Bimodal Nature of the Compactness Parameter
Collaborators: Stan Woosley(UCSC),Alex Heger(UM) and Bill Paxton(UCSB)
The compactness of the core of a massive star is one of the important global characteristics, which determine the fate of its death. Except few talks given by Zalman Barkat and Stan Woosley back in 1990s (Barkat's proceeding), the variation of the compactness as a function of mass and metallicity and their causes remain an important unexplored issue. Recently O'Connor and Ott reported a bimodal variation of the compactness parameter (basically the radius enclosing inner 2.5Msol) in their study of black hole formation in failing core-collapse supernovae (O'Connor and Ott 2010).
The Compactness Parameter as defined in the O'Connor and Ott (2010), calculated for KEPLER models in the range 12-30 Msol
We are creating a large grid of models mainly using 1D implicit hydrodynamic code KEPLER and to some extent the open source stellar evolutionary code MESA. So far we have found lots of interesting details in the variation of the compactness parameter and now working hard to find their intrinsic causes.
Overshooting in the Upper Main Sequence
Collaborators: Casey Meakin(LANL and UA), Dave Arnett(UA)
Turbulent Mixing and Mass Loss are the 2 most 'serious' issues with the current theory of stellar evolution. Our distant goal in this project is to tackle the problem of mixing at the boundaries. Traditionally such situations are handled with the Mixing Length Theory (MLT) with one of its free parameters: alpha_overshoot. This parameter is usually constrained by detached eclipsing binaries(dEBs), open clusters, asteroseismology and apsidal motion studies. However, since this picture is not really based on physics, the parameter is not constrained well:
Overshoot parameter estimates from dEBs (diamonds) and asteroseismological data (triangles). The values adopted by Girardi et al. (2000) and Pietrinferni et al. (2004) for populations synthesis are labeled G2000 and P2004. The mass uncertainties for the eclipsing binary data is negligible on the log(M) scale used. Overshoot parameters inferred from asteroseismic data are from Soriano & Vauclair (2010), Di Mauro et al. (2003), Sua´rez et al. (2009), Briquet et al. (2007), Dupret et al. (2004), Aerts et al. (2006), Desmet et al. (2009), and Mazumdar et al. (2006); and the values from eclipsing binary data are from Claret (2007).
In this study we are particularly looking at the convective core overshooting problem. So far we have calculated more than 25,000 models using MESA and TYCHO stellar evolutionary codes, to constrain the parameter using very high precision data from dEBs presented in Torres et al. (2010). Once we're done with this analysis we will move on to compare different mixing schemes for this problem: semiconvection, diffusive mixing and mass entrainment. The summary of this work is discussed in this paper.
This project was partially funded by Arizona Astronomy Board Grant
Machine Learning in Astronomy
Collaborators: Michael Shavlovsky(UCSC),Connie Rockosi(UCSC)
Following the ever increasing size of already huge survey databases, the role of Machine Learning in astronomy is growing naturally. Future optical and near-infrared surveys will cover billions of sources, so the more of the analyzing part has to be done directly on the base, in order to handle massive amounts of data (i.e. effective extracting of information from high dimentional database). In the past couple of years, people have been successfully implemented the advanced machine learning tools in several branches of astronomy: source detection in gamma-ray images (Campana et al. 2007), spectral classification with images (Richards et al. 2004) and inferring parameters from spectra (Re Fiorentin et al. 2007). Ball and Brunner (2010) provides a nice broad summary of this new direction in astronomy.
In this project we are basically pushing Re Fiorentin et al. (2007) work further. Instead of synthetic spectra, we are training the non-linear regression models with real SDSS data and implementing additional constraints, notably the S/N ratio variance, in order to extract all possible information as accurately as possible from the given real spectra.
Analytic Solution to the Lane-Emden Equation
Collaborators: Hassen Yesuf(UCSC)
As we all know form undergraduate physics class, the Lane-Emden equation basically describes the gravitational potential of a self-gravitating, spherically symmetric polytropic fluid. Its a special case of the elliptic type PDE, connecting the potential with the density, otherwise known as Poisson's equation. Polytropes of n=0,1,5 can be solved analytically (Chandrasekhar 1967, p. 91):
This is really not a 'serious' research project, but in my spare times with my friend Hassen, we're trying to find analytic solutions for the polytropic indexes of n=2,3,4. Extra knowledge never hurts. ;-)