Search for GeV Gamma-Ray Emission from Possible TeV-bright Red Dwarfs with Fermi-LAT

Red dwarfs have been suggested to be among the possible astrophysical species accelerating particles and emitting TeV γ-rays. In an effort to search for the GeV γ-ray counterparts of the suggested TeV emission from eight red dwarfs, we analyze the 0.2–500 GeV γ-ray emission of the regions covering them, exploiting the ∼13.6 yr Pass 8 data from the Fermi Large Area Telescope (LAT). A GeV γ-ray emission excess with a significance of 3.8σ is detected in the direction of the red dwarf V962 Tau. This emission contains V962 Tau in a 1σ error radius and is independent of the catalog source. However, the stellar flare scenario can hardly explain the total energy and lightcurve (LC) derived from the γ-ray emission in view of the spectral analysis. We also analyze the LCs in the positions of the eight red dwarfs, and no time bin with a significance >5σ is found. Therefore, no significant emission from the red dwarfs could be concluded to have been detected by Fermi-LAT.


Introduction
A large number of studies have been conducted to understand the origin of cosmic rays (CRs) since their discovery (Ackermann et al. 2012;Banik & Ghosh 2022;Abe et al. 2023).Radio synchrotron radiation from supernova remnants (SNRs) proves that there are relativistic electrons that have accelerated in SNRs (Ginzburg et al. 1954), which means SNRs might be the potential source of Galactic CRs.However, whether SNRs are the primary place where the acceleration of Galactic CRs takes place is still ambiguous, although piondecay bumps, an important characteristic of the proton-proton interaction shown in γ-ray spectra, have been detected in SNRs (Giuliani et al. 2011;Ackermann et al. 2013).If Galactic supernovae solely sustain the observed CR energy density, they require energy conversion efficiency, with an energy ratio of CRs to the ejecta of supernova as high as 10%, which is yet unproven (Bell 2004;Strong et al. 2010;Vink 2020).Sources other than SNRs, such as stellar winds and flares, are also believed to be capable of accelerating particles to high energy (Benz & Güdel 2010).Some research has shown that large flares in the Sun can produce γ-ray emission with energy up to tens of MeV by bremsstrahlung from energetic particles (Lysenko et al. 2019) and >100 MeV by the decay of neutral pions (Omodei et al. 2018;Tang et al. 2018;Gopalswamy et al. 2020).
It has recently been reported that TeV emissions have been detected in the direction of the eight red dwarfs ranging from 800 GeV to ∼20 TeV in the SHALON long-term observations, and thus, red dwarfs are considered a possible origin of CRs (Sinitsyna et al. 2019).The red dwarf is a kind of mainsequence star, which is shown in the bottom right of the H-R diagram, with a mass of ∼(0.075-0.5)M e and a surface temperature of 2500-5000 K.Although red dwarfs have very low masses compared to the Sun, their stellar activities, M dwarfs in particular, are more frequent and violent due to the strong magnetic activity associated with their convective envelopes (Chang et al. 2017).It has been shown that the frequency of the occurrence of flares from Sun-like stars or M dwarfs can be characterized by the power law ~a dN dE E (Hilton et al. 2011;Yang & Liu 2019;Aschwanden & Güdel 2021) and vary by orders of magnitude for different activity levels.The total output energy of one flare in a red dwarf is 1032-1035 erg, thousands of times higher than that of a solar flare (Yang et al. 2017).Hence, it is plausible that red dwarfs, which are more active than the Sun, may be potential γ-ray sources.A powerful outburst from the flaring dwarf DG CVn has been detected by Swift with associated optical emission (Drake et al. 2014) and radio emissions (Fender et al. 2015).DG CVn has been observed with the Fermi-Large Area Telescope (LAT) at 0.1-100 GeV for possible γ-ray emission (Loh et al. 2017).Ohm & Hoischen (2018) simulate the expected GeV γ-ray emission from DG CVn using the X-ray properties of the superflare.Recent observation of the M dwarf TVLM 513-46546 shows a γ-ray pulse with a power-law index of 2.59 ± 0.22, and its γ-ray period is consistent with optical observations (Song & Paglione 2020).It is known that red dwarfs are the most numerous stars and account for more than 70% of Galactic stars.The total energy of stellar flares from all Galactic red dwarfs may be up to ∼10 51 erg (Sinitsyna et al. 2019), which is comparable to the estimation of the CR energy budget in the Galactic disk (Stozhkov 2011).Therefore, it is conjectured that red dwarfs may be among the CR sources with energy up to ∼10 14 eV (Sinitsyna et al. 2021).
To explore the ability of red dwarfs to accelerate particles, analyzing the accompanying γ-ray emission is necessary.In this study, we perform a detailed GeV γ-ray analysis of eight red dwarfs that are reported as TeV sources (Sinitsyna et al. 2021) by using ∼13.6 yr of Fermi-LAT data.The sample of red dwarfs with the observational physical parameters is listed in Table 1.We find that only V962 Tau and GJ 1078 may have GeV emission.This paper is organized as follows.In Section 2, we present the data analysis and the results.In Section 3, we discuss the possible association between the GeV source and V962 Tau.Finally, a summary is provided in Section 4.
First, the data selection is made with the command gtselect with the maximum zenith angle of 90°.We apply the command gtmktime to the data with the recommended filter string "(DATA_QUAL > 0)&&(LAT_CONFIG==1)" to choose good time intervals.The entire energy range from 0.2-500 GeV is divided into 10 logarithmic bins per decade for the count cube and exposure cube.The appropriate Instrument response function is "P8R3_SOURCE_V3," and was used for this data set, and the Galactic interstellar diffuse background emission model and isotropic background spectral template "gll_iem_v07" and "iso_P8R3_SOURCE_V3_v1" are applied, respectively.Then, we use the 4FGL-DR3 catalog, the Fermi-LAT 12 yr source catalog, and the two background models to define our source model by the user-contributed tool make4FGLxml.py,4and the corresponding list of 4FGL sources within a radius of 25°centered at a target source is obtained.After that, we use the Python module pyLikelihood with the NewMinuit optimizer to perform the binned likelihood analysis and get the best-fit results.In this step, we free the spectral parameters of the catalog sources within 5°f rom the ROI centers and the normalization of the two diffuse background components.In addition, a Python package fermipy v1.25 (Wood et al. 2017) is employed in the position of the fitting process and the lightcurve (LC) analysis.

Results
To search for the GeV counterparts from the suggested TeV bright red dwarfs listed in Table 1, we generate their residual test statistic (TS) maps in the energy range of 0.2-500 GeV.
The TS value for each pixel is evaluated by TS = 2ln(L1/L0), where L0 is the maximum likelihood of the null hypothesis, and L1 is the maximum likelihood of the test model that a putative point source is located in this pixel.
Besides some nearby excesses, no GeV emission >3σ is found to be coincident with any of the eight red dwarfs in our spatial analysis, and all of them are outside the 95% error ellipse of nearby 4FGL catalog sources.In order to investigate the possible association between the targets and the nearby excesses, we use the 1-500 GeV data with better angular resolution to generate the 2°× 2°TS maps where only the catalog sources and two diffuse backgrounds are modeled.We found that there are >3σ excess near V962 Tau and GJ 1078 with an angular separation of a few 0°.1, which are shown in Figure 1.A detailed analysis of V962 Tau and GJ 1078 is presented below.The TS maps for the remaining sources can be found in the Appendix.

V962 Tau
For V962 Tau, there is some excess east of the field and a nearby catalog source 4FGL J0544.4+2238 in the southwest (see the left panel of Figure 1), which may affect the result.Thus, we first generated a 5°× 5°TS map in the energy range of 1-500 GeV by excluding 4FGL J0544.4+2238from the source model.As shown in Figure 2(a), a significant excess is present in the nearby southwest region of V962 Tau.To eliminate the influence from this source, we add a point source p1 with a simple power-law spectrum at the peak pixel (R.A. J2000 = 84°.285, decl.J2000 = 22°.040) to the source model and reproduce the TS map shown in Figure 2(b).There is some residual emission with two peaks near V962 Tau, as shown in Figure 2(c).Due to the small separation between the two peaks, we use another point source, p2, to model the residual emission and use the localize method in fermipy to fit its position.The best-fit position of p2 is R.A. J2000 = 86°.161,decl.J2000 = 22°.617 with a 1σ error radius of 0°.033, very close to that of 4FGL J0544.4 + 2238, which means that p2 is precisely 4FGL J0544.4+2238.After subtracting the contribution of p1 and p2, the residual TS map is displayed in Figure 2(d), which still shows an excess to the southeast of V962 Tau with a peak TS value of ∼17.Therefore, we add the third point source, p3, and fit its position, resulting in R.A. J2000 = 86°.562,decl.J2000 = 22°.820 with a 1σ error radius of 0°.113.The corresponding TS values of p1-p3 are TS p1 = 72.1,TS p2 = 22.3, and TS p3 = 18.9, respectively.To further check the significance of p3, we calculate the likelihood ratio of the three-point-source  9) Stephenson (1986).
2ps , obtaining TS model = 17.5, which corresponds to a significance of 3.8σ above 1 GeV.Although the significance of p3 is not too high, it may be the possible signal of a marginal detection.Thus, we adopt the three-point-source model in the following analysis for V962 Tau.
In the three-point-source model, both p2 and p3 are in the vicinity of V962 Tau with angular distances of 0°.389 and 0°.109, respectively.Due to the small 1σ statistical error radius (∼0°.03),however, V962 Tau is obviously outside the 3σ positional uncertainty radius 6 of p2 even if the systematic error is taken into account, 7 while V962 Tau is located within the 1σ error radius of source p3 after considering the systematic error.Compared with p2, source p3 is more likely related to V962 Tau given the spatial distribution.
To further explore the property of source p3 and its relation to V962 Tau, we perform a spectral analysis at 0.2-500 GeV.It is noted that the distance between p3 and Crab is about 2°.8, while the 68% containment range of point-spread function (PSF) at an energy of 0.2 GeV is about 3°, which may affect the flux below 1 GeV.To reduce the influence of Crab's pulsar, we only use the off-pulse (0.45-0.85) interval of Crab in phase space based on the ephemeris from Abdo et al. (2010) to calculate the energy flux between 0.2 and 500 GeV.With a power-law spectrum, the photon index Γ = 3.08 ± 0.08 and the energy flux of (7.59 ± 1.15) × 10 −12 erg cm −2 s −1 are obtained in the global fitting.Assuming a distance of 710 pc (Gaia Collaboration 2020), the luminosity of p3 is 4.58 × 10 32 erg s −1 .The spectral energy distributions (SEDs) of p3 are produced by the sed method in fermipy in five logarithmically spaced energy bins based on the maximum likelihood analysis.During the fitting process, the free parameters only include the normalization parameters of the sources with a significance 5σ within 5°from the ROI centers as well as the Galactic and isotropic diffuse background components, while all other parameters are fixed to their best-fit values in the global fitting.For the energy bins with TS 4, the 95% confidence level upper limits are calculated.
In order to examine the long-term variability of source p3, a 3 month binned LC is constructed over the whole time and energy interval by using the LIGHTCURVE method in fermipy.The LC is shown in Figure 3, in which, for the bins with TS 4, the upper limits of the 95% confidence level are displayed.According to the criterion in Nolan et al. (2012), a variable source can be identified at a 99% confidence level if the variability index (TS var ) is greater than 88.6 for the 55 time bins.In view of the TS var = 59.5 obtained for p3 in this study, no significant γ-ray variability can be counted as being detected.

GJ 1078
For GJ 1078, there are no other contaminating sources, and 4FGL-DR3 sources are far away (see Figure 1).Thus, we directly use one point source (p4) with a power-law spectrum to model the excess to the southwest of GJ 1078 in the 1-500 GeV band and fit its position, yielding R.A. J2000 = 80°.852, decl.J2000 = 22°.333 with a 1σ error radius of 0°.066.The angular separation between p4 and GJ 1078 is 0°.23, which is greater than the 3σ positional uncertainty (0°.15) of p4.So, it is hard to associate p4 with GJ 1078, and thus no further analysis for p4 is performed.

Physical Association between p3 and V962 Tau
In our Fermi-LAT data analysis described above for the eight red dwarfs, we find that only V962 Tau may have long-term GeV emission according to the possible spatial association between p3 and V962 Tau.Here, we discuss whether there may be a physical association between them in terms of radiation mechanism.
As one of the most studied objects, the Sun has been observed by Fermi-LAT in the past years (Ajello et al. 2014;Ackermann et al. 2017), showing hundreds of MeV to GeV γ-ray emission during some solar flares.The flares associated with γ-ray emission are generally accompanied by fast coronal mass ejections (CMEs).In addition to the Sun, hard X-ray and/or soft γ-ray emission are also detected from stellar 6 The 2σ and 3σ error radii are calculated as 1.6407r 1σerr and 2.2699r 1σerr with 2 degrees of freedom (Mattox et al. 1996 flares/superflares of nearby active stars, e.g., DG CVn (Drake et al. 2014;Osten 2016).The magnetic reconnection and the CME-driven shock waves are invoked to explain the energetic particles that are responsible for the hard X-ray and/or γ-ray emission (Cliver et al. 2022).The former is generally related to the impulsive (prompt) phase of flares, and it is hard to accelerate particles beyond a few GeV (Takahashi et al. 2016).After the peak of the impulsive phase, flares of a longer duration (from several hours to weeks) follow, which can be attributed to the CME-driven shock waves.
Due to the very short duration of the impulsive phase, here we only adopt the CME-driven shock wave scenario, in which the shock-accelerated protons with a fraction, η, of the CME kinetic energy collide with the CME matter to produce piondecay γ-rays.Taking the superflare of DG CVn as a prototype, Ohm & Hoischen (2018) calculated the expected γ-ray emission from the nearby flaring stars.Following their treatment, for the CME kinetic energy, we take an optimistic value of E CME,kin = 10 37 erg as a reference, which corresponds to a CME mass of 2.2 × 10 20 g and a CME velocity of 3000 km s −1 .With these parameters, the average density of the CME particles as the target of the relativistic protons is n 11 = 2 in units of 10 11 cm −3 within a few hours of evolution after the flaring.The accelerated protons are assumed to have an exponentially cutoff power-law spectrum with an index of α p and a cutoff energy of E p,c .We adopt the Python package naima8 v0.10.0 with the proton-proton cross section from Kafexhiu et al. (2014) to calculate the pion-decay γ-rays.In the calculation, we found that the parameters are degenerated and cannot be constrained by the current data points.Thus, we  consider two cases: (1) the index is fixed as 2.0, which is the typical value predicted by shock acceleration theory, and (2) the cutoff energy is fixed as 1 TeV, which is the possible maximum energy in the flares (Ohm & Hoischen 2018).At a distance of 710 pc (Gaia Collaboration 2020), we obtain E p,c = 10 GeV and η = 1.5 in the former case and α p = 3.2 and η = 2.5 in the latter case to explain the Fermi-LAT data of source p3.The corresponding SED is presented in Figure 4.
On the one hand, even with the optimistic CME kinetic energy range, the energy conversion fraction η > 1 indicates that one flare cannot alone maintain the GeV γ-ray luminosity of p3.Given the short lifetime of the accelerated protons, n 2.6 11 1 hr (Ohm & Hoischen 2018), and the optimistic assumption that the CME can transfer 10% of its total energy to accelerate particles and all of them interact with the surrounding medium for γ-ray emission in a duration comparable to the proton-proton loss time, at least 15 superflares are needed to produce the observed flux.However, V962 Tau has the largest distance in our sample.If it has a few tens of parsecs like other dwarfs, the energy budget can decrease by 3 orders of magnitude, which could be supplied by the CME kinetic energy.On the other hand, considering the low variability of LC of p3, the superflares should occur very frequently, which seems unreasonable according to the current statistics of flares (Chang et al. 2017;Yang & Liu 2019).Thus, it is difficult for source p3 to be physically related to the flares from V962 Tau.
Besides the above flare scenario, red dwarfs could be a potential passive γ-ray source: the background CRs could penetrate their atmosphere and emanate γ-ray emission.Following the work for the case of the Sun (Zhou et al. 2017), the passive γ-ray flux from V962 Tau is estimated as ∼10 −29 erg cm −2 s −1 , far below the flux of p3 (∼10 −13 erg cm −2 s −1 ).Thus, the passive γ-ray emitter scenario for p3 can be excluded.In addition, we search for other possible counterparts within the 3σ error radius of p3 in SIMBAD (Wenger et al. 2000) and find that there is no source that belongs to the types of known γ-ray-bright sources.Due to the low significance of ∼4σ and the low Galactic latitude |b| ∼ 3°, p3 appearing near V962 Tau may likely be background emission in nature.

Constraints for Upper Limits
Based on the above analysis and discussion, there is, in fact, no long-term GeV γ-ray emission for the eight red dwarfs, including V962 Tau.So, we calculate the upper limits to constrain some physical properties.Assuming a point source and subtracting the nearby excess for each source, the upper limits are calculated in five energy bins based on a power-law spectrum with a spectral index of 2.0 in each bin and are displayed in Figure A2.With E CME,kin = 10 37 erg, α p = 2.0, and E p,c = 10 GeV, the energy conversion fraction can be constrained to η  10 −4 .In the paradigm of SNRs as the main sources of Galactic CRs, the particles accelerated by the shock should carry 10% of the explosion energy (e.g., Blasi 2013, and references therein).If the CME shocks can also accelerate particles with the same energy conversion fraction, then the kinetic energy of CMEs can be reduced to the order of 10 34 erg.
For flares with such energy, the frequency can only be reached several times per year.Thus, the long-term GeV γ-ray emission from red dwarfs may be hard to detect by the current telescope.
With an occurrence frequency of stellar flares (ν ∼ 36 yr −1 ) and the average flare energy (∼10 35 erg), it has been suggested that flares of active dwarf stars could also provide enough energy to maintain the luminosity of Galactic CRs (Kopysov & Stozhkov 2005).The energy density of Galactic CRs is about w ∼ 1 eV cm −3 (e.g., Gaisser 1990).By adopting a radius of 10 kpc and a thickness of 300 pc, the volume of the Galactic disk is V gal ∼ 3 × 10 66 cm −3 .Considering the lifetime of CRs in the disk τ ∼ 10 7 yr, the luminosity of the Galactic CRs is L = wV gal /τ ∼ 1.4 × 10 40 erg s −1 .In a Galaxy, there are n s ∼ 2 × 10 11 stars, and most of them are the G-M spectral classes.Assuming the accelerated particles take up 10% of the flare energy, the power of CRs contributed by flares of the active dwarf stars is 0.1 n s νE CME,kin .To explain the luminosity of CRs, n ~´--( ) E n 1.4 10 erg s 10 CME,kin 30 1 s 11 1 is required.According to our constraints of E CME,kin < 10 34 erg and the occurrence frequency of such flares of ν < 10 yr −1 (e.g., Yang & Liu 2019), flares of the active dwarf stars only make a limited contribution to the Galactic CRs.
In addition, if the particle index is α p > 2.0 and the maximum energy is E p,c > ∼ 10 TeV, the SHALON data are obviously higher than the theoretical expectation constrained by the Fermi-LAT upper limits.This means that the TeV emission seen by SHALON may not be associated with red dwarfs, which can be verified by a next-generation telescope, e.g., the Cherenkov Telescope Array (CTA).

Flare-like Events
Although no long-term GeV γ-ray emission is found for the eight red dwarfs, there may be flares in the GeV band, like in the case of the Sun reflected in the LC.Based on the best-fit source model derived from the binned likelihood analysis in Section 2, we construct the 1 week binned LC for each red dwarf over the entire data.For V962 Tau, V1589 Cyg, and GJ 1078, the surrounding excesses are included in the source model and are treated as background sources.We first search for the flare-like candidate events by seeking the time intervals in which the γ-ray emission is detected with large significance (e.g., TS 25).But no such intervals are found for all of the eight red dwarfs.Due to the blind search, the period of a flare may have been divided into two time bins, reducing the significance of the γ-ray signal.We thus deleted the first 3.5 days of data and rebuilt the 1 week binned LCs over the remaining data, but, again, no periods with a significant γ-ray signal were found.Thus, we conclude that no flare is detected by Fermi-LAT for the eight red dwarfs based on the current observational data.

Summary
In order to search for potential GeV γ-ray emission from red dwarfs, we analyze the 0.2-500 GeV γ-ray emission of the regions covering V388 Cas, V547 Cas, V780 Tau, V962 Tau, V1589 Cyg, GJ 1078, GJ 3684, and GL 851.1 with 13.6 yr of Fermi-LAT data and find significant excesses projected near V962 Tau and GJ 1078.The spatial analysis shows that V962 Tau is in the range of a 1σ error radius of the nearby γ-ray emission after taking the systematic error into consideration, while GJ 1078 is outside of the 3σ error radius of nearby emission, meaning that it is hard to associate them with the nearby excess.A spectral analysis shows that the γ-ray emission near V962 Tau can be fitted by exponentially cutoff power-law proton distribution models.However, based on the optimistic assumption of CME kinetic energy (10 37 erg), we obtain the energy conversion efficiency of η > 1, which is impossible for a single flare.Considering the low variability of the LC of p3, the flares should be very frequent, which is unreasonable according to the statistics of the flare.As a result, the GeV γ-ray emission presented should be irrelevant for V962 Tau.We also constructed a 1 week binned LC for all of the eight red dwarfs, but no periods with significant emission were found.Therefore, further observation of high-energy processes is still necessary to explore nearby flaring stars and is expected to increase our understanding of the physics of stellar energetic eruption events.

Figure 1 .
Figure 1.TS maps of 2°× 2°regions centered at V962 Tau (left) and GJ 1078 (right) in the energy range of 1-500 GeV.The green pluses mark the positions of the 4FGL-DR3 catalog sources, with the 95% error ellipses shown in green.The cyan stars mark the positions of red dwarfs.The white contours show the emission excess with a 3σ significance, which corresponds to TS = 11.83 with 2 degrees of freedom.

Figure 2 .
Figure 2. TS maps centered at V962 Tau in the energy range of 1-500 GeV.(a) The 5°× 5°region, excluding 4FGL J0544.4+2238from the source model.The white circle in the lower-left corner of the top left panel shows the 68% containment range of the PSF of Fermi-LAT at 1 GeV.(b) Same as (a), but point source p1 is included in the source model.(c) Same as (b) but for a 2°× 2°region.(d) Same as (c), but p2 is added to the source model.The yellow solid and dashed circles represent the 1σ and 2σ error radii of source p3, respectively.

Figure 3 .
Figure 3. 3 month binned γ-ray LC of p3 near V962 Tau.The horizontal dashed line represents the constant flux.For the bins with a TS 4, the 95% upper limits are presented.

Figure 4 .
Figure 4. SEDs of p3 near V962 Tau.The black dots with the 1σ error bars or the 95% upper limits represent the Fermi-LAT data obtained.The red squares with 1σ error bars represent the TeV spectral data from SHALON toward these red dwarfs (Sinitsyna et al. 2021).The gray bowtie represents the 68% confidence range of the LAT spectra.The orange (α p = 3.2, E p,c = 1 TeV, and η = 2.5) and light blue (α p = 2.0, E p,c = 10 GeV, and η = 1.5) lines represent the fitting spectra of p3.The blue solid line and dashed line show the differential energy flux sensitivities of the CTA for the exposure duration of 5 and 50 hr (Observatory & Consortium 2021).

Table 1
Parameters of the Red Dwarfs