The change of GRB polarization angles in the magnetic-dominated jet model

The polarimetric measurement on the prompt phase of GRB 100826A shows that the polarization angle changes $\sim 90^{\circ}$ between two adjacent time intervals. We will show that this phenomenon can be naturally interpreted in the framework of the magnetic-dominated jet (MDJ) model. The MDJ model suggests that the bulk Lorentz factor of the outflow increases as $\Gamma\propto r^{1/3}$, until reaching a saturated value $\Gamma_{\rm sat}$. Electrons move in the globally ordered magnetic field advected by the jet from the central engine and produce synchrotron photons. The polarized synchrotron photons travel alone the jet direction and then collide with the cold electrons at the front of the jet. After the Compton scattering process, these photons escape from the jet and are detected by the observer locating slightly off-axis. If photons are emitted before the bulk Lorentz factor saturates, the change of polarization angle is a natural result of the acceleration of the outflow.Comment: 7 pages, 2 figure

Glauber gluons in pion-induced Drell-Yan processes

We point out that the existence of Glauber gluons in the $k_T$ factorization theorem can account for the violation of the Lam-Tung relation, namely, the anomalous lepton angular distribution, observed in pion-induced Drell-Yan processes. Radiations, that balance the lepton-pair transverse momentum, cause the responsible spin-transverse-momentum correlation in the Glauber-gluon background. It is argued that the Glauber effect is significant in the pion due to its unique role of being a Nambu-Goldstone boson and a $q\bar q$ bound state simultaneously. This mechanism is compared to other resolutions in the literature by means of vacuum effects and Boer-Mulders functions. We propose to discriminate the above resolutions by measuring the $p\bar p$ Drell-Yan process at GSI and J-PARC.Comment: power counting of Glauber divergences added; more references include

Enumerations of Permutations by Circular Descent Sets

The circular descent of a permutation $\sigma$ is a set $\{\sigma(i)\mid \sigma(i)>\sigma(i+1)\}$. In this paper, we focus on the enumerations of permutations by the circular descent set. Let $cdes_n(S)$ be the number of permutations of length $n$ which have the circular descent set $S$. We derive the explicit formula for $cdes_n(S)$. We describe a class of generating binary trees $T_k$ with weights. We find that the number of permutations in the set $CDES_n(S)$ corresponds to the weights of $T_k$. As a application of the main results in this paper, we also give the enumeration of permutation tableaux according to their shape

Effect of GRB spectra on the empirical luminosity correlations and the GRB Hubble diagram

The spectra of gamma-ray bursts (GRBs) in a wide energy range can usually be well described by the Band function, which is a two smoothly jointed power laws cutting at a breaking energy. Below the breaking energy, the Band function reduces to a cut-off power law, while above the breaking energy it is a simple power law. However, for some detectors (such as the Swift-BAT) whose working energy is well below or just near the breaking energy, the observed spectra can be fitted to cut-off power law with enough precision. Besides, since the energy band of Swift-BAT is very narrow, the spectra of most GRBs can be fitted well even using a simple power law. In this paper, with the most up-to-date sample of Swift-BAT GRBs, we study the effect of different spectral models on the empirical luminosity correlations, and further investigate the effect on the reconstruction of GRB Hubble diagram. We mainly focus on two luminosity correlations, i.e., the Amati relation and Yonetoku relation. We calculate these two luminosity correlations on both the case that the GRB spectra are modeled by Band function and cut-off power law. It is found that both luminosity correlations only moderately depend on the choice of GRB spectra. Monte Carlo simulations show that Amati relation is insensitive to the high-energy power-law index of the Band function. As a result, the GRB Hubble diagram calibrated using luminosity correlations is almost independent on the GRB spectra.Comment: 13 pages, 7 figures, 5 tables, accepted by MNRA

Tutte polynomial and G-parking functions

Let $G$ be a connected graph with vertex set $\{0,1,2,...,n\}$. We allow $G$ to have multiple edges and loops. In this paper, we give a characterization of external activity by some parameters of $G$-parking functions. In particular, we give the definition of the bridge vertex of a $G$-parking function and obtain an expression of the Tutte polynomial $T_G(x,y)$ of $G$ in terms of $G$-parking functions. We find the Tutte polynomial enumerates the $G$-parking function by the number of the bridge vertices

Gamma-ray polarization induced by cold electrons via Compton processes

The polarization measurement is an important tool to probe the prompt emission mechanism in gamma-ray bursts (GRBs). The synchrotron photons can be scattered by cold electrons in the outflow via Compton scattering processes. The observed polarization depends on both the photon energy and the viewing angle. With the typical bulk Lorentz factor $\Gamma \sim 200$, photons with energy $E>10$ MeV tend to have smaller polarization than photons with energy $E<1$ MeV. At the right viewing angle, i.e. $\theta \sim \Gamma^{-1}$, the polarization achieves its maximal value, and the polarization angle changes $90^{\circ}$ relative to the initial polarization direction. Thus, the synchrotron radiation plus Compton scattering model can naturally explain the $90^{\circ}$ change of the polarization angle in GRB 100826A.Comment: 19 Pages, 5 figures, 1 tabl

Polarization of photons scattered by electrons in any spectral distribution

Based on the quantum electrodynamics, we present a generic formalism of the polarization for beamed monochromatic photons scattered by electrons in any spectral distribution. The formulae reduce to the components of the Fano matrix when electrons are at rest. We mainly investigate the polarization in three scenarios, i.e., electrons at rest, isotropic electrons with a power law spectrum and thermal electrons. If the incident beam is polarized, the polarization is reduced significantly by isotropic electrons at large viewing angles, and the degree of polarization due to thermal electrons is about one times less than that of electrons in a power law. If the incident bean is unpolarized, soft $\gamma$-rays can lead to about 15% polarization at viewing angles around $\pi/4$. For isotropic electrons, one remarkable feature is that the polarization as a function of the incident photon energy always peaks roughly at 1 MeV, this is valid for both the thermal and power law cases. This feature can be used to distinguish the model of the inverse Compton scattering from that of the synchrotron radiation.Comment: 17 pages, 4 figures. to be published in Ap

Model-independent distance calibration of high-redshift gamma-ray bursts and constrain on the Λ\LambdaCDM model

Gamma-ray bursts (GRBs) are luminous enough to be detectable up to redshift $z\sim 10$. They are often proposed as complementary tools to type-Ia supernovae (SNe Ia) in tracing the Hubble diagram of the Universe. The distance calibrations of GRBs usually make use one or some of the empirical luminosity correlations, such as $\tau_{\rm lag}-L$, $V-L$, $E_p-L$, $E_p-E_{\gamma}$, $\tau_{\rm RT}-L$ and $E_p-E_{\rm iso}$ relations. These calibrating methods are based on the underling assumption that the empirical luminosity correlations are universal over all redshift range. In this paper, we test the possible redshift dependence of six luminosity correlations by dividing GRBs into low-$z$ and high-$z$ classes according to their redshift smaller or larger than 1.4. It is shown that the $E_p-E_{\gamma}$ relation for low-$z$ GRBs is consistent with that for high-$z$ GRBs within $1\sigma$ uncertainty. The intrinsic scatter of $V-L$ relation is too larger to make a convincing conclusion. For the rest four correlations, however, low-$z$ GRBs differ from high-$z$ GRBs at more than $3\sigma$ confidence level. As such, we calibrate GRBs using the $E_p-E_{\gamma}$ relation in a model-independent way. The constraint of high-$z$ GRBs on the $\Lambda$CDM model gives $\Omega_M=0.302\pm 0.142(1\sigma)$, well consistent with the Planck 2015 results.Comment: 10 pages, 4 figures, 3 table

Gamma-ray burst polarization via Compton scattering process

Synchrotron radiation and Compton scattering are widely accepted as the most likely emission mechanisms of some astrophysical phenomena, such as gamma-ray bursts (GRBs) and active galactic nuclei (AGNs). The measurement on polarization of photons provides a useful tool to distinguish different emission mechanisms and structures of the emission region. Based on the differential cross section of a polarized photon scattered by an unpolarized electron of any initial momentum, we derive analytical formula of polarization for beamed photons scattered by isotropic electrons with a power law distribution. Numerical calculations are carried out in four special cases: electrons at rest, Thomson limit, head-on collision and monochromatic electrons. It is found that the maximum polarization can be as high as $100\%$ for low energy photons, if the electrons are at rest. Although polarization is highly suppressed due to the isotropic electrons, a maximum value of \sim 10\% \-- 20\% can still be achieved. Compton scattering process can be used to explain the polarization of GRB 041219A and GRB 100826A.Comment: 22 pages, 5 figure

The significance of anisotropic signals hiding in the type Ia supernovae

We use two different methods, i.e., dipole-fitting (DF) and hemisphere comparison (HC), to search for the anisotropic signals hiding in the Union2.1 data set. We find that the directions of maximum matter density derived using these two methods are about $114^{\circ}$ away from each other. We construct four Union2.1-like mock samples to test the statistical significance of these two methods. It is shown that DF method is statistically significant, while HC method is strongly biased by the distribution of data points in the sky. Then we assume that the anisotropy of distance modulus is mainly induced by the anisotropy of matter density, which is modeled to be the dipole form $\Omega_M=\Omega_{M0}(1-\cos\theta)$. We fit our model to Union2.1, and find that the direction of maximum matter density is well consistent with the direction derived using DF method, but it is very different from the direction previously claimed. Monte Carlo simulations show that our method is statistically more significant than HC method, although it is not as significant as DF method. The statistical significance can be further improved if the data points are homogeneously distributed in the sky. Due to the low quality of present supernovae data, however, it is still premature to claim that the Universe has any preferred direction.Comment: 11 pages, 12 figures, accepted by MNRA