Identifying the population of T-Tauri stars in Taurus: UV–optical synergy

Abstract

With the third data release of the Gaia mission, Gaia DR3 with its precise photometry and astrometry, it is now possible to study the behavior of stars at a scale never seen before. In this paper, we developed new criteria to identify T-Tauri stars (TTS) candidates using UV and optical color-magnitude diagrams (CMDs) by combining the GALEX and Gaia surveys. We found 19 TTS candidates and five of them are newly identified TTS in the Taurus molecular cloud (TMC), not cataloged before as TMC members. For some of the TTS candidates, we also obtained optical spectra from several Indian telescopes. We also present the analysis of distance and proper motion of young stars in the Taurus using data from Gaia DR3. We found that the stars in Taurus show a bimodal distribution with distance, having peaks at $130.17_{-1.24}^{1.31}$ pc and $156.25_{-5.00}^{1.86}$ pc. The reason for this bimodality, we think, is due to the fact that different clouds in the TMC region are at different distances. We further showed that the two populations have similar ages and proper motion distribution. Using the Gaia DR3 CMD, we showed that the age of Taurus is consistent with 1 Myr.

Appendices

Appendix A. Sturges’ rule

Sturges’ rule (Sturges 1926) provides a simple method of binning the data based on the number of data points, n. Sturges’ rule makes the assumption that the histogram consists of normally distributed data points, approximated as a binomial distribution. The optical number of bins, k, using the Sturges’ rule (Sturges 1926) is given as:

$$\begin{aligned} k= 1 + \log _2(n). \end{aligned}$$

(A.1)

Appendix B. Rice rule and the rule of square roots

Other methods based on the number of data points in the sample are Rice rule² and the rule of square roots. The number of bins, k, as given by Rice rule is $k=\root 3 \of {n}\times 2$ and from the rule of square roots is $k=\sqrt{n}$. The issue with these methods is that they do not consider the inherent skewness of the data.

Appendix C. Doane’s rule

If the data points are not normally distributed, we can use a modification of the Sturges’ rule, known as Doane’s rule (Doane 1976). Doane’s rule tries to account for the skewness of the data. The number of bins, k, is given as:

$$\begin{aligned} k = 1 + \log _2( n ) + \log _2 \left( 1 + \frac{ |g_1| }{\sigma _{g_1}} \right) , \end{aligned}$$

(C.1)

where $g_{1}$ is the estimated 3rd-moment-skewness of the distribution and is given as:

$$\begin{aligned} g_{1}=\frac{\Sigma _{i=1}^{n} (X_i - \bar{X})^3}{[\Sigma _{i=1}^{n} (X_i - \bar{X})^2]^{3/2}}. \end{aligned}$$

(C.2)

Here, $X_i$ are the data points and $\bar{X}$ is the mean of the sample. $\sigma _{g_{1}}$ is given as:

$$\begin{aligned} { \sigma _{g_{1}}={\sqrt{\frac{6(n-2)}{(n+1)(n+3)}}}}. \end{aligned}$$

(C.3)

Appendix D. Scott’s rule

Scott’s rule (Scott 1979) is based on the standard deviation, $\sigma$, of the data. Unlike previous methods, Scott’s rule gives us the optimal bin width, h, and not the number of bins, k. The bin width, w, is correlated with the number of bins by $k={R}/{w}$, where R is the range in the distribution. The bin width is given as follows:

$$\begin{aligned} h = \frac{3.49 \sigma }{\root 3 \of {n}}. \end{aligned}$$

(D.1)

Appendix E. Freedman–Diaconis rule

The Freedman–Diaconis rule (hereafter FDR; Freedman & Diaconis 1981) has a similar approach as that of Scott’s rule, wherein the optimal bin width is considered instead of the number of bins. The optimal number of bins in the FDR rule depends on the interquartile range ${\text {IQR}}(x)$. The ${\text {IQR}}(x)$ is less sensitive to deviant outlier points than the usual standard deviation estimations. Standard deviation calculation depends on the mean of the data, where outlier data points are included. This may affect the accuracy of the result, and hence ${\text {IQR}}(x)$ will be the best way to estimate the bin size. The optical bin width is estimated as:

$$\begin{aligned} h=2{{\text {IQR}}(x) \over {\root 3 \of {n}}}. \end{aligned}$$

(E.1)