a new technique of detection and inversion of magnetic fields in stars: pca-zdi
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
A new technique of detection and inversion
of magnetic fields in stars:
PCA-ZDI
Julio Ramirez Velez Meir Semel
It is possible to decrease the noise level by:
-- Adding spectral lines (e. g., Zeeman Doppler Imaging)
-- Using PCA-ZDI
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
What are these
signals??
How do we analise them??
Scalar product
Scalar product
Scalar product
Scalar product
Scalar product
Scalar product
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.
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??
Why principal components??
Why correlations??
Why principal components??
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.
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??
Why principal components??
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.
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!
We have no restrictions !
The PCA-ZDI technique
LOS
BPosition of the magnetic element
in the stellar surface (µ)
Strength and orientationof the magnetic field.
(B,
Modelling of the stellar atmosphere to construct the data base
Following the original ideas expressed in ZDI (Semel 1989),we consider a unique isolated magnetic agent.
We use the COSSAM (Stift 2000) code to calculate the synthetic spectraof the star covering around 3000 A
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 atA wavelength range going from 450 to 750 nm.
S (Y) = (I,Q,U,V)
Very high resolution 10 mA.
300 000 points in wavelength !! Spectral Range=[450,750] nm
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 PCA-ZDI technique
Let M the matrix containing the 255 Stokes vectors
M =[300000,255,4]
The {Pn} is the base of the eigenvectors (principal components).
Pn will be the DETECTORS
Y N = 0 , 1 ,.., 254
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:
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:
The PCA-ZDI technique
Pseudo profiles
hd155555 IIpeg
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:
The PCA-ZDI technique
Pseudo profiles
hd155555 IIpeg
WE ARE ABLE TO DETECT SIGNALS USING THE PCA-ZDI TECHNIQUE
Not only circular but also LINEAR polarizationHas been detected using this technique!!
SPW4 The first detections of magnetics fields in stars using the PCA-ZDI technique
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.
Gives rise to polarization due to a
PHYSICAL MECHANISM that we can model.
ZEEMANSTOKES PROFILES
+ PCA-ZDI method
PSEUDO-PROFILES
Second Part of the talk
How do we analise the PCA-ZDIpseudo-profiles?
Is there the information of themagnetic field?
The center gravity method The pseudoline PCA inversions
The DISCRET multi line case(ZDI)
The CONTINUM case
(PCA-ZDI)
PCA inversions of the pseudo-profiles
The DISCRET case
In order to study if it is possible toretrieve the magnetic field vector from
the observations by means of the “addition of lines” (ZDI) technique, we perform somesynthetic tests considering the following
spectral lines:
Adding all these Fe lines, we construct the pseudoline:
The DISCRET case
The center gravity method The pseudoline PCA inversions
The DISCRET multi line case(ZDI)
The CONTINUM case
(PCA-ZDI)
PCA inversions of the pseudo-profiles
B (G)
B (G)
Using the pseudo line
The center gravity method
The DISCRET case
The center gravity method The pseudoline PCA inversions
The DISCRET multi line case(ZDI)
The CONTINUM case
(PCA-ZDI)
PCA inversions of the pseudo-profiles
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.
The DISCRET case
Line Fe Parameter(A) Btrength B Angle Azitmuth Angle LOS
6141 3,14 4,01 0,616232 3,13 3,67 0,626246 3,07 3,64 0,66301 2,87 2,86 0,616302 2,91 3,72 0,646336 2,69 3,71 0,596400 3,03 2,53 0,66408 2,21 2,59 0,746411 2,88 2,88 0,61
Pseudo line 3,01 4,01 0,61
When no noiseis added, the errors..
Inversions of noisy profilesThe DISCRET case
Inversions of noisy profilesThe DISCRET case
Line Fe Parameter(A) Strength B Angle Azitmuth Angle LOS
6141 132 34 176232 126 33 156246 149 35 166301 205 45 176302 97 27 146336 94 27 136400 185 40 196408 174 40 176411 185 39 17
Pseudo line 55 15 10
In the most noisy case,the best retrieval of themagnetic field is the one
of the pseudo-line.
The DISCRET case
In the most noisy case,the best retrieval of themagnetic field is the one
of the pseudo-line.
The DISCRET case
THE INFORMATION OF THE MAGNETIC FIELD VECTOR IS WELL CONTAINEDIN THE PROFILES OF THE PSEUDO-LINE
Line Fe Parameter(A) Strength B Angle Azitmuth Angle LOS
6141 132 34 176232 126 33 156246 149 35 166301 205 45 176302 97 27 146336 94 27 136400 185 40 196408 174 40 176411 185 39 17
Pseudo line 55 15 10
The center gravity method The pseudoline PCA inversions
The DISCRET multi line case(ZDI)
The CONTINUM case
(PCA-ZDI)
PCA inversions of the pseudo-profiles
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
The CONTINUM case
Example of a pseudo-profile of the data basis.
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
The CONTINUM case
- 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.
CONCLUSIONS
Detections are possiblefor all the Stokes parameters
Inversions are also possible.