Spectral disentangling with XTgrid
XTgrid (Németh et al., 2012 MNRAS, 427, 2180) applies a steepest-gradient chi-square minimization algorithm to fit synthetic spectra to observations and derive absolute surface parameters for hot stars and binaries. The procedure takes an observation and a set of free parameters, and iteratively varies the parameters to converge a best-fit. All parameters are changed in every iteration and weighted by their respective contribution to improve the goodness of fit.
Although the method is computationally intensive and the required large number of iterations (50 - 80) make it rather slow compared to grid-search methods, its major advantage is the ability to solve problems with excessive number of free parameters. One can easily track about 30 parameters in spectral modeling, which allows to attack more complex problems or fit individual element abundances.
Spectral decomposition was included in XTgrid from its early versions. Within the GALEX survey (Vennes et al., MNRAS 410, 2095) it became obvious that neary 20% of hot subdwarf stars are found in composite spectra with F-G-K type main-sequence companions. In such systems both components of the binary have comparable luminosities in the visible and contribute to the observed spectrum. While H, He and the strongest metal lines are clearly visible in such spectra, the strong contribution of the companion makes reliable parameter determination impossible with single-star models. To solve this issue, we included a secondary template to the subdwarf synthetic spectrum and we iterate the linear combination of the two models until the best-fit is reached. This step added at least 5 new parameters to the fits (Teff, logg, [Fe/H], dilution and projected rotation of the secondary), but further parameters, such as alpha or carbon enhancements can be added, if a suitable grid provides such models. The observed template spectra for the cool companions were taken from the MILES library (Cenarro et al., 2007, MNRAS, 374, 664). In the beginning, the precise characterization of the secondary star was not considered. As long as a generic template could describe the spectrum, no further interpolations or error analysis were attempted. This was adequate, because we were most interested in the parameters of the hot component of the binary.
Later developments included a more sophisticated spectral disentangling of binaries, that also finds the radial velocities of the stars. This information is important to confirm binarity and provide input for orbital solutions. The secondary spectrum is now extracted from a pre-calculated grid, such as the BOSZ spectral library (Bohlin et al., 2017 AJ, 153, 234) or the PHOENIX v2 library (Husser et al., 2013 A&A, 553, 6). A set of example fits to high-resolution spectra are available within the VLT/UVES sample of long-period hot subdwarf binaries by Vos et al., 2018 MNRAS, 473, 693 (https://astroserver.org/KW32YZ). The decomposition does not use any assumptions for the luminosities of the members, just tries to reproduce the observation with two models. This approach is useful to remove spectral contamination due to foreground or background stars in crowded fields. Such an application was performed by Reed et al., 2020 MNRAS (in press, https://astroserver.org/FC6QRB).
In contrast, the approach included in XTgrid use models calculated on-the-fly. This method follows the chi-square field to the minimum, which is at the very bottom of the valley. This is a computationally demanding task, but able to provide more precise final parameters. However, one must pay attention to various correlations, that may skew the accuracy of the method. This we attempt to achieve with constraints from SED data. Another important advantage of this approach is the ability to change any model parameters individually without interpolating synthetic spectra. This is important because the method of interpolation is another factor that adds systematics to the final results.
Figures 2 - 5 demonstrate the starting and final models of a fit procedure. The animations in Fig 6 and 7 show how XTgrid does approach the best fit composite model of a LAMOST observation. The synthetic composite model (green) is normalized to the observation (red) at 8000 Å. The composite model is the sum of a hot subdwarf component (Tlusty model in green) and a cool main sequence star component (Atlas model in red). The residuals (grey) at the bottom show how the goodness of fit improves with iterations. The procedure started from a 28000 K + 5000 K (sdB+K2V) binary and converged on a 53700 K + 5850 K (sdO+G2V) binary.
From start to best-fit model (global)
Fig 2: Starting sdB+K2V type to model a composite spectrum binary from LAMOST DR6.
Fig 3: Best-fit sdO+G2V model after 31 iterations.
From start to best-fit model (zoomed)
Fig 4: Starting sdB+K2V type to model a composite spectrum binary from LAMOST.
Fig 5: Best-fit sdO+G2V model after 31 iterations.
Animated fit procedure with 31 iterations
Fig 6: Animation of a fit procedure with 31 iterations.
Fig 7: Animation of a fit procedure with 31 iterations.