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MODE IDENTIFICATION MODE IDENTIFICATION ▸ extraction of frequencies → we need to know what pulsation mode gives rise to each frequency = Mode Identification ▸ Mode identification techniques assign values to the discrete spherical harmonic quantum numbers (l, m) of each of the detected pulsation modes. ▸ The amount of astrophysical information that can be derived from the observed pulsations depends directly on the number of successfully identified modes. 1 MODE IDENTIFICATION METHODS FOR MODE IDENTIFICATION ▸ Detection of (regular) frequency (p-modes) or period (g-modes) spacings is a comparatively simple way for slow rotating stars ▸ Sun, solar-like oscillators, white dwarfs, few δ Scuti stars 2 3 MODE IDENTIFICATION REGULAR FREQUENCY SPACINGS HD 144277 - a δ Scuti star Zwintz et al. (2011) MOST light curves amplitude spectra 4 MODE IDENTIFICATION REGULAR FREQUENCY SPACINGS HD 144277 - a δ Scuti star Zwintz et al. (2011) frequency spectrum 5 MODE IDENTIFICATION REGULAR FREQUENCY SPACINGS HD 144277 - a δ Scuti star Zwintz et al. (2011) frequency spectrum frequency spacings 6 MODE IDENTIFICATION REGULAR FREQUENCY SPACINGS Zwintz et al. (2013) HD 144277 - a δ Scuti star 7 MODE IDENTIFICATION REGULAR FREQUENCY SPACINGS Zwintz et al. (2013) HD 144277 - a δ Scuti star 8 MODE IDENTIFICATION REGULAR FREQUENCY SPACINGS Zwintz et al. (2013) HD 144277 - a δ Scuti star MODE IDENTIFICATION 9 METHODS FOR MODE IDENTIFICATION ▸ Detection of (regular) frequency (p-modes) or period (g-modes) spacings is a comparatively simple way for slow rotating stars ▸ Sun, solar-like oscillators, white dwarfs, few δ Scuti stars ▸ Does not work for ▸ a limited number of modes ▸ no regular patterns ▸ very dense or complicated (e.g., due to rotation) frequency spectrum ▸ 2 possibilities: mode-identification from multi-color time series photometry or from line profile variations from time series spectroscopy MODE IDENTIFICATION PHOTOMETRIC MODE IDENTIFICATION ▸ stellar pulsations cause changes in temperature and geometry over a pulsation cycle ▸ we measure the intensity of the star light through various filters, i.e., in a certain wavelength range ▸ blackbody curves: wavelength dependent effect of the temperature variation on the light variability in a pulsator 10 MODE IDENTIFICATION 11 PHOTOMETRIC MODE IDENTIFICATION ▸ stellar pulsations cause changes in temperature and geometry over a pulsation cycle ▸ we measure the intensity of the star light through various filters, i.e., in a certain wavelength range ▸ blackbody curves: wavelength dependent effect of the temperature variation on the light variability in a pulsator → intensity change is larger in the blue than in the red → most pulsating stars have larger photometric variations in the blue than in the red MODE IDENTIFICATION 12 PHOTOMETRIC MODE IDENTIFICATION ▸ Additionally, light variations in different wavelengths depend on the geometry of the temperature variations, i.e., on the spherical harmonic of the pulsation mode, and on the change in geometrical cross section which also depends on the pulsation mode. ▸ Pulsation amplitude and phase are a function of wavelength and are affected by the geometry of the temperature and cross section changes ▸ Observations of pulsation amplitudes and phases in different photometric passbands (=filters) can constrain the mode identification. 13 MODE IDENTIFICATION PHOTOMETRIC MODE-ID METHOD ▸ based on time variations of the stellar magnitude measured with different filters of a photometric system ▸ for mode-ID: consider only oscillation frequencies that are found in all different filters B2 β Ceph star F2 γ Dor star 14 MODE IDENTIFICATION AMPLITUDE DIFFERENCES Theoretically predicted amplitude ratios for various degrees l F2 γ Dor star B2 β Ceph star l=4 l=3 l=0 l=2 l=1 l=4 l=3 l=2 l=1 Comparison with observations allows identification of l 15 MODE IDENTIFICATION B2 β Ceph star l=4 l=3 l=0 l=2 l=1 F2 γ Dor star l=4 l=3 l=1 l=2 Model Observations MODE IDENTIFICATION MODEL UNCERTAINTIES ▸ Theoretical amplitude ratios and phase differences depend on the stellar flux. ▸ The stellar flux is determined by the metallicity, the effective temperature, the mass and the radius, or equivalently, by the gravity, of the star. ▸ Parameters are often not well known; their errors propagate into the final selection of the best l value. 16 MODE IDENTIFICATION 17 NECESSARY STEPS 1. compute stellar models with appropriate Teff and log g: need to cover the observational error box 2. compute the theoretical phase lag and the variation of the local effective temperature and of the gravity for different degrees l ▸ restriction to l = 0, 1, 2, 3, 4; observational cancellation for higher degree modes 3. for each filter and each degree l compute the theoretical amplitude 4. define a reference filter to compute the amplitude ratios 5. compare the theoretical and the observed amplitude ratios for all stellar models that pass through the error box in Teff and log g