5 Relationship between the polarimetric and photometric data

5.1 Polarization and optical photometry

Only four stars in our sample show a clear correlation between brightness and polarimetry. These are V350 Ori (probably a HAEBE star with Algol-like minima), VY Mon (a HAEBE star or FU Ori type star), the peculiar star WRA 15-535 and the TTS RY Lup; in these cases the polarization was larger when the star was faint. For other stars which show polarimetric variability these variations are not accompanied by changes in brightness. However if the dominant source of photometric variability in HAEBE stars with Algol-like minima is variable extinction (i.e. obscuration by proto-planetary clouds) then the requirement that such systems are only observed with their discs nearly edge-on for all such systems is highly unlikely. Note however that some objects were observed in our survey only at high (or low) levels of brightness. However we know that the photometric amplitudes for many of these stars are large (see Tables 1 and 2). Thus in order to draw any conclusions on the correlation between the photometry and polarization additional observations at a different light curve levels are needed.

5.2 Polarization and near IR excesses

As mentioned in Sect. 1 the correlation between polarization and IR excess was established for young TTS by Bastien (1982, 1985) and for HAEBE and TTS by Yudin (1988) in the sense that stars with a large IR excess also have large polarization. This fact suggests that the IR excess in young stars, as well as the polarization, are produced by the same agent. While it is now well established that dust grains are responsible for IR excess longward of the L (3.5 $\mu$m) band, the observed polarization in young stars in many cases is also connected with scattering on the dust grains. Note that the data obtained here indicate that circular polarization was not statistically detected in most of the early type stars in our survey. Therefore we can refute the suggestion that multiple scattering, or scattering on aligned nonspherical dust grains, is a significant process in the CS shells of at least some of the investigated stars having large detected polarization. Furthermore, in most of the stars with large polarization, it is likely that the contribution of interstellar polarization is large.

To explain large values of polarization by the presence of dust envelopes in terms of single scattering we must suppose that the geometrical distribution of grains is not spherical, i.e. the dust is concentrated mostly in CS discs. But in this case large values of polarization will be observed only if the dust discs are have large inclination to the line of sight. While we cannot assert that all the observed stars have dust discs which are oriented edge-on there will be some stars with small polarization and large IR excesses but not vice versa. The latter case (large polarization and a small IR excess) may occur only if the contribution of interstellar polarization is large, or an additional mechanism of polarization is at work. For example, as was shown by Yudin (1988), classical Be stars do not fit the relation on the $\log~p - (V-L)_{*}$ diagram obtained for young stars and in general they have small IR excess due to the dust (in the L band) but show polarization at the 1% - 2% level. This leads to the possibility of discriminating between stars that are undergoing PMS evolution and stars at later stages of evolution.

It is well known that the linear polarization of Be stars has been interpreted in terms of electron scattering by free CS electrons whose distribution is not spherically symmetrical (Waters & Marlborough 1992). With such a model it has been shown that it is not easy to produce a degree of optical polarization above $\approx$1.5%, which is indeed is about the maximum degree of polarization observed in Be stars (see McLean & Brown 1978; Poeckert et al. 1979). Waters & Marlborough (1992) have pointed out that, for a model in which the optical depth for electron scattering is large, multiple scattering will tend to reduce the degree of observed polarization. Note however that there is no evidence for circular polarization in most of the stars in our survey and that there is therefore no evidence for multiple scattering in their CS shells. Some Be stars in the relation derived by Yudin (1988) and which show polarization above the 1.5% limit probably have an additional component of polarization, such as scattering by grains, or interstellar polarization. In addition Waters & Marlborough (1992) have claimed that the bulk of the linear polarization is produced in layers within 2 or 3 stellar radii,which can produce polarimetric variability on a time-scale of few minutes due to illumination effects. This conclusion is in good agreement with the results obtained here.

Combination of near IR continuum observations and optical linear and circular polarization may provide constrains on (i) the geometrical distribution of scatterers, (ii) selection of stars at different stages of evolution and (iii) the different mechanisms of polarization. This conclusion can be applied to HAEBE and Be stars, but we can not discriminate between HAEBE and B[e] stars by using this method, as near IR excesses in both classes of stars are explained by the presence of hot dust. Moreover, according to Zickgraf & Schulte-Ladbeck (1989) and Magalhaes (1992) in some cases dust is the main polarizing agent in B[e] stars envelopes. Nevertheless, as was shown above, such a separation can be made by using the IRAS two-colour diagram.

To obtain additional information on the possible classification of programme stars, and to estimate roughly the inclination of the dust discs around them, we collect available data on the IR photometry in the L band (see Tables 1 and  2). Note that Yudin (1988) has found a significant (k=0.94) correlation between polarization in the R band and the optical-IR colour excess (V-L)_*, where $(V-L)_{*}=(V-L)_{\rm obs}-(V-L)_{0}-(A_{ V}-A_{ L})$; here (V-L)₀ is the normal colour index corresponding to the spectral class of the star, and (A _V and A _L) are the interstellar extinction in the respective photometric bands. It is easy to show that (V-L)_* determines the relative contribution of the CS shell to the IR emission in comparison with the stellar photosphere in the given IR photometric band (Yudin 1988). In our study we have obtained numerous polarimetric data, mainly in the V band. Since the values of polarization in the V and R bands are often strongly correlated (see for example Bastien (1985), and since our data also suggest a strong correlation between p _V and $p_{ R_{\rm c}}$, we can use the polarimetric data obtained in the V band, which are more numerous. More significant is the fact that we have estimates of interstellar extinction for only 19 stars in our survey, whereas the IR data are available for 36 of the programme stars. Note however that a significant correlation of polarization with $(V-L)_{\rm obs} - (V-L)_{0}$, or even with $(V-L)_{\rm obs}$, was also established for young stars, but the correlation coefficient is smaller ($k\approx0.7$). Therefore we construct for the objects from our survey two diagrams, namely $\log p_{ V} - (V-L)_{*}$ and $\log~p - \{(V-L)_{\rm obs} - (V-L)_{0}\}$ (see Figs. 26, 27).

  

Figure 26: Polarization-photometry diagram for the objects from our survey

  

Figure 27: Polarization-near IR excess diagram for the objects from our survey

The following conclusions can be drawn from the analysis of the location of the programme stars on the above mentioned diagrams.

1.

For most objects there is a tendency to show large polarization with large near IR excess.

2.

Some stars, such as He3-672, EW CMa, HD37411, He3-331, HD37357, MWC158, MWC148, AS160, LkH$\alpha$18, do not fall on the dependence obtained for young stars, and some of them are located in the field occupied by Be stars. Thus it is likely that they are not young objects, or are at a stage of evolution close to the main sequence, in good agreement with our conclusion based on an analysis of the IRAS two-colour diagram (see above).

3.

The stars V350 Ori, VV Ser, S CrA, V599 Ori, RY Ori, NX Pup, He 3-365, WRA 15-535 all fall approximately on the dependence derived for young stars.

4.

The locus of VY Mon on the diagram due to the variability of polarization and visual flux takes place parallel to, but above, the dependence relation for young stars, suggesting the presence of a large component of interstellar polarization ($\approx$ 5%).

5.

The locus of V350 Ori and WRA 15-535 on the diagram takes place in the strip occupied by the majority of young stars.

6.

The position of He3-597, MWC137, MWC272, MWC863, together with the presence of a large but nonvariable component of polarization, also suggests a significant component of interstellar polarization.

7.

The position of RCW 34 is peculiar. This O-type star shows a small near IR excess, together with large polarization; however its far IR excess is large. Taking into account data obtained by Jain et al. (1995) we can deduce the presence of an interstellar component of polarization at the level of $\approx3$%, but even in this case the intrinsic polarization would exceed 2.5%.

As noted in Sect. 3, five stars in our sample which are binary (ZCMa, NXPup, MWC 863, KK Oph and SCrA) show the PA of observed polarization close to the PA between the components. If the components in the above mentioned systems are physically connected and at least one of the components is surrounded by a CS disc then such a disc must be oriented in the direction between the components. In all the cases mentioned above the observed polarization is parallel (or close) to the disc plane. However, it is well known that for optically thin discs the polarization has a direction perpendicular to the disc plane (see for example Whitney & Hartmann 1992). According to Whitney & Hartmann (1993) "for optically thick envelopes, with rotation or wind-driven holes the net system polarization is parallel to the disc plane since more singly scattered light escapes from the polar regions". We conclude that the observed behavior (at least for KKOph and MWC863) can be explained in terms of the model discussed by Whitney & Hartmann (1993). On the other hand for the stars V350 Ori, He 3-672, HD 132947 and RY Lup the data on the U-Q diagram are concentrated along a line that is also evidence of non-spherically symmetrical envelopes.