A&A 377, 672-676 (2001)
Department of Physics, University of Haifa at Oranim, Tivon 36006, Israel
Received 11 June 2001 / Accepted 8 August 2001
We propose a model based on ionization shadows to explain the formation of the long and narrow strings of Carinae. Five strings are known, all located along the symmetry axis outside the Homunculus. The model assumes that each string is formed in a shadow behind a dense clump near the symmetry axis. The surrounding gas is ionized first, becomes much hotter, and compresses the gas in the shadow. This leads to the formation of a radial, dense, long, and narrow region, i.e., a string. Later the neutral material in the strings is ionized, and becomes brighter. Still later it re-expands, and we predict that in the strings will fade. The condition for the model to work is that the ionization front, due to the diffuse ionizing recombination radiation of the surrounding gas, proceeds into the shadow at a velocity slower than the compression speed, which is about the sound speed. From that we get a condition on the mass loss rate of the mass loss episode that formed the strings, which reads . The model can also explain the strings in the planetary nebula NGC 6543.
Key words: stars: early-type - stars: mass loss - stars: individual: Carinae - ISM: planetary nebulae: individual: NGC 6543 - ISM: reflection nebulae
There are several open questions regarding the formation of the nebulosity around the massive star Carinae (Davidson & Humphreys 1997; hereafter DH97). Some of the questions concern the nature and formation process of the strings (Weis et al. 1999, hereafter WDC; Weis 2001). WDC identified 5 strings, which are long, 0.1, and narrow, width of 0.002, almost straight filaments, denser than their environment, and located close to the symmetry (major) axis of the Homunculus, but outside the Homunculus. They expand radially, following a Hubble-type law, with velocity increasing from 450 kms-1 in the parts closest to the central star, to 900 kms-1 at their ends away from the central star (WDC; Weis 2001). From their kinematics it seems that the material in the strings was expelled during the Great Eruption of 1850, or just prior or after the eruption. Interestingly, the planetary nebula (PN) NGC 6543 has filaments similar in many properties to those of Car (WDC); they have the same general shape, same relative location, i.e., outside the main nebula near the symmetry (major) axis, and they are also much fainter than the main shell. Kinematically, they expand at much lower velocities 50 kms-1 (Balick & Preston 1987), as expected in PNe, and their distance to the central star of NGC 6543 is about half the distance of the filaments of Car to the center. As discussed later, the proposed model can also explain the formation of the filaments in the PN NGC 6543.
In the present paper we propose a model for the formation of the strings. The explanation for the Hubble-type expansion law of the strings is beyond its scope. We only propose a model for the formation of the long and narrow radial strings, assuming they are formed from material that is already expanding by a Hubble-type law. We propose that each string was formed by the compression of neutral cool gas in an ionization shadow. The surrounding gas was ionized first, and its temperature and pressure became larger by a factor of 10 than the still cool gas in the shadow. Hence the surrounding gas compresses the gas in the shadow, forming a radially long and narrow tail in the shadow, a string. Garcia-Segura et al. (1999) include photoionization in their gasdynamical numerical simulations of PNe evolution, and convincingly show that ionization shadow is capable of forming dense, radial, straight, and narrow filaments. Nor do we deal with the origin of the material, which could have been expelled by Car itself, or was first accreted by a companion and then expelled by the companion (Soker 2001). The proposed model is outlined in Sect. 2. In Sect. 3 we show that it is quite possible that the companion (if it exists) also played a role in the ionization process. The conditions for the formation of the strings from ionization shadows are derived in Sect. 4. A summary of main results is in Sect. 5.
The proposed model for the formation of the strings is that of an ionization shadow behind a dense clump. The ionization front proceeds much slower inside the dense clump, hence the clump shades the region behind it from the ionizing radiation, at least during part of the time until it is completely evaporated (e.g., Lopez-Martin et al. 2001). The shadow stays cool, at , while its surroundings are ionized and heated, hence it is compressed to a higher density (Cantó et al. 1998; Pavlakis et al.2001). An ionization shadow model for the formation of radially aligned narrow structures was discussed in the context of PNe (Soker 1998, 2000). The strings of Car are different in several respects from the situations studied by Soker (1998, 2000). First, the strings in Car are very narrow, hence a steady-state neutral tail behind a dense clump cannot be reached (Cantó et al. 1998, Fig. 4; Pavlakis et al. 2001). Second, the structures studied by Soker were located in a dense region in the PN shell, unlike the strings of Car, which are located in relatively low density regions outside the main shell of the nebula. The very narrow strings of the PN NGC 6543 (WDC) are also located in a (relatively) low density region outside the dense shell of NGC 6543. Third, the material in Car expands with velocities of , much faster than the sound speed, unlike in PNe, where the two speeds are comparable.
Because of these differences, the proposed model does not deal with
a steady-state model, where a neutral shadow exists until the
shadowing clump is ionized; instead it is a dynamic model, where
the strings exist for a relatively short time.
Before describing the model, we emphasize that the relevant mass
loss rates are those along the polar directions
(mass loss rate per unit solid angle) were the strings are found,
and not the average or equatorial mass loss rates.
The scenario has four main phases.
Phase 1 (20 years): during the 20 years of the Great Eruption of 1850 the star lost (DH97). Because of the large optical depth during the eruption, the gas in the wind recombined and cools, down to , after leaving the star and expanding. From the shape of the nebula, it seems that the mass loss rate along the polar directions was lower than average, allowing earlier ionization along these directions at later times.
Phase 2 (50 years): after the eruption, the average mass loss rate probably dropped to something like its present value of (DH97; Corcoran et al. 2001b). The mass loss rate increased for a short period of time during the lesser eruption of 1890, but we ignore this mass loss episode (we have no data on the polar mass loss rate, which is relevant for us). As the dense material from the great eruption expanded, the ionization front moved outward. With ionization of fresh neutral material being disregarded, the ionization front is given by the equality of the photon luminosity to the total recombination rate
The proposed model involves ionization by the central source along and
near the polar directions, as discussed in the previous section.
This section examines the possibility that the companion (if it exists)
plays a role, even a dominant one, in the ionization
Let the mass loss rate from the primary star (
and the expansion velocity during the relevant ionization epoch
respectively, so that the wind's density
in a spherical geometry is
Neglecting ionization of new material, assuming spherical symmetry,
and neglecting material from the Great Eruption, we find that
the ionization front
is given by the equality of the photon
with the total recombination rate.
The recombination rate is given by Eq. (1), with the mass loss rate
and velocity being
is the stellar radius,
Substituting other typical values we obtain the condition for ionization
of the entire nebula
By comparing the conditions for full ionization along the polar directions, Eq. (4) for the primary and Eq. (7) for the secondary, we see that in principle both can be the ionization source, during the phases when the mass loss rate is , the third and fourth phases in the scenario plotted in the previous section. Which of the two ionizing source dominates depends on details such as the departure of mass loss from sphericity and the properties of the wind blown by the companion. In any case, the proposed model for the strings can hold for the cases where no binary companion exists. Two phenomena suggest that the companion indeed plays a role. (1) All the presently known strings are located to the same side of the long axis of the Car nebula (WDC). This departure from axisymmetry hints at a role played by a companion in their formation (Soker 2001). (2) The ionization structure near the central source changes on a time scale of 5.5 years (e.g., Smith et al. 2000), which is taken to be the orbital period of the binary system (Damineli 1996; Damineli et al. 2000).
The proposed model for the formation of the strings is described in
Sect. 2. We now derive the conditions for the model to work.
Most of the basic physics used below can be found, e.g.,
in Cantó et al. (1998).
Let the proton and electron number densities in the strings'
respectively, and let be neutral hydrogen number density in the neutral shadow.
At phase 3 of the model (see Sect. 2), the surrounding gas is
fully ionized and optically thin to ionzing photons.
The recombination of the surrounding gas yields a diffuse ionizing flux
is the size of the
recombining region, which we take to be of the order of the radius r,
is the recombination coefficient to the ground state
The ionization front proceeds into the neutral shadow at a speed of
For the shadow to be compressed we require
is the sound speed of the ionized
Therefore, our condition for the compression of a long dense tail
in the shadow reads
The condition on the mass loss rate may seem very stringent, since the average mass loss rate during the great eruption was much higher, . But noting the following we argue that this requirement is quite reasonable. First, the strings are located near the long axis of the nebula - the polar directions - and outside the dense part of the nebula. In the main nebula the mass loss rate per unit solid angle along the polar directions is lower than near the equatorial plane, and the mass loss rate which formed the regions outside the main nebula - the Homunculus - were much lower. Therefore, it is likely that the mass loss rate that formed the strings was relatively low. Indeed, from Chandra X-ray observations Seward et al. (2001) deduce a density of in the outskirts of Car. Second, WDC show that the PN NGC 6543 contains strings which are similar, in their shape, location, and relative brightness, to those in Car. The maximum mass loss rates from asymptotic giant branch progenitors of PNe are . NGC 6543 does not contain a dense equatorial flow, and the mass loss rate of its progenitor was probably lower, say < . The strings of NGC 6543, which are much fainter than the shell, were formed from a much lower mass loss rate, . We conclude that condition (9) for the formation of the strings of Car by ionization shadow is reasonable.
The immediately surrounding gas enters the shadow while compressing the material in the shadow. The recombining time of this material is , which is longer than any other relevant time scale. However, the neutral material in the shadow is compressed to an order of magnitude of larger densities, and after being ionized, and before re-expanding, the recombination time is comparable to the re-expansion time . The recombination of the dense material of the strings makes their formation process more efficient, since their ionization time by the diffuse ionizing radiation takes somewhat longer.
The typical width of the filaments is (Weis 2001). If the material was compressed to a density 10 times higher, the initial width of the material in the long strings was 3 times larger, i.e. . As discussed above, the closest to the central star parts of the strings were at when the ionization of their surroundings started according to the proposed model. This means that the typical size (diameter if spherical) of the shadowing clumps was . This is a reasonable size for clumps formed by instabilities, e.g., from winds collision (Dwarkadas & Balick 1998). Narrower filaments, if formed, are short lived. First, the shadowing clump is small and it will evaporate in a short time (assuming it is more or less spherical). Second, even if a compressed tail is formed, it will be ionized and re-expand in a short time. Wider strings can in principle be formed. The question is whether dense clumps of such larger sizes exist. Since the formation process of the dense clumps is beyond the scope of the present paper, we will not comment on this further (see Garcia-Segura et al. 1999).
We proposed a model to explain the formation of the long and narrow strings of Car, which are located along the symmetry axis outside the Homunculus. Five such strings were identified by WDC in Carinae, and similar strings exist in the PN NGC 6543 (WDC). The Hubble-type expansion law of the strings was beyond the scope of the present paper, and we assumed that the material in the strings had the Hubble-type expansion law before it was compressed. The model assumes that dense clumps near the symmetry axis form an ionization shadow behind them. The surrounding gas is ionized first, becomes much hotter, and compresses the gas in the shadow. This leads to the formation of a radial, dense, long, and narrow region, i.e., a string (Garcia-Segura 1999). Later the neutral material in the strings is ionized, and becomes brighter. Still later it re-expands, and we predicted that in the string would fade.
We also showed that the companion, if it exists, may play a significant role in the ionization of the strings' surroundings. The condition for the model to work is that the ionization front, due to the diffuse ionizing recombination radiation of the surrounding gas, proceeds into the shadow at a velocity slower than the compression speed, which is about the sound speed. From this we obtain a condition on the density of the strings' surroundings (electron density in Eq. (8)), or on the mass loss rate of the mass loss episode that formed the strings (Eq. (9)). The mass loss rate is much below the average mass loss rate during the Great Eruption of 1850, but we argue that is is quite reasonable along and near the major axis and for material outside the Homunculus.
I thank the referee, A. Raga, for his helpful comments. This research was supported in part by grants from the US-Israel Binational Science Foundation.