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Register a new userAre long-term $N$-body simulations reliable?
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David M. Hernandez
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$N$-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be established. We address this reliability by running a three-body planetary system over about $200$ e-folding times. Using nearby initial conditions, we can construct statistics of the long-term phase-space structure and compare to rough estimates of resonant widths of the system. We compared statistics for a wide range of numerical methods, including a Runge--Kutta method, Wisdom--Holman method, symplectic corrector methods, and a method by Laskar and Robutel. Improving an integrator did not increase the phase space accuracy, but simply increasing the number of initial conditions did. In fact, the statistics of a higher order symplectic corrector method were inconsistent with the other methods in one test.
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Many barred galaxies harbor small-scale secondary bars in the center. The evolution of such double-barred galaxies is still not well understood, partly because of a lack of realistic N-body models with which to study them. Here we report the generation of such systems in the presence of rotating pseudobulges. We demonstrate with high mass and force resolution collisionless N-body simulations that long-lived secondary bars can form spontaneously without requiring gas, contrary to previous claims. We find that secondary bars rotate faster than primary ones. The rotation is not rigid: the secondary bars pulsate, with their amplitude and pattern speed oscillating as they rotate through the primary bars. This self-consistent study supports previous work based on orbital analysis in the potential of two rigidly rotating bars. We also characterize the density and kinematics of the N-body simulations of the double-barred galaxies, compare with observations to achieve a better understanding of such galaxies. The pulsating nature of secondary bars may have important implications for understanding the central region of double-barred galaxies.
Through synthetic observations of a hydrodynamical simulation of an evolving star-forming region, we assess how the choice of observational techniques affects the measurements of properties which trace star formation. Testing and calibrating observational measurements requires synthetic observations which are as realistic as possible. In this part of the paper series (Paper I), we explore different techniques for how to map the distributions of densities and temperatures from the particle-based simulations onto a Voronoi mesh suitable for radiative transfer and consequently explore their accuracy. We further test different ways to set up the radiative transfer in order to produce realistic synthetic observations. We give a detailed description of all methods and ultimately recommend techniques. We have found that the flux around 20 microns is strongly overestimated when blindly coupling the dust radiative transfer temperature with the hydrodynamical gas temperature. We find that when instead assuming a constant background dust temperature in addition to the radiative transfer heating, the recovered flux is consistent with actual observations. We present around 5800 realistic synthetic observations for Spitzer and Herschel bands, at different evolutionary time-steps, distances and orientations. In the upcoming papers of this series (Paper II, Paper III and Paper IV), we will test and calibrate measurements of the star-formation rate (SFR), gas mass and the star-formation efficiency (SFE) using our realistic synthetic observations.
We report results of N-body simulations of isolated star clusters, performed up to the point where the clusters are nearly completely dissolved. Our main focus is on the post-collapse evolution of these clusters. We find that after core collapse, isolated clusters evolve along nearly a single sequence of models whose properties are independent of the initial density profile and particle number. Due to the slower expansion of high-N clusters, relaxation times become almost independent of the particle number after several core collapse times, at least for the particle range of our study. As a result, the dissolution times of isolated clusters exhibit a surprisingly weak dependence on N. We find that most stars escape due to encounters between single stars inside the half-mass radius of the cluster. Encounters with binaries take place mostly in the cluster core and account for roughly 15% of all escapers. Encounters between single stars at intermediate radii are also responsible for the build up of a radial anisotropic velocity distribution in the halo. For clusters undergoing core oscillations, escape due to binary stars is efficient only when the cluster center is in a contracted phase. Our simulations show that it takes about 10^5 N-body time units until the global anisotropy reaches its maximum value. The anisotropy increases with particle number and it seems conceivable that isolated star clusters become vulnerable to radial orbit instabilities for large enough N. However, no indication for the onset of such instabilities was seen in our runs.
Tormen and Bertschinger have presented an algorithm which allows the dynamic range of N-body simulations to be extended by adding long-wavelength power to an evolved N-body simulation. This procedure is of considerable interest as it will enable mock galaxy catalogues to be constructed with volumes as large as those of the next generation of galaxy redshift surveys. Their algorithm, however, neglects the coupling between long-wavelength linear modes and short-wavelength non-linear modes. The growth of structure on small scales is coupled to the amplitude of long-wavelength density perturbations via their effect on the local value of the density parameter Omega_0.The effect of neglecting this coupling is quantified using a set of specially tailored N-body simulations. It is shown that the large-scale clustering of objects defined in the evolved density field such as galaxy clusters is strongly underestimated by their algorithm. An adaptation to their algorithm is proposed that, at the expense of additional complexity, remedies the shortcomings of the original one. Methods of constructing biased mock galaxy catalogues which utilise the basic algorithm of Tormen and Bertschinger, but avoid the pitfalls are discussed.
We present a comprehensive investigation of main-sequence (MS) binaries in the DRAGON simulations, which are the first one-million particles direct $N$-body simulations of globular clusters. We analyse the orbital parameters of the binary samples in two of the DRAGON simulations, D1-R7- IMF93 and D2-R7-IMF01, focusing on their secular evolution and correlations up to 12 Gyr. These two models have different initial stellar mass functions: Kroupa 1993 (D1-R7-IMF93) and Kroupa 2001 (D2-R7-IMF01); and different initial mass ratio distributions: random paring (D1-R7-IMF93) and a power-law (D1-R7-IMF93). In general, the mass ratio of a population of binaries increases over time due to stellar evolution, which is less significant in D2-R7-IMF01. In D1-R7-IMF93, primordial binaries with mass ratio $q approx$ 0.2 are most common, and the frequency linearly declines with increasing $q$ at all times. Dynamical binaries of both models have higher eccentricities and larger semi-major axes than primordial binaries. They are preferentially located in the inner part of the star cluster. Secular evolution of binary orbital parameters does not depend on the initial mass-ratio distribution, but is sensitive to the initial binary distribution of the system. At t = 12 Gyr, the binary fraction decreases radially outwards, and mass segregation is present. A color difference of 0.1 mag in $F330W-F814W$ and 0.2 mag in $NUV-y$ between the core and the outskirts of both clusters is seen, which is a reflection of the binary radial distribution and the mass segregation in the cluster. The complete set of data for primordial and dynamical binary systems at all snapshot intervals is made publicly available.
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