Issue |
A&A
Volume 519, September 2010
|
|
---|---|---|
Article Number | L8 | |
Number of page(s) | 4 | |
Section | Letters | |
DOI | https://doi.org/10.1051/0004-6361/201015238 | |
Published online | 17 September 2010 |
LETTER TO THE EDITOR
The origin of peculiar molecular bands in cool DQ white dwarfs
P. M. Kowalski
Helmholtz Centre Potsdam, GFZ - German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Received 18 June 2010 / Accepted 25 August 2010
Abstract
Aims. The DQ white dwarfs are stars whose atmosphere is enriched with carbon, which for cool stars (
)
is indicated by the Swan bands of
in the optical part of their spectra. With decreasing effective
temperature these molecular bands undergo a significant blueshift (
100-300 Å).
The origin of this phenomenon has been disputed over the last two
decades and has remained unknown. We attempt to address this problem by
investigating the impact of dense helium on the spectroscopic
properties of molecular carbon, the electronic Swan band transition
energy
and the vibrational frequency
,
under the physical conditions encountered inside helium-rich, fluid-like atmospheres of cool DQ white dwarfs.
Methods. In our investigation we use a density functional theory based quantum mechanical approach.
Results. The electronic transition energy
increases monotonically with the helium density (
). This causes the Swan absorption to occur at shorter wavelengths compared with unperturbed
.
On the other hand the pressure-induced increase in the vibrational
frequency is insufficient to account for the observed Swan bands
shifts. Our findings are in line with the shape of the distorted
molecular bands observed in DQp stars, but the predicted photospheric
density required to reproduce these spectral features is one order of
magnitude lower than the one predicted by the current models. This
indicates pollution by hydrogen or reflects incomplete knowledge of the
properties of fluid-like atmospheres of these stars.
Conclusions. Our work shows that at the physical conditions
encountered in the fluid-like atmospheres of cool DQ white dwarfs the
strong interactions between
and helium atoms cause an increase in
,
which should produce a blueward shift of the Swan bands. This is
consistent with the observations and indicates that the observed
Swan-like molecular bands are most likely the pressure-shifted bands of
.
Key words: atomic processes - dense matter - stars: atmospheres - white dwarfs
1 Introduction
A DQ white dwarf is a star with a helium-dominated atmosphere enriched
with carbon, which is believed to be dredged-up from the core by the
deep helium convection zone (Pelletier et al. 1986). In the cool DQ white dwarfs (
)
carbon shows its presence by the
Swan bands in the optical spectrum. The two until now unexplained
phenomena are observed in the local samples of these stars. There is a
cutoff in their cooling sequence at
(Koester & Knist 2008; Dufour et al. 2005) and an appearance of ``peculiar'' DQ stars (following Hall & Maxwell 2008,
we call them DQp white dwarfs) at lower temperatures. These peculiar
stars show Swan-like bands that are blueshifted by 100 to 300
(Schmidt et al. 1995; Bergeron et al. 1997; Hall & Maxwell 2008).
The representative spectra of normal and peculiar cool DQ stars are given in Fig. 1.
In the detailed analysis of DQp stars Schmidt et al. (1995,1999) and Hall & Maxwell (2008)
doubt the possibility that the shifts of the Swan bands observed in
spectra of these stars are solely due to a strong magnetic field, which
is not observed to be stronger than in ``normal'' DQ stars. Observing
identical shifts of the bands in all at that time known DQp stars, Schmidt et al. (1995)
concluded that a different molecular species could produce the observed
bands.
Analyzing the abundances of chemical species in the H/He/C mixture
under the physical conditions found in the atmospheres of helium-rich
stars, they proposed the
molecule as a source of the optical spectral features in the DQp stars.
The idea that hydrogen is responsible for the spectra of DQp stars is
consistent with two findings regarding the chemical evolution of cool
white dwarf atmospheres. The already mentioned observation of DQ
DQp
transition indicates some sort of transformation of the physical or
chemical properties of the atmospheres of these stars. Also the
analyses of the local populations of white dwarfs by improved
atmosphere models, which account for physics and chemistry of dense
media, show the decrease in number of the helium-rich atmosphere stars
with
(Bergeron et al. 1997; Kowalski & Saumon 2006; Bergeron et al. 2001) and the appearance of white dwarfs with
atmospheres highly enriched in hydrogen (Kilic et al. 2008,2009a,b; Kowalski & Saumon 2006).
Subsequent work on the coolest stars indicates that the stars at the
end of the white dwarf cooling sequence posses pure hydrogen
atmospheres (Hall et al. 2008; Kilic et al. 2010).
Both these findings indicate that the accretion of hydrogen from the
interstellar medium may change the composition of a helium-dominated
atmosphere into a hydrogen-rich one,
and shows that the appearance of DQp stars may be somehow connected to
this process. However, in the recent work of Hall & Maxwell (2008) the authors ruled out the possibility that
molecule or other carbon and hydrogen bearing species are responsible
for the absorption in the optical spectra of DQp stars and concluded
that
itself is a reasonable candidate for producing the observed features.
This claim is supported by matching of the long-wavelength edges of the
observed bands in DQ and DQp stars, as indicated in Fig. 1. Hall & Maxwell (2008)
postulate that the Swan bands distortion could be produced by the high
pressure or the high excitation of the rotational states of
.
This claim is however purely speculative and is not based on strong theoretical or experimental evidence.
The majority of DQ star atmospheres are highly depleted with hydrogen,
and the dominant constituent species is helium. With cooling, an
atmosphere of a helium white dwarf becomes more charge-neutral, less
opaque and more dense at the photosphere. Also the amount of carbon,
which significantly contributes to the opacity by delivering free
electrons, diminishes with the effective temperature (Koester & Knist 2008; Dufour et al. 2005),
causing an increase in the photospheric density. The photospheric
densities as a function of effective temperature for DQ white dwarfs
with representative amounts of carbon are given in Fig. 2. The atmospheres of these cool stars (
)
posses extreme densities (as high as few
)
and represent a dense fluid, in which strong inter-particle interactions affect the chemistry and physics (Kowalski 2006; Bergeron et al. 1995; Kowalski et al. 2007; Kowalski & Saumon 2004).
Plotting the photospheric densities of a DQ star cooling sequence in Fig. 2, which is based on the carbon abundances derived by Dufour et al. (2005),
we see that the atmospheres of DQ stars reach fluid-like densities and
therefore high pressures at the temperatures of the observed DQ
DQp
transition. This suggests the pressure effects as a good candidate to
be responsible for the spectral distortions observed in DQp stars.
In order to understand the origin of the spectral features
observed in DQp stars, we investigate the impact of dense helium fluid
on the spectroscopically important properties of
molecule. We performed ab initio calculations of
in dense helium, looking for changes in quantities that shape the optical spectrum of
,
the electronic transition energy
,
and the vibrational frequency
.
![]() |
Figure 1:
Optical spectra of the white dwarfs LHS179 (DQ, upper panel) and LHS290 (DQp, lower panel) (Bergeron et al. 1997). The solid line represents the fit to the spectrum of LHS179. The parameters of the fits are:
|
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![]() |
Figure 2:
Left panel: density at the photosphere (the Rosseland mean optical depth
|
Open with DEXTER |
2 Computational approach
The most widely used method for the quantum mechanical treatment of
dense, extended many-particle systems is the density functional theory
(DFT, Koch & Holthausen 2000).
Over the last decade DFT methods proved to be very useful in
calculations of various chemical and physical properties of atoms,
molecules, solid states and matter under high compression.
In our work we used one of the most common DFT version, the generalized
gradient approximation (GGA) with PBE exchange-correlation functional (Perdew 1996).
The calculations were performed by the plane-wave DFT ABINIT code (Gonze et al. 2005,2002) with the ultra-soft pseudopotentials (Vanderbilt 1990) (PAW method and the energy cutoff of
).
In order to obtain the distributions of helium atoms around
we derived the
interaction potential using a combined DFT, molecular dynamics, and classical theory of fluids approach.
First we performed Car-Parrinello simulations (Car & Parrinello 1985) of
emerged in dense helium at density of
and the temperature of
(equiv. of
). The periodically repeated simulation box contained one
molecule and 64 He atoms. As the ABINIT code is not well suited for these calculations, they were performed
with the CPMD code (Marx & Hutter 2000; Car & Parrinello 1985),
keeping the same psuedopotentials, DFT functional and energy cutoff. We
checked that using the same computational setups both DFT codes give
the same answers for the total energies (within
). A trajectory of one million configurations was generated (
long). The
interaction potential was derived by solving the Ornstein-Zernike equation in the Percus-Yevick approximation (Martynov 1992), taking as input the pair-distribution function obtained from the simulation. In order to calculate the energies of
in dense helium in
and
states, which constitute the Swan band transition,
for a given T and
we calculated the ground state energies of a set of 50 ionic
configurations obtained from the classical Monte Carlo simulations of
helium fluid with one
molecule, performed using Allen & Tildesley (1987) Monte Carlo code with the derived
interaction potential and
interaction of Ross & Young (1986). We used this approach because
an explicit quantum molecular dynamics (QMD) simulations would
be computationally much more demanding, and be undoable for extended systems with hundreds of atoms.
The relevant
and
states are constructed according to the electronic configurations given by Ballik & Ramsay (1963). The symmetries of the five lowest KS orbitals of
molecule are:
,
,
,
,
,
in agreement with Ballik & Ramsay (1963). The lower
state (
)
is obtained by fixing the occupation of spin-up orbitals as 11100 and spin-down 11111.
The upper
state (
)
is obtained by fixing the occupation of spin-up orbitals as 10101 and
spin-down 11111.
Then the Swan Band electronic transition energy is given as the
difference of these two calculations. The obtained equilibrium
separations for these two states,
,
and the electronic transition energy
agree well with the experimental values (
,
and
respectively, Ballik & Ramsay 1963), which justifies the usage of DFT.
The impact of dense helium on the vibrational frequencies of
was investigated by computing the vibrational density of states by the Fourier transform of the velocity
autocorrelation function (Egelstaff 1994) derived from the velocities obtained from Car-Parrinello molecular dynamic runs for selected densities and
in a ground
state.
In order to compute the atmosphere models we used our own stellar
atmosphere code that accounts for various dense medium effects such as
refraction, the non-ideal equation of state, and chemical equilibrium.
The internal partition functions of carbon molecule is that of Irwin (1981).
For the carbon atom and ion we set the
values. This approximation is justified because the electronic
excitation energies of both carbon species are high, and for
temperatures of a few thousand degrees the populations of the
electronic excited levels are extremely small.
Hydrocarbon species are not considered.
3 Results and discussion
It is well known that in helium fluid the interaction energies at
the considered densities can be significant and may reach values of eVs (for instance the internal energy of atoms in dense helium is 0.5 eV/atom at
and
).
The interaction energy should in principle be higher for the species
in the higher excited states, because their electronic charge is
located farther away from the center of the atom/molecule. This should
lead to an increase in an electronic transition energy. We computed the
electronic transition energy of the Swan transition in
that emerged in dense He at different densities and representative for the atmospheres of DQp stars temperature
.
The obtained shift in the electronic transition energy,
is given in Fig. 2. With the increase in the density of helium,
increases and the increase for densities up to
is linear and given by
.
This increase shows the smaller slope at densities between 0.5 and
and a similar increase at higher densities. The increase in the
electronic transition energy should produce a blueshift in the Swan
band spectrum, which is qualitatively consistent with the shifts
observed for DQp stars. Positions of the band minima in the spectra of
DQp stars imply a shift of
0.08 eV. This indicates that the bands form at a density of
0.05 g/cm3, which is one order of magnitude smaller than the predicted photospheric densities in the models of these stars (
0.4 g/cm3, Fig. 2).
![]() |
Figure 3:
Left panel: the vibrational density of states of |
Open with DEXTER |
On the other hand the change in the vibrational frequency is prominent,
but appears at significantly higher densities. The result in terms of
the vibrational density of states of
in
state is given in Fig. 3. The vibrational frequency is barely affected up to a density of
and shifts toward higher frequencies
at higher densities. This can be explained looking at the impact of compression on the mean inter-atomic separation in
.
In Fig. 3
we present the variation of this value as a function of density
together with the mean inter-particle separation in the fluid helium.
The distance between carbon atoms that constitute the molecule remains
unaffected up to a density of
,
and decreases slowly
at higher densities. The decrease is correlated with the mean
inter-particle distance in fluid helium. The weak density-dependence of
the inter-particle distance in
(for considered densities) justifies the usage of fixed inter-particle distance in the
molecule in the calculations of
.
We also notice that to reproduce the observed shifts by the increase in
the vibrational frequency, the difference in this increase should be at
least
(
), which could occur at densities higher than
.
Potential rotational excitation, as proposed by Hall & Maxwell (2008)
for the reason of the shifts, is difficult to explain, because this is
a temperature effect and should be stronger at higher temperatures,
which is opposite to the temperature trend of the DQ
DQp
transition. Therefore, we conclude that the dynamical motion of carbon
atoms is unlikely to be responsible for the distortion of Swan bands.
Our results show that the distortion of the
bands in DQp stars is caused by the pressure-induced increase in
.
After computing the shifts in the electronic transition energy for the
Swan band transition we attempted to reproduce the spectrum of a DQp
star.
We did this by using the standard Swan band spectrum, shifted at a
given atmospheric level by the derived value of
.
We note that although this is a quantitatively meaningful
approximation, its validation would require the modeling of the
absorption by
in dense helium, which is a complex task, restricted by the limited
applicability of quantum methods beyond DFT to many particle systems.
In Fig. 4 we show the optical spectrum of the cool DQp white dwarf LHS290 (Bergeron et al. 1997) together with a set of synthetic spectra.
The overall spectral energy distribution of that star is best reproduced by models with
(Fig. 5), and we assume this temperature
in our analysis and fix the gravity at
.
The C/He and H/He abundances are fitted to best reproduce the peaks of the
bands.
Assuming pure He atmosphere the strength of the Swan bands is reproduced with
,
but with the computed correction for
the spectrum is far too distorted
. The observed spectrum can be fairly well reproduced by a model with photospheric density
0.05 g/cm3, or assuming that the
dependence on the density is weaker,
.
The first case is realized by the addition of hydrogen to the
atmosphere, which increases the opacity and lowers the photospheric
density. The required amount of hydrogen is
.
In both cases the observed spectrum is fairly well reproduced. The
minima of the bands are blueshifted, as most of the absorption occurs
close to the photosphere (Fig. 5).
The long-wavelength parts of the bands resemble those of the standard
Swan absorption, because part of the absorption occurs in the less
dense upper atmospheric layers, where
is unperturbed. We notice that the abundances of molecular carbon and
the resulting strength of its molecular bands could also be affected by
high density, which could eventually impact the reported carbon
abundances.
![]() |
Figure 4:
Fits to the optical spectrum of the DQp white dwarf LHS290 (thick solid line).
All the fits are with
|
Open with DEXTER |
![]() |
Figure 5:
Left panel: fits to the entire spectral energy distribution of the DQp white dwarf LHS290 (thick solid line)
given by BVIJHK photometry of Bergeron et al. (2001) (bars). The parameters of the fits are the same as in Fig. 4. Right panel: density profiles of the discussed models. The vertical dotted line marks the photosphere (
|
Open with DEXTER |
4 Conclusions
The so-called DQp stars represent a puzzle in the understanding of
evolution of cool, helium-dominated white dwarf atmospheres. The DQ stars disappear at
,
and few stars with apparently distorted Swan bands were detected at lower effective temperatures.
All explanation through the formation of different species, like
,
magnetic fields, or roto-vibrational excitations failed to explain the
spectral features of these stars or definitely assign them as the distorted bands of
.
We show that the distortion of Swan bands originates in the
pressure-induced increase in the electronic transition energy between
states involved in the transition. This results in a blueshift of the
molecular bands minima, and explains why the red edges of the bands
match the spectra of normal DQ stars (Swan bands).
Our results, when applied to the current atmosphere models, predict
Swan bands shifts that are too large compared with the observed ones.
This indicates that the density at the photosphere of DQp stars does
not excess
,
and the input physics in the models or the understanding of
the atmospheres of these stars, especially the pollution by hydrogen, requires further improvements.
I thank Sandy Leggett for providing me with the spectra of DQ and DQp stars, Didier Saumon for comments on the manuscript, the referee Patrick Dufour for constractive comments, suggestions and sharing the details of his DQ white dwarf atmosphere models, and Richard Freedman for providingopacities.
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Footnotes
- ... distorted
- We note that it resembles the spectrum observed for a star
G240-72 in Bergeron et al.
(1997), Fig. 30, which opens the possibility that
this star (
, Bergeron et al. 1997) is not only magnetic, but also shows the extremely pressure-shifted Swan bands.
All Figures
![]() |
Figure 1:
Optical spectra of the white dwarfs LHS179 (DQ, upper panel) and LHS290 (DQp, lower panel) (Bergeron et al. 1997). The solid line represents the fit to the spectrum of LHS179. The parameters of the fits are:
|
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Left panel: density at the photosphere (the Rosseland mean optical depth
|
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Left panel: the vibrational density of states of |
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Fits to the optical spectrum of the DQp white dwarf LHS290 (thick solid line).
All the fits are with
|
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Left panel: fits to the entire spectral energy distribution of the DQp white dwarf LHS290 (thick solid line)
given by BVIJHK photometry of Bergeron et al. (2001) (bars). The parameters of the fits are the same as in Fig. 4. Right panel: density profiles of the discussed models. The vertical dotted line marks the photosphere (
|
Open with DEXTER | |
In the text |
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