<figure><img src="image_1.png" /></figure>

# Planet Formation in AB Aurigae: Imaging of the Inner Gaseous Spirals Observed inside the Dust Cavity

Ya-Wen Tang<fnref n="1" />, Stephane Guilloteau<fnref n="2" />, Anne Dutrey<fnref n="2" />, Takayuki Muto<fnref n="3" />, Bo-Ting Shen<fnref n="4" />, Pin-Gao Gu<fnref n="1" />, Shu-ichiro Inutsuka<fnref n="5" />, Munetake Momose<fnref n="6" />, Vincent Pietu<fnref n="7" />, Misato Fukagawa<fnref n="8" />, Edwige Chapillon<fnref n="2" />,<fnref n="7" />, Paul T. P. Ho<fnref n="1" />, Emmanuel di Folco<fnref n="2" />, Stuart Corder<fnref n="9" />, Nagayoshi Ohashi<fnref n="1" />, and Jun Hashimoto<fnref n="1" />

Received 2016 November 30; revised 2017 March 14; accepted 2017 March 30; published 2017 May 2

## Abstract

We report the results of ALMA observations of a protoplanetary disk surrounding the Herbig Ae star AB Aurigae. We obtained high-resolution (0.′′1; 14 au) images in $^{12}$CO $J = 2 - 1$ emission and in the dust continuum at the wavelength of 1.3 mm. The continuum emission is detected at the center and at the ring with a radius ($r$) of ~120 au. The CO emission is dominated by two prominent spirals within the dust ring. These spirals are trailing and appear to be about 4 times brighter than their surrounding medium. Their kinematics is consistent with Keplerian rotation at an inclination of 23°. The apparent two-arm-spiral pattern is best explained by tidal disturbances created by an unseen companion located at $r$ of 60–80 au, with dust confined in the pressure bumps created outside this companion orbit. An additional companion at $r$ of 30 au, coinciding with the peak CO brightness and a large pitch angle of the spiral, would help to explain the overall emptiness of the cavity. Alternative mechanisms to excite the spirals are discussed. The origin of the large pitch angle detected here remains puzzling.

**Key words:** planet–disk interactions – protoplanetary disks – stars: individual (AB Aurigae)

## 1. Introduction

Recent large facilities such as ALMA, HiCIAO/SUBARU, and SPHERE/VLT have revealed complex gas and dust structures, such as large cavities, asymmetries, and spiral patterns in protoplanetary disks, thanks to their high sensitivity and resolving power. The spiral-like features, either observed in the millimeter (mm) and sub-millimeter wavelengths or in the optical and infrared (IR) scattered light, are found around, for example, HD163296 (Grady et al. 2000; Fukagawa et al. 2010), HD100546 (Grady et al. 2001; Quanz et al. 2011), HD142527 (Fukagawa et al. 2006; Christiaens et al. 2014), HD97048 (Doering et al. 2007), MWC758 (Isella et al. 2010; Grady et al. 2013; Benisty et al. 2015), HD135344B (Muto et al. 2012), Elias 2–27 (Pérez et al. 2016), and HD 141569A (Clampin et al. 2003; Perrot et al. 2016).

These spirals may appear reasonably regular, asymmetric or more reminiscent of faint discontinuous disks. The origin is basically due to gravitational disturbances, either via planet–disk interactions (e.g., Zhu et al. 2015) or gravitational instabilities inside a massive disk (Kratter & Lodato 2016). The resulting structures can be very complex (Dipierro et al. 2014; Dong et al. 2015; Flock et al. 2015; Pohl et al. 2015). Nevertheless, spiral-like features are expected to reveal disturbers, such as embedded planets, which cannot be yet directly observed when the gas of the disk is not fully dissipated.

Located at 140 pc, AB Aurigae (hereafter AB Aur) is one of the closest Herbig Ae stars of the A0 spectral type $V_e (2.4 \pm 0.2 M_\odot, DeWarf et al. 2003)$ and it shows an extended reflection nebula at large scales (100s au). This young star is unique, because it exhibits a very small inner disk (~2–5 au) observed in near-IR (NIR) and mid-IR interferometry (di Folco et al. 2009), surrounded by a large cavity of radius ~70 au based on the CO and mm continuum observations (Piétu et al. 2005), and a CO gas and dust-rotating ring from which external spirals are observed both in the NIR (Fukagawa et al. 2004) and in the mm domain (Tang et al. 2012). The inclination of the inner and outer disks slightly varies from 23° at 20 au to 29° at 100 au scales (Tang et al. 2012). The accretion rate observed for AB Aur ($1.3 \times 10^{-7} M_\odot \text{ yr}^{-1}$; Garcia Lopez et al. 2006; Salyk et al. 2013) is still high given the estimated age of the star (about 4 Myr).

The large-scale spirals detected at optical/NIR wavelengths (Grady et al. 1999; Fukagawa et al. 2004) extend from 100 au up to 500 au. The extended CO emission mapped by the IRAM array also reveals large-scale spirals. Tang et al. (2012) found that, surprisingly, the excess of CO gas along the spirals is apparently counter-rotating with respect to the gaseous disk that Tang et al. (2012) attributed to residual gas being accreted from the envelope high above the disk mid-plane. Such a scenario is also reminiscent of the asymmetric accretion suggested for some Class 0 sources by Tobin et al. (2011).

At small scales, the wide dust gap, the warped disk (change in inclination from small to large scales by about 6°–10°), and

<footnote n="1">¹Academia Sinica, Institute of Astronomy and Astrophysics, Taipei, Taiwan; ywtang@asiaa.sinica.edu.tw</footnote>

<footnote n="2">²Laboratoire d'astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, alle Geoffroy Saint-Hilaire, F-33615 Pessac, France</footnote>

<footnote n="3">³Department of Physics, National Taiwan University, Taiwan</footnote>

<footnote n="4">⁴Division of Liberal Arts, Kogakuin University, 1-24-2 Nishi-Shinjuku, Shinjuku-ku, Tokyo 163-8677, Japan</footnote>

<footnote n="5">⁵Department of Physics, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan</footnote>

<footnote n="6">⁶College of Science, Ibaraki University, 2-1-1 Bunkyo, Mito, Ibaraki 310-8512, Japan</footnote>

<footnote n="7">⁷IRAM, 300 rue de la Piscine, Domaine Universitaire, F-38406 Saint-Martin-d'Hères, France</footnote>

<footnote n="8">⁸Division of Particle and Astrophysical Science, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan</footnote>

<footnote n="9">⁹National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA</footnote>

<footnote n="10">¹⁰Subaru Telescope, National Astronomical Observatory of Japan, 650 North Aohoku Place, Hilo, HI 96720, USA</footnote>

<footnote n="11">¹¹Astrobiology Center of NINS 2-21-1, Osawa, Mitaka, Tokyo, 181-8588, Japan</footnote>
the asymmetric dust ring (an intensity contrast of 3 is observed inside the mm dust ring) suggest the existence of at least one undetected companion with a mass of 0.03 $M_{\odot}$ at a radius of 45 au (Tang et al. 2012).

Motivated by such complex structures, we obtained ALMA observing time in Cycle 3 to image at very high angular resolution ($<0''1$) the close environment of AB Aur in CO and in the mm continuum. In this paper, we report the observations (Section 2) and the results (Section 3) of these data and then discuss them with respect to recent studies and models of planet-disk interactions (Section 4). For simpler comparison with previous work, we assume a distance of 140 pc, although the GAIA DR1 release indicates $153 \pm 10$ pc (Gaia Collaboration et al. 2016).

## 2. Observations

The observations were carried out with ALMA in Cycle 3 (project "2015.1.00889.S") with two execution blocks on 2015 November 5 and 10, respectively. The array included 45 and 46 of the 12 m antennas, respectively. The baselines ranged from 78.1 m to 15.5 km. The gain calibrator (phase) is J0512+2927, which is $3^\circ$83 away from AB Aur and was observed with a cycle time between AB Aur and J0512+2927 of 1 minute. The bandpass calibrator was J0510+1800. The absolute flux level is referenced to J0423$-$0120 and J0510+1800 for which flux densities of 0.77 Jy and 3.42 Jy, respectively, were determined by the ALMA monitoring program. The flux calibration is expected to be accurate at the 10% level.

The calibrations were done by EA ARC using CASA 4.5. A secondary calibrator, J0518+3306, was observed every 15 minutes in order to verify the position accuracy. It lies $5^\circ$38 eastward of AB Aur, and is $3^\circ$83 away from the phase calibrator J0512+2927. After standard calibration, the position difference between the known coordinate and the apparent position of the secondary calibrator is $0''$019 and $0''$036 for the two execution blocks. We conclude that the absolute positioning accuracy of this experiment is limited to $\sim 0''$03.

After calibration, the data were exported to the GILDAS package for further analysis. The detected central continuum peak of AB Aur at 1.3 mm is offset by ($-5 \pm 0.3, -10 \pm 0.4$) mas from the stellar location, taken from the *Hipparcos* reduction of van Leeuwen (2007). As this offset is of the same order as that seen for the secondary calibrator, it is likely due to the absolute position uncertainties. We assume that the continuum peak and the stellar positions are identical.

The presented data have been corrected for the proper motion with the values of (2.63, -24.73) mas yr$^{-1}$ given by van Leeuwen (2007), and shifted to the epoch of 2000.0 for comparison with earlier work. All the presented maps are centered on the 1.3 mm continuum peak, which is at $(\alpha, \delta) = (04:55:45.85, 30:33:04.30)$. The maps of $^{12}$CO 2–1 have a spectral resolution of 0.71 km s$^{-1}$ and a sensitivity of 1.60 mJy per $0''$11 × $0''$08 beam (4.6 K). The effective sensitivity ($1\sigma$, including dynamic range limitations) of the continuum emission is 33 µJy per $0''$14 beam (0.04 K).

## 3. Results

### 3.1. Continuum Emission

The continuum emission at 1.3 mm is detected at the $60\sigma$ level toward the center, and is clearly detected at the dust ring (Figure 1(b)). The total detected flux density is 16.4 mJy, which is 20% of the reported flux density of 80 mJy at 1.3 mm from

our previous detection with shorter baselines (Tang et al. 2012). This suggests that the missing 80% of the flux is at a scale larger than $2''$1, which is determined by the shortest baseline of our observation. This missing flux at a scale larger than $2''$1 corresponds to a maximum brightness of the dust ring of $\sim 0.2$ mJy per $0''$14 beam. Accounting for this missing flux, the contrast in the dust ring between the brightest regions in the South-eastern part and the rest can be as low as about 3, although Figure 1(a) displays an apparent contrast around 5. The dust ring is consistent with a circular structure of radius $\sim 120$ au, inclined at $\sim 23^\circ$ with the same axis as that derived from the gas kinematics by Piétu et al. (2005), and centered on the star. More precise values of the ring parameters are actually derived from higher sensitivity, lower angular resolution observations at 0.9 mm (Y.-W. Tang et al. 2017, in preparation).

We model the central continuum peak with an elliptical disk in the visibility plane. The best-fit disk diameter is found to be $\sim 11$ au. The flux density is 2.1 mJy, which is larger than the previous detected value of 1.3 mJy with the IRAM interferometer (Tang et al. 2012). The difference is at a $3\sigma$ level when accounting for the flux calibration accuracy. Furthermore, the different spatial filtering properties of the two observations may also contribute to the measured differences, especially since the IRAM observations did not clearly separate the central continuum from the dust ring emission. We note that the total central continuum emission is about 3.4 mJy within the inner $0''$6 region and the emission appears extended at the level of SN ratio of 3.

The nature of the central continuum emission is unclear. There is an elongated emission at 3.3 cm that was detected with signal-to-noise ratio of 4 along PA of $\sim 170^\circ$ and was suggested as free-free jet by Rodríguez et al. (2014). The total flux density of the jet is reported to be 0.8 mJy at 7 mm. Assuming a spectral index of 0.6 for the jet, this free-free emission would give 2.2 mJy at 1.3 mm within the central $1''$. About 65% of the emission at 1.3 mm (2.1 mJy from the inner disk and 1.3 mJy from the faint emission) can come from free-free emission.

### 3.2. CO Gas

Previous observations of AB Aur in CO 2–1 and 3–2 at angular resolutions of $\sim 0''$5 – $1''$ (Piétu et al. 2005; Lin et al. 2006) revealed that most of the gas was in a large outer disk surrounded by an extended envelope (Tang et al. 2012). The disk displayed an inner radius of 45–77 au (Piétu et al. 2005) depending on the isotopologue being observed, although some $^{12}$CO emission was associated with the unresolved inner dust disk (Tang et al. 2012). Large-scale CO “spirals,” extending outside the dust ring into the envelope, were reported in Lin et al. (2006) and Tang et al. (2012). Their kinematics suggest that these features trace gas infalling onto the ring from well above and below the disk mid-plane (Tang et al. 2012). On the other hand, a recent analysis of the NIR images, which uses the spectral-energy-distribution fitting, argued that these large-scale spirals can be disk-related (Lomax et al. 2016). In any case, all structures reported in these earlier studies are at $r > 100$ au and beyond.

In contrast, the new high angular resolution (about $0''$1) and high sensitivity (noise of 4.6 K) $^{12}$CO 2–1 images obtained with ALMA (Figure 1) reveal that most of the detected emission here is inside the dust cavity, within 90 au from the star. The $^{12}$CO 2–1 emission at various velocities $v_{LSR}$ (i.e.,
<figure><img src="image_2.png" /><figcaption>**Figure 1.** (a) Moment 0 map of CO 2–1 (contours) and 0.9 mm continuum (color scale; units of mJy per 0.′′3 beam; Y.-W. Tang et al. 2017, in preparation). The cyan box marks the zoomed-in area shown in panels (c) and (d). The triangle marks the possible locations of the planets. (b) Continuum emission at 230 GHz (1.3 mm) (contours) and the moment 0 map of CO (color scale; units of mJy/beam km s⁻¹, where the beam is 0.′′11). The contours are −6σ, −3σ, 3σ, 15σ, 30σ, and 50σ, where 1σ is 33 µJy per 0.′′14 beam (0.04 K). (c) Moment 0 (black contours) and moment 1 with $v_{sys}$ subtracted (color scale; units of km s⁻¹) maps of CO with an angular resolution of 0.′′11. Continuum emission at 1.3 mm with 0.′′03 × 0.′′07 beam (marked in the lower right corner) is shown in thin blue contours at 10σ, 20σ, 30σ and 40σ, where 1σ is 27 µJy/beam. The white and black arcs mark the best-fit spirals. (d) Moment 0 map of CO (white contours) and a polarized intensity image at NIR (color scale, arbitrary units; adopted from Hashimoto et al. 2011). The cyan contours are the same as those in panel (c). A scale bar of 30 au is marked at each upper left corner. In panels (a), (c), and (d), the black contours are 2, 4, 6, 8, and 10 × 6.15 (mJy/beam km s⁻¹). The angular resolutions of the color image and contour image are marked as ellipses in the lower left and lower right corners, respectively, in panels (a), (b), and (c).</figcaption></figure>

channel maps) is shown in Figure 2. Figure 1 clearly shows that the CO gas is inside the dust ring and there is no apparent connection with the large CO disk and the extended CO spirals mentioned in the previous works. This apparent lack of connection may, however, be partly an artifact due to our uv coverage. Any extended and smooth emission larger than about 2.′′1 would have been filtered out. Only compact CO features, such as spirals or rings, remain detectable.

Some idea of the impact of this filtering can be obtained by comparing with the results from Tang et al. (2012), which included short spacings from the IRAM 30 m single dish map. Smoothing our data to the same angular resolution as in Tang et al. (2012)

(0.′′56 × 0.′′42) shows that we are only recovering 25% of the line flux in the $v_{LSR}$ range of 2–5 and 7–10 km s⁻¹. Near the systemic velocity ($v_{sys}$ of 5.85 km s⁻¹) in $v_{LSR}$ of 5–7 km s⁻¹, the missing flux problem is more severe. Given the typical brightness measured by Tang et al. (2012) of 50 K, we estimate that the measured brightness (at the velocity where the emission peaks) should be de-biased by adding about 20–30 K, as a first-order correction for missing flux.

### 3.2.1. General Features

The detected ¹²CO 2–1 gas emission peaks at position P1 (see Figure 1), about 30 au from the star, where the peak
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Channel maps of $^{12}$CO 2 − 1. The contours denote the brightness temperature from −6σ, −3σ, 3σ to 15σ by 3σ, where 1σ is 4.6 K (or 1.6 mJy per 0.′′11 × 0.′′08 beam). The segments mark the major (PA of 54°) and minor axes (PA of −36°) of the disk. $v_{LSR}$ is labeled in the lower right corner of each panel.</figcaption></figure>

brightness temperature, $T_B$, is 70 K at $v_{LSR}$ of 8.32 km s$^{-1}$. At this distance, following Piétu et al. (2005), we assume CO traces gas at a temperature of 140 K. With a line width of 1 km s$^{-1}$ and optically thin emission, the column density of CO gas is $10^{17}$ cm$^{-2}$ (surface density, $\Sigma_{gas}$, $10^{-2}$ g cm$^{-2}$) for a $T_B$ of 70 K, which, for a CO gas abundance of $10^{-4}$ with respect to H$_2$, gives a total gas mass of 0.03 $M_\oplus$ in one beam. As the CO gas emission is at least partially optically thick, this gas mass is only a lower limit. The non-detection of C$^{18}$O 3–2 (3σ upper limit) indicates an upper limit for the mass that is 180 times larger (an abundance ratio of CO to C$^{18}$O of 560), 5.4 $M_\oplus$.

The integrated intensity (moment 0) map of the $^{12}$CO 2 − 1 emission appears asymmetric with respect to the central star (Figure 1). The emission is patchy, especially in the fainter part, but appears to be spiral-like to the first order. We separate the CO emission into an eastern arm and a western arm for further analysis. The total gas mass of the eastern and western spirals is estimated to be of the order of 1 $M_\oplus$ or more.

To display the radius dependence of these structures, we present in Figure 3(b) the deprojected moment 0 map (see description below) in polar coordinates (r, θ), where r is the distance from the 1.3 mm continuum peak, and θ is the Azimuth counted eastwards from North. Both spirals appear to have a smaller r as azimuth increases, and are thus trailing given the known sense of rotation of the AB Aur disk. The eastern spiral consists of two separated structures, with the structures around an azimuth of 180° having a clearer r dependence.

We further analyze the CO emission as follows. First, the moment 0 map is deprojected with an inclination of 23.2° assuming the position angle (PA) of the disk rotation axis of −36° and is centered on the 1.3 mm continuum peak (Figure 3(a)). We then take the maximum locations of the $^{12}$CO moment 0 image every 5° in θ. We first fit the eastern and western arms with logarithmic spirals in order to search for the best description. For the eastern spiral, the best-fit function is $r(\theta) = 0.′′85 \exp(-21.0\theta)$, where θ is in degrees, and the origin is at (−0.′′01, −0.′′09) from the continuum peak. Note that the data at r < 30 au in the eastern spiral are clearly deviating from the best-fit function. In all the figures the best-fit function of the eastern spiral is not shown at r < 30 au. For the western spiral, the best-fit function is $r(\theta) = 0.′′38 \exp(-12.5\theta)$ and the origin is at the central continuum peak. The results are marked in Figure 3.

### 3.2.2. Kinematics

The highest velocities at which CO gas is detected are $v_{LSR}$ of 0.46 and 15.47 km s$^{-1}$ for the blueshifted and redshifted gas (see Figure 1(a)), respectively. We note that the position centroid of the emission at these high velocities is consistent (within the uncertainty) with the location of the central continuum peak detected at 1.3 mm. Because the peak locations of the high-velocity CO gas appear along the disk plane, this suggests that the high-velocity gas traces the inner CO disk in
explain the observed structures. Such an object located inside
the dust cavity may create both the observed mm cavity and
spiral-like pattern (for example, Zhu et al. 2015).

In Dong et al. (2015), the adiabatic model with a 6 $M_J$ planet orbiting at 50 au of $M_* = 1 M_\odot$ seems to produce structures similar to what we observe here in $^{12}$CO. Scaling to the mass of AB aur ($M_*$ of 2.4 $M_\odot$), the planet would need to have a mass of 14 $M_J$ and be located at an $r$ of 30 au (location P1; see Section 3.2.1; Figure 1(c)), in order to create the observed features if we adopt this model.

This possibility is supported by several unusual features
detected near the location of this putative inner planet at P1.
First, the pitch angle of the eastern spiral becomes large near
this point: large pitch angles are only obtained near the driving
object in planetary-induced spirals. Second, there is a compact
CO emission between velocities $v_{LSR}$ of 9.04 and 11.18 km s⁻¹
(see Figure 2) and the line width is larger than it is elsewhere,
as expected for the streaming motions (gas accretion and jet at
the circumplanetary disk) around the planet (see Gressel
et al. 2013, for example). Finally, there is 1.3 mm continuum
emission with a flux of 110 µJy/beam at the location P1. This
matches the predicted flux densities of the circumplanetary
disks of known planet candidates, of the order of 100 µJy at
1.3 mm (Zhu et al. 2016). However, because the 3.3 cm
continuum flux is 35.9 µJy/beam at this position, we cannot
rule out that the 1.3 mm continuum emission has a contribution
from free-free emission.

However, this scenario faces some difficulties. In an analysis
of the multi-epoch NIR images, Lomax et al. (2016) found no
apparent rotation of the spiral patterns within the 5.8 year time
span of the images. If the spiral patterns are induced by a planet
or companion, this suggests that such an object is located at
$r > 47$ au. However, their first epoch data, using Stokes I only,
is not sensitive to the region around P1 discussed here, so this
result only applies to the other arms. Furthermore, a planet at
P1 cannot simply explain the western spiral, because outward
from the orbit of the driving planet, the perturbation is mostly a
(usually tightly wound) one-armed spiral.

On the contrary, two-armed spirals are easily produced
inside the orbit of the perturbing planet (see Fung &
Dong 2015, for example). In this second scenario, another
possible location of the planet, P2, is at the outer tip of the
western spiral (i.e., at a PA of 180° and $r = 80$ au). In this case,
the spirals seen here are inner spirals, and the two arms are
explained by a single perturber. A planet at this location can
also explain the sharp inner edge of the dust ring seen at
1.3 mm, while there is still a significant amount of µm-sized
dust particles (Hashimoto et al. 2011) within the mm dust
cavity. This is consistent with the picture of dust filtration,
where dust grains larger than 0.1 mm are trapped at the radius
outside of the planet and only small dust grains and gas can
accrete toward the inner disk (Zhu et al. 2012). This location is
also far enough to be consistent with the lack of apparent
rotation of the NIR spiral patterns found by Lomax
et al. (2016).

The main difficulty in this scenario is its failure to explain
the large pitch angle between P1 and the star location. One
possibility would be that the inner disk part of the system is
warped compared to the outer part. Indeed, attributing a single
inclination to the AB Aur system appears challenging. The
inclination angle of the dust ring is 23°, while NIR
interferometric results suggest an inclination of only 20° for

the inner dust disk (Eisner et al. 2004). The larger scale
observations from Piétu et al. (2005) suggest higher inclina-
tions, but fail to reproduce the expected Keplerian velocities. It
appears that the variation of inclination as a function of scale
cannot explain the large pitch angle.

All the spirals induced by planets in simulations appear to
have limited contrast, the maximum being 2:1 in Dong et al.
(2015), for example. The ¹²CO spiral is detected at about the
12σ level (see Figures 3(c) and (d)). Using a 3σ non-detection
of the surroundings, the observed spirals have a contrast of 4:1,
much higher than predictions. However, the missing flux (see
Section 3.2) can easily bring this contrast down to 2:1.
Furthermore, the models predict density contrasts, while we
observe a brightness contrast in the CO $J = 2-1$ line.

The simplest interpretation of the observed contrast is linked
to the vertical thermal gradient in the disk and the expected CO
opacity. The spirals have larger column densities, and the
$\tau = 1$ layer is reached at higher heights in the spirals.
Therefore, the spirals are warmer gas and far from being dense
enough to affect the local scale height. We note that from a
comparison between ¹²CO and ¹³CO, Piétu et al. (2005)
indicated a temperature difference of about a factor of 2
between the lower layer traced by ¹³CO and the ¹²CO surface.
Additionally, the NIR opacity toward the star is much larger
than the CO line opacity along our line of sight. We expect the
scattered light to trace the inner side of the spiral structures,
exactly as seen in Figure 1(d).

These spiral-like patterns are reminiscent of the patterns
expected for planet-induced structures in disks, although the
pitch angle seems relatively large (about 20° for the Western
spiral). Indeed, it is difficult to fit the analytical shape
prescriptions of Rafikov (2002) and Muto et al. (2012) to our
measurement. For the south part of the eastern spiral, we find a
planet location near 28 au at PA 180° (i.e., near the brightest
spot), but the best-fit values for parameters *h/r* at the planet
radius and *β* (the exponent of the velocity law of the sound
speed) are 0.4 and 0.9, respectively. This is inconsistent with
the measured radial temperature profile and expected thickness
of our disk, as derived from hydrostatic equilibrium. The
Western spiral analysis leads to similar difficulties, although a
solution with a planet near 20 au is possible, assuming $\beta = 0$.

Another exciting mechanism of the spiral wave was
suggested by Montesinos et al. (2016), where shadows cast
by a tilted inner disk onto the outer disk cause a drop in
illumination and thus lower temperature locally. The pressure
imbalance further causes a density enhancement. As suggested,
this mechanism could create spiral waves with an opening
angle 10°–15° in the outer disk. We note that the CO spirals
detected here are within the cavity. Furthermore, there is no
evidence for strong tilt of the inner (few au) disk of AB Aur
compared to the observed spirals, so this mechanism is unlikely
to apply to our case.

Spiral patterns can also develop under external disturbances,
like asymmetric accretion (Hennebelle et al. 2017, 2016).
Again, these studies assume a centrally condensed disk,
different from the spirals detected here within the dust ring.
Indeed, for AB Aur, accretion from the outer envelope was
invoked by Tang et al. (2012) to explain the apparent counter-
rotation of the gas in the outer (150–400 au) spirals. However,
the opening angle of the induced spiral pattern is expected to be
on the order of *h/r* in the Hennebelle et al. (2016) model, again
much smaller than our 0.3 radian value.
Thus, while our trailing spirals are highly suggestive of disturbances due to planet-disk interaction or external disturbances, their pitch angle seems difficult to explain. We point out, however, that this apparent opening angle is only defined through a relatively limited range of azimuth (less than 180°). Furthermore, it may be affected by differential filtering of the extended emission at various velocities (see Section 3.2), especially near $v_{sys}$, where the missing flux is largest. The effect of missing flux on the morphology of the detected spirals can be studied by combining new ALMA observations with shorter baselines covering the size-scale of the spirals.

In summary, we report the detection of gaseous spirals within a dust gap for the first time in the transitional disk AB Aur. In contrast to previous detections of the spirals in continuum emission, we are able to probe the kinematics of the spirals, which is mainly Keplerian. We argue that the spirals are most likely triggered by embedded object at two possible locations, either at 60–80 au and/or at around 30 au from the star.

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2015.1.00889.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. This research was partially supported by MOST grant MOST105-2112-M-001-025-MY3. This research was supported in part by the “Programme National de Physique Stellaire” from INSU/CNRS, France.

Facility: ALMA.

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