A radio continuum study of the ‘Engraved Hourglass’ nebula, MyCn 18

Abstract

We present the first radio continuum images of the ‘Engraved Hourglass’ planetary nebula (PN) MyCn 18 from multifrequency observations with the Australia Telescope. The radio emission is strongly core-dominated at all frequencies investigated. At the three higher observing frequencies, the radio emission is seen to trace the optically-visible hourglass lobes. In the highest resolution image, the position of peak radio brightness is found in a region which we show to be geometrically off-centre in the same sense as the offset of the ‘central’ star seen in the WFPC2 HST images of Sahai et al. The brightness temperatures measured are surprisingly low and this is interpreted as an effect of beam dilution and nebular clumpiness. We have attempted to separate the contributions to the integrated flux density from the lobes and the core and we present individual plots of the radio spectrum for these regions and also for the total nebular emission. These plots are used to obtain (lower, upper) limits to the turnover frequency of the core and the lobes, which in turn are used to derive (lower, upper) limits to the emission measure, density and ionized mass of the respective regions. Assuming the PN is at a distance of 2.4 kpc, we derive (lower, upper) limits to the total ionized mass of the PN of (0.2, 0.8) M_⊙.

circumstellar matter, planetary nebulae: individual: MyCn 18 (PN G307.5-04.9), radio continuum: stars

1 Introduction

A continuing question in the study of planetary nebulae (PN) is the origin of the varied and complex morphologies they are observed to display. The generalized interacting stellar winds (GISW) model (e.g. Frank et al. 1993) attempts to account for this by invoking density inhomogeneities in the circumstellar envelope (CSE) of the progenitor asymptotic giant branch (AGB) star, which are amplified on interaction with the fast wind that is predicted to switch on between the AGB and PN phases. Models based on this (e.g. Mellema & Frank 1995, and references therein) are successful in reproducing many of the large-scale structures and dynamical characteristics seen in evolved PN. However, the physical explanations for such features as point-symmetric knots (e.g. López, Meaburn & Palmer 1993) and high velocity outflows (e.g. Bryce et al. 1997) remain unclear.

MyCn 18 was discovered by Mayall & Cannon (1940). It is thought to be at a distance of ∼2.4 kpc (Corradi & Schwarz 1993). It shows an extreme bipolar morphology, with a tightly pinched waist from which emanate the open-ended outer ‘hourglass’ structures (Sahai et al. 1999) with their intricate ‘etchings’ and filaments. These features, and the high velocity outflows the PN displays, have aroused much curiosity as to its origins. These characteristics make it an ideal candidate to study in order to investigate evolutionary morphologies of young PN.

Previous studies of MyCn 18 at optical and infra-red wavelengths have led to conflicting opinions regarding the nature of the central star; is it a single or multiple system? A study by Corradi & Schwarz (1993) discounted the possibility that MyCn 18 was a post-PN symbiotic nebula. Based on optical and near-infrared diagnostic diagrams, they found that it falls in the locus occupied by young and compact PN. However, they also found that MyCn 18 falls in the dusty symbiotic locus of the emission line diagram of Schwarz (1988). Sahai et al. (1999) note that the ‘central’ star of MyCn 18 is visibly off-centre within the main structure. They measure the major axis of MyCn 18 to have a position angle of and find that the star does not lie on this major axis but is offset along the minor axis, roughly westward from the geometric centres of the inner rings and the two hourglasses. In discussing the possible reasons for this offset, they conclude that binarity of the central stellar system would provide a successful explanation. A binary system is also suggested by Bryce et al. (1997) and O'Connor et al. (2000) who reported the discovery of a bipolar, knotty outflow from MyCn 18 with velocities ⅽ630 km s⁻¹. They discuss several possible explanations for the ejection mechanism and favour a (possibly recurrent) nova-like ejection from a central binary system.

From spatial and kinematical constraints, Dayal et al. (2000) infer that the inclination of its southeastern lobe towards the observer is θ∼ 30°–35° and O'Connor et al. (2000) find θ∼ 38°. From their model, Dayal et al. (2000) derive electron densities of greater than 10⁴ cm⁻³ in the compact core region to 1350 cm⁻³ in the lobes; from [S ii] ratios, Corradi ' Schwarz (1993) measure densities ranging from 10⁴ cm⁻³ to 500 cm⁻³ in the same respective regions. Dayal et al. (2000) calculate dynamical time-scales of about 1000 yr along the waist and about 2500 yr at the rim of the hourglass lobes. Bryce et al. (1997) determine a kinematical age of 1250 yr for the furthest knots.

No neutral molecular species have been found in the environment of MyCn 18. Vibrationally-excited H₂ is associated with the photodissociation regions around some PN (e.g. Latter et al. 2000), but no 2.12-μm emission has been detected in this object (Webster et al. 1988). Dayal et al. (2000) did not detect any CO emission either and they use these molecular non-detections to suggest that MyCn 18 is mainly density bounded and that molecular material, if present, may be too cold and/or diffuse to be detected. They infer from the observed Hα flux that the PN may be ionization bounded in the compact core and that any molecular material may exist in this waist region.

MyCn 18 was selected as a target for study in order to follow up the recent HST WFPC2 observations (Sahai et al. 1999) as no radio images of this object existed in the literature. The published radio observations of MyCn 18 are primarily concerned with flux density measurements (e.g. Milne & Webster 1979; Milne & Aller 1982; Calabretta 1982). As PN are intrinsically dusty (e.g. Woodward et al. 1992), radio images can provide a useful probe of their structure, revealing the full extent of the ionized matter without suffering from extinction effects.

To facilitate the comparison of the new radio images with the randomly-oriented HST images of Sahai et al. (1999), some of the HST data were obtained from the archive and are presented in Fig. 1. We choose to show the [O iii] 5007-Å image as this high ionization line clearly shows the core structure and the inner parts of the outer hourglass that are most useful for comparing with the radio structures discussed in this paper. [O iii] emission is confined to a particular ionization zone and does not faithfully trace the origins of the radio emission as does Hα emission. The WFPC2 Hα image is not displayed here because part of the core region in the Hα image is affected by saturation. However, the regions of MyCn 18 that are traced by [O iii] in Fig. 1 are similarly traced by the Hα emission (Sahai et al. 1999). The ‘central’ star is also visible in Fig. 1 as the ‘kink’ to the east of the third-highest contour and to the west of the centre of the geometrical structures that comprise the PN (Sahai et al. 1999). Note that we shall refer to the central ∼5 arcsec core region that contains the ‘inner hourglass’ and two elliptical rings (Sahai et al. 1999) simply as the ‘core’. The bipolar lobes that emanate from the core in Fig. 1 trace the inner parts of the outer hourglass structure seen in the composite images of Sahai et al. (1999); we shall refer to these as the ‘lobes’.

Figure 1

(a) The WFPC2 HSTnarrowband image of MyCn 18 in the light of [O iii] 5007 Å, observed on July 30 1995 (Proposal I.D. 6221, Trauger, J; published in Sahai et al. 1999). The image is comprised of two 700 s exposures that have been combined and cosmic ray rejected. The scale is ∼0.1 arcsec pixel⁻¹. The contours are plotted at −1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 768 and 960 × 0.1per cent of the peak surface brightness of 0.425 erg s⁻¹ cm⁻² sr⁻¹. The three highest contours are plotted in white to facilitate viewing. The ‘central’ star is visible as a ‘kink’ to the east of the third highest contour and to the west of the centre of the geometrical structures that comprise the PN (Sahai et al. 1999). To the east of the central star, a local minimum of emission is seen within the core region. (b) The same as (a) but enlarged so that the central region and the star are more apparent.

2 Observations and Data Reduction

The observations presented in this paper were made using the Australia Telescope Compact Array (ATCA). The observations utilized all of the available observing bands in order to make a comprehensive continuum study of MyCn 18; the observing details are given in Table 1. In addition, observations were made in spectral line mode to search for mainline OH maser emission; the details are given in Table 2.

Table 1

Continuum observations of MyCn 18 with the ATCA. Column (1) gives the date of the observations, (2) the central observing frequency, (3) the observing bandwidth, (4) the antenna configuration (see Sault & Killeen 1998) and (5) gives the total time spent observing MyCn 18.

Table 2

Spectral line observations of MyCn 18 with the ATCA. The columns are as in Table 1 apart from (4) which gives the observing bandwidth in terms of velocity and (5) which gives the number of correlator channels.

The primary amplitude calibrators observed were 1934-638 or 0823-500. The scan time on the target source was either 15 or 30 min depending on the atmospheric stability associated with the observing frequency being used, and interleaved between each scan on target was a 3.5-min scan on 1352-63, the phase reference calibrator. In order to calibrate for the feed leakage terms (Sault & Killeen 1998), the continuum data were observed in full polarization mode (XX, YY, XY, YX). The final images, however, are all in total intensity (Stokes I).

The MyCn 18 continuum data were reduced using the ATCA-specific miriad package (see Sault & Killeen 1998). The initial calibration routines were applied in the standard way. The known flux density of the primary amplitude calibrator (Duncan, Kesteven & Manchester 2002) was used to scale that of 1352–63 (Table 3). The target data were then self-calibrated and the derived solutions were applied to the data set. The first round of self-calibration solved for phase only, using a point source model at the phase centre. Subsequent rounds of phase-only, and then phase and amplitude self-calibration were performed using the clean components derived from the previous round as a model in each iteration. Three confusing sources were found to be in the field of view and so the emission from the nebula and the confusing sources was carefully boxed for the cleaning process. The final images were made with uniform weighting.

Table 3

The flux densities of the phase reference calibrator, 1352–63, found at each frequency by calibrating against the known flux density of one of the standard flux calibrators, 1934–638 or 0823–500. The errors are of order 5 per cent.

Table 4gives the full width at half-maximum (FWHM) parameters of the restoring beam used at each frequency. Table 5 gives the flux measurements made from each image. The integrated flux densities and rms off-source noises were measured using miriad task cgcurs. The errors on the peak brightness and integrated flux density measurements are typically of the order of 5 per cent of the respective measurements.

Table 4

FWHM beam dimensions and position angles at each frequency.

Table 5

Flux measurements taken from the images. Column (1) gives the frequency of the observations, (2) the peak flux density per beam area, (3) the total integrated nebular flux density, (4) the off-source 1σ rms noise level (5) the theoretical sensitivity for observations of equivalent duration at each frequency.

The fact that none of the images attain the theoretical noise levels can be explained by the offset of the phase centre (α_J2000= 13 : 39 : 34.10, δ_J2000=−67 : 22 : 00.00) of the PN observations by about −50 arcsec in declination from the position of the PN (measured in Section 4.1) itself. This offset was used because it was thought that sampler harmonics might lead to artefacts in the centre of the field. The use of self-calibration, using a point source model at the phase centre, effectively ‘pulled’ the data to this position and decreased the wrapping rate of the phases so that the resulting signal-to-noise ratio within a solution interval improved and the faint nebular lobe structure became more apparent. Nevertheless, a consequence of the offset was that the data were still quite noisy. The noise levels were also increased by the presence of the three confusing sources in the field. Two of these sources are at angular distances of ∼100 arcsec and the other is ∼250 arcsec from the phase centre. At these distances, they are too far out in the primary beam for cleaning to work effectively. The sidelobes arising from one of the confusing sources are seen clearly in the north-east to south-west stripes visible in Fig. 2(a). The 1384-MHz image is particularly noisy, probably because of ionospheric effects which can be quite serious at this frequency.

Figure 2

ATCA images of MyCn 18 with logarithmic grey-scales from the 1σ noise level to the nebular peak radio brightness on each map (Table 5): (a) 1384 MHz. Contours plotted at −1, 1, 2, 4, 8, 12, 16, 24, 32 and 36 × the 3σ level of 0.97 mJy beam⁻¹; (b) 2496 MHz. Contours plotted at −1, 1, 2, 4, 8, 16, 32, 48, 64, 96, 128, 160 and 192 × the 3σ level of 0.20 mJy beam⁻¹. Note that in this image, the contours that enclose positions −3, 4 and 1, 6.5 arcsec represent a dip in the 2496 MHz emission; (c) 4800 MHz. Contours plotted at −1, 1, 2, 4, 8, 16, 32, 48, 64, 96 and 128 × the 3σ level of 0.22 mJy beam⁻¹; (d) 8640 MHz. Contours plotted at −1, 1, 2, 4, 8, 16, 32, 48, 64, 80 and 92 × the 3σ level of 0.20 mJy beam⁻¹. In each image, the few highest contours are plotted in white to facilitate viewing. The scale bars are in Jy beam⁻¹ and correspond to the individual grey-scale ranges of each map. Dotted contours indicate negative flux. The beam is shown to the bottom right of each image.

The integrated flux density of the PN measured from the 4800-MHz image and given in Table 5 is lower than that given in Milne & Aller (1982) of 0.106±0.010 Jy at 6 cm. This discrepancy is unlikely to be due to the resolving out of any extended emission as the minimum baseline length used should enable emission up to an extent of ∼38 arcsec to be detected at this frequency. The explanation more likely lies in the different beamsizes used in the respective observations. The Milne & Aller (1982) beamsize was 2.1 arcmin; with such a beam, the inner two confusing sources that were found in the field of view of the new observations will have contributed to their flux density measurement. A measurement of the integrated flux density of these sources was made from the new image and yielded a figure of 18.56 mJy. When added to the integrated flux density measured from the nebula, the new total integrated flux density measurement due to all of the objects within the beam of Milne & Aller (1982) is consistent with their measured flux density. However, the magnitude of the new 4800-MHz integrated flux density still supports the assertion by Dayal et al. (2000) that faint and therefore unobserved Hα emission may exist from ionized gas outside of the hourglass walls.

The spectral line data sets were also reduced using the miriad package. These data were observed in dual orthogonal polarization mode (XX, YY). The YY polarization data were completely wiped out due to interference. No OH maser emission was found down to a 3σ noise level of ∼4 mJy beam⁻¹ in the XX data. This molecular non-detection is consistent with the assertion by Dayal et al. (2000) that the PN is mainly density bounded.

3 The Radio Continuum Images

The images made at each observing band are displayed in Fig. 2 in terms of offsets in arcsec from the phase centre (Section 2). The emission is seen to be strongly core-dominated at each frequency. For this reason, a logarithmic grey-scale is used because the lobes are effectively invisible on a linear grey-scale plot. Where the extent of the nebular emission is commented upon, this has been measured from the 3σ contours on each of the images.

3.1 Radio structure

The PN is resolved at all frequencies investigated, although at 1384 MHz (Fig. 2a) the beamsize is such that the PN appears as nothing more than a blob of maximum extent ∼18 arcsec. The two background stripes crossing the field in this image are the result of sidelobe artefacts emanating from one of the confusing sources and have been effectively ‘magnified’ by the logarithmic grey-scale used to display the image. At this frequency, the smooth brightness distribution is likely to be caused by both the relatively large beamsize and the nebula tending to optical thickness. The variation of optical depth with frequency in the optically thick regime effectively means that different parts of the PN are being observed at different frequencies.

As the observing frequency and resolution increase, the radio emission from the PN increasingly resembles the optical structure seen in Fig. 1(a). The compact core region is clearly resolved at the three higher observing frequencies and is seen to be distinct from the two extended bipolar lobes that emanate from the core to the north-west and south-east. These radio lobes trace the optical lobes seen in Fig. 1(a).

At 2496 MHz (Fig. 2b), the north-west lobe is seen as an arc with a depression between itself and the core that makes it more clearly delineated than its counterpart to the south-east. There is a pinched feature resolved at the north-east tip of the minor axis and the length of this axis is ∼11 arcsec. The nebular emission is of maximum extent ∼20 arcsec if the curious extended feature to the south is included. At 4800 MHz (Fig. 2c) and 8640 MHz (Fig. 2d), the resolution and limb brightening effects combine to separate most of the lobe structures from the main body of the core. Any emission from the region in between is either too faint or too smooth to detect. At 4800 MHz, the north-west lobe forms an incomplete, open-ended arc. The south-east lobe is brighter and in the form of a complete arc, an appearance possibly due to the inclination of this part of the PN towards the line-of-sight (O'Connor et al. 2000; Dayal et al. 2000). The width of the arcs that form the lobes at 4800 MHz is ∼2–3 arcsec. The maximum extent of the emission is ∼15 arcsec and the length of the minor axis is ∼8 arcsec. In the highest resolution radio image, the lobes show structure of dimension ∼1 arcsec, the maximum extent of the nebular emission is ∼12 arcsec and the minor axis is of dimension ∼8 arcsec.

4 Analysis

4.1 Position of peak radio brightness

Inspection of the radio images in Fig. 2 reveals that as the resolution increases, the elliptical core becomes resolved and the position of peak radio brightness is clearly not located at the centre of this region. To investigate this, the position of nebular peak brightness was measured at each observing frequency using miriad task maxfit; the results are given in Table 6. Note that the fits were made to the maps that were constructed prior to the self-calibration stage, when the PN was at its ‘true’ phase referenced position (see Section 2).

6

The variation in position of peak radio brightness (Table 5) with observing frequency. The range of error in each position, σ_p, is based on the given range of the position error of the phase reference calibrator (Duncan et al. 2002) and the error due to the beamsize at each frequency.

The fits show that as the resolution increases, the position of peak radio brightness is found generally further westwards. Interestingly, this apparent geometrical offset is consistent in direction with the position of the peak in the [O iii] emission (Fig. 1) and the Hα emission (Fig. 2c of Sahai et al. 1999) and also with the offset of the ‘central’ star from the geometrical centre of the hourglass structures (Sahai et al. 1999). To further illustrate this, the HST image of Fig. 1 was convolved down to the resolution of the 8640-MHz radio image (Table 4) and aligned with it as shown in Fig. 3. Note that the alignment was in the form of a best approximation as there is no feature common to both images that can be used as a definite reference point. In this convolved-down HST image, the peak contours of the [O iii] emission are clearly skewed in the same sense as those in the 8640-MHz radio image.

Figure 3

Grey-scale of the 8640-MHz radio image overlaid with contours of the HSTWFPC 2 [O iii] narrowband (F502N) image (Fig. 1) that has been convolved down and regridded to the parameters of the 8640-MHz image and shifted into alignment. The grey-scale range is as in Fig. 2(d). The contours are at −1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 768 and 960×0.1 per cent of the peak optical surface brightness. The 5 highest contours are plotted in white to facilitate viewing. Note that the contours that enclose positions 1.5, −3.5 and −1, 5 arcsec represent dips in the optical emission. The negative contours to the bottom left of the plot are an artefact of the rotation process used when rationalizing the optical axes.

The geometrical offset of the star is a puzzle. The fact that the offset in peak radio brightness is consistent with it is worth commenting on. Sahai et al. (1999) attribute the prominence of ‘ring 2’ in Hα and [O iii], and its near-invisibility in [O i] and [N ii], to the likelihood that it contains more highly excited gas than ‘ring 1,’ presumably because of its greater proximity to the central star. They also suggest that the greater relative brightnesses of the western sides of rings 1 and 2 in Hα and [O iii] appear to be consistent with the offset of the central star to the west. However, the proximity of the central star cannot account for the position of peak radio brightness. Some unknown process, e.g. denser gas, is producing brighter radio emission in this region. If the ‘inner hourglass’ seen in the HST images is due to a second interacting winds event, as suggested by Sahai et al. (1999), then it is possible that we are seeing shock-excited radio emission in the vicinity of the visible star.

There is no dip in radio emission (Fig. 2) corresponding to the dip seen in the optical emission (Fig. 1) in the core region. This could indicate that the optical emission is being obscured; Sahai et al. (1999) suggest that dust in the core region could explain their lower-than-expected K-band flux measurement. Indeed, the GISW models account for bipolar PN by invoking an equatorial density enhancement in the progenitor AGB wind that would be expected to be intrinsically dusty. However, it is difficult to clarify this given the constraints on the resolution of the radio images. No dip is visible in the optical emission that has been convolved to the 8640-MHz beamsize either (Fig. 3). Additionally, the fact that the star is clearly seen in the HST images suggests that there is a local minimum of extinction in its immediate environs, an effect that is possibly due to the favourable inclination of the PN with respect to the line-of-sight.

4.2 The radio spectrum of MyCn 18

Using the images shown in Fig. 2, separate spectral index images were made between 8640-4800 MHz (Fig. 4), 4800-2496 MHz and 2496-1384 MHz (not shown) in order to examine the spectral index variation across the face of the nebula. In order to do this, the higher frequency image in each spectral index pair was first convolved down to the parameters of the lower frequency image. The 2496-1384 MHz and 4800-2496 MHz spectral index images show that the compact core is more optically thick than the lobe regions between these observing frequencies. The 8640-4800 MHz spectral index image indicates that between these frequencies, both the core and the lobe regions are optically thin.

Figure 4

The 8640-4800 MHz spectral index image of MyCn 18. The contours are plotted at spectral indices of −2.8, −2.4, −2, −1.6, −1.2, −0.8, −0.4, 0, 0.4, 0.8, 1.2, 1.6 and the linear grey-scale (indicated by the scale bar) is from −2.88 to 1.76. The dotted contours indicate a negative spectral index. The beam is shown to the bottom right of the image. The extreme spectral index values are found in the edge regions, where one of the component radio images slightly overhangs the other. For the most part, in both the lobes and the core, the spectral index is between ∼−1 and 0 indicating between 4800 MHz and 8640 MHz, the whole PN is optically thin.

Analysis of the radio spectrum of a PN can reveal model-dependent information regarding its physical properties (e.g. Wright & Barlow 1975; Terzian 1978; Kwok, Purton & Keenan 1981; Taylor, Pottasch & Zhang 1987; Calabretta 1991; Aaquist & Kwok 1991). In the case of MyCn 18, the obvious density variations between the core and the lobes suggest that the spectral behaviour of these two regions should be studied separately.

Gaussian fitting was used to separate the integrated flux density contribution due to the core from that of the lobes. However, in comparing flux density measurements from maps of different resolution that contain unresolved structure (such as the core in Fig. 2a), the variation in the beamsize between the observing frequencies cannot be ignored. Ideally, the observations would have taken place with the array configuration adjusted so that equivalent beamsizes were obtained at each frequency; in practice the cost to the resolution in the higher frequency radio images would have been too great. In an attempt to minimize the effects of the beamsize in the analysis of the radio spectrum, the three higher resolution maps were first convolved down to the same resolution, that of the 1384-MHz observations.

An elliptical Gaussian was fitted to the core region of the convolved-down maps at each frequency using miriad task imfit. The results of the fits are given in Table 7. In addition, the residual PN flux density (greater than the 3σ level) that was left after the Gaussian fitting was measured using cgcurs and is also given in Table 7; this was taken to be the contribution from the lobes. The errors on the flux density measurements are typically 5 per cent. The flux density contributions from the core and lobes and the total nebular emission (Table 5) are plotted versus observing frequency in the log—log plots in Fig. 5.

7

Parameters of the Gaussians fitted to the core and the flux densities of the core and lobe regions. Column (1) is the observing frequency, (2) the angular size of the fitted elliptical Gaussian FWHM major axis, (3) the angular size of the FWHM minor axis, (4) the integrated flux density within the fitted Gaussian, (5) the integrated flux density from the lobes. The errors on the flux density measurements are typically 5 per cent.

Figure 5

The radio spectra of the (a) lobe regions (Table 7), (b) core region (Table 7) and (c) total nebular emission (Table 5). The errors on the flux density measurements are typically 5 per cent.

It is interesting to note that the angular sizes of the fitted elliptical Gaussians (Table 7) decrease with frequency even though the maps have been convolved to the same beamsize. This implies that the size of the core emitting region really does change with frequency, a result also implied by the higher frequency images in Fig. 2 where the core is resolved. Given the apparent difference in size between the core (where resolved) in Fig. 2 and the fits in Table 7, it is likely that the Gaussian fits to the core also include some contribution from the flux density of the lobes.

With only 4 data points, the turnover frequency ν_t cannot be uniquely determined. Our observations did not reach sufficiently low frequencies to enable us to witness the PN in a highly optically thick state. However, given the results of the spectral index maps and the plots in Fig. 5, we can say in all likelihood that the (lower, upper) limits to ν_t for both the core and the total nebular emission are (2496 MHz, 8640 MHz), whilst those for the lobes are (1384 MHz, 4800 MHz).

If the morphological evolution of the PN has been governed by the presence of an equatorial density enhancement, as the GISW models predict for such bipolar PN as MyCn 18, then the core region would be expected to be more optically thick than the lobes. A binary system can produce both an accretion disc and high velocity outflows (e.g. Soker & Livio 1994), such as those seen in MyCn 18 (Bryce et al. 1997), as can the presence of magnetic fields (e.g. Garcia-Segura 2002, and references therein). Alternatively, if the second CSE ejection event hypothesis is favoured (Sahai et al. 1999), we would expect to see a more dense, swept-up shell of gas in this region which would also lead to the localized greater optical depth that we observe.

4.3 Brightness temperature

Brightness temperatures T_B can be derived directly from individual radio maps by application of

(1)

where B_ν is the specific intensity in W m⁻² Hz⁻¹ sr⁻¹, c is the speed of light, k is Boltzmann's constant and ν is the observing frequency. The peak B_ν was measured for each of the images in Fig. 2 using the relevant values of elliptical beam area calculated from Table 4 and S_peak given in Table 5. The peak T_B values so derived are given in Table 8. These temperatures have an associated ∼5 per cent error. For thermal bremsstrahlung, the measured T_B is related to the electron temperature T_e by

(2)

where τ_ν is the optical depth of the source at frequency ν. When the emission is optically thick, τ_ν≫1 and so T_B∼T_e.

8

Peak brightness temperatures T_B derived from the radio images. The errors are typically 5 per cent.

The canonical T_e of a PN is taken to be of order 10⁴ K and in young PN it can be expected to be higher. Given that MyCn 18 is thought to be a young PN and the results of Section 4.2 suggest it is tending to optical thickness at 1384 MHz, the peak T_B derived at this frequency is particularly low; in this region of the radio spectrum T_B should be approaching T_e. This low value of T_B probably occurs as a result both of the PN not being completely optically thick at 1384 MHz and also because of beam dilution effects. The 1384-MHz beamsize appears to be larger than the core area (Fig. 2) and so the peak T_B derived here will include a contribution from the lobe regions as well as the core. The lobes are likely to be at a lower temperature than that of the core, given their larger distance from the central star, as well as being less optically thick (Section 4.2). In addition, the HST images suggest that the core is inherently clumpy. Therefore, it is likely that beam dilution effects will act to average the temperatures of the clumps in the core to something lower than their actual peak.

4.4 Estimates of some physical parameters

As distance determinations for PN are notoriously inaccurate, where relevant the following calculations will be made for both a normalized distance of 1 kpc and the published distance of 2.4 kpc (Corradi & Schwarz 1993). We assume an average T_e of 10⁴ K.

4.4.1 Clumps

If beam dilution due to nebular clumpiness is the correct explanation for the anomalous temperatures (Section 4.3), the number of clumps N_cl intersecting the beam at 1384 MHz can be estimated. If a random distribution of clumps intersects the beam, the aggregate of which subtends at the telescope a solid angle Ω_cl, which is less than the beam solid angle Ω_B (Table 4), then

(3)

where T_B is the measured brightness temperature (Table 8) and T_cl is the actual aggregate clump brightness temperature. Given that the PN is tending towards optical thickness at this frequency (Section 4.2), T_cl is assumed to be 10⁴ K, yielding Ω_cl=2.6 arcsec². The filling factor at 1384 MHz is then 0.15. If the diameter in the plane of the sky of a typical single nebular clump is ∼10⁻³ pc (Meaburn et al. 1998), then at a distance of 1 kpc (2.4 kpc), N_cl becomes 80 (450).

4.4.2 Emission measure

The emission measure is defined as

(4)

where n_e is the electron density along the differential path length dl. Following the analysis given in Osterbrock (1989), the emission measure is given by

(5)

At the turnover frequency ν_t, the optical depth is unity. Using the (lower, upper) limits to ν_t given in Section 4.2, the limits to the emission measure are (2, 28) × 10⁷ cm⁻⁶ pc for the core region and (6, 82) × 10⁶ cm⁻⁶ pc for the lobes.

4.4.3 Density

If the core is assumed spherical and of diameter 5.5 arcsec (Table 7 and Fig. 2), equation (4) gives limits to n_e in the core of (3, 10) × 10⁴ cm⁻³ at 1 kpc or (2, 7) × 10⁴ cm⁻³ at 2.4 kpc. These densities are comparable with those obtained by Corradi & Schwarz (1993) and Dayal et al. (2000).

If the lobes are assumed to be 2 cylinders of diameter 8 arcsec (the PN minor axis dimension in Figs 2c and d), the limits to n_e within them are (1, 5) × 10⁴ cm⁻³ at 1 kpc or (8, 30) × 10³ cm⁻³ at 2.4 kpc. These densities are somewhat higher than those obtained by Corradi & Schwarz (1993) and Dayal et al. (2000) and this could be because we have not deprojected the PN; the inclination of its major axis to the line-of-sight will lead to an apparent increase in path length through the lobes.

4.4.4 Ionized mass

Assuming the PN matter is mainly ionized hydrogen, the ionized mass of a spherical core (not including the central star) is

(6)

where m_p is the mass of a proton and d is the diameter of the ionized region. This yields limits to M_c of (7, 25) × 10⁻³ M_⊙ at 1 kpc or (6, 23) × 10⁻² M_⊙ at 2.4 kpc. The ionized mass of the 2 cylindrical lobes is

(7)

where the height of each cylinder h ∼ 5 arcsec (Fig. 2). This yields limits to M_l of (0.02, 0.07) M_⊙ at 1 kpc or (0.2, 0.6) M_⊙ at 2.4 kpc. The limits to the total ionized mass of the PN then become (0.03, 0.09) M_⊙ at 1 kpc or (0.2, 0.8) M_⊙ at 2.4 kpc.

5 Summary

The first radio continuum images of the ‘Engraved Hourglass’ planetary nebula, MyCn 18, have been presented and discussed. At the higher observing frequencies, the radio structure is seen to trace the hourglass shape seen at optical wavelengths, with a compact core region and two outer, less dense lobe regions. The resolution afforded by the higher frequency images also shows that the position of peak radio brightness occurs in a geometrically off-centre region which is consistent with the direction of the ‘offset’ of the ‘central’ star seen in the HST images of Sahai et al. (1999).

The brightness temperatures derived from the radio images are lower than expected and this has been interpreted as being due to beam dilution and nebular clumpiness. A model for the clumps has been used to calculate a filling factor of 0.15 at 1384 MHz.

From spectral index maps, the core is found to be more optically thick than the lobes between 1384 and 4800 MHz. Between 4800 and 8640 MHz, both the core and lobe regions are optically thin. Separate analyses of the radio spectra of the core and lobe regions of the PN have enabled (lower, upper) limits to the turnover frequencies of (2496, 8640) MHz for the core and (1384, 4800) MHz for the lobes to be estimated. These measurements have been used to estimate limits to the emission measure, density and ionized mass of the respective regions. The limits to the total ionized mass of the PN are (0.03, 0.09) M_⊙ at 1 kpc and (0.2, 0.8) M_⊙ at 2.4 kpc.

Acknowledgments

The authors thank the staff of the Australia Telescope for their assistance during these observations. The Australia Telescope Compact Array is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. The HST data are based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. Thanks are also due to A. M. S. Richards, M. P. Redman, N. E. B. Killeen and A. Zijlstra for their helpful comments and suggestions. IB and AMS acknowledge the support of PPARC studentship and PDRA grants. MB acknowledges a University of Manchester fellowship.

This paper has been typeset from a TEX/LATEX file prepared by the author.