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Package ivs :: Package asteroseismology :: Module redgiantfreqs
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Module redgiantfreqs

source code

Functions for Red Giant Seismology.

Contents:

This library contains several functions which allow to identify modes in the power-spectra of red giants. For the description of the pressure modes, the formulism of Mosser et al. (2011A&A...525L...9M) for the 'Universal Oscillation Pattern' is available.

For the description of the frequencies and rotational splitting of the mixed dipole modes, the formalism of Mosser et al. (2012A&A...540A.143M) and (2012arXiv1209.3336M) has been scripted. To apply this method, one needs to know the value of the true period spacing. The modulation of the mixing between pressure- and gravity-dipole modes is described through a Lorentzian profile. This approach assumes a constant Period Spacing for all radial orders. Comparing the modelled frequencies with the real frequencies, found in an spectrum, will work well for the several radial orders but deviations can be found in other regions of the spectrum. A similar Lorentzian description is valid for rotational splitting.

Contents:

* purePressureMode: calculates the position of the pure pressure pressure mode of a spherical degree \ell and radial order.

* universalPattern: creates an array with the frequencies of all pure pressure modes with \ell=0,1,2 and 3, whereby the index i selectes all m odes of the same spherical degree: e.g.: asymptoticRelation[0] = all \ell=0, asymptoticRelation[2] = all \ell=2, asymptoticRelation[-1] gives an array with the radial orders (as float).

* asymptoticRelation: returns an array with the frequencies of the pure pressure modes of the pure pressure modes

* rotational splitting: calculates the expected rotational splitting of a dipole mode based on the degree of mixing

Example: KIC 4448777

This star is a H-shell burning red giant with rotational splitting. The powerspectrum can be found here: ...

>>> import ivs.asteroseismology.redgiantfreqs as rg
>>> centralRadial=  226.868     # [muHz], Frequency of the central radial mode
>>> largeSep    = 17.000                # [muHz], large Frequency separation in powerspectrum
>>> smallSep    = 2.201                 # [muHz], small Frequency separation in powerspectrum
>>> 
>>> DeltaPg             = 89.9                  # [seconds],    true period spacing of dipole modes
>>> dfMax               = 0.45                  # [muHz], normalized rotational splitting (i.e. |freq_{m=0} - freq_{m=+/-1}|
>>> 
>>> qCoupling= 0.15; lambdaParam = 0.5; beParam = 0.08 #Default values

First model the frequencies of the pure pressure modes.

>>> frequenciesUniversalPattern = rg.universalPattern(largeSep, smallSep, centralRadial)

Next, we calculate the frequencies of the mixed dipole modes:

>>> mixedModesPattern = rg.asymptoticRelation(centralRadial,largeSep, DeltaPg, qCoupling)
>>> rotationalSplittingModulation = rg.symmetricRotationalModulation(dfMax, largeSep, frequenciesUniversalPattern, mixedModesPattern, lambdaParam, beParam)
Functions [hide private]
 
purePressureMode(nnn, centralRadial, largeSep, smallSep, epsilon, ell)
Calculates and returns the frequency of a single pure pressure mode for a spherical (\ell=0,1,2, and 3)[Nota Bene: 3 to be implemented].		 source code
 
universalPattern(largeSep, smallSep, centralRadial, numberOfRadialOrders=3)
Calculates and returns an array containing frequencies the frequencies of the pure pressure modes of the degrees spherical degrees \ell= 0,1,2 and 3 for a defined range of radial orders.		 source code
 
asymptoticRelation(centralRadial, largeSep, DeltaPg, qCoupling=0.15, approximationTreshold=0.001, numberOfRadialOrders=4)
Calculates and returns the frequencies mixed dipole modes in the powerspectrum of a red-giant star.		 source code
 
symmetricRotationalModulation(dfMax, largeSep, frequenciesUniversalPattern, mixedModesPattern, lambdaParam=0.5, beParam=0.08)
Calculates and returns rotational splitting		 source code
Variables [hide private]
  format = ''
  datefmt = ''
  logger = logging.getLogger('IVS.RG')
Function Details [hide private]

purePressureMode(nnn, centralRadial, largeSep, smallSep, epsilon, ell)

source code 

Calculates and returns the frequency of a single pure pressure mode for a spherical (\ell=0,1,2, and 3)[Nota Bene: 3 to be implemented].

smallSep can be set to an abitrary value if not calculating \ell=2 modes.

Parameters:
  • nnn (float or integer) - radial order of the mode with respect to the radial order of the central radial mode.
  • largeSep (float) - large Frequency separation in powerspectrum, in muHz
  • smallSep (float) - small Frequency separation in powerspectrum, in muHz
  • centralRadial (float) - Frequency of the central radial mode, in muHz
  • epsilon (float) - echelle phase shift of the central Radial mode: epsilon = centralRadial / largeSep - centralRadial // largeSep
  • ell (float or integer @return frequency in muHz @rtype float array) - spherical degree of a mode

universalPattern(largeSep, smallSep, centralRadial, numberOfRadialOrders=3)

source code 

Calculates and returns an array containing frequencies the frequencies of the pure pressure modes of the degrees spherical degrees \ell= 0,1,2 and 3 for a defined range of radial orders.

When slicing, the index number is equal to the spherical degree \ell, universalPattern[0] = all \ell=0, universalPattern[2] = all \ell=2, The number of the radial order is given as output[-1]. If desired, the array can also be printed to the screen.

Parameters:
  • largeSep (float) - large Frequency separation in powerspectrum, in muHz
  • smallSep (float) - small Frequency separation in powerspectrum, in muHz
  • centralRadial (float) - Frequency of the central radial mode, in muHz
  • numberOfRadialOrders (float or integer

    @return array with frequencies in muHz, [-1] indicates the radial order. @rtype float array

    ) - for how many radial orders above and below the Central Radial Mode should the frequencies be calculated.

asymptoticRelation(centralRadial, largeSep, DeltaPg, qCoupling=0.15, approximationTreshold=0.001, numberOfRadialOrders=4)

source code 

Calculates and returns the frequencies mixed dipole modes in the powerspectrum of a red-giant star.

This function the modulation of the mixing between pressure- and gravity-dipole and derives the frequencies of the mixed modes from it.

Parameters:
  • centralRadial (float) - Frequency of the central radial mode, in muHz
  • largeSep (float) - large Frequency separation in powerspectrum, in muHz
  • smallSep (float) - small Frequency separation in powerspectrum, in muHz
  • DeltaPg (float) - value of the true period spacing
  • qCoupling (float) - coupling factor
  • approximationTreshold (float) - prefiltering of the solution. if modes seem to be missing, increase this parameter
  • numberOfRadialOrders (float or integer @return frequencies of the m=0 component of the mixed dipole modes @rtype float array) - for how many radial orders above and below the Central Radial Mode should the frequencies be calculated.

symmetricRotationalModulation(dfMax, largeSep, frequenciesUniversalPattern, mixedModesPattern, lambdaParam=0.5, beParam=0.08)

source code 

Calculates and returns rotational splitting

This function the modulation of the mixing between pressure- and gravity-dipole and derives the frequencies of the mixed modes from it.

Parameters:
  • dfMax (float) - the largest rotational splitting measured for a given star
  • largeSep (float) - large Frequency separation in powerspectrum, in muHz
  • frequenciesUniversalPattern (array, float) - output from rg.universalPattern
  • mixedModesPattern (array, float) - output from rg.asymptoticRelation
  • lambdaParam (float) - parameter for fitting, Default: lambdaParam = 0.5
  • beParam (float

    @return array with the rotational splitting @rtype array, float

    ) - parameter for fitting, Default: beParam = 0.08

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