11institutetext: School of Physics, University College Dublin, Dublin 4,
Ireland
11email<EMAIL_ADDRESS>22institutetext: School of Cosmic
Physics, The Dublin Institute for Advanced Studies, Dublin 2, Ireland
33institutetext: Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
44institutetext: Observatoire de Paris, PSL University, Sorbonne Université,
CNRS, LERMA, F-75014, Paris, France 55institutetext: INAF, Osservatorio
Astrofisico di Arcetri, Largo E. Fermi 5, 50125, Firenze, Italy
66institutetext: INAF, Osservatorio Astrofisico di Torino, Via Osservatorio
20, 10025, Pino Torinese, Italy 77institutetext: SKA Organisation, Jodrell
Bank Observatory, Lower Withington, Macclesfield, Cheshire, SK11 9FT, UK

# Launching the asymmetric bipolar jet of DO Tau

J. Erkal 11 C. Dougados 33 D. Coffey 1122 S. Cabrit 4433 F. Bacciotti 55 R.
Garcia-Lopez 11 D. Fedele 5566 A. Chrysostomou 77

###### Abstract

Context. The role of bipolar jets in the formation of stars, and in particular
how they are launched, is still not well understood.

Aims. We probe the protostellar jet launching mechanism, via high resolution
observations of the near-IR [Fe ii]$\lambda$1.53,1.64 $\mu$m emission lines.

Methods. We consider the case of the bipolar jet from Classical T Tauri star,
DO Tau, and investigate the jet morphology and kinematics close to the star
(within 140 au), using AO-assisted IFU observations from GEMINI/NIFS.

Results. We find that the brighter, blue-shifted jet is collimated very
quickly after it is launched. This early collimation requires the presence of
magnetic fields. We confirm velocity asymmetries between the two lobes of the
bipolar jet, and also confirm no time variability in the asymmetry over a 20
year interval. This sustained asymmetry is in accordance with recent
simulations of magnetised disk-winds. We examine the data for signatures of
jet rotation. We report an upper limit on differences in radial velocity of
6.3 and 8.7 km s-1 for the blue and red-shifted jets, respectively.
Interpreting this as an upper limit on jet rotation implies that any steady,
axisymmetric magneto-centrifugal model of jet launching is constrained to a
launch radius in the disk-plane of r0 $<$ 0.5 and 0.3 au for the blue and red-
shifted jets, respectively. This supports an X-wind or narrow disk-wind model.
However, the result pertains only to the observed high velocity [Fe II]
emission, and does not rule out a wider flow launched from a wider radius. We
report detection of small amplitude jet axis wiggling in both lobes. We rule
out orbital motion of the jet source as the cause. Precession can better
account for the observations but requires double the precession angle, and a
different phase for the counter-jet. Such non-solid body precession could
arise from an inclined massive Jupiter companion, or a warping instability
induced by launching a magnetic disk-wind.

Conclusions. Overall, our observations are consistent with an origin of the DO
Tau jets from the inner regions of the disk.

###### Key Words.:

ISM: jets and outflows – Stars: pre-main sequence, low-mass – ISM: individual
objects: DO Tau

##  1 Introduction

Jets and outflows from newly forming stars are a commonly observed phenomenon,
but whether they play a critical role in the star formation process is still
an open question. Principally, they are invoked to explain the removal of
angular momentum from the newly forming star-disk system, allowing the star to
spin-down and the disk to accrete. Furthermore, if jets do indeed play this
critical role, identifying the launching mechanism may have implications for
the disk physics in the region where planets are formed (see reviews by
Baruteau et al. (2014) and Turner et al. (2014)).

Early magnetohydrodynamic (MHD) models of bipolar jets, based on the work of
Blandford & Payne (1982), reveal a link between jet launching and the magnetic
fields threading the accretion disk (for e.g. Shu et al. 2000; Ferreira 1997).
Furthermore, mass outflow and angular momentum removal can occur along
magnetic field lines within the inner regions of the disk (Uchida & Shibata
1985). Casse & Keppens (2002) present the first global simulations of jet
launching from a resistive disk, finding that collimation occurs as the jet
propagates outwards from the star at a nearly constant rate, and that the jet
removes a significant portion of the energy released by accretion (Casse &
Keppens 2004). While the theory is broadly supported by numerical simulations,
observational support has been tricky to obtain due to the small spatial
scales involved (i.e. tens of au, equivalent to sub-arcseconds for the nearest
star-forming regions).

Recent decades have seen ever higher spatial and spectral resolution
observations provide much needed constraints on proposed models by probing the
initial jet channel i.e. within 100 au from the star (see review by Frank et
al. (2014)). For example, the jet collimation zone ($<$100 au from the star)
reveals that jets from both T Tauri (Class II) stars and younger sources
(Class 0 and I) are already collimated by the time they propagate to z=50 au
(Dougados et al. 2000; Cabrit et al. 2007). These observed similarity in jet
widths, independent of evolutionary stage, suggest magnetic collimation
processes which in turn implies a magnetohydrodynamic (MHD) jet launch model
(e.g. Cabrit et al. 2007). Indeed, most recently, cylindrical collimation as
early as z=30 au has been observed in the DG Tau jet (Bacciotti et al. 2002;
Maurri et al. 2014).

In addition, the initial jet channel has been observed to trace out a
systematic wiggling pattern in a number of cases (see for example HH 30
(Anglada et al. 2007), HH 24 (Terquem et al. 1999), ZCMa (Antoniucci et al.
2016), RY Tau (Garufi et al. 2019)). The fact that this wiggle pattern is
observed close to the star suggests that, rather than being an effect of
interactions with the environment, it is either produced by orbital motion of
the jet source in the binary system, see e.g. the study of the HH 30 bipolar
jet wiggling by (Anglada et al. 2007) or that the cause of the jet wiggling is
intrinsic to the launching mechanism.

Furthermore, observations have identified asymmetries between the two lobes of
the bipolar jet in terms of velocity, density and opening angle as well as
time-variability in velocity. Examples include the bipolar jets from HH 30, RW
Aur, DO Tau, DP Tau, DG Tau and DG Tau B (Hirth et al. 1994; Woitas et al.
2002 Melnikov et al. 2009; Hartigan & Hillenbrand 2009; Agra-Amboage et al.
2011; Podio et al. 2011). The question is whether bipolar asymmetries
originate in the launching mechanism itself, or as a result of interaction
with an asymmetric environment. If such asymmetries could be observed soon
after launching (i.e. $<$ 100 au from the star), this would render the latter
less likely.

Numerical simulations have risen to the challenge of reproducing observed jet
wiggling and other asymmetries. Studies have investigated the launching of
intrinsically asymmetric high velocity jets from stellar magnetospheres (for
e.g. Lovelace et al. 2010; Lii et al. 2014; Dyda et al. 2015) and magnetised
disks (Fendt & Sheikhnezami 2013). It has been shown that the presence of a
companion star or interactions with the interstellar magnetic field can cause
the jet axis to curve and bend (Fendt & Zinnecker 1998). However, many
simulations consider the larger scales. Few focus on the initial jet channel
which is more likely to better constrain the launching mechanism. Examples
include recent 3D MHD simulations of jet precession caused by a warped disk in
a binary system (Sheikhnezami & Fendt 2015; 2018). These latter studies find
that the differential tidal effects of a close companion could generate
asymmetries between jet and counter-jet collimation and axis wiggling.

Intriguingly, observational support for magneto-centrifugal jet launch models
was also pursued through investigations of kinematic signatures interpreted as
jet rotation (and hence evidencing angular momentum transport). This wave of
studies was initiated by HST observations of Classical T Tauri jets in optical
and near-UV atomic tracers (Bacciotti et al. 2002; Coffey et al. 2004, 2007,
2012), and was soon followed by similar studies from the ground in near-IR
atomic lines (Chrysostomou et al. 2008; White et al. 2014, Coffey et al. 2011,
Coffey et al. 2015). However, debate continues over the interpretation of
observed kinematic signatures which may have other causes, among them
asymmetric shocks and/or jet wiggling (Soker 2005; Cerqueira et al. 2006;
Fendt 2011; Staff et al. 2012). Most recently, the high resolution of ALMA
helped lend excitement to claims of rotation signatures in molecular tracers
of high velocity jets (Lee et al. 2017). This assumes, of course, that the
molecules can actually survive the MHD launching process (Panoglou et al.
2012). Then, the main concern when using molecular versus atomic tracers is
that molecular emission may be contaminated or dominated by emission from the
cavity walls and entrained ambient material, rather than the flow itself (e.g.
Hirota et al. 2017). Thus, a combined approach is required, whereby the atomic
and molecular tracers are observed at several wavelengths to give a complete
picture (Coffey 2017).

Clearly, observations close to the jet base are critical to probe intrinsic
launching signatures and minimise ambient contamination. Such jet studies
within 100 au of the star are observationally demanding, requiring sub-
arcsecond resolution often in combination with a long slit or integral field
unit. So inevitably they occur on a case-by-case basis, and for the brightest
targets. In this vein, here we present the case of Classical T Tauri star, DO
Tau, using adaptive-optics assisted spectro-imaging observations of near-
infrared atomic tracers, close to the base of the flow.

DO Tau, lies in the Taurus cloud at a distance, $d$, of 139$\pm$7 pc (Gaia
Collaboration et al. 2018). We adopt the stellar properties listed in Long et
al. (2019): stellar mass $M_{\star}\sim$ 0.59 $M_{\sun}$, stellar age
$t_{\star}$ $\sim$ 5.9 $\rm Myr$ and extinction $A_{v}\sim 0.75$. Spectral
type is given as M0.3 (Herczeg & Hillenbrand 2014). From modelling of the UV
excess flux, Gullbring et al. (1998) derives a disk accretion rate, $M_{acc}$
$\geq$ 1.44 $\times$ 10-7 $M_{\sun}yr^{-1}$. Similarly, Eisner et al. (2014)
derives from the observed Brγ flux an accretion luminosity $L_{acc}$ $\sim$
1.5 $L_{\sun}$, yielding a mass accretion rate $M_{acc}$ $=$ 2.1 $\times$ 10-7
$M_{\sun}yr^{-1}$ with the adopted stellar parameters. However, recently,
Simon et al. (2016) derived from optical veiling measurements an order of
magnitude lower Lacc ($\sim$ 0.1 $L_{\sun}$), suggesting possible strong
accretion variability in this source.

The disk of DO Tau was recently mapped with ALMA in the continuum at high
angular resolution by Long et al. (2019). The dust continuum emission was
modelled to reveal a compact, smooth disk with effective radius, encompassing
95% of encircled flux, of $r_{\rm eff,95}=$ 0$\aas@@fstack{\prime\prime}$263
(37 au), inclination angle of $i_{\rm disk}$ $\sim$ 27.6∘ $\pm$ 0.3 to the
line-of-sight, and position angle, PAdisk $\sim$ 170∘ $\pm$ 0.9. The quoted
uncertainties on the disk parameters are formal uncertainties in the fitting
procedure. True uncertainties are probably larger especially in the case of a
face-on disk. Recently, Fernández-López et al. (2020) derived an inclination
angle of 19∘ from ALMA data. We therefore adopt an inclination of 23.5∘ (the
average of Long et al. (2019) and Fernández-López et al. (2020)) and a more
conservative estimate of 5∘ for the disk inclination uncertainty.

The jet from DO Tau was originally revealed through optical forbidden emission
lines (Edwards et al. 1987). A radial velocity asymmetry in the bipolar jet
was identified of -92 and +210 km s-1 at 1$\aas@@fstack{\prime\prime}$5 along
the blue- and red-shifted jets respectively in [S II] (Hirth et al. 1997).
More recent observations, which spectrally resolve high and low velocity
components of the blue-shifted jet, show no velocity variation over time for a
given tracer (Simon et al. 2016; Giannini et al. 2019), and reveal plasma
conditions in the inner 100 au from the disk surface, including a typical
electron temperature ($T_{e}\sim$ 8000 K), a lower than usual ionisation
fraction ($x_{e}<<$ 0.1), and a hydrogen number density in the low and high
velocity components $n_{H}\sim 10^{6-7}{\rm cm}^{-3}$ (Giannini et al. 2019).
Most recently, Fernández-López et al. (2020) report a ringed pole-on outflow
based on CO data from ALMA.

On parsec scales, DO Tau is associated with HH objects HH 831A, HH 831B and HH
832 (McGroarty et al. 2004), all of which are located to the northeast as far
as 11′ i.e. $\sim$ 90 pc. With position angles of $\sim$74-78$\degr$, they are
well-aligned with the red-shifted jet (PA${}_{jet}\sim$70$\degr$, Hirth et al.
1997). Also coinciding with this position angle is an extended reflection
nebulosity to the north-east of DO Tau (Magakian 2003). Observed near-infrared
emission, extending to the northeast as far as 1$\aas@@fstack{\prime\prime}$7
with an inner boundary at 1$\aas@@fstack{\prime\prime}$1, was interpreted as
scattering from a cleared cavity (Itoh et al. 2008). Observed far-infrared
emission extending in the same direction (Howard et al. 2013), forms an arc
which connects DO Tau to neighbouring Classical T Tauri star, HV Tau, to the
east at $\sim$7′ ($\sim$1 kpc). When interpreted as a ’bridge’ of dust
emission, it prompted the suggestion of a disk-disk encounter (Winter et al.
2018).

Here, we present our study of the DO Tau jet and disk system at high
resolution. In section 2, we outline the observations and archival data
presented. In section 2.3, we describe the data reduction and analysis. In
section 3, we set out our main findings and in section 4 we discuss the
implications in the context of relevant modelling. Section 5 summarises our
conclusions.

##  2 Observations and data reduction

###  2.1 NIFS observations

The bipolar jet of T Tauri star DO Tau was observed in the H-band using the
Gemini-North NIFS instrument, with Altair adaptive optics (AO) correction
(Program ID: GN-2009B-Q-43), on 2009 Nov 11, Dec 17, 23 and 24.

The star was offset from the center of the NIFS field-of-view (3$\arcsec$
$\times$ 3$\arcsec$) in order to include as much of the bright blue-shifted
jet as possible while also observing the stellar PSF. This was to facilitate a
PSF deconvolution of the jet image, to maximise the spatial resolution of the
jet. Fortunately, the dimmer red-shifted jet also appeared within the field-
of-view.

NIFS spatial sampling is 0$\aas@@fstack{\prime\prime}$043 $\times$
0$\aas@@fstack{\prime\prime}$103\. The direction with the smallest spatial
sampling (detector x-axis) was aligned perpendicular to the jet position
angle, in order to achieve the highest spatial sampling in the direction
transverse to the jet axis. This corresponded to an instrument position angle,
PAIFU=160∘. Observations were also conducted with an anti-parallel position
(i.e. PAIFU=340∘), to facilitate identification of any contamination by PSF
artefacts. The use of AO correction yielded angular resolution of
FWHM=0$\aas@@fstack{\prime\prime}$15-0$\aas@@fstack{\prime\prime}$175,
determined by measuring the FWHM of the continuum. The NIFS H-band covers
1.49-1.80 $\mu$m, which includes the jet emission lines of [Fe II] 1.53, 1.60
and 1.64 $\mu$m. NIFS spectral sampling is 1.6 Å, giving a two-pixel velocity
resolution of 56 km s-1. The observations were conducted using the standard
ABA nodding technique. A total of 96 short exposures were obtained, reaching
an on-target total exposure time of 3.2 hours.

###  2.2 ALMA observations

Archival ALMA observations were retrieved in order to study the disk rotation
sense. We use in this paper observations of the DO Tau disk in the
C${}^{18}{\rm O}({\rm J}=2-1)$ line at 219.560 GHz from ALMA program
2016.1.00627.S (P.I. K. Oberg) presented in Bergner et al. (2019).
Observational and data reduction details are given in Huang et al. (2017). The
resulting beam is $0.72^{\prime\prime}\times 0.46^{\prime\prime}$ at PA=30∘
and the sensitivity (1 $\sigma$ rms) is 5 mJy/beam per 0.2 km s-1channel.

###  2.3 NIFS data reduction

The standard GEMINI calibration pipeline was used to reduce the NIFS data.
Each night was processed individually. Due to a deterioration in observing
conditions during one of the four nights, there are fewer exposures for the
anti-parallel slit (2009 Dec 23, PAIFU=340∘). The exposures for this one night
were not included in further analysis. A second night (2009 Nov 11,
PAIFU=160∘) was also excluded due to a time interval of several weeks between
it and the other observations. In this data, a small change in jet velocity of
5-10 km s-1 was measured. Such small variability in jet velocity is expected,
especially when there is a time interval of several weeks between
observations. However, since we are investigating small changes in velocity on
this order, it was deemed prudent to discard these exposures.

For the two remaining nights, 2D Gaussian fits to the individual continuum
images were used to exclude exposures with poorer seeing, in an attempt to
maintain higher spatial resolution. Although parallel and anti-parallel slit
positions were requested in order to identify artefacts, the challenge of
achieving sufficient signal-to-noise in the jet borders meant we were
compelled to combine these two slit orientations. Any artefacts would be
cancelled out in this way, with a resulting improvement in the quality of the
data.

Thus, since we used only two of four datacubes (2009 Dec 17 (PA=340∘) and Dec
24 (PA=160∘)), we achieve a total on-target exposure time of about one hour,
and a PSF of 0$\aas@@fstack{\prime\prime}$15.

To form the datacubes, co-adding the individual exposures first required
aligning the exposures via a 2D Gaussian fit of the stellar PSF. Then, co-
adding was conducted via sub-pixel shifts using the IRAF tool imshift. The
data were flux calibrated using the telluric standards.

A dedicated continuum subtraction procedure was employed to optimize
subtraction of the bright stellar contribution and better isolate the faint
jet line emission in its immediate vicinity. We followed the method outlined
in Agra-Amboage et al. (2011). This method allows us to correct both from the
photospheric spectrum and telluric absorption features close to the central
source. However, it also removes any unresolved [Fe II] emission close to the
star, and so we cannot study [Fe II] closer than
0$\aas@@fstack{\prime\prime}$1 to the source. The datacubes were then rotated
to align the jet axis with the horizontal, to facilitate eventual analysis
using 1D Gaussian fitting.

The next steps in the data reduction saw the procedure branch in two, with one
approach deemed more appropriate for analysis of the morphology and the other
for the kinematics. To facilitate analysis of the jet morphology, we first
combined the datacubes for the parallel and anti-parallel slit positions. We
then spectrally binned the [Fe II] 1.64 $\mu$m line, integrated over
vLSR=[-122-228] $\rm km\leavevmode\nobreak\ s^{-1}$, to create 2D images of
the approaching and receding jets, respectively. We then further improved
angular resolution via deconvolution using the IRAF Lucy routine. The PSF was
constructed by summing the continuum emission, near the [Fe II] 1.64 $\mu$m
line, over a number of spectral channels similar to the width of the [Fe II]
1.64 $\mu$m line (5 channels). The deconvolution improved resolution further
to $\leq$ 0$\aas@@fstack{\prime\prime}$06 (FWHM). For both the jet and
counter-jet images, we conducted 1D Gaussian fitting across the jet intensity
profile, yielding jet axis position and jet width as a function of projected
distance from the source.

Meanwhile, for analysis of the jet kinematics, PSF deconvolution was avoided
for fear of contaminating the kinematic signature. However, critically, a
correction was required for a possible uneven slit illumination effect. Non-
uniform illumination within an IFU slitlet introduces a wavelength shift in
the spectrum at that position which can be up to a few km s-1, (Agra-Amboage
et al. 2014). The uneven slit correction was conducted on datacubes for both
the parallel and anti-parallel IFU positions, PAIFU, before combining them. We
found this to be the optimum procedure to remove all possible instrumental
effects, and fundamental to a jet rotation study. This is because the
differences in radial velocity under investigation are on the same order as
those expected from uneven illumination effects, i.e. a few km s-1. The uneven
slit illumination effect was modelled in each IFU spaxel by estimating the
displacement of the centroid of the brightness distribution within the spaxel
with respect to the slitlet center. From this a 2D velocity map correction was
estimated and subtracted from the observed 2D centroid velocity maps. As a
double-check, the uneven slit 2D correction map was also computed from a
photospheric absorption line near the [Fe II] 1.64 $\mu$m emission, by
estimating at each spaxel position the velocity shift of the centroid of the
line with respect to the spectrum located at the continuum centroid position
(i.e. the defined star center). The required correction was found to be
typically of a few km s-1 and up to $\pm$ 8 km s-1 at
0$\aas@@fstack{\prime\prime}$1 from the star (see Appendix, figure 11).

The datacubes for the parallel and anti-parallel slit positions were then
combined, and Gaussian profile fitting was conducted at each spatial position
to retrieve the jet peak centroid velocity map in [Fe II] 1.64 $\mu$m. Lastly,
all velocities were corrected to the LSR velocity frame, using for DO Tau the
systemic LSR velocity of +6.47 $\pm$ 0.14 km s-1 (Guilloteau et al. 2016).

The differences in radial velocity under investigation are expected to be on
the same order as the residuals from wavelength calibration. Although the
absolute velocity calibration accuracy is not critical for this study, the
relative accuracy within the IFU spaxels and over a wavelength range close to
the line of interest is crucial. A detailed analysis of telluric sky emission
lines close to the [Fe ii]1.64 $\mu$m line is described in a similar study for
RY Tau (Coffey et al. 2015), which was observed during the same period and
with the same instrument configuration. From this study, we estimate an
internal relative calibration 1$\sigma$ error of $\sim$ 1.6
$\rm{km\leavevmode\nobreak\ s^{-1}}$ (Coffey et al. 2015) over the IFU field
of view. We also estimate a 1$\sigma$ error on the global absolute velocity
calibration scale of 10 km s-1. When performing Gaussian fitting to derive the
line velocity centroids, errors in centroid velocity are a combination of the
error in velocity calibration and that of Gaussian fitting. The former remains
constant, while the latter is signal-to-noise dependent. Fitting errors were
calculated in accordance with the equation for the accuracy of a Gaussian
centroid fit as applied to cases of high signal-to-noise such that photon
noise dominates, and assuming that the profile is well-sampled (Whelan &
Garcia 2008):

$\centering\sigma_{centroid}=\frac{\text{FWHM}}{2\sqrt{2\leavevmode\nobreak\
\text{ln}\leavevmode\nobreak\ 2}\leavevmode\nobreak\
\text{SNR}}\@add@centering$ (1)

where FWHM represents the width of the fitted profile, (here our spectral
resolution of 56 km s-1), and SNR is the signal-to-noise ratio at the Gaussian
peak. For our observations, we thus derive typical centroid velocity 3$\sigma$
accuracy of 2-5 km s-1, depending on the signal to noise. Combining this in
quadrature with the internal relative calibration error gives the error bars
in figure 6.

##  3 Results

###  3.1 Jet Morphology

Figure 1: Deconvolved image of the DO Tau receding (left) and approaching
(right) jet in Fe II 1.64 $\mu$m line, integrated over
$\text{v}_{\text{LSR}}=[-122,228]\leavevmode\nobreak\
\text{km\leavevmode\nobreak\ s}^{-1}$. The contour floor is $3\sigma$
increasing in log intervals of 0.5 (where $1\sigma$ is
$1.43\leavevmode\nobreak\ \times\leavevmode\nobreak\
10^{-18}\leavevmode\nobreak\ \text{erg\leavevmode\nobreak\
s}^{-1}\leavevmode\nobreak\ \text{cm}^{2}\leavevmode\nobreak\ \text{\AA}$. The
derived jet axis position is overlaid in black dots with associated error
bars. Rotating to the horizontal yields a blue-shifted jet position angle,
PA${}_{\text{jet}}$ = 260$\degr$. Blue and red contours trace C18O emission
integrated over $\text{v}_{\text{LSR}}=[4.21,5.01]\leavevmode\nobreak\
\text{km\leavevmode\nobreak\ s}^{-1}$ and
$\text{v}_{\text{LSR}}=[7.01,7.61]\leavevmode\nobreak\
\text{km\leavevmode\nobreak\ s}^{-1}$ respectively. The contour floor is
$3\leavevmode\nobreak\ \sigma$ (13 mJy/beam), increasing in linear intervals
of $1\leavevmode\nobreak\ \sigma$ (4.5 mJy/beam).

We present the first high spatial resolution images of the DO Tau bipolar jet
close to the star. Figure 1 shows a deconvolved intensity maps of the red- and
blue-shifted jets in [Fe II] 1.64 $\mu$m emission. (Recall the map is
deconvolved as described in section 2.3.) The blue-shifted jet is brighter
(right side of figure 1). Overlaid are intensity contours of C18O molecular
emission, from ALMA archival data, which traces the gaseous disk.

Rotating the jet image to the horizontal provided a revised estimate of the
blue-shifted jet PA = 260$\degr\pm$ 3$\degr$ (compared to 250$\degr\pm$
10$\degr$ (Hirth et al. 1997)). This is in very good agreement with the recent
determination of Fernández-López et al. (2020) from HST imaging and with the
large scale disk $PA=170\pm 0.9^{\circ}$ derived by Long et al. (2019) from
ALMA high-angular resolution continuum observations. There may be a small
misalignment of the red-shifted jet PA by $\simeq$ 1$\degr$, but changes in
the jet trajectory makes it difficult to claim with certainty.

The blue-shifted jet is detected as close as 0$\aas@@fstack{\prime\prime}$1
from the star and extends to 1$\aas@@fstack{\prime\prime}$2\. The dimmer
counter-jet does not appear until 0$\aas@@fstack{\prime\prime}$5, aside from a
small emission at $\sim$ 0$\aas@@fstack{\prime\prime}$35, and then similarly
extends to 1$\aas@@fstack{\prime\prime}$5\. Given the disk inclination angle
to the line-of-sight of 28∘ (Long et al. 2019), it seems that the base of the
red-shifted jet may be obscured by a disk of projected radius
0$\aas@@fstack{\prime\prime}$5 (70 au), or deprojected radius of
0$\aas@@fstack{\prime\prime}$57 (79 au). Long et al. (2019) derive a dusty
disk radius of 0$\aas@@fstack{\prime\prime}$263 (which converts to 39 au),
which is very compact with respect to other disks in their survey, and too
compact to obscure the red-shifted jet out to 0$\aas@@fstack{\prime\prime}$5\.
Similarly, Fernández-López et al. (2020) report a dusty disk radius of 47 au
(which converts to 0$\aas@@fstack{\prime\prime}$33). We note, however, that
continuum disk sizes in ALMA observations only probe millimetre-sized grains,
which appear to undergo significant inward migration relative to the gas. On
the other hand, near-infrared extinction is dominated by small sub-micron
grains expected to remain well-coupled to the gas. Referring to Figure 1 of
Fernández-López et al. (2020), we see that the Keplerian curve of the 12CO
emission is traced roughly out to 1$\arcsec$ (i.e. 150 au). This shows that
the gas disk, and therefore the associated small grains, are extended enough
to explain occultation of the base of the red-shifted jet in our data.

The jet image highlights morphological asymmetries between the two jet lobes:
the blue-shifted jet appears to maintain the same width as it propagates to
-1$\aas@@fstack{\prime\prime}$2, while the red-shifted jet, though initially
maintaining the same width, becomes a broad bow-shock type structure at
1$\aas@@fstack{\prime\prime}$2\. The bow-shock location appears to coincide
with the location of reported H-band emission from
1$\aas@@fstack{\prime\prime}$1 to 1$\aas@@fstack{\prime\prime}$7 to the
northeast of DO Tau (Itoh et al. 2008).

Gaussian fitting to intensity profiles allowed extraction of the jet axis
position and jet width. In Figure 1, the jet axis position is over-plotted
with black dots. There is a clear wiggling of both the blue- and red-shifted
jets. The wiggle appears to increase in amplitude with distance from the
source. From the wiggle pattern of the blue-shifted jet, we derive an observed
(projected) spatial wavelength $\lambda_{\text{obs}}=90\pm
5\leavevmode\nobreak\ \text{au}$, and semi-opening angle
$\theta_{\text{obs}}=1.3\pm 0.5\degr$. While the spatial wavelength is not
well constrained on the red-shifted side (with $\lambda_{\text{obs}}\simeq
100-200\leavevmode\nobreak\ \text{au}$), the wiggles seem to carve out a semi-
opening angle of $\theta_{\text{obs}}\simeq 2.6-4.7{\degr}$, which is clearly
larger than on the blue-shifted side. The origin of the wiggling will be
investigated further in section 4.3.

Figure 2 shows the jet widths for both jet and counter-jet as a function of
deprojected distance from the source. Full symbols show the jet widths
directly measured on the deconvolved images, while open symbols show the same
values deconvolved from the PSF width, taking the first measure as an estimate
of the PSF FWHM. These values give upper and lower limits respectively on the
intrinsic jet width. Indeed, since the deconvolution is performed on the
continuum subtracted images, no precise knowledge of the PSF in the final
deconvolved images is available. An upper limit on the PSF width is obtained
by assuming that the jet width is not resolved at distances closest to the
source. Halving the FWHM values, we obtain estimates of the jet radius. The
blue-shifted jet reveals a radius of $r\leavevmode\nobreak\
\leq\leavevmode\nobreak\ 4\leavevmode\nobreak\ {\rm au}$ at distances from the
star of $z=40\leavevmode\nobreak\ {\rm au}$. This increases steadily to
$r=8-9\leavevmode\nobreak\ {\rm au}$ at $z=300\leavevmode\nobreak\ {\rm au}$.
Both jets maintain the same jet width in their inner regions, which steadily
increases with distance. However, the red-shifted jet reveals an increased
width at the location of its apparent bow-shock feature as it propagates from
$z=$300 to 400 ${\rm au}$.

Comparing to the literature (figure 2), it appears that the DO Tau blue-
shifted jet is very narrow and strongly collimated with respect to other Class
II T Tauri jet targets. Indeed, it is similar to the well-known narrow jet of
the very active T Tauri star, RW Aur (Woitas et al. 2002), and to the higher
velocity component of the jet from DG Tau (Agra-Amboage et al. 2011). We
derive a semi-opening angle $\simeq$ 1.1-1.4∘ for the blue-shifted jet, for
deprojected distances along the jet axis z0 = 40$\leavevmode\nobreak\ -$300
au. No significant change in opening angle is observed over these distances.
Thus, our results confirm previous claims that jets already achieve strong
collimation on scales of a few tens of au after launching has occurred (Ray et
al. 2007). Furthermore, the DO Tau blue-shifted jet appears very narrow at its
base, with an upper limit on its radius of only r $<$ 4 au for a deprojected
distance along the jet axis z0=35 au from the star. This upper limit is very
similar to the collimation of the base of the HH 212 Class 0 jet seen with
ALMA (Lee et al. 2017). Finally, the derived value of the blue-shifted jet
semi-opening angle ($\leq 1.4^{\circ}$) is significantly smaller than the
estimated Mach semi-opening angle, $c_{s}/V_{jet}$ = 4.4∘ assuming
$T=8000\leavevmode\nobreak\ K$, indicating the necessity of an additional
collimation agent. These observations provide direct confirmation that atomic
jets originate from the very inner au of the star-disk system, as originally
shown by Hartigan et al. (2004). We also note that the collimation is similar
for the inner portions of both lobes of the bipolar jet, in spite of a strong
jet velocity asymmetry.

Figure 2: Jet FWHM versus deprojected distance from the source. Full circles
show the DO Tau FWHM directly measured on the deconvolved images (upper limit
to jet diameter) while open circles give the same values corrected for the
estimated PSF FWHM (=0$\aas@@fstack{\prime\prime}$06), giving a lower limit to
the jet diameter. All measurements from the other jets have been corrected for
their respective estimated PSF FWHM. Errors bars for DO Tau are 3$\sigma$. For
DO Tau, we assume an inclination of the jet axis to the line of sight of
i=23.5∘. The full and dashed lines are fits of the jet FWHM for z=35-300 au
with deprojected semi-opening angles of 1.1∘ and 1.4∘ respectively. We also
show FWHM for the DG Tau [Fe ii] HVC (blue lobe) from Agra-Amboage et al.
(2011), for the RW Aur jet (red lobe) from Woitas et al. (2002), and for the
HH 212 jet from Lee et al. 2017. Adopted jet inclination to the line of sight
are i=37∘ for DG Tau (Bacciotti et al. 2018), i=55.5∘ for RW Aur (Rodriguez et
al. 2018).

.

###  3.2 Jet Kinematics

####  3.2.1 Bipolar velocity asymmetry

Figure 3: Position-velocity diagram of the DO Tau bipolar jet in [Fe II] 1.64
$\mu$m emission along PA=160∘ in a pseudo-slit of width
$0\aas@@fstack{\prime\prime}3$. The contour floor is $3\sigma$ (solid line)
and increases in log intervals of 0.3. Note that $2\sigma$ is also marked
(dashed line), and $1\sigma=3.5\times 10^{-16}\text{erg\leavevmode\nobreak\
s}^{-1}\text{cm}^{-2}\text{\AA}^{-1}$. The horizontal solid line marks the
star position. The horizontal dashed lines mark the spatial resolution. The
blue dashed line shows the variation of the peak velocity centroids, derived
from Gaussian fitting to the line profiles. The green diamonds represent the
centroid velocities found by Hirth et al. (1997); red triangle represents the
velocity found by Giannini et al. (2019).

Radial velocities were measured by Gaussian fitting the spectrally binned [Fe
II] 1.64 $\mu$m line at each spatial position. Figure 3 shows a position-
velocity (PV) diagram of the bright blue-shifted jet and dimmer red-shifted
counter-jet.

Radial velocities are measured to be -103 $\pm$ 1 km s-1 and +173 $\pm$ 4 km
s-1 for the jet and counter-jet respectively, when we average over the entire
length of the jet. A similar radial velocity asymmetry of -92 km s-1 and +210
km s-1, at 1$\aas@@fstack{\prime\prime}$5 along the jet and counter-jet, was
previously reported by Hirth et al. (1997) \- see datapoints overplotted in
Figure 3. More recent results for the blue-shifted jet include Giannini et al.
(2019) who report well-resolved low and high velocity components (which remain
spectrally unresolved in our PV diagram), with the latter dominating the
emission, and having peak velocity $\sim$ -102 and -87 km s-1 for [O
I]$\lambda$6300 and [Fe II]$\lambda$16440 respectively. Simon et al. (2016)
report similar two-component results with centroid velocities of $\sim$ -97 km
s-1 for the [O 1]$\lambda$6300 higher velocity component. Comparing all these
measurements, we see that each species traces a slightly different velocity,
but within 10-15 km s-1and so no time variability is apparent across epochs.
Thus, our measurements confirm previous reports in the literature of the jet
velocity asymmetry, and show a limited time variability $\leq 10\%$ in the
blue-shifted jet velocity over a 20 year interval, and $\leq 20\%$ in the red-
shifted jet velocity.

The striking velocity asymmetry between the jet and counter-jet may be caused
by an interaction with the environment as the jet propagates, or it may be
intrinsic to the jet launching mechanism (see below). In our data, the
velocity asymmetry is observed in all positions where both jets are observed,
including as close as $z_{\rm proj}$ =0.5′′ (deprojected distances of 140 au).
Furthermore, although the red-shifted jet is not detected closer to the star
(likely due to obscuration by the dusty disk), the blue-shifted jet reaches
its terminal velocity even closer, at $z_{\rm proj}\leq 0.1^{\prime\prime}$,
corresponding to deprojected distances of z=28 au. These two results strongly
support a velocity asymmetry originating in the launching process itself,
rather than resulting from an interaction with the environment.

At each projected distance along the jet, $z_{\text{proj}}$, we compute the
launch time of the gas parcel of line of sight velocity
$V_{\text{rad}}(z_{\text{proj}})$ assuming constant ballistic motion since
origin:
$t_{\text{launch}}-t_{\text{obs}}=z_{\text{proj}}/(V_{\text{rad}}\times\tan(\text{i}))$,
where $t_{\text{obs}}$ is 2009.97 (average of the two observing epochs).
Figure 4 shows the deprojected velocities as a function of their time of
launch for both jets. This figure represents a reconstructed history of
ejection velocities. The plot has a time resolution, $\Delta t=\Delta
z/(V_{\text{rad}}\times\tan(\text{i}))$, on the order of 0.7 years on the
blue-shifted side, and 0.4 years on the red-shifted side. The non-detection of
the red-shifted jet emission, which would have been launched over the past 4
years, may be due to extinction by the circumstellar disk, as per section 3.1.
The blue-shifted jet shows an average deprojected velocity of 112 $\pm$ 3 km
s-1over the past 20 years, while the red-shifted jet shows an average
deprojected velocity of 190 $\pm$ 8 km s-1over 8 years. Launching of both jets
co-existed for at least 8 years, and the velocity asymmetry (with an almost
constant factor of $\simeq$ 1.7) is sustained over at least that period of
time. Since we concluded that the velocity asymmetry is likely to originate in
the launching process, the duration of the sustained asymmetry provides a
useful constraint on jet launch models (see section 4.2).

Figure 4: Jet deprojected velocities as a function of their time of launch
(measured from the average observation date tobs=2009.97) assuming ballistic
motion at constant velocity (see text for more details). Error bars include
uncertainties on the jet inclination and centroid line of sight velocities.

####  3.2.2 Jet shocks

While we do not identify any great velocity variations over time (thus lending
a stability to the velocity asymmetry of the bipolar jet), the fact that our
data is spatially resolved allows a snapshot of velocity variations within the
jet at a fixed point in time. Considering velocity variations along the jet
(for this epoch), Figure 5 shows a radial velocity map of the bipolar jet,
with an associated error map. We can see that the blue-shifted jet has a
radial velocity of -110 km s-1 at 0$\aas@@fstack{\prime\prime}$1 from the star
which decreases to -90 km s-1 at 0$\aas@@fstack{\prime\prime}$4, before
increasing again at 0$\aas@@fstack{\prime\prime}$5 to -100 km s-1 and more or
less maintaining this velocity further downstream. Such changes in velocity
are expected at shock fronts, where the gas is collisionally excited. However,
we do not clearly identify emission knots in the blue-shifted jet, and these
20 km s-1 variations in velocity do not correspond to any measurable change in
intensity or morphological feature at this distance, recall Figure 1.
Intriguingly, the initial decrease in velocity occurs over similar distances
as a jump in electron number density (see section 3.3). However, the gradient
in velocity is significantly smoother. This behaviour is not compatible with a
shock as the velocity would be expected to drop sharply at the location of the
shock front, which is not observed here.

####  3.2.3 Jet rotation

We consider velocity variations across the jet, which may indicate a rotation
of the flow or alternatively may be caused by a wiggling of the jet. We first
note that the borders of the jet travel at a lower velocity to the on-axis
component, dropping by $\sim$ 5 km s-1. This reflects the onion-like layered
velocity structure observed in other high resolution case studies (e.g.
Bacciotti et al. (2000)). At a distance larger than
0$\aas@@fstack{\prime\prime}$6 along the blue-shifted jet, the SE border of
the jet appears to be more red-shifted. These distances coincide with the
location of a wiggle in the jet axis. Meanwhile, at the same distances along
the red-shifted jet, the SE border is more blue-shifted.

Figure 5: Centroid velocity map of the DO Tau bipolar jet, derived from
Gaussian fitting the [Fe II] 1.64 $\mu$m line profile at each spaxel (see text
for more details). Brightness contours from figure 1 are overlaid, along with
the jet axis centroids. 3$\sigma$ errors are given in the bottom panels.

A closer examination of a possible asymmetry in radial velocity across the jet
first requires identification of the jet axis position. At a given distance
from the star, the jet axis position was identified by spectrally binning the
[Fe II] 1.64 emission line and fitting a Gaussian profile to determine the
peak centroid. The jet radial velocity was measured at each transverse
position from the jet axis, via Gaussian profile fitting. Measurements
equidistant from the axis were compared to identify differences in radial
velocity. Systematic asymmetries may be interpreted as a signature of a
rotation of the flow. A comparison with the disk rotation sense, if possible,
is a fundamental consistency check on the interpretation, i.e. the disk and
both lobes of the bipolar jet should all be seen to rotate in the same
direction.

Figure 6: Radial velocity profiles across the jet at various distances, z,
from the star. The vertical line marks the measured jet axis position at this
distance z, whereas the zero position on the x-axis marks the nominal jet axis
position according to the jet PA. The compass orientation of the x-axis is
from SE to NW. A jet rotation signature should reveal itself as a systematic
gradient in radial velocities across the jet in a sense that matches the disk
rotation sense. (Recall the kinematics were measured on data before PSF
deconvolution i.e. PSF FWHM = 0$"$15.) No systematic gradient is observed.
Errors are 3$\sigma$.

Figure 6 shows the transverse radial velocity profile at a selection of
projected distances, z, from the star. In the inner jet region
($<0\aas@@fstack{\prime\prime}5$), we would expect that the NW side of the jet
is less blue-shifted (redder), as this would match the sense of disk rotation,
Figure 1. However, it is clear that we cannot identify a gradient in the
Doppler profile, between positions symmetric about the jet axis, as would be
expected if due to rotation, due to the large error bars. Since errors on
centroid velocity fits are signal-to-noise dependant, measurements in the
borders of the jet suffer. This hampers our ability to detect small
differences in radial velocity between the jet borders.

Meanwhile, recall in figure 5 that from 0$\aas@@fstack{\prime\prime}$6 along
the jet, the SE border of the approaching jet seems more red-shifted. While
this does not agree with the disk rotation sense, the redder velocities
coincide with the location of a wiggle in the jet axis. By contrast, the
receding jet shows bluer velocities in the SE border, in agreement with the
disk rotation sense. Unfortunately, error bars on jet velocities, as well as a
wiggle of the jet axis, forbid certainty in any claim to observe jet rotation.
We can, however, provide an upper limit on a possible rotation signature based
on our calculated error bars (see section 4.1).

###  3.3 Electron Number Density of the Jet

A direct measure of the electron number density, $n_{e}$, can be obtained from
the emission line ratio [Fe II] 1.53$\mu$m/1.64$\mu$m (Pradhan & Zhang 1993).
To increase signal-to-noise, emission line fluxes were binned spatially across
the jet. This allowed a 1D plot of flux ratio along the jet axis from which
the electron number density was derived. Unfortunately, the [Fe II] 1.53$\mu$m
emission for the red-shifted jet was too faint, and so the electron number
density could not be estimated here. Figure 7 shows estimates for the blue-
shifted jet. We caution that our $n_{e}$ measurement closest to the star may
still be contaminated by photospheric subtraction residuals. We see that
derived $n_{e}$ values range from $1\leavevmode\nobreak\
\text{to}\leavevmode\nobreak\ 5\times 10^{4}$ cm-3 close to the star, and drop
to a plateau at $\simeq 10^{4}$ cm-3 beyond projected distances along the jet
of z=0.4-1′′. These values are lower than the $n_{e}$ values of 104.5 to 105
cm-3, derived by Giannini et al. (2019), from a spectrum on source with seeing
of 0$\aas@@fstack{\prime\prime}$8 (i.e. not spatially resolved along the jet).
Giannini et al. (2019) values are likely strongly dominated by the very inner
denser regions of the jets, which we do not probe here due to strong continuum
residuals. Hence, it is likely that $n_{e}$ remains high closer to the star,
i.e. our first datapoint may be discounted. Such high values are also
typically found at the base of other T Tauri jets (see e.g. Coffey et al.
2008).

Figure 7: Top: Blue-shifted jet centroid velocities with 3$\sigma$ errors.
Bottom: Electron number density, $n_{e}$, derived from the line ratio [Fe II]
1.53$\mu$m/1.64$\mu$m at various distances along the blue-shifted jet. [Fe II]
1.53$\mu$m emission close to the source was contaminated by residuals from
continuum subtraction.

###  3.4 Bipolar jet mass flux

A critical parameter in modelling jet physics is the mass flux of the jet.
Using our measurements, the jet mass flux was estimated with two methods,
described in detail in Nisini et al. (2005) and Agra-Amboage et al. (2011).

Method 1: For a jet uniformly filled with a number density of hydrogen nuclei,
nH, the mass flux is given by (see Eq. 2 in Agra-Amboage et al. 2011):

$\begin{split}\dot{\text{M}}_{J}=1.3\times
10^{-9}\text{M}_{\odot}\leavevmode\nobreak\
\text{yr}^{-1}\left(\frac{\text{n}_{H}}{10^{5}\leavevmode\nobreak\
\text{cm}^{-3}}\right)\\\
\times\left(\frac{\text{D}_{J}}{14\leavevmode\nobreak\
\text{au}}\right)^{2}\left(\frac{\text{V}_{J}}{100\leavevmode\nobreak\
\text{km}\text{s}^{-1}}\right)\end{split}$ (2)

where DJ is the jet diameter and VJ the jet velocity. The electron number
density $n_{e}$ and ionisation fraction $x_{e}$ together allow an estimate of
the hydrogen number density, $\text{n}_{H}=\text{n}_{e}/\text{x}_{e}$. For DO
Tau blue-shifted jet, the ionisation fraction, $\text{x}_{e}$, was reported as
0.01 at velocities of -100 km s-1 from high spectral resolution data (see Fig.
10 Giannini et al. 2019). Since there is no spatial information (i.e. how the
ionisation fraction changes with distance along the jet), we adopt this value
for all positions along the blue-shifted jet. The jet diameter is taken as the
jet FWHM directly measured in the deconvolved maps. This gives an upper limit
on the jet diameter (in the sense that we we do not correct for the PSF FWHM).
The deprojected jet velocity is given by
$\text{V}_{J}=\text{V}_{r}/\text{cos}(i_{jet})$, where $\text{i}_{jet}$ is the
jet inclination angle to the line of sight, and $\text{V}_{r}$ is the radial
velocity of the jet. The deprojected blue-shifted jet velocity is thus
$\text{V}_{J}=-109$ km s-1. Method 1 gives an upper limit on the mass flux.
Indeed, in addition to the upper limit on the jet radius, we also likely over-
estimate the hydrogen number density, given that we assume a constant
ionisation along the jet whereas the ionisation may vary (e.g. Bacciotti &
Eislöffel 1999). Indeed, the value taken from Giannini et al. (2019) is
probably dominated by the inner brighter regions close to the star, and so
better represents the base of the jet.

Method 2 allows us to derive an estimate of the jet mass flux from the [Fe II]
line luminosity and electronic density estimates. This method assumes
optically thin emission, uniform excitation conditions within the emitting
volume and iron fully singly ionized (Fe+/Fe=1). The [Fe II] line luminosity
per unit length can then be directly related to the mass flux with the
following equation (eq. 4 in Agra-Amboage et al. 2011):

$\begin{split}\dot{\text{M}}_{J}=1.45\times 10^{-8}\leavevmode\nobreak\
\text{M}_{\odot}\leavevmode\nobreak\ \text{yr}^{-1}\left(1+\frac{3.5\times
10^{4}}{\text{n}_{e}(\text{cm}^{-3})}\right)\left(\frac{\text{L}_{[\text{Fe}{\sc
ii}]}}{10^{-4}\leavevmode\nobreak\ \text{L}_{\odot}}\right)\\\
\times\left(\frac{\text{V}_{t}}{150\leavevmode\nobreak\
\text{km}\text{s}^{-1}}\right)\left(\frac{\text{l}_{t}}{210^{15}\text{cm}}\right)^{-1}\leavevmode\nobreak\
\left(\frac{[\text{Fe}/\text{H}]}{[\text{Fe}/\text{H}]_{\odot}}\right)^{-1}\end{split}$
(3)

where Vt is the jet tangential velocity projected on the plane of the sky, and
lt the length of the aperture both projected onto the plane of the sky. We
take vt=43.5 km s-1(calculated from $i=$23.5∘ and $v_{r}$=-103 km s-1) and lt
= 0$\aas@@fstack{\prime\prime}$05 = 1014 cm (at 140 pc). This method also
depends on the Fe gas phase abundance. Giannini et al. (2019) has shown that
the Fe gas phase abundance is close to solar in the DO Tau blue-shifted jet at
higher velocities, with [Fe/H] $\simeq$ 70% [Fe/H]☉. No spatial information is
available for the evolution of this ratio along the jet so we take here a
ratio value of 1 at all positions along the jet. No correction for extinction
was included either, since the already low visual extinction towards DO Tau,
Av= 0.75, has even less impact in the near-IR. Method 2 gives a lower limit on
the mass flux. Here, a lack of correction for extinction leads to an under-
estimated luminosity. Also, we do not correct for iron depletion, which again
yields a lower limit on the mass flux.

Figure 8 shows our results for the derived mass flux along the blue-shifted
jet. Errors are on the order of 30%, increasing to $>$ 50% beyond
0$\aas@@fstack{\prime\prime}$9 from the source. Since Method 1 provides an
upper limit and Method 2 a lower limit to the mass flux, we take an average of
the two methods. Note that the mass flux values presented in Figure 8 rely on
a one-dimensional plot of the electron number density along the jet (see
Figure 7). Given the faintness of the 1.53 $\mu$m line, it was not possible to
produce a 2D map of the density. Additionally, the total density is not
accessible without a measure of the ionisation fraction for which we have used
an estimate measured by Giannini et al. (2019) near the star (since they do
not spatially resolve the jet). Note that, with the assumption of a constant
ionisation fraction, the variation in mass flux with distance from the star
reflects the variation in electron number density. However, we caution that
spatially resolved measurements of ionisation fraction in other Class II jets
show that this quantity can fluctuate spatially by a factor of ten within a
few 100 au of the source (e.g. Lavalley-Fouquet et al. 2000; Bacciotti et al.
2002; Hartigan et al. 2007; Maurri et al. 2014). Therefore, we cannot exclude
that the fluctuations in Figure 8 could be caused by underlying spatial
variations in ionisation fraction, rather than a true change in mass flux. So
only the average value of mass flux will be considered hereafter. Thus, we
estimate 5 $\times$ 10-9 M⊙ yr-1 for the blue-shifted jet.

When considering the red-shifted jet, we note that the [Fe ii] 1.64 $\mu$m
line is about ten times fainter than in the blue-shifted jet, and the 1.53
$\mu$m line is not detected in the red-shifted jet in our data. Instead, to
estimate the mass flux in the red-shifted jet, we use the value for electron
density found by Hirth et al. (1997). In the red-shifted jet, an average
electron density of 5000 cm-3 is found between 2-4$\arcsec$ from the star.
Assuming the ionisation fraction is similar, this suggests a possible mass
flux on the order of 10-8 M⊙ yr-1 in the red-shifted jet. The mass loss rates
compare well with typical values derived for similar high accretion targets.
In particular, RW Aur reveals 2.6 and 2 $\times$ 10-9 M⊙ yr-1 for the red- and
blue-shifted jet, respectively (Melnikov et al. 2009).

We calculate a mass accretion to ejection ratio by using the mass accretion
rate, $\dot{M}_{acc}$ $\geq$ 1.44 $\times$ 10-7 $M_{\sun}yr^{-1}$ (Gullbring
et al. 1998). Summing our mass flux estimate for the red- and blue- shifted
jets, and comparing this to the mass accretion rate, we obtain a ratio of
0.10. Alternatively, since our red-shifted jet mass flux estimate is less
accurate, we assume that the red-shifted jet has the same mass flux as the
blue-shifted jet (an assumption for asymmetric jets supported by Melnikov et
al. (2009), we double our one-sided value of $\dot{M}_{jet}$ $\sim$ 5$\times$
10-9 M⊙ yr-1 to achieve a ratio for the bipolar jet of
2$\dot{M}_{jet}$/$\dot{M}_{acc}$ $\sim$ 0.07. These ratios are in line with
literature values for the HVC component in similar targets, such as e.g. DG
Tau (Maurri et al. 2014), RY Tau (Agra-Amboage et al. 2011), RW Aur (Melnikov
et al. 2009) and compatible with predictions from MHD launching models
(Ferreira et al. 2006).

Figure 8: Top panel shows the [Fe II] 1.64$\mu$m line luminosity per unit
length for the blue-shifted jet. (The red-shifted jet has a typical value of
$\sim$ 3 $\times$ 10-8 L${\sun}$ per unit length) Bottom panel shows the jet
mass flux calculated using two methods: method 1 (black) based on nH and jet
radius estimate, method 2 (green) based on the [Fe II] 1.64 $\mu$m line
luminosity per unit length and the electronic density ne to find the emitting
mass. Both methods are described in more details in the text. Method 1 gives
an upper limit, while method 2 is a lower limit.

##  4 Discussion

###  4.1 The Origin of the Bipolar Jet

Assuming the magneto-centrifugal mechanism of jet launching, our observations
can potentially provide a way of differentiating between competing models. The
main long-standing contenders in this class of model are: accretion powered
stellar winds launched from open magnetic field lines anchored at the stellar
surface (Matt & Pudritz 2005); winds launched from the interaction of the
stellar magnetosphere and inner disk from r $\sim$ 0.05 au (Shu et al. 2000;
Romanova et al. 2009; Zanni & Ferreira 2013); disk-winds launched from a range
of radii in the disk (Pudritz et al. 2007; Ferreira 1997).

Our high resolution observations of the jet base allowed us to probe a
possible jet rotation signature, which can be used to indicate the launch-
point of the jet. Unfortunately, the size of the error bars on radial
velocities measured across the jet prevent any claim of a jet rotation
detection. We can nevertheless impose an upper limit on any rotation present.
The errors in our measurements allow us to provide an upper limit on the jet
toroidal velocity, and hence provide constraints on jet launching models.

However, these models critically rely on an assumption of a steady,
axisymmetric flow. Clearly, evidence of jet wiggling may call into question
this assumption. Indeed, Cerqueira et al. (2006) showed that a precessing and
variable velocity jet can present transverse asymmetries in velocities similar
to rotation signatures. However, these simulations include strong velocity
variability at the source (with $\Delta V=\pm 100$ km s-1). The observed line
of sight velocity variations along the DO Tau jets do not exceed $\pm 5$km
s-1in the blue, $\pm 13$km s-1in the red, in the central 150 au. In addition,
our observations do not show any clear evidence for shock formation (no
emission knot detected) or brightness asymmetries across the blue-shifted jet.
Therefore, we assume that despite the small wiggling detected (with a
deprojected semi-opening angle of 0.5∘ more than twice smaller than the jet
beam semi-opening angle of 1.1-1.4∘, see Section 3.1), the low level of
velocity variability does not produce shocks strong enough to introduce
significant departure from axisymmetry for the global flow. No simulations of
jet propagation with such conditions exist to our knowledge, and would be
required to fully test this hypothesis. For DO Tau, the wiggling introduces
possible changes in the inclination angle of the flow axis to the line of
sight of $<0.5^{\circ}$ for the blue-shifted jet, and $<2.5^{\circ}$ for the
red-shifted jet. These variations are smaller than the assumed global
uncertainty of $5^{\circ}$ taken for the jet inclination to the line of sight.
We therefore apply the method outlined below to derive an upper limit on the
launching radius.

Assuming a steady, axisymmetric and cold MHD ejection process, the radius in
the disk-plane where the jet originates can be calculated using the method of
Anderson et al. (2003). This method relies on the general conservation
principles of total specific energy and momentum along each magnetic surface,
thus removing the magnetic term and so allowing a calculation of the launch
radius from observed velocities alone. The approximation below is valid when
the observed jet poloidal velocity is much greater than the Keplerian velocity
at the launch point, which is verified a-posteriori, see below. Hence, the jet
launch radius in the disk plane, $\bar{r}_{0}$, is given by:

$\begin{split}\bar{r}_{0}\simeq 0.7\leavevmode\nobreak\
\text{au}\left(\frac{\,\bar{r}_{\infty}}{10\leavevmode\nobreak\
\text{au}}\right)^{2/3}\left(\frac{\text{v}_{\phi,\infty}}{10\leavevmode\nobreak\
\text{km\leavevmode\nobreak\ s${}^{-1}$}}\right)^{2/3}\\\
\times\left(\frac{\text{v}_{p,\infty}}{100\leavevmode\nobreak\
\text{km\leavevmode\nobreak\
s${}^{-1}$}}\right)^{-4/3}\left(\frac{\text{M}_{*}}{1\leavevmode\nobreak\
\text{M}_{\odot}}\right)^{1/3}\end{split}$ (4)

where $\bar{r}_{\infty}$ is the radius from the jet axis of the observation
(at a distance from the disk plane of effectively infinity, z=$\infty$), vϕ,∞
is the toroidal velocity observed at z=$\infty$, vp,∞ is the poloidal velocity
observed at z=$\infty$, and M∗ is the mass of the star.

The poloidal velocity can be derived from the radial velocity,
$\bar{{\text{v}}}_{\text{r}}$ = $\text{v}_{p}$ cos($i_{\rm jet}$) while the
toroidal velocity can be derived from the difference in radial velocities
either side of the jet, $\Delta\text{V}_{\text{r}}$ = 2 vϕ sin($i_{\rm jet}$),
where the jet inclination angle is with respect to the line of sight. We make
our calculations based on velocity measurements at a distance along the jet of
z$\sim$0$\aas@@fstack{\prime\prime}$4 (corresponding to a deprojected distance
z0=112 au). We want to observe as close to the jet base as possible, to
maximize signal-to-noise and minimise effects of jet wiggling further
downstream, but far enough from the base to resolve the jet in the transverse
direction (without deconvolution). We take measurements at a distance across
the jet from the jet axis of r = 0$\aas@@fstack{\prime\prime}$1\. We avoid
using measurements very close to the jet axis because it is expected that, as
we draw closer to the jet axis, any radial velocity gradients across the jet
will be washed-out by beam convolution effects (Pesenti et al. 2004; Tabone et
al. 2020).

Referring to Figure 6, we see that for z$\sim$0$\aas@@fstack{\prime\prime}$4
(top right panel) we measure an average radial velocity of -95 km s-1 which
gives a jet poloidal velocity, $\text{v}_{p}$ = -103.6 km s-1 $\pm$ 7.5 km
s-1. For r = 0$\aas@@fstack{\prime\prime}$1 (outer datapoints), the error bars
give us an upper limit on the difference in radial velocity,
$\Delta\text{v}_{r}$ $<$ 5 km s-1. This gives us a 3 $\sigma$ upper limit on
toroidal velocity of $\text{v}_{\phi}$ $<$ 6.3 km s-1 $\pm$ 0.7 km s-1. We
thus achieve an upper limit on the specific angular momentum, r $\times$ vϕ,
carried by the jet of $<$ 87 au km s-1 $\pm$ 19 au km s-1. For a stellar mass
$M_{\star}\sim$ 0.59 $M_{\sun}$ (and assuming an uncertainty of 30% on the
stellar mass), we calculate an upper limit on the launch radius in the disk-
plane of $\bar{r}_{0}$ $<$ 0.5 $\pm$ 0.1 au. We perform the same calculation
for the red-shifted jet at a position of
z$\sim$0$\aas@@fstack{\prime\prime}$8, i.e. before variations in the jet axis
position become too large. At this position, we find an average radial
velocity of 170 km s-1 giving a poloidal velocity of 185 km s-1 $\pm$ 12 km
s-1. From the upper limit on the difference in radial velocity,
$\Delta\text{v}_{r}$ $<$ 7 km s-1 at a jet radius of r =
0.1$\aas@@fstack{\prime\prime}$, we derive an upper limit on the toroidal
velocity $\text{v}_{\phi}$ $<$ 8.7 km s-1 $\pm$ 0.9 km s-1 and specific
angular momentum $r{\rm v}_{\phi}$ $<$ 122 au km s-1 $\pm$ 27.1 au km s-1.
From these values for the poloidal velocity and specific angular momentum, we
infer an upper limit on the launching radius of the red-shifted jet to
$\bar{r}_{0}$ $<$ 0.3 au $\pm$ 0.06 au. Our derived upper limits on the
launching radii differ between the two lobes (r0 $<$ 0.5 $\pm$ 0.1 au for the
blue lobe, r0 $<$ 0.3 $\pm$ 0.06 au for the red lobe). However, since these
values are _upper limits_ , they do not exclude the same launching radius for
both sides of the jet. We note, however, that in each lobe we measure
different terminal velocities very close to the source. This points to a
possible asymmetric launching process which could imply different launch radii
for the two jet lobes. Possible origins and effects of an asymmetric jet
launch are discussed in Section 4.2.

Figure 9: Parameter space of the magnetic lever arm parameter,
$\lambda_{\phi}$, and jet launching radius, $r_{0}$, predicted for steady
magneto-centrifugal disk winds, based on the relationship between jet
kinematics, $rv_{\phi}$ and $v_{p}$ (see Ferreira et al. 2006). DO Tau blue-
and red-shifted jet kinematics are plotted, with 1$\sigma$ errors, revealing
theoretical $\lambda_{\phi}$ and $r_{0}$ upper limits.

Besides the launch point, $r_{0}$, another important parameter that can be
extracted from observed kinematics to constrain the MHD launching mechanism is
the ”magnetic lever arm parameter” $\lambda$ (Anderson et al. 2003 and
Ferreira et al. 2006). This parameter measures the total specific angular
momentum extracted by the wind in units of the Keplerian value at its
footpoint in the disk. It may be shown from steady MHD theory that $\lambda$
$\simeq$ ($r_{A}$/$r_{0}$)2 where $r_{A}$ is the Alfvén radius111The Alfvén
radius of the magnetic streamline is the distance along the outflow at which
the accelerating plasma reaches the velocity of the Alfvén wave propagating
along the flow, $v_{A}$=(Bp/(4$\pi\rho$))1/2. (Blandford & Payne 1982).
Therefore, the asymptotic level of wind rotation is the same as if matter was
forced to co-rotate rigidly with the field up to the Alfvén radius $r_{A}$,
and conserve its angular momentum beyond this point. The lever arm is,
therefore, a measure of the efficiency of the mechanism for extracting angular
momentum from the disk. (In reality, however, the conversion of field torsion
into outflow rotation takes place over scales $>$ $r_{A}$ so that the observed
$\lambda_{\phi}$ estimated from the specific angular momentum of the matter
only gives a lower limit to the true $\lambda$ (Pesenti et al. 2004, Ferreira
et al. 2006)). Note that $\lambda_{\phi}$ reaches $\lambda$ when all the
magnetic energy is converted to kinetic energy, i.e. when all angular momentum
has been transferred to the matter. This typically occurs when $z/r_{0}>>100$
(Tabone et al. 2020). Given the distance at which we make our measurements, z
= 0$\aas@@fstack{\prime\prime}$4-0$\aas@@fstack{\prime\prime}$8 ($\sim$ 60-120
au), and the small inferred values of $r_{0}<$ 0.3-0.5 au, we would thus
expect $\lambda_{\phi}\sim\lambda$. Using Equation 10 from Ferreira et al.
(2006), we retrieve an upper limit on $\lambda_{\phi}$ independently of
$r_{0}$ from observed values of $rv_{\phi}$ and $v_{p}$. (For graphical
derivation, see Figure 9.) We find $\lambda_{\phi}\sim\lambda\leq$ 6.25 and
11, for the blue- and red-shifted jets respectively.

Our derived upper limit for the DO Tau blue-shifted launching radius is
consistent with the low Fe gas phase depletion observed in this jet (Giannini
et al. 2019), suggesting that the Fe jet originates from close to the dust
sublimation radius in the disk, estimated to be $\sim$ 0.13 au by Eisner et
al. (2014). Our derived upper limit on $\bar{r}_{0}$ also matches the computed
upper limits of $r_{0}$ = 0.44 and 1.6 au for the RW Aur blue- and red-shifted
jet respectively (Woitas et al. 2005), and of $r_{0}<0.45$ au for the RY Tau
blue-shifted jet (Coffey et al. 2015). Moderate $\lambda$ values such as the
one derived here have been also favoured for the DG Tau jet (Pesenti et al.
2004). They correspond to warm MHD disk-wind solutions such as the ones
computed by (Casse & Ferreira 2000).

Our results do not allow discrimination between the competing launching
mechanisms. However, they confirm that the high-velocity jets originate from,
at most, 0.5 au $\pm$ 0.1 au from the star in the disk plane. We caution
however that these results only relate to the very narrow jet component which
is traced by the high velocity [Fe II] line. It is possible that there co-
exists a lower velocity, broader outflow component which is launched from
larger radii in the disk-plane. Indeed, a low-velocity component is also
detected in DO Tau in some typical jet emission lines (Giannini et al. 2019).
These authors have shown that physical properties (excitation temperature,
densities, ionisation fractions) vary continuously with velocities across the
line profiles suggesting a common physical origin for both the lower and
higher velocity components. Furthermore, Fernández-López et al. (2020)
estimate a larger upper limit of $\leq$ 15 au on the launching radius for the
wind component driving the ringed CO outflow which they recently identified.

###  4.2 The origin of the velocity asymmetry

In section 3.2.1, we report that the velocity asymmetry between the DO Tau
blue- and red-shifted jets is traced close to the source, indicating that it
is likely to be caused by the jet launch mechanism. We also report that the
asymmetry is constant at a factor 1.7 and sustained for around 7 years. For a
typical inner disk truncation radius of 0.05 au, the Keplerian orbital
timescale at the inner disk around a 0.59 M☉ star is 0.014 yrs ($\simeq$ 5
days). Therefore, the velocity asymmetry in the DO Tau bipolar jet is
sustained over a duration of at least 500 times the orbital period of the
inner disk. We investigate below the constraints brought by these results on
asymmetric jet launching models.

Lovelace et al. (2010), Dyda et al. (2015) and Lii et al. (2014) have all
studied the launching of asymmetric outflows from the magnetospheres of
rapidly rotating stars in the propeller regime. They find that the presence of
a small dipole component leads to the formation of one-sided accretion funnel
flows accompanied by episodic outflows in the opposite hemisphere. The
dominant direction of ejection changes stochastically on timescales of
$\simeq$ 30-50 inner disk orbital periods. The inclusion of a disk magnetic
field does not significantly affect these results (Dyda et al. 2015; Lii et
al. 2014). On longer timescales, the jets will therefore look essentially
symmetric. Such models therefore cannot account for the velocity asymmetry
sustained over typically an order of magnitude longer timescales observed in
the DO Tau bipolar jet.

A more promising scenario is provided by recent numerical works studying the
launching of outflows from magnetised disks. If originating from an MHD disk-
wind, a difference of a factor 4 in launching radius would account for a
difference of a factor 2 in terminal velocities. Alternatively, different
lambda values could be achieved between the two surfaces of the disk. The
pioneering studies of Fendt & Sheikhnezami (2013) and Dyda et al. (2015),
using a simplified $\alpha$ prescription for the disk viscosity, have shown
that indeed asymmetric high velocity jets can develop and endure over long
lasting timescales, $\simeq$ a few hundred orbital timescales at the inner
disk radius, depending on the disk magnetic properties. Bipolar jet velocity
asymmetries of up to a factor 2-2.5 are observed in such models.

Recent global non-ideal MHD simulations of magnetised disks, including more
comprehensive disk microphysics and evolving both hemispheres, have confirmed
these early results and shown that pronounced asymmetries between the lower
and upper disk halves of the disk can develop and launch asymmetric outflows
which persist over timescales of at least 1000 times the orbital period at the
inner disk radius (Béthune et al. 2017; Bai 2017; Gressel et al. 2020; Riols
et al. 2020). However, most of these recent simulations do not currently
include the very central regions of the disk (r $\leq$ 1 au) from which the
high-velocity jets are launched.

###  4.3 The Origin of Jet Axis Wiggling

As seen in Section 4.1, the DO Tau bipolar jet shows a quasi sinusoidal small
amplitude wiggling of its axis. Similar wiggling has been recently revealed at
the base of other T Tauri jets (e.g. Dougados et al. 2000; Anglada et al.
2007; Garufi et al. 2019). This wiggling is often interpreted as tracing the
dynamical perturbation due to an unseen companion. A companion can induce
wiggling of the jet axis in two different ways. The first one is orbital
motion of the jet source (Masciadri & Raga 2002; hereafter ‘orbital
scenario’). Alternatively, a mis-aligned companion can cause retrograde
precession of the disk rotation axis around the orbital axis Papaloizou &
Terquem (1995), and hence of the associated jet axis ((Terquem et al. 1999);
hereafter ‘precession scenario’). Sheikhnezami & Fendt (2018) have studied the
onset of jet/disk precession in a binary system and showed that moderate mis-
alignments between the binary and disk orbital planes ($<10^{\circ}$) are
required for persistent MHD jet launching. The small wiggling angle detected
here would therefore be consistent with such scenario. We discuss below the
two possible binary wiggling mechanisms, and show that both scenarii met
difficulties in reproducing the pattern of the DO Tau bipolar jet wiggle. We
then discuss an alternative jet precession mechanism related to a possible
warping instability in disks launching magnetically-driven outflows, proposed
by Lai (2003).

####  4.3.1 Wiggling due to binarity

In principle, we can distinguish between the orbital and precession motion
induced by a companion by examining the symmetry pattern of the wiggling
between the jet and counter-jet: orbital motion produces a mirror-symmetry,
while jet precession produces an S-shaped symmetry (Masciadri & Raga 2002).
For DO Tau, however, the effect is complicated by the velocity asymmetry
between the two jet lobes, and by the limited field of view of our NIFS
observations. To examine these two scenarii, we use the formalism and
equations first introduced by Masciadri & Raga (2002), and further developed
in Anglada et al. (2007) and Estalella et al. (2012), to model the wiggling in
the HH 30 bipolar jet.

##### i) Orbital scenario

Figure 10: Wiggle in the jet axis of DO Tau: Black dots with associated error
bars show the jet axis displacement, measured with respect to the blue-shifted
jet PA. On the red-shifted jet side (left), grey dots show measurements before
correction for a possible misalignment of 1∘ of the red-shifted jet. Top
panel: The red solid curve shows the orbital solution fitted to the blue-
shifted jet axis wiggling. Bottom panel: The solid cyan curve shows the
precession solution fitted to the blue-shifted jet axis wiggling. The dashed
cyan curve shows the same precession solution computed for the red-shifted
jet, but adjusted for a phase shift and an increased precession angle (by a
factor 2.5). See text for more details.

In the orbital scenario, the launching point of the jet moves as the jet
source orbits the center of mass of the system (where the jet source can be
either the primary or secondary component). We further assume that the jet
axis and the binary orbital axis coincide, i.e. the binary orbital plane and
the disk plane of the jet source are aligned.

Following Anglada et al. (2007), we define m1 as the mass of the jet source
and $\mu=\text{m}_{2}/\text{m}_{\text{tot}}$ as the ratio between the mass of
the companion and the total mass of the system. Let $a$ be the binary
separation and r0 the orbital radius of the jet source with respect to the
center of mass of the system ($\text{r}_{0}=\mu a$). Using the wiggling
parameters on the blue-shifted side with equations (6) & (7) from Anglada et
al. (2007), and including an uncertainty of $5^{\circ}$ for the jet
inclination and 5 km s-1for the blue-shifted jet line of sight velocity, we
derive for the jet source an orbital velocity of v0=1. $\pm$ 0.45 km s-1and an
orbital radius of r0=0.32 $\pm$ 0.13 au. The orbital period is then $\tau_{\rm
orb}$=9.5 $\pm$ 5.6 years. This best-fit solution is represented in Figure 10,
top panel. This solution reproduces the amplitude and spatial wavelength of
the jet axis wiggling on the blue-shifted side but fails to reproduce the
amplitude of the wiggles on the red-shifted side.

Indeed, the larger amplitude wiggling on the fastest jet side is in
contradiction with the expectation from the orbital model. In the orbital
scenario, the amplitude of the wiggles is set by the ratio between $V_{0}$,
the orbital velocity of the jet source around the center of mass of the
system, and $V_{jet}$. Given that the receding jet has roughly twice the
velocity of the approaching jet, we expect the opening angle of the wiggles to
be two times smaller on the red-shifted side, which is clearly not observed.

This orbital solution also predicts a periodic variation in line-of-sight
velocity of amplitude $\text{v}_{0}\times\sin{\text{i}}$ = 0.2-0.7 km s-1,
which is an order of magnitude smaller than the observed radial velocity
variations along the blue-shifted jet ($\pm 5$ km s-1over the inner 200 au)
and within our estimated uncertainties on the centroid velocities. So such a
variation could be hidden in larger amplitude variations due to, for example,
time variability in the ejection velocity.

##### ii) Precession scenario

Wiggling of the jet axis could also be the signature of precession driven by
tidal interactions between the disk and a companion in a non-coplanar orbit.
This scenario has been investigated in the context of the HH 30 bipolar jet by
Anglada et al. (2007); Estalella et al. (2012). We assume that the jet axis
precesses with a precession angle $\beta$ and precession period
$\tau_{\text{pre}}$ and that the jet precession axis coincides with the
average jet PA. We show in Figure 10 (solid blue curve) the equivalent
precession solution obtained by setting the precession period equal to the
period of the orbital solution ($\tau_{\text{pre}}=9.5\pm 5.6$ yrs) and the
precession angle $\beta$ such that $\tan(\beta)$ =
$\tan(\theta_{\text{obs}})\times\sin{\text{i}}$, which gives $\beta$= 0.52
$\pm$ 0.22 $\degr$ for the approaching jet.

Similar to the orbital solution, the spatial wavelength of the wiggles is
expected to be twice as large on the receding side as on the approaching side.
However,contrary to the orbital scenario, the apparent opening angle of the
wiggles does not depend on the jet velocity since it is set by the precession
angle. Such a solution also predicts a periodic variation of the line of sight
velocity of amplitude $\pm v_{j}\sin(\beta)\sin(i_{\text{jet}})\simeq 0.4$ km
s-1, very similar to the orbital case. These variations are much smaller than
both our estimated uncertainties and the observed radial velocity variations
along the jet.

Again, the agreement is not good on the receding jet side. A better match can
be obtained by introducing a phase shift between the precession of the red-
and blue-shifted jets and increasing the precession angle by a factor $\simeq$
2-2.5 for the red-shifted jet (dashed blue curve in Fig.10). Such a solution
would be possible if the red- and blue-shifted jets originate from annuli at
different radii in a warped disk (each disk annulus would make a different
angle in 3D with respect to the orbital plane).

In the case of a companion in an inclined orbit perturbing the circumstellar
disk of the jet source, a general expression for the precessional period was
originally derived by Papaloizou & Terquem (1995) and Terquem et al. (1998)
for arbitrary disk surface density distributions and rotation curves, assuming
rigid body precession and a circular orbit. The orbital period of the
companion is found to be significantly smaller than the disk precession
period, by at least one order of magnitude if $\mu<1$ (see Equation 24 in
Terquem et al. (1998)). In the DO Tau case, however, this would imply orbital
periods shorter than one year, which would be inconsistent with an orbit 2-4
times wider than DO Tau’s disk (which has $R_{d}$ ¿ 150 au, see Section 3.1).

An alternative scenario is a planetary mass companion in a misaligned orbit
within the primary disk itself. Recent works have studied the impact of such a
companion on the disk (Xiang-Gruess & Papaloizou 2013; Nealon et al. 2018; Zhu
2019). For sufficiently massive planets, a gap is created at the orbital
radius which can divide the disk in two parts. The inner disk then precesses
at a much faster rate than the outer disk. The relationship between the
companion orbital period $\tau_{\text{orb}}$ and the inner disk precession
period $\tau_{\text{pre}}$ is then given by a similar expression than in the
distant binary scenario (see Eq. 27 in Zhu (2019)):

$\frac{\tau_{\text{orb}}}{\tau_{\text{pre}}}=\frac{3}{8}\text{cos}(\text{i}_{\text{p}})\left(\frac{\mu}{\sqrt{(}1-\mu)}\right)\sigma^{3/2}$
(5)

where $\text{i}_{\text{p}}$ is the angle between the disk and the companion
orbital angular momentum vectors and $\sigma=\text{R}_{\text{d}}/\text{a}$ the
ratio of the radius of the inner disk to the companion separation. In the mis-
aligned planetary mass companion scenario $\sigma\simeq 1$. While this ratio
is 5 times larger than in the previous ”distant binary” scenario (where
$\sigma\simeq$ 1/3), it is still much smaller than 1 for $\mu<<1$ (planetary
mass companion). In the case of DO Tau, with
$\text{i}_{\text{p}}\simeq\beta=0.5\degr$, we thus have:

$\frac{\tau_{\rm orb}}{\tau_{\rm pre}}\simeq
0.37\frac{\mu}{\sqrt{(}1-\mu)}\simeq 0.37\mu\leavevmode\nobreak\
\text{for}\leavevmode\nobreak\ \mu<<1$ (6)

Additional constraints can be obtained by requiring that the angular effect
produced by the orbital motion of the jet source is negligible compared to the
precession angle, i.e.
$\frac{\text{V}_{0}}{\text{V}_{\text{j}}}\leq\text{tan}(\beta)$, which
translates here into v${}_{0}\leq 1.4$ km s-1(taking into account
uncertainties on $\text{V}_{\text{j}}$ and $\beta$). The total mass of the
system $\text{m}_{\text{tot}}$ and orbital velocity $\text{V}_{0}$ can be
expressed as a function of the orbital parameters by:

$\begin{split}\left(\frac{\text{m}_{\rm
tot}}{\text{M}_{\odot}}\right)=\mu^{-3}\left(\frac{\text{r}_{0}}{\rm
au}\right)^{3}\left(\frac{\tau_{\text{orb}}}{\rm yr}\right)^{-2}\end{split}$
(7)

$\begin{split}{V}_{0}=2\pi\frac{\text{r}_{0}}{\tau_{\text{orb}}}\end{split}$
(8)

Combining these equations, the requirements that $\text{v}_{0}\leq 1.4$ km
s-1and $\text{m}_{\text{tot}}\simeq 0.6$ M⊙ then imply $\mu\leq 0.02$, ie.
companion masses $\leq$ 12 MJup, and separations $\text{a}\leq$ 0.15 au.

Therefore the precession scenario requires a massive planetary mass companion
in a very close orbit (separation less than 0.15 au) with a small mis-
alignment of its orbit (a few degrees). It is not clear how such small
misalignments could be preserved over long timescales. Zhu (2019); Xiang-
Gruess & Papaloizou (2013) show that, in standard disk conditions, a massive
enough planet ($>$ 6 $M_{J}$) is required for the inclination damping
timescale to exceed the precession timescale at small misalignments. With this
additional constraint, the precession solution requires a companion mass in
the range 6-12 MJup with separations 0.1-0.15 au. Such a solution would still
allow the launching of the jet but seems unlikely as the survival of the inner
disk may be affected at such small separations. It is also not clear how the
red- and blue-shifted jets would precess with slightly different solutions
since this scenario predicts solid body precession of the inner disk.

####  4.3.2 Precession induced by magnetic torques

Given that the binary models face significant issues in reproducing the
observed wiggling in the DO Tau bipolar jet, we investigate an alternative
mechanism. Lai (2003) recently proposed that magnetic torques associated with
the outflow may cause warping instability of the accretion disk, and hence
precession of the disk rotation axis and associated jet axis. This study finds
that the growth timescale for the disk warp, and so the precession period, is
of the order of the radial accretion time of the disk, r/—vr—. The study
suggests that a warped, precessing disk-outflow system may be an alternative
(and preferred) state for an accretion disk threaded by large-scale magnetic
fields.

Here, we apply this idea to the case of DO Tau. We find the disk radial
accretion timescale, r/—vr—, by taking the radial distance travelled, r, as
the outer limit on our jet launching radius, r0 = 0.5 au $\pm$ 0.1 au. In a
standard viscous $\alpha$-disk model (Shakura & Sunyaev 1973), the radial
accretion velocity is given by vr $\sim$ $\alpha$ (h/r) $c_{s}$ under the
assumption of a thin disk (i.e. h/r $<<$ 1). Typically,
$\alpha=10^{-2}-10^{-3}$ and h/r$=0.1$, giving radial velocities which are
very subsonic ($\simeq 10^{-3}c_{s}$). However, in a disk launching a jet
through magneto-centrifugal processes, accretion radial velocities are
significantly increased with respect to the standard viscous case, due to the
efficient extraction of angular momentum provided by the magnetised wind. In
such as case, radial velocities are typically expected to fall between 0.1 and
1 cs (see e.g. Combet & Ferreira 2008). Taking a gas temperature of 1000 K,
which gives a sound speed $c_{s}$ $\sim$ 3 km s-1, we obtain a typical radial
accretion timescale ranging from $0.7$ to $7$ yrs. This rough estimate is
marginally compatible with the derived jet precession period of 10 $\pm$ 2.7
years, suggesting that such a mechanism could be at work in the DO Tau disk.
This disk warp could also account for a difference in PA of 1° between the
blue- and red-shifted jets, as well as for a slightly different precession
solution for the two jets if they arise from annuli at different radii in the
disk.

##  5 Conclusions

We present a case study of the DO Tau bipolar jet, examining the jet base with
high resolution spectro-imaging, in order to constrain jet launching models.
The main conclusions are the following:

\- The DO Tau blue-shifted jet is among the narrowest and initially most
collimated Class II jets identified so far. Strong collimation (with semi-
opening angle $\leq$ 1.5∘) is achieved within deprojected distance from the
source $z_{0}$=40 au. The derived opening angle is twice smaller than the
estimated Mach opening angle. The jet base is very narrow, with a jet radius
$<$ 4 au at $z_{0}$=40 au. This is similar to recent observations at the base
of the Class 0 HH 212 SiO jet (Lee et al. 2017). These results strongly
support a collimation mechanism independent of evolutionary stage, as already
suggested by Cabrit et al. (2007), which in turn strongly supports a magnetic
collimation mechanism.
\- The DO Tau red-shifted jet is not detected until projected distances from
the source z $\geq$ 0.5′′, consistent with occultation by the gaseous disk
observed with ALMA. It then shows a similar collimation to its blue-shifted
counter-part.
\- For the DO Tau blue-shifted jet, terminal velocities are reached within
$z_{0}$=40 au and show only small variability (less than 20%) thereafter on a
time-span of 15 years. This suggests weak shocks, if present at all. Indeed,
no emission knots can be clearly identified in the blue-shifted jet [Fe II]
emission.
\- We measure a blue-shifted jet electron number density of $5\times 10^{4}$
cm-3 close to the source (z$\sim$0$\aas@@fstack{\prime\prime}$3) followed by a
sharp decline and plateau to $1\times 10^{4}$ cm-3 at z
$\sim$0$\aas@@fstack{\prime\prime}$4-1$\arcsec$ from the source. Combined with
our velocity measurements, we derive a jet mass flux of $\dot{M}_{jet}$ $\sim$
5 $\times$ 10-9 M⊙ yr-1 for the DO Tau blue-shifted jet. Assuming a similar
mass flux for the red-shifted jet yields an overall ejection to accretion mass
flux ratio of $\dot{M}_{jet}$ $\times$2/$\dot{M}_{acc}$ $\sim$ 0.07.
\- No systematic difference in peak centroid velocity is observed across the
blue-shifted jet. Our observations put a 3 $\sigma$ upper limit on jet
rotation velocities of Vϕ $\leq$ 6.3 and 8.7 km s-1 for the blue and red-
shifted jets, respectively, at jet radii of r=14 au. This yields specific
angular momentum of $r\times V_{\rm phi}\leq$ 87 and 122 au km s-1 for the
blue and red-shifted jets, respectively. Under a _steady_ and _axisymmetric_
MHD disk-wind launching process assumption, this implies a jet launch radius
in the disk plane of r0 $\leq$ 0.5 au and r0 $\leq$ 0.3 au for the blue and
red-shifted jets, respectively. We discuss the possibility that such
difference derives from an asymmetric launch mechanism in the two disk
hemispheres. An origin so close to the star of the [Fe II] jet is consistent
with the absence of significant Fe gas phase depletion. However, we note that
the detection of wiggling in the jet may call into question the assumption of
axisymmetry, under which these values have been determined.
\- We confirm the previously reported striking velocity asymmetry between jet
and counter-jet, of a factor 1.7. This asymmetry is established close to the
source and stays constant over a time span of at least 7 years corresponding
to $\simeq$ 500 orbital timescales at the inner disk region. This long lasting
asymmetry is in accordance with predictions from recent simulations of
magnetised disk-winds.
\- We identify jet axis wiggling in both lobes with an apparent semi-opening
angle of 1.3 $\pm$ 0.5∘ and spatial wavelength of 90 $\pm$ 5 au on the blue-
shifted side. The spatial wavelength of the wiggles is poorly constrained on
the red-shifted side but the opening angle appears larger at 2.6-4.7∘. The
larger amplitude wiggling observed for the faster (red-shifted) jet excludes
orbital motion of the jet source as the origin of the wiggling. Precession of
the jet axis can be fitted to the observed wiggling on both sides if different
precession angles and precession phases are assumed. Such a solution would
require the blue- and red-shifted jets to originate from rings at different
radii in the disk, and to precess slightly differently. A warping instability,
induced by the launching of magnetic disk-wind, is a promising mechanism to
explain the disk precession and wiggling in the DO Tau bipolar jet.

Overall, the observed properties of the DO Tau bipolar jet are consistent with
properties of a disk-wind model for jet launching, provided it originates in
the inner regions of the disk. Our study shows the power of high resolution
spectro-imaging observations close to jet base in imposing constraints on
competing jet launching models. However, further case studies are required to
build statistics on asymmetric bipolar jets, if jet launching is to be fully
understood with all its consequent implications for magnetic field strengths
in the inner regions of protoplanetary disks.

###### Acknowledgements.

This work has benefited from the ULYSSES PHC France Ireland cooperative
program. This work was supported by the ”Programme National de Physique
Stellaire” (PNPS) of CNRS/INSU co-funded by CEA and CNES. JE acknowledges
funding from the UCD Physics Scholarship in Research and Teaching. FB
acknowledges support from the project PRIN-INAF-MAIN-STREAM 2017
“Protoplanetary disks seen through the eyes of new-generation instruments”.
Based on observations obtained at the Gemini Observatory, which is operated by
the Association of Universities for Research in Astronomy, Inc., under a
cooperative agreement with the NSF on behalf of the Gemini partnership: the
National Science Foundation (United States), National Research Council
(Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación
Productiva (Argentina), Ministério da Ciência, Tecnologia e Inovação (Brazil),
and Korea Astronomy and Space Science Institute (Republic of Korea).

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##  Appendix A Uneven slit illumination

For accurate rotation measurements, our derived Fe II velocity centroid maps
need to be corrected for spurious velocity shifts due to uneven-slit
illumination. The slicing mirrors in NIFS/GEMINI behave like a long-slit
spectrograph, for which off-axis light suffers from a shift in wavelength on
the detector with respect to on-axis light. The magnitude of this effect
depends on both the centering and gradient of light distribution within the
“slitlet”. In our observations, the total light distribution is dominated by
the PSF of the stellar continuum, which has a FWHM on the order of the
“slitlet” width (0.1′′). Therefore, one might expect this effect to be
significant over the spatial extent of the PSF wings which, due to imperfect
adaptive optics (AO) correction, cover a significant fraction of the NIFS
field of view.

We followed the method outlined in appendix A of Agra-Amboage et al. (2014) to
model the uneven slit illumination effect. We take, as the incoming light
distribution, an image in a wavelength band which includes the relevant
emission line plus the nearby continuum. This is obtained by spectrally
integrating the datacube in a narrow wavelength domain centered on the line of
interest, here [Fe II]$\lambda$1.64 $\mu$m, and over-sampled by a factor 5. In
each spaxel, we then estimate the location of the brightness centroid and its
displacement with respect to the slitlet center. The velocity shift induced by
the uneven slit illumination effect on a given spaxel is then given by the
following formula, adapted from Marconi et al. (2003):

$\Delta v(x_{0},y_{0})=\frac{\delta v}{\delta x/2.}\times\frac{\iint
I_{mod}(u,v)\times(u-x_{0})\,du\,dv}{\iint I_{mod}(u,v)\,du\,dv}$

where $\delta v$ is the spectral pixel sampling, $\delta x$ the width of the
slit, and $I_{\rm mod}$ is the model infalling light intensity integrated over
the current spaxel of detector coordinates (x0,y0).

Figure 11: Maps of velocity corrections required as a result of uneven slit
illumination, for both PA 160 °(left) and PA 340 °(right). Top panels are
computed by modelling the uneven slit illumination effect in each spaxel.
Bottom panels are measured velocity centroid shifts relative to the central
spectrum for the photospheric line near 16755Å, as a double-check on the model
output. Black contours show the position of the approaching jet.

Figure 11 shows the resulting 2D maps of the velocity corrections around the
[Fe II]$\lambda$1.64$\mu$m line for the datacubes corresponding to the two
instrument position angles used. These velocity corrections reach 7-10 km s-1
close to the stellar peak position, and rapidly decrease to a few km s-1 at
larger distances. As expected the velocity corrections have a stronger
variation along the $x$ (dispersion) direction.

We also determined empirically the velocity shifts induced by the uneven slit
effect by looking at a photospheric absorption line near 16755 Å, located in
the vicinity of the [Fe II] 1.64$\mu$m line. Figure 11 shows the centroid
velocity shifts relative to the central spectrum ($v_{\rm cen}(x,y)-v_{\rm
cen}(x_{0},y_{0})$), derived by Gaussian fitting of the line profile. Although
these maps are more noisy, they show very good agreement with the computed
model velocity correction maps above, Figure 11.