11institutetext: Instituto de Astrofísica de Canarias (IAC), E-38205 La Laguna, Tenerife, Spain
11email: vperezme@iac
22institutetext: Departamento de Astrofísica, Universidad de La Laguna (ULL),
E-38206 La Laguna, Tenerife, Spain
33institutetext: Laboratoire Univers et Particules de Montpellier, Université
de Montpellier2, CNRS, 34095 Montpellier, France
44institutetext: Consejo Superior de Investigaciones Científicas (CSIC), E-28006
Madrid, Spain
55institutetext: Monash Centre for Astrophysics, School of Physics and Astronomy,
Monash University, VIC3800, Australia
66institutetext: Konkoly Observatory, Research Centre for Astronomy and Earth Sciences,
Hungarian Academy of Sciences, 1121 Budapest, Hungary
Rubidium and zirconium abundances in massive Galactic asymptotic giant branch stars revisited
V. Pérez-Mesa
1122
O. Zamora
1122
D. A.
García-Hernández
1122
B. Plez
33
A. Manchado
112244
A. I. Karakas
55
M. Lugaro
5566
(Received September 15, 1996; accepted March 16, 1997)
Abstract
Context. Luminous Galactic OH/IR stars have been identified as massive
(> 4-5 M⊙) asymptotic giant branch (AGB) stars experiencing hot
bottom burning and Li production. Their Rb abundances and [Rb/Zr] ratios, as
derived from classical hydrostatic model atmospheres, are significantly higher
than predictions from AGB nucleosynthesis models, posing a problem to our
understanding of AGB evolution and nucleosynthesis.
*Aims. *We report new Rb and Zr abundances in the full sample (21) of massive
Galactic AGB stars,
previously studied with hydrostatic models, by using more realistic extended
model atmospheres.
Methods. For this, we use a modified version of the spectral synthesis code
Turbospectrum and consider the presence of a circumstellar envelope and radial
wind in the modelling of the optical spectra of these massive AGB stars. The Rb
and Zr abundances are determined from the 7800 Å Rb I resonant line and the
6474 Å ZrO bandhead, respectively, and we explore the sensitivity of the
derived abundances to variations of the stellar (Teff) and wind (M˙,
β and vexp) parameters in the pseudo-dynamical models. The Rb and Zr
abundances derived from the best spectral fits are compared with the most
recent AGB nucleosynthesis theoretical predictions.
Results. The Rb abundances derived with the pseudo-dynamical models are much lower
(in the most extreme stars even by ∼1-2 dex) than those derived with the
hydrostatic models, while the Zr abundances are similar. The Rb I line profile
and Rb abundance are very sensitive to the wind mass-loss rate M˙
(especially for M˙ ≥ 10-8 M⊙yr−1) but much less
sensitive to variations of the wind velocity-law (β parameter) and the
expansion velocity vexp(OH).
*Conclusions. *We confirm the earlier preliminary results based on a smaller sample of
massive O-rich AGB stars, that the use of extended atmosphere models can
solve the discrepancy
between the AGB nucleosynthesis theoretical models and the observations of
Galactic massive AGB stars. The Rb abundances, however, are still strongly
dependent of the wind mass-loss M˙, which, unfortunately, is unknown in
these AGB stars. Accurate mass-loss rates M˙ (e.g., from rotationally
excited lines of the CO isotopologues in the radio domain) in these massive
Galactic AGB stars are needed in order to break the models degeneracy and get
reliable (no model-dependent) Rb abundances in these stars.
Key Words.:
**stars: AGB and post-AGB –
stars: abundances –
stars: evolution –
nuclear reactions, nucleosynthesis, abundances –
stars: atmospheres –
stars: late-type
**
1 Introduction
The asymptotic giant brach (AGB; Herwig 2005; Karakas & Lattanzio 2014)
is occupied by low- and
intermediate-mass (0.8 ≤ M ≤ 8 M*⊙) stars in the last
nuclear-burning phase. At the end of the AGB phase, these stars develop
thermal pulses (TP) and suffer extreme mass loss. AGB stars are thus
one of the main contributors to the enrichment of the
interstellar medium (ISM) of light elements (e.g. Li, C, N, F) and heavy
(slow neutron capture, s-process) elements and so to the
chemical evolution of galaxies (Busso et al., 1999). AGB stars are also one of
the most prominent source of dust in galaxies and the site of origin of the
vast majority of meteoritic stardust grains (e.g. Hoppe & Ott, 1997; Nittler et al., 1997; Lugaro et al., 2017). In low-mass AGB stars (M < 4 M⊙) 12C is produced
during the TP-AGB phase, and carried to the stellar surface via the third
dredge-up (TDU) that can occur after each TP, transforming originally O-rich
stars in C-rich stars (C/O>1) (e.g. Herwig, 2005; Karakas & Lattanzio, 2007; Lugaro & Chieffi, 2011).
However, the more massive AGB stars (M > 4-5 M⊙*) are O-rich (C/O<1)
because the so-called ”hot bottom burning” (hereafter, HBB) process is activated.
The HBB converts 12C into 13C and 14N through the CN cycle via proton
captures at the base of the convective envelope, thus preventing the formation of
a carbon star (Sackmann & Boothroyd, 1992; Mazzitelli et al., 1999).
The s-process allows the production of neutron-rich elements heavier than
iron (s-elements such as Sr, Y, Zr, Ba, La, Nd, Tc, etc.) by s
-process. In the low-mass AGB stars (roughly ¡ 4 M*⊙), the 13C(α,
n)16O reaction is the dominant neutron source (e.g. Abia et al., 2001). In the
more massive AGB stars instead, neutrons are mainly released by the 22Ne(α,
n)25Mg reaction, resulting in a higher neutron density (up to 1013* n/cm3)
and temperature environment than in lower mass AGB stars (García-Hernández et al., 2006).
The Rb produced depends on the probability of the 85Kr and 86Rb capturing a
neutron before decaying and acting as ”branching points” (see van Raai et al., 2012, for more
details). The probabiliy of this happening depends on the local neutron density
(Beer & Macklin, 1989). The 87Rb/85Rb isotopic ratio is a direct indicator
of the neutron density at the production site but it is not possible to distinguish
individual 87Rb and 85Rb from stellar spectra (García-Hernández et al., 2006).
However, the relative abundance of Rb to other nearby s-process elements such
as Zr is very sensitive to the neutron density, and so a good discriminant of the stellar
mass and the neutron source at the s-process site (Lambert et al., 1995; Abia et al., 2001; García-Hernández et al., 2006; van Raai et al., 2012). In other words, [Rb/Zr]<0 is observed in low-mass
AGB stars where the main neutron source is the 13C(α, n)16O
reaction (Plez et al., 1993; Lambert et al., 1995; Abia et al., 2001), while [Rb/Zr]>0 is observed in more
massive AGB stars, where the neutrons are mainly released through the
22Ne(α, n)25Mg reaction (García-Hernández et al., 2006, 2007, 2009).
Chemical abundance analyses using classical MARCS hydrostatic atmospheres
(Gustafsson et al., 2008) revealed strong Rb overabundances (∼103-105
times solar) and high [Rb/Zr] ratios (⩾ 3-4 dex) in massive AGB stars
(generally very luminous OH/IR stars) of our own Galaxy and the Magellanic Clouds
(MC; García-Hernández et al. 2006, 2007, 2009). This
observationally confirmed for the first time that the 22Ne neutron source dominates
the production of s-process elements in these stars. However, the extremely
high Rb abundances and [Rb/Zr] ratios observed in most the massive stars (and especially
in the lower metallicity MC AGB stars) have posed a ”Rb problem”; such extreme [Rb/Fe]
and [Rb/Zr] values are not predicted by the s-process AGB models,
(van Raai et al., 2012; Karakas et al., 2012), suggesting fundamental problems in our present
understanding of AGB nucleosynthesis and/or of the complex extended dynamical atmospheres of
these stars (García-Hernández et al., 2009).
Zamora et al. (2014) constructed new pseudo-dynamical MARCS model atmospheres by considering
the presence of a gaseous circumstellar envelope with a radial wind and
applied them to a small sample of five O-rich AGB stars with different expansion
velocities and metallicities. The Rb abundances and [Rb/Zr] ratios obtained were
much lower than those obtained with classical hydrostatic models; in better
agreement with the AGB nucleosynthesis theoretical predictions. In this paper,
we use the Zamora et al. (2014) pseudo-dynamical model atmospheres to obtain the abundances
of Rb and Zr in the full sample of massive Galactic AGB stars previously
analyzed with hydrostatic models (García-Hernández et al., 2006, 2007).
These Rb and Zr abundances are then compared with the more recent AGB
nucleosynthesis theoretical predictions available in the literature.
2 Sample and observational data
Our sample is composed by 21 massive Galactic AGB stars (most of them very
luminous OH/IR stars) previously analyzed by García-Hernández et al. (2006, 2007); we use their high-resolution (R∼40,000−50,000)
optical echelle spectra (see García-Hernández et al., 2006, 2007, for further observational details)111The high-resolution spectra
were obtained using the Utrecht Echelle Spectrograph (UES) at the 4.2 m William
Herschel Telescope (La Palma, Spain) and the CAsegrain Echelle SPECtrograph
(CASPEC) of the ESO 3.6 m telescope (La Silla, Chile) during several observing
periods in 1996-97 (see García-Hernández et al., 2007).. The signal-to-noise (S/N)
ratios achieved in the reduced spectra strongly vary from the blue to the red
(typically ∼ 10-20 at 6000 A˚ and >100 at 8000 Å). The Rb and
Zr abundances were determined from the resonant 7800 A˚ Rb I line and the
6474 A˚ ZrO bandhead, respectively, by using classical MARCS hydrostatic
model atmospheres (García-Hernández et al., 2006, 2007). The Rb
abundances and [Rb/Zr] ratios obtained from this chemical analysis are mostly in
the range [Rb/Fe]∼0.6−2.6 dex and [Rb/Zr]∼0.1−2.1 dex. The
atmospheric parameters and Rb abundances derived with the hydrostatic models as
well as other useful observational information like the OH expansion velocity,
variability period, and the presence of Li are listed in Table 1.
3 Chemical abundance analysis using pseudo-dynamical models
3.1 Modified version of the Turbospectrum spectral synthesis code
We have used the v12.2 version of the spectral synthesis code
Turbospectrum (Alvarez & Plez, 1998; Plez, 2012), which considers the presence
of a circumstellar gas envelope and a radial wind, as modified by Zamora et al. (2014).
The main modifications are the following: (i) the Doppler effect due to the
extended atmosphere and velocity field is introduced in the routines that
compute the line intensities at the stellar surface; (ii) the source
function of the radiative transfer is assumed to be the same as computed in the
static case (Gustafsson et al., 2008). The validity of this approximation was tested
by comparing with Monte Carlo simulations (see Zamora et al., 2014); (iii)
the scattering term
of the source function (∝σλJλ) is not shifted
to save computing time and it is only incorporated for the continuum.
This scattering term is computed as in the static case
using the Feautrier method (Nordlund, 1984; Gustafsson et al., 2008); and (iv) the velocity field
is taken into account through a shift of the absorption coefficient
κλ; the source function is built using the static
σλJλ and the shifted κλBλ.
The emerging intensity is then computed in the observer frame by a direct quadrature
of the source function.
3.2 Extended atmosphere models
For the analysis of each star in our sample, we have adopted the atmosphere
parameters from García-Hernández et al. (2006, 2007) and the solar
reference abundances by Grevesse et al. (2007). We constructed our pseudo-dynamical models
from the original MARCS hydrostatic atmosphere model structure. We expanded the
atmosphere radius by a wind out to ∼5 stellar radii and a radial velocity
field (Zamora et al., 2014). In the MARCS hydrostatic model, the R∗ is the
radius corresponding to r(τRoss=1), where r is the distance from the
center of the star and τRoss is the Rosseland optical depth. We have
computed the stellar wind following the mass conservation (Eq. 1), radiative
thermal equilibrium (Eq. 2) and a classical β-velocity law (Eq. 3),
[TABLE]
[TABLE]
[TABLE]
where ρ(r) is the density of the envelope radius r, M˙ is the
mass-loss rate and v(r) is the velocity of the envelope, which is calculated
by means of Eq.(3). In Eq.(3), v0 is a reference velocity for the
beginning of the wind and β is an arbitrary free parameter. We take
v0=v(R∗) for the onset of the wind and the extension of the envelope
begins from the outer radius of the hydrostatic model. Using Eq.(2) the envelope
is extended, layer by layer, out to the distance rmax, which corresponds to
the maximum radius in our calculations, with Tmin=1000 K.
Turbospectrum cannot compute lower temperatures due to numerical
reasons (Zamora et al., 2014).
3.3 Resulting grids of synthetic spectra
The synthetic spectra are generated with the modified version of
Turbospectrum by using the extended pseudo-dynamical model atmospheres as
input. We constructed a mini-grid of synthetic spectra for each sample star by
adopting the atmospheric parameters (e.g., effective temperature,
macroturbulence333The synthetic spectra are convolved with a Gaussian
profile (with a certain FWHM typically between 250 and 400 mÅ) to account for
macroturbulence as well as instrumental profile effects.) from
García-Hernández et al. (2006, 2007). Basically, the stellar mass,
gravity log g, microturbulent velocity ξ, metallicity [Fe/H], and C/O ratio
are fixed to 2 M*⊙, −0.5 dex, 3 kms-1*, 0.0, and 0.5 dex,
respectively (see García-Hernández et al., 2007, for more details). On the other
hand, for the mass-loss rate M˙ and the exponent β, we use values
between M˙∼10−9−10−6M⊙yr−1 in steps of
0.5×10−1 M⊙yr−1 and β∼0.2−1.6 in steps of 0.2.
We have not considered the case where β=0.0 because the expansion
velocity would be constant at any r. We assume the OH expansion velocity
(vexp(OH); see Table 1) as the terminal velocity
because the OH maser emission is found at very large distances of
the central star (see e.g., Decin et al., 2010). Figure 1 shows examples
of the β-velocity laws used in our pseudo-dynamical models based on the MARCS
hydrostatic models. Finally, for the Rb and Zr abundances we used
[Rb/Fe]∼−2.6 to +3.0 dex, and [Zr/Fe]∼−1.0 to +1.0 in steps of 0.1
and 0.25 dex, respectively.
The resulting mini-grid (∼4400 models) is compared to the observed
spectrum in order to find the synthetic spectrum that best fits the 7800 A˚
Rb I line and the 6474 A˚ ZrO bandhead profiles and their adjacent
pseudocontinua. In order to obtain the best fits, we made use of a procedure
based on the comparison between synthetic and observed spectra, while in
Zamora et al. (2014) the observed spectra were fitted by eye. The method is a
modified version of the standard χ2 test,
[TABLE]
where Yobsi and Ysynthi are the observed and synthetic data points,
respectively, with N the number of data points, and M the number of free
parameters. On the other hand, w is a vector that gives a stronger weight to
the detailed spectral profiles of the Rb I line and the ZrO bandhead. This
way, the lowest value of χ2∗ gives us the best fitting synthetic
spectrum from the mini-grid for each sample star.
The use of the χ2∗ test to find the best fits to the observed
spectra
reveals the presence of important
degeneracies in the resulting grids of pseudo-dynamical synthetic spectra; i.e., very
similar synthetic spectra are obtained from different sets of wind parameters
(see below for more details). Moreover, in a some cases (IRAS 04404−7427,
IRAS 05027−2158, IRAS 05098−6422, IRAS 06300+6058, IRAS 10261−5055,
IRAS 18429−1721, IRAS 19059−2219 and
IRAS 20343−3020) the use of the χ2∗ test is not enough for obtaining the
synthetic
spectrum that best reproduces the observed one and the best fits have to be
found by eye. Unfortunately, the wind model parameters M˙ and β are
generally not known for stars in our sample (see below), complicating the
abundance analysis. Thus, here we study the sensitivity of the synthetic spectra
and the abundance results to variations of the stellar and wind parameters.
3.4 Sensitivity of the synthetic spectra to variations of the model
parameters
Here, we analyze how the variations in stellar (Teff) and wind
(M˙, β and vexp(OH)) parameters influence the output synthetic
spectra. Figures 2 and 3 show examples of
synthetic spectra for different stellar and wind parameters in the spectral
regions around the 7800 A˚ Rb I line and 6474 A˚ ZrO bandhead,
respectively. We note that the fraction of the absortion at 7800
Å due to other species (e.g., TiO) is tipically around 20%.
The Rb I line profile is very sensitive to the wind mass-loss rate M˙
(especially for M˙ ≥ 10*-8* M⊙yr−1); the Rb I line is
significantly deeper and blue-shifted with increasing M˙ (Figure
2, top-left panel). However, the Rb I line profile is much
less sensitive to changes of the wind velocity-law (β parameter);
being only slightly deeper with increasing β (Figure 2,
bottom-left panel). In addition, for β values higher
than ∼1.2 (shallower velocity profiles), the Rb I line profile is
not sensitive to variations of the expansion velocity vexp(OH) because the
velocity profiles are very similar in our extended model atmosphere (up to
∼1014 cm; see Figure 1). Variations in the expansion velocity
vexp(OH) mainly affect the blue-shift of the Rb I line and, in addition,
for large vexp(OH) values the core of the Rb I line is less deep (Figure
2, bottom-right panel). Finally, the Rb I absorption line is
stronger with decreasing effective temperature Teff (as expected; Figure
2, top-right panel) but this time the wealth of TiO molecular
lines and the pseudo-continua are also affected. We note that all these effects
(variations in the Rb I profile in terms of depth and blue-shift) are more
evident for extreme mass-loss rates (M˙ ≥ 10*-7*
M⊙yr−1) and higher Rb abundances.
On the other hand, the ZrO bandhead profile is not sensitive to the wind
parameters M˙, β, and vexp(OH) (see Figure 3;
top-left, bottom-left, and bottom-right panels, respectively). The ZrO bandhead
profile (as well as the adjacent TiO lines and pseudo-continuum) are, again as
expected, stronger with decreasing Teff (Figure 3,
top-right panel). This is because ZrO is formed deeper than Rb I in the
atmosphere, being much less affected by the circumstellar envelope and radial
wind.
4 Results
As we have mentioned above, there are important degeneracies in the resulting
mini-grids of synthetic spectra for each star.
Two synthetic spectra with the same Teff, logg and vexp(OH), but
different β, M˙, and [Rb/Fe] abundances could be practically identical
in spite of the different wind parameters. This complicates the abundance
analysis because the wind model parameters M˙ and β are generally
not known for
stars in our sample. In any case, we can use some observational constraints and
previous results on a few similar OH/IR stars to limit the possible variation
range of these wind parameters (in particular for the mass-loss rates M˙,
see below).
By using multiple rotationally excited lines of both 12CO and 13CO,
De Beck et al. (2010) provide accurate mass-loss rates M˙ for a large sample
of Galactic AGB stars. Unfortunately, only one star (IRAS 20077−0625) from our
present sample of Rb-rich OH/IR massive AGB stars is included in their work and
we cannot fit this star with our pseudo-dynamical models (see below). There are seven
massive AGB stars of OH/IR type (WX Psc, V669 Cas, NV Aur, OH 26.5+0.6, OH
44.8−2.3, IRC −10529 and OH 104.9+2.4) previously studied in the optical by
García-Hernández et al. (2007). Their variability periods and mass-loss rates range
from 552 to 1620 days444The variability periods of our sample stars are
also lower, from ∼320 to 580 days (only two stars display periods in excess
of 580 days; see Table 1). and from 1.8×10*-5* M⊙yr−1 to
9.7×10*-6* M⊙yr−1, respectively. Interestingly, all these
stars are extremely obscured in the optical, being too red or without optical
counterpart555The only exception is WX Psc as already noted by
Zamora et al. (2014). This star (with a mass-loss rate of ∼1.8 ×
10*-5* M⊙yr−1, De Beck et al. 2010; Justtanont et al. 2013) has an
extremely faint optical counterpart. The S/N around 7800 Å is too low for
an abundance analysis but a strong Rb I absorption line is clearly detected in
its optical spectrum.; they likely already have entered the superwind phase.
Thus, the M˙ values in optically obscured OH/IR AGB stars can be taken as
upper limits (i.e. <10*-6* M⊙yr−1) for our sample of OH/IR
massive AGB stars with optical counterparts; i.e. with useful spectra around the
7800 Å Rb I line. Indeed, we generally find that lower mass-loss rates
(∼10−7−10*-8* M⊙yr−1) give superior fits to the
observed Rb I line profiles. Mass-loss rates of ∼10*-6* M⊙yr−1
(or higher) give strong Rb I absorption lines for solar Rb abundances (see also
Zamora et al. 2014) with the consequence that all stars in our
sample of OH/IR massive AGB stars would be Rb-poor. By combining the variability
periods from Table 1 and the mass-loss rates estimated from the Rb I line
profiles (mainly in the range ∼10−7−10*-8* M⊙yr−1; see
Table 2) into the AGB mass-loss formula by Vassiliadis & Wood (1993) (their Eq. (5)), we obtain
reasonable current stellar masses in the range ∼2.5−6 M⊙.
In Table 2 we show the mass-loss rates obtained from the best spectral
fits (M˙fit) and the current stellar masses by using the mass-loss
expression from Vassiliadis & Wood (1993).
The β parameter in our models (only up to ∼1014 cm from the
photosphere; see Figure 1) cannot be directly compared with other estimations of
this parameter in the literature (e.g. Decin et al., 2010; Danilovich et al., 2015), which
map much outer regions in the circumstellar envelope and that usually obtain
quite high and uncertain values (0 ≤ β ≤ 5.0). However, the
effect of the β parameter on our synthetic spectra is minor compared
to the mass-loss rate M˙ and we keep it as a free parameter in our
abundance analysis. We note also that the velocity profiles are very similar
in our extended model atmosphere for β ≥ 1.2; i.e., the Rb I line
profile is not more sensitive to variations of the expansion velocity and the
abundance results are very similar for β ≥ 1.2. We generally
find better fits with low β values (or steeper velocity profiles; see
Table 3).
As mentioned above, the parameters of the hydrostatic models providing
the best fit to the observations and the Rb abundances derived are shown in
Table 1. The static models use the solar abundances from
Grevesse & Sauval (1998) for computing the Rb abundances
(see García-Hernández et al., 2006, 2007), while our pseudo-dynamical
models use the more recent solar abundances from Grevesse et al. (2007). In
Zamora et al. (2014) we compared the Rb abundances from static models using
Grevesse & Sauval (1998) and Grevesse et al. (2007), and the Rb abundances obtained agree
within ∼0.2 dex in most cases.
Figure 4 shows that our pseudo-dynamical atmosphere models reproduce the
observed 7800 A˚ Rb I line profile much better than the classical hydrostatic
models in four sample stars (see Appendix A for the rest of sample stars).
On the other hand, the Zr abundances derived from the extended models
are similar to those obtained with the hydrostatic models because the 6474 A˚
ZrO bandhead is formed deeper in the atmosphere and is less affected by the
radial velocity field (Zamora et al., 2014). We could obtain the Rb and Zr abundances
(or upper limits) for 17 sample stars. The rest of sample stars (IRAS
07222−2005, IRAS 09194−4518, IRAS 19426+4342 and IRAS 20077−0625) seem
to display different Rb I line profiles (e.g., with more than one circumstellar
contribution or anomalously broad profiles with red-extended wings; see e.g.,
Figure 5) that cannot be completely reproduced by our present
version of the spectral synthesis code. In the two stars (IRAS 07222−2005 and
IRAS 09194−4518) shown in Figure 5 we cannot fit the two Rb I
components (circumstellar and photospheric) at the same time; e.g., we only might
fit partially the blue-shifted circumstellar component using a larger
mass-loss rates (>10*-6* M⊙yr−1). Curiously, these two stars
present the largest periods (see Table 1) and they may be
the more extreme and evolved stars in our sample, where our extended models do
not not work so well (e.g., due to even more extended atmospheres). It is not
completely clear,
however, if the observed profiles are real because these four sample stars
have the lowest quality spectra (S/N < 30 at 7800 Å; see Table
1).
For the two sample stars with unknown OH expansion velocity, IRAS 16030−5156
and IRAS 17034−1024, we explore the velocity range displayed by other stars
with similar variability periods (see Table
1). Similar fits can be obtained for vexp(OH)
∼ 7−12 and 7−9 kms*-1* (in combination with sligthly different
wind parameters) for IRAS 16030−5156 and IRAS 17034−1024, respectively,
and we thus adopt average velocities of 10 and 8 kms*-1*, respectively, in
the abundance analysis (see Table 3).
Table 3 shows the atmospheric and wind parameters as well as
the Rb and Zr abundances (or upper limits) from the best fits to the observed
spectra when the wind parameters M˙ and β are not fixed. In most
cases, the best fit is obtained for both low β (∼0.2) and M˙
(∼10*-9*-10*-7* M*⊙* yr*-1*) values. The new Rb abundances
obtained from extended models are lower than those obtained using the hydrostatic
models, and the difference is larger for stars with higher hydrostatic Rb
abundances. In addition, this difference is smaller for lower vexp(OH) and
increases with increasing vexp(OH), as expected. On the other hand, in the
case of Zr we obtain upper limits mostly between 0.0 and +0.25 dex, as derived
from the hydrostatic models. Figure 6 displays the hydrostatic
and pseudo-dynamical Rb abundances versus the OH expansion velocity for the wind
parameters that provide the best fits (Table 3.
We plot the Rb abundances versus the expansion
velocity because the vexp(OH) can be used as a mass indicator independent
of the distance in OH/IR stars (García-Hernández et al., 2007).
In addition, in Figure 6 we have marked the Li-rich stars
(García-Hernández et al., 2007) by squares. About half of the stars with vexp(OH)
> 6 km/s are Li-rich and most of these stars are also the more Rb-rich ones.
We get pseudo-dynamical abundances lower than the hydrostatic ones and a
worse correlation between666The correlation coefficients are r= 0.84 and
0.54 for the hydrostatic and pseudo-dynamic cases, respectively. the Rb abundances
and vexp(OH); the Rb-vexp(OH) relationship is flatter (with a higher
degeneration) for the pseudo-dynamical case (see also Sect. 5).
Also, we have carried out several tests with different β and M˙
values in order to check the sensitivity of the derived abundances to variations
of the wind parameters. In Table 4 we present the wind
parameters and Rb abundances obtained when fixing β to 0.2 and 1.2.
Basically, the Rb abundances are lower in the β = 1.2 case because a
higher β deepens the Rb I 7800 A˚ line for the same Rb abundance (see
Figure 2); in a few cases, however, the M˙ of the best
fit also changes, further affecting the determination of the Rb abundance. The
Zr abundances (or upper limits) are similar in most cases; the upper limits only change
when the M˙ is not the same for the β = 0.2 and 1.2 cases. Figure
7 represents the Rb abundances obtained versus vexp(OH)
for β = 0.2
and β = 1.2
. By comparing the Rb abundances from Figure
6 and Figure 7, it is clear that the Rb
abundances are slightly lower in the β = 1.2 case. Moreover, the correlation
between the pseudo-dynamical Rb abundances and vexp(OH) for different β values
is worse (e.g., flatter) than the hydrostatic case. In addition, the dispersion seems
to be larger for the β = 1.2 case.
On the other hand, Figure 8 displays the Rb results when
M˙ is fixed to 10*-8*, 10*-7* and 10*-6* M*⊙* yr*-1*.
This could be equivalent to consider that our AGB sample stars have a similar
evolutionary stage in terms of the mass loss; of course we have a strong
degeneracy between the progenitor masses and mass loss/evolutionary stage.
In the particular case of the Li-rich AGB stars, statistical arguments
suggest that these stars should have a narrow initial mass range
(see Di Criscienzo et al., 2016); 4-5 or 5-6 M*⊙* according to
the most recent ATON (Di Criscienzo et al., 2016) or Monash (Karakas & Lugaro, 2016)
AGB nucleosynthesis models, respectively. The current stellar masses from
Table 2
show, however, that there is a complicated interplay (degeneracy) between
Li enhancement, progenitor mass and mass-loss rate and that the progenitor
mass range of these stars may be actually broader; e.g., their current
stellar mass and Li abundance ranges are ∼2.7-5.6 M*⊙* and
∼logε(Li)∼0.7-2.6 dex. Figure
8 shows that the Rb abundances decrease with increasing
M˙ and the dispersion of the Rb abundances is much lower when fixing
M˙. The slopes (and correlation coefficients) of the Rb-vexp(OH)
correlations are more
similar to the one obtained with hydrostatic models. The Rb abundances from
extended models approach the hydrostatic ones with decreasing M˙ (both
sets of Rb abundances are identical for M˙ ≤ 10*-9* M*⊙*
yr*-1*) because the atmosphere is less extended with decreasing M˙, as
expected.
Finally, we fixed M˙ and β, which could be equivalent to consider
that our AGB sample stars have the same mass loss stage and velocity profile.
Figure 9 displays the pseudo-dynamical Rb abundances versus
vexp(OH) for β = 0.2 and M˙ values of 10*-8*, 10*-7* and
10*-6* M*⊙* yr*-1*. The Rb results when fixing both M˙ and
β are very similar (with a slightly tighter correlation with vexp(OH))
to those obtained when only fixing M˙ (see Figure 8)
because β = 0.2 is the most common value obtained from the best spectral
fits (all wind parameters free); an exception is the AGB star IRAS 15193+3132
(with the lowest vexp(OH) and high β) for which only an upper limit
to the Rb abundance ([Rb/Fe]≤0.7) could be obtained because the pseudo-dynamical
model does not converge for such unusual combination of wind parameters (M˙=10*-6*
M*⊙* yr*-1*; β=0.2; vexp(OH)=3 km s*-1*) coupled with
[Rb/Fe]<0.7 dex (see Figure 9).
Figure 10 displays the [Rb/Fe] abundances from the best spectral
fits versus the variability periods P. As already mentioned, our sample is
composed by AGB stars of different progenitor masses and evolutionary stages.
Most stars with P > 400 days are Li-rich and present some Rb
enhancement888The only exceptions are IRAS 04404−7427 and IRAS
19059−2219, whose optical counterparts are too red to estimate their Li
abundances (i.e., the S/N at 6708 Å is too low;
see García-Hernández et al., 2007), which suggests that, on average, these stars are
more massive stars experiencing HBB and/or more evolved stars (because of the
longer periods) than the group of non Li-rich (and generally Rb-poor) stars with
P < 400 days. The stars IRAS 05027−2158 (P=368 days) and IRAS
20343−3020 (P=349 days) are exceptions in the latter group. IRAS 05027−2158
is slightly Li-rich and Rb-poor, suggesting that it is a relatively massive AGB
star (say ∼3.5−4.5 M*⊙999The initial mass for HBB
activation is model dependent; i.e., at solar metallicity HBB is activated at
∼3.5 and 4.5 M⊙* depending on the mass-loss and convection
prescriptions used in the models (see e.g. García-Hernández et al., 2013, for more
details).) at the beginning of the TP phase (e.g., in an
inter-pulse period just before or after the super Li-rich phase) but it is not
evolved enough for efficient Rb production (see García-Hernández et al., 2013). On
the other hand, IRAS 20343−3020 is slightly Rb-rich and Li-poor, which
suggests a more advanced evolutionary stage and a slightly higher initial mass
(say ∼4.0−5 M*⊙*) than IRAS 05027−2158 (see Fig. 1
in García-Hernández et al., 2013).
5 Comparison with AGB nucleosynthesis models
In Figure 11 we compare our new [Rb/Fe] abundances and [Rb/Zr]
ratios with solar metallicity massive (3−9 M*⊙*) AGB predictions from
several nucleosynthesis models: van Raai et al. (2012), Karakas et al. (2012),
Karakas & Lugaro (2016) (Monash), Pignatari et al. (2016) (NuGrid/MESA)
and Cristallo et al. (2015) (FRUITY101010FUll-Network Repository of
Updated Isotopic Tables and Yields: http:// fruity.oa-teramo.inaf.it/.). The
predicted [Rb/Fe] abundances and [Rb/Zr] ratios ranges are 0.00−1.35 and
−0.45−0.52 dex, respectively.
The Monash models (van Raai et al., 2012; Karakas et al., 2012; Karakas & Lugaro, 2016) use the stellar
evolutionary sequences calculated with the Monash version of the
Mount Stromlo Stellar Structure Program (Frost & Lattanzio, 1996), which uses
the Vassiliadis & Wood (1993)
mass-loss prescription on the AGB. A post-processing code is used to obtain
in detail the nucleosynthesis of a large number of species, including the
s-process abundances. Due to convergence difficulties, the stellar
evolution models used in the calculations are not always evolved until the end of the
superwind phase and synthetic models have been used to estimate the effect of
remaining TPs and to completely remove the envelope. We refer the reader to
van Raai et al. (2012), Karakas et al. (2012) and Karakas & Lugaro (2016) for more details
about the theoretical models. Here, we only report the main differences between these
models and that are basically the following: i) the use of different nuclear
networks; i.e., the
total number of nuclear species considered and the values of some reaction rates and
neutron-capture cross sections (see below); and ii) the use by Karakas et al. (2012) of a
modified Vassiliadis & Wood (1993) mass-loss prescription, which delays the
beginning of the superwind phase until the pulsation period reaches values of
700-800 days (instead of the value of 500 days used in the other models), resulting
in a higher Rb production.
The NuGrid/MESA and FRUITY models assume AGB mass-loss
prescriptions, nuclear physics inputs and treatments of convection
different from the Monash models. In particular, the Blöcker (1995) and
Straniero, Gallino & Cristallo (2006) mass-loss formulae for the AGB phase are assumed by the
NuGrid/MESA and FRUITY models, respectively. Furthermore, these models produce
self-consistently the 13C neutron source as a result of the different
convective boundary mixing scheme and treatments of the convective borders,
while in the Monash models the mixing required to produce the 13C neutron
source is included in a parametrized way during the post processing and it is
typically not included in massive AGB stars, following theoretical (Goriely & Siess, 2004)
and observational indications (García-Hernández et al., 2013)
(see also Pignatari et al., 2016; Cristallo et al., 2015; Karakas & Lugaro, 2016, for more details). In relation
to the main results: i) the NuGrid/MESA solar metallicity massive AGB models are
qualitatively similar to the Monash models in terms of HBB and light s-process
element production (of the elements from Rb to Zr) are seen at the stellar surface,
the latter due to the activation of the 22Ne neutron source and the subsequent
operation of the TDU; and ii) the FRUITY solar metallicity
massive AGB models are different to the Monash and NuGrid/MESA models because
these models experience very inefficient TDU, hence the signature of the nucleosynthesis
due to the 22Ne neutron source is not visible at the stellar surface.
Figure 11 shows that the FRUITY massive AGB models predicts final
[Rb/Fe] < 0.15, which does not explain the observed range of Rb abundances and
[Rb/Zr] ratios; specifically the [Rb/Zr] ratios remains negative for all masses.
Another difference of the FRUITY models with the Monash and NuGrid models
is that the FRUITY models do not predict HBB to occur in AGB stars, unless the metallicity
is very low, at least ten times lower than solar. However, spectroscopic
observations of massive AGB stars demonstrate that they experience HBB; as evidenced by: i)
strong Li overabundances observed in massive AGB stars in the Galaxy
(Fe/H=0.0; e.g., García-Hernández et al., 2007, 2013), the
Magellanic Clouds (Fe/H=−0.7-−0.3; e.g., Plez et al., 1993; Smith et al., 1995; García-Hernández et al., 2009)
and the dwarf galaxy IC 1613
(Fe/H=−1.6; e.g., Menzies, Whitelock & Feast, 2015); ii) N enhancements and low
12C/13C ratios in Magellanic Cloud Li-rich massive AGBs
(e.g., Plez et al., 1993; McSaveney et al., 2007).
The lack of HBB in the FRUITY predictions is also at
odds with the observations of the so-called type I planetary nebulae in very
different metallicity environments and galaxies; which are expected to be the
descendants of HBB massive AGB stars based on their strong N and He
overabundances (see e.g. Stanghellini et al., 2006; Karakas et al., 2009; Leisy& Dennefeld, 1996; García-Rojas et al., 2016, and references therein).
It is to be noted here that the several Monash AGB models
(van Raai et al., 2012; Karakas et al., 2012; Karakas & Lugaro, 2016) mentioned above notably use different
rates for the 22Ne(α,n)25Mg reaction, which drives the production
of s-process elements in massive AGB stars. In particular,
Karakas & Lugaro (2016) use the 22Ne(α,n)25Mg reaction from
Iliadis et al. (2010), neutron-capture cross section of the Zr isotopes (Lugaro et al., 2014), and a
more extended nuclear network of 328 species (from H to S, and then from Fe to
Bi). The van Raai et al. (2012) models, instead, use a nuclear network of 166 species (up to
Nb) and the 22Ne(α,n)25Mg reaction rate from Karakas et al. (2006),
while Karakas et al. (2012) explored different networks (166, 172 and 320 species)
and 22Ne(α,n)25Mg reaction rates; from Karakas et al. (2006),
Iliadis et al. (2010) and Angulo et al. (1999), NACRE.
The van Raai et al. (2012) models (from 4 to 6.5 M*⊙* at Z = 0.02; Fig.
11) show that both the [Rb/Fe] abundances and [Rb/Zr] ratios
increase with the initial mass of the AGB star, as the star becomes hotter and
the 22Ne(α,n)25Mg reaction is more efficiently activated. However,
the [Rb/Fe] abundances from the last computed TP are too low (ranging from 0.0 to
0.26 dex). The corresponding Rb abundances ([Rb/Fe]∼0.0−1.0 dex) from the
synthetic evolution calculations cover most of the Rb abundances observed;
although they cannot explain the star IRAS 05151+6312 with [Rb/Fe]=1.3 dex.
Such high Rb abundances can be reached by the synthetic calculations of the
solar metallicity 6 and 7 M*⊙* AGB models with delayed superwinds of
Karakas et al. (2012) when using the faster NACRE rate for the 22Ne(α,n)25Mg reaction.
Finally, the Karakas & Lugaro (2016)
models (from 4.5 to 8 M*⊙* at Z = 0.014111111According to the more
recent solar abundances from Asplund et al. 2009; Fig. 11)
predict lower Rb abundances than the Karakas et al. (2012) models of the same mass
and similar metallicity, mostly due to the implementation of the delayed superwind
and the use of the NACRE rate in Karakas et al. (2012).
The NuGrid/MESA models (from 3 to 5 M*⊙* at Z = 0.02; Fig.
11) reproduce the observed [Rb/Fe] and [Rb/Zr] ranges,
up to 0.9 and 0.4 dex, respectively. However, we note that only in the 5
M*⊙* case the NuGrid/MESA models see signature of HBB and predict O-rich stars.
The 3 and 4 M*⊙* cases become C-rich stars and do not experience HBB, which
is at odds with our sample of O-rich stars (García-Hernández et al., 2006).
Regarding the [Rb/Zr] ratios, obviously also in this case
the higher [Rb/Zr] ratios are obtained from the models
with delayed superwind (P = 700-800), however, these [Rb/Zr] ratios are still lower than our
observed values. The maximum value from the AGB models is [Rb/Zr] = 0.52 for
M = 5 M*⊙*, and the maximum value from our observations is [Rb/Zr] = 1.05.
A possible explanation is that Zr could be depleted
into dust (see e.g. van Raai et al., 2012; Zamora et al., 2014), producing the differences between
the theoretical and observational [Rb/Zr] ratios. Abundance measurements of similar
s-elements such as Sr and Y would be needed in order to clarify this problem.
6 Conclusions
We have reported new Rb and Zr abundances determined from the 7800 A˚ Rb I line and
the 6474 A˚ ZrO bandhead, respectively, in a complete sample of massive
Galactic AGB stars, previously studied with hydrostatic models, using more
realistic extended atmosphere models and a modified version of the spectral synthesis
code Turbospectrum, which considers the presence of a circumstellar envelope
with a radial wind. The Rb abundances are much lower (in some cases even 1-2 dex)
with the pseudo-dynamical models, while the Zr abundances are close to the
hydrostatic ones because the 6474 Å ZrO bandhead is formed deeper in the atmosphere and
is less affected than the 7800 Å Rb I resonante line by the circumstellar effects.
We have studied the sensitivity of
the determined abundances to variations in the stellar (Teff) and wind
(M˙, β and vexp) parameters. The Rb abundances are very
sensitive to the mass loss rate M˙ but much less to the β
parameter and vexp(OH). The
Zr abundances, instead, are not affected by variations of the stellar and wind
parameters. The Rb abundances from extended models are lower than those obtained from the
hydrostatic ones, and the difference is larger in the stars with the highest
Rb abundances in the hydrostatic case. We have represented the hydrostatic
and pseudo-dynamical Rb abundances against the vexp(OH), which can be used as a
mass indicator independent of the distance, and we have observed
a flatter correlation. The difference between the hydrostatic and
pseudo-dynamical Rb abundances increases with increasing the vexp(OH),
due to the fact that the presence of a circumstellar envelope affects more strongly the
more massive stars. Furthermore, the dispersion of the correlation between the Rb abundance
and vexp(OH) is larger in the pseudo-dynamical case. When we fix the wind parameters
M˙ (i.e., equivalent to assuming that our AGB sample stars have a similar
evolutionary stage in terms of mass loss), and/or β (the same velocity profile)
the dispersion is lower.
The Monash nucleosynthesis theoretical predictions reproduce the range of new
Rb and Zr abundances although [Rb/Fe] values above 1.0 can be matched only if
the superwind is delayed to after the period reaches 700-800 days. We also note
that the rate of the 22Ne(α,n)25Mg reaction is crucial, but
still hampered by large systematic uncertainties (see e.g. Bisterzo et al., 2016; Massimi et al., 2017).
Underground measurements, planned, e.g., at LNGS-LUNA (Laboratory for Underground
Nuclear Astrophysics) will help to resolve the current issues. The FRUITY
massive AGB models predict Rb abundances much lower than observed and negative
[Rb/Zr] ratios, at odds with the observations. The NuGrid/MESA models of 4 and
5 M*⊙* predict [Rb/Fe] as high as 0.9 dex, however, the 4M*⊙* model
do not experience HBB and becomes C-rich, while our sample stars are clearly O-rich. The
maximum observed [Rb/Zr] ratios are still more than a factor of two larger than predicted
by the nucleosynthesis models. A possible explanation to this difference
between the observations
and the predictions is that Zr could be depleted into dust. Observations of other
s-process elements Sr and Y belonging to the same first peak as Rb and Zr will
help clarifying this mismatch.
In summary, the [Rb/Fe] abundances and [Rb/Zr] ratios previously
derived with hydrostatic models are certainly not
predicted by the most recent theoretical models of AGB nucleosynthesis. In
particular, the highest [Rb/Fe] abundances and [Rb/Zr] ratios observed in
massive Galactic AGBs are much larger than theoretically predicted. The new
[Rb/Fe] abundances and [Rb/Zr] ratios as obtained from our simple (but more
realistic) pseudo-dynamical
model atmospheres are much lower in much better agreement with the theoretical
predictions, significantly resolving the mismatch between the observations and the
nucleosynthesis models in the more massive AGB stars. This confirms the earlier
Zamora et al. preliminary results on a smaller sample of massive O-rich AGB
stars but here we find that the Rb abundances are strongly dependent of the wind
mass-loss M˙, which is basically unknown in our AGB stars sample.
Follow-up radio observations (e.g. the rotational lines of the several CO
isotopologues) of these massive Galactic AGB stars are encouraged in order to
get precise mass-loss rates estimates, which are needed to break the actual
models degeneracy and obtain more reliable (no model-dependent) Rb abundances in
massive AGB stars.
Acknowledgements.
This work is based on observations at the 4.2 m William Herschel Telescope
operated on the island of La Palma by the Isaac Newton Group in the
Spanish Observatorio del Roque de Los Muchachos of the Instituto de
Astrofisica de Canarias. Also based on observations with the ESO 3.6 m
telescope at La Silla Observatory (Chile). We thank Marco Pignatari and
Umberto Battino for providing information about the Nugrid/MESA models.
V.P.M. acknowledges the financial support from the Spanish Ministry of Economy
and Competitiveness (MINECO) under the 2011 Severo Ochoa Program MINECO
SEV-2011-0187. D.A.G.H. was funded by the Ramón y Cajal fellowship number
RYC-2013-14182. V.P.M., O.Z., D.A.G.H. and A.M. acknowledge support provided by
the MINECO under grant AYA-2014-58082-P. M.L. is a Momentum
(“Lendület-2014” Programme) project leader of the Hungarian Academy of
Sciences. M. L. acknowledges the Instituto de Astrofísica de Canarias for
inviting her as a Severo Ochoa visitor during 2015 August when part of this work
was done. This paper made use of the IAC Supercomputing facility HTCondor
(http://research.cs.wisc.edu/htcondor/), partly financed by the Ministry of
Economy and Competitiveness with FEDER funds, code IACA13-3E-2493. This work
benefited from discussions at The 12th Torino Workshop on Asymptotic Giant
Branch Stars in August 2016 supported by the National Science Foundation under
Grant No. PHY-1430152 (JINA Center for the Evolution of the Elements).
Appendix A Complete sample
Figure 1
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