4. Chisquare analysis of the Li I 6708 resonance line: 6Li 7Li

1
Lithium isotopic abundance ratios in metal-poor
star a chi-square analysis of Subaru/HDS
stellar spectra
Ana Elia García Pérez1, Wako Aoki2, Susumu Inoue2
and Sean Ryan1 1 University of Hertfordshire,
Hatfield, UK 2 National Astronomical Observatory
of Japan, Mitaka, Tokyo, Japan
Abstract Lithium is an element of great
importance from a cosmological point of view.
Observations of its light isotope lithium-6 (6Li)
are very delicate. Detections for only a handful
of metal-poor stars are found in the literature.
Using the Subaru 8.2-m optical telescope and the
High Dispersion Spectrograph (HDS), we have taken
high quality spectra (S/N 360-600, R 100 000)
of the Li I 6708 Å resonance line for a sample of
several metal-poor stars. We present here the
1D-LTE analysis of the metal-poor stars
BD-04?3208 and BD26?3578. The isotopic
contribution of 6Li, due to the possible presence
of this isotope in the stellar atmospheres, is
included in the analysis. The best fit to the
observed spectra of these two stars suggest
lithium isotopic abundance ratio (6Li/ 7Li)
values of the order of 0.04 and 0.05
respectively. The fits are based on a minimum
chi-square fitting procedure with three free
parameters the wavelength shift, the total
lithium abundance and the lithium isotopic
abundance ratio.
1. Stellar atmospheres of halo stars Most of the
chemical elements in the Universe are synthesised
in stellar interiors (Burbidge et al. 1954).
According to Big Bang calculations, only the
light nuclei of hydrogen, deuterium, helium-3 and
helium-4, and lithium-7 were synthesised in the
epoch of nucleosynthesis. Hence, we are
interested to study the chemical composition of
the light elements in non-evolved stars of very
low metal content whose composition resembles the
primordial one. The two stable lithium
isotopes are 6Li and 7Li. 6Li is not produced in
the Big Bang, and furthermore has a larger
cross-section for destruction by proton fusion,
and therefore is less abundant and difficult to
detect in the spectra of metal-poor stars. There
are published detections for only a handful of
metal-poor stars (Smith et al 1998, Asplund et
al. 2006 etc). The isotopic ratio 6Li /7Li has
something to say about the discrepancy which
exists between the 7Li abundance observed in
metal-poor stars (Spite Spite 1982) and the
higher predicted value based on recent
determinations of baryon-to-photon ratio ? (see
Fig. 1). If the explanation for the discrepancy
is depletion in stars, why is 6Li, which is more
fragile than 7Li, detected in some metal-poor
stars? These detections of 6Li are challenging.
It is important to confirm them and to add new
detections to the picture. This may also help to
discriminate between different models of 6Li
production cosmic-ray spallation processes
associated to supernovae, to cosmological
structure-formation shocks etc. 2. Measurement
of lithium isotope ratio In the spectra of the
Li I resonance line, the presence of the
lithium-6 isotope is seen as a slightly asymmetry
in the profile of the red wing. Detections of
this isotope are based on fitting the observed
spectra with synthesised spectra, and requires
high quality data, both, observed and
synthesised. Observational data High quality
Subaru/HDS spectra, resolving power (R) 100 000
and signal-to-noise ratios (S/N) of 620 and 480
for BD-04?3208 and BD26?3578,
respectively. Synthetic spectra 1D-LTE
synthesis was done using the spectral synthesis
code BSYN and MARCS plane-parallel model
atmospheres. The stellar parameters values
effective temperature (Teff) and surface gravity
(log g) were taken from the literature. We
calculated the metalliciy (Fe/H)) after
measuring the equivalent widths of several Fe II
lines from our spectra. The values of (Teff /
logg / Fe/H / microturbulence) were BD-04?3208
(6338/4.00/-2.21/1.5) and BD26?3578
(6239/3.87/-2.25/1.5). Method Fitting was based
on minimising the differences between the
observations and the spectral synthesis. The
minimum chi-square (?2) procedure. 3.
Chi-square analysis of Ca I and Fe I lines
broadening parameter We used a set of Ca I and
Fe I lines (see Fig. 2) to fix the free parameter
associated with the line broadening. This method
has another free parameter, the element abundance
(A(Ca) or A(Fe)). The broadening parameter (?)
is the combination of the macroscopic stellar and
instrumental broadening. The left panel in Fig. 2
shows the variation of minimum ?r2 with ? for the
Ca I 6122 Å line and BD-04?3208. The right panels
show the observations and the spectral synthesis
associated to the minimum ?r2 value.
Fig.2 Left Reduced chi-square ?r2 for
BD-04?3208. Right The observed Ca I 6122 Å
profile of BD-04?3208, together with the computed
lines for three different values for ? (6.30, 6.6
and 6.90). Red bars indicate the wavelength
range for the ?r2 calculations.
Fig. 1. Big Bang nucleosynthesis predictions
based on a standard cosmological model (Coc et
al. 2004).

• 4. Chi-square analysis of the Li I 6708 Å
  resonance line 6Li/ 7Li
• Our best estimate of the lithium isotopic
  abundance corresponds to the minimum of the
  curves in the left panels of Fig. 3. Each 6Li/
  7Li point there has associated a wavelength shift
  (??) and a total lithium abundance (A(Li)) such
  that minimises the chi-square. The contour plots
  in Fig.3 shows ?r2 for our best ?? estimate. In
  the right panels, synthesis and observations are
  compared. Three different synthetic spectra are
  plotted the fits for 6Li/ 7Li0.00 and 0.10 and
  the best fits, 6Li/ 7Li0.04 and 6Li/ 7Li0.05
  for BD-04?3208 and BD26?3578, respectively.

?2 ?(Oi Si)2/?2 , ?r2 ?2 /(n-np) (Oi
observed data , Si synthetic data, ? data noise,
n number of points, np number of free
parameters)
G64-37