Lecture 4 Danny Steeghs University of Warwick
Reconstruction techniques Danny Steeghs University of Warwick
Non-parametric methods Astro-tomography reconstruction tools: - Eclipse mapping Doppler Tomography Roche Tomography Echo Tomography
Eclipse Mapping Baptista (2015)
Regularized image reconstruction Baptista (2015)
Temperature profiles Baptista (2015)
The observers toolbox : spectroscopy accretion in compact binaries ; broad emission lines
Emission lines from a disk
Emission line diagnostics The presence of strong and Doppler broadened emission lines is indeed a key characteristic of accretion flows line emissivity radial velocity (km/s)
Doppler tomography using line profiles Time-dependent line profiles provide a powerful diagnostic as the binary components go through their orbits Each spectrum provides a snapshot of the binary dynamics at a given orbital phase = orientation Phase-resolved spectroscopy can build up a dataset of line profiles that contain sufficient information to invert these into images resolving the dynamics of accretion = image reconstruction through (de)projection = tomography Marsh & Horne (1986), Marsh (2001), Steeghs (2004)
Medical CAT: from sample to tomogram sample tomogram tomogram data scanne r computerized axial tomography
Imaging through fast spectroscopy time velocity we can observe the time dependent line profiles as a function of the binary orbit! The tomogram reconstructs the mean emission line distribution in the co-rotating frame Since our diagnostic is Doppler shift, our projection space is in velocity and not Cartesian coordinates
The inversion from data to image Just like CT-scanning, the inversion problem in its simplest form represents a Radon transform One performs a back-projection through the data I(Vx,Vy) = D(v, ) d Generally this is done together with Fourier-filtering to sharpen up the PSF of the reconstruction ; filtered backprojection Data is not perfect (noise, limited sampling, gaps) and often produced significant back-projection artifacts A more robust (but computationally expensive) reconstruction is obtained using regularised maximum likelihood methods
Iterative and regularised reconstruction Default DATA Entropy Goodness of fit Minimisation problem: IMAGE Lagrange multiplier represents balance between realism versus simplicity Q2 = 2 S
Numerical implementation Iterate the image values along a MEM trajectory until the maximum entropy solution is reached for the chosen Local 2 and entropy gradients are evaluated each iteration in order to steer the image =0 visualisation of a twoparameter problem best fit, complex image after Horne (1994) = poor fit, simplest image A numerical convergence criterion is evaluated in order to test whether the current solution is indeed the maximum entropy one
Reconstruction techniques compared observed data filtered straightback-projection back-projection
Entropy regularised fitting maximum (image) entropy serves as our Occam s razor in regularising the fit
Doppler coordinates angular resolution = time resolution Since our diagnostic is Doppler shift, our projection space is in velocity and not Cartesian coordinates Sensible compromise between spectral resolution, time resolution and S/N radial resolution = spectral resolution (after Horne 1991)
Mapping the accretion disks in binaries binary phase H velocity (km/s)
An accreting white dwarf (IP Peg) hydrogen helium the donor star in emission ionized helium (from Steeghs, 2001) the extended accretion disc
Tidal asymmetries revisited Smak 2001 Ogilvie 2002 Danny Steeghs
Modeling in Doppler space Do data versus model comparison in velocity space ; either (Vr, ) or (Vx,Vy) Danny Steeghs
Tidally induced and spiral in shape Model simulation Synthetic data from Steeghs & Stehle (1999) Dynamics easy to compare, quantitative emissivity modelling much harder Danny Steeghs
The 2001 outburst of WZ Sge ~35 nights with spectroscopy Period: 82 minutes White dwarf: M1~ 1 M Donor: 0.03 < M2 < 0.11 Distance: ~ 45pc
Time-lapsed reconstructions
Key snapshots day 3: two armed spiral, donor star, orbital humps day 13: weakened asymmetries, faded donor star, super-humps re-brightening of disc AND mass donor star day 19: cooler disk, strong donor star plus major growth in stream emission. Steeghs (2004) Danny Steeghs
Extra continuum & line emission near stream/spot start of super-humps, re-brightening prominent donor irradiation peak of gas stream feature in maps Apparent bright spot eclipse strength in photometry (Patterson et al. 2002) Danny Steeghs
Extra mass transfer, stream-disc interaction, or pure disc? emission lies along the ballistic stream which is independently fixed by the donor star the donor star is irradiated evolution is strictly along the stream amplitude of the event much stronger than the modulations on the super-cycle that correspond to the stream-disc interaction due to flexing disc and standard stream Day 19 a similar sequence of events in both photometry (bright spot like humps) as well as spectroscopy (stream like emission) certainly looks like a mass transfer burst Danny Steeghs
Mass transfer variations do happen Long-term AM Her Hessman et al. (2000) Low-states in BB Dor Rogriguez-Gil et al. 12 Danny Steeghs
From disks to binary parameters Ca II triplet reveals mass donor star L. van Spaandonk (2011)