Rotational velocity and velocity fields Spring School of Spectroscopic Data Analyses 812 April 2013 Astronomical Institute of the University of Wroclaw Wroclaw Poland Giovanni Catanzaro ID: 560844
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Slide1
Spectral lines analysis
Rotational velocity and velocity fields
Spring School of Spectroscopic Data Analyses
8-12 April 2013
Astronomical Institute of the University of Wroclaw
Wroclaw, Poland
Giovanni Catanzaro
INAF - Osservatorio Astrofisico di CataniaSlide2
equator
Projected rotational velocity
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Because
the Doppler
effect
we
can
see
only
the component of the
equatorial
velocity
parallel
to the line of
sightSlide3
equator
Special case:
i
=90º
All rotational velocity is parallel to line of sight: star
appears
to rotate with
v
eq
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equator
Special case:
i
=0º
All rotational velocity is perpendicular to line of sight: star appears not rotate
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Rotation shapes line profile
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Rotational profileSlide6
limb darkening
Rotational
profile
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Profile fitting for v sin i
Observed spetrum with several synthetics overimposed. Each synthetic spectrum was computed for different value of rotational velocity.
Instrumental profile
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Importance of Resolution
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Example: FeII 5316.615 Å
T
eff
= 7000 K
Log g = 4.00
HERMES
R = 80000Slide9
Fourier analysis
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~0,007
Slide10
Limb darkening
Limb darkening shifts the zero to higher frequency
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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
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Velocity fields
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Motions of the photospheric gases introduce Doppler shifts that shape the profiles of most spectral linesTurbulence 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.Slide13
Macroturbulence
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
n
= I
n
0
*
Q(Dl
)
I
n
0
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
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Radial-Tangent model
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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 limbSlide15
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Assume that a certain fraction of the stellar surface, A
T
, has tangential motion, and the rest, A
R
, radial motion
Q
(
Dl
) = A
R
Q
R
(
Dl
) + A
T
Q
T
(
Dl)
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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.Slide16
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Macro
10 km/s
5 km/s
2.5 km/s
0 km/s
Pixel shift (1 pixel = 0.015
Å)
Relative Intensity
Effect of Macroturbulence
It does not alter the total absorption of the spectral lines, lines broadened by macroturbulence are also made shallower.
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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)
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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.Slide18
Example: b
Comae (Gray et al., 1996)09/04/2013
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d(
s) individual lines
h(
s
) thermal profile
i(
s
) instrumental profile
d(
s
) a
veraged and divided by
i(s
) Slide19
Microturbulence
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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:
Slide20
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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 (>10
5
), high SNR spectra and slow rotators stars (a few km s-1) are needed.Slide21
Blackwell diagrams
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1998, A&A, 338, 1041
FeII
CrIISlide22
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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 FeISlide23
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Thanks for your attention