We use two model-independent methods to standardize long gamma-ray bursts (GRBs) using the E iso − E p correlation (log E iso = a + b log E p ), where E iso is the isotropic-equivalent gamma-ray energy and E p is the spectral peak energy. We update 42 long GRBs and attempt to constrain the cosmological parameters. The full sample contains 151 long GRBs with redshifts from 0.0331 to 8.2. The first method is the simultaneous fitting method. We take the extrinsic scatter σ ext into account and assign it to the parameter E iso . The best-fitting values are a = 49.15 ± 0.26, b = 1.42 ± 0.11, σ ext = 0.34 ± 0.03 and Ω m = 0.79 in the flat ΛCDM model. The constraint on Ω m is 0.55 < Ω m < 1 at the 1σ confidence level. If reduced χ 2 method is used, the best-fit results are a = 48.96 ± 0.18, b = 1.52 ± 0.08, and Ω m = 0.50 ± 0.12. The second method uses type Ia supernovae (SNe Ia) to calibrate the E iso − E p correlation. We calibrate 90 high-redshift GRBs in the redshift range from 1.44 to 8.1. The cosmological constraints from these 90 GRBs are Ω m = 0.23 +0.06 −0.04 for flat ΛCDM and Ω m = 0.18 ± 0.11 and Ω Λ = 0.46 ± 0.51 for non-flat ΛCDM. For the combination of GRB and SNe Ia sample, we obtain Ω m = 0.271 ± 0.019 and h = 0.701 ± 0.002 for the flat ΛCDM and the non-flat ΛCDM, and the results are Ω m = 0.225 ± 0.044, Ω Λ = 0.640 ± 0.082, and h = 0.698 ± 0.004. These results from calibrated GRBs are consistent with that of SNe Ia. Meanwhile, the combined data can improve cosmological constraints significantly, compared to SNe Ia alone. Our results show that the E iso − E p correlation is promising to probe the high-redshift Universe.

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In this work, 1272 superflares on 311 stars are collected from 22,539 solar-type stars from the second-year observation of the Transiting Exoplanet Survey Satellite (TESS), which almost covered the northern hemisphere of the sky. Three superflare stars contain hot Jupiter candidates or ultrashort-period planet candidates. We obtain γ = −1.76 ± 0.11 of the correlation between flare frequency and flare energy ( ) for all superflares and get β = 0.42 ± 0.01 of the correlation between superflare duration and energy (T duration ∝ E β ), which supports that a similar mechanism is shared by stellar superflares and solar flares. Stellar photometric variability (R var) is estimated for all solar-type stars, and the relation of is included. An indicator of chromospheric activity (S-index) is obtained by using data from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) for 7454 solar-type stars. Distributions of these two properties indicate that the Sun is generally less active than superflare stars. We find that saturation-like feature of R var ∼ 0.1 may be the reason for superflare energy saturating around 1036 erg. Object TIC 93277807 was captured by the TESS first-year mission and generated the most energetic superflare. This superflare is valuable and unique in that it can be treated as an extreme event, which may be generated by different mechanisms than other superflares.

Young neutron stars (NSs) born in core-collapse explosions are promising candidates for the central engines of fast radio bursts (FRBs), since the first localized repeating burst FRB 121102 happens in a star forming dwarf galaxy, which is similar to the host galaxies of superluminous supernovae (SLSNe) and long gamma-ray bursts (LGRBs). However, FRB 180924 and FRB 190523 are localized to massive galaxies with low rates of star formation, compared with the host of FRB 121102. Meanwhile, the offsets between the bursts and host centers are about 4 kpc and 29 kpc for FRB 180924 and FRB 190523, respectively. These properties of hosts are similar to short gamma-ray bursts (SGRBs), which are produced by mergers of binary neutron star (BNS) or neutron star-black hole (NS-BH). Therefore, the NSs powering FRBs may be formed in BNS mergers. In this paper, we study the BNS merger rates, merger times, and predict their most likely merger locations for different types of host galaxies using population synthesis method. We find that the BNS merger channel is consistent with the recently reported offsets of FRB 180924 and FRB 190523. The offset distribution of short GRBs is well reproduced by population synthesis using galaxy model which is similar to GRB hosts. The event rate of FRBs (including non-repeating and repeating), is larger than those of BNS merger and short GRBs, which requires a large fraction of observed FRBs emitting several bursts. Using curvature radiation by bunches in NS magnetospheres, we also predict the observational properties of FRBs from BNS mergers, including the dispersion measure, and rotation measure. At late times (t ≥ 1yr), the contribution to dispersion measure and rotation measure from BNS merger ejecta could be neglected.