Doppler Imaging & Doppler Tomography. Ilian Iliev Institute of Astronomy & Rozhen NAO

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1 Doppler Imaging & Doppler Tomography Ilian Iliev Institute of Astronomy & Rozhen NAO

2 Indirect imaging of stellar surfaces and flattened structures means restoring spatial distribution of some physical parameters using time-dependent spectroscopic and/or photometric observational data. Stars: Light Curve Modeling Budding; Vogt; Strassmeier; Kjurkchieva Doppler Imaging (a.k.a. Doppler Mapping) Deutsch; Khokhlova; Vogt & Penrod; Piskunov, Accretion disks: Eclipse Mapping Horne subject of this talk Doppler Tomography Marsh, Horne, Richards,

3 Our Sun is the only star we can look at its surface directly.

4 No chances to observe spots at the same size like solar on any other star, but fortunately, there are much larger stars and spots. Strassmeier et al., 2003

5 The idea that other stars could also have spots is more than three centuries old Spottedness as (one of many) cause(s) for stellar variability. Stellar rotation modulates both photometric and spectroscopic behavior of the objects we observe Regular Rotation & Irregular Spots Enterprise, established 1667 Why studying spots is so important? Crucial information about the stellar magnetic fields, because magnetic fields can make surface structures to appear or to vanish.

6 The idea that other stars could also have spots is more than three centuries old Spottedness as (one of many) cause(s) for stellar variability. Stellar rotation modulates both photometric and spectroscopic behavior of the objects we observe Regular Rotation & Irregular Spots Enterprise, established 1667 Why studying spots is so important? Crucial information about the stellar magnetic fields, because magnetic fields can make surface structures to appear or to vanish.

7 The idea that other stars could also have spots is more than three centuries old Spottedness as (one of many) cause(s) for stellar variability. Stellar rotation modulates both photometric and spectroscopic behavior of the objects we observe Regular Rotation & Irregular Spots Enterprise, established 1667 Why studying spots is so important? Crucial information about the stellar magnetic fields, because magnetic fields can make surface structures to appear or to vanish.

8 Late type active stars (RS CVn, BY Dra, FK Com, W UMa, T Tau, G-K giants, UV Cet, single MS, Algols & CVS secondaries): = cool spots because the convection is extinguished = surface structures changeable (few weeks, months, years?) = weak and complex magnetic fields (few tens of Gs, rarely observed); stellar dynamo generated fields. Early type magnetic chemically peculiar stars (Ap, Bp elemental abundances differ from solar): = abundance spots because the particle transport is restricted = surface structures stable (no changes for decades) = strong and ordered (poloidal) magnetic fields (few kgs, directly observed); fossil magnetic fields.

9 Doppler Imaging: to gain information about stellar surface structures from spectral line profiles and their variations due to rotation. As a spot moves across the star, line profile changes. An image of the stellar surface can be reconstructed from the observed line profile. without spot with spot Vogt & Penrod, 1983

10 Cool spot, temperature

11 Higher concentration spot, elemental abundances Kochukhov, 2005

12 Magnetic activity produced by the very complex inteplay between rotation and convection. => fast rotation + deep convection = large spots RS CVn stars: evolved stars in binary systems that are tidally locked. Young (PMS) stars that have not yet lost their angular momentum.

13 RS CVn type star Strassmeier et al.

14 RS CVn type star

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16 II Peg, RS CVn type star, flip-flop activity Berdyugina et al., 1999

17 a 2 CVn, Ap star Kochukhov et al., 2002

18 HR3831, magnetic Ap star Kochukhov et al., 2004

19 Stars: Doppler Imaging Zeeman-Doppler Imaging Semel; Donati; Brown II Peg, RS CVn type star An extension of the temperature and abundance mapping Strassmeier et al., 2007

20 V374 Peg, Teff = 2900 K, ~1 kgs, solid body rotation!?! V circular polarization Donati et al., 2006

21 LINEAR POLARISATION CIRCULAR POLARISATION

22 HD24712, magnetic Ap star Lüftinger et al., 2008

23 AB Dor, dwarf, compact emmitting high-latitude spot Jardine et al. 2002

24 Velocity Distribution spherical harmonics with quantum numbers n,l,m (radial, angular, azimuthal) l = number of nodes m = number of nodes intersecting pole l-m = number of nodes parallel to equator Slide credit A. Hatzes

25 l = number of nodes m = number of nodes intersecting pole l-m = number of nodes parallel to equator l = 2, m = 1 l = 8, m=3 l = 3, m = 0 animations Tim Bedding

26 Asteroseismology

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29 Observational constraints: Vsini ~ km/s, i ~ 20 o - 70 o ; S/N higher is better, good phase coverage 40+ different rotational phases, S/N ~ , spectral resolution ~ and this is the ultimate price for Probably the best spatial resolution method ever used Effective spatial resolution at the equator: N res ~ 4R star Vsini/c = , or ~10-11 arcsec DVrad [m/s] = constant (S/N) 1 R 3/2 (D ) 1/2 Large, larger, and even larger telescopes, more, and even more efficient spectrographs

30 Power of Doppler Imaging Mapping the low latitude spots on RS CVn is the equivalent of seeing the о on 10 KČ coin from a distance of about 100 km! feat. A. Hatzes

31 Computer matters: Spatial restoration using line profiles is an ill-posed problem, it has no unique solution and needs additional information. = Maximum Entropy Method Vogt; Rice; Brown; Strassmeier = Tikhonov Regularization Khokhlova; Piskunov = CLEAN Kürster = Occamian Approach Berdyugina; Savanov = Radio Astronomy Approach Yankov The GOOD news is that the difference is diminished when the data used are of high quality

32 Tau Scorpii HOT MASSIVE STAR

33 SU Aur YOUNG STAR

34 V374 Peg Jardine & Donati

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36 Tomography = imaging by sections, or sectioning pineapple or banana?

37 Tomography = to reconstruct N-dimensional object from its (N-1)-dimensional projections (or slices) Observations = to collect slices through the object or projections around it. Lunar eclipse picture credit Anthony Agiomamitis Only a spherical object can cast such a shadow: therefore, the Earth has spherical shape. Aristotle

38 Johann Radon ( ) 3D object Radon transform 2D projection Děčín back-projections: Reconstructed image: inverse Radon transform slide credit M.T.Richards

39 rho=x*cos(theta)+y*sin(theta) g(x,y) ğ(x,y)

40 Cataclysmic Variable Stars (CVS) or Nice Things That Explode (from time to time) Close binary systems that consist of a white dwarf primary and mass transferring (donor) secondary star. Orbital periods from hours to days. Matter is transferred from donor star to the white dwarf through L1. Due to angular momentum conservation law, an accretion disk is formed. A bright spot is created in the place where the hot gas stream enters the disc. No astronomical instrument can resolve the disks optically. BUT

41 Earth

42 L1 L1 inside out

43 IP Peg spiral structures Schwarz et al. 2005

44 TT Ari disk asymmetries Stanishev et al. 2001

45 H-alpha Doppler Tomograms of Algols accretion ring transient disk gas stream chromosphere accretion disk Richards, 2004

46 Observational constraints: An old spectroscopic game: how to rise the time resolution keeping S/N and spectral resolution as-high-as-possible. Solution is not easy, not unique, and not always successful. Blurring factor 360 o t/p; t/p ~ 1/2π*ΔV/K P period, t exposure time, K feature speed, km/s ΔV spectral resolution, km/s Δφ = t/p phase resolution P = 16 hours (app. 0.7 days) t < 2.5 minutes K = 400 km/s ΔV = 6 km/s, sp.res. = Δφ < m 8-m class telescopes

47 Danke Thank you Благодаря Díky

48 Most parts in CV s are moving at a few 100 to a few 1000 km/s so lines are shifted to few tens of angstroems, i.e. we can detect it With Doppler Tomography a 2D data set consisting of a time series of line profiles is then converted to a 2D Doppler tomogram A tomogram is a map of velocities without translating these into positions An intensity-distribution in the two-dimensional velocity space is created X-axis points in the direction from the accretor to the donor and the y-axis points in the direction of motion of the donor

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