- 105 Views
- Uploaded on
- Presentation posted in: General

Learning from spectropolarimetric observations

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Learningfrom

spectropolarimetricobservations

A. Asensio Ramos

Instituto de Astrofísica de Canarias

aasensio.github.io/blog

@aasensior

github.com/aasensio

Learningfromobservationsisanill-posedproblem

Followthesefoursteps

- Understandyourproblem
- Understandthemodelthat ‘generates’ your data
- Define a meritfunction
- Compute the‘best’ fitbyoptimizingorsamplethismeritfunction

Thesolutiontoanymodelfitting

has to be probabilistic

Understandyourproblem

- Your data has beenobtainedwithaninstrument
- Yoursyntheticmodelmightnotexplainwhatyousee
- You are surelynotunderstandingyourerrors
- Systematics
- …

Understandyourgenerativemodel

Thisisthemostimportantand complexpart of theinference

Example

Generativemodel

Assumptions

- Weassumethat xi are fixed and givenwithzerouncertainty
- Uncertainty in themeasurementisGaussianwithzero meanand diagonal covariance

Fromthegenerativemodeltothemeritfunction

Likelihood

Probabilitythatthemeasured data has been

generatedfromthemodel

Why do we do thec2fitting?

Thestandardleast-squaresfitting comes fromthe

maximization of a Gaussianlikelihood

Somesubtleties

- Weights
- Do notchangethe position of themaximum
- Modifythecurvature at themaximum

- Ifnoisestatisticschange, modifythelikelihood

Be aware of theassumptions

- Errors are Gaussian
- Youknowtheerrors itisdifficulttoestimateuncertaintiesin theerrorsbecauseerrors are already a 2ndorderstatistics
- Errors are onlyonthe y axis x locations are givenwithinfiniteprecision
- Themodelincludesthetruth

Whatifwe break theassumptions?

Any of ourassumptionsmight be broken

- Errors are notGaussian
- Wedon’tknowtheerrors
- Errors are alsoonthex axis
- Themodeldoesnotincludethetruth

Withoutoutliers

Withoutliers

Wegetbiasedresults

Modeleverything

Ifyoumodelthe data points and theoutliers, youautomatically

have a generativemodel and a meritfunctiontooptimize

pointsfromthe line

badpoint

Fitting He I 10830 Å profiles

Hazel

github.com/aasensio/hazel

MIT license

Assumptions+ properties

- Multi-term atom
- Simplified but realistic radiativetransfer effects
- One or two components (along LOS or inside pixel)
- Magneto-optical effects
- MIT license
- MPI using master-slavescheme
- Scalesalmostlinearlywith N-1 (testedwithup to 500 CPUs)
- Pythonwrapperforsynthesis

3d3D

3p3P

3s3S

2p3P

10830 Å

2s3S

Forward modelling

Problemswithinversion

- Robustness
- Sensitivitytoparameters
- Ambiguities

Robustness: 2-step inversion

Global convergence DIRECT

Refinement Levenberg-Marquardt

Step 1

Step 2

Step 3

DIRECT algorithm (Jones et al 93)

Sensitivitytoparameters: cycles

Modifyweights and do cycles

Cycle 1

Invertthermodynamicalproperties

t, Dvth, vDopp, …

Stokes I

Cycle 2

Invertmagneticfield vector

Stokes Q, U, V

Ambiguities

Ambiguities: off-limbapproach

- Do a firstinversionwithHazel
- Saturationregime findtheambiguoussolutions (<8)

In thesaturationregime(above~40 G for He I 10830)

Ambiguities: off-limbapproach

- Do a firstinversionwithHazel
- Saturationregime findtheambiguoussolutions (<8)
- Foreachsolution, use Hazelto refine theinversion
- NowalmostautomaticallywithHazel

Wheretogofromhere?

- Do full Bayesianinversion
- Modelcomparison
- Inversionswithconstraints

Modeleverything, includingsystematics, and

integrateoutnuisanceparameters

Bayesianinference

PyHazel+PyMultinest

Modelcomparison

H0 : simple Gaussian

H1 : twoGaussians of equalwidthbutunknownamplitude ratio

Modelcomparison

H0 : simple Gaussian

H1 : twoGaussians of equalwidthbutunknownamplitude ratio

Modelcomparison

Modelcomparison

ln R=2.22 weak-moderateevidence

in favor of model 1

Constraints

Central stars of planetarynebulae

Bayesianhierarchicalmodel

Model

FV

B1,μ1

Model

FV

b0

B2,μ2

Model

FV

B3,μ3

Bayesianhierarchicalmodel

Are solar tornadoes and barbsthesame?

Coreof the He I line at 1083.0 nm (~0.8’’)

- Full Stokes He I line at 1083.0 nm (VTT+TIP II)
- Imaging at thecore of the Hα line (VTT - diffractionlimited MOMFBD)
- Imaging at thecore of the Ca II K (VTT - diffractionlimited MOMFBD)
- Imagingfrom SDO

Coincidencewithtornadoes in AIA

``Vertical’’ solutions

Field inclination

``Horizontal’’ solutions

Field inclination

Magneticfieldisrobust

- Fields are statisticallybelow 20 G
- Someregionsreach 50-60 G
- Filamentary vertical structures in magneticfieldstrength

Conclusions

- Be aware of yourassumptions
- Modeleverythingifpossible
- Hazelisfreelyavailable
- Ambiguities can be problematic
- More worktoputchromosphericinversionsat thelevel of photosphericinversions

Announcement

IAC Winter SchoolonBayesianAstrophysics

La Laguna, November 3-14, 2014