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The "Breakthrough Starshot" program is planning to send transrelativistic probes to travel to nearby stellar systems within decades. Because the probe velocity is designed to be a good fraction of the light speed, Zhang & Li recently proposed that these transrelativistic probes can be used to study astronomical objects and to test special relativity. In this work, we propose some methods to test special relativity and constrain photon mass using the Doppler effect with the images and spectral features of astronomical objects as observed in the transrelativistic probes. We introduce more general theories to set up the framework of testing special relativity, including the parametric general Doppler effect and the Doppler effect with massive photons. We find that by comparing the spectra of a certain astronomical object, one can test Lorentz invariance and constrain photon mass. Additionally, using the imaging and spectrograph capabilities of transrelativistic probes, one can test time dilation and constrain photon mass. For a transrelativistic probe with velocity v ∼ 0.2c, aperture D ∼ 3.5 cm, and spectral resolution R ∼ 100 (or 1000), we find that the probe velocity uncertainty can be constrained to σv ∼ 0.01c (or 0.001c), and the time dilation factor uncertainty can be constrained to (or 0.001), where is the time dilation factor and γ is the Lorentz factor. Meanwhile, the photon mass limit is set to mγ ≲ 10−33 g, which is slightly lower than the energy of the optical photon. [ABSTRACT FROM AUTHOR]

By fitting the bolometric light curves of 31 superluminous supernovae (SLSNe) with the magnetar engine model, we derive the ejecta masses and magnetar parameters for these SLSNe. The lower boundary of magnetic field strengths of SLSN magnetars can be set just around the critical field strength of the electron Landau quantization. In more details, SLSN magnetars can further be divided into two subclasses of magnetic fields of and , respectively. It is revealed that these two subclasses of magnetars are just associated with the slow-evolving and fast-evolving bolometric light curves of SLSNe. In comparison, the magnetars harbored in gamma-ray bursts (GRBs) and associated hypernovae are usually inferred to have much higher magnetic fields with a lower boundary of about . This robustly suggests that it is the magnetic fields that play the crucial role in distinguishing SLSNe from GRBs/hypernovae. The rotational energy of SLSN magnetars is found to be correlated with the masses of supernova ejecta. This possible correlation provides a clue to explore the nature of their progenitors. Moreover, the distribution of ejecta masses of SLSNe is basically intermediate between those of normal core-collapse supernovae and hypernovae. This could indicate an intrinsic connection among these different stellar explosions. [ABSTRACT FROM AUTHOR]