3 Polarization and near IR excess

As was mentioned above the investigation of p and IR colour indices was fulfilled by Bastien ([1985]) for 85 TT stars, however the correlation coefficients for "p-colour indices" dependencies were calculated by him only for about 50 of the stars from his sample. Further, Yudin ([1988]) studied similar correlations for a sample of about 70 TT and HAEBE stars and calculated the correlation coefficients for his dependencies for about 50 stars too. In spite of the fact that Yudin ([1988]) has studied not only TT but also HAEBE stars the same number of used stars was justified due to a limited (at that time) data on interstellar absorption and IR photometry. Here we should try to construct a similar $\log p/E(V-L)$ diagram adding all new available data which have been collected since 1988.

3.1 Sample of stars

All collected data are presented in the Appendices 1-5 for HAEBE stars: [1], Vega-type and post HAEBE stars: [2], HAEBE and TT stars with synchronous photometric and polarimetric measurements: [3], TT stars: [4], and young solar-type stars: [5]. The columns in these Tables give the star's name, the weighted average value of p(preferable in V, R bands for all published data) in percent, the full amplitude of polarimetric variability and the references, the spectral class of a star and the references, the average value of the observed colour index $(V-L)_{\rm obs}$ in magnitudes and the references, the average value of $v\sin{i}$ in km s^-1 and the references, the calculated value of colour excess E(V-L) in magnitudes and remarks. As may be noted from the Appendices 1-5 the number of HAEBE stars (including candidate members and Vega- and $\beta$ Pic type stars) and TT stars (including young solar-type stars) which are used in this study is 264 and 232 respectively. The number of stars with all data which are needed for statistical analysis (i.e. $(V-L)_{\rm obs}$, Sp classes, p and A_V) is about 400, eight times greater than in previous studies.

3.2 The new $\log p/E(V-L)$ diagram

First of all we plotted, in Fig. 1, the observed polarization for the sample of selected young stars against their observed $(V-L)_{\rm obs}$ colour index. We emphasize that pronounced correlation between $\log p$ and $(V-L)_{\rm obs}$for a sample of 402 young stars is evident. On the other hand Fig. 1 demonstrates no noticeable differences in position of different types of young objects (HAEBE and TT stars) on the diagram. It is easy to explain while the values $(V-L)_{\rm obs}$ are composed of normal colour indices corresponding to the spectral type of stars and biased by interstellar absorption. However, it follows even from this relation that most of the Vega-type and young solar-type stars are well concentrated in the left side of the diagram and represent a separate group.

Figure 1: $\log p$/ $(V-L)_{\rm obs}$ diagram for HAEBE, TT type, Vega-type and young solar-type stars. The number of stars used is indicated. The solid line represents a linear fit for the region $1^{\rm m}<(V-L)_{\rm obs}<15^{\rm m}$

Figure 2: $\log p/E(V-L)$ diagram for HAEBE, Vega-type stars and standard early-type stars from Serkowski et al. ([1975]). The dashed lines indicate the bounded region of the diagram in which 85% of HAEBE stars are located

Figure 3: $\log p/E(V-L)$ diagram for TT stars, young solar-type stars and Mira Ceti-type stars and stars within 50 pc from the Sun from Leroy ([1993]). The dashed lines indicate the bounded region of the diagram in which 80% of TT stars are located

Figure 4: The common $\log p/E(V-L)$ diagram for HAEBE, TT, Vega-type stars and young solar-type stars. The boxes 1 and 2 indicate the position of supergiants from Serkowski et al. ([1975]) and MS stars from Leroy ([1993]) respectively. The dashed lines indicate the bounded region of the diagram in which 85% of HAEBE and TT stars are located. The solid line represents a linear fit for the dependence: Eq. (3)

In the next step we construct the diagram $\log p/E(V-L)$ separately for HAEBE stars (Fig. 2) and for TT stars (Fig. 3), where E(V-L) was calculated in the same way as mentioned in Sect. 2 (i.e. corrected for the normal colour index corresponding to the spectral type of the star and the amount of interstellar absorption, see (1)).

From Fig. 2 we conclude that most HAEBE stars (as many as 85%) show a clear dependence between the polarization degree and near IR excess. The behaviour for TT stars is not so apparent. However some tendency to increase p with increasing near IR excess exists, (see Fig. 3) and more than 80% of TT stars are concentrated at the same region of the diagram as HAEBE stars.

In Fig. 4 all data for young stars from our sample are plotted together.

It is clear that most young stars are well concentrated along a line with the pronounced positive correlation between $\log p$ and E(V-L).
As was suggested by Herbig ([1960]), the so-called HAEBE stars are intermediate mass analogues of young TT stars in the mass range between 2 and 8 $M_{\hbox{$\odot$ }}$. From that time numerous observational and theoretical confirmations of this suggestion have been discussed and there is no doubt at present that the CS environment of TT and HAEBE stars is rather similar (in the sense of non-spherical symmetry). Note however that some significant differences in physical conditions in CS shells exist. For example Grinin ([1998]) noted that "HAEBE stars are more massive objects than TT stars and their CS disks are geometrically thicker". Besides he also noted that for TT stars the model of magnetospheric accretion is successfully adopted whereas their application for HAEBE stars faced several problems. Moreover, Pogodin ([1998]) have pointed out several main distinctions between the disks around classical TT stars and HAEBE stars as follows:

1.

The inner boundary of the HAEBE star's disk is not as close to the star as in the case of TT stars;

2.

The gas density is lower in the case of the HAEBE disk; and

3.

Matter infall in HAEBE stars is discrete rather than continuous.

In addition note that although we know that TT stars are surrounded by CS accretion disks, there is still active debate going as to whether or not HAEBE stars have accretion disks (see for example B $\rm\ddot{o}$hm & Catala [1994]).

The $\log p/E(V-L)$ diagram discussed here provides additional information on similarities and differences in CS shells in both kinds of young objects because the polarization and near IR excesses both originate mainly in the inner part of CS shells and are sensitive in general to the presence of hot dust in the CS environment.

The main conclusions drawn from the diagram constructed here (see Figs. 2-4) are as follows:

First, most of HAEBE and TT stars show a common linear dependence between the $\log p$ and near IR excess. In the range of E(V-L) from $1^{\rm m}$ to $8^{\rm m}$ the best fit for this dependence (solid line in Fig. 4) may be depicted by the following equation:

$$p\approx 0.22~{\rm e}^{0.58~E(V-L)}$$ (2)

or

$$\log~p\approx0.25~E(V-L)-0.66.$$ (3)

This is in good agreement with earlier results of Yudin ([1988]) (taking into account the much lower statistics in the previous study). In the range $E(V-L)<1^{\rm m}$ the relation is quite different. The behaviour for this region is more complicated and probably may be depicted by the equation in the form:

$$p\approx k\times E(V-L).$$ (4)

More detailed analysis of this behaviour will be considered in Sect. 6.

Second, on average HAEBE stars (131 objects) exhibit larger near IR excesses than TT stars (153 objects) (see Figs. 5-6). For HAEBE stars the mean value of E(V-L) is about $\approx3\mbox{$\,.\!\!\!^{\rm m}$ }48$ (with the standard deviation $\sigma_{E(V-L)}\approx1\mbox{$\,.\!\!\!^{\rm m}$ }67$) and 76% of stars exhibit E(V-L) excesses ranging between $2^{\rm m}$ and $6^{\rm m}$. For TT stars the mean value of E(V-L)is about $\approx1\mbox{$\,.\!\!\!^{\rm m}$ }85$ ( $\sigma_{E(V-L)}\approx1\mbox{$\,.\!\!\!^{\rm m}$ }33$) and 90% of TT stars exhibit $0^{\rm m}<E(V-L)<3^{\rm m}$.

Third, clear differences are found also in the polarization distribution for the groups of TT (174 objects without young solar-type stars) and HAEBE stars (149 objects without Vega-type stars) in common (see Figs. 7-8). Note, that the polarization distribution has been investigated for 122 TT stars and related objects by Menard & Bastien ([1992]) (it is peaked at 0.75% with the average polarization of 1.7%) and the distribution constructed here for 174 TT stars is very similar. For TT stars the mean value of polarization is about 1.6% (with the standard deviation 1.8%) and for HAEBE stars the mean value of p is $\approx3.0$% ( $\sigma_{p}\approx3.4$%). For both TT and HAEBE stars the polarization distributions are broad and there are tails in the distributions, as is evident from the fact that the standard deviation in both cases is greater than the mean. The differences are much pronounced in numerical form (see Table 1). It is easy seen that a significant fraction (1/3) of HAEBE stars exhibit polarization degree at a level higher than 3% whereas among TT stars only 1/8 show the same level of polarization.

 

Table 1: Numerical differences between polarization distributions for HAEBE and TT stars

	p<1.5%	p>1%	p>2%	p>3%	p>4%
TT	67.9%	48.5%	23.8%	11.7%	6.5%
HAEBE	49.6%	64.5%	41.0%	27.6%	19.2%

Fourth, most of the young early-type stars which might be classified as Vega-type, $\beta$-Pic type or post HAEBE stars (i.e. comparable young stars near the end of the pre-MS evolutionary phase or young MS stars) show statistically smaller near IR excesses and polarization than HAEBE stars (see Fig. 2). The same conclusion can be made for young solar-type stars (see Fig. 3). The histograms of near-IR excess and polarization distributions for Vega-type and young solar-type stars are presented in Figs. 9 and 10. As follows from Fig. 9 about 65% of Vega-type and solar-type stars exhibit near-IR excess less than $0\mbox{$\,.\!\!\!^{\rm m}$ }25$, 72% - less than $0\mbox{$\,.\!\!\!^{\rm m}$ }5$ and 85% - less than $1^{\rm m}$. In the polarization distribution about 63% of Vega-type and solar-type stars show polarization degree less than 0.1%, 71% - less than 0.25% and 90% of them have p<0.75%. Note that a portion of post HAEBE and Vega-type stars in our sample are stars in the Orion region and they exhibit relatively large observed polarization at the level of $p_{\rm obs}\approx0.4-1$% that is not consistent with their small near IR excesses (see Appendix 2). However, the analysis of interstellar polarization in the Orion region yields $p_{\rm is}\approx0.25$% for the majority of cluster stars (Breger et al. [1981]). Taking into account this value, the intrinsic polarization for most of these Orion stars would not exceed 0.2%. This leads to the a significant improvement in the correlation in the sense that these stars would transit to the lower left region of the diagram. Besides, in the polarization distribution the number of post HAEBE and Vega-type stars with the polarization degree less than 0.25% would reach a value of about 80%.

Figure 5: Histogram of near IR excesses for HAEBE stars

Figure 6: Histogram of near IR excesses for TT type stars

Figure 7: Histogram of polarization for HAEBE stars

Figure 8: Histogram of polarization for TT type stars

Figure 9: Histogram of near IR excesses for Vega-type stars and young solar-type stars

Figure 10: Histogram of polarization for Vega-type stars and young solar-type stars

One can note however that the spread of the data points for young stars around the average is not small. There are a few reasons to account for such behaviour:
1. In spite of significant photometric variability taking place in many young stars the average value of $(V-L)_{\rm obs}$ indices may be well determined. Some spread in estimates of Sp types and interstellar extinction taken from the literature is more significant. However for our statistical investigation this is not so important since as a rule in the modelling of the SED the use of an earlier Sp type requires one the large value of reddening. Few typical examples for the stars with strong discrepancy in determination of Sp type and A_V are given in Table 2. As can be seen in Table 2 no strong variations in E(V-L) occurred due to different estimates of Sp types and A_V. Note however that for some objects (especially for TT stars) uncertainties in estimates of Sp classes and A_V may lead to the significant scattering of the data points;
2. More important is that, in contrast to photometric observations, the polarimetric data are very limited. The values of p which are presented in the Appendices are often an average from 2-3 measurements or even a single one. However, as has been pointed out by Menard & Bastien ([1992]) and Yudin & Evans ([1998]), about 100% of all young stars are polarimetrically variable. This may lead to the displacement of their location on the diagram;
3. In some cases averaging of polarization over a long period is not correct since a star may usually possess small polarization and show an increase of p from time to time on a short time scale. Such behaviour is observed in HAEBE stars with Algol-like minima. Their location on the diagram will be considered in the next section;
4. For most of the stars we use the observed values of polarization without allowance for interstellar polarization;
5. Finally the scattering of the data points on the diagram may be due to a specific orientation of nonspherical dust shells surrounding some stars. This possibility will be considered in Sect. 4.
To investigate the influence of interstellar polarization on our resulting dependence we try to calculate an interstellar polarization component for a few stars which lie far from the average line and/or on the edge of the region. The values of interstellar and intrinsic components for some stars were derived by the field stars method using the VizieR Service at the CDS (using the catalogues of Mathewson et al. [1978] and Axon & Ellis [1976]) or were taken from literature and are tabulated in Table 3. The results of these calculations were used to investigate the changes in the position of stars on the diagram. As can be seen in Fig. 11 the plotting of the values of intrinsic polarization results in the transition of a few selected stars close to the average line into the region occupied by most young stars. For TT stars which usually exhibit relatively low levels of intrinsic polarization the estimate of interstellar components is very important. The objects whose positions strongly deviate from others on the diagram are mainly TT stars and they usually show much higher values of polarization than might be expected from their near IR excesses (see for example: LkH$\alpha$ 338, LkH$\alpha$ 332-20, Sz 30, Sz 45, CT Cha, VV Cha, Haro 1-1, CHX 10A, CED 110, ROX 7, ROX 39, ROX 42B, ROX 43AB, P1540, P 1724 and AZ Ori). However most of these "peculiar" stars are located in the Chamaeleon and Ophiuhus regions or in the Orion nebula and their large observed polarization may be due to significant interstellar polarization (see for example Whittet et al. [1991]; Breger [1976], [1977]). As follows from Whittet et al. ([1994]) namely for Cha I the considerable uniformity of polarization vectors in this region is observed and the large group of young stars in Cha I show unexpectedly high polarization degree in comparison with their relatively low near IR excesses. This fact has been discussed for CHX 10A by Whittet et al. ([1994]) who suggested that "for this weak-lined TT star the interstellar polarization component dominates over any intrinsic component". Other "peculiar" stars were measured polarimetrically on a single occasion and estimates of their polarization may be doubtful. Moreover, Sz 30, VV Cha, CHX 10, LkH$\alpha$ 332-20 are well-known close binaries which may also affect on their observed polarization. Nevertheless the fraction of stars which deviate from the general dependence is not large and there is no need to invoke another mechanism of polarization instead of the scattering in nonspherical dust shells for the majority of young stars.

 

Table 2: The calculated values of E(V-L) for different estimates of spectral types and interstellar extinction for selected stars

name	Sp	ref.	AV	ref.	$(V-L)_{\rm obs}$	E(V-L)
LkH$\alpha$ 208	B7	1	1.7	1	5.5	4.2
	F0	2	0.4	2	5.5	4.3
V 376 Cas	F0	1	2.9	1	11.1	6.75
	B5	2	5.2	2	11.1	7.55
T Ori	B9	1	1.7	1	5.3	4.00
	A3	3	1.1	3	5.3	3.92

 

Table 3: Estimates of intrinsic polarization for some stars

name	$p_{\rm obs}$, $\theta_{\rm obs}$	$p_{\rm is}$, $\theta_{\rm is}$	$p_{\rm int}$, $\theta_{\rm int}$	rem.
MWC 137	6.0% 163$^\circ$	4.0% 162$^\circ$	2.0% 162$^\circ$
HD 45677	1.0% 166$^\circ$	0.8%  75$^\circ$	1.7% 166$^\circ$	1
HD 316285	2.9% 166$^\circ$	2.5% 165$^\circ$	0.4% 165$^\circ$
HD 150193	5.0%  48$^\circ$	2.5%  21$^\circ$	4.2%  65$^\circ$
HD 100546	0.2%  60$^\circ$	0.6% 117$^\circ$	0.8%  30$^\circ$	4
HD 259440	3.5% 165$^\circ$	1.5% 165$^\circ$	2.0% 165$^\circ$
HD 163296	0.2%  28$^\circ$	0.6% 175$^\circ$	0.6%  75$^\circ$	2
BHJ 71	4.0% 128$^\circ$	2.5% 100$^\circ$	3.3% 145$^\circ$	5
IL Cep	4.6% 115$^\circ$	2.5% 100$^\circ$	2.8% 128$^\circ$	5
HD 142666	0.6%  78$^\circ$		0.5%  70$^\circ$	6
HD 141569	0.6%  90$^\circ$		<0.15% 105$^\circ$	6
HD 53367	0.6%  44$^\circ$		0.2%  44$^\circ$	1
HD 37806	0.5% 120$^\circ$	0.4%  76$^\circ$	0.6% 138$^\circ$	1
HD 87643	0.9% 165$^\circ$	2.2% 155$^\circ$	1.3%  65$^\circ$
RCW 34	5.6%  59$^\circ$	3.5%  95$^\circ$	5.0%  75$^\circ$	3
HD 98922	0.2% 160$^\circ$	0.3% 120$^\circ$	0.33%  12$^\circ$

Figure 11: Changes in the position on the $\log p/E(V-L)$ diagram of some young stars taking into account their intrinsic polarization

3.3 HAEBE and TT stars with Algol-like minima

It is also interesting to investigate the behaviour on the $\log p/E(V-L)$diagram for the stars with available data of synchronous polarimetry and photometry. Most of these objects (so-called HAEBE stars with Algol-like minima of brightness, hereafter UXOrs) were investigated by Grinin and coauthors (Grinin [1991]; Grinin et al. [1991]) and some objects by Yudin ([1992]), Yudin & Evans ([1998]). One can readily see in Fig. 12 that most of them are transferred along the main dependence within the region in which 90% of all young stars are located. For each of the objects we use average values of p and colour excesses for a few stages of brightness. Moreover, for BF Ori, CQ Tau, RR Tau and BM And we use the values of intrinsic polarization which were calculated using the estimates of interstellar components (see references to the objects in Appendix 3). Of course in some cases the changes in polarization during the optical fading may have more complicated behaviour (see for example Grinin [1988]; Grinin et al. [1991]; Voshchinnikov & Grinin [1988]; Grinin et al. [1995]). Nevertheless, for the most part this behaviour substantiates the validity of the dependence discussed here. The only assumption has been made here, namely that the IR fluxes of these stars are not changing strongly in comparison with the optical variations during the optical fading. Variations of IR fluxes for some HAEBE stars (including UXOrs: BF and UX Ori) were detected by Hutchinson et al. ([1994]). However examination of the Kilkenny et al. ([1985]) catalogue indicates that the amplitude of photometric variability of young stars in the optical region of spectra is in general much larger than that of variability in the IR region. The same conclusion is evident from the paper of Davies et al. ([1990]). Thus the above mentioned assumption would not affect strongly the behaviour of the stars with Algol-like minima on the diagram. Finally note that behaviour like that observed for UXOrs has been detected in few TT stars (see Appendix 3) and their transfer on the diagram takes place again within the same region and along the main dependence. This fact indicates again similarity of polarization mechanisms at least in some TT and HAEBE stars.

Figure 12: $\log p/E(V-L)$ diagram for HAEBE stars with Algol-like minima

3.4 Young solar-type and Vega-type stars

Our sample of young stars has also included a small group of young solar-type stars (see Appendix 5). Most of them are young MS stars and no near IR excesses are observed for them. The absence of hot dust in their envelopes led to the suggestion that the main mechanism of polarization is not connected with dust and the intrinsic polarization in U and B bands is caused by magnetic activity of these stars. However in the red (R and I bands and possibly in V) the polarization can originate in CS shells with large scattering particles (see Huovelin [1985]). Since all selected stars are located within 50 pc from the Sun, the interstellar extinction and interstellar polarization are negligible. An inspection of the catalogue of Leroy ([1993]) immediately indicates a small level of polarization for all stars of this type (p<0.05%) and these stars are located in the lower left side of the diagram (see Fig. 3). One can note that these stars may be later spectral type analogues of Vega-type or $\beta$ Pic type stars (see Appendix 2) which are located in the same region of the diagram (see Figs. 2 and 4). The prototypes for these stars (Vega, $\beta$ Pic and Fomalhaut) are classified as the young MS stars and they are characterized by the existence of disk-like dust envelopes. A brief discussion on polarimetric properties of some $\beta$ Pic-type stars has been presented recently by Yudin et al. ([1999]). In spite of the presence of cool dust in their CS disks the polarization of these stars is very small even for $\beta$ Pic itself for which the CS disk is viewed edge-on. Two possibilities to explain this behaviour exist:
- an absence of a sufficient amount of hot dust (which is a primary source of polarization in most young stars) in their CS shells i.e. the disks are optically thin and the unpolarized starlight dominates; and
- small geometrical thickness of the disks around them, that is unfavorable for producing polarization (see for example Dolginov et al. [1995]).
Note however, that the group of Vega-type stars is not homogeneous. Some objects might be considered as genuinely MS stars and they have small polarization (p<0.1%) and near-IR excess $0^{\rm m}<E(V-L)<1^{\rm m}$, whereas others have $1^{\rm m}<E(V-L)<3^{\rm m}$ and a higher level of polarization ( $0.1\%<p<0.7$%). The latest group includes the stars: HD31648, HD34282, HD37411, HD38120, HD57150, 51 Oph, HD139614, HD142666, HD144432, HD 169142 and others. Most of them have been studied early as the members of HAEBE group and there are no doubts on their youth. Some stars have been investigated recently as Vega-type candidates by Coulson et al. ([1998]) who suggested that "these stars are on an earlier evolutionary state then the archetypes". It is felt that these objects are in the transition stage from HAEBE stars to young MS stars (see further discussion in Sect. 7). The same suggestion has been made recently for HD142666 and HD139614 by Yudin et al. ([1999]). In addition note that HD31648 and HD163296 (these stars also show polarization at the level of about 0.2% and the value of $E(V-L)\approx3^{\rm m}$) were recently considered as members of "baby" $\beta$ Pic type stars (Sitko et al. [1999]).

The important conclusions from this section may be emphasized as follows: most young MS stars and stars in the stage of evolution close to MS exhibit very small levels of intrinsic polarization as well as small (or even absence of) near IR excesses. However some differences between young MS stars and young stars close to the end of the PMS stage of evolution may be seen in the sense that the latter exhibit larger intrinsic polarization and near-IR excesses.