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Astron. Astrophys. 355, 922-928 (2000)

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2. FIR-radio correlation of WR galaxies

WR galaxies are extragalactic sources that exhibit broad emission lines characteristic of WR stars in their spectra (Conti 1991). Their typical burst ages are [FORMULA]-8 Myr. The 50 WR galaxies that show a good FIR-radio correlation, as shown in Fig. 1a, have detected flux at 1.4 GHz in NVSS Catalog (Condon et al. 1998) and 60[FORMULA] in IRAS (Moshir et al. 1992) among 139 known sources (Schaerer et al. 1999). Such a correlation of WR galaxies is apparently nonlinear, with a regression coefficient of about 1.20, as obtained before for other samples of galaxies (e.g. Fitt et al. 1988; Cox et al. 1988).

[FIGURE] Fig. 1. a FIR-radio correlation of WR galaxies, denoted by open triangles. Model predictions are shown by lines: solid line for warm dust component at the burst age of 6 Myr; dashed lines for models containing both warm and cool dust components, see the text for details.b Same correlation as Fig. 1a, added several sources at the burst age of 107 - 108 yr. Model predictions for the age of 2[FORMULA]107 yr are indicated by lines: dotted line for dust-to-gas ratio of 1/100; dashed line for dust-to-gas ratio of 1/20; dot-dashed line for containing shock-heating phase but with same parameters as those for dashed line, see text for further details.

This correlation can be understood in the framework of starburst phenomenon (Moorwood 1996; Lisenfeld et al. 1996). For simplicity, we take the stars/dust geometry to be close to a star-free shell of dust surrounding a central dust-free sphere of stars (Mas-Hesse & Kunth 1999). In this scenario, the radiation from the nuclear starburst (the optical, ionizing and non-ionizing photons) heats the dust grains, and the UV photons emitted from the nuclear massive stars photoionize the gas.

The radio flux at 1.4 GHz consists of thermal bremsstrahlung emission from photoionized gas and synchrotron radiation from supernova remnants. The luminosities of the two radiation mechanisms are respectively given by Rubin (1968)


where [FORMULA] is electron temperature in units of 104K and [FORMULA] ionizing photons per second, and by Colina & Pérez-Olea (1992)


where [FORMULA] is the Type II supernova rate.

The FIR radiation at 60µm is assumed to be composed of two parts: the warm dust component caused by the same starburst event, and the cool dust component outside the starburst region heated by the general interstellar radiation. Xu et al. (1994) modelled the contribution of cool and warm components in FIR - radio correlation for late-type galaxies Several authors have virtually tried correcting or linearizing the FIR-radio correlation (Condon 1992; also see Fitt et al. 1988; Devereux & Eales 1989). The luminosity of the FIR radiation is described by


where [FORMULA] and [FORMULA] are the warm and cool dust temperatures, [FORMULA] and [FORMULA] the total number of warm and cool dust grains, a is the average radius of dust grains, [FORMULA] the absorption efficiency of dust grains, and [FORMULA] the Planck function. We adopt the "astronomical silicate" dust model (Draine & Lee 1984), which is most likely suitable to starburst galaxies (Mas-Hesse & Kunth 1999).

Assuming a "steady-state" case for the dust grains, the dust temperatures can be derived from the equilibrium between dust absorption and dust emission,


where [FORMULA] is the energy density of a diluted radiation field that heats the dust, which is satisfied with


where W is the dilution factor, and [FORMULA] the equivalent effective temperature for the radiation field generated by starburst activities. Using the [FORMULA] dependence for [FORMULA], one can yield the dust temperature from equa. (4): [FORMULA] (Spitzer 1978). The FIR luminosity at 60µm can be obtained from equa. (3), scaling the value of [FORMULA] to fit the Draine & Lee (1984) model at [FORMULA]: [[FORMULA]2.5.

At any given burst age, the evolutionary synthesis model, GISSEL95 (Bruzual & Charlot 1996), is used to provide the relevant quantities such as [FORMULA], [FORMULA], and the bolometric corrections for deriving the effective temperatures. Considering the discussion by Mas Hesse & Kunth (1999), we have assumed 50% of [FORMULA] are absorbed by dust.

We have estimated the possible values of the dilution factor in various ways and adopt their average, 10-14, which is compatible with the usual interstellar value (Spitzer 1978). The radiation transfer is not taken into account. A dust-to-gas mass ratio [FORMULA] is assumed. We also assume that the gas mass is comparable to the star mass in the starburst region ([FORMULA]) (namely the gas-to-star mass ratio is roughly unity). The total grain number is interpreted as [FORMULA] where the density of the `astronomical silicate' is adopted as [FORMULA] (Draine & Lee 1984).

For calculating the cool dust temperature, we assume that the cool dust component may be heated by the general interstellar radiation field that arises from a past starburst event with a typical burst age [FORMULA] 1 Gyr. The mass of the cool component is a free parameter, and we try fixing its value, 106 [FORMULA] or [FORMULA], for any [FORMULA]. It means that the contribution from the cool component is relatively significant for small burst strength (small [FORMULA]), and relatively unimportant for ultraluminous infrared galaxies (ULIGs; large [FORMULA]). Generally, we have [FORMULA] K, similar to the assuming cool dust temperature by Fitt et al. (1988).

To perform the calculations, we take [FORMULA] as an independent variable, which is in the range of [FORMULA]-[FORMULA]. The upper end of [FORMULA] corresponds to the case of ULIGs (e.g. Genzel et al. 1998). The stronger the starburst (i.e., the larger [FORMULA]), the higher the FIR and radio luminosities. With various adopted parameters (burst ages, dust-to-gas ratio, etc.), we obtain linear FIR-radio correlations if taking only the warm dust component into consideration, or a nonlinear correlations if both the warm and cool dust components. The model curves are plotted in Fig. 1a, the model parameters are listed in Table 1.


Table 1. Model parameters

The solid line I in Fig. 1a represents the linear part of our model prediction at the burst age of 6 Myr, in which the contribution of cool dust emission is neglected and thermal (bremsstrahlung) emission is dominant at 1.4 GHz. The dashed lines in Fig. 1a illustrate the lower-right envelopes for models, in which the contribution of cool dust emission is taken into account. For lines IIa and IIb, the cool dust mass is taken as [FORMULA] and [FORMULA] at the age of 3 Myr, respectively, and for line IIc, the cool dust mass is [FORMULA] at the age of 6 Myr. As expected, counting the cool dust emission reproduces the nonlinear trend in the correlation lines. It is quite reasonable to see in Fig. 1a that the cool dust component makes significant contribution in the case of small burst strength, while it is negligible compared with warm component for large burst strength. Satisfactorily, the majority of WR galaxies are located in a "passage" escorted by the upper and lower envelopes in the diagram. Reasonably, this passage may be considered to be typical of the positions of the SB-dominated galaxies.

In Fig. 1b, we have added two prototypical starburst galaxies, M 82 and NGC 253, corresponding to a burst age of 107-108 yr. The dotted line Ia in Fig. 1b indicates our model prediction (with a dust-to-gas ratio of 1/100) at the burst age of 2[FORMULA]107 yr, which represents the upper end of age for the supernova, set by GISSEL95. The non-thermal (synchrotron) radiation dominates at 1.4 GHz in this case. Considering the enrichment of the dust grains by supernova explosions at this age, the dust-to-gas ratio can increase by several times, up to an order of magnitude (Hirashita 1999), so it would be reasonable to replace the dust-to-gas ratio of 1/100 with 1/20. As a result, the model curve will shift to a position indicated by the dashed line Ib in Fig. 1b.

In order to fit the galaxies that exhibit ongoing star formation, such as a transition object NGC 5194 (Heckman 1980; Larkin et al. 1998), we tried to add a shock wave (that may be related with the supernova explosions and/or outflowing winds from starburst) as additional mechanism for heating the dust, following Dwek (1986) and Contini et al. (1998). The model curve containing a shock-heating phase is represented by the dot-dashed line Is in Fig. 1b, which is below the lower border of the passage mentioned above. Here, we have adopted a shock velocity [FORMULA], a shock covering fraction 1/10, and a dust-to-gas ratio 1/20 at the age of [FORMULA] yr. It is worth noting that a strong near-infrared [Fe II ] line has been observed in NGC 5194, and the shock excitation in supernova remnants is probably the mechanism responsible for this line (Larkin et al. 1998). This excitation mechanism may be consistent with our consideration of shock-heating of dust in this galaxy, with [FORMULA] in order [FORMULA].

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Online publication: March 21, 2000