Download Cool Star Atmospheres and Spectra for GAIA

GAIA Spectroscopy, Science and Technology
ASP Conference Series, Vol. XXX, 2002
U.Munari ed.
Cool Star Atmospheres and Spectra for GAIA: MARCS
models
Bertrand Plez
GRAAL, cc72, Université Montpellier II, F-34095 Montpellier cedex 05,
France
Abstract. After general considerations on the use of model atmospheres
and spectra, with special attention to the expected GAIA spectral harvest, I expose the general characteristics of classical line-blanketed model
atmospheres (1D, LTE, static). The history and current status of MARCS
model atmospheres, initially developed by Gustafsson et al. (1975), are
then briefly described, with a few recent achievements in photometry
and spectroscopy of cool stars. It seems that the MARCS models have
reached their ultimate level of sophistication, within their set of limiting
hypotheses. Further progress require more elaborate modeling, including
non-LTE, and hydrodynamics. Synthetic spectra of M and S stars calculated for the GAIA spectral range are shown and discussed. I demonstrate
that important work is necessary on the existing line lists before we can
reliably extract stellar parameters from GAIA spectra.
1.
On the use of model spectra
GAIA will provide us with millions of stellar spectra, as well as with broad- and
narrow-band photometry, for stars of all spectral types. This wealth of data
will have to be understood, and stellar parameters extracted from it (T eff , logg,
metallicity, and if possible more detailed abundance patterns). In the actual
phase of instrument design, it is necessary to assess, .e.g, what resolution of
the spectrograph will allow a given accuracy on the determination of stellar
parameters. Huge efforts have thus been devoted to build libraries of observed
stellar spectra in the GAIA range (Munari & Tomasella, 1999; Maresse, Munari
& Boschi, 2003; Munari et al., 2003). These are extremely helpful, but lack
completeness for obvious reasons. Model spectra can be used to complete these
libraries with, e.g., rare spectral types, or extremely metal poor stars. Model
spectra have the additional advantage that they can be built at any spectral
resolution, for any spectral range, and at any special chemical composition, for
any combination of Teff , logg... in principle at least. Various problems may
be encountered: necessary physics not implemented in the code (highly ionized
species must be included for hot stars, molecules have to be included in very cool
stars, etc), approximations not appropriate (to compute an O star spectrum in
LTE is futile), inadequate line lists (missing lines, incorrect gf-values, etc), or
even numerical problems. With model spectra, we can also check the effect of
a change of the C abundance on the spectrum of a carbon star, or of the Zr
abundance on an S star. We can determine the amount of absorption due to
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a haze of lines, or to some given continuous opacity. For these exercises to be
useful there is however a necessary condition: that our models are sufficiently
good that we trust them to reproduce real star spectra.
We know real star atmospheres are not simple spherically symmetric layers,
at hydrostatic equilibrium and LTE. We know from detailed observations and
modeling of the Sun that hydrodynamics, magnetic fields, non-LTE, all must
enter the picture if we have the ambition of reproducing the solar spectrum.
We know that our line lists are incomplete, or suffer from uncertainties in line
strength or broadening parameters. This latter point is however improving,
thanks to the enormous work done by our colleagues in atomic and molecular
spectroscopy (see Wahlgren & Johansson 2003, for problems directly related to
the planed GAIA spectral range). We have detailed models of the solar atmosphere (e.g. Asplund et al. 2000), that accurately reproduce most features
of the solar spectrum (line strengths, shifts, and asymmetries, granulation distribution of shapes and intensities, etc). These 3D radiative-hydrodynamics
models are extremely costly, and cannot yet be used for routine analysis of
a large number of stars. They also still need to be tested in detail for stars
different from the Sun (much lower metallicities, and lower temperatures and
gravities). Recently, the first 3D model of the atmosphere of the supergiant
Betelgeuse was computed by B. Freytag (Freytag & Mizuno-Wiedner 2003, see
also http://www.astro.uu.se/b̃f), showing enormous convection cells, moving at
supersonic velocities, on time-scales of months. This looks extremely promising,
and such models will eventually be used to carry detailed analyses of giant and
supergiant stars, but they need to be refined and tested extensively. No doubt
such models will be available at the time we get the GAIA spectra, and we
should bear that in mind when the time comes for their detailed analysis. Note
also the recent full non-LTE models of cool stars of Hauschildt et al. (1999),
and the new pulsation models for long-period variables of Höfner (1999), that
will be indispensable to process mira spectra.
In the mean time, we must use what we have at hand, that can be used
easily on a large scale: we want thousands of model spectra spread all over the
HR diagram, to carry various tests on instrument design, spectra extraction,
photometric system design, and stellar parameter determination. I will show
that, the existing classical models have reached a high level of sophistication,
within their own limited hypotheses (in the following I call classical models,
models built assuming a 1D stratification of the atmosphere, i.e. without horizontal structure, in hydrostatic equilibrium, at LTE, and with conservation of
the radiative and convective luminosity). Actually, it is probably not useful to
further develop classical models. Instead, one must focus efforts towards the
development of models that relax the classical hypotheses.
2.
Classical model atmospheres and spectra
We have seen that model spectra are a complement to observed spectra, when
building libraries, and that they allow extensive experiments on the impact of
the variation of stellar parameters. Their basic use, the one they were initially
developed for, is to interpret observed spectra. The extraction of chemical abundances requires the comparison of the observations to a model spectrum. Adjust-
MARCS models
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ment of the line profiles (or equivalent widths, when it is possible), provides the
abundances, if the model atmosphere used reflects the actual stellar atmosphere
thermodynamical conditions sufficiently well. At this stage it is important to
clearly make the difference between a model atmosphere and a model spectrum.
A classical model atmosphere provides the run of temperature, pressure of gas,
electrons, and radiation, convective velocity and flux, and more generally of
all relevant quantities, as a function of some depth variable (geometrical, or
optical depth at some special frequency, or column mass). Such a model is computed assuming conservation of the luminosity (no energy production nor sink in
the atmosphere), hydrostatic equilibrium (radiative and gas and turbulent pressure balance gravity), with radiative transfer treated in LTE, using some theory
for the convective transport (usually mixing-length theory, or some refinement
of it). As these hypotheses, combined with the 1D (plane-parallel or spherical) geometry, are relatively computationally cheap to deal with (despite strong
non-linearities, and numerical problems to take care of), it is possible to treat
the radiative field in a much elaborate way. While 3D radiative-hydrodynamics
models treat the radiative field with a handful of frequencies, current classical
models evaluate intensities at 105 wavelengths taking into account 10 8 spectral
lines, in minutes, on workstations.
Once we have built a model atmosphere, we can use it to generate synthetic
spectra, like the calcium IR triplet region for GAIA, or larger chunks that may
be used to compute synthetic colors. The synthetic spectrum quality will be
affected by the quality and adequacy of the atmosphere model, but also by the
details of the line list adopted, its accuracy, and completeness. To build a good
model atmosphere requires an extensive account of the opacity sources, but the
exact position of lines is not so critical, as long as they appear approximately
a the right place and strength. The situation is different when computing a
synthetic spectrum at a resolution of 100 000: line positions really matter. It is
that latter situation that may not be fully satisfactory for molecular lines in the
GAIA spectral range, even if the opacities are sufficiently good and complete
to construct model atmospheres (for the atomic line situation see Wahlgren &
Johansson 2003).
3.
MARCS models
The MARCS models were initially developed in Uppsala by Gustafsson et al.
(1975), as plane-parallel, convective and radiative flux conservative, LTE, lineblanketed models. The line opacity was treated through opacity distribution
functions (ODF). The first grids were for solar-type dwarfs and giants of various metallicities. Carbon star models were produced by Eriksson et al. (1984),
after inclusion of additional carbon-bearing molecular opacities, and extension
of the chemical equilibrium to a larger number of species. A major update was
done by Plez, Brett, & Nordlund (1992), who included spherical symmetry, the
opacity sampling (OS) treatment of line opacities, further extended the chemical equilibrium to a few hundreds molecular species, and added opacity for TiO
and H2 O, to allow the modeling of M type stars. In parallel, Edvardsson et al.
(1993) introduced better continuous and atomic line opacities. Later, continuous
opacities were further refined and completed, to build H-deficient and R CrB
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type models. The current version of the MARCS code is a final evolution merging all these changes with newer updates of the opacities, and a new chemical
equilibrium including all the neutral and first ions, and some second ions of the
atoms, and about 600 molecular species. The atomic lines are based on VALD
(Kupka et al. 1999), with collisional broadening by hydrogen following Anstee,
Barklem and O’Mara (see Barklem, Piskunov, & O’Mara 2000). The molecular
opacities comprise extensive line lists for CH, NH, OH, C 2 , CN, CO, CaH, FeH,
MgH, SiH, SiO, TiO, VO, ZrO, H2 O, HCN, C3 , C2 H2 . The data comes primarily
from calculations, supported by laboratory data when available (Jørgensen 1997,
Jørgensen et al. 2001, Plez 1998). The opacities are sampled with a resolution
of 20 000, between 91 and 20 000 nm (more than 150 000 points).
The new models were recently presented by Gustafsson et al. (2003a, b),
and Plez et al. (2003), where more details can be found, as well as discussions of
the thermal structure of the models. No future extensive updates are foreseen
for these models. They are, and will be, used for systematic, detailed analyses
of cool stars, and will also provide a reference for more elaborate 3-D, non-LTE
modeling.
4.
Recent results
The updated MARCS models have been used in recent years for a variety of
purposes from abundance analyses of cool stars, to the analysis and calibration of
ISO-SWS spectra, or calibration of photometric systems. This utilization of the
models in various conditions, shows that they provide a remarkably consistent
description of cool star atmospheres. In some cases, however, the models may
still be improved: in very cool carbon stars, failure to accurately reproduce the
whole IR spectrum is probably due to persistent uncertainties in polyatomic
opacities, esp. C2 H2 . In very cool stars in general (Teff <2500 K), the absence of
dust condensation and opacities is a limitation. The ambition of the new grid of
model is therefore to cover all spectral types with 2500< T eff <8000 K, with any
metallicity, or chemical peculiarity (esp. CNO abundances). Among recent uses
of the MARCS models, Bessell, Castelli, & Plez (1998), established a calibration
of the Johnson-Cousin broad-band photometric system (also for the Kurucz’s
ATLAS models, see Nesvacil et al. 2003). The models reproduce well most
of the color-color relations, and the temperature-color relations. Bolometric
corrections are also provided. Figure 1 shows one example of the match of a
model spectrum to a flux calibrated observation.
In a series of papers, Decin et al. (2000, 2002a,b,c) studied in detail ISOSWS spectra of A to M stars, contributing to the final calibration of the instrument. A nice consistency check of the models and their calculated emergent
spectra is provided by the fact that temperatures derived from the photometry of
the stars using the Teff -color relations established with the models, luminosities
derived from bolometric corrections from the models, distances from Hipparcos,
and angular diameters from interferometry or from the ratio of ISO absolute
flux and model flux, are all consistent.
Recently, Plez et al. (2003) computed a grid of models with parameters
appropriate for M and S giants (3000 < T eff < 4000 K, 0.5<C/O<0.99). They
studied the effects of varying C/O, Fe/H, and the s-element abundances on the
MARCS models
Figure 1.
Observed spectra of M giants from Serote Roos, Boisson,
& Joly 1996 (full line), and MARCS model spectra (dotted line), for
Teff =3800 K, log g=1.5 and Teff =3500 K, log g=0.9. The model spectra
were computed with a solar chemical composition. (From Alvarez &
Plez 1998)
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thermal structure of the models and on their spectra. They also computed
narrow-band TiO and ZrO indices, as well as broad-band colors. They could
predict, from the model calculations, that the T eff -scale of S stars is different of
that of M stars, but that a combination of broad-band colors and narrow-band
indices allows to estimate simultaneously T eff , C/O and Zr/Fe of M and S stars.
This is confirmed by the first comparisons to observations. Further work is in
progress.
5.
The GAIA spectral window, and a few lessons we can learn from
models
It is interesting to use some specific models to calculate theoretical spectra in the
GAIA window, to check e.g. the impact of spectral resolution, or how different
opacity contributors react to changes of T eff . I made this exercise for models of
the Sun, of Arcturus, and a few M and S giants and dwarfs. The idea was to
take the appropriate MARCS model, an atomic line list from VALD, as extracted
from their web site, and the molecular line lists used in our MARCS models. I
then computed the spectrum between 848 and 874 nm, at a resolution of more
than 800 000. It was then degraded to the required resolution, if needed.
5.1.
The Sun
A comparison of the Solar spectrum to the full resolution absolute flux atlas
of Neckel (1999) shows that the model performs well on average (see Fig. 2),
but that mismatches appear at closer examination: (i) the continuum flux of
the model is slightly below the observations. This must be looked at, as it
could be due to a calibration problem of the observations, or to some problem
with the continuous opacity of the model. The effect is small however (less
than 2 percent). This stresses the importance of comparing the models to well
calibrated (absolute flux) observations, as this would not appear in comparisons
with observations normalized to the continuum. (ii) some lines appear in the
observations that are absent in the model spectrum, and conversely. This shows
that work needs to be done on the line lists (line identifications, positions, gfvalues). Wahlgren & Johansson (2003) provide a more extensive discussion of
this aspect, and propose solutions. (iii) further, a comparison of model and
observed spectra degraded to a resolution of about 20 000, shows that as lines
blend with their neighbors, it becomes more difficult to recover the information
on what lines are missing, misplaced, or of erroneous strength. In addition
faint lines tend to behave like a pseudo-continuum (see the right wing of the
Ca II line on Fig. 2). (iv) and finally, at low resolution, line profiles become
unrecoverable, and most information on velocity fields is lost. This may impact
the radial velocity (supergiants show velocity gradients of up to 20 km/s in their
atmospheres, Josselin, Plez, & Mauron 2003), and abundance determinations.
5.2.
Cool M and S stars
Similar comparisons for Arcturus (T eff = 4300 K, log g=1.5) lead to the same conclusions as for the Sun, with more complications due to the greater crowding,
also by molecular lines. This crowding is best illustrated by series of calculated
spectra for Teff = 3600 and 3200 K (Fig. 3). I have separated the contributions of
MARCS models
Figure 2.
Upper panel: detail of the full resolution spectrum of the
Sun, around the λλ8498 Ca II line. Full line: observed absolute flux
from Neckel (1999), dotted line: computed spectrum using a MARCS
model and existing line lists. Note the mismatches in line positions and
strengths, and the missing lines.
Lower panel: same spectra degraded to R≈20 000. Note how lines
get smoothed out to a point where faint lines totally disappear into
a pseudo-continuous opacity. In particular the red wing of the Ca
line seems perfectly matched, whereas inspection of the high resolution
spectrum shows it is not the case (this seems to be due to a slight
difference in absolute flux level).
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B. Plez
Figure 3.
Synthetic spectra for M and S giants, at R≈20 000, computed using MARCS models (see text), and normalized to the continuum. The full spectrum is the thick line. Contribution from TiO alone
is the full thin line, and CN alone produces the dotted line spectrum.
Upper panel: Teff = 3600 K, log g=1.0, C/O=0.5, corresponding to an
early-type M giant. Note the lowering of the apparent continuum due
to TiO. Many atomic lines are still easily seen.
Middle panel: Teff = 3200 K, log g=0.35, C/O=0.5, a late-type M giant.
TiO dominates the spectrum. The flux level is between 20% and 60%
of the continuum only! Very few atomic lines, among which the Ca II
lines, are detected.
Lower panel: Teff = 3200 K, log g=0.35, C/O=0.99, a late-type S giant. The molecular veiling is much decreased compared to the M giant
of identical temperature. CN and TiO contribute equally. Atomic
lines are more prominent than in the early-type M giant model. These
changes are due to the displacement of the chemical equilibrium caused
by the disappearance of almost all oxygen into CO, and the associated
decrease of the TiO an H2 O opacity. Many lines above 8690Å are from
FeH.
MARCS models
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the main species acting in that spectral range (TiO, CN, FeH, and atomic lines).
FeH only appears redwards of the Ca II lines, and becomes more prominent in
dwarfs. TiO totally dominates the spectrum, except for C/O ratios close to one,
where CN takes over. The haze of molecular lines at these low temperatures
forms a pseudo-continuum, relative to which the strength of atomic line absorptions must be gauged. Inspection of Fig. 3 shows also that the slope of the
spectrum carries information, even in the restricted GAIA range. The influence
of Teff , C/O, Ti/H, and log g on the appearance of the spectrum is strong in
cool stars. Stellar parameters cannot probably be recovered from GAIA spectra
only, for the coolest stars.
6.
Conclusions
In conclusion, it is crucial to carefully carry out detailed comparisons of model
and observed spectra, at very high resolution, before we can be sure that our
model spectra have the required quality that enables the recovery of stellar
parameters from low resolution spectra. This will imply hard work on line lists.
The model atmospheres themselves must be tested on a much broader set of data
(photometry, spectra at other wavelengths, etc), to ensure that they adequately
represent the conditions in the real star atmosphere. Preliminary tests of the
new generation MARCS models shown above are comforting in that sense.
Finally, we should keep in mind that the actual GAIA data will probably
be processed using more elaborate models, accounting for non-LTE, if not for 12- or 3D hydrodynamics.
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