A new technique of detection and inversion of magnetic fields in stars: PCA-ZDI

A new technique of detection and inversion of magnetic fields in stars: PCA-ZDI Julio Ramirez Velez Meir Semel

The polarization that we can detect in solar-type stars is the one integrated over the whole surface. It is not surprising that in the majority of the cases the circular or linear polarization signals per spectral line are hidden below the noise level. Multiline analysis • It is possible to decrease the noise level by: • - Adding spectral lines (e. g., Zeeman Doppler Imaging) • - Using PCA-ZDI How do we analise them?? What are these signals??

Scalar product

Scalar product • The addition of lines gives reliable results if the profiles are SIMILAR • The technique is restricted to the NO BLENDED lines that would be in the • WEAK FIELD REGIME. • Restricted to Stokes V profiles. In order to overcome all these difficulties, we propose the PCA-ZDI technique.  We use the eigenvectors coming from a data base of synthetic Stokes profiles instead of delta functions.

Why correlations?? Scalar product • The addition of lines gives reliable results if the profiles are SIMILAR • The technique is restricted to the NO BLENDED lines that would be in the • WEAK FIELD REGIME. • Restricted to Stokes V profiles. In order to overcome all these difficulties, we propose the PCA-ZDI technique.  We use the eigenvectors coming from a data base of synthetic Stokes profiles instead of delta functions.

Why correlations?? Scalar product • The addition of lines gives reliable results if the profiles are SIMILAR • The technique is restricted to the NO BLENDED lines that would be in the • WEAK FIELD REGIME. • Restricted to Stokes V profiles. Why principal components?? In order to overcome all these difficulties, we propose the PCA-ZDI technique.  We use the eigenvectors coming from a data base of synthetic Stokes profiles instead of delta functions.

Why correlations?? To add coherently the spectral lines that have the same (or very similar) Doppler shifts.  We can differenciate the distincts plasma movements coming from different parts of the star of from the different components of a star system. Why principal components?? Illustrative examples: ZDI will give a null signal. The principal components contain the physical information and the correlations will be different from zero  we will detect the signal!

Why correlations?? To add coherently the spectral lines that have the same (or very similar) Doppler shifts.  We can differenciate the distincts plasma movements coming from different parts of the star of from the different components of a star system. Why principal components?? We have no restrictions ! Illustrative examples: ZDI will give a null signal. The principal components contain the physical information and the correlations will be different from zero  we will detect the signal!

LOS B Position of the magnetic element in the stellar surface (µ)‏ Strength and orientation of the magnetic field. (B,  The PCA-ZDI technique Modelling of the stellar atmosphere to construct the data base We use the COSSAM (Stift 2000) code to calculate the synthetic spectra of the star covering around 3000 A Following the original ideas expressed in ZDI (Semel 1989), we consider a unique isolated magnetic agent.

S (Y) = (I,Q,U,V)‏ Very high resolution 10 mA. Spectral Range =[450,750] nm The PCA-ZDI technique Let Y be a vector containing the variables of our stellar atmosphere Y =[ µ, B,  ]. The data base consists in 255 Stokes vectors with 255 combinations of the parameters at A wavelength range going from 450 to 750 nm.  300 000 points in wavelength !!

Y N = 0 , 1 ,.., 254 The PCA-ZDI technique Let M the matrix containing the 255 Stokes vectors M =[300000,255,4] We diagonalise the matrix M in order to obtain the Principal Components in which the Stokes vectors of the data base can be decomposed: The {Pn} is the base of the eigenvectors (principal components). Pn will be the DETECTORS

The PCA-ZDI technique The spectral dispersion is different for each wavelength  We change the wavelength axis to the velocity one: Where X is the velocity. We assume that our data base is complete enough (contains enough physical ingredients) and we perform the cross-correlation beween the observed (VERY NOISY) Stokes vector and one of the detectors:

Pseudo profiles IIpeg hd155555 The PCA-ZDI technique We assume that our data base is complete enough (contains enough physical ingredients) and we perform the cross-correlation beween the observed (VERY NOISY) Stokes vector and one of the detectors:

Pseudo profiles IIpeg hd155555 The PCA-ZDI technique We assume that our data base is complete enough (contains enough physical ingredients) and we perform the cross-correlation beween the observed (VERY NOISY) Stokes vector and one of the detectors: WE ARE ABLE TO DETECT SIGNALS USING THE PCA-ZDI TECHNIQUE

Not only circular but also LINEAR polarization Has been detected using this technique!! SPW4  The first detections of magnetics fields in stars using the PCA-ZDI technique

Gives rise to polarization due to a PHYSICAL MECHANISM that we can model. THEY ARE NOT THE REAL PROFILES! The information of the atmospheric variables is encoded in these profiles (that we will call the pseudo profiles) in a more complicated way than in the typical Zeeman profiles. + PCA-ZDI method ZEEMAN STOKES PROFILES PSEUDO-PROFILES

Second Part of the talk How do we analise the PCA-ZDI pseudo-profiles? Is there the information of the magnetic field?

The DISCRET multi line case (ZDI)‏ The center gravity method The pseudoline PCA inversions The CONTINUM case (PCA-ZDI) PCA inversions of the pseudo-profiles

The DISCRET case In order to study if it is possible to retrieve the magnetic field vector from the observations by means of the “addition of lines” (ZDI) technique, we perform some synthetic tests considering the following spectral lines: Adding all these Fe lines, we construct the pseudoline:

The DISCRET case

Using the pseudo line B (G)‏ B (G)‏ The DISCRET case The center gravity method

The DISCRET case Using the Milne-Eddington approximation, we compute a data base for each one of the spectral lines.  Adding each profile of all data bases we have the data base for the pseudo-line. We consider as free parameters: B=[0,5000] Gauss, Angle Azimuthal=[0,180] et Angle LOS=[0,90] We synthesize 500 profiles of the pseudo-line and we invert them developing a PCA inversion code.

The DISCRET case Using the Milne-Eddington approximation, we compute a data base for each one of the spectral lines.  Adding each profile of all data bases we have the data base for the pseudo-line. We consider as free parameters: B=[0,5000] Gauss, Angle Azimuthal=[0,180] et Angle LOS=[0,90] We synthesize 500 profiles of the pseudo-line and we invert them developing a PCA inversion code.  When no noise is added, the errors..

The DISCRET case Inversions of noisy profiles

The DISCRET case  In the most noisy case, the best retrieval of the magnetic field is the one of the pseudo-line.

The DISCRET case  In the most noisy case, the best retrieval of the magnetic field is the one of the pseudo-line. THE INFORMATION OF THE MAGNETIC FIELD VECTOR IS WELL CONTAINED IN THE PROFILES OF THE PSEUDO-LINE

The CONTINUM case DATA BASE of S(Y) DATA BASE of fS Inversions are performed in the space of the pseudo-profiles of the principal components.

The CONTINUM case Example of a pseudo-profile of the data basis.

The CONTINUM case Using (I,V) is possible to obtain * position of the magnetic agent in the stellar surface, (Mu)‏ * the magnetic field strength * the Angle in the LOS

Detections are possible for all the Stokes parameters Inversions are also possible. CONCLUSIONS - We do not employ the weak field approximation (we are not restricted by the psysical conditions that MIGHT be included in the data base) - We are able to detect LINEAR polarization signals. - The most important fact is that the analysis of both profiles coming from the addition of lines or from the PCA-ZDI techniques are RELIABLE. The information of the magnetic field vector is contained in the pseudo-profiles.

A new technique of detection and inversion of magnetic fields in stars: PCA-ZDI