2 Observations and data reduction

  
2.1 Observations

5-16.5 $\mu$m imaging spectroscopy was performed on six target fields in four low-mass star formation regions using the ISOCAM-CVF, on various dates between April 1996 and February 1997. This instrument made use of 2 variable width filters to take images at a number of different wavelengths, using a $32\times32$ pixel gallium-doped silicon array. Exposure times of 2.1 s per CVF step were used. Each was exposed repeatedly and the images were sequenced (in time) in decreasing order of wavelength, resulting in a total exposure time of $\sim$2500 s per target region for each CVF set. This procedure produced 2 datacubes for each target region. The first covered the wavelength range 5.0-9.4 $\mu$m (CVF1) and the other covered 9.3-16.3 $\mu$m (CVF2), with a mean spectral resolving power of $\lambda/\Delta\lambda\simeq40$. A brief summary of the characteristics of the observed regions is given below.

  
2.1.1 RCrA

The RCrA cloud is the name given to a molecular cloud of mass $\sim$120 $M_{\odot}$ (Harju et al. 1993) around the variable star R Coronae Australis, at a distance of 130 pc (Marraco & Rydgren 1981). It is a region of low-mass star formation located approximately 18 $\hbox{$^\circ$ }$ below the galactic plane (Olofsson et al. 1999), where it suffers little foreground obscuration. The previous K-band studies of Taylor & Storey (1984) and Wilking et al. (1997) and the sub-millimetre survey of Harju et al. (1993) revealed a number of embedded objects and other objects classified as YSOs. One field of view was observed in the RCrA cloud, using the 6 $\hbox{$^{\prime\prime}$ }$ pixel field of view (pfov). It was centred on 19$^{\rm h}$01$^{\rm m}$45 $\hbox{$.\!\!^{\rm s}$ }$1, -36 $\hbox{$^\circ$ }$58 $\hbox{$^\prime$ }$34 $\hbox{$^{\prime\prime}$ }$, immediately to the south-west of RCrA itself.

  
2.1.2 $\rho$ Ophiuchi

The $\rho$ Ophiuchi dark cloud complex is a complicated structure of several large molecular clouds near the bright star $\rho$ Ophiuchi. Its relatively high galactic latitude ( $b=17^{\circ}$) combined with its relative proximity (d=160 pc, Whittet 1974) result in comparatively little foreground obscuration, making it an ideal region in which to study star formation. Initially identified by Grasdalen et al. (1973), who identified 41 sources in a K-band map, it has since been studied extensively both in the infrared (Elias 1978; Greene & Young 1992; Strom et al. 1995; Abergel et al. 1996; Bontemps et al. 2001) and at millimetre wavelengths (Loren et al. 1990; André & Montmerle 1994). In particular, Loren et al. (1990) showed that the cloud consists of a number of smaller sub-structures. They identified 6 dense cores (labelled A-F) and observed significantly higher clustering of YSOs in three of these cores (A, B, and E/F). Two fields were observed in $\rho$ Oph, both with the 6 $\hbox{$^{\prime\prime}$ }$ pfov: one centred on 16$^{\rm h}$26$^{\rm m}$21 $\hbox{$.\!\!^{\rm s}$ }$4, -24 $\hbox{$^\circ$ }$23 $\hbox{$^\prime$ }$59 $\hbox{$^{\prime\prime}$ }$ (field $\rho$ Oph A) and one at 16$^{\rm h}$27$^{\rm m}$23 $\hbox{$.\!\!^{\rm s}$ }$7, -24 $\hbox{$^\circ$ }$40 $\hbox{$^\prime$ }$39 $\hbox{$^{\prime\prime}$ }$ (field $\rho$ Oph E). The positions correspond (approximately) to cores A and E/F above.

  
2.1.3 Serpens

The Serpens molecular cloud was initially identified by Strom et al. (1976). It has since been very well surveyed, both in the infrared (Churchwell & Koornneef 1986; Gomez de Castro et al. 1988; Eiroa & Casali 1992; Giovannetti et al. 1998; Kaas 1999) and the sub-millimetre (Casali et al. 1993), with as many as 163 sources identified in the $6'\times5'$ K-band map of Eiroa & Casali (1992). The cloud itself extends over a region of $\ge$ $20'\times\ge15'$ in CO line emission (Loren et al. 1979) and is at a distance of $\simeq$260 pc (Straizys et al. 1996). In addition to survey imaging, many individual objects in the cloud have been studied in detail: Eiroa & Casali (1989) studied the multiple outflow source SVS4; SVS2 has been shown to illuminate the Serpens Reflection Nebula (Gomez de Castro et al. 1988; Huard et al. 1997); SVS20 has been shown to be a close binary system (Huard et al. 1997). Two fields were observed in Serpens. Field Ser B, taken with the 6 $\hbox{$^{\prime\prime}$ }$ pfov, was of the region around SVS2 and SVS20 and was centred on 18$^{\rm h}$29$^{\rm m}$57 $\hbox{$.\!\!^{\rm s}$ }$6, 1 $\hbox{$^\circ$ }$12 $\hbox{$^\prime$ }$42 $\hbox{$^{\prime\prime}$ }$. Field Ser A was a higher resolution field (3 $\hbox{$^{\prime\prime}$ }$ pfov) of the multiple outflow source SVS4, centred on 18$^{\rm h}$29$^{\rm m}$57 $\hbox{$.\!\!^{\rm s}$ }$2, 1 $\hbox{$^\circ$ }$14 $\hbox{$^\prime$ }$25 $\hbox{$^{\prime\prime}$ }$.

  
2.1.4 Chamaeleon I

The Chamaeleon dark cloud complex is a complicated structure consisting of 3 large molecular clouds (designated Cha I, II, III by Hoffmeister 1963) and a number of smaller clumps and globules. Again, the relative proximity (d=160pc, Whittet et al. 1997) and high galactic latitude ($b\sim-$16 $\hbox{$^\circ$ }$) of the clouds result in little foreground obscuration and make them ideal for star formation study. The region has been well-surveyed at millimetre wavelengths (Mattila et al. 1989; Henning et al. 1993) and more recently in the near- (Kenyon & Gómez 2001) and mid-infrared (Persi et al. 2000). A single field was observed in the Cha I cloud, with the 6 $\hbox{$^{\prime\prime}$ }$ pfov, centred on 11$^{\rm h}$09$^{\rm m}$39 $\hbox{$.\!\!^{\rm s}$ }$4, -76 $\hbox{$^\circ$ }$35 $\hbox{$^\prime$ }$2 $\hbox{$^{\prime\prime}$ }$. The corresponds (approximately) to a previously observed dense core lying to the north of HD97300 (Jones et al. 1985; Persi et al. 1999).

  
2.2 Data reduction

Initial data reduction was performed using the auto-analysis package from the ISO data pipeline (OLP V10.0, Ott et al. 1997; Blommaert et al. 2001). This corrected the images for changes in the spectral response of the detector, as well as performing flatfielding and flux calibration. It should be noted that column 24 on the array was dead: this was corrected for by means of a simple linear interpolation from the adjacent pixels. Sources were identified "by eye'' and everything representing a local maximum in intensity in more than 75% of the frames was treated as a source. For each source identified the flux in each frame was evaluated as the total flux contained within a $18\hbox{$^{\prime\prime}$ }\times18\hbox{$^{\prime\prime}$ }$ ($3\times3$ pixel) aperture less the sky flux (evaluated as the mean flux per pixel over a designated sky region). This produced a spectrum for each source from both filter sets. These spectra were smoothed to match the resolution of the CVF and the 2 "halves'' taken from the 2 filter sets were then joined together. Unfortunately it was necessary to discard the data from positions 70-80 on CVF1 (8.94-9.43 $\mu$m), as the array "memory'' (a noted problem with ISO, see Blommaert et al. 2001) rendered these images useless. Consequently the spectra contain a small gap in their wavelength coverage at this point, from 8.94-9.33 $\mu$m. The spectra were also corrected for a systematic under-estimation of flux at long wavelength, which arose from the use of a fixed-size aperture to measure the total flux from diffraction-limited images.

  
2.3 Spectral features

Figure 1: A typical spectrum, with prominent spectral features annotated.

An example of a typical spectrum is shown in Fig. 1. The following spectral features were identified in the spectra:

• An absorption feature at 6 $\mu$m attributed to the bending mode of H₂O ice (Gerakines et al. 1995).
• An absorption feature at 6.8 $\mu$m, the well-known unidentified feature (Schutte 1997).
• A weak absorption feature at $\sim$7.6 $\mu$m which was not resolved at the low spectral resolution of the CVF. It is tentatively identified as the bending mode of CH₄ at 7.67 $\mu$m (Hudgins et al. 1993; Boogert et al. 1996; Boogert et al. 1998) but due to the low resolution of the CVF and the weak nature of the observed feature this identification is somewhat uncertain.
• A broad feature centred at $\sim$9.7 $\mu$m, seen in both emission and absorption, identified as the Si-O stretching mode of "astronomical silicate'' (Draine & Lee 1984; Simpson 1991; O'Donnell 1994).
• A broad absorption feature at $\sim$13 $\mu$m identified as the libration (or hindered rotation) mode of H₂O ice (Gerakines et al. 1995).
• An absorption feature at 15.2 $\mu$m attributed to the bending mode of CO₂ ice (Ehrenfreund et al. 1996).

Other spectral features were observed in individual sources, such as the apparent 10.5 $\mu$m emission feature in RCrA IRS5 (see Fig. 2) or the apparent 14 $\mu$m absorption feature in HH100-IR (see Fig. 4). These rarer features have been noted in the results tables where they occur, but the goal of this study was to look for general trends rather than individual curiosities. With this in mind, and also considering the large number of spectra obtained, it was decided to fit only the strongest and most commonly occuring features highlighted above.

  
2.4 Fitting the spectra

As many of these spectral features overlap, independent determinations of their strengths were not possible, so all of the features in the spectra were fitted simultaneously. This was achieved by fitting a spectrum of the form:

$$F_{\nu}(\lambda) = C(\lambda)\times\exp\left(-\sum_i s_i \alpha_i(\lambda)\right)$$ (1)

where $C(\lambda)$ is the continuum, s_i represents the absorbing column density of each species i and $\alpha_i(\lambda)$ are the absorption coefficients for each species i. This essentially treats the absorbing material as a cold absorbing screen. In order to account for possible silicate emission, the depth of the silicate feature, $s_{{\rm Si}}$, was allowed to run negative. Note however that this assumes that the same profile applies in both absorption and emission, so could result in errors if both are present. The absorption coefficients for H₂O ice and CO₂ ice were taken from the Leiden Observatory Database of Interstellar Ices (Gerakines et al. 1995; Ehrenfreund et al. 1996) and those coefficients evaluated at 10 K were used, as thermal variations are negligible at the spectral resolution of the CVF. It should be noted, however, that the depths of the 6 $\mu$m and 13 $\mu$m water ice bands did not correlate as expected, so they were fitted independently. The unidentified feature at 6.8 $\mu$m was fitted using an asymmetric Gaussian profile: a Gaussian profile with two different widths shortward and longward of the peak. The best-fitting profile for each 6.8 $\mu$m feature was measured, and the widths were then fixed as the means of the widths measured in all of the observed profiles ( ${\it FWHM}=500$ nm). The poorly resolved 7.6 $\mu$m feature was fitted using a Gaussian profile with a width equal to that of the CVF resolution element at that wavelength. A number of profiles exist in the literature for the silicate feature, obtained both theoretically and observationally, so the profile which provided the best fit to the observed data was used: profile 2 from Simpson (1991). However the profiles obtained by Simpson (1991) from IRAS observations extend shortward only to $\simeq$7.5 $\mu$m, and so shortward of this wavelength the optical constants for "circumstellar silicates'' from Ossenkopf et al. (1992) were used. It should be noted that the profiles from Simpson (1991), Ossenkopf et al. (1992) and Draine (1985) are almost identical away from the 9.7 $\mu$m peak: only the shape of the absorption band is dependent on the choice of optical constants.

The fitting procedure was iterative, with repeated fitting converging to a final profile. The fitting algorithm took the form:

1.

Fit initial continuum and divide out. The continuum was fitted as a 2nd-order polynomial through points at 5.6, 7.9 and 16.1 $\mu$m, so chosen as they best constrained the resulting fits.

2.

Measure the strength of each spectral feature at a number of points around the peak.

3.

Use these strengths and the optical constants for the different species to divide out the features from the spectra.

4.

Fit a new continuum to this "featureless'' spectrum.

5.

Iterate this procedure until the fit converged: typically 10-15 iterations were sufficient.

It should be noted that this allowed the continuum to drift away from the observed spectrum in some cases, due to absorption across the entire observed wavelength range. This is because the normalised silicate opacity over the range 5-7.5 $\mu$m is approximately constant at $\simeq$0.15, and towards the long wavelength end of the spectra the 18 $\mu$m bending feature begins to "cut in''. (The normalised opacity at 16 $\mu$m is approximately 0.3.) The effect of this can be seen in Fig. 2: although the continua are seen to deviate significantly from the observed spectra, appearing to diverge from the observed spectra in some cases, this is primarily due to silicate absorption across the entire wavelength range. With only the silicate features included, these "continuum plus silicate'' fits are seen to follow the observed spectra well. As a result, any possible systematic errors arising from the manner of the continuum fit will only affect the evaluation of the silicate optical depth; the measured strengths of the narrower features are not affected by the choice of continuum.

Figure 2: Examples of successful fits to GY265 in $\rho$ Oph (upper) and RCrA IRS5 (lower): fitted spectra are shown as solid lines and continua as dashed lines. The dotted lines are the "continuum plus silicate'' fits given by $C(\lambda)\times\exp\left(- s_{\rm Si} \alpha_{\rm Si}(\lambda)\right)$.

On inspection of the residuals from this fitting procedure a further feature was observed: a broad feature centred on $\simeq$11.2 $\mu$m, seen in both emission and absorption. This has a number of possible identifications, such as crystalline silicates (Bregman et al. 1987; Campins & Ryan 1989), the Unidentified (PAH) Band at 11.3 $\mu$m (Boulanger et al. 1996), or a shoulder on the silicate profile. Given the variation in possible identifications, it was decided to fit this feature independently using an asymmetric Gaussian profile, once again taking the widths to be the mean of those observed ( ${\it FWHM}=1700$ nm). This feature was then included in the algorithm and the fitting procedure repeated: examples of successful fits are shown in Fig. 2. Another similar residual around 8.5 $\mu$m was also observed, but the properties and strength of this were greatly affected by the choice of continuum point around 8 $\mu$m. Whereas the 11 $\mu$m feature was robust against small changes in the continuum this apparent 8.5 $\mu$m feature was not, so it was not included in the fitting procedure.

The 15.2 $\mu$m CO₂ ice feature is an interesting one and has been used in the past as a diagnostic of the ice environment. Gerakines et al. (1999) found that two distinct phases of CO₂ ice (polar and non-polar) show significantly different absorption profiles. The non-polar phase is characterised by a double-peaked profile, arising from the two-fold degeneracy of the bending mode, whereas the polar (H₂O-rich) phase shows a significant long wavelength wing. The spectral resolution of the CVF is too low to resolve the double-peak structure, but the CO₂ profiles were observed to vary noticeably from source to source. As a result it was decided to let the CO₂ profile vary, so it was fitted using an asymmetric Gaussian profile with the widths as variable parameters.

There are two forms of error associated with this fitting procedure. Firstly there are the ordinary statistical errors associated with the fits, evaluated by combining the statistical errors on the data points used to fit the features and the intrinsic uncertainties in the individual feature fits. These are typically around 5-10% for the stronger features (silicate, H₂O, CO₂) and around 15-20% for the less well constrained features, although in the case of some poor S/N spectra they are much larger. In addition to this, there are systematic errors associated with poor fits. These are usually due to the presence of "extra'' features in the spectra, or because of poorly fitting feature profiles, and are less easy to quantify. Consequently, the errors reported in the results tables are the statistical errors only; where fits are flagged as poor additional systematic errors also apply.

  
2.5 Dealing with poor fits

Figure 3: Examples of poor fits (solid lines) from 5-8 $\mu$m and around the CO2 ice feature.

Generally the procedure described above proved successful, but in some cases it led to poor fitting of certain features. This was primarily due to the manner in which the continuum was fitted, as shown in the examples in Fig. 3. The continuum was fitted as a 2nd-order polynomial through three sections on the spectrum expected to show the least absorption, as described above. However, constraining the continuum through these three points led in some cases to poor fitting elsewhere, particularly at the short end of the CO₂ ice band and immediately shortward of the silicate feature.

In such cases, the narrower features at the short end of the spectrum (6.0, 6.8 and 7.6 $\mu$m) were fitted in exactly the same way as before, only this time using a linear continuum through the points at 5.6 and 7.9 $\mu$m. As absorption due to the silicates is approximately constant over this wavelength range this removed complications due to the quadratic continuum fit. When tested on spectra which were fitted well, such as those in Fig. 2, this produced results which were the same as before, within the fitting errors. Also, the manner in which the continuum was fitted often led to the CO₂ feature fitting poorly, as seen in Fig. 3. As a result it was decided to measure the CO₂ absorption in all the sources by fitting a linear continuum from 14.5-16.1 $\mu$m, as the silicate absorption does not vary much over this range and the CO₂ is not blended with any other spectral feature. This procedure was only applied to these narrower features, however, as the broad silicate, 11 and 13 $\mu$m bands were deemed to be too heavily blended to deconvolve them meaning fully over a short section of the spectra. In addition, all features fitted in this manner are flagged as such in the results tables.

  
2.6 Spectral index

In order to take a standard measurement of the SED, the spectral index $\alpha$ was evaluated as a traditional IR spectral index (e.g. Kenyon & Hartmann 1995):

$$\alpha = \frac{\log \lambda_2 F_{\lambda_2} - \log \lambda_1 F_{\lambda_1}}{\log \lambda_2 - \log \lambda_1} \cdot$$ (2)

This sets $\alpha=0$ as the index of a flat $\nu F_{\nu}$ and $\alpha=-3$ as the index of a Rayleigh-Jeans spectrum. Equivalently, class I YSOs have $\alpha>0$, class II have $-3<\alpha<0$ and class III $\alpha \sim -3$, using the conventional definition of spectral class (Lada 1987), although more recent studies (e.g. André & Montmerle 1994; Greene et al. 1994) have found that the class II/III border lies at a higher value ( $\alpha \simeq -1.5$). Where previous K-band data exist in the literature the wavelengths were taken as $\lambda_2=14.0$ $\mu$m (our data) and $\lambda_1=2.2$ $\mu$m (K-band data from references in Table 1) and this was applied to both the observed spectrum and the calculated continuum for each source. (Where no K-band data exist, for sources not previously observed or with uncertain identifications, $\lambda_1=8.0$ $\mu$m was used.) This second ("continuum'') measurement of the spectral index is important, as many of the sources suffer significant absorption (including foreground absorption) and a straight application to the observed spectrum could result in sources being mis-classified in cases where deep absorption is present. In cases where the flux suffers little extinction the two give the same results, but where deep absorption is present the continuum spectral index derived is greater than that obtained from the observed spectrum. In such cases the continuum spectral index provides a truer measurement of the shape of the underlying continuum.