Post on 09-Feb-2016
description
transcript
Spectral lines analysisRotational velocity and velocity fields
Spring School of Spectroscopic Data Analyses8-12 April 2013
Astronomical Institute of the University of WroclawWroclaw, Poland
Giovanni Catanzaro INAF - Osservatorio Astrofisico di
Catania
π₯
π¦
π
equator
Projected rotational velocity
09/04/2013Spectroscopic School of Data Analyses 2
π£ππ sin π
Because the Doppler effect we can see only the component of the equatorial velocity parallel to the line of sight
π₯
π¦
πequator π£ππ
Special case: i=90ΒΊAll rotational velocity is parallel to line of sight: star appears to rotate with veq
09/04/2013Spectroscopic School of Data Analyses 3
π₯
π¦
equ ator
π£ππ
Special case: i=0ΒΊAll rotational velocity is perpendicular to line of sight: star appears not rotate
09/04/2013Spectroscopic School of Data Analyses 4
Rotation shapes line profile
09/04/2013Spectroscopic School of Data Analyses 5
Rotational profile
πΊ ( Ξπ )=π1[1β( ΞπΞ ππΏ)2]
12+π2[1β( ΞπΞ ππΏ)
2] limb darkening
Rotational profile
09/04/2013Spectroscopic School of Data Analyses 6
Profile fitting for v sin i
Observed spetrum with several synthetics overimposed. Each synthetic spectrum was computed for different value of rotational velocity.
π =πΞ π=57000
Instrumental profile
π· (π )=πΌ ( π )βπΉ (π)
09/04/2013Spectroscopic School of Data Analyses 7
Importance of Resolution
09/04/2013Spectroscopic School of Data Analyses 8
Example: FeII 5316.615 Γ
logπ πΉπ
ππππ‘=β4. 48 log
π πΉπ
ππππ‘=β4. 3 0
Teff = 7000 KLog g = 4.00HERMESR = 80000
Fourier analysis
09/04/2013Spectroscopic School of Data Analyses 9
~0,007
π (π )=π (π )βπ(π )
Limb darkening
Limb darkening shifts the zero to higher frequency
09/04/2013Spectroscopic School of Data Analyses 10
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
πΉ(π
)
π09/04/2013Spectroscopic School of Data Analyses 11
Velocity fields
09/04/2013Spectroscopic 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:β’ The size of the turbulent elements is large compared to
the unit optical depth Macroturbulent limit
β’ 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.
MacroturbulenceTurbulent cells are large enough so that photons remain trapped in them from the time they are created until they escape from the starLines 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: In = In0 * Q(Dl)
In0 is the unbroadened profile and Q(Dl) is the macroturbulent velocity distribution.
What do we use for Q?
09/04/2013Spectroscopic School of Data Analyses 13
Radial-Tangent model
09/04/2013Spectroscopic 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 β main contribution at disk center
Tangential motion β main contribution at limb
09/04/2013
Assume that a certain fraction of the stellar surface, AT, has tangential motion, and the rest, AR, radial motion
Q(Dl) = ARQR(Dl) + ATQT(Dl)
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.
09/04/2013
Macro
10 km/s
5 km/s
2.5 km/s
0 km/s
Pixel shift (1 pixel = 0.015 Γ )
Rel
ativ
e In
tens
ity
Effect of MacroturbulenceIt does not alter the total absorption of the spectral lines, lines broadened by macroturbulence are also made shallower.
Spectroscopic School of Data Analyses 16
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/sblue line for v sini = 0 km/s and x = 3 km/s R
elat
ive
Flux
Pixel (0.015 Γ /pixel)
Am
plitu
de
Frequency (c/Γ )
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.
Example: b Comae (Gray et al., 1996)
09/04/2013Spectroscopic School of Data Analyses 18
d(s) individual linesh(s) thermal profilei(s) instrumental profile
d(s) averaged and divided by i(s)
Microturbulence
09/04/2013Spectroscopic 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.
πΌ=πΌ β²βπ (π£)
Line absorption coefficient without microturbulence
Particles velocity distribution (gaussian)
π (π£ )ππ£= 1
π12 π
πβ( π£π )
2
ππ£The convolution of two gaussian is still a gaussian with a dispersion parameter given by:
π£2=π£ 02+π2
Ξ ππ·=ππ ( 2πΎπ
π +π2)12
09/04/2013Spectroscopic School of Data Analyses 20
Landstreet et al., 2009, A&A, 973
Typical values for x 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 x by fitting the line profile. Very high resolution (>105), high SNR spectra and slow rotators stars (a few km s-1) are needed.
Blackwell diagrams
09/04/2013Spectroscopic School of Data Analyses 21
1998, A&A, 338, 1041
FeII
CrII
09/04/2013Spectroscopic 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 Β± 150, log g = 4.0 Β± 0.1 71 lines FeI
09/04/2013Spectroscopic School of Data Analyses 23
Thanks for your attention