1. Spring School of Spectroscopic Data Analyses 8-12 April 2013 Astronomical Institute of the University of Wroclaw Wroclaw, Poland

2. equator 09/04/2013 Spectroscopic School of Data Analyses 2 Because the Doppler effect we can see only the component of the equatorial velocity parallel to the line of sight

3. equator All rotational velocity is parallel to line of sight: star appears to rotate with v eq 09/04/2013 Spectroscopic School of Data Analyses 3

4. equator All rotational velocity is perpendicular to line of sight: star appears not rotate 09/04/2013 Spectroscopic School of Data Analyses 4

5. 09/04/2013 Spectroscopic School of Data Analyses 5 Rotational profile

6. 09/04/2013 Spectroscopic School of Data Analyses 6

7. Observed spetrum with several synthetics overimposed. Each synthetic spectrum was computed for different value of rotational velocity. Instrumental profile 09/04/2013 Spectroscopic School of Data Analyses 7

8. 09/04/2013 Spectroscopic School of Data Analyses 8 Example: FeII 5316.615 Å T eff = 7000 K Log g = 4.00 HERMES R = 80000

9. 09/04/2013 Spectroscopic School of Data Analyses 9 ~0,007

10. Limb darkening shifts the zero to higher frequency 09/04/2013 Spectroscopic School of Data Analyses 10

11. The limb of the star is darker so these contribute less to the observed profile. You thus see more of regions of the star that have slower rotation rate. So the spectral line should looks like that of a more slowly rotating star, thus the first zero of the transform move to lower frequencies 09/04/2013 Spectroscopic School of Data Analyses 11

12. 09/04/2013 Spectroscopic School of Data Analyses 12 Motions of the photospheric gases introduce Doppler shifts that shape the profiles of most spectral lines Turbulence are non-thermal broadening We can make two approximations: The size of the turbulent elements is large compared to the unit optical depth Macroturbulent limit The size of the turbulent elements is small compared to the unit optical depth Microturbulent limit Velocity fields are observed to exist in photospheres oh hot stars as well as cool stars.

13. Turbulent cells are large enough so that photons remain trapped in them from the time they are created until they escape from the star Lines are Doppler broadened: each cell produce a complete spectrum that is displaced by the Doppler shift corresponding to the velocity of the cell. The observed spectra is: I = I 0 *  ) I 0 is the unbroadened profile and  is the macroturbulent velocity distribution. What do we use for  ? 09/04/2013 Spectroscopic School of Data Analyses 13

14. 09/04/2013 Spectroscopic School of Data Analyses 14 We could just use a Gaussian (isotropic) distribution of radial components of the velocity field (up and down motion), but this is not realistic: Rising hot material Cool sinking material Horizontal motion Convection zone If you included only a distribution of up and down velocities, at the limb these would not alter the line profile since the motion would not be in the radial direction. The horizontal motion would contribute at the limb Radial motion → main contribution at disk center Tangential motion → main contribution at limb

15. 09/04/2013 Assume that a certain fraction of the stellar surface, A T, has tangential motion, and the rest, A R, radial motion  (  ) = A R  R (  ) + A T  T (  ) Spectroscopic School of Data Analyses 15 The R-T prescription produces a different velocity distribution than an isotropic Gaussian. If you want to get more sophisticated you can include temperature differences between the radial and tangential flows.

16. 09/04/2013 Macro 10 km/s 5 km/s 2.5 km/s 0 km/s Pixel shift (1 pixel = 0.015 Å) Relative Intensity It does not alter the total absorption of the spectral lines, lines broadened by macroturbulence are also made shallower. Spectroscopic School of Data Analyses 16

17. 09/04/2013 At low rotational velocities it is difficult to distinguish between them: red line is computed for v sini = 3 km/s, x = 0 km/s blue line for v sini = 0 km/s and x = 3 km/s Relative Flux Pixel (0.015 Å/pixel) Amplitude Frequency (c/Å) Spectroscopic School of Data Analyses 17 There is a tradeoff between rotation and macroturbulent velocities. You can compensate a decrease in rotation by increasing the macroturbulent velocity. While, In the wavelength space the differences are barely noticeable, in Fourier space (right), the differences are larger.

18. 09/04/2013 Spectroscopic School of Data Analyses 18 d(  ) individual lines h(  ) thermal profile i(  ) instrumental profile d(  ) averaged and divided by i(  )

19. 09/04/2013 Spectroscopic School of Data Analyses 19 Contrarly to macroturbulence, we deal with microturbulence when turbulent cells have sizes small compared to the mean free path of a photon. In this case the velocity distribution of the cells molds the line profile in the same way the particle distribution does. Line absorption coefficient without microturbulence Particles velocity distribution (gaussian) The convolution of two gaussian is still a gaussian with a dispersion parameter given by:

20. 09/04/2013 Spectroscopic School of Data Analyses 20 Landstreet et al., 2009, A&A, 973 Typical values for  are 1-2 km s -1, small enough if compared to the other components of the line broadening mechanism. It is a very hard task to attempt the direct measurement of  by fitting the line profile. Very high resolution (>10 5 ), high SNR spectra and slow rotators stars (a few km s-1) are needed.

21. 09/04/2013 Spectroscopic School of Data Analyses 21 1998, A&A, 338, 1041 FeII CrII

22. 09/04/2013 Spectroscopic School of Data Analyses 22 Catanzaro & Balona, 2012, MNRAS, 421,1222 Other type of diagram: from a set of spectral lines, we require that the inferred abundance not depend on EW Example: HD27411, Teff = 7600 ± 150, log g = 4.0 ± 0.1  71 lines FeI

23. 09/04/2013 Spectroscopic School of Data Analyses 23 Thanks for your attention