Issue |
A&A
Volume 501, Number 1, July I 2009
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|
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Page(s) | 269 - 278 | |
Section | Interstellar and circumstellar matter | |
DOI | https://doi.org/10.1051/0004-6361/200911883 | |
Published online | 29 April 2009 |
A break in the gas and dust surface density of the disc around the T Tauri star IM Lupi
O. Panic1 - M. R. Hogerheijde1 - D. Wilner2 - C. Qi2
1 - Leiden Observatory, Leiden University, PO Box 9513, 2300
RA, Leiden, The Netherlands
2 - Harvard-Smithsonian Center for Astrophysics, 60 Garden Street,
Cambridge, MA 02138, USA
Received 19 February 2009 / Accepted 2 April 2009
Abstract
Aims. We study the distribution and physical properties of molecular gas in the disc around the T Tauri star IM Lup on scales close to 200 AU. We investigate how well the gas and dust distributions compare and work towards a unified disc model that can explain both gas and dust emission.
Methods. 12CO, 13CO, and C18O J=2-1 line emission, as well as the dust continuum at 1.3 mm, is observed at 1
8 resolution towards IM Lup using the Submillimeter Array. A detailed disc model based on the dust emission is tested against these observations with the aid of a molecular excitation and radiative transfer code. Apparent discrepancies between the gas and dust distribution are investigated by adopting simple modifications to the existing model.
Results. The disc is seen at an inclination of 54
and is in Keplerian rotation around a 0.8-1.6
star. The outer disc radius traced by molecular gas emission is 900 AU, while the dust continuum emission and scattered light images limit the amount of dust present beyond 400 AU and are consistent with the existing model that assumes a 400 AU radius. Our observations require a drastic density decrease close to 400 AU with the vertical gas column density at 900 AU in the range of
-1022 cm-2. We derive a gas-to-dust mass ratio of 100 or higher in disc regions beyond 400 AU. Within 400 AU from the star our observations are consistent with a gas-to-dust ratio of 100 but other values are not ruled out.
Key words: planetary systems: protoplanetary disks - stars: individual: IM Lup - stars: pre-main sequence - circumstellar matter
1 Introduction
Low-mass star formation is commonly accompanied by the formation of a circumstellar disc. The disc inherits the angular momentum and composition of the star's parent cloud, and is shaped by the accretion and other physical processes within the disc during the evolution that may result in a planetary system. Over the past two decades observations of circumstellar discs at millimetre wavelengths have been established as powerful probes of the bulk of the cold molecular gas and dust. Spatially resolved observations of the molecular gas with (sub) millimetre interferometers constrain the disc size and inclination, the total amount of gas, its radial and vertical structure, and the gas kinematics (e.g., Dartois et al. 2003; Isella et al. 2007; Qi et al. 2004; Piétu et al. 2007; Panic et al. 2008; Guilloteau & Dutrey 1998). In parallel, continuum observations of the dust at near-infrared to millimetre wavelengths provide the disc spectral energy distribution (SED), that through modelling (e.g., Chiang & Goldreich 1997; Dullemond et al. 2001; D'Alessio et al. 2005) yields the disc's density and temperature structure from the disc inner radius to a few hundred AU from the star. Studies of the gas through spatially resolved molecular line observations using results from the SED modelling (e.g., Raman et al. 2006; Panic et al. 2008) offer the means of addressing the gas-to-dust ratio, differences between the radial and vertical distributions of the gas and the dust, and the thermal coupling between the gas and the dust in the upper disc layers exposed to the stellar radiation (e.g., Jonkheid et al. 2004). Recent papers have suggested different disc sizes for the dust and the gas (e.g., HD 163296, Isella et al. 2007), which may be explained by sensitivity effects in discs with tapered outer density profiles (Hughes et al. 2008). Here, we present the results of a combined study using spatially resolved molecular-line observations and SED modelling of the disc around the low-mass pre-main-sequence star IM Lup.
Most pre-main-sequence stars with discs studied so far in detail are
located in the nearby star-forming region of Taurus-Aurigae,
accessible for the millimetre facilities in the northern
hemisphere. Much less is known about discs in other star-forming
regions such as Lupus, Ophiuchus or Chamaeleon. It is important to
compare discs between different regions, to investigate if and how
different star-forming environments lead to differences in disc
properties and the subsequent planetary systems that may result.
IM Lup is a pre-main-sequence star located in the Lupus II cloud for
which Wichmann et al. (1998) report a distance of pc using
Hipparcos parallaxes. From its M0 spectral type and estimated
bolometric luminosity of
,
Hughes et al. (1994) derive a
mass of 0.4
and an age of 0.6 Myr using evolutionary tracks
from Swenson et al. (1994), or 0.3
and 0.1 Myr adopting the
tracks of D'Antona & Mazzitelli (1994). In Pinte et al. (2008), a much higher value of 1
is derived using tracks of Baraffe et al. (1998).
IM Lup is surrounded by a disc detected in scattered light with the
Hubble Space Telescope (Pinte et al. 2008)
and in the
CO J=3-2 line with the James Clerk Maxwell Telescope by
van Kempen et al. (2007).
Lommen et al. (2007) conclude that grain growth up
to millimetre sizes has occured from continuum measurements at 1.4 and
3.3 mm. Recently, Pinte et al. (2008) present a detailed model for the disc
around IM Lup based on the full SED,
scattered light images at multiple wavelengths from the Hubble Space
Telescope, near- and mid-infrared spectroscopy from the Spitzer Space
Telescope, and continuum imaging at 1.3 mm with the Submillimeter
Array. They conclude that the disc is relatively massive,
with an uncertainty by a factor of a few, has an outer dust radius
not greater than
400 AU set by the dark lane and lower reflection lobe seen in
the scattered light images, and has a surface density
proportional to R-1 constrained by the 1.3 mm data. Furthermore,
they find evidence for vertical settling of larger grains by comparing
the short-wavelength scattering properties to the grain-size
constraints obtained at 1.4 and 3.3 mm by Lommen et al. (2007).
In this work, we present (Sect. 2) spatially resolved
observations of the disc around IM Lup in 12CO, 13CO and
C18O J=2-1 line emission, together with 1.3 mm dust continuum
data, obtained with the Submillimeter Array (SMA). Our results (Sect. 3) show that
the gas disc extends to a radius of 900 AU, more than twice the size
inferred by Pinte et al. (2008). A detailed comparison (Sect. 4.1)
to the model of Pinte et al. (2008) suggests a significant break in the
surface density of both the gas and the dust around 400 AU, and we
discuss possible explanations. We summarise our main conclusions in
Sect. 5.
2 Observations
IM Lup was observed with the SMA on 2006 May 21 in a 8.6 h
track, with a 4.3 h on-source integration time. The coordinates of the phase centre are
RA = 1556
09
17 and Dec
56
06
40 (J2000). Eight
antennas were included in an extended configuration providing a range
of projected baselines of 7 to 140 m. The primary beam
half-power width is
.
The SMA receivers operate in a double-sideband (DSB) mode with an intermediate frequency band of 4-6 GHz which is sent over fiber optic transmission lines to
24 ``overlapping'' digital correlator chunks covering a 2 GHz spectral window in each sideband. The DSB system temperatures ranged from 90 to 150 K.
The correlator was configured to include the 12CO J=2-1 line
(230.5380000 GHz) in the upper sideband and the 13CO 2-1
(220.3986765 GHz) and C18O 2-1 line (219.5603568 GHz) in the
lower sideband. Each of the three lines was recorded in a spectral
band consisting of 512 channels with 0.2 MHz spacing
(
0.26 km s-1). Simultaneously to the line observations,
the 1.3 mm dust continuum was recorded over a bandwidth of 1.8 GHz.
The data were calibrated and edited with the IDL-based MIR software package. The bandpass response was determined from Jupiter, Callisto and 3C 273. After the passband calibration, broadband continuum in each sideband was generated by averaging the central 82 MHz in all line-free chunks. Complex gain calibration was performed using the quasar J1626-298.
The absolute flux scale was set using observations of Callisto.
Subsequent
data reduction and image analysis was carried out with the Miriad
software package (Sault et al. 1995).
The visibilities were Fourier transformed with natural weighting,
resulting in a synthesized beam of
at a
position angle of
1 Jy/beam corresponds
to 15.9 K. The rms noise level is
125, 94 and 102 mJy beam-1 per channel respectively for the 12CO, 13CO
and C18O spectral line data and 4 mJy beam-1 for the continuum data.
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Figure 1:
Dust continuum image at 1.3 mm. The contours are at (2, 4, 8, 16)
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Figure 2:
a, b) First moment maps in the 12CO and 13CO
J=2-1 lines, from 1.9 km s-1 to 6.9 km s-1 observed towards IM Lup. These maps
are created using the Miriad task ``moment'' with clip levels of
0.5 and 0.3 Jy respectively. The integrated emission of 12CO J=2-1 is shown in
contours of 1, 2, 3, ... |
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3 Results
3.1 Dust continuum
Figure 1 shows the 1.3 mm continuum emission observed toward
IM Lup, previously reported in Pinte et al. (2008). The emission is centered on RA
56
09
20, Dec =-37
56
06
5 (J2000), offset by +0
4 in right ascension and by -0
1 in declination
from the pointing center. We adopt the peak of the
continuum emission as the position of IM Lup. The peak intensity of
the continuum emission is
mJy beam-1 and the total
flux
mJy. The emission intensity is fit to the precision of one sigma by an elliptical
Gaussian, yielding a source FWHM size of 1
and a position angle of
deconvolved with the
synthesized beam. This position angle, and the inclination in the range of 33
suggested by the deconvolved aspect ratio, agree well with the values obtained by Pinte et al. (2008)
of, respectively,
and 45
from scattered light imaging.
A fit to the 1.3 mm visibilities done in Pinte et al. (2008) provides a rough disc mass estimate of 0.1 ,
with an uncertainty of a factor of few, dominated by the adopted dust emissivity and gas-to-dust mass ratio in the model.
3.2 Molecular Lines
Emission of 12CO and 13CO J=2-1 was detected toward
IM Lup, and an upper limit on C18O 2-1
obtained. Figure 2 shows the zero moment (integrated emission,
contours) and first moment (velocity centroid, colour scale) of the
12CO and 13CO emission from IM Lup. Significantly detected
12CO emission extends to 5
from the star (roughly 900 AU for IM Lup).
This is more than double the size inferred from
the dust continuum image, and Sect. 4 discusses if
this is due to different sensitivity in these two tracers or if the
gas disc indeed extends further than the dust disc. The aspect ratio
(5/3), suggesting an inclination of
,
and
orientation PA =
of the CO disc, agrees with the continuum image
(Sect. 3.1) and scattered light imaging results (Pinte et al. 2008).
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Figure 3:
12CO, 13CO, and C18O J=2-1 line spectra
summed over
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The first moment images of Fig. 2 show velocity patterns
indicative of a rotating disc inclined with respect to the line of sight. This is also
seen in Fig. 3, which presents the 12CO, 13CO, and
C18O spectra averaged over
boxes around IM
Lup. The 12CO and 13CO lines are double-peaked and centered on
km s-1. Figures 4 and 5 show the channel maps of the 12CO and 13CO
emission,
respectively, revealing the same velocity pattern also seen from the
first-moment maps and the spectra. The Keplerian nature of the
velocity pattern is most clearly revealed by Fig. 6, which
shows the position-velocity diagram of the 12CO emission along
the major axis of the disc. In Sect. 4, we derive a stellar mass of 1.2
,
and, as an illustration,
the rotation curves for stellar masses of 0.8, 1.2, and 1.6
are plotted in Fig. 6.
Using single-dish 12CO 3-2 observations, van Kempen et al. (2007) first
identified molecular gas directly associated with IM Lup, but they
also conclude that the
-range of 4 to 6 km s-1 is
dominated by gas distributed over a larger (>30'') scale. In our
12CO 2-1 data this same
-range is also likely affected:
where the single-dish 12CO 3-2 spectrum from
van Kempen et al. shows excess emission over
km s-1, the red peak of our 12CO 2-1
spectrum, which lies in this
-range, is weaker than the blue
peak at +3.5 km s-1. We suspect that absorption by the same
foreground layer identified by van Kempen et al. is responsible
for this decrement, while its emission is filtered out by the
interferometer. The 13CO 2-1 spectrum is symmetric, suggesting
that the foreground layer is optically thin in this line.
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Figure 4:
The black contours show the observed 12CO J=2-1 emission in the velocity range from
2.46 to 6.42 km s-1. Alongside the observations, the panels with grey contours show the
calculated emission from the extended disc model described in
Sect. 4.2, with parameters
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Figure 5:
Channel maps of the observed 13CO J=2-1 emission at the velocities where the line is
detected are shown in black contours. For comparison, the line emission calculated from our
extended disc model described in Sect. 4.2 is shown in grey contours. The model
parameters are
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The spatial extent of the line emission is further explored in
Fig. 7 which plots the 12CO and 13CO J=2-1vector-averaged line fluxes against projected baseline length. The
12CO flux is integrated from 2.5 to 4.0 kms-1 to avoid the
range where foreground absorption affects the line. The 13CO flux
does not suffer from absorption and is integrated over its full extent
from 2.5 to 6.9 kms-1. Comparing the curves of Fig. 7 to
those of the continuum flux versus baseline lengths (Fig. 8) it
is clear that the line flux is much more dominated by short spacings (<40 k
). This profile may indicate the presence of a larger structural component (outer disc or envelope), combined with the disc emission (see Jørgensen et al. 2005, Fig. 2). We explore disc structure beyond 400 AU in the following section.
4 Discussion
The results of the previous section show that IM Lup is surrounded by a gaseous disc in (roughly) Keplerian rotation. The gas disc has a radius of 900 AU, and its surface density may have a break around a radius of 400 AU. In contrast, the size of the dust disc is constrained to a radius of 400 AU by our continuum data and the modelling of Pinte et al. (2008). This section explores if the gas and dust have the same spatial distribution (in which case different sensitivity levels need to explain the apparent difference in size) or if the gas and dust are differently distributed radially. First we investigate whether the model of Pinte et al. (2008) can explain the molecular line observations (Sect. 4.1). After we conclude that this is not the case, we construct new models for the gas disc (Sect. 4.2) describing their best-fit parameters, and compare them to the dust disc (Sect. 4.3).
4.1 Molecular-line emission from the dust-disc model
Recently, Pinte et al. (2008) present a detailed model for the disc around IM Lup based on the full SED, scattered light images at multiple wavelengths from the Hubble Space Telescope, near- and mid-infrared spectroscopy from the Spitzer Space Telescope, and continuum imaging at 1.3 mm with the Submillimeter Array.
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Figure 6:
Position-velocity diagram of the 12CO 2-1 line emission
along the disc's major axis. Contour levels are (1, 2, 3,
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Based on the two-dimensional density and temperature structure of the Pinte et al. model, with
M=0.1 ,
AU, and
,
we
calculate the resulting line intensity of the 12CO and 13CO
J=2-1 lines. To generate the input model for the molecular
excitation calculations, we adopt a gas-to-dust mass ratio of 100 and
molecular abundances typical for the dense interstellar medium
(Wilson & Rood 1994; Frerking et al. 1982): a 12CO abundance with respect to H2of 10-4 and a 12CO/13CO abundance ratio of 77. No
freeze-out or photodissociation of CO is included. The velocity of the
material in the disc is described by Keplerian rotation around a
1.0
star plus a Gaussian microturbulent velocity field with a
FWHM of 0.16 km s-1; the exact value of the latter parameter has little effect on the
results. Using the molecular excitation and radiative transfer code
RATRAN (Hogerheijde & van der Tak 2000) and CO-H2 collision rates from the
Leiden Atomic and Molecular Database
(LAMBDA
,
Schöier et al. 2005) we calculate the sky brightness distribution of
the disc in the 12CO and 13CO J=2-1 lines for its distance of
190 pc. From the resulting image cube, synthetic visibilities
corresponding to the actual (u,v) positions of our SMA data were
produced using the MIRIAD package (Sault et al. 1995). Subsequent Fourier
transforming, cleaning, and image restoration was performed with the
same software.
Figure 2 compares the zeroth-moment (integrated intensity;
contours) and first-moment (velocity-integrated intensity; colour scale) maps of
the resulting synthetic images to the observations. Clearly, the
Pinte et al. model produces 12CO and 13CO 2-1
emission with spatial extents and intensities too small by a factor close to two. In Fig. 7 it is clear that the Pinte et al. model fails to reproduce the 12CO and 13CO line fluxes at short projected baseline lengths, but is consistent with the observations longward of 40 k
that correspond to spatial scales
500 AU.
Our comparison with Pinte et al. model thus suggests that the gas extends much further
than 400 AU from the star.
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Figure 7:
The left and the right panel show vector-averaged 12CO and 13CO line flux (black symbols),
respectively. Dashed black lines represent the zero-signal expectation value of our line visibility
data. The calculated visibilities based on Pinte et al. model (full red line) and
our extended disc model described in Sect. 4.2 (dotted red line) are shown for comparison.
Our model parameters are
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The observed 1.3 mm continuum emission traces the extent of larger dust particles (up to millimetre in size). Pinte et al. (2008) show that their 400 AU model reproduces these observations well. In Sect. 4.3 we explore to what level larger particles can be present outside 400 AU.
4.2 Extending the gas disc beyond 400 AU
As mentioned in Sect. 3.2, the CO line flux as function of
projected baseline length suggests a possible break in the emission
around 40 k
(Fig. 7). Results of Sect. 4.1 show that the
Pinte et al. model, while providing a good description of line fluxes at small spatial scales (baselines
), requires a more extended component to match the observed line fluxes (baselines
). In this section we extend the Pinte et al. model by simple radial power laws for the gas surface density and temperature, and place limits on the gas
column densities in the region between 400 and 900 AU.
Table 1 lists the model parameters. For radii smaller than
400 AU, the radial and vertical density distribution of the
material follows the Pinte et al. model. As in Sect. 4.1 we adopt ``standard'' values of gas-to-dust mass ratio and molecular abundances, and a Gaussian microturbulent
velocity field with equivalent line width of 0.16 km s-1. Unlike the calculations of
Sect. 4.1 we add as free parameters the stellar mass and the gas kinetic temperature. For the latter, we follow the
two-dimensional structure prescribed by Pinte et al., but scale
the temperatures upward by a factor f with
.
This
corresponds to a decoupling of the gas and dust temperatures, as may
be expected at the significant height above the midplane where the
12CO and 13CO lines originate (see, e.g., Jonkheid et al. 2004; Qi et al. 2006). Because the highly red- and blue-shifted line emission (line wings)
comes from regions closer to the star than 400 AU and is optically thick, factor f is determined by the observed fluxes in the line wings. The molecular excitation and synthetic line data
are produced in the same way as described in Sect. 4.1.
Outside 400 AU we extend the disc to
900 AU, as suggested by the observed 12CO image of Fig. 2,
by simple radial power laws for the surface density and temperature,
and
.
At 400 AU, the surface density is
and the temperature is T400; the parameter p is assumed to be
.
To limit the number of free parameters,
we set
T400=30 K and q=0.5; we assume that the disc is
vertically isothermal and that the 12CO abundance is 10-4, constant throughout the disc. At R>400 AU, the disc thickness is set to
AU and the density
is vertically constant.
For our free parameters
and p, we assume that
g cm-2 (vertical gas column density of
cm-2),
the value at the outer radius of the Pinte et al. model. We have
run a number of disc models, with the inner 400 AU described by the
Pinte et al. model (with the gas kinetic temperature scaled as
described in the previous paragraph) and the region from 400 to 900 AU
described here by the disc extension. Figure 10 shows the surface density in the models that we have tested: within 400 AU it is the surface density as in Pinte et al. (blue line) and between 400 and 900 AU different combinations of
and p (black lines).
The models are tested against the observed 12CO and 13CO uv-data, channel
maps, spectra, and position-velocity plots. The comparison of modelled emission with uv-data for the line wings,
km s-1 for 12CO and
km s
km s-1 for 13CO is also examined.
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Figure 8:
Vector-averaged continuum flux as a function of projected
baseline length (black symbols). Error bars show the variance within
each annular bin. The dashed histogram shows the zero-signal
expectation value. The full red line shows the continuum flux calculated
from Pinte et al. model. The dotted red line corresponds to the extended disc model with
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Table 1: Model parameters.
Figure 10 shows the models that overproduce the observed emission with dashed black lines and those that underproduce it with dotted black lines. The full black lines correspond to the models that reproduce well our 12CO and 13CO data. The general area (beyond 400 AU) allowed by the models is shaded in Fig. 10 for guidance. It can be seen that the 12CO and 13CO
observations constrain the column density of 12CO at R=900 AU
to
cm-2,
where the lower bound follows from the requirement that the 12CO emission is sufficently extended and the upper bound from the requirement that the 12CO and 13CO peak intensity, and the
extent of the 13CO emission are not overestimated.
The corresponding surface density at 900 AU is
g cm-2, i.e.,
a vertical gas column density (0.05-
cm-2.
Our data do not constrain the parameters
and p, that determine how the surface density decreases from its value at the outer edge of the Pinte et al. model, to its value at 900 AU. This is either a marked change from the power-law slope of p=1 found
inside 400 AU to p=5 beyond 400 AU, or a discontinuous drop by a factor
10-100 in surface density at 400 AU.
Figure 7 compares observations to synthetic
12CO and 13CO line visibilities for our model
with
cm-2 and
p=1, plotted with dotted red lines. There is a good match between the model and the data for both
transitions. In particular, the model
reproduces well the change in the slope of visibilities, mentioned in Sect. 3.2.
The match between the model (red lines) and observations is also seen in the line spectra, Fig. 9.
Figures 4 and 5 show, respectively, the
12CO and 13CO channel maps (black contours) compared to our extended disc model (grey contours).
It can therefore be seen that our model provides a good description not only of the line intensity at each channel (spectra), but also a very close match in the spatial extent of the emission in each spectral channel.
A good fit to the wings of the 12CO and 13CO spectra (Fig. 9, red lines) and the spatial distribution of the respective line fluxes at highly blue- and red-shifted velocities (lower panels, Figs. 4 and 5) is found for temperature scalings f of 1.7 for 12CO and 1.4 for 13CO. These values of f suggest that the gas is somewhat warmer than the dust at the heights above the disc where the 12CO and 13CO emission originates, and more so at the larger height probed by the 12CO line compared to the 13CO line.
At the adopted disc inclination of
,
the line peak separation provides
a reliable constraint on the stellar mass. We find a best-fit of
,
where the uncertainty is dominated by
our limited spectral resolution. This value is consistent with the rough estimate of 1
from Pinte et al. (2008), but a few times higher than derived by Hughes et al. (1994).
We conclude that the surface density
traced through 12CO and 13CO has a discontinuity
around R=400 AU either in
or in its derivative
d
,
or both. This may, or may not be an indication of an overall
discontinuity of the gas surface density.
A break in the temperature T(R) cannot
explain the observations, since our model already adopts a low
temperature at the margin of 12CO freeze-out in the outer regions.
An alternative explanation for the observations is a radical drop in the
abundance of CO (with respect to H2 and H) or its radial derivative. Freeze-out onto dust grains or
photodissociation can significantly reduce the gas-phase abundance of
CO. In the next section we explore the limits that the dust emission
can give us on the gas content outside 400 AU, and compare them to the 12CO results.
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Figure 9:
12CO and 13CO J=2-1 line spectra averaged over a
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Figure 10:
Gas surface density in our disc models is plotted as a function of radius. Within 400 AU, it is identical to the Pinte et al. model shown with the full blue line. Outside 400 AU, we explore different power-law distributions, each plotted in black and marked with the corresponding slope p. The models which overestimate the observed 12CO emission are plotted with dashed lines, while those that underpredict it are shown in dotted lines. The full black lines represent the models that fit well the 12CO J=2 -1 emission, and define the shaded region which shows our constraint on
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4.3 Comparing gas and dust at radii beyond 400 AU
The previous section concluded that both the gas and the dust out to 400 AU in the
disc around IM Lup is well described by the model of
Pinte et al., with the exception of gas
temperatures that exceed the dust temperature at some height above the
disc midplane. It also found that the gas disc needs to be
extended to an outer radius of 900 AU, albeit with a significant
decrease in the surface density of CO,
,
or in its
first derivative, d
close to 400 AU.
Pinte et al. (2008) show that
some dust is present outside 400 AU as well, visible as an extended
nebulosity in their 0.8 m scattered light images. At the same time, the visible lower scattering disc surface places a stringent limit on the surface density
of small dust
particles outside 400 AU.
Requiring the optical depth
and adopting an emissivity per gram of dust of
cm2 g-1 at 0.8
m (see first row of Table 1, Ossenkopf & Henning 1994), we find
g cm-2. If we adopt the gas-to-dust mass ratio of 100, this corresponds to
cm-2.
Our limit differs from that given in Pinte et al. (2008) (0.2 g cm-2) because we use dust opacities representative of small dust, while they assume considerable grain growth in disc midplane and thus use much lower dust opacities at 0.8
m.
The limit on surface density we derive is two orders of magnitude lower than the column density at the
outer radius of 400 AU of the Pinte et al. model. This indicates that either the dust surface density drops sharply at 400 AU, or that efficient grain growth beyond 400 AU has caused a significant decrease in dust near-IR opacity.
As can be seen in Fig. 10, the upper limit on surface density of (
cm-2 is consistent with the gas surface density range inferred in Sect. 4.2 from our
CO data, using the canonical CO/H2 abundance of 10-4.
While 0.8 m imaging traces the small dust, our observations of 1.3 mm dust continuum emission, on the other hand, trace the millimetre-sized dust particles. In Fig. 8 we can see that the Pinte et al. model (full red line), with the radius of 400 AU, compares well to the observed continuum flux at all projected baseline lengths. On the other hand, the comparison of the 1.3 mm visibilities to our extended disc model with
cm-2 and p=1 shows that the model overestimates emission at short uv-distances (large spatial scales). A constant dust emissivity of 2.0 cm2 g-1 (emissivity of mm-sized grains, as in Draine 2006) was used throughout the disc in the calculation of 1.3 mm fluxes. Our model indicates that any dust present in the outer disc regions must be poor in mm-sized grains, i.e., have low millimetre wavelength opacities, while dust within 400 AU has likely undergone grain growth as found by Pinte et al. (2008). This further supports our choice of
at 0.8
m when estimating the upper limit on dust column (see above).
Therefore, a viable model for the disc of IM Lup consists of an
`inner' disc extending to 400 AU as described in Pinte et al.
augmented with an `outer disc' extending from 400 to 900 AU with a
significantly reduced surface density (with negligible mass) but standard
gas-to-dust mass ratio and CO-to-H2 ratios. The SED of this new model should not differ significantly to that of Pinte et al. model, and is therefore expected to provide a good match to the observed SED of IM Lup.
Hughes et al. (2008) find that the apparent difference between the extent of submillimetre dust and gas emission in several circumstellar discs can be explained by an exponential drop-off of surface density which naturally arises at the outer edge of a viscous disc. In Fig. 10 we show how, with a careful choice of parameters (
,
c1=340 AU and
cm-2), the model of Hughes et al. (2008) (red long-dashed line) can reproduce the surface density distribution of the models which describe well the 12CO 2-1 line emission. This model, and the one discussed below, are only examples. A proper modelling of IM Lup in the context of viscous disc models would require a revision of the entire disc structure both in terms of temperature and density, which is outside of the scope of the current work. We notice that the Hughes et al. models cannot simultaneously comply with the gas and dust constraints in the outer disc and the surface density derived by Pinte et al. (2008) in the inner disc. This is illustrated by the Hughes et al. (2008) model with parameters
,
c1=340 AU and
cm-2, shown with the red dash-dotted line in Fig. 10. The surface density of this model outside 400 AU is in agreement with observational constraints from gas and dust, but it is roughly two orders of magnitude lower than suface density from Pinte et al. (2008) within 400 AU.
In the standard theory of viscous discs (see Pringle 1981), irrespective of the initial density distribution, a radially smooth surface density distribution with a tapered outer edge is rapidly reached. If there is a significant change in the nature of the viscosity inside and outside of 400 AU, discontinuities in the equilibrium surface density may follow. Such changes could, for example, result from differences in the ionization structure of the disc or from a drop of the surface density below some critical level. Here we explore some scenarios that could explain this:
A young disc.
An extreme example of such a configuration is a disc where the inner
400 AU follows the standard picture of a viscous accretion disc, but
where the region outside 400 AU has not (yet) interacted viscously
with the inner disc. This outer region may be the remnant of the
flattened, rotating prestellar core that has not yet made it onto the
viscous inner disc. This configuration, reminiscent of the material
around the object L1489 IRS (Brinch et al. 2007),
suggests that IM Lup would only recently have emerged from the
embedded phase.
L1489 IRS showed clear inward motion in its rotating envelope. Our
observations limit any radial motions in the gas between 400 and
900 AU to <0.2 km s-1, or 20% of the Keplerian orbital
velocities at these radii. Furthermore, for the 900 AU structure to
survive for the lifetime of IM Lup of 0.1-0.6 Myr, inward motions cannot
exceed 10-2 km s-1. Any mass inflow is therefore small, and the
material between 400 and 900 AU is likely on Keplerian orbits.
A companion body.
Another explanation for the break in the disc density structure around
400 AU would be the presence of a companion near this radius. A companion
of
at 400 AU could open a gap in the disc and
affect the viscous disc spreading. No companions at this separation
are visible in the HST images of (Pinte et al. 2008) or in K-band direct
imaging (Ghez et al. 1997). Whether these observations exclude this
scenario is unclear: it requires modelling of the orbital evolution
of a companion in a viscously spreading disc and calculation of the
observational mass limits at the age of IM Lup. This is beyond the
scope of this paper.
Gas to dust ratio.
While our model is consistent with standard gas-to-dust and
CO-to-H2 ratios beyond 400 AU, this is not the only
solution. Instead of adopting these standard ratios, which requires
explaining the drop in
or d
around 400 AU, we can
hypothesize that the gas (H2 or H) surface density is continuous
out to 900 AU and that both the CO-to-H2 and dust-to-gas ratios
show a break around 400 AU. This scenario requires a drop between 400
and 900 AU of the CO abundance by a factor between 10 and 200, and of the
dust-to-gas mass ratio by a factor
90. These drops can be sudden,
with a discontinuity at 400 AU, or more gradual, with a rapid decline
of the two ratios from 400 to 900 AU. Since a low amount of dust
emission outside 400 AU is observed both at wavelengths of
mm
(our data) and
m (Pinte et al. 2008), the overall dust-to-gas
ratio is likely affected, and not just the individual populations of
small and large grains.
Dust radial drift and photoevaporation.
If a large fraction of the dust is removed from the disc regions
outside 400 AU, the increased penetration of ultraviolet radiation
could explain the drop in 12CO surface density through increased
photodissociation (van Zadelhoff et al. 2003). Radial drift of dust particles due to the gas drag force (Whipple 1972; Weidenschilling 1977) is a possible scenario in circumstellar discs. The difference in velocity between the dust, in Keplerian rotation, and gas, sub-Keplerian because of the radial pressure gradient, can cause dust particles to lose angular momentum and drift inward. The optimal drift particle size depends on the gas density, Keplerian rotation frequency and hydrostatic sound speed.
Most dust evolution models focus on the inner 100 AU of discs, relevant to planet
formation. In these regions, the grains from 100 m to about 0.1 m
efficiently migrate inwards on a timescale shorter than 2 Myr. However, the optimal grain size for
inward drift decreases with the gas density. Our modelling of the disc region from 400 AU to 900 AU, predicts
surface densities of
g cm-2, low enough even for
sub-micron-sized particles to drift inward (to <400 AU). For the
estimated age of IM Lup of 0.1-0.6 Myr, all particles larger than
0.1-0.02
m will have migrated inward.
This process leaves the outer disc unshielded by dust against UV radiation. Infrared emission of PAHs may be used to trace the disc surface in this scenario. However, Geers et al. (2007) do not detect PAH emission at 3.3
m in their VLT-ISAAC L-band observations of IM Lup. This may indicate that either there are not enough PAHs in the disc or that they are not exposed to a significant level of UV flux. The latter possibility allows the outer disc to remain molecular. Otherwise, the outer disc is exposed to photodissociating radiation, destroying much of the CO and likely also a significant
fraction of the H2 given the limit on the dust surface density of
1021 cm-2 corresponding to
.
In
this scenario, the outer disc between 400 and 900 AU would be largely
atomic and possibly detectable through 21 cm observations of
H I, or line observations of C I at 609 and 370
m or C II at
158
m. If photoevaporation is efficient in this region
it may remove the (atomic) gas and reduce the gas surface density further.
Therefore, a combined effect of efficient drift, photodissociation and photoevaporation in the outermost disc regions may be a reason for the low gas and dust density observed. The efficiency of these processes decreases with density and perhaps the density at 400 AU is high enough so that material is no longer efficiently removed from the disc. Only the detailed simultaneous modelling of drift, photodissociation and photoevaporation could test this scenario.
5 Conclusions
We probe the kinematics and the distribution of the gas and dust in the disc around IM Lup through molecular gas and continuum dust emission. Our SMA observations resolve the disc structure down to scales of 200 AU, and allow us to probe the structure of the inner disc (<400 AU) and the outer disc (400-900 AU). Our main conclusions can be summarized as follows.- The 12CO and 13CO emission extends to 900 AU from IM Lup, much further than the outer radius of 400 AU inferred earlier from dust measurements.
- The H2 gas surface density in the region between 400 and
900 AU lies in the range of
to 10 22 cm-2, using the standard CO-to-H2 ratio of 10-4.
- The disc is in Keplerian rotation around a central mass of
. Infall motions, if present in the outer disc, are negligible at <0.2 km s-1.
- The molecular line emission from the inner disc, within 400 AU, is well described by the model of Pinte et al. (2008), except that the gas temperature in the layers dominating the line emission of 12CO and 13CO exceeds the dust temperature by factors 1.7 and 1.4, respectively.
- Outside 400 AU, the surface densities of the molecular gas, as
traced through 12CO and 13CO, of small (
m) dust grains, and of larger (
mm) dust grains have a break in their radial dependence. At 400 AU, the dust surface density (in small grains) drops by a factor
100, while the gas surface density shows a comparable drop of a factor 10-200 or steepens its radial power-law slope from p=1 to
.


Acknowledgements
The research of O.P. and M.R.H. is supported through a VIDI grant from the Netherlands Organisation for Scientific Research. We would like to thank our Leiden colleagues Anders Johansen and Richard D. Alexander for valuable insights and discussions, as well as C. P. Dullemond, A. Juhász and others at the Star and Planet Formation Department of MPIA Heidelberg for their help and advice during the stay of O.P. in March 2008. Finally, we are grateful to E. F. van Dishoeck for her support and guidance throughout the writing of this paper.
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Footnotes
- ... Array
- The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica.
- ... package
- http://www.cfa.harvard.edu/~cqi/mircook.html
- ...
(LAMBDA
- http://www.strw.leidenuniv.nl/~moldata/
All Tables
Table 1: Model parameters.
All Figures
![]() |
Figure 1:
Dust continuum image at 1.3 mm. The contours are at (2, 4, 8, 16)
|
Open with DEXTER | |
In the text |
![]() |
Figure 2:
a, b) First moment maps in the 12CO and 13CO
J=2-1 lines, from 1.9 km s-1 to 6.9 km s-1 observed towards IM Lup. These maps
are created using the Miriad task ``moment'' with clip levels of
0.5 and 0.3 Jy respectively. The integrated emission of 12CO J=2-1 is shown in
contours of 1, 2, 3, ... |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
12CO, 13CO, and C18O J=2-1 line spectra
summed over
|
Open with DEXTER | |
In the text |
![]() |
Figure 4:
The black contours show the observed 12CO J=2-1 emission in the velocity range from
2.46 to 6.42 km s-1. Alongside the observations, the panels with grey contours show the
calculated emission from the extended disc model described in
Sect. 4.2, with parameters
|
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Channel maps of the observed 13CO J=2-1 emission at the velocities where the line is
detected are shown in black contours. For comparison, the line emission calculated from our
extended disc model described in Sect. 4.2 is shown in grey contours. The model
parameters are
|
Open with DEXTER | |
In the text |
![]() |
Figure 6:
Position-velocity diagram of the 12CO 2-1 line emission
along the disc's major axis. Contour levels are (1, 2, 3,
...) |
Open with DEXTER | |
In the text |
![]() |
Figure 7:
The left and the right panel show vector-averaged 12CO and 13CO line flux (black symbols),
respectively. Dashed black lines represent the zero-signal expectation value of our line visibility
data. The calculated visibilities based on Pinte et al. model (full red line) and
our extended disc model described in Sect. 4.2 (dotted red line) are shown for comparison.
Our model parameters are
|
Open with DEXTER | |
In the text |
![]() |
Figure 8:
Vector-averaged continuum flux as a function of projected
baseline length (black symbols). Error bars show the variance within
each annular bin. The dashed histogram shows the zero-signal
expectation value. The full red line shows the continuum flux calculated
from Pinte et al. model. The dotted red line corresponds to the extended disc model with
|
Open with DEXTER | |
In the text |
![]() |
Figure 9:
12CO and 13CO J=2-1 line spectra averaged over a
|
Open with DEXTER | |
In the text |
![]() |
Figure 10:
Gas surface density in our disc models is plotted as a function of radius. Within 400 AU, it is identical to the Pinte et al. model shown with the full blue line. Outside 400 AU, we explore different power-law distributions, each plotted in black and marked with the corresponding slope p. The models which overestimate the observed 12CO emission are plotted with dashed lines, while those that underpredict it are shown in dotted lines. The full black lines represent the models that fit well the 12CO J=2 -1 emission, and define the shaded region which shows our constraint on
|
Open with DEXTER | |
In the text |
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