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Supplementary Material:
Spectro-astrometric Technique The method by which any displacement in the emission lines of
-Oph 102 is measured, can be summarised as follows:
1. A simple script based on the IRAF task splot is used to determine the position of the
continuum emission at different wavelengths. The Image Reduction and Analysis Facility
(IRAF) is written and supported by the IRAF programming group at National Optical
Astronomy Observatories (NOAO), Tuscon Arizona. In particular one can easily use this
interactive task to extract a spatial profile from a 2D spectrum and then fit it with a
gaussian. This is illustrated in Supplemental Figure 1. The fitting routine outputs the
position centroid and the full width half maximum (FWHM) of the profile and estimates
the arbitrary flux in relative counts.
2. Once the position of the continuum is measured for the whole spectrum one can then
remove any curvature and/or tilt, caused by misalignment effects of the optics, which may
be present in the spectrum. The position of the continuum is represented by the centroid of
the spatial profile measured at each wavelength. The line of such centroids, in the
dispersion direction but excluding any region where emission lines are present, is fitted
with a 2nd order polynomial, over a range of typically 200-300 Å. In this way instrumental
curvature, with a characteristic frequency many times larger than the width of any line, is
determined. The fit, to the centre of the continuum, is then subtracted from the actual
measured centroids leaving residuals that are evenly scattered about the abscissa (i.e. the
fit defines the zero offset line). Supplementary Figure 2 shows the position spectrum of
the continuum in the vicinity of the [OI]6300 line, for -Oph 102, before and after
continuum straightening. The emission line offsets are also corrected for any tilt or
curvature in the continuum. Note that even without fitting, the spatial offset in the
[OI]6300 line is clearly present.
Supplementary Figure 1
Continuum fitting and removal, using a long-slit spectrum of a typical young star, with an outflow (in this case
DG Tau). The extraction of a 1D spatial profile from firstly the continuum emission and then from an emission
line region in the continuum subtracted spectrum is illustrated. Note how easily the continuum can be removed
leaving the pure line regions exposed.
3. The next step is the continuum subtraction. If one is considering for example only the
emission line regions (ELRs), the raw spectrum i.e. before the continuum subtraction, is
in effect “contaminated’’ by the continuum. The effect this contamination has on the
spectro-astrometric plot is that one measures an offset for the ELR + continuum which, of
course is closer to the star than that of the pure ELR. Essentially the displacements
measured are dragged towards the continuum emission. It is therefore important that the
continuum be subtracted so that the true offsets of the different ELRs can be recorded.
The continuum subtraction is easily done using the IRAF continuum task. For a strong
continuum, emission is spread over a substantial number of rows in the dispersion
direction (see again Supplementary Figure 1). Once the range of lines over which the
continuum emission is spread is specified, the continuum task selects the first line in the
range, fits a 2D polynomial to this line (ignoring the ELRs) and then subtracts this fit. In
this way the continuum is removed line by line. One ensures that the ELRs are not
included in the fit to the continuum by using the sample parameter to specify the parts of
the spectrum that are continuum emission and the parts that are line emission. One can
also check the fit, alter its order and even its functional form at each line. The continuumsubtracted spectrum of a typical Classical T Tauri star is shown in Supplementary Figure
1 part (b).
4. Once the continuum is subtracted, any displacement in the pure ELR relative to the center
of the continuum can be measured. Again the splot task is used, in exactly the same way
as described above, to extract a spatial profile from a pure ELR and fit it with a gaussian.
Again Supplementary Figure 1 part (b) illustrates this process. As mentioned above any
tilt or curvature in the spectrum is removed from the plot of the continuum position by
fitting the continuum points and subtracting the fit. Obviously it is necessary that this fit
also be applied to the position velocity diagrams of the ELRs.
5. In the vicinity of the [OI]λ6300,6363 lines emitted by -Oph 102, there were in fact
several night-sky lines within the velocity range Figure 1 in our Letter. For example
adjacent to the [OI]λ6300 ELR a very weak OH line, at around -122 kms-1, as well as the
strong, but narrow, [OI]λ6300 line at approximately -9 kms-1 are observed. These
velocities are of course with respect to the systemic velocity of the BD. The
instrumentally determined width of the [OI]λ6300 airglow line was 15 pixels or 17 kms -1
(Full Width Zero Intensity).
Supplementary Figure 2
Spectro-astrometric plots in the vicinity of the [OI]6300 line of -Oph 102, before (top) and after (bottom)
continuum straightening. Line offsets are measured after the continuum subtraction.
The continuum, or the BD [OI]λ6300,6363 emission was not fitted in the region of any
night-sky lines. This explains the gaps in the continuum data points in Figure 1 in our
Letter and in the supplementary figures presented here.
Note that the offsets plotted in all figures are measured with these night-sky lines still
present. However, if the night-sky lines are removed, and the displacement measured as
before, no difference in the plotted offsets is seen. This is not surprising given the narrow
width, and position with respect to the BD emission, of the night-sky lines.
Supplementary Figure 3 shows the position spectra of the [OI] λ6300, 6363 ELRs before
and after the night-sky line subtraction. The night-sky line subtraction was done in a
similar way to the continuum subtraction using the IRAF continuum task.
6. Binning the spectrum, such that each extracted spatial profile is actually the sum of
several adjacent profiles, increases the spectro-astrometric accuracy (as outlined below).
As explained in the Letter, a different binning factor is used for the continuum, in
comparison with the line, so as to achieve a similar signal/noise, and hence offset errors,
in both regions. Use of this method, allowed the common error lines shown in the original
and supplementary figures, to be defined. In addition, it is important to employ the
smallest possible bin, consistent with a reasonable signal to noise, to sample the emission
line region. In this way one can easily see how the offset varies with velocity. The
different binning factors for the continuum and line emission explains the different
frequency of points within the line and continuum regions. Our experience with Classical
T Tauri stars is that the forbidden emission line offset peaks within a certain velocity
range but decreases for higher and lower velocities as also seen for -Oph 102.
Additional ELRs. Spectro-astrometric plots are presented in the Letter for the [OI]6300,
6363, H and [SII]6731 emission lines only. The HeI6678 emission line and the Li6708
absorption line were also prominent in the spectrum of this BD. In Supplementary Figure 4
spectro-astrometric plots for the Li6708 and HeI6678 lines are presented.
No offset is
expected in the Li6708 and HeI6678 lines as they are photospheric and chromospheric
respectively and none is found.
Supplementary Figure 3
The [OI]6300, 6363 ELRs were initially fitted with the night sky (NS) lines still present (left panel). However in
order to check for any contamination by the NS lines to the measured displacements, they were removed as per the
continuum subtraction and the residual profiles were then fitted (right panel). There was no difference in the offset of
the [OI]6300, 6363 ELRs.
Supplementary Figure 5 shows the position spectra of the [OI]6300, 6363, H and HeI6678
lines. For each line the continuum is fitted across the whole of each order and this figure is
included here to emphasise that a significant displacement is only measured at the forbidden
emission line regions.
Supplementary Figure 4
Other lines present in the spectrum included HeI6678 and Li6706.
Supplementary Figure 5
Figure showing the displacement in the [OI]6300, 6363, [SII]6731 and HeI6678 ELRs, with respect to the
continuum measured across a large part of the individual orders. Note that at no other point in any of the lines do the
significant displacements measured at the forbidden ELRs occur.
. 1/2
The critical density for a forbidden line scales with M Jet To prove that the critical density for
. 1/2
.
a forbidden line roughly scales with, M Jet where M Jet is the mass loss flux through the jet, we
note first of all that:
.
M Jet  πr 2ρVJet
where r, ρ, and VJet are the jet radius, density and velocity respectively. The radius in turn is
related to the jet opening angle θ (in radians) by θ ≈ r/L where L is the distance to the source and
thus:
.
M Jet  πρVJet θ 2 L2
Now as mentioned in our Letter, the escape velocity, and hence the jet velocity, for a brown
dwarf and a T Tauri star should be approximately the same. Moreover the opening angle of such
jets seem to be close to their ballistic values, i.e. θ ≈ 1/MJet where MJet is the jet Mach number.
Since the gas temperature determines the sound speed, and this in turn depends on the line
emission, we expect the Mach numbers for jets from T Tauri stars and brown dwarfs to be close.
Thus we also expect their opening angles to be similar.
Finally the spatial offset we observe between the source and the centroid of emission for a
forbidden line roughly coincides with the point at which the critical density for the line is
. 1/2
reached. From the last formula, this offset is then expected to scale with M Jet .