Observational data analysed in this Chapter confirm that most T Tauri stars are variable also in infrared. Variations were found to be one order of magnitude smaller than in optical, but still significant, with a maximum amplitude of 0.6 magnitude in near infrared and 0.3 in mid infrared. Infrared variations are higher in bands W1 and W2, with a median of 0.29 and 0.32 mag respectively, which is larger than the typical fluctuation of 0.1 mag found by Flaherty et al. (2013) at the same wavelengths. Their sample, however, is in IC348, which is older than Taurus-Auriga by 1-2 Myrs, and the different age could explain the drop in the observed variations.
Variability was analysed through two different methods: Stetson index, whose thresh- old was taken at 0.9 following Rebull et al. (2014) prescription, andχ2. Based on Stetson
index, the percentage of variable star innear infrared is 66%, while it is only 28% inmid
infrared. However, the different statistics might be affected by the smaller number of data points for each star in bands W3 and W4. When using the same data set innear infrared as in mid infrared, the percentage of variable stars in the former case drops to 14%. If a less conservative threshold had been used, for example 0.21 as in Flaherty et al. (2013), 93% stars would have been classified as variable innear and 69% inmid infrared. Innear
infrared the percentage would be 62% in case the reduced sample were used. When vari- ability was analysed in each single band, throughχ2 values, 76% of the stars were variable
in W1, 86% in W2, 38% in W3 and 17% in W4. Overall, variability is present both in
near and mid infrared, although it tends to be more pronounced at 3.6 and 4.5µm rather than at longer wavelengths, when single bands are analysed. The same behaviour was confirmed in a larger samples of stars, taken as comparison from Luhman et al. (2010).
This work has then shown that the correlation between optical highly variable stars and infrared variations is rather weak, which would support the prediction that the infrared flux is mainly due to disc emission (Cody et al., 2014). However, there is a slight trend in favour of a correlation between optical and mid infrared variations, as shown in Fig. 4.8 in the Slope-χ2 plots for bands W3 and W4. In addition, based on theχ2 values listed in
Table 4.1, some of the most variable stars in optical show higher variability in infrared, especially mid-infrared, like DOTau, DR Tau, RU Lup. Nevertheless, the correlation between optical and infrared variability is still controversial: according to Flaherty et al.
4.6. Discussion
(2013) there is strong indication that optical and infrared are correlated, especially in case of irregular optical, while Cody et al. (2014) identified three groups of stars (well- correlated, non correlated and inverse correlated), but on the whole they found that optical and infrared data were not very well correlated in more that 50% of the cases. They gave two explanations for the uncorrelated group: on one hand there may be two separate mechanisms causing variability, on the star and in the disc; on the other one infrared variations may be due to changes in the disc scale height through magnetic turbulence, as initially proposed by Turner (2013). However, as reported by Cody et al. (2014), other factors may affect the variability and hence the correlations, as inclination, disc flux and geometry, types of variability mechanisms, which are difficult to be disentangled and quantified. Another interpretation recently presented by Pozo Nu˜nez et al. (2015) is based on the presence of a binary unresolved system, where the two stars have different mass and consequently different evolution. One would be a blue star, the other a red one, thus affecting optical and infrared emission separately. However, in the sample analysed in this work no correlation with binarity or inclination was found either in optical or infrared emission.
Regarding the origin of infrared variations, the colour-magnitude diagrams in bands W1 and W2, shown in Fig. 4.11, excluded interstellar extinction as the only cause of variability in near infrared, because the slope of the fitted line does not follow the slope of the reddening curve. 22 out of 29 stars in the sample becomes redder when fainter, the remaining 7 becomes bluer. Among the 76% which become redder, all have a shallower slope than the extinction law, thus showing that there has to be an additional source of reddening.
Only few stars become bluer when fainter, and they are: CQ Tau, CW Tau, DF Tau, FT Tau, Haro 1-16, RU Lup and UZ Tau E. CQ Tau and RU Lup belong to group A in the optical variability analysis, CW Tau to group B, while DF Tau and UZ Tau E are in binary or multiple systems. DF Tau, for example, was found to have gray stellar variations in optical, between B and I band (Chelli et al., 1999), hence independent of the wavelength. Variations were attributed to circumstellar extinction and less likely to cold spot. According to Grankin et al. (2007) optical variable circumstellar extinction could cause stars to become bluer when fainter, due to an increase of scattered light compared to direct star light, so if valid in infrared too, DF Tau variations could be explained through
this mechanism.
The origin of infrared variations has been discussed by many authors, and explained either through hot and cool spots (Carpenter et al., 2001, 2002), eclipses by circumstellar material (Bouvier et al., 2003), disc asymmetries (Flaherty & Muzerolle, 2010; Flaherty et al., 2013) or disc wind (Bans & K¨onigl, 2012).
In this work, a simple model was used to try explaining the infrared variability as due to hot spots. Without taking into account inclination or limb darkening, the hot spot was modelled as a blackbody and then reddened as the star. A grid of temperatures, higher than the stellar temperature, was used to test different possible hot spots. Using the amplitude of variations known from observational data, the area of the hot spot causing such variations was computed for each temperature. According to my results, the infrared variability cannot be explained only as a consequence of hot spots, because that would require too wide an emission area, not compatible with current models (Fernandez & Eiroa, 1996; Morales-Calder´on et al., 2009). This result confirms what found by Morales- Calder´on et al. (2009), although their approach was reversed, in that they first assumed a value for the hot spot area and then estimated the expected variation at 3.6µm. On the contrary, Flaherty et al. (2013) found it possible for a hot spot to cause the observed infrared variations, but only indirectly. The hot spot would heat the inner rim, cause dust to sublimate and thus increase the dust sublimation radius. The effect would be a change in the structure of the inner part of the disc and consequently in the infrared emission. Through this mechanism, the author found a hot spot coverage of about a few percentage of the stellar area.
Another mechanism for infrared variations could be disc wind emission, as proposed by Bans & K¨onigl (2012). The presence of wind would account for the observed NIR variations, which happen on a timescale shorter than one day. The movement of material caused by the wind, along with the rapid rotation period at the inner rim (2-3 days), would give rise to a range of different particles and consequently emission coefficients. However, Flaherty et al. (2011) discarded wind as a cause of infrared variations, because according to their models high wind should be accompanied by larger infrared emission, which did not find correspondence in their observations.