying on the same plane as the pre-existing disk,
without disrupting it, might be an unlikely coincidence. Lastly, the outermost
shells of the gas cloud can sometimes be detected as extended reflection
nebulosity near the star, as for the case of FU Orionis (Dullemond et al.,
2019) or SU Aur (Ginski et al., 2021). We did not observe similar features
around HD 34700 A, but the capture conditions are relevant in this regard and
may not apply to our case. Overall, the late infall scenario cannot be ruled
out.

##  5 Conclusions

We have reported the discovery of a new ring within the disk of the binary
star HD 34700 A. This new inner ring was detected thanks to SPHERE/ZIMPOL
instrument in the $H\alpha$ band, at shorter wavelengths than the already
known outer ring (which is bright also in the $J$, $H$ and $K$ bands). The
variety of substructures in this disk suggests the presence of several disk-
shaping mechanisms acting simultaneously. We argue that the disk inner
features (ring shapes, gaps, dust segregation, mm-dust asymmetry) may be
shaped by a not-yet-seen companion of a few Jupiter masses, whereas the outer
disk morphology and the extended spirals may be created by either cloudlet
capture or flybys. We summarise in the following the key findings of this
work:

  * •

We resolved an inner ring extending approximately from $65\text{\,}$ to
$120\text{\,}$, with a $PA\approx$$$. It is likely to be a slightly eccentric
ring, based on the centre offset with respect to the host stars.

  * •

The LoS inclination inferred for the inner ring ($None$) is compatible with
those of the outer ring and of the binary host (with the caveat of unknown PA
for this). This suggests a strong coplanarity of the whole system, up to large
radial separations of hundreds of au.

  * •

We find a sharp segregation in the dust populations of the two rings. Based on
the rings detection passbands and the effective scattering asymmetry
parameters, the typical grain sizes may differ by one order of magnitude
between the inner and outer ring, which may then consist of aggregates roughly
of $\lesssim$0.4\text{\,}$$ and $\gtrsim$4\text{\,}$$, respectively.

  * •

We detected two very extended spiral arms with similar shapes and high pitch
angle ($\gtrsim$$$), at opposite sides of the disk. We cannot rule out either
the flyby or the cloud capture scenarios as potential excitation mechanisms.

  * •

The outer ring appears as a spiral arm itself, with a varying radial distance
from the star and complex substructures. It is not clear whether the two rings
are spatially contiguous.

  * •

We obtained the CO velocity map for HD 34700 B and find that the latter
rotates with a completely different orientation than the A component. No CO or
mm-dust streamer could be resolved between A and B, from our ALMA data.

The mechanisms responsible for dust segregation still require further
investigation, but there are hints of intense hydrodynamical perturbations in
the disk of HD 34700 A. One or more compact objects with several Jupiter
masses could be responsible for carving the gap between the rings, creating
the mm-dust crescent and possibly segregating the dust grain sizes to some
extent. The dust inward migration, diffusion, and accumulation in the pressure
maxima could have a particular equilibrium, giving rise to the differentiated
rings of this system. In addition, the inner ring cavity is too large to be
carved by the tight binary star, so other processes must be at work to explain
that. We cannot rule out the presence of substellar companions, based on our
detection limits, but future observations with greater sensitivity instruments
(JWST or the future ELT) may hold the key. Alternatively, higher spectral and
spatial resolution ALMA data may find kinematic anomalies within the disk, or
_velocity kinks_ , as described by Perez et al. (2015). This technique has
already detected several potential signatures of giant planets and can be used
also for embedded bodies (see, e.g., Teague et al., 2018; Pinte et al., 2020,
2022). We save for future studies the further characterisation of some
features in the disk of HD 34700 A which were not yet conclusively framed and
that could be key elements for creating a complete physical model of this
system.

###### Acknowledgements.

This work has been partially supported by the Large Grant INAF 2022 YODA (YSOs
Outflows, Disks and Accretion: towards a global framework for the evolution of
planet forming systems). The LBT is an international collaboration among
institutions in the United States, Italy and Germany. LBT Corporation partners
are: The University of Arizona on behalf of the Arizona Board of Regents;
Istituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft,
Germany, representing the Max-Planck Society, The Leibniz Institute for
Astrophysics Potsdam, and Heidelberg University; The Ohio State University,
representing OSU, University of Notre Dame, University of Minnesota and
University of Virginia. We acknowledge the use of the Large Binocular
Telescope Interferometer (LBTI) and the support from the LBTI team,
specifically from Amali Vaz, Jared Carlson, Jennifer Power, Steve Ertel. This
publication makes use of VOSA, developed under the Spanish Virtual Observatory
project supported from the Spanish MICINN through grant AyA2008-02156. This
work has made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. T.B. acknowledges funding
from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme under grant agreement No 714769 and
funding by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under grants 361140270, 325594231, and Germany’s Excellence
Strategy - EXC-2094 - 390783311. S.F. is funded by the European Union under
the European Union’s Horizon Europe Research & Innovation Programme 101076613
(UNVEIL). Ch. Rab is grateful for support from the Max Planck Society and
acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) - 325594231. A.R. has been supported by the UK Science
and Technology research Council (STFC) via the consolidated grant ST/W000997/1
and by the European Union’s Horizon 2020 research and innovation programme
under the Marie Sklodowska-Curie grant agreement No. 823823 (RISE DUSTBUSTERS
project). This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation
programme (PROTOPLANETS, grant agreement No. 101002188), as well as under the
Horizon Europe research and innovation program (Dust2Planets, grant agreement
No. 101053020). A.Z. acknowledges support from ANID – Millennium Science
Initiative Program – Center Code NCN2021_080

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##  Appendix A Additional figures

We add to this appendix a few extra figures to complement the already numerous
figure within the text.

In Figure 10 we show for completeness the Stokes parameters frames for the
IRDIS H-band data of 2019. These have been illustrated with a composite
logarithmic colour scale that helps to highlight the faint features of the
frames.

In Figure 13 and Figure 14 we show the results of the phase fitting procedure
on other two datasets for the outer ring(in addition to the one shown within
the main text). These allow one to form a more complete panoramic of the
scattering properties of the outer dust, and extend the wavelength domain
where this study was performed.

We show the contrast limit curve for the IFS non-coronagraphic data reduction
of the 26-11-2021 in Figure 11. The relative signal-to-noise image map is
shown in Figure 12. These allowed us to search for stellar companions in the
vicinity of the central binary, as described in Sec. 3.2.3. The limits
obtained from the 14-11-2021 data were of worse quality, and we did not show
them.

Finally, in Figure 15 and Figure 16 we illustrate respectively the gas
velocity and continuum emission obtained from the ALMA data. These images show
both the A and B components of HD 34700 in the same FoV, to highlight their
differences.

Figure 10:  Stokes parameters frames for the polarimetric observation of HD
34700 A with IRDIS in the $H$ band. The subplots are, in order: the $Q$, $U$,
$Q_{\phi}$ and $U_{\phi}$ frames, as overlaid in white text. The colour scale,
shared between all four frames, is a symmetric logarithmic function, chosen to
display all the fainter details. The coordinates are reported as delta offsets
with respect to the nominal position of the central star.

Figure 11:  Contrast limit curves as a function of the distance from the
central star HD 34700 A, for the inner system region (see Figure 12). The blue
shaded area represents the inner ring (partially), while the coloured lines
the contrasts for the three IFS broad bands (see plot legend). These were
obtained from the IFS flux calibration frames, with no coronagraph. Below
$42\text{\,}\mathrm{m}\mathrm{a}\mathrm{s}$ self-subtraction becomes more
significant and thus this range was excluded.  Figure 12:  Map of the signal-
to-noise ratio, relative to the ADI-like reduction described in Sec. 3.2.3 on
the 26-11-2021 IFS observation of HD 34700 A. The central blue circle masks
the area within 1.3 $\lambda/D$, where self-subtraction is significant. The
colourbar indicates the SNR level. A couple of higher-SNR points on the
Western side may be spurious speckles; no reliable point-source is detected in
this reduction. North is up and East to the left.  Figure 13:  Analysis of the
total intensity scattering brightness of the outer ring on the iRDI K band
data. _Top:_ median radial brightness of the ring (yellow), as a function of
the azimuth angle on the disk plane ($None$ is North), normalised to the
maximum. _Middle:_ residues of the data to the best fit function, with grey
arrows pointing towards the candidate shadow features. _Bottom:_ IRDIS
$Q_{\phi}$ data transformed to polar-coordinates and corrected for the $r^{2}$
flux dilution, from which the median brightness of the top panel was
extracted. The best fit asymmetry parameter was $g=+0.04\pm 0.01$. Figure 14:
Analysis of the polarised scattering brightness of the outer ring on the
ZIMPOL data. _Top:_ median radial brightness of the ring (yellow), as a
function of the azimuth angle on the disk plane ($None$ is North), normalised
to the maximum. _Middle:_ residues of the data to the best fit function.
_Bottom:_ IRDIS $Q_{\phi}$ data transformed to polar-coordinates and corrected
for the $r^{2}$ flux dilution, from which the median brightness of the top
panel was extracted. The best fit asymmetry parameter was $g=-0.03\pm 0.01$.
Figure 15:  ALMA data velocity map, obtained from the 12CO molecular lines,
illustrating in the same FoV both HD 34700 A and B (on the right and on the
left, respectively). North is up and East is left. The yellow cross marks the
A star position. Gas rotation is detected in the B component as well, although
with a weaker SNR. The directions of rotation of the two gas disks are
different, as are their PA in the sky plane. The beam is $$$\times$$$ at a PA
of $None$. The gas speed values refer to the Local Standard of Rest.  Figure
16:  ALMA 1.3 mm continuum emission contours, including in the same FoV both
HD 34700 A and B (on the right and on the left, respectively). North is up and
East is left. The yellow cross marks the A star position. The emission around
A is asymmetric and off-centre, whereas around B is centred and elliptical.
The beam is $$$\times$$$ at a PA of $None$.