Context:

August 2010, at OHP spectral meeting, we have found criteria that may impact on EW's computation and we then defined some conventions about how to compute EW.

Possible criteria that may impact on EW's computation:

EW's definition is:

I(λ) : spectrum's intensity at wavelength λ Ic(λ) : continuum's intensity at wavelength λ

EW's computation needs continuum's intensities Ic which can be extracted from spectrum by several ways. So, it seems that there is no need to normalize the spectrum.

We have found the following criteria that should impact on EW's computation:

1. Wavelength bandwidth for integration;
2. Continuum extraction method;
3. Star's behaviour of course;
4. For the same date, EW depends on the observer (experimental bias, spectral reduction, ...);
5. Depends on software's version (id. algorithm used for computation).

Here are a pictures of white board used at OHP 2010 meeting workshop on EW:

Solutions to fixe criteria:

Workshop dealed with all points adn conclued to:

1. Wavelength bandwidth for integration:
   We have to fix wavelength's bandwidth for each stars. If unfixed, 6535-6595 is used. This bandwidth has to include all shapes of the line studed including wings. Wings' limits have to be discussed for each stars and depends on each spectrum's resolution (wider for low resolution spectra).
2. Continuum extraction method:
   We have to choose the continuum extraction method and apply it to each spectra. This is the main source of EW's dispersion with intrinsic star's activity variations.
   The continuum extracted needs to follow global slop of left edge and right edge stellar's continuum shape and needs to have the smallest curvature.
3. Star's behaviour of course:
   Stars' activity may vary through hours to mounths.
4. For the same date, EW depends on the observer:
   If preprocessing is well done and all EW's computation is made by only one observer, EW won't vary. Only weather conditions could then influence EW value.
5. Depends on software's version:
   Software's version and name have to be present in fits file's header in order to know witch algorithm have been used to compute EW and continuum. Software's EW computation result has to be compare one time with MIDAS's result.

It appears that the main reason for EW's variations is the continuum computed used for EW.

Continuum's extraction:

1. How to choose a continuum?

We can see bellow few continuum extracted from the same star and the EW obtained with it. Computation are done with SpcAudace's spc_ew command on this CI Cyg spectrum.

# Date: 2010-10-26T19:11:18.00 # JD: 2455496.2995138890 # EW(20.0=6550.0-6570.0)=-223.21 A. # Sigma(EW)=24.17 A. # SNR=11.	# Date: 2010-10-26T19:11:18.00 # JD: 2455496.2995138890 # EW(20.0=6550.0-6570.0)=-190.21 A. # Sigma(EW)=20.15 A. # SNR=11.	# Date: 2010-10-26T19:11:18.00 # JD: 2455496.2995138890 # EW(20.0=6550.0-6570.0)=-178.56 A. # Sigma(EW)=19.09 A. # SNR=11.	# Date: 2010-10-26T19:11:18.00 # JD: 2455496.2995138890 # EW(20.0=6550.0-6570.0)=-262.74 A. # Sigma(EW)=26.8 A. # SNR=11.
EW=-223.21 A	EW=-190.21 A	EW=-178.56 A	EW=-262.74 A
spc_ew _ci_Cyg_20101026_800 6550 6570 6 n 1	spc_ew _ci_Cyg_20101026_800 6550 6570 6 n 2	spc_ew _ci_Cyg_20101026_800 6550 6570 6 n 3	spc_ew _ci_Cyg_20101026_800 6550 6570 6 n
Low pass filter with deg 1 polynom.	Low pass filter with deg 2 polynom.	Low pass filter with deg 3 polynom.	Multi linear pieces smoothed with factor 10^6.

Continuum has a great impact on EW's value. So whitch continuum is the best?

With this star, multi linear pieces smoothed with factor 1000000 seems to be the best continuum fitting which takes care of global slop of left edge and right edge stellar's continuum and that has the smallest curvature.
But with an other star (the Crb spectrum), low pass filter with deg 2 polynom would be the best:

Command: spc_ew the_crb_20100315.fit 6535 6595 6 n 2

Low pass filter with deg 2 polynom that matches Ha line wing's edges.
Obtained with command: spc_ew the_crb_20100315.fit 6535 6595 6 n 2

Here is how SpcAudace works in automated mode:

1. It extracts continuum with non-linear methods (left picture);
2. It finds integrations limits by finding intersection between special smoothed spectrum and extracted continuum (right picture).

2. What makes continuum's extraction difficult?

Continuum extraction's main difficulty comes from continuum's SNR. In the last example, SNR was very low and algorithms have few possibilities how to find continuum median position in wide spread distribution of intensities.

Command: spc_ew the_crb_20100315.fit 6535 6595 6 n 2

However, when SNR is good, all algorithms find closed EW's values for the same bandwidth (6535-6595) on this zeta Tau spectrum:

Low pass filter with deg 1 polynom.	Low pass filter with deg 2 polynom.	Low pass filter with deg 3 polynom.	Multi linear pieces smoothed with factor 10^6.
EW=-13.69 A	EW=-13.7 A	EW=-13.2 A	EW=-13.74 A

3. Possible work after continnum's extraction method is defined for a star:

So, before beginning before launching a time study of EW's evolution, it is needed to select the more adapted method for continuum extraction witch depends on the star. After what a pipeline may be applyed.

Here is an example of such pipeline for EW time evolution:

EW evolution from 2010/02/05 to 2010/04/04. Obtained with command: spc_ewcourbe 6535 6595	EW's period computation by fiting with unscaled Levenberg-Marquardt algorithm.

A periodogramm (spc_periodogram SpcAudace command) may resolve the period too if there are anougth points:

Conclusions:

Finally, all criteria are fixed but continuum extraction is the critical step:

• Wavelength bandwidth has to be adapted to the star and spectrum's resolution;
• EW computation must be given with an error estimation;
• Continuum extraction must be done by an algorithm in order to avoid manual bias and time waste, and then makes available scripting for time evolution studies with graphs etc.;
• If star's behaviour doesn't change, the same continuum's extraction method will be applied;
• With cautions described below, starting choices can be shared with the whole survey's team and measurements can be done by anyone without any bias. Scientific tasks can then be shared.

With such methodoly, studing stars would be rather efficiency and sure.

BeSS database and dedicated surveys such as novae monitoring will then give a great amount of information.