Download Mode Identification

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.
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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
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MODE IDENTIFICATION
REGULAR FREQUENCY SPACINGS
HD 144277 - a δ Scuti star
Zwintz et al. (2011)
MOST light curves
amplitude spectra
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MODE IDENTIFICATION
REGULAR FREQUENCY SPACINGS
HD 144277 - a δ Scuti star
Zwintz et al. (2011)
frequency spectrum
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MODE IDENTIFICATION
REGULAR FREQUENCY SPACINGS
HD 144277 - a δ Scuti star
Zwintz et al. (2011)
frequency spectrum
frequency spacings
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MODE IDENTIFICATION
REGULAR FREQUENCY SPACINGS
Zwintz et al. (2013)
HD 144277 - a δ Scuti star
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MODE IDENTIFICATION
REGULAR FREQUENCY SPACINGS
Zwintz et al. (2013)
HD 144277 - a δ Scuti star
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MODE IDENTIFICATION
REGULAR FREQUENCY SPACINGS
Zwintz et al. (2013)
HD 144277 - a δ Scuti star
MODE IDENTIFICATION
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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
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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
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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.
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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
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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
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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.
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MODE IDENTIFICATION
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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