1. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Mathematical algorithms for spectral analysis within the VO framework A. Laruelo, P. Osuna, I. Barbarisi, J. Salgado, C. Arviset ESAVO team – European Space Agengy

2. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Spectral Analysis and VO Analysis utilities for astronomical data within the VO framework must be ready to deal with –wide variety of data –different sources –different energy ranges –different resolutions That implies dealing with –unevenly samplings –unequal ranges of definition –grids of theoretical models –variable dimension of parameters space –multi valued spectra –numerical calculus –interpolation techniques –spectral noise The development of tools capable of handling these issues is a cornerstone of the progress of the analysis of astronomical data.

3. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 VOSpec During last spectroscopy and VO EuroVO-DCA workshop, scientists asked to have more analysis functionalities in the VO applications http://esavo.esa.int/SpectroscopyAndVOWorkshopMarch2007 / We describe a series of algorithms for spectral analysis in the context of highly distributed data. These algorithms are integrated in VOSpec, the ESAVO tool for handling spectra.

4. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 VOSpeculator Arithmetic operations VOSpeculator allows you to add, subtract, divide and multiply spectra In order to not extrapolate and to not decrease resolution: The operations are performed at all wavelength positions of every involved spectra laying within the ranges where such spectra are defined * Convolution Between spectra Between spectrum and a selected region VOSpeculator is the tool of VOSpec to perform arithmetic and convolution operations among spectra Convolution of a spectrum and one of its lines Range where both spectra are defined Sum of two spectra The sum is performed at all the wavelength positions of both spectra inside this range

5. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 VOSpeculator (cont) To perform operations with VOSpeculator you just need to drag and drop the spectra and to select the desired operation

6. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Fitting Utilities Line fitting : - Polynomial Fits a selected spectral line to a n-grade polynomial using Least Squares fitting method. - Black-body Fits selected spectral line to a black-body continuum spectrum using Levenberg Marquardt Chi-Square minimization algorithm. -Gaussian - Lorentzian - Voight -Fits selected spectral line to a Gaussian, Lorentzian or Voight profile using Levenberg Marquardt Chi-square minimization algorithm. -Compare the goodness of the fits with their normalized Chi-square values

7. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Fitting Utilities -This tool helps us to find the theoretical model that best fits a given observational spectral energy distribution. -The search is performed by a modified version of the iterative Levenberg-Marquardt method. -Chi-square test is used to measurethe goodness of the fit. -The TSAP server and a starting model for the Levenberg- Marquardt method are selected by the user -Coming soon: possibility of fixing parameters SED fitting: -Fit to TSAP Server

8. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Bisector This tool deduces the bisector by evaluating the midpoint between the two halves of the spectral line at a number of flux levels The number of flux levels is selected by the user Useful for the interpretation of the distortions of the spectral lines Application examples –Presence of orbiting planetary companion –Photospheric velocity fields Very soon –Velocity span and bisector curvature parameters –Interactive/manual line previous preparation

9. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Mirroring Spectrum mirroring: Evaluates the mirrored spectrum with respect to an axis selected by the user. If no axis is selected, the tool considers the midpoint of the spectrum. Line PeakReference input position Application: Measure of radial velocities Proved to be useful for analysis of Be stars Gaussian mirroring: Given a spectral line, this method evaluates the axis (peak position) and returns the mirrored line respect to this axis.

10. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Mirroring simple application Two very close spectral lines Select the half of the line we want to study Line mirroring

11. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Equivalent width Interactive calculus of the equivalent width of a given spectral line The formula used by this tool is: Linear continuum considered Coming soon: more complex continuums Continuum flux Spectrum flux

12. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Flux Integrated flux: Estimates the area under the selected region of the spectrum using simple trapezoidal integration. Line Flux: Measures the area between a spectral line and a linear continuum Line flux Flux

13. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Tuning Multi valued spectra averaging: –Replaces all flux values at the same wavelength position by their mean value Re-binning: –Increase or decrease spectra resolution –Number of points of the output spectrum is selected by the user Reject zero and negative flux values –Allows you to remove zero and negative flux values from your spectra Multi valued spectra averaging Spectrum containing zero values Cleaned spectrum

14. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Wavelength to velocity Converts X values from wavelength to velocity and vice versa as follows: c is the velocity of the light in Km/s The reference wavelength is an input. No changes are made to the flux values. Applying bisector method to a spectral line converted to velocity coordinates

15. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 De-noising VOSpec offers many types of de-noising methods: –Averaging filters –Convolution filters Constant width IDS Adaptive width –Wavelet filters

16. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Averaging filters The averaging filters offered by VOSpec are: –Mean filter –Median filter These filters replace every flux value by the mean/median value of a number of adjacent flux values. The number of adjacent neighbours considered is determined by the user through two possible parameters: –Number of adjacent positions to be considered: Replaces every flux value by the mean/median value of such number of neighbours flux values. –Number of sub-ranges for dividing the range where the spectrum is defined: The output spectrum has such positions as input number of sub-ranges. The flux value for each position is the mean/median value of all the flux values inside the sub-range.

17. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Convolution filters Each flux value is replaced by a weighted average of its adjacent flux values. Such weighted average can be expressed by the convolution expression: is the input spectrum evaluated at the kth wavelength position is the weighting function evaluated at the jth wavelength position Available weighting functions are: -Gaussian -Lorentzian -Voight The width of these functions: -is constant at every position -can be introduced as input by two different ways: -real width: the user knows a suitable value for the width and the input width is used by the algorithm -fitted to range width: the input value is fitted to the range where the spectra is defined to obtain a suitable width value. It’s possible to use any weighting profile like: -selected line -continuum -other spectrum… making use of the convolution operation offered by the VOSpeculator

18. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Adaptive IDS filters IDS = Intensity dependant spread filters These are convolution filters where the width of the weighting functions is adapted to the shape of the spectrum. The width is narrower close to the peaks of the spectrum and wider close to the continuum. The aim of these filters is to preserve all the spectral lines, even the smoothest ones. Noisy spectrum Filtered spectrum IDS filters preserve the spectral lines, although the spectrum has much more values defining the continuum than the lines

19. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 Wavelet filters These filters use the properties of the wavelet transform to smooth the spectra. The technique works in the following way: when a data set is decomposed using wavelets, some of the resulting wavelet coefficients correspond to details (high freq.) in the data set. If those details are sufficiently small (smaller than a given threshold), they might be omitted without substantially affecting the main features of the data set. The result is a cleaned-up spectrum that still preserve the important details. Available wavelet functions are: –Daubechies –Coiflets –Symlets Donoho’s threshold Hard and soft thresholding methods.

20. European Space Astronomy Centre (ESAC) Villafranca del Castillo, MADRID (SPAIN) Andrea Laruelo IVOA Interoperability Cambridge September 2007 During last spectroscopy and VO EuroVO workshop @ ESAC, scientists point the need of some analysis utilities in VO applications Analysis algorithms have been included in VOSpec Basic (and no so basic) analysis can be executed within the application: Arithmetic operations with spectra, tuning, spectral line analysis, de-noising, etc Conclusions