Determining the luminosity function of Swift long gamma-ray bursts with pseudo-redshifts

The determination of luminosity function (LF) of gamma-ray bursts (GRBs) is of an important role for the cosmological applications of the GRBs, which is however hindered seriously by some selection effects due to redshift measurements. In order to avoid these selection effects, we suggest to calculate pseudo-redshifts for Swift GRBs according to the empirical L-E_p relationship. Here, such a $L-E_p$ relationship is determined by reconciling the distributions of pseudo- and real redshifts of redshift-known GRBs. The values of E_p taken from Butler's GRB catalog are estimated with Bayesian statistics rather than observed. Using the GRB sample with pseudo-redshifts of a relatively large number, we fit the redshift-resolved luminosity distributions of the GRBs with a broken-power-law LF. The fitting results suggest that the LF could evolve with redshift by a redshift-dependent break luminosity, e.g., L_b=1.2\times10^{51}(1+z)^2\rm erg s^{-1}. The low- and high-luminosity indices are constrained to 0.8 and 2.0, respectively. It is found that the proportional coefficient between GRB event rate and star formation rate should correspondingly decrease with increasing redshifts.Comment: 5 pages, 5 figures, accepted for publication in ApJ

Black hole hyperaccretion in collapsars. III. GRB timescale

Gamma-ray bursts (GRBs) are classified into long and short populations (i.e., LGRBs and SGRBs) based on the observed bimodal distribution of duration $T_{90}$. Multimessenger observations indicated that most SGRBs and LGRBs should be powered by ultrarelativistic jets launched from black hole (BH) hyperaccretion in compact object mergers and massive collapsars, respectively. However, the duration criterion sometimes cannot correctly reflect the physical origin of a particular GRB. In the collapsar scenario, a GRB can be observed when the jet breaks out from the envelope and circumstellar medium successfully. The observed GRB duration reflects only the time that the engine operates after the jet breaks out. This work studies the propagation of jets driven by the neutrino annihilation or Blandford-Znajek mechanism in massive collapsars. The signatures of the progenitors for producing LGRBs, SGRBs, and failed GRBs in the collapsar scenario are exhibited. The competition between the mass supply onto the BH hyperaccretion and jet propagation into the envelope are definitely dependent on the density profiles of the collapsars. We show that duration and isotropic energy $E_{\rm{\gamma,iso}}$ of GRBs can help constrain the density profiles of collapsars. Finally, we propose that a collapsar-origin SGRB, GRB 200826A, might originate from a neutrino-annihilation-dominated jet launched by a $\sim 10~M_\odot$ collapsar whose progenitor's envelope has been stripped.Comment: 9 pages, 4 figures, accepted for publication in Ap

Dynamic dissipative cooling of a mechanical oscillator in strong-coupling optomechanics

Cooling of mesoscopic mechanical resonators represents a primary concern in cavity optomechanics. Here in the strong optomechanical coupling regime, we propose to dynamically control the cavity dissipation, which is able to significantly accelerate the cooling process while strongly suppressing the heating noise. Furthermore, the dynamic control is capable of overcoming quantum backaction and reducing the cooling limit by several orders of magnitude. The dynamic dissipation control provides new insights for tailoring the optomechanical interaction and offers the prospect of exploring macroscopic quantum physics.Comment: accepetd in Physical Review Letter

Higher theta series for unitary groups over function fields

In previous work, we defined certain virtual fundamental classes for special cycles on the moduli stack of Hermitian shtukas, and related them to the higher derivatives of non-singular Fourier coefficients of Siegel-Eisenstein series. In the present article, we construct virtual fundamental classes in greater generality, including those expected to relate to the higher derivatives of singular Fourier coefficients. We assemble these classes into "higher" theta series, which we conjecture to be modular. Two types of evidence are presented: structural properties affirming that the cycle classes behave as conjectured under certain natural operations such as intersection products, and verification of modularity in several special situations. One innovation underlying these results is a new approach to special cycles in terms of derived algebraic geometry.Comment: Comments welcome