Amplitude transformation

The assumption that instrumental and environmental artifacts use to be additive in terms of intensity may create needs to transform amplitudes in mag from the comparison into the target spectra, if the conditional CINDERELLA mode is applied. The amplitude transformation is only performed to obtain conditional sigs.

Three different strategies to adjust comparison amplitudes are offered, according to the specifications in the .cnd file.

• In photometry, the photon statistics may be employed to transform comparison into target amplitudes, if the mean magnitudes of the stars are known (Reegen et al. 2008). If the keyword transam:mean is provided in the .cnd file, CINDERELLA uses the mean observables $\left< m_C\right>$, $\left< m_T\right>$ of the comparison and target time series, respectively, to transform the comparison amplitude $A_C$ into a target amplitude $A_T$ according to
  

  $$A_T = 2.5\log\left[ 1 + \frac{10^{-0.4\left(\left< m_C\right... ...-0.4\left< m_C\right>}}{10^{-0.4\left< m_T\right>}}\right]\: .$$ (32)

  
  

• If the keyword transam:rms is specified in the .cnd file, CINDERELLA interprets the residual rms errors $\sigma _C$, $\sigma _T$ of the comparison and target time series, respectively, as measures of the photon noise levels and evaluates the transformed amplitude according to
  

  $$A_T = 2.5\log\left[ 1 + \frac{\sigma _C^2}{\sigma _T^2}\left( 10^{0.4\,A_C} - 1\right)\right]\: .$$ (33)

  
  

• The keyword transam:ppsc in the .cnd file causes CINDERELLA to use Eq.5 employing residual point-to-point scatter instead of residual rms error for both $\sigma _C$ and $\sigma _T$.
• If the keyword transam:none is specified in the .cnd file, no amplitude transformation is performed at all, i.e., CINDERELLA assumes $A_T = A_C$.

Example. The sample project transam-mean contains the same input as the project CinderellaNative (p.). The time series data are considered to represent millimag photometry. The comparison dataset is assumed to refer to a 5 mag star, whereas the target datasets shall correspond to a 15 mag star. The resulting time series input files are 000000.transam-mean.dat 000001.transam-mean.dat to 000008.transam-mean.dat. The keyword

transam:mean

in the file transam-mean.cnd forces CINDERELLA to employ the mean magnitudes of the datasets for the amplitude transformation.

Example. The sample project CinderellaNative contains an amplitude transformation based on the rms residual, which is the default method.

Example. The sample project transam-ppsc contains the same input as CinderellaNative (p.). The line

transam:ppsc

in the file transam-ppsc.cnd forces CINDERELLA to employ the residual point-to-point scatters of the datasets for the amplitude transformation.

Example. The sample project transam-none contains the same input as CinderellaNative (p.). The line

transam:none

in the file transam-none.cnd switches off the amplitude transformation.