Strongly Misaligned Triple System in SR 24 Revealed by ALMA

The data analyzed here come from two observations taken in the ALMA Cycle 1 (projects 2013.1.000912.S and 2013.1.00498.S). These projects focused on the study of the SR24S disk properties as inferred from the 1.3 mm (227 GHz) continuum and several CO isotopologues. Here, we explain the geometry of the disks using the continuum emission and the ¹²CO (2-1) and C¹⁸O (2-1) lines. We also discuss the nature of the ¹²CO (2-1) extended emission in the SR24 triple system.

We built a 1.3 mm continuum image and a C¹⁸O (2-1) velocity cube using the data collected on 2015 September 26 (project 2013.1.000912.S). The time on source was 23.3 minutes. At that time, ALMA had 34 operative antennas with baselines ranging up to 2270 m. During the observations, the median system temperature was about 70 K. The phase center was at $(\alpha ,\delta ){\rm{J}}2000.0=({16}^{{\rm{h}}}{26}^{{\rm{m}}}58\buildrel{\rm{s}}\over{.} 506,-24^\circ 45^{\prime} 35\buildrel{\prime\prime}\over{.} 87$), and the FWHM of the primary beam of the telescope was $27^{\prime\prime}$ at the observing frequency. The ALMA digital correlator was set to have two continuum windows (2000 MHz width) and two additional spectral windows (1875 MHz width), most of which where line-free and were hence added to the continuum after removing the line channels. The four windows were centered at 219.550, 220.383, 234.507, and 232.987 GHz. Observations of the asteroid Pallas were used to set the absolute scale for the flux density calibration. The quasar J1517–2422 was used to correct for bandpass and the quasar J1617–2537, observed every 10 minutes, was used to extract the time-dependent gains and calibrate the phases and amplitudes. We self-calibrated and cleaned the final continuum image three times and applied a mask surrounding the two main sources detected in SR24. The data were calibrated, imaged, and analyzed using CASA (McMullin et al. 2007), KARMA (Gooch 1996), MIRIAD (Sault et al. 1995), and GILDAS⁴ packages. The final 7.5 GHz continuum image was obtained using natural weighting. Its synthesized beam is $0\buildrel{\prime\prime}\over{.} 18\times 0\buildrel{\prime\prime}\over{.} 12$ with a ${\rm{P}}.{\rm{A}}.\,=\,71\buildrel{\circ}\over{.} 5$ and its rms noise level is 44 μJy beam⁻¹. The C¹⁸O (2–1) velocity cube was obtained after applying the selfcal solution. The synthesized beam of the C¹⁸O data is $0\buildrel{\prime\prime}\over{.} 21\times 0\buildrel{\prime\prime}\over{.} 16$ with a ${\rm{P}}.{\rm{A}}.\,=\,76\buildrel{\circ}\over{.} 6$ and an rms noise level of 1.2 mJy beam⁻¹ per 1.35 km s⁻¹ channel.

The ¹²CO (2-1) data set was obtained on 2015 July 21 (project 2013.1.00498.S). SR24 was observed with 44 ALMA 12 m antennas for 12.6 minutes, with 946 baselines ranging from 15.1 to 1600 m. During the observations, the median system temperature was about 95 K. The phase center was at $(\alpha ,\delta ){\rm{J}}2000.0=({16}^{{\rm{h}}}{26}^{{\rm{m}}}58\buildrel{\rm{s}}\over{.} 499,-24^\circ 45^{\prime} 37\buildrel{\prime\prime}\over{.} 42$). The ALMA correlator setup included eight spectral windows ranging in frequency from 215 to 233 GHz. One of these windows, centered at 230.714 GHz, covers 469 MHz and contains the ¹²CO (2-1) transition (${\nu }_{\mathrm{rest}}=230.538$ GHz). This spectral window has 1920 channels, providing a spectral resolution of 244 kHz, which results in 0.3 km s⁻¹ at the observing frequency. In this case, Saturn's moon Titan was used as the absolute flux calibrator and the quasars J1517–2422 and J1627–2426 were used to get the bandpass and the gains corrections, respectively. CASA, KARMA, and Miriad were again used to calibrate, image, and analyze the ¹²CO data. Two ¹²CO velocity cubes were obtained. The first velocity cube was obtained after applying a uv-taper to stress the extended ¹²CO emission. This image has a synthesized beam size of $0\buildrel{\prime\prime}\over{.} 60\times 0\buildrel{\prime\prime}\over{.} 54$ with a ${\rm{P}}.{\rm{A}}.\,=\,89\buildrel{\circ}\over{.} 2$, and it has an rms noise level of 4.6 mJy beam⁻¹ in the binned channels of 0.6 km s⁻¹. A second velocity cube was made with a natural weighting, which results in a $0\buildrel{\prime\prime}\over{.} 25\times 0\buildrel{\prime\prime}\over{.} 21$ with a ${\rm{P}}.{\rm{A}}.\,=\,61\buildrel{\circ}\over{.} 3$ synthesized beam and an rms noise level of 5.2 mJy beam⁻¹ per 0.6 km s⁻¹ channel.

The observations were obtained with the Submillimeter Array⁵ during 2004 August 2, when the array was in its compact configuration. The data were taken with seven antennas and double-sideband receivers with an IF frequency of 225.494 GHz. The zenith opacity (τ at 230 GHz) measured with the NRAO tipping radiometer located at the Caltech Submillimeter Observatory was ∼0.1, which indicates good weather conditions. The ¹²CO(2-1) millimeter line at a frequency of 230.538 GHz was centered in the upper sideband. The digital correlator of the SMA was configured with 2 GHz bandwidth in each sideband and a spectral resolution of 1.06 km⁻¹ (∼0.8 MHz) per channel. The phase center was at $(\alpha ,\delta ){\rm{J}}2000.0=({16}^{{\rm{h}}}{26}^{{\rm{m}}}58\buildrel{\rm{s}}\over{.} 5,\,-24^\circ 45^{\prime} 36\buildrel{\prime\prime}\over{.} 67$. Both objects SR24S and SR24N fall well inside of the SMA FWHM ($57^{\prime\prime}$) for this wavelength. The total on-source integration time for SR 24 was 1.7 hr.

Observations of Uranus provided the absolute scale for the flux density calibration. The gain calibrators were the quasars J1743−038 and J1733−130, while Callisto was used for bandpass calibration. The uncertainty in the flux scale is estimated to be between 15% and 20%, based on the SMA monitoring of quasars.

The data were analyzed in the standard manner using the IDL-based MIR software package⁶ and MIRIAD. We used the ROBUST parameter of CLEAN set to 2 in order to obtain a better sensitivity, losing some resolution. The resulting line-image rms was 40 mJy beam⁻¹ per channel at an angular resolution of $2\buildrel{\prime\prime}\over{.} 0\times 1\buildrel{\prime\prime}\over{.} 5$ with $\mathrm{PA}=-42\buildrel{\circ}\over{.} 4$.

The left panel of Figure 1 shows the spatial distribution of the ALMA 1.3 mm continuum emission contours overlapped with an archival HST ACS 6000 Å image.⁷ As previously reported, the system SR24 consists of two circumstellar disks (SR24N and SR24S) imaged, for instance, at infrared wavelengths (Mayama et al. 2010). While SR24S is associated with a well-known millimeter continuum source (e.g., Andrews & Williams 2005; Pinilla et al. 2017), here we report for the first time the detection of SR24N in this wavelength domain. ALMA shows SR24S having a well-defined annular morphology. This ring of dust is seen as an annular ellipse in projection (see Table 1), with two brighter parts toward the Northwest and the Southeast. SR24N is unresolved with the ALMA resolution ($\sim 0\buildrel{\prime\prime}\over{.} 15$) and its position coincides with the position of the 2MASS disk within the positional uncertainty ($0\buildrel{\prime\prime}\over{.} 5$, see right panel of Figure 1). We measured a peak flux of 314 μJy beam⁻¹ (that is a $7\sigma$ detection) for the SR24N millimeter source, which has a size of the order of the angular separation of the binary contained in it (as measured by Correia et al. 2006). For comparison, an M or K spectral type star at the distance of the Ophiuchus molecular cloud would have a flux density⁸ of $\lesssim 0.5$ μJy beam⁻¹.

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Table 1.  Characteristics of the 1.3 mm Continuum Sources

Source	R.A.	Decl.	Flux Density	Semiajor Axisa	Semiminor Axisa	P.A.	ib	Mdiskc
	J2000	J2000	(mJy)	('')	('')	(°)	(°)	(${M}_{\odot }$)
SR24S	${16}^{{\rm{h}}}{26}^{{\rm{m}}}58\buildrel{\rm{s}}\over{.} 504$	−24°45'3721	211 ± 4	0.70 ± 0.06	0.50 ± 0.06	212 ± 3	44 ± 6	0.025 ± 0.001
SR24N	${16}^{{\rm{h}}}{26}^{{\rm{m}}}58\buildrel{\rm{s}}\over{.} 434$	−24°45'3224	0.34 ± 0.07	⋯d	⋯	⋯	⋯	4 × 10−5 ± 1 × 10−5

Notes.

^aDeconvolved semimajor and semiminor axis of the ring-shaped disk. ^bEstimated from the major and minor axis lengths as the $\arccos ({R}_{\min }/{R}_{\mathrm{maj}})$. ^cThe disk mass is estimated assuming a typical gas-to-dust ratio of 100. ^dThis disk is unresolved with the present ALMA resolution.

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Therefore, the detected millimeter source in SR24N is probably due to the dust emission from the protostellar disk(s). Assuming optically thin isothermal dust emission, a gas-to-dust ratio of 100, a dust opacity of 1.1 cm² g⁻¹ at 1.3 mm appropriate for dust with thin ice mantles (Ossenkopf & Henning 1994), an opacity spectral index with an exponent $\beta =0.4$ for both sources (Isella et al. 2009; Ricci et al. 2010; Pinilla et al. 2014), and a dust temperature of 30 K, we estimate a mass associated with the SR24N millimeter source of 4 × 10⁻⁵ M_☉ or 13 ± 7 M_⊕ (where we have estimated the statistical error based on the uncertainty of the flux density and a 5 K uncertainty for the temperature). Using the same approximate values, for SR24S we obtain a mass of 0.025 ± 0.007 M_☉, which is in good agreement with previous estimates (e.g., Isella et al. 2009; Andrews et al. 2010, 2011).

The ¹²CO molecular emission observed by ALMA in the SR24 system shows the kinematics of two gaseous rotating disks at the positions of SR24S and SR24N (Figure 2). The gas content and kinematics of the SR24N disk is reported here for the first time.⁹ Table 2 presents a summary of the properties of the disks found through the ¹²CO emission.

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Table 2.  ¹²CO Disks Properties

Column	2	3	4	5	6	7	8
Source	Size	P.A.	i	Vcentera	Vrangea	Vpeaksa	Vabsorptiona
	(${b}_{\mathrm{maj}}\times {b}_{\min };\,{\rm{P}}.{\rm{A}}.$)	(°)	(°)	(km s−1)	(km s−1)	(km s−1)	(km s−1)
SR24S	050 ± 006 × 017 ± 002;  41°	218 ± 2	70 ± 5	4.4 ± 0.3	[−3.5, 12.4]	−0.3/6.0	[2.2, 4.1]
SR24N	060 ± 010 × 031 ± 006; 111°	297 ± 5	121 ± 17	5.6 ± 0.3	[−0.3, 10.5]	1.6/7.3	[2.2, 4.8]

Note. Column 2: deconvolved FWHM of the semimajor and semiminor axis and position angle estimated from a 2D-Gaussian fit to the moment 0 image produced using the V_range specified in column 5. Column 3: estimated using a linear fit to the peak of the red- and blueshifted high-velocity channels. Column 4: derived from the semimajor and minor axis obtained in column 2. Column 5: measured from a Gaussian fit to the wings of the line profile integrated along the disk. Column 6: measured until no 3σ emission is detected in a velocity channel at the disk position. Column 7: velocities of the disk's double-peak spectrum. Column 8: velocity range of the self-absorption feature.

^aVelocities are V_LSR and are not corrected by the cloud velocity.

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A southwest–northeast (red- to blueshifted emission, respectively) velocity gradient indicative of rotation is observed in SR24S at a position angle,¹⁰ ${\rm{P}}.{\rm{A}}.\,=\,218^\circ \pm 2^\circ$, ranging for about 16 km s⁻¹. The disk rotation is centered at 4.4 km s⁻¹ and the spectrum integrated over the disk shows a double peak, as it is stronger the redshifted one (Figure 3). In addition, four slightly blueshifted spectral channels close to the cloud velocity (which we found to be the channel at ${V}_{\mathrm{cloud}}=4.8$ km s⁻¹, because it shows the typical interferometric pattern when extended emission is missed) show a significant absorption over the SR24S ring disk. This radial velocity range coincides exactly with the kinematics of the cloud 33 of the ρ-Ophiuchus region in which the SR24 system is embedded (de Geus et al. 1990). This absorption is possibly affecting the results of our 2D-Gaussian fit, which would explain the different inclination obtained, $70^\circ$, with respect to that obtained by analyzing the continuum emission, $44^\circ$.

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Centered at a different velocity (5.6 km s⁻¹, that is 1.2 km s⁻¹ away from that of SR24S), the fainter SR24N ¹²CO emission presents a velocity gradient. The red- to blueshifted emission gradient (west–east, respectively; Figure 3) goes along the ${\rm{P}}.{\rm{A}}.\,=\,297^\circ \pm 5^\circ$ with a velocity range of about 11 km s⁻¹. The integrated spectrum over the northern disk also presents a skewed double-peaked profile, with a stronger redshifted peak most probably due to the cloud absorption as in SR24S. Because the SR24N disk is not detected in less optically thick molecular tracers, we used the available ¹²CO information to make an order-zero estimate of the dynamical mass of the system. The left panel of Figure 4 shows a position–velocity diagram taken along the major axis of the SR24N disk. For comparison, we overlapped three Keplerian rotation curves produced with central masses ranging between 0.1 M_☉ and 1 M_☉, which encompass the emission from the disk. Another crude estimate of the dynamical mass for SR24N can be made by using the expression ${(M/{M}_{\odot })=0.00121\times (({\rm{\Delta }}v/\mathrm{km}{{\rm{s}}}^{-1})/2)}^{2}\times (r/\mathrm{au})$, where the parameters are ${\rm{\Delta }}v={V}_{\mathrm{range}}$ and r is equal to the geometric mean of the sizes given in Table 2. The resulting mass, 0.8 M_☉, is in good agreement with the total mass of the close binary system (0.95 M_☉, Correia et al. 2006). Compared with it, the mass of the SR24N disk is negligible.

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The C¹⁸O (2-1) line emission is only detected toward SR24S and not SR24N. Although fainter than the ¹²CO line, its emission is more optically thin and is less affected by the cloud absorption (Pinilla et al. 2017). This is the reason why the C¹⁸O (2-1) line is the best molecular proxy available to study the kinematics of the SR24S disk. We made a simple model of a rotating and accreting thin disk, which does not include radiative transfer, as the goal is to study the disk kinematics and geometry. The surface density is described by a tapered power law consistent with the theoretical predictions for accretion disks (Lynden-Bell & Pringle 1974; Hartmann et al. 1998; Facchini et al. 2017; Factor et al. 2017):

$$\begin{eqnarray*}&&{{\rm{\Sigma }}}_{\mathrm{gas}}(r)={{\rm{\Sigma }}}_{0}{\left(\displaystyle \frac{r}{{r}_{c}}\right)}^{-\gamma }\exp \left[-{\left(\displaystyle \frac{r}{{r}_{c}}\right)}^{(2-\gamma )}\right],\end{eqnarray*}$$

where ${{\rm{\Sigma }}}_{c}$ is proportional to the disk mass, r_c informs about the radial extent of the gas disk, and γ is the power law index that we fixed to 0.8 following Andrews et al. (2010). We implemented the kinematics of the rotating and accreting disk using the Miriad tasks velmodel and velimage and convolved the model with a 2D-Gaussian to match the observed synthesized beam. To build up the velocity cube with velimage, we assumed that both the rotation and the infall velocity have an ${r}^{-0.5}$ radial dependence. Our model of the velocity cube has nine free parameters: peak intensity, disk center $({x}_{0},{y}_{0})$, inclination with respect to the line of sight i, the characteristic radius r_c, the position angle P.A. (measured from north to east), the LSR velocity v_LSR, the rotation velocity v_rot, and the accretion velocity v_infall at a fiducial radius of $1^{\prime\prime}$ (120 au for the adopted distance). We used an optimization algorithm based on the AGA method developed by Cantó et al. (2009) to fit the observed velocity cube and ran it a 100 times in order to extract a standard deviation for the averaged parameters (Table 3).

Table 3.  C¹⁸O Fit Disk Parameters

Parameter	Fit Value
x0a	002 ± 002
y0a	−130 ± 003
i	46° ± 8°
rc	13 ± 02
$p.a.$	212° ± 6°
vLSRb	4.6 ± 0.2
vrotb	3.2 ± 0.5
vinfallb	0.3 ± 0.2
${F}_{0}\times {10}^{-5}$	4 ± 1

Notes. Results from the C¹⁸O velocity cube fitting to the SR24S disk.

^aThese offsets set the modeled disk center at 16:26:58.507, −24:45.37.17. ^bVelocities are in km s⁻¹.

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Figure 5 shows the good agreement between the simple model and the C¹⁸O (2–1) observed velocity cube, which displays the typical butterfly-shaped emission along the velocity channels, proper of a Keplerian disk. The blueshifted emission is located preferentially toward the Northeast, while the redshifted emission is found toward the Southwest, with the velocity center estimated at 4.6 ± 0.2 km s⁻¹. The inclination and position angle match the values found in Section 3.1 from the continuum emission, while the radius of the gaseous disk seems to be almost a factor of two larger than the radius of the dusty disk, which may be explained by differences in the optical depth of the CO line and the continuum emission (Facchini et al. 2017). The rest of the resulting parameters of the fit are summarized in Table 3. The model included the rotation velocity of the disk at a fiducial radius of 120 au (${v}_{\mathrm{rot}}=3.2\pm 0.5$ km s⁻¹), which we use to estimate the dynamical mass of the protostar ($M={v}_{\mathrm{rot}}^{2}r/G$) of 1.5 ± 0.5 M_☉. This mass makes a good fit to the position–velocity diagram taken along the disk's major axis (at ${\rm{P}}.{\rm{A}}.\,=\,212^\circ$) shown in the right panel of Figure 4. Additionally, it is similar to the value of 2 M_☉ reported by Andrews et al. (2010).

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The ¹²CO (2-1) ALMA and SMA velocity cubes show several regions of extended emission. The SMA data set has shorter baselines than the ALMA data set and therefore is more sensitive to extended emission; although, on the contrary, it has a coarser spectral resolution. We present both velocity cubes overlapped in Figure 6. There are three main features that we point out: (i) a gas reservoir extending north–northwest of SR24N, (ii) a bridge of gas connecting SR24N with the SR24S disks, and (iii) an elongated and blueshifted feature due southwest of SR24S.

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The northern gas reservoir spreads out $7\buildrel{\prime\prime}\over{.} 5$ east–west and extends for about $4^{\prime\prime} \mbox{--}5^{\prime\prime}$ north of SR24N. It embraces the SR24N disk and is probably associated with it, as it is detected from 5.4 to 7.9 km s⁻¹, part of the redshifted velocities at which the SR24N disk is seen. The elongated ¹²CO bridge connecting SR24N and SR24S disks extends for $\sim 5\buildrel{\prime\prime}\over{.} 5$ north–south. It is mainly detected between 5.4 and 6.0 km s⁻¹ with the SMA, although the ALMA observations also show a faint arc-like structure linking the northeast part of the SR24S ring-like disk, with the east edge of the SR24N disk and the Northern gas reservoir. There is another ¹²CO linearly elongated source due southwest from SR24S that is detected at blueshifted velocities ranging from −0.9 to 0.9 km s⁻¹.

We estimate the mass of the Northern gas reservoir and the gas bridge between the disks using the ¹²CO (2-1) SMA emission, assuming that the gas is in local thermodynamic equilibrium and its emission is optically thin. We derive them with the following expression:

$$\begin{eqnarray*}&&M{/M}_{\odot }=1.03723\times {10}^{-4}\,\displaystyle \frac{Q({T}_{\mathrm{ex}})\,{e}^{({E}_{u}/{T}_{\mathrm{ex}})}\,{d}^{2}\int {S}_{\nu }{dv}}{{\nu }^{3}\,S{\mu }^{2}\,({X}_{\mathrm{CO}}/{X}_{{{\rm{H}}}_{2}})},\end{eqnarray*}$$

in which we adopt an excitation temperature ${T}_{\mathrm{ex}}=30$ K, the partition function for the ¹²CO $Q(30\,{\rm{K}})=1.29$, the energy of the upper level of the ¹²CO (2-1) transition is E_u = 16.596 K, the fractional abundance ${X}_{\mathrm{CO}}/{X}_{{{\rm{H}}}_{2}}={10}^{-4}$, the distance is d = 0.12 kpc, the rest frequency $\nu =230.538\,\mathrm{GHz}$, the molecular dipolar momentum $S{\mu }^{2}=0.02423$ D, and the integrated flux density $\int {S}_{\nu }{dv}$ goes in Jy km s⁻¹. The resulting masses, 13 × 10⁻⁷ M_☉ and 2 × 10⁻⁷ M_☉ (see Table 4), for the Northern reservoir and the bridge, respectively, are of the order of half the mass of the planet Earth.

Table 4.  SMA ¹²CO Extended Emission

Source	Flux Density	Size	${M}_{{{\rm{H}}}_{2}}$
	(Jy km s−1)	(arcsec2)	(×10−7 ${M}_{\odot }$)
Northern reservoir	11.3 ± 0.3	16.5	13
Bridge	3.0 ± 0.1	37.5	3
Southern streamer	1.6 ± 0.1	7.0	2

Note. Column 2: integrated ¹²CO (2-1) flux densities from SMA observations with a synthesized beam of $2\buildrel{\prime\prime}\over{.} 0\times 1\buildrel{\prime\prime}\over{.} 5$; ${\rm{P}}.{\rm{A}}.\,=\,42\buildrel{\circ}\over{.} 2$. Column 3: approximated size of the source taken from the SMA data set. Column 4: mass of the gas estimated from the SMA integrated flux measurements.

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Having measured the P.A. and the inclination of a disk, the only information that is missing to completely characterize its geometry is to know the tilt of the protostellar disk (i.e., which end of the disk's minor axis is the nearest to the observer). This could be addressed indirectly by putting together the information about the approaching–receding side of the disk and the sense of the disk's rotation (an analogous problem to distinguish between leading and trailing spiral arms in galaxies, e.g., de Vaucouleurs 1958; Repetto et al. 2017).

For SR24S, the southwest side of the disk is receding (redshifted), while the northeast side is approaching (blueshifted). We can now derive the sense of rotation (and hence the tilt of the disk) in three ways. The first is achieved by admitting the indications of previous coronograph IR observations (Mayama et al. 2010), which show an extended arc of emission reported as a spiral arm of the SR24S disk. The curvature of the spiral arm would indicate that the disk is rotating counterclockwise (as seen in projection), which implies that the east side is its near side. Second, the same infrared observations show brighter emission toward the east side of the SR24S disk, which lead Mayama et al. (2010) to conclude that the near side is the east side (the same applies also for the SR24N disk). Along with the approaching/receding kinematic information, this implies a counterclockwise rotation for the SR24S disk. The third evidence supporting this sense of rotation comes from a close inspection of the velocity field of the C¹⁸O disk. Figure 7 presents two different velocity cuts perpendicular to the major axis of the SR24S disk. A subtle asymmetric pattern can be noticed in both position–velocity diagrams. On one hand, the northern pv-cut shows the blueshifted emission in a boomerang-shaped feature originated by the rotation, but the west arm of the boomerang is shorter than the east arm. On the other hand, the southern pv-cut shows the redshifted emission in another boomerang-shaped feature, but this time, the east arm is slightly shorter and fainter. The asymmetric length of the boomerang arms in both pv-diagrams is due to the non-zero infall velocity as supported by the following study that we present using some synthetic models. Actually, the asymmetry is more pronounced as the infall velocity is larger and the disk is closer to edge-on. Note that if outflow rather than infall motions are considered, the asymmetry would be reversed. In the case of the SR24 system, we assume infall motions based on the evidence of accretion provided by Paschen hydrogen recombination lines observations by Natta et al. (2006).

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In Figure 8, we show sketches for two rotating and accreting disks with inclinations separated by $180^\circ$ and a third rotating disk with no accretion (Cases I, II, and III, respectively). We simulated the kinematics of these disks using the toy model described in Section 3.3 for SR24S but changing the inclination and the accretion velocity while keeping the receding and approaching sides of the observations fixed. Two position–velocity cuts perpendicular to the major axis of the disks are presented for each case. Case I and III disks have their nearest side to the east (inclination $i=46^\circ$) and differ only in the accretion velocity: ${v}_{{\rm{I}}}=3.2$ km s⁻¹ and ${v}_{\mathrm{III}}=0.0$ km s⁻¹. Case II disk has $i=136^\circ$, ${v}_{\mathrm{II}}=3.2$ km s⁻¹ and its nearest side is west. Case I and II disks rotate in opposite directions (as seen in projection) so that they keep the receding and approaching sides the same. The pv-cuts perpendicular to the major axis of the disks show similar boomerang-shaped features as the SR24S observations. The boomerang shapes appear due to the gas rotation (Case III), but the asymmetries in the length of the boomerang arms are related to the accretion or infall motions (Cases I and II). Indeed, in the case of an accreting disk, the asymmetry pattern is also related with the inclination of the disk with respect to the plane of the sky. As evidenced by Figured 8, when $i\lt 90^\circ$ (Case I) the infall motions make the nearest blueshifted quarter of the disk to reach less blueshifted velocities, while the opposite applies for the farthest blueshifted quarter of the disk. Analogously, the farthest redshifted quarter appears less redshifted than the nearest redshifted quarter. On the contrary, when $i\gt 90^\circ$ (Case II) the asymmetries are just reversed, making it possible from the kinematic observations to determine which is the nearest side, the true inclination and the sense of rotation of the disk, given that the disk has infall motions. All of this analysis leads us to derive the sense of rotation (counterclockwise) and the location of the near edge (east edge) of the SR24S disk.

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For the SR24N disk, the lower signal-to-noise ratio and the foreground cloud absorption of the ¹²CO data prevent a similar analysis. Therefore, we assume that the sense of the disk rotation matches that of the close binary systems SR24Nb and SR24Nc (i.e., clockwise, see section Section 1 and Correia et al. 2006). Although there are examples of disks hosting counter-rotating stars (Bate et al. 2010; Vorobyov et al. 2016, and references therein), the simplest hypothesis is that both binary and disk rotate in the same sense.

Figure 9 sketches the SR24 system (note that it is not to scale and the gaps of the disks are not real), with the binary system SR24N rotating clockwise and with an inclination $\lt 90^\circ$, while the SR24S disk is rotating counterclockwise with an inclination $\gt 90^\circ$. Given the measured position angles and the inclinations of both disks (Tables 1–3), we derive an angle between the angular momentum vectors of the two disks¹¹ of $108^\circ \pm 25^\circ$. Even considering that the SR24N disk rotates in the opposite direction (it would have $i=59^\circ$) the disk's angular momentum vectors would be $66^\circ$ away from each other. Therefore, there is strong evidence suggesting that the SR24 system has two highly misaligned disks.

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Inspecting the HST optical emission of Figure 1, it is noticeable the bridges and/or streamers produced by light scattered in dust and gas (Potter 2003). There is a twisted bifurcation in the bridge joining the SR24N and SR24S disks, and a prominent curved arc south of SR24S thought to be a spiral arm (Mayama et al. 2010). The present ¹²CO (2-1) observations from ALMA and SMA do not perfectly match these structures. For instance, the southern optical/infrared spiral arm has no ¹²CO counterpart. The location of the molecular bridge between the two disks (Figure 6) is slightly east of the HST bifurcated bridge, but both seem to join the two disks of the system. The nature of this bridge is unknown, although it is well known from numerical simulations that multiple systems have bridges of material like the one observed here (e.g., Gabbasov et al. 2017). We have also noticed that the optical bridge between the disks of the system has a curvature and joins the west side of SR24S with the east side of SR24N. Models including two disks with the same sense of rotation (see Figure 1 in Mayama et al. 2010) seem to predict a reversed orientation of the linking bridge, and this is a point for further investigation of the geometry and kinematics of the system.

Regarding the Northern gas reservoir seen in the ¹²CO (2-1) maps (Figure 6), it is possible that it is connected (in space and velocity) with the bridge. It could be part of a spiral structure due to gravitational instabilities of the system (see, e.g., Tobin et al. 2016), the remnant of a circumbinary structure, or a reservoir of material found by SR24N in its orbital path. More sensitive ALMA observations are needed to further interpret the nature of this feature.

The ALMA observations and the previous work on the SR24 system make it clear that the two disks are misaligned, making this one more of a small sub-population of multiple systems with large separations (Jensen & Akeson 2014; Salyk et al. 2014; Williams et al. 2014). However, SR24 has another peculiarity: the two disks possibly rotate in opposite directions as seen from Earth (i.e., in projection, one rotates clockwise and the other counterclockwise). How this system originated is not a trivial question, and here we introduce a few suggestions into the discussion.

It is known that a highly misaligned multiple system is hardly formed via the collapse of a non-turbulent rotating cloud, and this has been previously stated by numerical simulations (e.g., Bate et al. 2010). Such non-turbulent clouds may produce disks that can undergo further fragmentation due to gravitational instabilities, being the most recent and clear example the triple system L1448 IRS3B (Tobin et al. 2016). Therefore, a cloud would need some degree of initial turbulent motions as to fragment into (at least two) pieces that would finally rotate in highly misaligned, or even opposite directions (i.e., antiparallel spins Offner et al. 2010; Tokuda et al. 2014).

Another possible explanation for the formation of a system with two strongly misaligned disks is the event of a close encounter of two previously isolated protostellar disks. However, in the thorough analysis by Salyk et al. (2014), adapting the expressions of Thies et al. (2005) to the Ophiuchus molecular cloud, they estimate a low encounter probability ($\lt {10}^{-5}$) for impact parameters under 500 au.

Whatever the multiple system formation mechanism was, at some point, one of the protostellar disk companions may undergo an event of external accretion from a reservoir of material (Vorobyov et al. 2016), which may impinge a tilt in this particular disk, resulting in a tilt with respect to its original inclination. Regarding the existence of a gas reservoir north of SR24N, this may provide a plausible explanation for the misalignment in SR24, which may erase the memory of the formation mechanism in this system.