Super-resolution Polarimetric Imaging of Black Holes using the Event Horizon Telescope

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1 Super-resolution Polarimetric Imaging of Black Holes using the Event Horizon Telescope MIT Haystack Observatory Mollie Pleau Mentors: Kazunori Akiyama Vincent Fish

2 The Event Horizon Telescope (EHT) Created to image black hole shadow of Sgr A* (55μas, 8kpc, 4x106M ) and M87 (36μas, 16 Mpc, 6.3x109 M ) A global effort: seven millimeter/submillimeter sites Objectives include: Testing general relativity Understanding jet generation and collimation in galaxies Understanding accretion around black holes

3 Increasing Image Fidelity A larger baseline increases resolution, and more telescopes increases sensitivity EHT UV Coverage (M87) Resolution goes as λ B As more telescopes are added to the EHT array, we can increase our image fidelity by increasing UV coverage Each measurement is called a visibility, and each is mathematically a Fourier Transform: (Honma et. al 2014)

4 Polarimetric Imaging Synchrotron emission is inherently polarized Polarimetric imaging can help characterize the magnetic field Stokes parameters: We image Q and U-map (linear polarization) as well as P-map (Q+iU) We require super-resolution (i.e. structure finer than the beam size can be reproduced) to accurately reconstruct linear polarimetric images

5 The Standard Imaging Technique In order to obtain a high fidelity reconstructed image, we must employ statistical imaging methods CLEAN (Jan Högbom 1974) Backward imaging technique, i.e. Fourier transform visibilities first to make dirty map Designed to image point sources (extensions exist to image extended structure) Cons User dependent Dirty beam (point spread function) is not conducive to producing super-resolution results Assumes that image can be broken down into many point sources

6 Sparse Modeling Forward imaging technique: works in visibility domain Tries to reconstruct images for which there are more pixels than data points Based on idea of sparsity, i.e. that the majority of pixels have a value of 0 There are thousands of images that mathematically fit the data well Though these images technically fit the data, they are overfitted Least squares fit with penalties (regularizers) to try to narrow down amount of images that are a good fit

7 Example A technique used in Magnetic Resonance Imaging (MRI) Same philosophy as CLEAN: reconstructing a sparse image w/o Sparse Modeling with Sparse Modeling MRI image of the cerebral blood vessel

8 Regularizers We impart regularization factors to solve images We must determine what type of regularization factor and how much of this factor to impart on the data χ2 Regularizers: L1-norm: Favors a sparse solution. TV-norm (Total Variation): Favors a smoother solution. Sparsity Regularization Less overfitting (With Penalties)

9 Cross Validation A statistical method used to assess how well a model will generalize to an independent data set The role of CV: To help determine how tune parameters, i.e. how much of each regularizer to use Used to train data in order to figure out which weights of the regularizer work best TV (Higher weight) We select the smallest value of 2 from the training data set compared to the validating data set L1 (Higher weight)

10 Methods We use data from simulated observations from EHT for M87 Employ different methods and solvers to image data Test image reconstruction for five different models Determine which L1+TV weights optimize each image Check results quantitatively Forward Jet Counter Jet

11 Images TARGET CLEAN Pure-L1 Pure-TV Forward Jet Model L1&TV

12 Images TARGET CLEAN Pure-L1 Pure-TV Counter Jet Model L1&TV

13 Fidelity Model CLEAN fails to reconstruct Electric Vector Position Angles (EVPA), fractional polarization, and the event horizon shadow, whereas L1&TV reconstructs them well CLEAN Sparse Modeling L1+TV 5 uas 15 uas 25uas Super Resolution

14 Conclusions We find that sparse modeling can reconstruct higher fidelity images than CLEAN by a factor of 10 At finer beam sizes, sparse modeling produces better images For polarimetric imaging, we must use L1+TV Whether we regularize P-map or (Q,U)-maps separately, our results are similar to within a few percent

15 A special thanks to: My mentors: Kazunori Akiyama and Vincent Fish REU Lecture Series speakers National Science Foundation The entire MIT Haystack Staff and summer group

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