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Aside from the grand-design stellar spirals appearing in the disk of M81, a pair of stellar spiral arms situated well inside the bright bulge of M81 has been recently discovered by Kendall et al. (2008). The seemingly unrelated pairs of spirals pose a challenge to the theory of spiral density waves. To address this problem, we have constructed a three component model for M81, including the contributions from a stellar disk, a bulge, and a dark matter halo subject to observational constraints. Given this basic state for M81, a modal approach is applied to search for the discrete unstable spiral modes that may provide an understanding for the existence of both spiral arms. It is found that the apparently separated inner and outer spirals can be interpreted as a single trailing spiral mode. In particular, these spirals share the same pattern speed 25.5 km s$^{-1}$ kpc$^{-1}$ with a corotation radius of 9.03 kpc. In addition to the good agreement between the calculated and the observed spiral pattern, the variation of the spiral amplitude can also be naturally reproduced.
We examine different phenomenological interaction models for Dark Energy and Dark Matter by performing statistical joint analysis with observational data arising from the 182 Gold type Ia supernova samples, the shift parameter of the Cosmic Microwave Background given by the three-year Wilkinson Microwave Anisotropy Probe observations, the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey and age estimates of 35 galaxies. Including the time-dependent observable, we add sensitivity of measurement and give complementary results for the fitting. The compatibility among three different data sets seem to imply that the coupling between dark energy and dark matter is a small positive value, which satisfies the requirement to solve the coincidence problem and the second law of thermodynamics, being compatible with previous estimates.
Using the data coming from the new 182 Gold type Ia supernova samples, the shift parameter of the Cosmic Microwave Background given by the three-year Wilkinson Microwave Anisotropy Probe observations, and the baryon acoustic oscillation measurement f rom the Sloan Digital Sky Survey, $H(z)$ and lookback time measurements, we have performed a statistical joint analysis of the interacting holographic dark energy model. Consistent parameter estimations show us that the interacting holographic dark energy model is a viable candidate to explain the observed acceleration of our universe.
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