7 Some astrophysical aspects of the $\log p/E(V-L)$ diagram

At the moment there is consensus on the changes in the masses of CS shells on the different stages of evolution. For detail discussions see for example:

1. Zuckerman & Beklin ([1993]) (the mass of dust in small grains is a sharply decreasing function of time from pre-MS to MS stars due to the coagulation of grains to planetesimal bodies);
2. Fuente et al. ([1998]) (there is a progressive dispersion of the dense gas associated with HAEBE stars in their evolution to the MS and there is good correlation between the ages of HAEBE stars and the observed dispersal on a large scale of CS material;
3. Coulson et al. ([1998]) (classical TT and HAEBE stars contain more dust ( $10^{-5}-10^{-2} M_{\hbox{$\odot$ }}$ and $10^{-2}-10^{0} M_{\hbox{$\odot$ }}$respectively) than Vega-type systems ( $10^{-7}-10^{-4} M_{\hbox{$\odot$ }}$).

On the other hand the evolutionary changes is CS masses are not so evident on a relatively short time-scale. Mannings & Sargent ([1997]) declared that the masses of the dust disks around Herbig Ae stars have changed little during their 5-10 Myr lifetime. Nata et al. ([1997]) claimed that "no systematic differences in $M_{\rm CSD}$ (CSD - circumstellar dust) between classical HAEBE stars and young stars with Algol-like minima, as well as no statistically significant correlations between $M_{\rm CSD}$ and stellar age is found, and the amplitude of photometric variability appears to be independent of age". They also noted that UXOr phenomena do not characterize a more evolved environment.

Thus we conclude that the changes in the envelope masses are clearly evident for objects which are at the significantly different stages of pre-MS evolution and we should try to consider all the above mentioned suggestions in the discussion below.

The next important point is to make a comparison of the polarization and photometric variability. According to Grady et al. ([1996]) "all of the stars which show photometric variability larger than $1^{\rm m}$ are stars with accreting gas detection and the accretion activity seen toward $\beta$ Pic began during the earlier PMS evolution of the star and its CS disk". Ancker et al. ([1998]) noted that no HAEBE stars with small IR excesses at 3.6 and 12 $\mu$m show strong photometric variability, whereas those with larger excesses show a large spread in $\delta H_{\rm p}$. They have also noted that $\beta$ Pic like systems with usually smaller IR excesses show a range in $H_{\rm p}$ less than $0\mbox{$\,.\!\!\!^{\rm m}$ }1$.

Analysis of polarimetric and photometric characteristics of early-type stars from our sample indicates that a few different groups of objects may be distinguished.

1. Objects with large, non-variable (on a short time scale - days) polarization and large near IR excesses $E(V-L)>5^{\rm m}$. These objects mainly show a high level of polarization (p>5%) over long periods. Large photometric and polarimetric variability in these objects may be observed but also on a large time scale;
2. Objects with intermediate near IR excesses $5^{\rm m}>E(V-L)>3^{\rm m}$ which exhibit large polarimetric variability on a short time scale (days) ( $\Delta p>3$%) and show essentially small polarization over long periods ($p\approx1$%). Variations in photometry are also significant (up to 2 $^{\rm m}-3^{\rm m}$);
3. Objects with small near IR excesses $3^{\rm m}>E(V-L)>1^{\rm m}$ and non-variable polarization ($p\approx1$% and $\Delta p<1$%). Photometric variability for these stars are rather small and does not exceed $0\mbox{$\,.\!\!\!^{\rm m}$ }5$;
4. Objects with small near IR excesses $E(V-L)<1^{\rm m}$, small polarization (p<0.5%) and small photometric variability $\Delta m\ll 1^{\rm m}$, or even non-variable in photometry and polarization.

We suppose that this differentiation is caused by the changes in structure and geometry of dust circumstellar shells around the stars and these changes are caused by evolution of the dust circumstellar environment.

It is interesting that some HAEBE stars with Algol-like minima of brightness and low values of $v\sin{i}$ show large photometric and polarimetric variations. If the value of $v\sin{i}$ in fact reflects the inclination of CS dust disks, the opening angle of these disks should not be small to explain the observed eclipses. For UXOrs' disks the opening angle was estimated to be of the order 35$^\circ$(see Nata et al. [1999]). In the case of the relatively large inclination angle the dust inhomogeneities which are responsible for the eclipse should have a size of the order of a stellar surface. However, these sizes of dust inhomogeneities are much less than those we can expect for younger objects (taking into account the time scale of their photometric and polarimetric variations). Conceivably, the formation of compact dust inhomogeneities in CS environments must reflect a definite stage of CS shell evolution. Ancker et al. ([1998]) noted that the patchy dust clouds are only present during the pre-MS evolution of a star. They either vanish or become more homogeneous when a star has reached the ZAMS. On the other hand, for extreme young IR sources (such as L1551 IRS5: Men'shchikov & Henning [1997], HL Tau: Men'shchikov et al. [1999], GSS 30: Chrysostomou et al. [1997] or R Mon: Magnier et al. [1999]) the opening angle of non-spherical dust envelopes was estimated to be of the order >50$^\circ$ or even $\approx 90$$^\circ$ whereas for $\beta$ Pic the opening angle was estimated to be 10$^\circ$ (Artymowicz et al. [1989]) or even 2$^\circ$ (Chini et al. [1991]).

To explain the observational behaviour in young stars we can suggest a two-component structure for CS dust shells: a large optically thin but geometrically thick disk-like envelope + a narrow optically thick (sometimes accretion) disk. Another possibility is to assume that the concentration of the dust particles significantly increases to the midplane of the disk-like envelope with the presence of optically thick dust condensations preferably in the midplane instead of the homogeneous and optically thick accretion disks. These two assumptions in principle may characterize different stages of CS shell evolution and/or reflect the differences in the CS shell configuration in TT and HAEBE stars. There is much evidence that the second case is more acceptable for classical HAEBE stars (see Discussion in Mitskevich [1995]).

The important conclusion which emerge from the above are as follows:

For the stars with geometrically thick dust disk-like shells which screen most of the nonpolarized stellar radiation we observe mainly scattered radiation from their nonspherical CS envelopes (i.e. high level of observed polarization). These geometrically thick disks are homogeneous i.e. not many clouds or holes exist in their circumstellar envelopes, or these clouds are very large (like that for R Mon, V 376 Cas, MWC349 etc. see for example Yudin [1996]; Matsumura et al. [1999]). Therefore large polarimetric and photometric variations for these objects are apparent in a time scale of tens of days and is not obvious for shorter periods (for a similar discussion see Matsumura et al. [1999] [for R Mon]). For UXOrs the disks are still relatively geometrically thick but their width is less than those for younger objects. These disks (or nonspherical envelopes) are rather optically thin but contain numerous optically thick condensations. Besides, the dust cloud size is comparable to the stellar radius. For these objects significant variations in polarization and photometry occur over a few days but over longer periods they show a low level of polarization and a small amplitude photometric variability. At the later stage of evolution the young stars exhibit geometrically thin disks and dust inhomogeneities with the size significantly less than the stellar surface. These disks and dust condensations cannot screen stellar radiation much so the observed polarization is small (even if the small-amplitude Algol-like minima are observed, see Vieira et al. [1999] for HD 100546). On the other hand the CS disks around Vega, Fomalhaut and $\beta$ Pic are still extended but geometrically and optically thin and homogeneous therefore no significant polarization occurs and no significant light variation exists in these objects (see for example Lecavelier des Etangs et al. [1997]).

It can be said with confidence that possible evolutionary changes in the geometry of CS disks are in good agreement with observational features, at least in early-type young stars.

The evolution of disks from optically and geometrically thick to optically and geometrically thin has been also suggested for TT stars by many authors (see for example Strom et al. [1989]).

First we compare the polarization values for TT stars with "active" and "passive" CS disks. In terms of the classification of Miyake & Nakagama ([1995]) these disks can be distinguished by different accretion rate $\dot{M}\geq 10^{-8}M_{\hbox{$\odot$ }}~{\rm yr}^{-1}$ and $\dot{M}\leq 10^{-9}M_{\hbox{$\odot$ }}~{\rm yr}^{-1}$respectively. Miyake & Nakagama ([1995]) have discussed the possible evolutionary sequence from "active" to "passive" class I disks. Using the available data on the polarimetry of TT stars, it is possible to compare the distribution of the polarization degree and near IR excesses for the objects with different kinds of CS disks.

In spite of the low statistics we may note the changes in the polarization degree from $\approx$2.5% for "active disks" through $\approx$1.1% for class I "passive" disks to $\approx$0.5% for class IV and II disks. Slightly better statistics for near IR excesses show the same decrease in E(V-L) respectively: "active" disks - $E(V-L)\approx2\mbox{$\,.\!\!\!^{\rm m}$ }15$, class I - $E(V-L)\approx1\mbox{$\,.\!\!\!^{\rm m}$ }60$, class IV - $E(V-L)\approx1\mbox{$\,.\!\!\!^{\rm m}$ }30$, class II - $E(V-L)\approx1\mbox{$\,.\!\!\!^{\rm m}$ }15$ and class III - $E(V-L)\approx0\mbox{$\,.\!\!\!^{\rm m}$ }2$.

The main conclusion from the above is the following: most TT stars which according to Miyake & Nakagama ([1995]), are accompanied by "active" CS disks, show significantly larger polarization and near IR excesses and possibly average polarization and IR excesses decrease with the disk's evolution.

At the latest stage of a TT phase (so-called weak-line TT stars) the disks become optically thin (low polarization and low near IR excesses), in good agreement with the results of Bastien et al. ([1996]) who have noted that "weak TT stars exhibit a small polarization averaging 0.7% and with no p in excess of 2.4% while classical TT stars exhibit an average polarization of 1.6% with a high polarization tail".