arXiv subjects

En-Wei Liang

Publications and source records attributed to En-Wei Liang.

At least 91 records · Page 5Linked to original sources

arXiv2024

The Energy Sources, the Physical Properties, and the Mass-loss History of SN 2017dio

We study the energy sources, the physical properties of the ejecta and the circumstellar medium (CSM), as well as the mass-loss history of the progenitor of SN 2017dio which is a broad-lined Ic (Ic-BL) supernova (SN) having unusual light curves (LCs) and signatures of hydrogen-rich CSM in its early spectrum. We find that the temperature of SN 2017dio began to increase linearly about 20 days after the explosion. We use the $^{56}$Ni plus the ejecta-CSM interaction (CSI) model to fit the LCs of SN 2017dio, finding that the masses of the ejecta, the $^{56}$Ni, and the CSM are $\sim$ 12.41 M$_\odot$, $\sim$ 0.17 M$_\odot$, and $\sim$ 5.82 M$_\odot$, respectively. The early-time photosphere velocity and the kinetic energy of the SN are respectively {$\sim$ 1.89 $\times 10^4$ km s$^{-1}$} and $\sim$ 2.66 $\times 10^{52}$ erg, which are respectively comparable to those of SNe Ic-BL and hypernovae (HNe). We suggest that the CSM of SN 2017dio might be {from an luminous-blue-variable-like outburst or} pulsational pair instability $\sim$ 1.2$-$11.4 yr prior to the SN explosion{, or binary mass transfer}. {Moreover,} we find that its ejecta mass is larger than those of many SNe Ic-BL, and that its $^{56}$Ni mass ($M_{\rm Ni}$) is approximately equal to the mean (or median) value of $M_{\rm Ni}$ of SNe Ic-BL in the literature, but lower than $M_{\rm Ni}$ of prototype HNe (e.g., SN 1998bw and SN 2003dh).

astro-ph.HE↗

arXiv2024

Multipole expansion of the gravitational field in a general class of fourth-order theories of gravity and the application in gyroscopic precession

A viable weak-field and slow-motion approximation method is constructed in $F(R,R_{μν}R^{μν}, R_{μνρσ}R^{μνρσ})$ gravity, a general class of fourth-order theories of gravity. By applying this method, the metric, presented in the form of the multipole expansion, outside a spatially compact source up to $1/c^3$ order is provided, and the closed-form expressions for the source multipole moments are all presented explicitly. The metric consists of the massless tensor part, the massive scalar part, and the massive tensor part, where the former is exactly the metric in General Relativity, and the latter two are the corrections to it. It is shown that the corrections bear the Yukawa-like dependence on the two massive parameters and predict the appearance of six additional sets of source multipole moments, which indicates that up to $1/c^3$ order, there exist six degrees of freedom beyond General Relativity within $F(R,R_{μν}R^{μν}, R_{μνρσ}R^{μνρσ})$ gravity. By means of the metric, for a gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velocities of the Thomas precession, the geodetic precession, and the Lense-Thirring precession are derived, and from them, the corrections to the angular velocities of the three types of precession in General Relativity can be read off. These results indicate that differently from $f(R)$ or $f(R,\mathcal{G})$ gravity, the most salient feature of the general $F(R,R_{μν}R^{μν}, R_{μνρσ}R^{μνρσ})$ gravity is that it gives the nonvanishing correction to the gyroscopic spin's angular velocity of the Lense-Thirring precession in General Relativity.

gr-qc↗

arXiv2024

Revisiting the Constraint on Equation of State of Neutron Star based on the Binary Neutron Star Mergers

The merger of neutron star (NS)-NS binary can form different production of the compact remnant, among which the supramassive NS (SMNS) could create an internal plateau and the followed steep decay marks the collapse of the SMNS. The proportion of SMNS and the corresponding collapse-time are often used to constrain the NS equation of state (EoS). This paper revisits this topic by considering the effect of an accretion disk on the compact remnant, which is not considered in previous works. Compared with previous works, the collapse-time distribution (peaks $\sim$100 s) of the SMNSs formed from NS-NS merger is almost unaffected by the initial surface magnetic ($B_{{\rm s},i}$) of NS, but the total energy output of the magnetic dipole radiation from the SMNSs depends on $B_{{\rm s},i}$ significantly. Coupling the constraints from the SMNS fraction, we exclude some EoSs and obtain three candidate EoSs, i.e., DD2, ENG, and MPA1. By comparing the distributions of the collapse-time and the luminosity of the internal plateau (in the short gamma-ray bursts) for those from observations with those obtained based on the three candidate EoSs, it is shown that only the EoS of ENG is favored. Our sample based on the ENG EOS and a mass distribution motivated by Galactic systems suggests that approximately $99\%$ of NS-NS mergers collapse to form a black hole within $10^7$s. This includes scenarios forming a BH promptly ($36.5\%$), a SMNS ($60.7\%$), or a stable NS that transitions into a BH or a SMNS following accretion ($2.1\%$). It also indicates that the remnants for GW170817 and GW190425, and the second object of GW190814 are more likely to be BHs.

astro-ph.HE↗

arXiv2024

GeV gamma-ray emission in the field of young massive star cluster RCW 38

We report the detection of gamma-ray emission by the Fermi Large Area Telescope (Fermi-LAT) towards the young massive star cluster RCW 38 in the 1-500 GeV photon energy range. We found spatially extended GeV emission towards the direction of RCW 38, which is best modelled by a Gaussian disc of 0.23$°$ radius with a significance of the extension is $\sim 11.4 σ$. Furthermore, the spatial correlation with the ionized and molecular gas content favors the hadronic origin of the gamma-ray emission. The gamma-ray spectrum of RCW 38 has a relatively hard photon index of $2.44 \pm 0.03$, which is similar to other young massive star clusters. We argue that the diffuse GeV gamma-ray emission in this region likely originates from the interaction of accelerated protons in the stellar cluster with the ambient gas.

astro-ph.HE↗

arXiv2024

AT2023lli: A Tidal Disruption Event with Prominent Optical Early Bump and Delayed Episodic X-ray Emission

High-cadence, multiwavelength observations have continuously revealed the diversity of tidal disruption events (TDEs), thus greatly advancing our knowledge and understanding of TDEs. In this work, we conducted an intensive optical-UV and X-ray follow-up campaign of TDE AT2023lli, and found a remarkable month-long bump in its UV/optical light curve nearly two months prior to maximum brightness. The bump represents the longest separation time from the main peak among known TDEs to date. The main UV/optical outburst declines as $t^{-4.10}$, making it one of the fastest decaying optically selected TDEs. Furthermore, we detected sporadic X-ray emission 30 days after the UV/optical peak, accompanied by a reduction in the period of inactivity. It is proposed that the UV/optical bump could be caused by the self-intersection of the stream debris, whereas the primary peak is generated by the reprocessed emission of the accretion process. In addition, our results suggest that episodic X-ray radiation during the initial phase of decline may be due to the patched obscurer surrounding the accretion disk, a phenomenon associated with the inhomogeneous reprocessing process. The double TDE scenario, in which two stars are disrupted in sequence, is also a possible explanation for producing the observed early bump and main peak. We anticipate that the multicolor light curves of TDEs, especially in the very early stages, and the underlying physics can be better understood in the near future with the assistance of dedicated surveys such as the deep high-cadence survey of the 2.5-meter Wide Field Survey Telescope (WFST).

astro-ph.HE↗

arXiv2024

Narrowly-Banded Spectra with Peak Frequency Around 1 GHz of FRB 20201124A: Implications for Energy Function and Radiation Physics

The radiation physics of fast radio bursts (FRBs) remains an open question. Current observations have discovered that narrowly-banded bursts of FRB 20201124A are active in 0.4-2 GHz and their spectral peak frequency ($ν^{\rm obs}_{p}$) are mostly toward $\sim 1$ GHz. Utilizing a sample of 1268 bursts of FRB 20201124A detected with the FAST telescope, we show that the $1σ$ spectral regime of 71.4\% events (in-band bursts) is within the FAST bandpass. Their intrinsic burst energies ($E^{\rm obs}_{\rm BWe}$) and spectral widths ($σ_s^{\rm obs}$) are well measured by fitting the spectral profile with a Gaussian function. The derived $E^{\rm obs}_{\rm BWe}$ and $σ_s^{\rm obs}$ distributions are log-normal and centering at $\log E^{\rm obs}_{\rm BWe}/{\rm erg}=37.2~ (σ=0.76)$ and $\log σ_s^{\rm obs}/{\rm GHz}=-1.16~ (σ=0.17)$. Our Monte Carlo simulation analysis infers its intrinsic $ν_p$ distribution as a normal function centered at $ν_{p,c}=1.16$ GHz ($σ=0.22$) and its intrinsic energy function as $Φ(E)\propto E^{-0.60}e^{-E/E_c}$ with $E_c=9.49 \times 10^{37}$ erg. We compare these results with that of typical repeating FRBs 20121102A and 20190520B that are active over a broad frequency range at several specific frequencies and discuss possible observational biases on the estimation of the event rate and energy function. Based on these results, we argue that FRB 20201124A likely occurs in a fine-tuned plasma for maser radiations at a narrow frequency range, while FRB 20121102A and FRB 20190520B could involve clumpy plasma conditions that make maser emission around several specific frequencies in a broad range.

astro-ph.HE↗

arXiv2024

X-Ray Polarization Variability of High Spectral Peak BL Lacertaes: Cases of 1ES 1959+650 and PKS 2155-304

The high-energy-peaked BL Lacertae objects (HBLs) are the main targets of the Imaging X-ray Polarimetry Explorer (IXPE) for investigating the mechanisms of radiation and particle acceleration in jets. In this paper, we report the first IXPE observations of two HBLs, 1ES 1959+650 and PKS 2155--304. Both sources exhibit X-ray polarization with a confidence level exceeding 99\%, as well as significant variability in polarization across different time intervals and energy ranges. Notably, PKS 2155--304 demonstrates the highest X-ray polarization among all blazars detected by IXPE within its entire energy band (2--8 keV), with a polarization degree of $Π_{\rm X}=21.9\%\pm1.9\%$ (MDP$_{99}\sim$6.0\%). An even higher polarization is observed in the 3--4 keV band, reaching $Π_{\rm X}=28.6\%\pm2.7\%$ (MDP$_{99}\sim$8.1\%) with a confidence level of 10.8$σ$. Furthermore, no polarization is detected above 5 keV energy band. For 1ES 1959+650, the highest detected polarization degree in the 2--8 keV band is $Π_{\rm X}=12.4\%\pm0.7\%$ (MDP$_{99}\sim$2.2\%), with an electric vector position angle (EVPA) of $ψ_{\rm X}=19.7^{\circ}\pm1.6^{\circ}$. The X-ray polarization of 1ES 1959+650 exhibits evident variability, accompanied by the variations of $ψ_{\rm X}$, flux, spectrum, and energy bin. We discuss possible implications of these observational findings, including the variability in polarization, rotation of EVPA, and transition between synchrotron and synchrotron-self-Compton. We speculate that the X-rays observed during different IXPE observations originate from distinct regions in the jet and may involve diverse mechanisms for particle acceleration.

astro-ph.HE↗

arXiv2024

A Channel to Form Fast-spinning Black Hole-Neutron Star Binary Mergers as Multimessenger Sources. II. Accretion-induced Spin-up

In this work, we investigate an alternative channel for the formation of fast-spinning black hole-neutron star (BHNS) binaries, in which super-Eddington accretion is expected to occur in accreting BHs during the stable mass transfer phase within BH-stripped helium (BH--He-rich) star binary systems. We evolve intensive \texttt{MESA} grids of close-orbit BH--He-rich star systems to systematically explore the projected aligned spins of BHs in BHNS binaries, as well as the impact of different accretion limits on the tidal disruption probability and electromagnetic (EM) signature of BHNS mergers. Most of the BHs in BHNS mergers cannot be effectively spun up through accretion, if the accretion rate is limited to $\lesssim10\,\dot{M}_{\rm Edd}$, where $\dot{M}_{\rm Edd}$ is the standard Eddington accretion limit. In order to reach high spins (e.g., $χ_{\rm BH} \gtrsim 0.5$), the BHs are required to be born less massive (e.g., $\lesssim3.0\,M_\odot$) in binary systems with initial periods of $\lesssim0.2-0.3\,{\rm days}$ and accrete material at $\sim100\,\dot{M}_{\rm Edd}$. However, even under this high accretion limit, $\gtrsim6\,M_\odot$ BHs are typically challenging to significantly spin up and generate detectable associated EM signals. Our population simulations suggest that different accretion limits have a slight impact on the ratio of tidal disruption events. However, as the accretion limit increases, the EM counterparts from the cosmological BHNS population can become bright overall.

astro-ph.HE↗

arXiv2024

Ejecta-circumstellar medium interaction in high-density environment contribution to kilonova emission: Application to GRB 191019A

The nearby long-duration GRB 191019A recently detected by Swift lacks an associated supernova and belongs to a host galaxy with little star formation activity, suggesting that the origin of this burst is the result of a merger of two compact objects with dynamical interactions in a high-density medium of an active galactic nucleus. Given the potential motivation of this event, and given that it occurs in such a high-density environment, the ejecta-circumstellar medium (CSM) interaction cannot be ignored as possibly contributing to the kilonova emission. Here, we theoretically calculate the kilonova emission by considering the contribution of the ejecta-CSM interaction in a high-density environment. We find that the contribution to the kilonova emission from the ejecta-CSM interaction will dominate at a later time, and a smaller ejecta mass will have a stronger kilonova emission from the ejecta-CSM interaction. Moreover, we try to apply it to GRB 191019A, but we find that it is difficult to identify the possible kilonova emission from the observations, due to the contribution of the bright host galaxy. On the other hand, less injected mass (less than $M_{\rm ej}=2\times10^{-5}M_{\odot}$) will be required if one can detect the kilonova emission associated with a GRB 191019A-like event in the future. The {\em r}-process-powered and spin energy contributions from the magnetar are also discussed.

astro-ph.HE↗

arXiv2024

Neutron Star Mergers as the Dominant Contributor to the Production of Heavy $r$-Process Elements

The discovery of the radioactively powered kilonova AT2017gfo, associated with the short-duration gamma-ray burst GRB 170817A and the gravitational wave source GW170817, has provided the first direct evidence supporting binary neutron star mergers as crucial astrophysical sites for the synthesis of heavy elements beyond iron through $r$-process nucleosysthesis in the universe. However, recent identifications of kilonovae following long-duration gamma-ray bursts, such as GRB 211211A and GRB 230307A, has sparked discussions about the potential of neutron star-white dwarf mergers to also produce neutron-rich ejecta and contribute to the production of heavy $r$-process elements. In this work, we estimate the contribution of binary neutron star mergers to the total mass of $r$-process elements in the Milky Way and investigate the possibility of neutron star-white dwarf mergers as alternative astrophysical sites for $r$-process nucleosynthesis through an analysis of the total mass of the $r$-process elements in the Milky Way. Our results reveal that binary neutron star mergers can sufficiently account for the Galactic heavy $r$-process elements, suggesting that these events are the dominant contributor to the production of heavy $r$-process elements in the Milky Way. Considering the total mass of $r$-process elements in the Milky Way and the higher occurrence rate of neutron star-white dwarf mergers, it is unlikely that such mergers can produce a significant amount of neutron-rich ejecta, with the generated mass of $r$-process elements being lower than $0.005M_{\odot}$.

astro-ph.HE↗

arXiv2024

Revisit the Emission Polarization of the Internal-shock for the blazars' Jet

Recent Imaging X-ray Polarimetry Explorer (IXPE) observations of blazars tend to support the shock model for the X-ray emission, but report a low polarization degree ($Π\sim 10\%$) in X-rays compared with the previous theoretical expectations in the shock model. In order to reconcile the theoretical expectations with observations, we revisit the polarization of the shock emission by considering different kind of direction distribution for the shock-generated magnetic fields (sgMFs). Here, $w'_{\rm sg}\propto(\sinθ')^{ζ_{\rm sg}}$ with $θ'=0$ along the shock normal direction is used to describe the direction distribution of the sgMFs in the shock co-moving frame. It is found that the polarization in the X-ray and radio emission for a general jet in blazars can be described as $Π\sim 44.5[1-\exp(-ζ_{\rm sg}/2.6)]\%$ and $Π\sim 20[1-\exp(-ζ_{\rm sg}/2.4)]\%$, respectively. Correspondingly, one can have $ζ_{\rm sg}\sim 1-1.5$ according to the IXPE observations. Besides the sgMFs, the magnetic fields generated by the Richmyer-Meshkov instability (rmMFs) is supposed to present in the jets. The direction of the rmMFs is mainly distributed along the shock normal in the simulations and thus $w'_{\rm rm}\propto(\cos θ')^{ζ_{\rm rm}}$ is adopted to describe the direction distribution of rmMFs. We find that the rmMFs is likely to significantly affect the polarization properties at the low-frequency emission, especially when the sgMFs decay rapidly. Based on the contemporaneous radio and X-ray observations, we find the the emission of the electrons in the rmMFs make a significant contribution in the low-frequency emission and the the ordered background magnetic fields (obMFs) can be neglected.

astro-ph.HE↗

arXiv2023

Radioactive Decay of Specific Heavy Elements as an Energy Source for Late-Time Kilonovae and Potential JWST Observations

Revealing the temporal evolution of individual heavy elements synthesized in the merger ejecta from binary neutron star mergers not only improves our understanding of the origin of heavy elements beyond iron but also clarifies the energy sources of kilonovae. In this work, we present a comprehensive analysis of the temporal evolution of the energy fraction of each nuclide based on the $r$-process nucleosynthesis simulations. The heavy elements dominating the kilonova emission within $\sim100$~days are identified, including $^{127}$Sb, $^{128}$Sb, $^{129}$Sb, $^{130}$Sb, $^{129}$Te, $^{132}$I, $^{222}$Rn, $^{223}$Ra, $^{224}$Ra, and $^{225}$Ac. It is found that the late-time kilonova light curve ($t\gtrsim20$~days) is highly sensitive to the presence of the heavy element $^{225}$Ac (with a half-life of 10.0~days). Our analysis shows that the James Webb Space Telescope (JWST), with its high sensitivity in the near-infrared band, is a powerful instrument for the identification of these specific heavy elements.

astro-ph.HE↗

arXiv2023

Unveiling the unconventional optical signatures of regular black holes within accretion disk

The optical characteristics of three types of black holes (BHs) surrounded by a thin accretion disk are discussed, namely the Schwarzschild BH, Bardeen BH, and Hayward BH. We calculate the deflection angle of light as it traverses the vicinity of each BH using numerical integration and semi-analytical methods, revealing that both approaches can effectively elucidate the deflection of light around the BH. We investigate the optical appearance of the accretion disk and its corresponding observational images at various viewing angles, discovering that the luminosity in the region near the BH on the inner side of the accretion disk is higher than that on the outer side owing to higher material density in closer proximity to the BH. We observe a significant accumulation of brightness on the left side of the accretion disk, attributed to the motion of matter and geometric effects. Our findings emphasize the significant influence of the observation inclination angle on the observed outcomes. An increase in the observation inclination angle results in the separation of higher-order images. With the improvement in EHT observation accuracy, we believe that the feature of a minimal distance between the innermost region of the direct image of the Hayward BH and the outermost region of the secondary image can be used as an indicator for identifying Hayward BHs.

gr-qc↗

arXiv2023

Searching for Associations Between Short Gamma-ray Bursts and Fast Radio Burst

The physical origin of fast radio bursts (FRBs) is still unclear. However, young magnetars associated with short-duration gamma-ray bursts (SGRBs) have been thought to be possible central engines for some FRBs. In this paper, we perform a systematic search for SGRBs that are associated with FRBs in a sample including 623 FRBs (601 one-off bursts and 22 repeaters) and 168 SGRBs with precise localizations. We find that FRB 190309A is spatially associated with GRB 060502B, with a chance probability of 0.05 when temporal and redshift information is taken into account. Considering the high chance probability (the statistical significance is < 3σ), we examine other observational properties such as the host galaxy, the dispersion measure, and the energy budget of the central engine to check the possibility of their association. Although the available observational information is insufficient to determine whether they are physically associated, it does not rule out such a possibility. As the only pair of FRB and GRB that are spatially associated, it remains an interesting case worthy of further attention

astro-ph.HE↗

arXiv2023

Constraining the Charge of a Black Hole with Electromagnetic Radiation from a Black Hole-Neutron Star System

Black hole-neutron star (BH-NS) mergers are expected to emit gravitational-wave (GW) and electromagnetic (EM) counterparts when the NS is tidally disrupted or plunges into the BH. Recently, GW 200105 and GW200115 were claimed as originating in BH-NS mergers, even GW 200105 remains in debate. Several optical source candidates are reported to possible associate with the two GW events, but not confirmed yet. In this work, we assume that the BH is charged (the NS is naturally charged) and try to constrain the charge of the BH by using the possible associated EM emission from the charged BH and NS system working in the inspiral regime. We adopt electric and magnetic dipole radiations for the binaries which power a Poynting-flux-dominated outflow to accelerate electrons. Then, it produces the observed EM radiation via synchrotron radiation. We find that the conversion efficiency in the X-ray band is much higher than that of the ultraviolet (UV), near-infrared, and radio bands. The estimated maximum charge-to-mass ratio (the charge for unit mass) of the BH is $1.12\times 10^{-6}$ and $1.53\times 10^{-6}$ esu for the binary systems of GW200105 and GW200115, respectively, if magnetic field strength $B_{p}\lesssim ~10^{16}$ G and period $P>~1$ ms for the NS spin.

astro-ph.HE↗

arXiv2023

Search for the gamma-ray spectral lines with the DAMPE and the Fermi-LAT observations

Weakly interacting massive particles, as a major candidate of dark matter (DM), may directly annihilate or decay into high-energy photons, producing monochromatic spectral lines in the gamma-ray band. These spectral lines, if detected, are smoking-gun signatures for the existence of new physics. Using the 5 years of DAMPE and 13 years of Fermi-LAT data, we search for line-like signals in the energy range of 3 GeV to 1 TeV from the Galactic halo. Different regions of interest are considered to accommodate different DM density profiles. We do not find any significant line structure, and the previously reported line-like feature at $\sim$133 GeV is also not detected in our analysis. Adopting a local DM density of $ρ_{\rm local}=0.4\,{\rm GeV\,cm^{-3}}$, we derive 95% confidence level constraints on the velocity-averaged cross-section of $\langle{σv}\rangle_{γγ} \lesssim 4 \times 10^{-28}\,{\rm cm^{3}\,s^{-1}}$ and the decay lifetime of $τ_{γν} \gtrsim 5 \times 10^{29}\,{\rm s}$ at 100 GeV, achieving the strongest constraints to date for the line energies of 6-660 GeV. The improvement stems from the longer Fermi-LAT data set used and the inclusion of DAMPE data in the analysis. The simultaneous use of two independent data sets could also reduce the systematic uncertainty of the search.

astro-ph.HE↗

arXiv2023

Studying X-ray spectra from large-scale jets of FR II radio galaxies: application of shear particle acceleration

Shear particle acceleration is a promising candidate for the origin of extended high-energy emission in extra-galactic jets. In this paper, we explore the applicability of a shear model to 24 X-ray knots in the large-scale jets of FR II radio galaxies, and study the jet properties by modeling the multi-wavelength spectral energy distributions (SEDs) in a leptonic framework including synchrotron and inverse Compton - CMB processes. In order to improve spectral modelling, we analyze Fermi-LAT data for five sources and reanalyzed archival data of Chandra on 15 knots, exploring the radio to X-ray connection. We show that the X-ray SEDs of these knots can be satisfactorily modelled by synchrotron radiation from a second, shear-accelerated electron population reaching multi-TeV energies. The inferred flow speeds are compatible with large-scale jets being mildly relativistic. We explore two different shear flow profiles (i.e., linearly decreasing and power-law) and find that the required spine speeds differ only slightly, supporting the notion that for higher flow speeds the variations in particle spectral indices are less dependent on the presumed velocity profile. The derived magnetic field strengths are in the range of a few to ten microGauss, and the required power in non-thermal particles typically well below the Eddington constraint. Finally, the inferred parameters are used to constrain the potential of FR II jets as possible UHECR accelerators.

astro-ph.HE↗

arXiv2023

White-light superflare and long-term activity of the nearby M7 type binary EI~Cnc observed with GWAC system

Stellar white-light flares are believed to play an essential role on the physical and chemical properties of the atmosphere of the surrounding exoplanets. Here we report an optical monitoring campaign on the nearby flaring system EI~Cnc carried out by the Ground-based Wide Angle Cameras (GWAC) and its dedicated follow-up telescope. A superflare, coming from the brighter component EI~CncA, was detected and observed, in which four components are required to properly model the complex decay light curve. The lower limit of flare energy in the $R-$band is estimated to be $3.3\times10^{32}$ ergs. 27 flares are additionally detected from the GWAC archive data with a total duration of 290 hours. The inferred cumulative flare frequency distribution follows a quite shallow power-law function with a slope of $β=-0.50\pm 0.03$ over the energy range between $10^{30}$ and $10^{33}$ erg, which reinforces the trend that stars cooler than M4 show enhanced superflare activity. The flares identified in EI~Cnc enable us to extend the $τ-E$ relationship previously established in the white-light superflares of solar-type stars down to an energy as low as $\sim10^{30}$erg (i.e., by three orders): $τ\propto E^{0.42\pm0.02}$, which suggests a common flare mechanism for stars with a type from M to solar-like, and implies an invariant of $B^{1/3}\upsilon_{\rm A}$ in the white-light flares.

astro-ph.SR↗