5 Discussion

  
5.1 Wind-luminosity thermalization

An important issue to consider is the thermalization efficiency of the wind kinetic energy. Even assuming that our estimates of the wind luminosities in NGC 2363 are highly accurate, the derived $t^2_{\rm kin}$ values should be corrected downward to take into account the fraction of the energy injected to the ISM which is eventually thermalized.

1-D hydrodynamical models of the bubble around OB associations indicate that such fraction is about 80% (Plüschke 2001; Plüschke et al., in preparation). An estimate of the thermalization efficiency in the case of NGC 2363 can be made by comparing the total kinetic energy injected into the region since the beginning of the starburst to the observed kinetic energy. Roy et al. (1991) observed in NGC 2363 a bubble with a 200 pc diameter, expanding with a velocity of 45 km s^-1, and calculated that the total kinetic energy involved is $E_{\rm kin}^{\rm obs}\sim 2 \times 10^{52}$ ergs, in agreement with the estimate made by Luridiana et al. (1999). Roy et al. (1992) found a high-velocity component in the gas, with a kinetic energy of $E_{\rm kin}^{\rm obs}\sim 10^{53}$ ergs. González-Delgado et al. (1994) confirmed the presence of this high-velocity gas, and estimated a kinetic energy of $E_{\rm kin}^{\rm obs}\sim 3 \times 10^{52}$ ergs.

These figures should be compared to the estimated values of the integrated wind kinetic energy, which are listed in Table 2 for the three considered cases. If we add the kinetic energy of the low-velocity bubble observed by Roy et al. (1991) to that of the high-velocity gas observed by González-Delgado et al. (1994), we find that the efficiency of the thermalization of wind kinetic energy is close to 0, lowering further the computed $t^2_{\rm kin}$ values.

An independent estimate of the efficiency of the thermalization of the wind energy can be done by considering the X-ray component in the spectrum of NGC 2363 detected by Stevens & Strickland (1998) with ROSAT; they found $L_x \gtrsim 6.6 \times 10^{37}$ erg s^-1 assuming a distance of 3.44 Mpc to the object, which becomes $L_x \gtrsim 7.3\times 10^{37}$ erg s^-1 rescaling to the distance of 3.8 Mpc assumed by Luridiana et al. (1999). Assuming that the origin of the X-ray component is the reprocessing of the wind kinetic energy, we can infer typical values for the thermalization efficiency of the order $\gtrsim$10%.

5.2 Pure photoionization component

The value of $t^2_{\rm str}$ could be higher if the ionizing spectrum turned out to be harder than supposed, as implied by the X-ray component detected by Stevens & Strickland (1998); in this case, the need for an extra-heating source to be added to the photoionization model would be proportionally smaller. To investigate this possibility, we computed a CLOUDY model with the analytical SED of the CMHK code, modified to account for the transformation of 20% of the kinetic energy into X-rays (Cerviño et al., in preparation). This experimental model is energetically equivalent to a hot-spot model in which the extra heating is provided by the wind kinetic luminosity thermalized with a 20% efficiency. Indeed, we found that for this model $t^2_{\rm str}=0.009$, i.e. the same as the Luridiana et al. (1999) to within 0.001, confirming that the wind kinetic luminosity is energetically insufficient to account for the observed temperature fluctuations.

5.3 Influence of stellar rotation

As it has been pointed out by Meynet & Maeder (2000), rotation dramatically changes the properties of massive-star models. In particular, it increases the mechanical energy released to the ISM (see, e.g., Maeder & Meynet 2001). Additionally, the winds of rotating massive stars can be highly non-spherical, with strong polar or equatorial structures, depending on the effective temperature and angular velocity of the star (Maeder & Desjacques 2001).

Rotation makes it possible to explain in several cases the observed features of individual stars, but, unfortunately, the evaluation of its effects on the integrated spectrum of star forming regions is not feasible yet. First, the distribution of angular velocities of the stars in the cluster should be known. Second, the distribution of inclination angles should also be known, since the emitted luminosity depends on the inclination angle. Third, it would be necessary to establish new homology relations in order to obtain the isochrones needed to compute the emission spectrum at any given time.

Thus, we can only predict qualitatively that rotating stars certainly produce a turbulent interstellar medium, possibly with strong density and temperature inhomogeneities, due to both the increased wind energy and the anisotropy of their winds. From the point of view of our study, the increased energy injected into the medium, would translate into a correspondingly higher $\Gamma ^{\rm kin}_{\rm heat}$ value, and the turbulence created in the ISM would possibly increase the thermalization efficiency of such energy, in such a way that the "actual'' $\Gamma _{\rm heat}$ of the region would approach its upper limit $\Gamma ^{\rm kin}_{\rm heat}$ (see also Sect. 5.1).

Thus, at a qualitative level, the effect of stellar tracks with rotation on our temperature-fluctuation model would be to increase the temperature fluctuation amplitude theoretically achievable through energy injection by stellar winds, as compared to non-rotating models.

5.4 Distance to NGC 2366

The distance to NGC 2366 plays several roles in our analysis. First, the average properties of a photoionization model constrained by observational data depend on the assumed distance in complex ways. Second, a smaller distance implies a smaller region, hence a relatively larger statistical dispersion. Third, the hot-spot model is calibrated to a specific model, so that, should the photoionization model change, the hot-spot model would also change.

In our analysis, based on the photoionization model by Luridiana et al. (1999), we assumed for the distance the value 3.8 Mpc determined by Sandage & Tammann (1976). However, there are a number of more recent distance determinations indicating smaller distances: Tikhonov et al. (1991) derived a distance of 3.4 Mpc to NGC 2366 through photographic photometry of its brightest stars; Aparicio et al. (1995) obtained the value of 2.9 Mpc with CCD photometry of its brightest stars; Tolstoy et al. (1995) determined a distance of 3.44 Mpc from Cepheid light curves and colors; Jurcevic (1998) obtained the value 3.73 Mpc, with an associated error of 0.04 dex, from a study of the period-luminosity relationship of the red supergiant variables in NGC 2366.

To illustrate how our conclusions would change under a different assumption on the distance, we consider a value of 3.4 Mpc, i.e. $\sim$10% less than the assumed distance. Given the observed H$\beta$ intensity, the smaller distance yields a 20% smaller rate of ionizing photons, Q(H⁰). Since in this case the region turns out to be smaller both in linear and in angular dimensions, more input parameters should be changed, in order to fulfill the observational constraint on the observed size of the nebula, even if the remaining constraints, such as the relevant line ratios, change negligibly. Though it is beyond the scope of this paper to calculate a full revised photoionization model, we can expect that a satisfactory fit could be obtained by means of relatively small adjustments in the density structure of the nebula surrounding the ionizing cluster, with the model stellar population rescaled to a total mass $M'_{\rm tot}=0.80 \times M_{\rm tot}$, and the other stellar parameters (e.g., SFR, IMF, etc.) left unchanged. These changes would translate into a $\Gamma ^{\rm kin}_{\rm heat}$smaller by 20%, with a statistical dispersion proportionally larger, due to the larger relative weight of the statistical fluctuations in the cluster.

The hot-spot model should also be accordingly modified, to take into account the properties of the revised model. However, we don't expect it too change too much, since the ionization parameter of the revised model would be essentially the same as the one of the old model. Summarizing, we estimate that a downward revision of the assumed distance would not significantly change our conclusions.

5.5 Temperature-fluctuation profile

In the interpretation of our results, it is important to take into account that they were obtained for a rather specific temperature-fluctuation pattern. As stated by Binette & Luridiana (2000), the model returns the correct results for fluctuations resembling those depicted in their Fig. 1, but for radically different patterns of hot spots (different in frequency, width, and/or amplitudes) the model would only provide a first order estimate of the relationship between t² and $\Gamma _{\rm heat}$; Binette & Luridiana (2000) estimate that the total uncertainty on $\Gamma _{\rm heat}$resulting from this approximation is less than 20%.