PACS numbers: 98.80. Es, 95.35.+d, 98.80.Jk

Constraints on the original Cardassian model and the modified polytropic Cardassian model are examined from the recently derived 42 gamma-ray bursts (GRBs) data calibrated with the method avoiding the circularity problem. The results show that GRBs can be an optional observation to constrain on the Cardassian models. Combining the GRBs data with the newly derived size of baryonic acoustic oscillation peak from the Sloan Digital Sky Survey (SDSS), and the position of first acoustic peak of the Cosmic Microwave Background radiation (CMB) from Wilkinson Microwave Anisotropy Probe (WMAP), we find $\Omega_{m0}=0.27_{-0.02}^{+0.02}, n=0.06_{-0.08}^{+0.07}$ ($1\sigma$) for the original Cardassian model, and $\Omega_{m0}=0.27^{+0.03}_{-0.02}$, $n=-0.09_{-1.91}^{+0.23}, \beta=0.82_{-0.62}^{+2.10}$ ($1\sigma$) for the modified polytropic Cardassian model.Comment: 11 pages, 4 figures, accepted for publication in Science in China

The power spectral densities (PSDs) for a sample of active galactic nuclei (AGNs) are analyzed in both the frequency domain and the time domain. We find for each object that for broadband noise a character timescale-bifurcation timescale of Fourier and time-domain PSD exists in the 10 3 -10 6 s range, below which the time-domain power spectrum is systematically higher than the corresponding Fourier spectrum. The relationship between bifurcation timescale, AGN mass and luminosity is studied. Compared with the fact that similar phenomena have been found for Galactic black hole candidates (GBHs) with bifurcation timescale ~0.1 s but not for accreting neutron stars, our finding indicates that AGNs and GBHs have common intrinsic nature in rapid X-ray variability with a character time parameter scaled with their masses.galaxies: nuclei, X-rays: galaxies, methods: data analysis Li & Muraki (2002) [1] analyzed the power spectra density for a sample of GBHs and neutron stars in both the Fourier frequency domain and the time domain, where the time domain power spectral density (PSD) was calculate based on the initial definition of the variation power in a time series. They found that for broadband noise, the two kinds of PSD in accreting neutron stars (4U0614+091, 4U1608-522, 4U1705-44, KS1731-260, GS1826-24) were generally consistent with each other, but the time-domain PSD for GBHs (Cyg X-1, GRS1915+ 105, GRO1655-40, GX339-4, XTE J1550-564) was systematically higher than the corresponding Fourier PSD in the timescale range shorter than a bifurcation timescale Δt b ≈ 0.1 s. Figure 1, as an example, shows the contract between PSD of Cyg X-1 and 4U0614+091. Simulation results show that for light-curves produced by a stochastic process model, random shots or autoregressive process, the bifurcation timescale of time-domain and Fourier power spectra corresponds to the character time of the stochastic process [1] , which indicates that random shots or other stochastic process with ~ 0.1 s character time parameter is a common nature of GBHs.In this study, power spectral analysis with both time-domain and Fourier PSD is made for a sample of AGNs. We find that the spectral bifurcation phenomenon also exists in AGNs in the timescale range of about 10 3 -10 6 s. We describe the used observations, data reduction procedure, and the used analysis methods, and present the analysis results and a brief discussion. Observations and data reductionLight-curves of 2-10 keV from a PCA detector aboard RXTE and pn aboard XMM-Newton are used in our study. The used observations are listed in Table 1. For NGC 5506's EXOSAT observation, the energy range sampled is 1-9 keV, which should have a similar shape and amplitude with RXTE, assuming the spectral shape is stationary on decade time scales.PCA/RXTE data are reduced with FTOOLS version 5.0.4. To minimize the background relative to source counts, we extract data only from the top layer. To exclude those ineffective data, we set the criteria as: ex-

For black hole binaries (BHBs) and active galactic nuclei (AGNs), bifurcation timescales (BTs) Δt b exist, below which time-domain power is significantly higher than the corresponding Fourier power. Quasi-periodic oscillations (QPOs) are removed from the Fourier spectra of BHBs. A relationship between BT, black hole mass and bolometric luminosity is derived. Strong anti-correlation between BT and luminosity of Cyg X-1 is found. After removing the QPOs, BTs are also obtained for two ultraluminous X-ray sources (ULXs), M82 X-1 and NGC5408 X-1. The results support that they harbor intermediate mass black holes (IMBHs).black hole binary, ultraluminous X-ray source, power spectral density, data analysis Power spectral densities (PSDs) in both the frequency and time domain have been jointly analyzed for a sample of BHBs and AGNs [1, 2]. All of them have similar phenomena: The time-domain PSDs are systematically higher than the corresponding Fourier PSDs in a short timescale regime in the time domain. Simulations show that BTs in PSDs represent the characteristic timescales of stochastic processes. They also estimated the BTs of AGNs by using the Lorentzian profile fitting method, and found that there is a positive correlation relationship between BT and black hole mass and an anti-correlation between BT and bolometric luminosity [2]. In this work, we analyze the PSDs of BHBs with more RXTE observations and give the relation among black hole BT, mass and bolometric luminosity, by fitting data of 6 AGNs and 4 BHBs. The relation supports that M82 X-1 and NGC 5408 X-1 harbor intermediate mass black holes.