High-resolution Near-infrared Polarimetry and Submillimeter Imaging of FS Tau A: Possible Streamers in Misaligned Circumbinary Disk System

3.1.1. Binary Orbit

In the Stokes I image shown in Figure 1(a), a bright source and one faint structure extending to the southeast can be seen, indicating that this binary is not resolved well in our near-infrared observations due to the limited seeing correction. Therefore, to derive the separation ρ and position angle (PA) θ of the companion star Ab we tried the following methods. First, we determined the center of the PSF via the IRAF center command, then we plotted the azimuthal profile relative to this center to help determine the PA of the binary. The averaged azimuthal profile, Figure 1(b), is drawn every 5° within 100 pixels. In this figure, the peak of the azimuthal profile appears at a PA of 110°, indicating that the PA of the companion star is about 110° ± 25.

Zoom In Zoom Out Reset image size

To determine the separation of this binary, we plotted and fit the radial profile along the direction of the binary, i.e., a PA of 110°, with an opening angle of 5°. The PSF after AO correction should include one core structure and one halo structure, which can be approximately represented as the sum of two Gaussian functions. In this case, the PSF of the primary star FS Tau Aa g_a can be expressed as

$$\begin{eqnarray}&&{g}_{a}={a}_{a}{e}^{-\tfrac{{x}^{2}}{2{\sigma }_{h}^{2}}}+{{sa}}_{a}{e}^{-\tfrac{{x}^{2}}{2{\sigma }_{c}^{2}}}.\end{eqnarray} \tag{ 2 }$$

Here, a_a, σ_h, s, and σ_c represent the amplitude of the PSF halo, deviation of the halo, ratio of the amplitude of the core to that of the halo, and deviation of the core, respectively. For FS Tau Ab, we assume that its PSF has the same s, σ_h, and σ_c as those of Aa, but a different amplitude a_b and a different projected distance of c pixels along PA = 110° from Aa. As a result, its PSF can be written as

$$\begin{eqnarray}&&{g}_{b}={a}_{b}{e}^{-\tfrac{{\left(x-c\right)}^{2}}{2{\sigma }_{h}^{2}}}+{{sa}}_{b}{e}^{-\tfrac{{\left(x-c\right)}^{2}}{2{\sigma }_{c}^{2}}}.\end{eqnarray} \tag{ 3 }$$

Therefore, the total PSF profile can be expressed as

$$\begin{eqnarray}&&G={g}_{a}+{g}_{b}.\end{eqnarray} \tag{ 4 }$$

The fitting is performed by the SciPy curve_fit command, which employs the Levenberg–Marquardt method. The initial guesses of all parameters are 1. The PSF fitting results, as well as their standard deviation errors, are listed in Table 1 (r² is the coefficient of determination) and shown in Figure 1(c); they do not have significant changes when we change the initial guesses of the parameters. To better describe how our results fit the observations, we also show the residual map. From the residual map, it can be seen that the relative residuals, calculated as observed value-fitted value/fitted value, of the fitting are smaller than 0.1 within a radius of ∼90 pixels, and are extremely small in the direction of Ab, indicating that our fitted PSF profile can be regarded as a good approximation of the observed profile. From the curve-fitting result, we derived separation c = −28.53 pixels, corresponding to 0271. As for the uncertainties of the binary separation, we consider the pixel scale, the accuracy of the image registration, and the errors of the fitting. The standard deviation error from the fitting is about 0.13 pixel. Also the radius is calibrated from the brightness peak, for simplicity we assume that the star Aa is at the same place (zero-point) as the brightness peak, however there is a ∼0.9 pixel offset between them in the fitting result. It is hard to make the fitted brightness peak just at the zero-point so we regard it as an error. In summary, we estimate that the astrometric error of the separation should not be larger than about 1 pixel or 9.5 mas.

Table 1.  PSF Fitting Results and Derived Binary Positions

Parameter	Value	Error
aa (ADU)	4650	43
σh (pixel)	41.52	0.16
s	2.79	0.03
σc (pixel)	13.10	0.06
ab (ADU)	1210	13
c (pixel)	−28.53	0.13(1)
r2	0.99833	⋯
ρ ('')	0.271	0.0095
θ (°)	110	2.5

Note. The errors are from the standard deviation errors. The error in the colon for c is the error after combining other possible uncertainties.

Download table as:  ASCIITypeset image

According to the orbit derived by Tamazian et al. (2002), the predicted position of FS Tau Ab should be at ρ = 0224 ± 002 and θ = 1124 ± 18°, which is not consistent with our result. Therefore, we tried to fit a new orbit. The MCMC algorithm of the code orbitize! (Blunt et al. 2019) is used to fit the orbit. Our data, as well as the data taken from the year 1996 to 2001 in Tamazian et al. (2002), are used for fitting. The 1989 year data used by Tamazian et al. (2002) were derived from lunar occultation; considering that this method has larger uncertainties, we do not use these results in our fitting. We set the parallax π of the binary to be 7.143 ± 0.001 mas. As for the system mass M_sys, we found out that the best solutions with the lowest chi-squared values (the chi-squared values of the orbits are calculated via $\sum {(O-E)}^{2}/E$, where O and E represent the observed positions and expected positions of the observed epoch, respectively) during the test runs tend to have a mass around 1.5M_⊙ so we set the initial mass at 1.5 ± 0.25 M_⊙. The Gaussian prior $\mathrm{log}(p(x| (\delta ,\mu ))\propto \tfrac{x-\mu }{\delta }$ is used for the parallax and system mass. As for other parameters, we do not set initial values. The semimajor axis a uses log uniform prior p(x) ∝ 1/x, the inclination i uses sine prior $p(x)\propto \sin (x)$, and the other parameters use uniform prior.

The fitting result is shown in Table 2, which is a sample including 1000,000 orbits following the convergence. The median, lower, and upper values correspond to 0.5, 0.16, and 0.84 percentile of the results, respectively, while the ${\chi }_{\min }^{2}$ indicates the best-fit result among the orbits, which has a ${\chi }_{\min }^{2}$ value of about 1.88, and is drawn in Figure 1(d). From this image, it can be seen that this result fits the observation results of 2001 and 2011 quite well. The corner map is also shown in Figure 2.

Zoom In Zoom Out Reset image size

Table 2.  Orbit Fitting Results

Parameter	Median	Lower	Upper	${\chi }_{\min }^{2}$
a (au)	34.3	28.0	46.9	38.5
e	0.374	0.220	0.512	0.269
i (°)	44.3	32.2	55.5	42.6
ω (°)	135	103	197	130
Ω (°)	158	110	211	170
tp (yr)	2101.39	2069.03	2195.44	2117.69
π (mas)	7.1430	7.1422	7.1438	7.1431
Msys (Msol)	1.54	1.36	1.74	1.71

Download table as:  ASCIITypeset image

3.1.2. Circumstellar Structures

We calculated the radial Stokes images relative to the brightness peak of the Stokes I image using the methods suggested by Avenhaus et al. (2014), based on the Stokes Q and U (Figure 3(a)). In the Q_ϕ radial Stokes image shown in Figure 3(b), it can be seen that this binary system is accompanied by nebula-like structures. Two symmetric, butterfly-like negative regions along a PA of about 55° and a radius of ∼05 can be seen, indicating that the polarization directions in these regions are along the radial direction. Since the instrumental polarization correction has been done via the method described by Joos et al. (2008), other mechanisms should be responsible for this butterfly pattern. One possibility is that it is caused by the uncorrected PSF halo of the stars (e.g., Oh et al. 2016).

Zoom In Zoom Out Reset image size

To test this we tried to generate the PSF halo for Stokes Q and U images using a method similar to that of Oh et al. (2016): first we derived the brightness ratio between Stokes Q/U images and the Stokes I image, by calibrating their brightness between radius 13.5–105 pixels relative to the brightness center position of the Stokes I image, to estimate the brightness of the PSF halos in Stokes Q and U images (about −0.3% and 0.5% relative to the Stokes I image, respectively). Then we generated the PSF halos based on the profile and brightness ratio we derived above, and we subtracted them from the origin Stokes Q and U images to get the PSF halo-subtracted Stokes Q and U images. Finally we recalculated the radial Stokes images after PSF halo subtraction (Figure 3(c)). From the Q_ϕ image in Figure 3(c), we note that the negative regions become smaller; however, many artifacts are also introduced into the image, especially the "dip," which was previously observed by Hioki et al. (2011), disappears in the PSF halo-subtraction image. Toward this, we suggest that an uncorrected PSF halo may not be the mechanism causing this butterfly pattern. Considering that the extinction of FS Tau A is high (A_V ∼ 5, Kraus & Hillenbrand 2009), the multiple scattering due to the dust in front of the stars could contribute to that. The following observations can tell us more about it and this time we will mainly focus on the other detected structures, i.e., structures outside ∼05 from the star.

In the composite image with the result of Hioki et al. (2011), Figure 4(a), it can be seen that we successfully revealed the structures within the 13 × 17 area where Hioki et al. (2011) did not resolved. In the Q_ϕ image, one structure, labeled "S1," was detected at the 5σ–6σ level in the southeast region (signal is from the Q_ϕ image, and the noise level was estimated from the standard deviation of the U_ϕ image at the same place). The structure starts from the south of the binary, and then turns to the northeast. From the azimuthal mapping image shown in Figure 4(b), its main part ranges from PA ∼ 70°–200° and extends to at least ∼15 from the stars. Another structure, labeled "S2," was detected at the 4σ–5σ level in the north. From Figure 4(a) it seems to be connected with the (2) structure of Hioki et al. (2011). It ranges from PA ∼ 300°–380° and extends to at least ∼17 from the stars. There is a dip centered on PA ∼ 50° between the S1 and S2 structures, whose position is consistent with the northeast dip (3) detected by Hioki et al. (2011; Figure 4(a)).

Zoom In Zoom Out Reset image size

From the channel map of FS Tau A CO (J = 2–1) image taken by ALMA shown in Figure 5 (beam size: 016 × 022; PA: 2624), it can be seen that emissions were detected in channels 1–8 (local standard of rest kinematic (LSRK) velocity: 1.19–5.64 km s⁻¹) and 12–25 (LSRK velocity: 8.17–16.43 km s⁻¹). No emission was detected in channels with LSRK velocities of 6.27, 6.90, and 7.54 km s⁻¹, corresponding to solar system barycentric radial velocities of 15.68, 16.31, and 16.94 km s⁻¹, respectively, indicating that two independent components were detected in the ALMA CO (J = 2–1) image. No calibration of FS Tau A's radial velocity was made. However, we noticed that its two nearby T Tauri stars, namely BD +26 718B and IP Tau, with separations of about 44' and 46' from FS Tau A, respectively, have barycentric radial velocities of 16.23 and 16.24 km s⁻¹, respectively (Nguyen et al. 2012). In this case, we suggest that the radial velocity of FS Tau A is not likely to be far from these values. Therefore, it is reasonable to assume that the heliocentric radial velocity of FS Tau A is 16.3 km s⁻¹, corresponding to an LSRK velocity 6.90 km s⁻¹. The detected structures can then be classified as blueshifted and redshifted parts.

Zoom In Zoom Out Reset image size

We integrated these two independent components individually. The blueshifted component was integrated from channels 1–8 (1.19–5.64 km s⁻¹); its moment 0 (integrated flux), 1 (velocity fields), and 2 (velocity dispersions) images and the signal-to-noise ratio (S/N) map are shown in Figure 6. In the moment 0 image, two obvious structures can be seen. One structure, labeled structure A, extends from the star Aa to about 04 or 56 au at the 3σ level (1σ ∼ 0.02 Jy beam⁻¹ · km s⁻¹) with a PA of about 190°; its brightest part is about 7σ. In the moment 1 map, it can be seen that the south part of structure A generally has a velocity of about 3.5 km s⁻¹, and at the position near the star Aa, there seems to be a velocity gradient. In the moment 2 map, there is clearly a larger velocity dispersion of about 1.6 km s⁻¹ near the star Aa. Another structure, a bar-like structure labeled structure B, is located at about 015 or 21 au from the star Ab. It has two cores: a large one in the northeast and a small one in the southwest. Both cores were detected at about 5σ, with a separation of about 07 or 98 au and a PA of about 30°. The connection between these two cores was barely detected (∼2σ). In the moment 1 map, structure B has a velocity of about 5 km s⁻¹, and the two cores have slightly larger velocity dispersions (∼0.6 km s⁻¹ for the north core and ∼0.8 km s⁻¹ for the south core) than their counterpart (∼0.3 km s⁻¹) in the moment 2 map.

Zoom In Zoom Out Reset image size

The redshifted component was integrated from channels 12–25 (8.17–16.43 km s⁻¹). Before analyzing the central structures, it is necessary to mention that some structures extending to about 55 (770 au) were barely detected in the southwest (Figure 7(a)). These structures seem to be located at the southwest boundary of the "2" and "3" structures in the image reported by Hioki et al. (2011), and have an LSRK velocity of about 9.5 km s⁻¹ and a small velocity dispersion (0.3 km s⁻¹). However, they are too faint (∼2–3σ, 1σ ∼ 0.03 Jy beam⁻¹ · km s⁻¹, Figure 7(b)) in this ALMA observation; further observation is needed for a detailed discussion. Here, we focus on the structures detected within 5'' from the stars.

Zoom In Zoom Out Reset image size

The moment 0, 1, and 2 images of the redshifted component within 5'' are shown in Figure 8. In the center of the moment 0 image, there is a very bright structure (∼9σ) close to the two stars in the northeast, and in the moment 1 and 2 maps, it can be seen that this structure has higher velocity (∼12 km s⁻¹) and velocity dispersion (∼1.3 km s⁻¹) than the surrounding structures. There is also an arm extending first to the north to ∼07 (98 au), and turning to the west to ∼06 (84 au) from the turning point at generally > 4σ. There is also some emission at ∼2σ extending from the end of the arm to the south, which may indicate that this arm finally turns to the south.

Zoom In Zoom Out Reset image size

The near-infrared observations and the submillimeter CO (J = 2–1) observations are compared in Figure 9. Figure 9(a) shows a comparison of the blueshifted component and the near-infrared observations (Q_ϕ image). It can be seen that the blueshifted component structures generally correspond to the S1 structure observed in the near-infrared band. We can see that structure B in the submillimeter band is consistent with the southeast part of structure S1 in the near-infrared band. As for structure A, it is smaller than the butterfly pattern (∼05), but from its shape it seems to correspond to the S1 part extending from the star FS Tau Aa.

Zoom In Zoom Out Reset image size

A comparison between the redshifted structures and the near-infrared observations is shown in Figure 9(b). The redshifted component arm first extends to the north, and then turns to the west. From Figure 9(b), it can be seen that the position of the north-extending part lies slightly east of the S2 structure detected in the near-infrared observations. However, the west-extending part of the redshifted component arm overlaps the S2 structure, indicating that there is some relationship between the structures detected in the different bands. Future observations can tell us more about this.

We have shown that the near-infrared polarimetry observations and CO (J = 2–1) observations resolved some structures around FS Tau A. In this section, we briefly discuss these structures.

Simulations such as Facchini et al. (2018) suggested that in the circumbinary disk systems, the inner region of the disk could be warped or broken from the outer disk, resulting in a misaligned inner circumbinary disk relative to the outer one. We first investigate if this can be the case. From Figure 6(c) it seems that structure A has relatively large velocity dispersion. To check whether this indicates a near-edge-on protoplanetary disk misaligned with the outer one, we drew a position–velocity (P–V) map of structure A and its opposite redshifted component structures. In the following discussion, we assume that the inclination of the possible disk is ∼90°; the conclusions would be similar for other near-edge-on inclinations. The P–V map is drawn along a PA of 99, a radius of 05 (70 au), and a 1 pixel width from the primary star Aa, as shown by the red line in Figure 10(a). From the P–V map, we can see that two different velocity components exist: one is at the bottom left of the P–V map, corresponding to the A structure in the blueshifted component, and the other is at the top right of the P–V map, corresponding to part of the redshifted component. We also show the Keplerian rotation curve in this image, assuming the central mass range we derived and an LSRK velocity of 6.9 km s⁻¹. The rotation map can barely fit the P–V map at the outer radius. However, in the inner region, e.g., at radius ∼20 au, both components keep their velocities at the outer radius and are slower than the Keplerian velocity.

Zoom In Zoom Out Reset image size

In the P–V map, no component with a velocity larger than the Keplerian velocity is observed. The velocities of the structures do not fit well with the rotation velocity. In this case, the existence of a disk is doubtful. The outer boundary of structure A is only at 04 or 56 au, and the semimajor axis of this binary system is about 28–46.9 au. Therefore, even if the slower velocity in the inner radius is due to the viscosity from the gas, it is a circumbinary disk around both stars instead of a circumstellar disk. For the disk to exist, the gap size opened by the binary should be smaller than the circumbinary disk.

The gap size relative to the binary orbital semimajor axis depends on the binary mass ratio, binary orbital eccentricity and misaligned angle between the binary orbit and the disk. The orbital inclination range of FS Tau A in our MCMC result is about 322–555. Therefore, if we assume that the disk is edge-on (e.g., inclination equals to 90°) to us, the misaligned angle between the disk and the binary orbital plane is 345–578 and the orbital eccentricity is about 0.22–0.512. Miranda & Lai (2015) suggested that in a circumbinary disk system, a binary with misaligned angle of 45° relative to the circumbinary disk, close to our case should open a gap at least twice of the binary semimajor axis, i.e., larger than 56 au. Therefore, we suggest that such a misaligned inner circumbinary disk does not exist, i.e., structure A does not indicate a protoplanetary disk.

As mentioned in Section 1, a binary can open gaps in its circumbinary disk. Streamers, which usually come in pairs, can penetrate this gap, sustaining the circumstellar disks around each of the binary stars. After comparing our observations with simulated streamers, such as those reported by Farris et al. (2014) and Nelson & Marzari (2016), we found that the shape of the detected structures, especially the near-infrared structures, resembles that of simulated streamers around binaries, which makes us believe that these structures are actually streamers triggered by the binary. We consider that the S1 structure and the blueshifted component indicate a streamer to the star Aa, since structure A in the submillimeter band is connected to Aa. The north arm S2 and the redshifted component indicate another streamer to Ab. Regarding the very bright part shown in the redshifted component near the binary, we suggest that it represents the streamer connecting the binary.

Based on ALMA observations, the southeast structure shows blueshifted characteristics, indicating that the materials in S1 are moving toward Earth. The redshifted component indicates that some materials in the north are moving away from Earth. In Figure 4, the southeast structure S1 is brighter than the north structure S2, which is consistent with the image derived by Hioki et al. (2011), in which the southeast part of the disk is brighter than the northwest part. Considering that the disk is large (∼600 au), we suggest that this difference in brightness is simply due to the southeast side being nearer to Earth, rather than that the dust surface density in the southeast part being much higher. If we assume that the streamers are flowing to the stars, then star Aa should be in front of the southeast side of the outer circumbinary disk, such that the streamer will move toward Earth to reach Aa, and Ab should be farther than the northwest side of the disk, such that the materials will move away from Earth to reach it. In a simple model of this situation, the outer circumbinary disk is highly misaligned with the binary orbit, Aa is in front of the disk, and Ab is behind the disk, as shown in Figure 11(a). Simulations such as that by Nixon et al. (2013) have proven that streamers to a binary can happen in a disk-binary misaligned system with a misalignment angle of up to 60°, supporting this scenario.

Zoom In Zoom Out Reset image size

To make this scenario true, the southeast inner edge of the circumbinary disk should be behind Aa, while the northwest inner edge of the circumbinary disk should be in front of Ab. Hioki et al. (2011) suggested that the ∼600 au circumbinary disk around FS Tau A has a PA of 15°–40°, an inclination of 30°–40°, and its southeast side nearer to Earth. While the binary has a semimajor axis 28–46.9 au, inclination 322–555. In this case, if we consider the circumbinary disk is "flat," i.e., the disk is not severely truncated by the binary, the southeast part of the circumbinary disk, even at 140 au, is closer to Earth than the binary, so this configuration conflicts with this scenario. However, if the inner region of the circumbinary disk is severely truncated by the binary, it is still possible that the streamers are moving to the stars.

Another interpretation is that the streamers are moving away from the stars. A simulation by Shi et al. (2012) suggests that while some materials move toward the central binary black hole, some other materials in the streamers move out from the stars to the disks; this should also happen in circumbinary disk systems. Considering FS Tau A, the southeast side of the disk is nearer to Earth, so observers on Earth will see the materials moving from Aa show a blueshift and those from Ab show a redshift, as shown in Figure 11(b). This interpretation fits well with the current suggested inclinations of binaries and disks given by Tamazian et al. (2002) and Hioki et al. (2011). We thus consider this to be the best explanation of the detected structures now. However, it does not indicate that materials will keep moving from the stars and there will be no circumstellar disks around each of the binaries. Simulations such as Muñoz & Lai (2016) show that the streamers triggered by the binary vary with time; even in one period, streamers are destroyed and regenerated, while material may be moving toward the star at some time, and moving away from the star at some other time. Therefore, it is difficult to connect the instantaneous kinematics in the streamers to the observed accretion rate onto the star, as the two can have a phase difference. There could still be a compact circumstellar disk around the star to sustain accretion, replenished by the streamers and other cross-cavity flows from time to time, but planet formation in such hostile environment might be hard.

Gravitational instability may also produce large-scale spirals and streamers in disks with sufficiently high mass (M_disk/M_star > ∼0.1; e.g., Vorobyov & Basu 2005, 2010; Kratter & Lodato 2016). These structures can be visible in near-infrared scattered light and millimeter dust emission (Dong et al. 2016a). If the disk can cool efficiently, it may also fragment to form self-gravitating objects, including protostars (Gammie 2001; Rafikov 2009). The protostar system L1448 IRS3B may be an example of this (Tobin et al. 2016). The Subaru Telescope image of the FS Tau A system appears to have a similar morphology. However, the total millimeter flux of the system (2.72 mJy at 1.3 mm) indicates a low disk mass, M_disk/M_star ∼ 0.5 (Akeson et al. 2019), assuming a dust opacity of τ_1.3mm = 2.3 cm² g⁻¹ (Beckwith et al. 1990), an average dust temperature of 20 K, and a gas-to-dust mass ratio of 100:1. The measured accretion rate is more than an order of magnitude smaller than the expected value for a gravitationally unstable disk ($\dot{M}\gt \sim {10}^{-7}\ {M}_{\odot }$ yr⁻¹; Dong et al. 2015). We thus consider that the observed structures in the FS Tau A system are unlikely to have been produced by gravitational instability.