$\mathrm{H}{\alpha }$ chromospheric activity of F-, G-, and K-type stars observed by the LAMOST medium-resolution spectroscopic survey

Abstract

The distribution of stellar $\mathrm{H}\alpha$ chromospheric activity with respect to stellar atmospheric parameters (effective temperature $T_{\mathrm{eff}}$, surface gravity $\log \,g$, and metallicity $\mathrm{[Fe/H]}$) and main-sequence/giant categories is investigated for the F-, G-, and K-type stars observed by the LAMOST Medium-Resolution Spectroscopic Survey (MRS). A total of 329,294 MRS spectra from LAMOST DR8 are utilized in the analysis. The $\mathrm{H}\alpha$ activity index ($I_{\mathrm{H}{\alpha }}$) and $\mathrm{H}\alpha$ $R$-index (${R_{\mathrm{H}{\alpha }}}$) are evaluated for the MRS spectra. The $\mathrm{H}\alpha$ chromospheric activity distributions with individual stellar parameters, as well as in the $T_{\mathrm{eff}}$ – $\log \,g$ and $T_{\mathrm{eff}}$ – $\mathrm{[Fe/H]}$ parameter spaces, are analyzed based on the ${R_{\mathrm{H}{\alpha }}}$ index data. It is found that: (1) for the main-sequence sample, the ${R_{\mathrm{H}{\alpha }}}$ distribution with $T_{\mathrm{eff}}$ has a bowl-shaped lower envelope with a minimum at about 6200 K, a hill-shaped middle envelope with a maximum at about 5600 K, and an upper envelope continuing to increase from hotter to cooler stars; (2) for the giant sample, the middle and upper envelopes of the $R_{\mathrm{H}{\alpha }}$ distribution first increase with a decrease of $T_{\mathrm{eff}}$ and then drop to a lower activity level at about 4300 K, revealing different activity characteristics at different stages of the stellar evolution; (3) for both the main-sequence and giant samples, the upper envelope of the $R_{\mathrm{H}{\alpha }}$ distribution with metallicity is higher for stars with $\mathrm{[Fe/H]}$ greater than about −1.0, and the lowest-metallicity stars hardly exhibit high $\mathrm{H}\alpha$ indices. A dataset of $\mathrm{H}\alpha$ activity indices for the LAMOST MRS spectra analyzed is provided with this paper.

Appendices

Appendix A: Distribution of the $\mathrm{[Fe/H]}$ values in the $T_{\mathrm{eff}}$ – $\log \,g$ parameter space

In Fig. 10, we show the distribution of the $\mathrm{[Fe/H]}$ values in the $T_{\mathrm{eff}}$ – $\log \,g$ parameter space for the MRS spectra of F-, G-, and K-type stars analyzed in this work. The values of the stellar atmospheric parameters ($T_{ \mathrm{eff}}$, $\log \,g$, and $\mathrm{[Fe/H]}$) are provided by the LAMOST Stellar Parameter Pipeline (LASP) and are determined by matching the observed MRS spectra with the reference spectra. Panel (a) of Fig. 10 mainly shows the distribution of the positive $\mathrm{[Fe/H]}$ values (displayed in red) in the $T_{\mathrm{eff}}$ – $\log \,g$ parameter space, and panel (b) mainly shows the distribution of the negative $\mathrm{[Fe/H]}$ values (displayed in blue). The result exhibited in Fig. 10 does not suggest a degeneracy (apparent correlation) between the values of $\mathrm{[Fe/H]}$ and the values of $T_{\mathrm{eff}}$ (or $\log \,g$) provided by the LASP, demonstrating the reliability of the stellar parameter values.

Fig. 10

Distribution of the $\mathrm{[Fe/H]}$ values in the $T_{\mathrm{eff}}$ – $\log \,g$ parameter space for the MRS spectra of F-, G-, and K-type stars analyzed in this work. The value of $\mathrm{[Fe/H]}$ is indicated by the color scale (red for positive and blue for negative). In panel (a), the data points are stacked in ascending order of their $\mathrm{[Fe/H]}$ values, with the maximum value at the highest layer and the minimum value at the lowest layer. In panel (b), the data points are stacked in reverse order of their $\mathrm{[Fe/H]}$ values, with the minimum value at the highest layer and the maximum value at the lowest layer. The horizontal and vertical lines in the two panels are the dividing lines for the main-sequence and giant samples (same as in Fig. 3)

Appendix B: Relationship between the magnitudes of $v \sin i$ and $\Delta I_{\mathrm{H}{\alpha}}$

We estimate the relationship between the magnitudes of $v \sin i$ (projected rotational velocity) and $\Delta I_{\mathrm{H}{\alpha}}$ (increment of $I_{\mathrm{H}{\alpha}}$ caused by rotational broadening) by using the nine example spectra shown in Fig. 1. These spectra are from different stellar types and at different $\mathrm{H}\alpha$ activity levels, and hence are representative.

For an input spectrum of the $\mathrm{H}\alpha$ line and a given $v \sin i$ value, the spectral profile after rotational broadening can be calculated by using the formula given by Gray (2008). For each of the spectra displayed in Fig. 1, we calculate a series of spectra after applying rotational broadening for a series of $v \sin i$ values from 0 km/s to 30 km/s,³ and then evaluate $I_{\mathrm{H}{\alpha}}$ values for each of the calculated spectra. The $\Delta I_{\mathrm{H}{\alpha}}$ values corresponding to the series of $v \sin i$ values are obtained by subtracting the $I_{\mathrm{H}{\alpha}}$ value of the original spectrum from the newly evaluated $I_{\mathrm{H}{\alpha}}$ values. (Note that the value of $\Delta I_{\mathrm{H}{\alpha}}$ is positive for the $\mathrm{H}\alpha$ absorption line profile and negative for the $\mathrm{H}\alpha$ emission line profile.)

The plots of $v \sin i$ – $\Delta I_{\mathrm{H}{\alpha}}$ relation for all the nine example spectra are shown in Fig. 11. It can be seen from Fig. 11 that, for $v \sin i$ values less than 30 km/s, the absolute magnitude of $\Delta I_{\mathrm{H}{\alpha}}$ is generally below about $0.02 \thicksim 0.05$ for higher $I_{\mathrm{H}{\alpha}}$ values (panels (a)–(f)) and below about $0.06 \thicksim 0.08$ for lower $I_{\mathrm{H}{\alpha}}$ values (panels (g)–(i)).

Fig. 11

Plots of $v \sin i$ – $\Delta I_{\mathrm{H}{\alpha}}$ relation (red curve) for the nine example spectra shown in Fig. 1. The horizontal line in the plots represents $|\Delta I_{\mathrm{H}{\alpha}}|=0.05$. The $I_{\mathrm{H}{\alpha}}$ values of the original spectra (corresponding to $v \sin i=0\text{ km}/\text{s}$ in the horizontal axis) are given in the plots. In panel (c), $\Delta I_{\mathrm{H}{\alpha}}$ takes a negative value owing to the emission profile of the $\mathrm{H}\alpha$ line

It should be noted that a comparison between the $v \sin i$ values obtained by the LAMOST MRS and by the Apache Point Observatory Galactic Evolution Experiment (APOGEE; Majewski et al. 2017) shows that the $v \sin i$ of the MRS is slightly larger than that of the APOGEE (see the data release documents of LAMOST for more details), and the original MRS spectra used for analyzing the $v \sin i$ – $\Delta I_{\mathrm{H}{\alpha}}$ relation might have a small but nonzero intrinsic $v \sin i$. Therefore, the $v \sin i$ – $\Delta I_{\mathrm{H}{\alpha}}$ relation and the upper limit of $\Delta I_{\mathrm{H}{\alpha}}$ displayed in Fig. 11 can be regarded as an estimate of magnitude rather than a precise result.

Appendix C: Algorithm for $\delta \chi$ estimation

The $\chi$ factor defined in equation (6) is a function of stellar atmospheric parameters $T_{\mathrm{eff}}$, $\log \,g$, and $\mathrm{[Fe/H]}$, thus the uncertainty of $\chi$ (i.e., $\delta \chi$) depends on the uncertainties of the three stellar atmospheric parameters $\delta T_{\mathrm{eff}}$, $\delta \log \,g$, and $\delta \mathrm{[Fe/H]}$.

We use $\delta \chi (T_{\mathrm{eff}})$, $\delta \chi (\log \,g)$, and $\delta \chi (\mathrm{[Fe/H]})$ to denote the uncertainties of $\chi$ caused by the uncertainties of the three stellar atmospheric parameters. To estimate $\delta \chi (T_{\mathrm{eff}})$, we first calculate three $\chi$ values corresponding to $T_{\mathrm{eff}}$, $T_{\mathrm{eff}}-\delta T_{\mathrm{eff}}$, and $T_{\mathrm{eff}}+\delta T_{\mathrm{eff}}$, which are denoted by $\chi (T_{\mathrm{eff}})$, $\chi (T_{\mathrm{eff}}-\delta T_{\mathrm{eff}})$, and $\chi (T_{\mathrm{eff}}+\delta T_{\mathrm{eff}})$, respectively. Then, the value of $\delta \chi (T_{\mathrm{eff}})$ is calculated by the following equation:

$$\begin{aligned} &\delta \chi (T_{\mathrm{eff}}) \\ & = \frac{\big|\chi (T_{\mathrm{eff}}-\delta T_{\mathrm{eff}}) - \chi (T_{\mathrm{eff}})\big| + \big|\chi (T_{\mathrm{eff}}+\delta T_{\mathrm{eff}}) - \chi (T_{\mathrm{eff}})\big|}{2}. \end{aligned}$$

(7)

$\delta \chi (\log \,g)$ and $\delta \chi (\mathrm{[Fe/H]})$ can be estimated similarly.

The value of $\delta \chi$ is calculated from the values of $\delta \chi (T_{\mathrm{eff}})$, $\delta \chi (\log \,g)$, and $\delta \chi (\mathrm{[Fe/H]})$ by the following formula:

$$ \delta \chi = \sqrt{ \big[{\delta \chi}(T_{\mathrm{eff}})\big]^{2} + \big[{\delta \chi}(\log \,g)\big]^{2} + \big[{\delta \chi}( \mathrm{[Fe/H]})\big]^{2} }. $$

(8)

In Fig. 12a, we compare the histograms of $\delta \chi (T_{\mathrm{eff}})$, $\delta \chi (\log \,g)$, $\delta \chi (\mathrm{[Fe/H]})$, and $\delta \chi$ for the MRS spectra analyzed in this work. It can be seen from Fig. 12a that the value of $\delta \chi$ is mainly affected by $\delta \chi (T_{\mathrm{eff}})$, and $\delta \chi (\log \,g)$ has the least effect on the $\delta \chi$ result.

Fig. 12

(a) Histograms of $\delta \chi$, $\delta \chi (T_{\mathrm{eff}})$, $\delta \chi (\mathrm{[Fe/H]})$, and $\delta \chi (\log \,g)$ for the MRS spectra analyzed in this work. (b) Histograms of $\delta R_{\mathrm{H}{\alpha}}/R_{\mathrm{H}{\alpha}}$, $\delta I_{\mathrm{H}{\alpha}}/I_{\mathrm{H}{\alpha}}$, and $\delta \chi /\chi$ for the MRS spectra analyzed in this work

In Fig. 12b, we compare the histograms of the relative uncertainties of $\chi$, $I_{\mathrm{H}{\alpha}}$, and ${R_{\mathrm{H}{\alpha}}}$ (i.e., $\delta \chi /\chi$, $\delta I_{\mathrm{H}{\alpha}}/I_{\mathrm{H}{\alpha}}$, and $\delta R_{\mathrm{H}{\alpha}}/R_{\mathrm{H}{\alpha}}$) for the MRS spectra analyzed in this work. It can be seen from Fig. 12b that the relative uncertainty of ${R_{\mathrm{H}{\alpha}}}$ ($\delta R_{\mathrm{H}{\alpha}}/R_{ \mathrm{H}{\alpha}}$) is mainly affected by $\delta I_{\mathrm{H}{\alpha}}/I_{\mathrm{H}{\alpha}}$, and for most MRS spectra $\delta \chi /\chi$ is much smaller than $\delta I_{\mathrm{H}{\alpha}}/I_{\mathrm{H}{\alpha}}$. The influence of $\delta \chi /\chi$ on $\delta R_{\mathrm{H}{\alpha}}/R_{\mathrm{H}{\alpha}}$ is only prominent for a small number of spectra with relatively large uncertainties of $T_{\mathrm{eff}}$.