Planetary Nebula M1-92920, 1998 September 10Planetary Nebula M1-92 We present high-resolution (1
0) maps of 13CO J = 21 in the protoplanetary nebula M1-92, Minkowski's Footprint, obtained with the Institut de Radioastronomie Millimétrique (IRAM) interferometer at Plateau de Bure. We confirm the main components found in our previous works: a central disklike condensation, a bipolar double-shell structure with axial outward velocity increasing with the distance to the star, and two opposed features at the tips of the nebula where the maximal deprojected velocity is attained, 
70 km s-1. The major quality of the present data allows us to estimate the very small width of the double-shell walls, 06 (2 × 1016 cm), and the diameter of the central disk, 2
3 (1017 cm). The whole structure is probably the remnant of the previous asymptotic giant branch (AGB) shell after being shocked by the bipolar post-AGB jets. The mass of the molecular envelope is about 0.9 M
, and its kinetic momentum and energy (released by the wind interaction) are 3 × 1039 g cm s-1 and 7 × 1045 ergs, respectively. Since the interaction time must be significantly smaller than the age of the nebula, 900 yr, these figures imply very energetic post-AGB jets that cannot be driven by radiation pressure. We also notice that the inner disklike structure is too large for collimating the very narrow post-AGB jets. We propose that reaccretion of material, ejected during the previous AGB phase, is the most likely mechanism to explain the strongly bipolar and very energetic post-AGB ejections.
Subject headings: circumstellar matter
ISM: jets and outflowsplanetary nebulae: individual (M1-92)stars: AGB and post-AGB
M1-92, Minkowski's Footprint, is an oxygen-rich protoplanetary nebula (PPN) that has been well observed in the optical and IR (see, e.g., Herbig 1975; Calvet & Cohen 1978; Bujarrabal et al. 1998). The temperature of the central star is about 20000 K, and its total luminosity and distance have been estimated to be about 104 L and 2.5 kpc, respectively. The optical image has an extent of about 10 (5 × 1017 cm) and consists of two lobes defining a conspicuous axis of symmetry (Trammell & Goodrich 1996; Bujarrabal et al. 1998). The orientation of this axis in the plane of the sky is approximately northwest-southeast; it is also inclined with respect to the plane of the sky (by about 35°), the northwest lobe pointing toward the observer. Optical spectroscopy (Herbig 1975; Solf 1994) has shown the existence of flows of excited gas in the axial direction, with expansion velocities between 200 and 500 km s-1; such flows seem to be due to a presently active process of mass loss. High-spatial resolution imaging with the Hubble Space Telescope (HST) reveals the existence of atomic line emission from compact knots in both lobes along the nebula axis, probably associated with shocks propagating in the bipolar flow (Bujarrabal et al. 1998). The shape of the two-lobe structure suggests the presence in the center of the nebula, and perpendicular to the axial flow, of an oblate dust condensation yielding a strong extinction. In fact, a torus-like structure about 3 wide has been inferred from IR color index images (Eiroa & Hodapp 1989) and 1667 MHz OH maser emission (Seaquist, Plume, & Davis 1991).
M1-92 has been observed in 12CO and 13CO J = 10 (2.6 mm wavelength) with a resolution of about 2 (Bujarrabal et al. 1994; 1997). These observations have revealed a double, empty shell that surrounds the knots of atomic line emission seen with the HST and that shows an extent comparable to the bipolar optical image. These shells were found to be particularly massive (1 M) and cool (about 15 K); their kinematics is dominated by high axial velocities (up to 70 km s-1). They are likely the remnant of the asymptotic giant branch (AGB) envelope accelerated by the passage of a bowlike shock wave. Very probably, this forward shock and the shocked knots detected in the post-AGB flow are both the result of the interaction between the AGB and post-AGB winds, a process that is thought to be responsible for the shaping of planetary nebulae.
We have conducted observations of M1-92 in the 13CO J = 21 line at 1.3 mm (rest frequency 220.399 GHz) using the IRAM interferometer located at Plateau de Bure (French Alps) during two winter periods (19951996 and 19961997). The instrument consists of five antennas of 15 m diameter equipped with dual-band SIS heterodyne receivers. Other characteristics of the array have been described in detail by Guilloteau et al. (1992). The observations were performed in the D, C1, C2, B1, B2, and A standard five-antenna configurations; the resulting synthesized beam, for natural weighting, has the largest negative (positive) sidelobes at a level of -10 (-6) dB, and major and minor axes at half-power of 10 and 09 (the major axis being at a position angle of 153°). This beam size was later used for the restoring of the maps after their CLEANing. As spectral back end we used a digital correlator providing a frequency resolution of 0.625 MHz (0.85 km s-1); however, to ease the comparison with our previous maps of this source (Bujarrabal et al. 1994; 1997), we have resampled the data to obtain exactly the same velocity channels (3.25 km s-1 velocity resolution).
Data reduction (passband, phase, and amplitude calibration, map restoring and CLEANing) was done as in Bujarrabal et al. (1994, 1997); the resulting maps are shown in Figure 1. The rms noise in the maps is 7 mJy beam-1, and the peak flux is 320 mJy beam-1. The conversion factor from flux units to antenna temperature is 29 K per Jy beam-1. Using these maps and this conversion factor, we have computed the spectrum that would have been observed at the central position of M1-92 using a single-dish antenna of 30 m diameter. This spectrum has been compared with data taken with the Pico de Veleta telescope, revealing that no flux is lost at any velocity in our interferometric data.
Fig. 1
In Figure 1 we show our CLEANed maps of the 13CO J = 21 line for the different LSR velocity channels where emission has been found. Our observations confirm the structure of the double, bipolar shell of cool molecular gas occupying the whole nebula. The hollow structure of the shells is clearly seen in the images for all velocities, except for the extreme ones, for which only the fast tips of the nebula (at which the hollow shells close up) are detected. At the central velocities (0 km s-1), both hollow shells are seen. As we show in the velocity-position diagram along the symmetry axis of the nebula (Fig. 1), there is a very clear velocity gradient in this direction. After deprojection of the inclination with respect to the plane of the sky (see § 1) the axial expansion velocity reaches values up to 70 km s-1. In Figure 1 we also show the velocity-position diagram along a central cut perpendicular to the symmetry axis.
From the maps for the central velocity and, particularly, from the double central maximum in both cuts, we can deduce the presence of a central and dense torus-like or disklike structure with a diameter of about 23. Such a size is very similar to that of the ring detected at other wavelengths (§ 1), and corresponds to 1017 cm at a distance of 2.5 kpc (§ 1). Our data show that this structure is essentially in expansion, with a typical velocity of about 8 km s-1 (after deprojection); no sign of rotation is seen in such a torus (or disk) with an upper limit to the rotation velocity at 2 km s-1.
The walls of the hollow shell are found to be particularly narrow. Cuts of the images, in the direction perpendicular to the symmetry axis and at the center of the observed holes, have been performed for all velocity channels. The deconvolution of the synthesized beam in most of such profiles reveal that the width of the observed walls is typically 0507 (2 × 1016 cm, to be compared with a total size of the nebula 
4 × 1017 cm). In a few cases, the walls appear to be still narrower, and their width is only tentatively detected.
Finally, in the tips of the nebula we detect two narrow high-velocity features. The deconvolution of their size in the direction perpendicular to the axis yields values comparable to the width of the walls given above.
We have tried to fit our 13CO J = 21 observations by means of a model of a CO-emitting nebula similar to the one presented in previous papers (Bujarrabal et al. 1994; 1997). We recall that in our model the kinetic temperature corresponds to the excitation (rotational) temperature in the whole rotational ladder of CO, since thermalization can be assumed (see discussion in Bujarrabal et al. 1997). We also mention here that the opacity effects and the interaction of different (perhaps distant) parts with similar velocities in the line of sight are taken into account in the calculation of the predicted intensities. In Figure 2 we give the general structure and velocity field of the model nebula that fits the 13CO J = 21 and J = 10 observations (data for the latter line taken from Bujarrabal et al. 1997). The temperature of the model nebula is 15 K for the central disk (Fig. 2) and 10 K for the other regions. The total density is 3 × 105 cm-3 in the central disk , and varies linearly in the lobes from 3 × 105 (equator) to 5 × 104 cm-3 (tips). The 13CO/H2 relative abundance is chosen to be 2 × 10-5 in the whole source. The velocity field has two components, one radial and one axial, both increasing linearly with the distance to the equatorial plane where only the radial component persists; a sketch of the model velocity is given in Figure 2. Note the great simplicity of this model. The flux distribution calculated for the model nebula is shown in Figure 3, in the same units as for Figure 1; as we see, the agreement is quantitatively good, which shows that the general structure of the molecular nebula (at least of the region responsible for the 13CO J = 21 emission) is well represented by our model. The fitted parameters and nebula structure are quite similar to those deduced in our previous works. The main difference is that the new observations imply that the width of the different components of the nebula (shell walls, ending clumps, and central disk) must be smaller than previously assumed. It is also remarkable that, while the density varies along the nebula, the temperature must be almost constant, which is imposed by the relatively constant J = 21/J = 10 line ratio (see Bujarrabal et al. 1997).
Fig. 2 
Fig. 3
We have mentioned that the fitting of the observations by our model is satisfactory; however, it is clear that the quality of the data would allow a fine tuning of the parameters, at least of those giving the dynamics and structure. Such a process (that would practically be equivalent to an image deconvolution) is out of the scope of this paper. For such a purpose we are already developing a systematic procedure that is giving a three dimensional image of the M1-92 molecular nebula (Alcolea et al. 1998). We must also note that the narrowness of the nebula structures detected in 13CO J = 21 implies that in our previous 13CO J = 10 observations, a relatively strong dilution of the emitting region could be present if both lines come from the same region. This is the reason that in the model presented here the rotational temperature is slightly lower than in our previous models. This temperature is however too low to also allow the fitting of the intense 12CO J = 10 transition (see reasoning by Bujarrabal et al. 1997) with only one component. A temperature gradient in all the parts of the nebula is necessary to fit all three transitions. We have checked that a temperature variation from about 30 to 10 K in the three components of the nebula would suffice. In this case, however, the treatment of the radiative interaction between the different regions and the discussion on the uniqueness of the fitting is hampered because of the strong self-absorption effects in the opaque 12CO J = 10 transition.
A discussion of a more detailed model for M1-92 becomes therefore too complex. Some parameters determined from our calculations, like the temperature, may just represent some kind of average, but we think that others are reliable. This is the case of the total mass of the molecular nebula and therefore of its momentum and kinetic energy. It is easy to show that the emissivity of the 13CO J = 10 and J = 21 transitions is close to the maximum for the rotational temperatures we are assuming. Even in the extreme excitation case in which only the involved levels (J < 3) are populated, the conversion factor from observed brightness to column density is only 1.5 times smaller than for the rotational temperatures taken in our model. Therefore, possible overestimations of the 13CO column densities from our calculations (even in the case of complex distribution of components or extreme excitation conditions) cannot be significant. Underestimations can, on the other hand, be important if the rotational excitation is much higher than expected (since this leads to a significant population of a high number of levels), or if the opacity is high. (Both possibilities are, however, improbable; see Bujarrabal et al. 1997. The excitation is bounded by the relatively low J = 21/1 0 line ratio and high opacities are not expected in 13CO J = 10 since 12CO J = 10 is significantly more intense.) The conversion from mass in 13CO to total mass is also affected by the assumed relative abundance of this molecule, 2 × 10-5, a value that is already quite high for a PPN (Bujarrabal et al. 1997). The 13CO abundance could be lower, since it is known that molecules tend to be photodissociated in PPNs, owing to the stellar UV field. In this case we would have underestimated the total molecular mass in M1-92; however, we do not think that a large underestimation is possible since molecular emission is intense even relatively close to the star and, moreover, the nebular mass we are obtaining (about 1 M; see next section) is already very high for what is expected in this kind of nebulae. In summary, we conclude that the values of the mass we derive for M1-92 could be overestimated only by factors smaller than 2; we cannot rule out a strong underestimation of the mass distribution, but we believe it to be a factor <5.
We can compare the structure and kinetics given by our observations with the results of detailed hydrodynamical calculations for wind interaction. In general, wind interaction models explain the bipolar structure observed in PPNs, with two well-developed cavities in the axial direction (Mellema 1993, 1995, 1997; Icke, Balick, & Frank 1992; Socker & Livio 1989). However, several theoretical results are not in agreement with our observations: (1) we detected a thin inner disk separating both lobeson the contrary, most calculations do not predict such a structure but rather a central cavity well detached from the star; (2) the sharp tips of the cavities observed are not reproduced by the calculations that tend to yield relatively rounded lobe ends; and (3) we note in the predictions a relatively high velocity component in the direction perpendicular to the axis, and the absence of a clear axial gradient, in contradiction to our data on M1-92 and recent results on the PPN OH 231.8+4.2 (Sánchez Contreras, Bujarrabal, & Alcolea 1997).
Point (1) can be due to the assumption that the post-AGB wind is collimated only by the dynamical interaction with the inner AGB layers, which are in the quoted models supposed to be much more dense in the equatorial plane (an assumption that is not confirmed from observations of AGB envelopes). Under these conditions, a strong acceleration also appears in such a plane, which yields a significant expansion of the central "waist" of the nebula. Note that the post-AGB jets are found to be very narrow (Bujarrabal et al. 1997; see also § 5) and, in any case, cannot be collimated by the observed central ring. This contradiction between observations of theory could be relaxed if the post-AGB wind is collimated by the development of conical shocks (see Borkowski, Blondin, & Harrington 1997; see also Mellema & Frank 1997). Collimation due to magnetic fields (Chevalier & Luo 1994; García-Segura 1997) seems a more promising mechanism, although it has not yet been extensively studied.
Points (2) and (3) could arise as a result of the assumption of adiabatic interaction made in most model calculations. In spite of the scarce theoretical investigation of the protoplanetary evolution in the presence of strong radiative cooling, general results on quasi-isothermal (or "momentum driven") wind interaction suggest that, in this case, the nebula should show dominant axial velocities and sharp opening angles in its tips (see, e.g., Masson & Chernin 1993; Blondin, Fryxell, & Königl 1990). Also, it is a classical result that the width of the walls of shocked gas are narrower when the cooling is fast (see, e.g., Frank & Mellema 1994; Blondin et al. 1990); this is qualitatively interesting in view of the very thin CO shells, although the comparison of our data with the calculations yields no clear conclusion on this topic. We recall that the temperature of the shocked molecular gas has apparently dropped to a very low value (about 15 K) in a few hundred years, which also indicates strong cooling effects (the total kinetic age of the nebula is only 900 yr, and the shock interaction time is probably much shorter; see § 5).
Finally, we note that in most models the kinetic momentum and energy assumed to be carried by the post-AGB colliding wind is much smaller than those deduced from the observed kinetics of the molecular shell (see § 5). Also, the interaction time assumed in theoretical works is usually significantly larger than the very short one indicated by our data. It is obvious that the consequences on the calculations of the presence of a post-AGB wind satisfying these properties must be important and should be studied. In the next section we discuss the constraints that the very high kinetic energy deduced to be carried by the post-AGB wind (at least during a short time) impose on its ejection mechanism.
We have seen that there is a strong and almost constant velocity gradient along the symmetry axis of M1-92 (Fig. 1). Such a kinematics is predicted by certain simple and well founded models, and often observed in PNs (Shu et al. 1991; Pottasch 1984). Under such a framework, the envelope suffered a strong axial acceleration during a time period much shorter than the whole post-AGB lifetime of the source. After this event, the different parts of the nebula continued its expansion without further acceleration, which is the simplest way to explain the constant velocity/distance ratio along the axis. From the displacement along the axis of the emission centroid for the different velocities (see also Bujarrabal et al. 1994), we estimate a total kinetic age for the M1-92 nebula to be 900 yr.
We estimated the inner diameter of the central disk or torus from the separation between the central maxima seen in Figure 1, obtaining 1, 4 × 1016 cm. This figure may not actually correspond to an inner diameter, since two maxima are also expected from a thin disk with an almost constant density and velocity, even if there is no central hole. But we note that, for a post-AGB life of 900 yr and a disk expansion velocity of 8 km s-1, the empty region left by the subsequent expansion accurately coincides with the above figure. Also, the inner radius measured by Eiroa & Hodapp (1989) and Seaquist et al. (1991) for their central tori are in agreement with this size. It is important to note that a disk with this inner radius and the width (
3 × 1016 cm) derived by our fitting is unable to collimate the very narrow post-AGB jets seen in the optical (Bujarrabal et al. 1998).
From our model parameters we can also calculate the total mass of the different components of the nebula, as well as their kinetic momentum and energy. The calculated total mass of the molecular nebula is equal to 0.9 M, in good agreement with our previous estimations. This was to be expected, since the determination of the total mass per projected velocity does not practically depend on the assumed geometry. This high mass value indicates that we are probing the bulk of the nebular material. We also calculate that the nebula has increased its energy by 7 × 1045 ergs and its momentum in the axial direction by 3 × 1039 g cm s-1. By "axial momentum" we mean the integration of the mass multiplied by the absolute value of the velocity in the axial direction. The increase in momentum and energy is calculated with respect to the AGB (isotropic) expansion before wind interaction, assuming that the central disk of M1-92 still keeps the original kinematics of the AGB shell and therefore that its velocity is practically equal to that of the AGB envelope. Similar values of the kinetic energy and momentum and of the interaction time have also been deduced for another well studied PPN, OH 231.8+4.2 (Sánchez Contreras et al. 1997).
Such high amounts of energy and momentum were gained by the molecular envelope owing to the PPN wind interaction, and were therefore provided by the bipolar post-AGB wind, in a time period significantly shorter than 900 yr. How the bipolar jets can be so powerful is not understood. The pressure of the stellar radiation, thought to drive the ejection of the AGB envelope, cannot supply the observed large momentum: for a total stellar luminosity 104 L, i.e., 1.2 × 1045 ergs yr-1, the momentum carried by the star's radiation is only 4 × 1034 g cm s-1 yr-1. This discrepancy is strengthened by the fact that we are dealing with kinetic momentum in the axial direction, while radiation is mostly isotropic; the problem persists even if we relax the energy conversion time to the whole lifetime of the source of the PPN, or if we take into account that the conversion factor from radiation to kinetic momentum may be slightly larger than one due to multiple scattering (see, e.g., Knapp 1986). Note that errors in the distance to M1-92 do not affect this comparison, since the distance affects in the same way as the determination of the stellar luminosity and of nebular mass and momentum. Other possible mechanisms, like the sudden ejection of the pulsating layers of the AGB star in its latest evolutionary phases, or the release of gravitational energy in a binary system, also cannot explain under reasonable conditions the kinetic energy of the bipolar ejection. We instead propose the reaccretion of previously ejected material (at least 0.05 M) by the now compact star (present radius 1012 cm) as a mechanism that could explain the observed outflow kinetics, at least from the point of view of energy and momentum conservation. It is well known that gravitational collapse on a compact object can efficiently lead to bipolar ejections of material along the magnetic field lines as a way to release angular momentum excess (see, e.g., Shu 1993). Mass accretion is probably responsible for the driving of bipolar outflows from very young stars, which on the other hand show many observational features in common with post-AGB outflows, including the very high collimation and momentum excess with respect to radiation pressure. Note that the presence of a stellar companion of the post-AGB star is not required; the nonexpanding innermost shells of the AGB envelope, kept "in levitation" by the star pulsation (see, e.g., Hinkle, Hall, & Ridgway 1982), could provide enough material for the postulated collapse once pulsation has stopped and the size of the star has decreased to its present value. Reaccretion of material has been also invoked for explaining anomalies of atmospheric element abundances in post-AGB objects (see, e.g., Van Winckel, Waelkens, & Waters 1995).
This paper has been partially supported by DGES, project PB96-0104.
. 1997, A&A, 320, 540 First citation in article | ADS. 1995, MNRAS, 277, 173 First citation in article | ADS. 1997, A&A, 321, L29 First citation in article | ADS
Full image (255kb) | Discussion in textUpper panels: Maps of the 13CO J = 21 intensity in M1-92 for the LSR velocities indicated in the upper lefthand corners; up is north and left is east. We also include the CLEANed beam (half-power contour), the dirty beam (contours: -10%, 10%, 20%, 30%, and 50%), and the directions "A" and "B" used for cuts below. Lower panels: Intensity as a function of the LSR velocity and position along the symmetry axis of the nebula, axis "A" shown above, and along the perpendicular axis, "B." The color and level scales are shown in the column, and negative contours are shown in red.
Full image (62kb) | Discussion in textStructure of the nebula deduced from our model fitting of the 13CO J = 21 data. The velocity field is indicated by the arrows. The density and temperature are described in the text.
Full image (117kb) | Discussion in textResults of our model fitting to the observed 13CO J = 21 intensity maps per velocity, to be compared with Fig. 1. The velocity, spatial offsets, and intensity scales are the same as in Fig. 1.