Physical Properties of Radio Stars Based on LAMOST Spectral Survey

: Radio emission has been detected for all types of stars in the Hertzsprung Russell diagram. Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) low and medium-resolution spectroscopic surveys provide a good opportunity to obtain the spectroscopic properties of radio stars. We cross-matched big data from the LAMOST DR7 low resolution spectral survey with a catalogue of radio stars, and obtained 449 stellar spectra of 258 stars. We detected 185 spectra with H α emission. There are a total of 108 objects with repeated low resolution spectral observations, of which 63 show variations in the H α line over a long time, about several months. We cross-matched LAMOST DR7 medium resolution spectra with the radio star catalogue. We obtained 1319 LAMOST medium-resolution spectra of the 156 radio stars and then calculated their equivalent widths ( EWs ) of the H α line. Among them, 93 radio stars with H α emission were found from the LAMOST medium resolution spectra, and 63 objects showed short and long-term variabilities, especially on a short time scale of approximately 20 min. Finally, we estimated the minimal detectable radio ﬂux of the FAST telescope and provided a scientiﬁc plan for studying radio stars.


Introduction
Radio waves have been detected in all types of stars across the Hertzsprung-Russell (HR) diagram [1,2]. Radio stars are defined as stars with continuum radiation at the radio wavelength. Radio emission has been detected from the accretion disks of young stellar objects [3], star-planet interactions between host stars with extra-solar planets [4], magnetic activity in T Tau stars [5], ultracool dwarfs [6], low-mass [7] and RS CVn stars [8], and binary interactions in eclipsing binary systems [9]. Thermal or non-thermal physical processes explain such detection. The most direct probes of physical non-thermal processes are stellar magnetic field activities or shock, wind-wind interaction, jets, stellar pulsation, particle acceleration, and energy release on stars. Thermal radio emissions include mass transport, stellar wind outflows, and circumstellar disk emission [2]. Bai et al. (2012) [10] used a 25 m radio telescope in Urumqi, China and made continuum and polarization observations on two RS CVn binaries, V772 Her and Beta Per. They detected two radio flares and determined their polarization fractions. The detection of radio emissions from nearby stars is one of the earlier scientific projects of the Five-Hundred-Meter Aperture Spherical Radio Telescope (FAST) [11,12]. Observations of radio stars can both enrich our understanding of their physical parameters and active phenomena and promote the development of stellar theory in the radio domain with cm wavelengths.
Wendker [13,14] released an updated catalogue of 3699 single radio stars and binary systems. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) has recently offered stellar parameters from low and medium-resolution spectra [15][16][17], which are extremely useful for studying the chromospheric activity of solar-like stars and other chromospheric active stars in the Hα and Ca II IRT lines [18][19][20][21][22]. Zhang et al. (2017) [23] analyzed 147 spectra of 89 active radio stars in the catalogue of radio stars using the LAM-OST low resolution survey DR2. They found that 28 stars exhibited long-term variation of chromospheric activity among 36 objects. Gizis et al. (2002) [24] and Lee et al. (2010) [25] found that approximately 30% of low mass stars showed variations in the Hα emission in short time scales of minutes to hours. In this study, we determined the nature of the physical parameters and optical properties of radio stars using LAMOST, particularly the time series of medium-resolution spectra. The relationship between the optical and radio wavelengths of nearby radio stars should be determined in the future.
The remainder of this paper is organized as follows. Based on the LAMOST low and medium resolution spectral surveys, we provide updated parameters of radio stars in Section 2. Then, we analyze the spectroscopic properties and variations in the Hα line in Section 3. Finally, we discuss the variation in the Hα line and provide an observational plan of the FAST telescope in Section 4.

Data
LAMOST is a reflecting Schmidt optical telescope with an effective aperture of 4 m and a field view of approximately 5 square degrees which is operated by the National Astronomical Observatories of China (NAOC); it is designed for low-and medium-resolution spectroscopic surveys [26,27]. In 2018, it was used to obtain a time series of the mediumresolution spectral survey [28]. More than 9.16 million LAMOST stellar spectra with a signal-to-noise ratios (SNR) above 10, and 6.20 million stellar parameters, were published on 30 June 2019 from the low resolution LAMOST DR7 [15,17]. There are two observational modes for the surveys of the LAMOST medium resolution spectra, namely, non-time domain and time-domain modes. A total of 0.67 million spectra of 0.51 million stars with an SNR of above 10 have been reported, and 0.51 million stellar parameters have been published as non time-domain data under the medium resolution. In addition, there are 1.61 million spectra of 0.29 million objects with SNR above 10. In total, 2.28 million spectra with an SNR above 10 and 0.81 million stellar parameters have been published. A standard reduction process was used to obtain the stellar parameters (e.g., the effective temperature, surface gravity, and metallicity) [15,29].
The LAMOST low-and medium-resolution spectra provide useful information for studying the chromospheric activity and parameters of radio stars. We cross-matched the LAMOST DR7 catalogue with the radio stars which were detected at least once and those with upper limits [13,14]. We obtained 449 stellar spectra of 258 radio stars with an SNR greater than about 10. We have listed the parameters of all the spectra of the radio stars in Table 1 and the repeated observations in Table 2. We have listed the LAMOST name (first column), number of radio stars (second column), other names (third column), observational HJD date (fourth column), exposure time (fifth column), spectral type (sixth column), and SNR using an R filter (seventh column). In addition, we cross-matched the radio stars with the medium spectra of LAMOST DR7. We obtained 1319 stellar spectra of 156 radio stars with an SNR above 10. In Table 3, we have listed the LAMOST name (first column), radio star number (second column), other names (third column), HJD (fourth column), exposure time (fifth column), and SNR (sixth column). We have listed only those parameters important for radio stars.  We list several parameters of radio stars with repeated observations. All parameters are available in the online journal. There may be multiple mechanisms for Hα line on radio stars, which are from the published paper [13,14] and our data. The cause of the Hα emission can not be ascertained, and needs more data prior to confirmation. Here, we list several parameters of radio stars. All parameters are available in the online journal.

LAMOST Low-Resolution Spectroscopic Analyses
For the LAMOST low resolution spectra, we obtained the continuum using the two sides of different chromospheric active indicators based on the Hammer program, which was published in 2007 [30,31]. The regions of these two sides of these indicators are listed in previously published papers [31,32]. We used a similar method to reduce the spectra from the LAMOST survey [15]. This method has previously been used to reduce the SDSS spectra by other astronomers [33]. The published LAMOST radial velocity was used to revise the spectrum and determine the position of the Hα line. We calculated the equivalent widths (EWs) in the Hα, Hβ, Hγ, Hδ, and Ca II H&K and IRT lines using the integration method within the region of ±10 Å around the core of the spectral lines. Simultaneously, we used the Gaussian function to fit the Hα line and obtained the Hα EW. The EW difference between the two methods is the uncertainty of the Hα EW. We listed the EWs (eighth column) and heights (ninth column) of Hα. Using the EWs of the Hα indicator, we determined the behavior of the absorption or emission (10th column). For the OBAFGK stars, we used the criterion of EW 0 Å. If the EW value of the Hα line was above 0 Å and simultaneously larger than the errors and the value of the height of the Hα line was three times larger than the standard error [34], we considered the behavior of the Hα line to be emission. However, the EW must be larger than 0.75 Å, because there are numerous molecular lines for M-type stars [23,31]. We have listed the EW of Hβ in the 11th column of Table 1 and the radio intensities at 4.8 GHz and 23 GHz in the 12th and 13th columns of Table 1. The printed versions of the tables include other values of all active chromospheric active indicators, and will be made available in the online database at the CDS. Among the 150 radio stars with single spectra, 77 radio stars had emissions. Several examples of radio stars with single spectra are plotted in the left-hand panels in Figure 1. There are obvious emissions of the Hα, Hβ, Hγ, Hδ, H8, Ca II H&K and IRT lines. In addition, there are 299 spectra of 108 objects with repeated observations of radio stars. Similar to Table 1, we list the parameters of the radio stars with repeated spectra in Table 2. The amplitude of the Hα EW variability is three times larger than the error, and we considered the radio star as a variable [23]. Among them, 69 objects show a long time variation in their Hα intensity. We plotted two examples and marked different chromospheric activity indicators in the right panels of Figure 1. In the small window of the right panel, the details of the Hα variation are clearly presented.

LAMOST Medium-Resolution Spectroscopic Analyses
For the total coadd spectra from LAMOST medium-resolution spectra, cosmic rays have been reduced. To discuss the variation in the Hα line of the radio star on a short time scale of approximately 20 min, we used the single exposure spectra. However, there are cosmic rays in these single spectra of the DR7 released data of the LAMOST. First, we needed to detect and remove the cosmic rays from the single exposure spectra. We calculated the ratio of the data above the mean of the surrounding wavelengths. If there were typical values five times or higher than the standard deviation of the background, we considered the points as cosmic rays and removed them for numerous runs. The detected cosmic rays were replaced by the average value of the neighboring pixels. Multiple detection passes are required to detect and replace cosmic ray events. As there are many repeated observations for LAMOST medium spectra, we reduced the cosmic rays using the cross-judgement method. In Figure 2, we provide several examples of the observed medium-resolution LAMOST spectra with cosmic rays (left) and the results of our reduction with no cosmic rays (right). We obtained the continuum spectra of the radio stars by 5or 6-order polynomial function fitting and normalised spectra after normalisation. We plotted the observed (right panel) and normalised (left panel) LAMOST spectra, as shown in Figure 3. The methods used for obtaining the EWs and their uncertainties were similar to those reported by Zhang et al. (2020) [21].

Comparison between Low-Resolution and Medium-Resolution LAMOST Spectra
By cross-matching the LAMOST low-and medium-resolution catalogue of radio stars, we found 102 objects with both low and medium resolution spectroscopic observations. Figure 4 shows several examples of FP Tau, FX Tau, DL Tau, and DM +25 1065 with two spectral observational modes. In Figure 4, it can be seen that there is a single peak emission of the low-resolution spectra. However, there are two or more peaks in the mediumresolution spectra because of the higher resolution of 7500. These emissions are caused by the substructures of the stellar disk, different regions of the chromospheric active region, or different components of binaries. Medium-resolution spectra are extremely important for investigating the details of spectroscopic binaries and special physical phenomena.    Figure 6. The variation in the Hα EW is shown in the right panel of Figure 6. We can observe the increase and decay phases of the Hα variation. Similar to Figure 6, we show examples with obvious long-term variations in the EW of the Hα line in Figure 7. More data on the Hα intensity are required to detect the chromospheric activity cycle in the future.

Discussion and Conclusions
We have investigated the Hα behavior of the detected radio stars and discussed the properties of short and long-term variations. We have additionally considered the radio stars in the observational region of the FAST.

Behavior of the Hα Line and Variation
We detected 449 low-resolution spectra for 258 objects. There were 185 objects with emissions above the continuum of the Hα line. There were 108 objects with the repeated observations, with 63 objects exhibiting long-term variations. We additionally obtained 1319 LAMOST medium-resolution spectra of 156 radio stars. Comparing the low-and medium-resolution LAMOST spectra, the medium-resolution spectra show more detailed behaviour. There are 93 radio stars with medium-resolution spectra with Hα emissions. Among them, 63 objects exhibited short-and long-term variability, particularly at a short time scale of approximately 20 min. The properties of Hα emission and spectral line variation of the radio stars are due to different physical mechanisms, including photo-star disks, stellar activity, and binary systems. For our data, we have provided the possible mechanism in the last columns of Tables 1 and 3. The cause of the Hα emission cannot be ascertained in the present paper, as we need more data to confirm it.
Most of our objects are young stars (such as FP Tau, FW Tau, DH Tau, HBC 230, etcetera). For young objects, the Hα emission can be explained by strong stellar winds, circumstellar discs, and outflow activity [35][36][37]. For solar-like and cool dwarf stars (such as UX Com,...), the short and long-term variations are due to magnetic phenomena. The short term variations can be explained by chromospheric activity of plages or flares, prominence, post-flare loops, and other chromospheric activity phenomena [38]. Several of our objects are eclipsing binaries, such as AC Cnc, DM +16 516), in which case the variations are caused by the activity of the two components or their interactions [39]. The chromospheric variation might be explained by orbital phase modulation of chromospheric emission [39] or chromospheric activity longitudes [40]. Long-term chromospheric variation was found on RX J0437.4+1851A and JH 56, which was explained by stellar Hα activity evolution [41]. As data from the time series LAMOST medium-resolution survey accumulated, we were able to detect the chromospheric activity cycles. There is an obvious EW decrease for CY Tau and an EW increase for BP Tau in the short time scales in Figure 6. If the intensity of the Hα emission shows a rapid increase followed by a gradual decrease, the phenomenon might be due to a flare event [42]. We expect to search for flare events with rise and decay in the future.
There were numerous objects (FP Tau, FX Tau, FQ Tau, DM +25 1065,...) observed in the low and medium-resolution spectral surveys. The medium-resolution spectra are more detailed than the low resolution spectra. We can see self-absorption in the Hα emission of early stars in Figure 4, which might be caused by accretion and outflow regions of circumstellar discs [43]. While we were able to confirm that the disks were more complex [37], we need more spectral data on the complete orbital phases to determine the disk structure. Meng et al. (2021) [44] identified two emissions from the primary and secondary components of eclipsing binary 2MASS J04100497+2931023 using the LAMOST medium spectra. This binary with both blended emissions and double Hα emissions might be caused by the two components of the active binaries [45]. The medium LAMOST spectral survey only started a few years ago, and thus the data for each object are insufficient. Here, we provide the complex and detailed theoretical mechanism and discuss the relationship between the optical and radio radiation.

Observational Plan of Radio Stars Using FAST
Wendker [13,14] published an updated catalogue of 3699 radio stars or binary systems. Owing to its excellent radio detection capability, we anticipate using the FAST telescope to observe radio stars, especially the nearby radio stars, in the future. Our project is dedicated to revealing the nature of radio emissions. Based on the latitude coverage of the sky from −14.6 to 65.6 Dec for FAST, we plotted the distribution of the radio stars in Figure 8, where the red points are within the observation region of FAST. The formula for the minimal detection flux density of the radio telescope is as follows: where K is the Boltzmann constant, K = 1.38 × 10 −23 erg/k, T sys is the telescope system temperature, T sys = 27 k. η is the aperture efficiency of the telescope, η min = 0.55. A is the effective aperture area of the radio telescope (the effective aperture area of FAST is 300 m in diameter), η p is a fixed value, η p = 2, ∆ bandwidth is 500 MHz, t is the sampling time, and we take t = 1 s. Based on these parameters [46], we can estimate the minimal detectable radio flux (S min ∼ 60 µJy) of the FAST telescope. We compared the flux of radio stars at 1.4 GHz with the minimal radio observational flux of FAST. We show the observational ability of FAST in Figure 9, where the horizontal axis is the number of radio stars in descending order of declination and the vertical axis is the intensity of the radio stars. For data points, the magenta five-pointed stars represent the real value of the radio flux, the green circles represent the upper limit of the radio flux, and the red line represents our estimated limit of the radio flux of FAST. It can be seen that FAST can theoretically detect the flux for the samples of radio stars above the limited line. In addition, the detection frequency band of the FAST telescope is limited to [47] (70 MHz∼3 GHz), and the limitation of the observation sky is Dec: −14.5∼65.6. We were thus able to obtain samples from the yellow region, as shown in Figure 9. The horizontal axis represents the serial number according to the size of the declination of the radio stars. The red dots in Figure 9 are above the detection limit of FAST, and are thus easy to detect. For the green points, the maximum possible value of the radio stars is above the detection limit of FAST, and we thus need to use FAST to conduct further validation checks. We have listed these in Table 4, as they are likely to be detected by FAST.   Figure 9. Distribution of the radio flux of radio stars in the 1.4 GHz frequency; the red line is the detection limit of the FAST telescope.
We have selected several interesting candidates from among the radio stars, such as the active stars from the LAMOST survey [21], ultracool dwarfs [48], and host stars with an extra-solar planet [49]. We intend to trace them over 4-6 h using FAST [28] and then attempt to detect their possible radio radiations. We might detect flare events and star-planet and binary interactions [9]. In the future the study of radio stars will be able to use both FAST and the upcoming SKA platform [50]. We intend to study non-thermal radio emission due to shock acceleration from the wind collision region of massive stars, the high energy emission process of young stellar objects [51,52], the generation and dissipation of kG-strength magnetic fields of ultra-cool dwarfs [53][54][55], and stellar and planetary magnetosphere interactions [56]. FIn the future, we will analyze the relationship between radio radiation and stellar physical parameters, as radio and optical emissions are required to determine the relationship between chromospheric and coronal emissions. The use of the FAST, SKA, and LAMOST platforms has the potential to unlock a great deal of new science concerning radio stars.
Author Contributions: Conceptualization, L.Z.; software, Y.C., B.L. and Z.Z.; investigation, Q.P.; writing-review and editing, L.Z., X.L.H. and P.M. All authors have read and agreed to the published version of the manuscript.