Transcript Spectral lines analysis

Spring School of Spectroscopic Data Analyses
8-12 April 2013
Astronomical Institute of the University of Wroclaw
Wroclaw, Poland
Because the Doppler
effect we can see only
the component of the
equatorial velocity
parallel to the line of sight
𝑦
𝑖
𝑣𝑒𝑞 sin 𝑖
𝑥
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All rotational velocity
is parallel to line of
sight: star appears to
rotate with veq
𝑦
equator
𝑖
𝑣𝑒𝑞
𝑥
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All rotational velocity
is perpendicular to
line of sight: star
appears not rotate
𝑣𝑒𝑞
𝑦
𝑥
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Rotational profile
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Δ𝜆
𝐺 Δ𝜆 = 𝑐1 1 −
Δ𝜆𝐿
2
1
2
+ 𝑐2
Δ𝜆
1−
Δ𝜆𝐿
2
𝑐1 , 𝑐2 = 𝑓 𝜖 limb darkening
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𝐷 𝜆 = 𝐼 𝜆 ∗ 𝐹(𝜆)
Instrumental
profile
𝜆
𝑅=
= 57000
Δ𝜆
Observed spetrum with several synthetics overimposed. Each synthetic
spectrum was computed for different value of rotational velocity.
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Example:
FeII 5316.615 Å
log
Teff = 7000 K
Log g = 4.00
HERMES
R = 80000
𝑁𝐹𝑒
= −4.48
𝑁𝑇𝑜𝑡
log
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𝑁𝐹𝑒
= −4.30
𝑁𝑇𝑜𝑡
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𝑑 𝜎 = 𝑖 𝜎 ∗ 𝑔(𝜎)
~0,007
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Limb darkening shifts the zero to higher frequency
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𝐹(𝜆)
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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𝜆
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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.
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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: In = In0 * Q(Dl)
In0 is the unbroadened profile and Q(Dl) is the macroturbulent
velocity distribution.
What do we use for Q?
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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:
Horizontal motion
Convection zone
Rising hot material
Cool sinking material
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
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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)
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.
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It does not alter the total absorption of the spectral lines, lines
broadened by macroturbulence are also made shallower.
Macro
Relative Intensity
10 km/s
5 km/s
2.5 km/s
0 km/s
Pixel shift (1 pixel = 0.015 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.
At low rotational velocities it is difficult to
distinguish between them:
Relative Flux
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
While, In the wavelength space the
differences are barely noticeable, in
Fourier space (right), the differences
are larger.
Amplitude
Pixel (0.015 Å/pixel)
Frequency (c/Å)
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d(s) individual lines
h(s) thermal profile
i(s) instrumental profile
d(s) averaged and divided by
i(s)
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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.
Particles velocity distribution (gaussian)
𝛼 = 𝛼′ ∗ 𝑁(𝑣)
𝑁 𝑣 𝑑𝑣 =
The convolution of two gaussian is
still a gaussian with a dispersion
parameter given by:
1
𝜋
1
2
𝜉
𝑣
−( )2
𝑒 𝜉 𝑑𝑣
𝑣 2 = 𝑣02 + 𝜉 2
Δ𝜆𝐷 =
𝜆 2𝐾𝑇
+ 𝜉2
𝑐 𝑚
1
2
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Line absorption coefficient
without microturbulence
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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 (>105), high SNR
spectra and slow rotators stars
(a few km s-1) are needed.
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1998, A&A, 338, 1041
FeII
CrII
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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
Catanzaro & Balona, 2012, MNRAS, 421,1222
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Thanks for your attention
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