Magnetic Activity of Millions of G-type Stars Based on the LAMOST DR10 Low-resolution Spectral and TESS Light-curve Surveys and the Future CSST Survey

The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) data release 10 (DR10) provides over 3 million G-type stellar spectra, which are important for the study of chromospheric activity of solar-like stars. We have used the iSpec program to perform spectral subtraction on the G-type stellar spectra obtained from LAMOST DR10 with a signal-to-noise ratio greater than 10. We have calculated the magnetic activity of G-type stars using Hα lines and analyzed the Hα variation. Among the more than 3 million spectra from more than 2.3 million stars, a total of 220,000 stars show excess chromospheric activity. There were a total of about 480,000 stars with repeated observations. About 390,000 stars were found to exhibit variations in the Hα line, and 14,000 stars showed changes in their radial velocity. By using the Gaia data, we determined the distances of these stars above the Galactic disk. We first concluded that the fraction of G-type active stars decreases with increasing distance above the Galactic disk. By using the Transiting Exoplanet Survey Satellite light curves, we obtained the effective fluctuation range of the light curve caused by the starspot and confirmed that there was a positive correlation between the starspot and chromospheric activity. We also concluded that RHα′ tends to be stable for Rossby number (Ro) < 0.13 and that RHα′ decreases as Ro increases in the region Ro ≥ 0.13.


Introduction
There are many stellar activity indicators, such as starspots, flares, chromospheric activity, and coronal mass emissions.Stellar activity is a common phenomenon in late-type stars that is affected by stellar magnetic fields, rotation, and convection.These activity indicators are related to processes like acoustic wave heating, magnetohydrodynamical convection, and magnetic reconnection (Parnell & De Moortel 2012;Charbonneau 2014).Such processes are closely associated with the stellar dynamo (Parker 1955;Babcock 1958;Middelkoop 1982).The study of stellar activity indicators is crucial for advancing the stellar dynamo theory.
There are many well-known indicators of stellar chromospheric activity, which include the presence of Ca II H and K lines (Saar & Schrijver 1987), Ca II infrared triplet (IRT) lines (Soderblom et al. 1991(Soderblom et al. , 1993)), and the Hα line (Hirayama 1974).Emission and absorption features in these lines are closely tied to the stellar effective temperature (T eff ), which greatly affects their states (Schrijver et al. 1989).Noyes et al. (1984) introduced the R HK ¢ parameter based on the Ca II H and K lines, unaffected by T eff , to obtain chromospheric activity.This parameter was similarly applied to the Hα emission lines (Soderblom et al. 1993;Hawley et al. 1996), which provided a more precise indicator of chromospheric activity.Skumanich (1972) established the age-rotation-activity relationship using Ca II H and K lines, suggesting a strong link between chromospheric activity and stellar age and rotation.This relationship was extended to the Hα line; Herbig (1985) analyzed the Hα emission flux of the F8-G3 main-sequence stars by subtracting the low-activity standard star spectra, which demonstrated a decay in the Hα emission intensity with age and were characterized by a power-law index of around −0.4.Pasquini & Pallavicini (1991) studied the effects of the absolute fluxes of Hα and Ca II H and K lines on G-and K-type stars and found that the fluxes of these two chromospheric activity indicators were higher on colder stars.They also found that the increase in the Hα intensity was slightly slower than that of the Ca II H and K intensity.In addition, they found that the flux of giant stars was significantly lower than that of dwarf stars.Delfosse et al. (1998) investigated the Hα, Hβ, and X-ray emissions of 118 M-type stars, which indicated that there was significant excess emission associated with fast-rotating stars.Reiners et al. (2012) explored projected rotational velocities, V sin i, and Hα emission in 206 M-type stars, which confirmed the relationship between stellar rotation and activity in both partially and fully convective stars.Several studies, such as those by Rebassa-Mansergas et al. (2013), Douglas et al. (2014), Newton et al. (2017), and Zhang et al. (2019), observed age-activity or rotation-activity relationships using the Hα emission.Noyes et al. (1984) used the Ca II H and K line to discuss the relationship between chromospheric activity and the ratio of the rotation period and the convective overturn time, i.e., the relationship between chromospheric activity and Rossby number (Ro).By using the Hα emission line, Reiners et al. (2009) discovered that the relationship between Ro and the intensity of the chromospheric activity exhibited two distributions.In an unsaturated state, when the value of Ro is greater than 0.1, the stellar activity decreased with an increase of the Ro value, while in a saturated state, when Ro is less than 0.1, the stellar activity did not change with Ro.
Due to the advent of the era of astronomical big data, such the Sloan Digital Sky Survey (SDSS; York et al. 2000), Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Su & Cui 2004), Kepler (Koch et al. 2010), and Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2014), we are now able to perform large-sample studies and determine the precise statistical properties of stars.West et al. (2004West et al. ( , 2006) ) utilized the Hα line from the SDSS data to investigate the chromospheric activity of M-type stars.They found that the activity decreases with increasing distance from the Galactic disk.Zhao et al. (2013) studied high signal-tonoise ratio (S/N) spectra of over 13,000 FGK-type stars by using the Ca II H and K lines in the SDSS data and found lower S HK indices for subgiants and higher activity in cooler stars.They also concluded that the activity of K dwarf stars decreases with increasing distance from the Galactic disk.Zhao et al. (2015) investigated activity in nearly 120,000 FGK-type stars using LAMOST and SDSS data and discovered that the activity-Galactic disk distance correlation disappears at temperatures above 5500 K. Zhang et al. (2020) derived the brightness variation amplitude due to the starspot coverage modulation (R eff ) from the Kepler light curves and R HK + from the LAMOST spectra of the FGK-type stars, which confirmed that both chromospheric and photospheric activity depended on stellar rotation.For the F-, G-, and K-type stars, many astronomers have used the Ca II H and K lines to study chromospheric activity (Zhao et al. 2015;Zhang et al. 2020).However, the Hα line, as one of the important indicators of stellar chromospheric activity, still has research significance (Linsky 2017).By employing the Hα line as a stellar activity indicator, we used the spectral subtraction approach of Herbig (1985) to comprehensively investigate chromospheric activity on millions of G-type stars from the low-resolution survey released by LAMOST data release 10 (DR10).We have divided our study into five sections in this paper.We introduce the LAMOST and TESS data in Section 2. In Section 3, we describe the data processing methods, and in Section 4, we analyze the chromospheric activity in millions of G-type stars.Finally, in Section 5, we provide a summary of our results.

LAMOST Spectra
LAMOST is a new reflective Schmidt telescope located at the Xinglong Observation station of China.It has a large field of view of 5° (Deng et al. 2012;Luo et al. 2012Luo et al. , 2015) ) and an effective aperture of 3.6-4.9m (Wang et al. 1996;Su & Cui 2004;Cui et al. 2012;Zhao et al. 2012).LAMOST is equipped with a total of 16 spectrometers, each consisting of 250 optical fibers (Xing et al. 1998), which can record the spectra of 4000 celestial bodies simultaneously.The spectral observations of LAMOST are mainly divided into two modes.One is the low-resolution observation mode, with a resolution of about 1800 and coverage bandwidth of 3700-9000 Å.The magnitude of the low-resolution survey was in the range 9-17.8 mag for the r band (Cui et al. 2012).The other is the medium-resolution observation mode, with a resolution of about 7500 that covers two sections of widths 4950-5350 and 6300-6800 Å (Liu et al. 2020).The magnitude of the mediumresolution survey was 9-15 mag in the r band.The LAMOST DR10 survey has released a total of 11,817,430 low-resolution spectra and 10,486,216 medium-resolution spectra.

LAMOST Data and Analysis
In the present study, we have utilized the low-resolution spectral data of LAMOST DR10 to study the chromospheric activity of G-type stars.Due to the large number of LAMOST spectra and the abundance of available data, in order to obtain more accurate data and results, we screened the S/N of the data.In this work, we have mainly studied the relationship between Hα emission lines and the stellar chromospheric activity.The center wavelength of the Hα emission line is 6562.8Å, which is in the r band.In order to obtain more accurate data and consistent results, we selected the spectral data with S/N r 10 as our objects for investigation.In Figure 1, we display the statistically analyzed S/N of each band of ugriz provided by the LAMOST data.The five panels on the left show results with S/N from 10 to 100 in intervals of 10.The right panel shows the corresponding S/N distribution from 100 to 800 in intervals of 100.We have removed the data with S/N r < 10 during the statistical process.Eventually, we obtained about 3.06 million spectra from about 2.3 million stars.Among them, there are about 480,000 stars with repeated observations, with a total of 1.2 million spectra.The distribution of our samples in Galactic coordinates is shown in the left panel of Figure 2. The right panel plots their corresponding positions in the Galaxy by using the Gaia DR2 We have listed the stellar parameters of our samples, such as radial velocity (RV), surface gravity ( g log ), effective temperature (T eff ), and metal abundance ([Fe/H]), in Table 1.In the right panel of Figure 3, we have plotted the statistical results and error distribution of the different atmospheric parameters obtained by the Laboratory for Atmospheric and Space Physics (LASP; Luo et al. 2015;Wang et al. 2019).The statistical results of atmospheric parameters are akin to trends observed in previous statistical analyses of stars with repeated spectra (Long et al. 2021).In order to compare the Gaia DR3 and the LASP stellar parameters (T eff , RV, and g log ), we have plotted the relationship between Gaia DR3 and LAMOST in Figure 4.These stellar parameters are consistent with each other.Figure 5 shows the Hertzsprung-Russell (H-R) diagram for our sample.Since our sample only involves G-type stars, the figure includes the parts near the G-type stars in the H-R diagram.We have obtained the data for the top panel using Gaia DR3.Gaia DR3 provided us with G-band magnitude, parallax, and BP-RP colors.We have calculated the absolute magnitude M G using the following formula (Pogson 1856): where m G is the apparent magnitude, and Plx is the parallax in milliparsecs.In Figure 6, we show the relationship between the errors of the different parameters and the corresponding S/N.The left panel shows the relationship between all data with S/N r 10 and the associated errors.The red dots in the figure show the results obtained by taking the median value for every 10 S/N.At S/N < 80, the errors of various atmospheric parameters significantly decrease as S/N increases; beyond S/N = 80, the errors appear to stabilize.The RV also shows an initial decrease and subsequently exhibits a flattening trend as the S/N increases, but the decrease is not significant.Akin to Ding et al. (2022), we have classified the number of errors with S/N between 10 and 160 into different T eff regions and    (This table is available in its entirety in machine-readable form.)plotted the results in the right panel.We divided the groups into different parts for every five S/N, whereby the midpoint represents the median of each part.The right panel of Figure 6 shows the relationship between the errors of different atmospheric parameters and the S/N for three different temperature ranges in small boxes.The error trends of the atmospheric parameters for the different temperature regimes are consistent with each other.

TESS Light Curve
TESS is a space telescope launched by NASA with a main scientific objective of searching for transit phenomena to discover new exoplanet systems.TESS primarily selects stars with magnitudes below 13 as its observational targets (Kossakowski et al. 2019).It has observed over 200,000 bright stars in the nearby sky and obtained nearly 1 million light curves, which include 2 minute and 20 s cadence data.We have used the TESS 2 minute light curves and calculated the brightness variation amplitude due to the starspot coverage modulation (R eff ).We extracted the observational coordinates of each light curve from TESS and performed crossmatching with the coordinates of the G-type star sample from LAMOST DR10 using Topcat.Stars within 2″ are considered as the same source.If multiple data points can be matched within 2″, we consider the brightest source as the one observed by TESS.By crossmatching the millions of G-type stars from the LAMOST low-resolution survey and the TESS 2 minute data in the first 62 sectors, we have obtained a total of about 23,000 light curves from about 15,000 G-type stars.

iSpec
iSpec is an automated spectral processing software to determine stellar atmospheric parameters and elemental chemical abundances, which include spectral normalization, reducing spectral resolution, RV measurements, telluric line identification, equivalent width (EW) calculations, spectral synthesis and subtraction, etc. (Blanco-Cuaresma et al. 2014;Blanco-Cuaresma 2019).We have used iSpec for spectral trimming, selecting to identify the core of the line and the line width, continuum fitting, and calibration of the RV.These operations are applicable to low-, medium-, and high-resolution spectra.The calculation of EW is carried out in a similar manner as in Su et al. (2022) and Zhang et al. (2023).

Template
To analyze stellar activity based on the spectral subtraction method, we need a library of standard stars as a template with different stellar parameters.As we all know, there are many stellar spectral template libraries, such as UVES-POP (Bagnulo et al. 2003), INDO-US (Valdes et al. 2004)  (Prugniel & Soubiran 2001), etc. Due to differences in wavelength coverage, inconsistency in atmospheric parameter coverage, and varying resolutions across different surveys, it is necessary for us to select a template that is suitable for the LAMOST low-resolution survey.Ultimately, we selected the template library developed by Du et al. (2019) based on LAMOST DR5 data.The T eff range of this template covers 3700 to 8500 K with intervals of 150 K, g log ranges from 0 to 5 with intervals of 0.25 dex, and [Fe/H] ranges from −2.5 to 1.0 with intervals of 0.15 dex.This approach completely covers the parameter space of G-type stars.For each spectrum, we can then find the corresponding template to fit from the template library.

Spectral Subtraction
In the present work, we did not use the complete lowresolution wavelength range of LAMOST and only used the region of the Hα line corresponding to stellar chromospheric activity.According to the procedure adopted by Xiang et al. (2022), we first selected the wavelength range 6370-6770 Å of our objects for spectral subtraction.The resolution of the spectrum was fixed to 1800 using iSpec.Subsequently, the spectra were normalized by a polynomial fit to the observed continuum.During the continuum process, we did not use the core range of Hα lines from 6552.8 to 6572.8 Å in order to avoid the influence of the strong Hα emission line on the continuum normalization fitting.Next, each observed LAMOST spectrum was matched with the standard spectrum using similar atmospheric parameters ( g log , T eff , [Fe/H]) and the optimal template chosen for spectral subtraction.In this method, the synthesized spectra were constructed from the artificial rotationally broadened RV shift of the standard spectra.After hundreds of runs, we found the best result with the smallest χ 2 .We show the spectral subtraction results of LAMOST J045614.62+101506.9 in Figure 7.The atmospheric parameters of this star are as follows: T eff = 5872, g log = 4.304, and [Fe/H] = 0.117.It is a typical mainsequence star.The results of the spectral subtraction indicate that the Hα line exhibits obvious emission.The panel in the top left corner of Figure 7 displays the results of the Hα spectral line at a resolution of 1800, which includes the observed spectra (blue line), synthesized standard spectra (red line), and subtracted spectra (green line).The subtracted spectra represent the excess chromospheric contribution of each G-type star.For some stars, there is an excess emission in form of the Hα line, which indicates that the chromosphere is active.

Hα EW Calculation
The Hα spectral line is one of the important indicators of stellar magnetic activity.We calculate the Hα EW using the subtracted spectra, which is the value of the EW H ¢ a introduced by Fang et al. (2016Fang et al. ( , 2018)).We have used the following formula to calculate EW H ¢ a (West et al. 2004): where F λ is the intensity of the Hα line and F c is the intensity of the continuum region on both sides of the Hα line.The error in EW H ¢ a was obtained using Monte Carlo simulation.A Gaussian distribution can be used to generate random values.
The random values of all data points within a 95% confidence interval were combined to form a simulated spectrum.We then generated 1000 simulated spectra and calculated the EW H ¢ a line from them.The standard deviation of these 1000 EW H ¢ a values was used as the final error.For the spectrum of R ∼ 1800, we used the region 6552.8-6572.8Å with a length of 20 Å as the Hα range, which is slightly longer than the region of 6562.8Å at two adjacent regions of the Hα center and 14 Å as the Hα center on M stars in West et al. (2004).This is because the Hα line of G-type stars is much stronger and wider than that of the M-type star.We used the two 50 Å regions of 6500-6550 and 6575-6625 Å on both sides of the Hα line as the continuum region, which is consistent with those of West et al. (2004) and Xiang et al. (2022).Finally, we obtained the EW H ¢ a of over 3 million spectra as chromospheric contributions and listed them in Table 1.Our criteria for judging active G-type stars are as follows.
1. Due to the low resolution of the spectra, the adjacent lines of the Hα line are affected, which impacts the uncertainty of the observational and synthesized spectra during the spectral subtraction operation.By plotting many subtracted spectra and inspecting them visually, we found that when EW H ¢ a is greater than 0.2, the spectral line emission can be seen in the subtracted spectrum.Thus, when EW 0.2 H  ¢ a , it indicates the presence of excess chromospheric emission in G-type stars.
2. The value of EW H ¢ a 3 × EW H ,err a ¢ .

The height of EW H
¢ a is greater than 2 times the standard deviation of both continuum regions of the Hα line.
Finally, we obtained a total of more than 220,000 spectra with chromospheric activity.These spectra are defined as active spectra.We calculated the fraction of active G-type stars and the corresponding stars present in different spectral subtypes of G-type stars and plotted the relationship of the fraction and G subtypes in Figure 8.It can be seen from this figure that the activity ratios of different G-subtype stars are similar.The activity ratios of all G subtypes are found to be stable at around 8%.

Hα Variability
The variability of the Hα line is significant for searching the stellar chromospheric activity cycle and exploring the relationship between the Hα emission and the stellar orbital phase and has been studied by Kruse et al. (2010), Lee et al. (2010), Bell et al. (2012), and Kumar et al. (2023).Due to the limitations of observational data, we consider the long-timescale variation of the EW H ¢ a line by using the LAMOST low-resolution repeated observations.Among our samples studied, there are 481,010 stars with at least two observations.For stars with two or more observations, we take into account the variability of the Hα emission line.The observational distribution is illustrated in Figure 9, where the left panel shows the statistical results with the observational times, of which 70.68% were only observed twice, 26.73% were observed 3-5 times, 1.7% were observed 6-10 times, and 0.89% were observed more than 10 times.The middle panel shows the EW H ¢ a distribution of the individual EW H ¢ a measurements of the subsample of stars with repeated observations.The right panel displays the distribution of δ EW H ¢ a , which represents the difference in the maximum EW H ¢ a and the minimum values of our objects with repeated observations.We have used the following formula to determine where σ is the Stefan-Boltzmann constant with a value of 5.6704 × 10 −5 erg s −1 cm −2 K −4 .Douglas et al. (2014) obtained F bol using the method of Walkowicz et al. (2004), which is slightly higher than the true value as seen by comparison with many works.Therefore, we utilized another commonly used method to obtain F bol using the function et al. 2008), which is consistent with the results of Douglas et al. (2014).To ensure the consistency of the results, we used the same spectral template as Douglas et al. (2014) to calculate the F Hα value.We calculated the F Hα of stars with different atmospheric parameters based on the PHOENIX ACES spectral template (Husser et al. 2013).We selected two adjacent regions near the Hα line as continuum windows (6500-6550 Å, 6575-6625 Å).
The PHOENIX ACES templates we used covered a T eff range of 3100-8400 K. Within this range, the interval is 100 K from 3100 to 7000 K and 200 K from 7000 to 8400 K.The g log covers 0-5 dex, with an interval of 0.5 dex.The [Fe/H] covers −3 to 1 dex, with intervals of 1.0 dex from −3 to −2 dex and 0.5 dex from −1 to 1 dex.By using this method, we obtained the χ for nearly 3000 spectra with different atmospheric parameters.Finally, the following formula was used to obtain R H ¢ a : Since we have already performed the spectral subtraction process for calculating EW H ¢ a , it can be directly used to calculate R H ¢ a .Fetherolf et al. (2023) determined the rotational periods on timescales of 0.01-13 days for over 80,000 stars using TESS data.The International Variable Star Index (VSX) is a continually updated and maintained catalog that has the basic stellar parameters listed, such as the period and variability type (Watson et al. 2006).Therefore, we crossmatched our samples with the VSX catalog (Watson et al. 2006) and the TESS variability catalog (Fetherolf et al. 2023) to obtain the stellar period.For crossmatching of the catalogs, we also adopted the range of 2″ as the same source.If there were multiple stars within 2″, we considered the brighter one to be the source we needed.To obtain the precise relationship between the period and R H ¢ a , we removed the binary stars from the VSX catalog that were marked with EA, EB, EW, RS, etc. in the VSX catalog, where EA, EB, and EW are different binary eclipses based on the shape division of the light curve.RS stands for RS CVn binary.RS CVn binary systems are characterized by an active chromospheric component, typically a subgiant or giant star, and a smaller companion star.The relationship between the period and R H ¢ a is shown in Figure 13.Stellar activity tends to stabilize if the period is less than 3 days.For stars with a rotation period greater than 3 days, the stellar activity gradually decreases with an increase in period.

Starspots
It is well known that starspots are also an indicator of stellar magnetic activity phenomena.Notsu et al. (2015) found that the variation in stellar brightness is closely related to the intensity of the Ca II IRT lines, while Karoff et al. (2016) found that the S HK values obtained from Ca II H and K lines are positively correlated with the variation of stellar brightness.He et al. (2015) introduced the R eff of light curves to describe the activity of starspots.Our work investigated the relationship     between the intensity of the Hα line and R eff .We crossmatched the LAMOST spectral survey with the TESS data to obtain the light curves of G-type stars.We used an approach similar to He et al. (2015) to calculate the effective range of the light-curve fluctuation caused by a starspot.First, the TESS light curves are simply reduced to obtain a set of relative fluxes, where F i is the value of each point in the light curves.F med is the median value of the light curves.Next, we performed a low-frequency filtering based on Fourier transformation to remove the high-frequency noise in F i .We also obtained the cutoff frequency of the filter based on the empirical formula (He et al. 2015;Mehrabi et al. 2017;Zhang et al. 2020) f P  where P rot is the period of stellar rotation obtained from the VSX star catalog.Finally, the brightness change of the light curves is given by the following formula: where f rms is the rms value of the relative flux for each star required to remove noise (García et al. 2010;Chaplin et al. 2011) and 2 is the correction introduced by He et al. (2015).We plotted the relationship of R eff and stellar T eff in the left panel of Figure 14, where it can be seen that R eff decreases as stellar temperature increases.Therefore, colder stars would exhibit stronger stellar magnetic activity, while hotter stars exhibit lower magnetic activity.At the same time, we have plotted the relationship between R H ¢ a and R eff in the middle panel of Figure 14.We found that there is a positive correlation between R eff and the Hα intensity.Our results are similar to the relationship observed between the chromospheric activity S HK and R eff of solar-type stars based on the LAMOST and Kepler surveys (Zhang et al. 2020).Our results are also consistent with those based on the LAMOST DR7 survey and the top 30 sectors of TESS (Zhang et al. 2023).It is well known that there is a close correlation between the stellar magnetic activity and the stellar rotation period.For example, Zhang et al. (2020) used the parameter S HK and found that the S HK activity of F-, G-, and K-type stars decreases as the rotation period increases.The right panel of Figure 14 shows the relationship between P rot and R eff in our sample data.The following formula is the basis for fitting the lines in Figure 14  When the stellar rotation period is greater than 3 days, R eff decreases with an increase in stellar period.When the rotation period is less than 3 days, starspots hardly vary with a change in period.The trend of our sample is consistent with the results reported by Zhang et al. (2020).The power-law index of our result is β = −1.52 ± 0.10, and their result is −3.64 ± 0.01 (Zhang et al. 2020).The difference might be caused by the following reasons.The duration of the light curve of the Kepler mission is longer, about 90 days, while the duration of the TESS mission is about 27 days.The first reason is that the rotation periods of the Kepler samples are generally longer than those of the TESS sample.For example, the median value of the stellar rotation period of the Kepler sample is 5 days, and the mean is 12 days, while the median of the period of our TESS sample is 3 days, and the mean is 5 days.Second, the observational wavelength of TESS is 600-1000 nm, while for Kepler, it is 420-880 nm.

Rossby Number
In addition to stellar rotation periods, several studies suggest that the magnetic activity of late-type stars is caused by differential rotation in the latitude direction and a spiral effect in the radial direction (Mohanty & Basri 2003;Pizzolato et al. 2003), which is known as the α-Ω dynamo model (Babcock 1961;Leighton 1969).Therefore, the convective turnover time τ is also an important indicator of magnetic activity.The value of Ro is defined as the ratio between the rotation rate and the convective turnover time, i.e., Ro = P/τ (Noyes et al. 1984;Maggio et al. 1987;Montesinos et al. 2001), where P is the rotation period obtained from the VSX catalog and τ is the convective turnover time.However, due to the difficulty in obtaining τ, Wright et al. (2011) provided an empirical formula to derive τ from the stellar mass and revised it in Wright et al. (2018): We calculated the Ro value for a total of 14,000 stars.Previous studies have shown that Ro is typically divided into two intervals: saturated and unsaturated.In the saturated regime, the Ro value corresponds to a constant level of stellar activity.However, in the unsaturated regime, the level of stellar activity varies with changes in the value of Ro.The critical point separating the saturated and unsaturated regimes is commonly considered to be when Ro = 0.1 (Douglas et al. 2014;Zhang et al. 2023).Therefore, based on the characteristics of Ro and the stellar activity, we adopt the following fitting scheme for the relationship graph between Ro and R H ¢ a : where Ro sat represents the turning point between saturation and unsaturation.In fact, it is controversial that the value of Ro sat is always around 0.1.For example, Newton et al. (2017) studied the relationship between Hα emission from nearby M dwarfs and stellar rotation.The best-fit results of Newton et al. (2017) showed Ro sat = 0.21 ± 0.02.Based on previous research, Ro sat is usually in the larger range between 0.1 and 0.3 (Newton et al. 2017;Fang et al. 2018).The value of Ro sat for the Hα line is about 0.19, and the Ro sat for the Ca II H and K lines was about 0.25 (Fang et al. 2018).In order to find a more suitable Ro sat , we referred to the method proposed by Fang et al. (2018) and did not use the χ 2 model to fit our sample data.We searched the best value of Ro sat from 0.1 to 0.3 in steps of 0.01.The final fitting results showed that β gradually decreased between 0.1 and 0.13 and gradually increased between 0.13 and 0.3.Therefore, the best-fit result for our sample is Ro sat = 0.  West et al. (2004) discovered that the proportion of M-type active stars decreases as the vertical distance of stars above the Galactic disk increases.In their article, they conducted a statistical analysis of stars located at a distance of 250 pc from the Galactic disk (West et al. 2004).West et al. (2008) used data from over 38,000 stars released by SDSS to investigate the activity proportion of M-type stars within 500 pc from the Galactic disk.The proportions of active stars generally decreased as the distance from the Galactic disk increased.Zhang (2021) studied 622,523 M-type stars from the LAMOST DR7 survey and found that the proportion of stellar activity decreases with increasing distance from the Galactic disk.However, for certain spectral types, the activity proportion does not consistently decrease with increasing distance from the Galactic disk.Furthermore, in the results of all the studies mentioned above, it is seen that within the range of 0-250 pc from the Galactic disk, there is a noticeable decrease in stellar activity as the distance from the Galactic disk increases.However, beyond 250 pc, this decreasing trend gradually diminishes and becomes more stable, with occasional instances of a slight increase in certain results.Zhao et al. (2013) studied the relationship between the activity of the K-type stars and their distance from the Galactic disk using the values of S HK .Their results did not include cases within 200 pc from the Galactic disk.However, beyond 200 pc, the K-type stars exhibited a trend where their activity proportionally increased with increasing distance from the Galactic disk.The peak of this activity proportion was observed at approximately 500-600 pc.However, beyond 600 pc, the activity proportion continued to decrease with further distance from the Galactic disk.
We investigated the distribution of the activity of G-type stars in the Milky Way and determined the relationship between the activity fraction and the distance above the Galactic disk.To obtain a more accurate relationship between stellar activity and distance from the Galactic disk, we selected data with S/N greater than 80 in the r band (see Figure 6).We calculated the position of stars in the Milky Way using Gaia data, and the specific results are shown in Table 3.We then divided the data into G0-G9 spectral types and obtained the proportions of active stars of different G spectral subtypes.The two-dimensional distribution of activity proportions is displayed in Figure 15.It is observed that almost every plot within 2 kpc from the Galactic disk shows a general decrease in the overall stellar activity proportion as the distance from the Galactic disk increases.The one-dimensional variation of activity proportions with Galactic disk distance is shown in Figure 16.For almost all results, the activity proportion shows a significant decreasing trend within the range of 0-400 pc, which is consistent with previous studies of M stars (West et al. 2004;Pineda et al. 2013) and K stars (Zhao et al. 2013).The activity fraction increases with radius and can be explained by a decreasing stellar age with increasing distance from the Galactic center (Pineda et al. 2013).Beyond 400 pc, the overall data and some spectral types continue to show a decreasing trend.However, the results of some spectral subtype stars exhibit a trend of initially increasing and then decreasing activity proportions between 400 and 600 pc, which is similar to the active fraction trend in K-type stars (Zhao et al. 2013).This phenomenon might be explained by the dynamics of the Galaxy.Widrow et al. (2012) discovered that stars have velocities perpendicular to the plane of the Galactic disk, gradually moving away from the Galactic disk.And the vertical velocity changes with the distance of the stars from the Galactic  disk.It is worth mentioning that Widrow et al. (2012) detected a small peak of the velocity at a distance of 500 pc from the north of the disk.Similarly, the peak also appeared in Lin et al. (2024), and there was also a peak near 300 pc in the south of the disk.This results in the age distribution of the stars in the Galaxy exhibiting oscillations in the region over 500 pc away from the north of the Galactic disk and in the region over 300 pc away from the south of the disk.This corresponds to an oscillation of the number density of young stars in the region about 400-600 pc.Therefore, the active fraction might be undergoing oscillations.More data and analysis are needed for confirmation.

Summary
In this work, we have used the LAMOST DR10 lowresolution spectra to study the chromospheric activity of more than 3 million spectra of over 2.3 million stars by using the spectral subtraction method and the Hα line.We obtained a total of over 270,000 G-type stars with marked chromospheric activity.We also found that the Hα EW H ¢ a of over 390,000 stars with repeated observations had variability, and the RV values of 14,000 stars exhibit variability as well.We found that the activity of the G-type stars is related to their rotation and convection.The activity of G-type stars decreases with an increase in their rotation period.The value of the R H ¢ a of G-type stars decreases as the Ro value increases in an unsaturated state and is stable with Ro in saturated states.We found that the stellar activity of G-type stars decreases as the vertical distance from the Galactic disk increases.This relationship is similar to the previously discovered decrease in activity of M-type and K-type stars with increasing distance from the Galactic disk.

Perspective
The Chinese Space Station optical Telescope (CSST) is a 2 m space telescope with a field of view larger than 1.1 deg 2 equipped with photometric multicolor imaging and spectroscopic slitless sky surveys (Zhan 2011;Gong et al. 2019;Yuan et al. 2021).CSST plans to publish high-quality low-resolution slitless spectra for hundreds of millions of targets with a limited magnitude of about 21 mag and a large survey area of about 17,500 deg 2 .The wavelength coverage range is 255-1000 nm, and the resolution is 200.In this work, we have used the LAMOST low-resolution spectra to simulate the CSST stellar spectra at R = 250 and investigated their capability to study chromospheric activity.We reduced the resolution of the LAMOST spectra to 250, obtaining a data set comparable to future CSST data, and processed the spectra of R ∼ 250 using the method proposed in the current paper.During the process of reducing the resolution, we referenced Xiang et al. (2022) and used the range of the Hα line between 6550 and 6575 Å.The upper right panel in Figure 7 shows the results of the same source at R ∼ 250, and the emission of the Hα line can still be seen.In addition to the Hα line, we also tested the other chromosphere activity indicators, the Ca II H and K line and the Ca II IRT line.For the Ca II H and K line, we selected 3968 and 3934 Å as the center wavelengths of the H and K lines, respectively, and 10 Å as the line width, and the results are shown in the middle panels of Figure 7.For the Ca II IRT line, the center wavelengths are 8498, 8542, 8662, and 15 Å for the line width.We plotted the values in the lower panels of Figure 7.There are also excess chromospheric emissions associated with the Ca II H and K line and the Ca II IRT line.In addition, to further assess whether CSST spectra can be used to study stellar chromospheric activity, we also reduced the resolution of all spectra with S/N r above 80 and calculated their EW H ¢ a values at a resolution of 250.In order to compare with each other, we plotted the measured EW H ¢ a values between the R = 250 spectra and the R = 1800 spectra in Figure 17.It can be seen from Figure 17 that there is a good linear relationship between the LAMOST 1800 resolution spectra and the simulated CSST 250 resolution spectra.This in turn means that the Hα line with a resolution of 250 can also be used to study stellar chromospheric activity.For the 250 resolution spectrum, we used the same criteria with the LAMOST spectra to determine whether it is active.Finally, we only detected about 1.44% of the active spectra using the simulated CSST 250 resolution spectra, which is lower than the value of 8% of the LAMOST 1800 resolution.In order to predict the number of observable active G-type stars in the CSST, we randomly selected 5 million stars from Gaia DR3 for prediction.Among them, over 94% of the stars have a G-band magnitude brighter than 21, which means that the number of stars observable by CSST in the same region is 94% of the total Gaia observations.Based on this proportion, it is estimated that the Gaia data contain approximately 1.7 billion stars with magnitudes brighter than 21.Gaia conducted observations across the entire celestial sphere, covering 30,000 deg 2 , with a strategy focused on the uniform distribution of stars on the celestial sphere.In contrast, CSST will observe approximately 17,500 deg 2 .Therefore, it is expected that CSST will observe around 1 billion G-band stars with magnitudes brighter than 21.We conducted a statistical analysis of all spectra from LAMOST DR10 and found that the G-type stars make up approximately 43.6% of the total sample.Thus, it is predicted that CSST will observe more than 400 million G-type stars.
According to the G-type star activity ratio determined in this work, it is estimated that CSST will detect approximately 5.7 million active G-type stars.

Figure 1 .
Figure 1.The left panels show the S/N distributions for G-type stars in the ugriz bands from 10 to 100 in intervals of 10.The right panels show the S/N distributions in the ugriz bands from 100 to 800 in intervals of 100.

Figure 2 .
Figure 2. The left panel displays the distribution of data with S/N r above 10 in LAMOST DR10 G-type stars.The right panel displays their spatial distributions in the Galaxy.

Figure 3 .
Figure 3.The left panel shows the statistical results of spectral subtypes for the sample.The number above each bin indicates the number of corresponding spectral subtypes.The right panel shows the statistical results of the sample atmospheric parameters and their errors.The parameters for both panels come from data provided by LAMOST DR10.

Figure 4 .
Figure 4. Comparison of stellar parameters T eff (left panel), g log (middle panel), and RV (right panel) between the LAMOST DR10 and Gaia DR3 data sets.The color bars of each panel represent the number density, where the density increases as the color changes from blue to red.The black line in each subplot represents x = y.

Figure 5 .
Figure 5. H-R diagram of the sample stars.The top panel is the color-magnitude diagram of our samples, where the color bar represents the number density.The lower left panel shows the position of each star on the H-R diagram, where the color bar represents the value of [Fe/H].The lower right panel shows the distribution of the sample density on an H-R diagram, where the color bar represents the count density.

Figure 6 .
Figure 6.The left panels display the relationship between the errors of different atmospheric parameters and S/N in the r band, where red dots represent the median values within each region with a bin of 10.The red dashed line in this panel indicates S/N = 80.The right panels show the relationship between the errors of different atmospheric parameters and S/N for three different temperature ranges in small boxes, where the points in the right panel are the median values of each bin and different colors represent the different temperature regions.

Figure 8 .
Figure 8.The fraction of active G-type stars in different spectral subtypes.

Figure 9 .
Figure 9.The left panel displays statistical plots of data with repeated exposure times, with the inset showing cumulative histograms.The middle panel displays the calculation of the EW H ¢ a of the sample.The right panel displays the distribution of δEW¢, and the inset shows the details in the larger EW¢.

Figure 10 .
Figure 10.The left panel shows the RV distribution for the entire LAMOST DR10 G-type star sample.The right panel shows the distribution of RV for the sample with multiple observations.The inset shows details of the data where RV is greater than 40.

Figure 12 .
Figure 12.Examples of G-type stars with variability in both EW¢ Hα and RV.The four groups of panels from left to right are normalized spectra, subtracted spectra, and EW¢ Hα and RV curves, respectively.The names of the three corresponding stars from top to bottom are LAMOST J085615.70+165152.6,J061921.71 +224432.3, and J085952.64+180053.3,respectively.

Figure 13 .
Figure 13.Left panel: the relationship between R H ¢ a and rotation period.The red point is the median value of each bin.Right panel: the relationship between R H ¢ a and Ro.The black dotted line represents the results of Newton et al. (2017), the blue dotted line represents the results of Douglas et al. (2014), and the red dotted line is the result of this work.The color bars in both panels represent the T eff scale.

Figure 14 .
Figure 14.The left panel displays the relationship between R eff and T eff .The middle panel displays the relationship between R H ¢ a and R eff .The right panel displays the relationship between period and R eff .

Figure 15 .
Figure 15.The two-dimensional distribution of the fraction of active G-type star in the Galaxy.Different panels represent different G subtypes.The color bars in the figures represent the proportion of active stars.

Figure 16 .
Figure16.The relationship between the ratio of active G-type stars and the distance above the Galactic disk.The error bars in these figures are 95% confidence intervals.

Figure 17 .
Figure 17.The EW H ¢ a relationship between the LAMOST 1800 resolution spectra and the simulated CSST 250 resolution spectra.The color bar represents the number density, where the density increases as the color changes from blue to red.
(Casagrande et al. 2008;Reiners et al. 2012;Fang et al. 2018;Long et al. 2021a , respectively.By employing the same method, we also calculated the variability of RV by using a formula similar to the one used to determine the variability of EW H ¢ a : Spectral subtraction results of J045614.62+101506.9 with resolutions of 1800 and 250.From top to bottom, these are the Hα, Ca II H and K, and Ca II IRT lines.The number distribution of RV is shown in Figure10.The left panel illustrates the number distribution of the RV on G-type stars with repeated observations, and the right panel displays the number distribution of the δRV values.We have used the δRV to search for the second or third bodies.Qian et al.Walkowicz et al. (2004)first introduced a method for calculating R H ¢ a independent of distance and introduced a factor χ.After that, many astronomers used χ to study chromosphere activity(West & Hawley 2008;Boyajian et al. 2012).We have used the following formula to calculate χ(Casagrande et al. 2008;Reiners et al. 2012;Fang et al. 2018;Long et al. 2021): (Hawley et al. 1996;Walkowicz et al. 2004;Douglas et al. 2014;Frasca et al. 2016inary candidates using LAMOST low-resolution spectra with δRV > 10 km s −1 .Mu et al. (2022)obtained 35 compact object candidates using δRV > 150 km s −1 of LAMOST DR5 low-resolution spectra and the TESS light curves.There are a total of 88,573 G-type stars with δRV > 10 km s −1 and 46 G-type stars with δRV > 150 km s −1 in our sample.We also calculated the coefficient of variation (CV) of EW H ¢ a and RV with repeated observation data.CV is a measure of evaluation of the degree of dispersion of the probability distributions.The CV is defined as the ratio of the standard deviation to the average value(Long et al. 2021).The results are shown in Figure11, where the left panel is the distribution of the CV of EW H ¢ a and the right panel is the distribution of the CV of the RV.Using Equations (eff .We obtained R H ¢ a by determining the ratio of the luminosity of the Hα lines to the bolometric luminosity using the following formula(Hawley et al. 1996;Walkowicz et al. 2004;Douglas et al. 2014;Frasca et al. 2016):

Table 2
Low-resolution Spectral Parameters of G-type Stars with Multiple Observations from LAMOST DR10