Physical Parameters and Activity Properties of K-type Stars Based on the LAMOST Spectral Survey

Abstract K-type stars are important objects of our Galaxy. It is interesting to determine the stellar physical parameters and magnetic activity properties of K-type stars. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope DR10 provides more than 1 million spectra of K-type stars. We have used spectra with a signal-to-noise ratio greater than 10 as our objects in the large amount of spectral data that we have analyzed. We used the spectral subtraction method to reduce the observational spectra by utilizing the iSpec program. We have determined the chromospheric activity of K-type stars using the H α line. Among more than 1.33 million spectra associated with about 1.06 million stars, there are a total of 150,000 stellar spectra that have excess chromospheric activity. For K stars with rotation periods above 6.20 days, the chromospheric activity decreases rapidly as the period increases. We calculated the solar Rossby number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">n</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1.85</mml:mn> </mml:math> , and conclude that when the Rossby number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>O</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>Sun</mml:mi> </mml:msub> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>0.07</mml:mn> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> remains stable; when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">n</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mspace width="0.25em"/> <mml:mo>≥</mml:mo> <mml:mspace width="0.25em"/> <mml:mn>0.07</mml:mn> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> decreases as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">n</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> increases. By crossmatching with the Gaia survey, we also determined their distances and found that the active fraction decreases as the distance above the Galactic disk increases.