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Astron. Astrophys. 364, 741-762 (2000)

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3. Infrared continuum

3.1. ISO observations

3.1.1. SWS and LWS continuum

The ISO spectrum of L1551 IRS 5 is shown in Fig. 3. The shape of the continuum in the LWS spectral region can to first order be fitted by a 50 K blackbody. There is however no reason to believe that the entire central region can be described by blackbody emission at this single mean temperature. In fact, the emission at short wavelengths exceeds the expected blackbody values, indicating that higher temperature dust grains must be present, and that the absorption efficiency of dust grains falls off with wavelengths (see e.g., Fig. 9).

[FIGURE] Fig. 3. L1551 IRS 5 spectrum. The two graphs show the same data, but using either linear or log scales, so as to emphasise the dynamic range of the spectrum, whilst showing weak features. The upper figure is overplotted with the positions of detected lines in the LWS range, and the locations of various features in the SWS range discussed in the text. The lower figure is overplotted with the locations of molecular emission lines which have been detected by ISO towards other sources.

There is a discontinuity in the continuum flux level between 40 and 50µm - where the SWS and LWS spectra join together (see Fig. 9 for the error bars). This may be due either to a calibration mismatch between the SWS and LWS spectrometers, or a consequence of the different beamwidths.

It is known that the size of L1551 IRS 5 at 50 µm is less than 6" FWHM (Butner et al. 1991), and so it should appear point-like to both the SWS and LWS. One should keep in mind, however, the fact that the beam size of the KAO observations was 14", much smaller than the apertures used in this study. Since larger beams probe different volumes of the circumstellar envelope, the observations cannot be compared directly, unless a detailed radiative transfer model for the object is developed. In fact, our detailed model of L1551 IRS 5 presented later in this section, shows that this continuum level break could be entirely due to the difference in beam sizes for SWS and LWS spectrometers - although of course there is still systematic uncertainty between the calibrations of the LWS and SWS as discussed earlier.

3.1.2. Solid state features

The ISO spectra are shown in Fig. 4 and Fig. 5. These include a number of features which are attributable to solid state carriers, as well as several gas phase lines.

[FIGURE] Fig. 4. Lines detected in the L1551 IRS 5 spectrum. The H2O lines indicated in the lower right pane show the expected wavelengths, but do not to necessarily indicate detections.

[FIGURE] Fig. 5a-f. Optical depth in various lines, superimposed by model fits to various gas phase lines. These models are run for a gas temperature of 200 K and Doppler width [FORMULA] = 2 km s-1, and column densities of a 1021 cm-2, b 5[FORMULA]1019 cm-2, c 6[FORMULA]1020 cm-2 (uppermost model curve at the top of the figure was run for a temperature of 200K, the lower model curve was for the higher temperature of 2500 K, and shows the bandhead more clearly), d 1021 cm-2, e 716 cm-2, f 5[FORMULA]1019 cm-2. All data and models have an effective resolution of 700.

The spectral region from 2.8 to 3.8 µm has a broad absorption feature extending across it, made up from contributions from ices at [FORMULA] 3.1 µm, O-H stretching band of H2O from 3 to 3.4 µm, and solid CH3OH at 3.54, 3.84 and 3.94 µm (Dartois et al. 1999), which sits on the long wavelength side of the H2O line.

The column density, N, of an absorbing species producing a feature of peak optical depth [FORMULA] and width [FORMULA] is given by

[EQUATION]

where A is the integrated absorption cross section per molecule (also known as the band strength) and [FORMULA] is the full-width at half maximum intensity, expressed in units of wavenumbers. The lower limit to the column density of solid H2O is 7.7[FORMULA]1018 cm-2 (the lower limit is a consequence of the available signal-to-noise ratio (S/N), baseline uncertainty and blending with the nearby CH3OH emission). Examples showing the optical depth in other solid state features are presented in Fig. 5.

It proved difficult to unambiguously separate the contributions of CH3OH from the O-H stretching band of H2O, however from first order Gaussian fitting, we estimate the solid CH3OH column density is 2.6[FORMULA]1018 cm-2.

The CO2 [FORMULA] 4.27 stretching mode and CO2 [FORMULA] 15.2 bending mode lines are clearly seen in absorption with optical depths [FORMULA] 2 and 1 respectively. The CO2 [FORMULA]15.2 line has an integrated line flux of [FORMULA]0.5[FORMULA]10-18 W cm2 and an optical depth of 0.4. Taking values of band strengths from Gerakines et al. (1995), the column densities in these CO2 stretching and bending modes are 5.5[FORMULA]1017 cm-2 and 5.3[FORMULA]1017 cm-2 respectively.

The ´XCN´ [FORMULA]4.619 line reported by Tegler et al. (1993) was not seen in our data, despite detection of the nearby CO2 [FORMULA]4.38 line. Similarly, the [FORMULA]4.68 line detected by Pendelton et al. (1999) was also not convincingly present towards L1551 IRS 5.

An absorption feature is seen close to 6 µm (see also Fig. 5), which is probably due to a combination of water ice, HCOOH and PAH features. Absorption at these wavelengths has previously been proposed by Tielens et al. (1984) and identified by Keane et al. (1999) towards several sources, and seen towards several of the infrared sources towards the Galactic Centre by Chiar et al. (2000), where it is suggested to indicate the presence of a mixture of H2O, NH3, HCOOH and an aromatic C-C component.

An absorption feature associated with the 7.66 µm CH4 [FORMULA] ´deformation mode´ line is clearly visible, with an optical depth [FORMULA] = 0.07. Using a band strength of A = 7.3[FORMULA]10-18 cm molecule-1 (Boogert et al. 1996), we estimate the column density of solid methane to be 7.6[FORMULA]1016 cm-2. Boogert et al. (1996) suggest that the CH4 is embedded with a mixture of polar molecules (such as H2O, CH3OH, CH4 or other species) in the icy grain mantle. However, despite the availability of models of CH4 in various mixtures of polar molecules, the S/N of the present data is insufficient to discriminate between various mixtures.

The column densities estimated above for the various solid state features are summarised in Table 2.


[TABLE]

Table 2. Summary of solid state column densities


3.1.3. Spectral shape

Compared to many pre-main sequence objects with outflows which have been observed with the ISO LWS, it is striking how few lines have been detected in these very deep spectra (Saraceno et al. 1999). The low intensity of the C II line and the relative invariance of its strength with distance from IRS 5 shows that the UV field must be weak, even close to IRS 5 and the HH 29 region. The non-detection of high-J CO lines suggests that the outflow gas is neither very hot ([FORMULA] [FORMULA] 200 K), nor very dense ([FORMULA] 104 cm-3).

3.2. HST NICMOS images

A composite showing images taken from the HST archive is shown in Fig. 6.

[FIGURE] Fig. 6. HST images of IRS 5 obtained with the NICMOS 2 camera (total field of view 19[FORMULA] [FORMULA] 19[FORMULA] pixel size 0[FORMULA] The area shown here has dimensions of 8[FORMULA] [FORMULA] 8[FORMULA] and the diffraction limited resolution is [FORMULA] 0[FORMULA] The peak intensity on the continuum subtracted images is 2 % of the peak flux of the direct 2.12 µm image.

The spatial distribution of radiation (Fig. 6) shows a nebular structure with an opening angle of [FORMULA] 60o. In two of the filters - the [Fe II] and 1.12 µm broad filters, emission from the ´jet´ is clearly visible - most prominently in the [Fe II] filter (this contains the [FORMULA]1.64 [FORMULA] line). It is notable that three [Fe II] lines are also seen in the ISO SWS spectra (see Sect. 4.1), and that the ´jet´ is not detectable in the narrowband [FORMULA]2.12 H2 filter. To attempt confirm the lack of H2 emission from the jet, a first order continuum subtraction, the [FORMULA]2.12 H2 + CO broad filter was scaled and subtracted from the narrowband [FORMULA]2.12 H2 filter. The ´continuum subtracted image´ formed in this way showed no evidence of H2 emission from the jet down to a level of 2 % of the peak [FORMULA]2.12 emission. This may be due to the fact that either there is no detectable H2 emission from the jet, or that the H2 emission is exactly cancelled out by the CO bandhead emission contained in the 2.12 H2 + CO broad filter. Resolution of this will require sensitive echelle spectroscopy which is not yet available. By contrast, [Fe II] emission is clearly visible without any attempt to ´continuum subtract´.

The mass of the torus was estimated to be 0.1-0.3 [FORMULA], the full opening angle was [FORMULA] 100-110o, and the radius 630 AU (Lucas & Roche 1996). A similar bipolar geometry of L1551 IRS 5 has been found also by MH97 in extensive modelling which, among other things, has shown that the actual size and mass of the dusty surroundings of IRS 5 is at least an order of magnitude larger ([FORMULA] AU and [FORMULA] 10 [FORMULA], respectively). The distribution of near-IR emission has been studied towards this source by Lucas & Roche (1996), who used image sharpening techniques to obtain a deconvolved angular resolution with a FWHM of 0[FORMULA] Based on Monte Carlo modelling, they suggested that the light originated from the scattered light associated with a circumstellar torus with an evacuated bipolar cavity.

3.3. Two-dimensional radiative transfer model

In order to interpret the observations in a quantitative way, we constructed a self-consistent two-dimensional (2D) radiative transfer model for L1551 IRS 5. Whereas MH97 have already presented a comprehensive model for this object, their calculations were affected by numerical energy conservation problems resulting from very high optical depths of the model and incomplete convergence of the iterations. The problem, which mainly affected the total luminosity of the central object and the near- to mid-IR part of the SED in the MH97 model, has now been improved (see, e.g., the model of HL Tau by Men'shchikov et al. 1999, hereafter MHF99).

In this paper, we have recomputed the model using the modified version of the code and the new constraints provided by the ISO and HST observations presented above. Our approach and the model are basically the same as those in MH97 and MHF99. We refer to the papers for more detailed discussion of our approach, computational method, model parameters, and ´error bars´ of the modelling.

3.3.1. Geometry

Following MH97, we assume that the central star (or a binary) is surrounded by a dense core (with a radius of [FORMULA] 100 AU), which is embedded within a much larger non-spherical envelope (outer radius of [FORMULA] AU). A conical cavity has been excavated by the bipolar outflow, and has a full opening angle of [FORMULA]. This axially-symmetric geometry is the same for both the core and the surrounding material. The geometry is shown in Fig. 7.

[FIGURE] Fig. 7. Geometry of L1551 IRS 5. Schematically shown are three regions of the model - the innermost dense torus (dark color), the constant-density part of the envelope (medium color), and the outer extended envelope containing most of the mass (light color). The bipolar geometry is defined by the opening angle of the conical outflow cavities,[FORMULA]90o ([FORMULA]90o) and the viewing angle, [FORMULA]44o, between the equatorial plane and the line of sight. The polar outflow regions are less dense than the torus.

The density distributions inside the torus and in the bipolar cavities are functions of only the radial distance r from the centre, where the source of energy is located. We neglect in this model the putative binary system inside the dense core, because its semi-major axis ([FORMULA] 20 AU) would be much smaller than the radius of the core. If the binary does exist, it is unlikely that there is a very large cavity around it, with a radius of [FORMULA] 20 AU. Our modelling has shown that in the presence of such a dust-free cavity, most of the inner dust boundary would have temperatures of only [FORMULA] 150 K, far too low to explain the observed SED of L1551 IRS 5. In fact, the near- and mid-IR fluxes would be (many) orders of magnitude less than the observed ones. Instead of assuming that the entire binary fits into the dust-free cavity, we adopt the view that a substantial amount of gas and dust exists deeper inside the core, as close as [FORMULA] 0.2 AU to the central source(s) of energy (see Sect. 4.1.1 later).

3.3.2. Grain properties

Assuming a similarity between HL Tau and L1551 IRS 5, we adopted for the latter the dust properties proposed by MHF99. The only difference is that magnesium-iron oxide grains ([FORMULA]) are absent, because there is no evidence of an emission/absorption sugnature close to 18 µm that would warrent introdcuing another free parameter to into the model (Fig. 8).

[FIGURE] Fig. 8. Opacities for our IRS 5 model. Three upper curves show the wavelength distribution of optical depths (total, absorption, and scattering) towards the central source, through both the envelope and the dense torus. The other curves display dust opacities of the core-mantle grains (which exist only in the envelope), for three representative sizes, as well as the total opacity of the entire size distribution.

(1) The large dust particles have an unspecified composition, radii 100-6000 µm, size distribution exponent [FORMULA], dust-to-gas mass ratio [FORMULA] = 0.01, average material bulk density [FORMULA] = 2.0 g cm-3, sublimation temperature [FORMULA] 1700 K. They show a gray (i.e., independent of wavelength) extinction efficiency for [FORMULA] 600 µm, whereas at longer wavelengths it falls off as [FORMULA].

(2) Core-mantle grains are assumed to contain silicate cores ([FORMULA]) with [FORMULA] = 3.2 g cm-3, covered by dirty ice mantles. The ratio of the total core-mantle grain radii to those of the pyroxene cores is 1.4, and their total radii are 0.11-0.7 µm, [FORMULA], [FORMULA] = 0.0037. The dirty mantles consist of water ice polluted by small amorphous carbon grains. The sublimation temperature of the mantles was assumed to be [FORMULA] 100 K.

(3) Amorphous carbon grains with radii 0.08-0.5 µm, [FORMULA], [FORMULA] = 0.0063, [FORMULA] = 2.0 g cm-3.

The contibutions to the extinction towards L1551 IRS 5 are shown in Fig. 8.

The first component of very large grains is present only inside the dense torus (0.2 AU [FORMULA] 250 AU), where all of the smaller grains are assumed to have grown into the large particles. The two other grain components exist only outside (250 AU [FORMULA] AU), in the extended envelope of much lower density. As in any model, the results depend on the accuracy of the input parameters and the assumptions made. A major source of uncertainty in a model such as the one used here, will be the assumptions adopted for the grain properties. Further details on the choice of grain properties and their effect on the model results have been discussed by MHF99 and references therein.

3.3.3. Parameter space

As has been discussed in detail by MH97 and MHF99, the parameter space available to numerical modelling is very large. There are many poorly constrained parameters, few of which can be fixed a priori, to reduce the space. This situation requires that all available observational information has to be taken into account to better constrain the models. As in the earlier modelling, we have used as observational constraints all existing photometry data with different beam sizes (from optical to millimetre wavelengths), intensity profiles at 50 µm, 100 µm, 1.25 mm, 1.3 mm, and visibility curves from interferometry at 0.87 mm and 2.73 mm (see references in MH97). In addition to the constraints, we used in the new modelling our HST image at 2.12 µm and the SWS and LWS spectrophotometry presented above.

Table 3 lists the main input parameters of our model. The opening angle has not been varied, being fixed at the value found by MH97. Likewise, the viewing angle and the outer boundary also have not been varied extensively in our new modelling. We varied mainly the radial density profile and the total mass (or the total optical depth in the mid-plane). The dust grain parameters, the primary source of uncertainties in this kind of modelling, was also mostly fixed at the values adopted by MHF99 for HL Tau.


[TABLE]

Table 3. Main input parameters of the IRS 5 model


Numerical parameters related to the accuracy of the model are the number of radial points (277), the number of azimuthal angles for the integration of intensity moments (10), the number of azimuthal angles for the observable flux calculation (50), the number of wavelengths (217), the number of points for convolved intensity maps (600 [FORMULA] 600), and that for the visibility calculations (4000 [FORMULA] 4000). Conservation of the total luminosity for both the equivalent spherical envelope and the 2D model was better than about 7 % at all radial points, certainly good enough compared to the total uncertainties involved in the modelling.

3.3.4. Spectral energy distribution

The model SED is compared to the observations of L1551 IRS 5 in Fig. 9 and Fig. 10. Only one, best-fitting SED corresponding to the viewing angle of 44[FORMULA] (measured from the mid-plane) is displayed. As has been extensively discussed by MH97 and MHF99 (see, e.g., their Fig. 5), the optical to mid-IR parts of the SEDs of bipolar embedded sources depend strongly on the viewing angle. The viewing angle derived on the basis of 2D radiative transfer calculations depends, among other factors, on the density distribution in the polar direction inside the dense disc and the surrounding material. Since the real density structure in the vertical direction is generally unknown, we adopted a density distribution independent of the polar angle. This introduces some degree of uncertainty in the derived value of the viewing angle, although the fact that the source is hidden behind the ´wall´ of extinction produced by the core and the torus (and close to the apex of the conical cavity) seems to be well established both by observations and by the modelling.

[FIGURE] Fig. 9. Comparison of the new IRS 5 model with the ISO SWS, LWS spectrum, and various, mostly ground-based, photometric points. The individual fluxes (taken from MH97) are labelled by different symbols, to distinguish between old observations (before 1980, circles), recent ones (1980-1990, diamonds), and new data (after 1990, triangles). Error bars correspond to total uncertainties of the observations. The stellar continuum (which would be observed, if there were no circumm- stellar dust, is also displayed. The model assumes that we observe the torus at an angle of 44[FORMULA] (relative to its midplane). The effect of beam sizes is shown by the vertical lines and by the difference between the dotted and solid lines in the model SED. Whereas only the lower points of the vertical lines are relevant, we have connected them to the adjacent continuum by straight lines, to better visualise the effect. To i llustrate the influence of the bipolar outflow cavities, the SED for the equivalent spherical envelope is also shown.

[FIGURE] Fig. 10. Same as in previous figure but it shows in more detail the SWS and LWS spectrophotometry (2-200 µm). The small insert displays in even greater detail the region of the ´mismatch´ between the SWS and LWS data (38-50 µm). The effect of beam sizes is also visible in this plot, as the difference between the dotted and the solid lines in the model SED. To illustrate the influence of the bipolar outflow cavities, the SED for the equivalent spherical envelope is also shown.

The overall quantitative agreement of the model SED with the entire set of observations of L1551 IRS 5 is obvious. The total model fluxes corrected for the beam sizes (solid lines in Fig. 9 and Fig. 10) coincide well with the observed fluxes, except for those in the near IR, although the shape of the SED is still very similar to the observed one. The effect of different apertures is evident everywhere, except for only the mid-IR wavelengths, where the source is very compact and most of its radiation fits into the SWS beam. Note that at millimetre waves the model predicts significantly larger total fluxes compared to the observed ones, indicating that the outer envelope is very extended and sufficiently massive.

The insert in Fig. 10 shows that the ´jump´ between the SWS and LWS data at [FORMULA] 45 µm is a consequence of the different beam sizes. The model shows a clear water ice absorption feature at 3 µm which is very similar to the observed profile. The agreement of the model with SWS in the 7-9 µm region is not very good; there are also smaller deviations in the 15-40 µm part of SWS. As we mostly fixed the grain properties, we have not attempted to find a better fit by varying the dust model (it would be extremely time-consuming). It seems very likely, however, that small changes in the dust chemical composition or temperature profile would be sufficient to fit the SED almost perfectly. We do not believe, however, that such an adjustment makes sense, given the much higher overall uncertainties of the problem at hand.

3.3.5. Densities and temperatures

The structure of our model of L1551 IRS 5, which is very similar to that presented by MH97, is illustrated in Fig. 11. The distribution of densities and temperatures in the model were chosen to be similar to those of HL Tau (MHF99), except for the flat density area between 250 and 2000 AU which is very likely to exist in IRS 5. The density structure in the inner few thousand AU is constrained by the SED (Sect. 3.3.4), the submm/mm visibilities (Sect. 3.3.6), and the long-wavelength intensity maps (Sect. 3.3.7). The visibilities suggest that the density structure consists of a dense core inside a lower density envelope. On the other hand, the intensity maps might also imply high densities are present at distances of [FORMULA] 4000 AU from the central source. Both requirements can however only be reconciled by adopting a flat density distribution. We have no clear understanding of the physical significance of this deduction (also inferred by MH97), which needs to be tested by other observations.

[FIGURE] Fig. 11. Density and temperature structure of the IRS 5 model. The jump in temperature profiles (upper curves) is due to the difference of grain properties between the dense torus and the outer envelope. See text for more details.

There are three regions that make up the torus: the innermost very dense core with a [FORMULA] density gradient, and low-density outer parts with a broken power-law ([FORMULA], [FORMULA]) density profile. A steep [FORMULA] transition zone between them (having a half-width at half-maximum of 70 AU) effectively forms the outer boundary of the inner dense torus. The boundary of the torus extends from [FORMULA] 80 to 250 AU and is effectively truncated by the exponential at about 200 AU, very similar to the density profile of HL Tau (MHF99). Conical surfaces of the bipolar outflow cavities define the opening angle of the torus to be [FORMULA]. Dust evaporation sets the inner boundary at [FORMULA] 0.4 AU, while the outer boundary is arbitrarily put at a sufficiently large distance of [FORMULA] AU. The polar outflow cones with a [FORMULA] density distribution have much lower density than the torus.

In the absence of any reliable constraints, the conical outflow regions are assumed to have a [FORMULA] density profile which is consistent with available data. The temperature profile displays a jump at 250 AU, where the hotter normal-sized dust grains of the envelope are assumed to be coagulated into the large grains of the dense core. We refer to MH97 and MHF99 for a more detailed discussion of the density structure and of the uncertainties of our model.

3.3.6. Submillimetre and millimetre visibilities

The model visibilities for two directions in the plane of sky, parallel and orthogonal to the projected axis of the torus (MH97, MHF99) are compared to the available interferometry data in Fig. 12. The model shows good agreement with the spatial information contained in the observed visibilities. The latter do not constrain, however, density distribution in the outer envelope. Instead, intensity maps over a larger area, obtained with large beams, should be useful in determining the density structure on the largest scales, thus giving an idea of the total mass of the circumstellar material. In fact, our model gives much larger mass ([FORMULA] 13 [FORMULA]) and extent ([FORMULA] 3[FORMULA]104 AU) of the envelope compared to other simplified models which do not take into account all available observations.

[FIGURE] Fig. 12. Comparison of the model visibilities at 0.87 mm and 2.7 mm with observations of Lay et al. (1994), Keene & Masson (1990), and Looney et al. (1997). The latter data set was not used in the search through the parameter space of the model (see Sect. 3.3.6). The upper and lower curves show the visibilities for two directions in the plane of sky, parallel and orthogonal to the projected axis of the outflow.

The observations by Looney et al. (1997) were added to the figure after our modelling has been completed; they show noticeably lower visibilities compared to those presented by Keene & Masson (1990), which were fit by the model reasonably well. This is clearly a consequence of the assumed [FORMULA] slope of the opacities by very large grains in this wavelength range (Sect. 3.3.2). The slope has been chosen in our model on the basis of the best fit to both 870 µm (Lay et al. 1994) and 2.73 mm visibilities (Keene & Masson 1990). The Looney et al. (1997) data suggest that the wavelength dependence of opacity may actually be slightly steeper (closer to [FORMULA]). This alone or together with a slight modification of the density profile would let the model visibility go through the cloud of the observed points. Given the uncertainties of the different data sets and of our model assumptions, however, we do not feel this would make sense.

3.3.7. Far-IR and millimetre intensity profiles

Model intensity profiles at 50 µm, 100 µm, 1.25 mm, and 1.3 mm (perpendicular to the outflow direction) are compared with the available observations in Fig. 13 and Fig. 14. The model intensity profiles have been convolved with the appropriate circular Gaussian beams. Unconvolved intensity distributions are also shown for reference. As in MH97, the new model shows very good agreement with the measurements, suggesting that the density and temperature distributions of the model are realistic.

[FIGURE] Fig. 13. Far-IR intensity profiles for our model of IRS 5 compared to the observations of Butner et al. (1991). Dotted line shows also unconvolved model intensity distribution (normalised to 0.75) that is dominated by the emission of the dense compact torus.

[FIGURE] Fig. 14. Millimetre intensity profiles of our model of IRS 5 compared to the observations of Keene & Masson (1990) and Walker et al. (1990). Dotted line shows also unconvolved model intensity distribution (normalised to 0.75) that is dominated by the emission of the dense compact torus.

Note that the temperature of the outermost parts may be controlled by the external radiation field, which is assumed to be a 5 K blackbody in our model. The radiation field defines the lower limit for the dust temperature in the distant parts of the torus. Thus, it is a key parameter that determines how extended the envelope would appear to millimetre observations after subtraction of the background radiation field. In fact, if the outer radiation field keeps the torus warm (e.g. [FORMULA] 20 K), then the millimetre intensity maps, which are sensitive to much cooler material, would reveal very little radiation from the envelope. One cannot conclude, however, that an envelope has very little mass on the basis of a few millimetre fluxes alone, without a careful analysis of its density and temperature structure.

3.3.8. HST image at 2.12 µm

An additional check of our model at short wavelengths is enabled by the HST NICMOS image of IRS 5 at 2.12 µm. In Fig. 15 we compare the model intensity profiles along the same orthogonal directions on the sky, parallel and perpendicular to the axis of the outflow, with the corresponding intensity strips taken from the observed images (Sect. 3.2). The model images were convolved with the HST point-spread function of 0[FORMULA] the unconvolved model intensity distributions are also shown for reference. Distortion of the observed profile in the lower panel (plateau and widening of the left wing) is caused by the removal of the intensity spike due to a bright knot slightly off the jet axis on the HST image.

[FIGURE] Fig. 15. Comparison of the HST 2.12 µm image with our model of IRS 5 in terms of normalised intensity profiles for two orthogonal directions in the plane of sky. In the top diagram, the x-shift of the observed profile is arbitrary, since the absolute positional co-ordinates of the HST are not known to sufficient accuracy - however it is the shape of the distribution that is predicted - and well matched by the model. As in previous figures, we also plotted the unconvolved model intensity distribution (normalised to 0.75) that is dominated by the radiation scattered and emitted by the dense compact torus.

The model of L1551 IRS 5 predicts that the observed intensity peak should be displaced by approximately 1[FORMULA] along the outflow direction from the completely obscured central energy source. This also has been suggested on the basis of the morphology of the optical and radio images (Campbell et al. 1988). Similar displacements in the near-IR images have been found in the recent modelling of HL Tau (see MHF99 for more discussion). Unfortunately the HST/NICMOS images do not have the astrometric accuracy needed to test this idea.

Taking into account the approximations involved in the model geometry and in the radiative transfer method, which should affect our results especially at short wavelengths, the agreement is good. The remaining discrepancies can be explained by a more complex density distribution around IRS 5, which in reality should depend also on the polar angle (MHF99).

In Fig. 16 we have presented near-IR model images of L1551 IRS 5 with a 0[FORMULA] resolution (equivalent to the HST image of the source at 2.12 µm, Fig. 15). The intensity profiles predicted by our model can be tested by future high-resolution observations.

[FIGURE] Fig. 16. Predictions of our model for [FORMULA], and N band images of IRS 5 with the adopted point-spread-function of 0[FORMULA] (FWHM). These predictions are included in this paper, because they are now able to be tested using large telescopes such as Gemini with adaptive optics.

3.3.9. Average density estimates

Table 4 compares average densities of our model with the observational estimates. The density reported by Keene & Masson (1990) (see MH97) from 2.7 mm interferometry was an overestimate because they assumed a steep long-wavelength absorption efficiency of dust grains [FORMULA]. Corrected for the higher opacity of large grains adopted in our work, the estimate would be about a factor of 4 times lower, in much better agreement with our result. The model is consistent with observations, given the approximations involved in the problem (see MHF99 for more discussion).


[TABLE]

Table 4. Average density estimates for L1551 IRS 5 from observations compared to the predictions of our model (references are given in MH97, Table 2).


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Online publication: January 29, 2001
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