Stellar Chromospheric Activity Database of Solar-like Stars Based on the LAMOST Low-resolution Spectroscopic Survey. III. Calibrating the Chromospheric Basal Flux and the Connection to Stellar Rotation

Abstract Based on the Ca ii H and K lines observed by the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, we employ the photospheric ( <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">HK</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> ) and basal ( <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">HK</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> ) flux-calibrated chromospheric activity indices to examine the relationship between chromospheric activity and the stellar rotation rate. We identify the rotation periods of 11,108 stars observed by Kepler and the Transiting Exoplanet Survey Satellite by crossmatching our chromospheric activity catalog with previous studies. Our statistical results show that chromospheric activity increases with the rotation rate until it reaches a saturation level. As the stellar effective temperature increases from 4950 to 5850 K, the saturation values of the rotation period ( P rot ) vary correspondingly from 4.38 to 1.23 days for <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">HK</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> and from 9.88 to 1.33 days for <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">HK</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> . Similarly, the corresponding saturation Rossby number (Ro) ranges from 0.200 to 0.032 for <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">HK</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> and from 0.302 to 0.107 for <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">HK</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> . The saturation is also found to be significant in stars with thick convective zones, whereas it is less apparent in stars with higher effective temperatures. For solar-like stars in the T eff range of 4800–6000 K, the values of chromospheric activity indicators are saturated when P rot &lt; 1.45 days (Ro &lt; 0.100) and P rot &lt; 2.85 days (Ro &lt; 0.097) for <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">HK</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> and <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">HK</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> , respectively.