1 Introduction

Dust grains absorb stellar ultraviolet-optical light and emit far-infrared (FIR) light, thereby affecting the spectral energy distributions of galaxies (e.g., Takagi et al. 1999). Since the spectral energy distribution is frequently analysed to infer the star formation history (SFH) that provides us with a key to understand the evolutionary history of galaxies, the research on the origin of the interstellar dust is important to this issue. A key quantity concerning grains is the dust-to-gas mass ratio, $\cal{D}$. Oort & van de Hulst (1946) have observationally shown a strong correlation between the densities of gas and dust. This indicates that dust traces dense environments, which should be rich in heavy elements. Thus, it is worth examining the evolution of $\cal{D}$ in the context of the chemical evolution of galaxies.

The condensation of heavy elements is an important process for the formation of grains. One of the environments where condensation takes place is the atmosphere of a cool giant star (Hoyle & Wickramasinghe 1963). High-dispersion spectroscopic observation of C₂ in post AGB stars may indicate the condensation process on C₂ as a dust kernel (Crawford & Barlow 2000; Kameswara Rao & Lambert 2000). Another environment for condensation is a supernova (SN). Dwek & Scalo (1980) have shown that SNe can be the dominant source of dust grains. This is partly because of a rich metal content in SNe. Indeed, a significant amount of dust is observed within hot SN remnants (Dwek et al. 1983; Moseley et al. 1989; Kozasa et al. 1989) and theoretical work by Todini & Ferrara (2001) has explained some principal features of dust formation in SN 1987A. Hirashita (1999a) has shown that observational dust amounts suggest that $\sim$$10\%$ (the fraction in mass) of the heavy elements ejected from stars condense into dust grains. Since his model prediction reproduces the observed trend between dust-to-gas ratio and metallicity of dwarf galaxies, we adopt this fraction for dust condensation.

The processes of dust destruction should also be considered. As shown in Dwek & Scalo (1980), dust grains are not only made from heavy elements but also destroyed in SN shocks (see also McKee 1989; Jones et al. 1996) in a cycle of the birth and death of stars. In short, $\cal{D}$ of a galaxy reflects its SFH via the regulation of dust formation and destruction. To investigate what determines the value of $\cal{D}$, investigation of a star-forming galaxy is the most interesting since SNe are expected to affect most largely their dust amount.

One of the observational features which give us a key to understand the regulation of $\cal{D}$ is the variance of $\cal{D}$ itself (e.g., Lisenfeld & Ferrara 1998, hereafter LF98). In this paper we examine the variance of $\cal{D}$ among galaxies. According to LF98, there is a large variance in $\cal{D}$ for a sample of blue compact dwarf galaxies (BCDs). By definition, galaxies categorised as BCD more or less show active star-forming activity. Therefore, dust formation and destruction are expected to occur in BCDs. Since grains are composed of heavy elements, application of the theory of galactic chemical evolution is useful and interesting. Then, we particularly consider the variance of $\cal{D}$ in BCDs by using the chemical evolution model developed by LF98 and Hirashita (1999b, hereafter H99).

LF98 applied a chemical evolution model to explain $\cal{D}$ of dwarf galaxies including BCDs. They have suggested that if the dust-to-gas ratio in outflow (galactic wind) is different from that in the interstellar medium (ISM), the large dispersion of $\cal{D}$ of dwarf galaxies can be explained. In this scenario, a significant outflow of gas is indispensable to explain the observed variance of dust-to-gas ratio of BCDs. However, is the variance of $\cal{D}$ determined simply by mass outflow? In this paper, after further investigation in the framework of LF98, we answer this question and point out that other factors are also important to explain the value and variance of $\cal{D}$.

Indeed, a recent analysis by Tajiri & Kamaya (2002) has suggested that outflow is not so efficient for BCDs. They estimated the current momentum supply from SNe by using H$\alpha$ luminosity, and concluded that the supplied momentum is not sufficient to blow away the H I envelopes surrounding star-forming regions and that BCDs do not currently suffer significant mass loss. Legrand et al. (2001) also suggested that low density halos around BCDs can be an obstacle for the ISM to escape from the galaxies themselves. Thus, it is worth examining mechanisms other than mass outflow. Since Tajiri & Kamaya (2002) adopted a sample in Sage et al. (1992), we also use the sample. Moreover, the sample in LF98 is also included because this paper is an extended study of LF98.

This paper is organised as follows. First, in Sect. 2 we explain the model that describes the evolution of dust content in a galaxy. In Sect. 3, we consider dust destruction, which is the most important process in this paper. Then, in Sect. 4, model predictions are presented in comparison with observations. In Sect. 5, we discuss the results and propose a physical mechanism that can explain the observations. Finally, we summarise the contents of this paper.