K.-P. Schröder

An improved mass-loss description for dust-driven superwinds and tip-AGB evolution models

We derive an improved description of dust-driven stellar mass-loss for the cool winds of carbon-rich tip-AGB stars. We use pulsating wind models in which the mass loss is driven by radiation pressure on dust grains, for C-rich chemistry. From a larger set of these models, selected for representative dynamical (pulsational velocity amplitudev ,p eriodP ) and chemical (theC=O abundance ratio) input parameters, an improved approximative mass-loss formula has been derived which depends only on the stellar parameters (eective temperature Te, luminosity L and mass M). Due to the detailed consideration of the chemistry and the physics of the dust nucleation and growth processes, there is a particularly strong dependence of the mass-loss rate _ M (in M=yr) on Te :l og _ M =8 :86 1:95logM=M 6:81logT=K+2:47logL=L. The dependence of the model mass-loss on the pulsational period has explicitly been accounted for in connection with the luminosity dependence, by applying an observed period{luminosity relation for C-rich Miras. We also apply the improved mass-loss description to our evolution models, and we revisit their tip-AGB mass-loss histories and the total masses lost, in comparison to our earlier work with a preliminary mass-loss description. While there is virtually no dierence for the models in the lower mass range of consideration (Mi =1 : 0t o 1:3M), we now nd more realistic, larger superwind mass-loss rates for larger stellar masses: i.e., _ M between0: 4a nd 1:0 10 4 M/yr for Mi between 1.85 and 2.65 M, removing between 0.6 and 1.2 M, respectively, during the nal 30 000 yrs on the tip-AGB.

Distant future of the Sun and Earth revisited

We revisit the distant future of the Sun and the Solar system, based on stellar models computed with a thoroughly tested evolution code. For the solar giant stages, mass loss by the cool (but not dust-driven) wind is considered in detail. Using the new and well-calibrated mass-loss formula of Schroeder & Cuntz, we find that the mass lost by the Sun as a red giant branch (RGB) giant (0.332 Msun, 7.59 Gyr from now) potentially gives planet Earth a significant orbital expansion, inversely proportional to the remaining solar mass. According to these solar evolution models, the closest encounter of planet Earth with the solar cool giant photosphere will occur during the tip-RGB phase. During this critical episode, for each time-step of the evolution model, we consider the loss of orbital angular momentum suffered by planet Earth from tidal interaction with the giant Sun, as well as dynamical drag in the lower chromosphere. As a result of this, we find that planet Earth will not be able to escape engulfment, despite the positive effect of solar mass loss. In order to survive the solar tip-RGB phase, any hypothetical planet would require a present-day minimum orbital radius of about 1.15 au. The latter result may help to estimate the chances of finding planets around white dwarfs. Furthermore, our solar evolution models with detailed mass-loss description predict that the resulting tip-AGB (asymptotic giant branch) giant will not reach its tip-RGB size. Compared to other solar evolution models, the main reason is the more significant amount of mass lost already in the RGB phase of the Sun. Hence, the tip-AGB luminosity will come short of driving a final, dust-driven superwind, and there will be no regular solar planetary nebula (PN). The tip-AGB is marked by a last thermal pulse, and the final mass loss of the giant may produce a circumstellar (CS) shell similar to, but rather smaller than, that of the peculiar PN IC 2149 with an estimated total CS shell mass of just a few hundredths of a solar mass.

Dust-driven winds and mass loss of C-rich AGB stars with subsolar metallicities

Aims. We investigate the mass loss of highly evolved, low- and intermediate mass stars and stellar samples with subsolar metallicity. We give a qualitative as well as quantitative description which can be applied to LMC/SMC-type stellar populations. Methods. For that purpose we apply the same approach as we did for solar metallicity stars and calculate hydrodynamical wind models including dust formation with LMC and SMC abundances under consideration of an adapted model assumption. In particular, we improved the treatment of the radiative transfer problem in order to accommodate larger non-local contributions occurring with smaller opacities. For each wind model we determine an averaged mass-loss rate. The resulting, approximate mass-loss formulae are then applied to well-tested and calibrated stellar evolution calculations in order to quantify the stellar mass loss. Results. The dynamical models for LMC and SMC metallicity result in mass-loss rates of the same order of magnitude as the solar metallicity models which is in this basic approach in agreement with observations. The hydrodynamical properties like e.g. the outflow velocity differ (for fixed C/O abundance ratio) noticeably, though. While critical luminosities of LMC and solar metallicity models fairly coincide, the SMC models need higher luminosities to develop dust-driven winds.

A critical test of empirical mass loss formulas applied to individual giants and supergiants

To test our new, improved Reimers-type mass-loss relation, given by Schroder & Cuntz in 2005 (ApJ, 630, L73), we take a look at the best studied galactic giants and supergiants – particularly those with spatially resolved circumstellar shells and winds, obtained directly or by means of a companion acting as a probing light source. Together with well-known physical parameters, the selected stars provide the most powerful and critical observational venues for assessing the validity of parameterized mass-loss relations for cool winds not driven by molecules or dust. In this study, star by star, we compare our previously published relation with the original Reimers relation (1975, Mem. Roy. Soc. Liege 6. Ser. 8, 369), the Lamers relation (1981, ApJ, 245, 593), and the two relations by de Jager and his group (1988, AA 1990, A&A, 231, 134). The input data, especially the stellar masses, have been constrained using detailed stellar evolution models. We find that only the relationship by Schroder & Cuntz agrees, within the error bars, with the observed mass-loss rates for all giants and supergiants.

What a local sample of spectroscopic binaries can tell us about the field binary population

We study a volume-limited sample of spectroscopic binaries (SBs) to find, in absolute terms, the period P, primary mass m1, and mass ratio q (=m2/m1) distributions of the local population of field binaries. The sample was collated using the Batten 8th catalogue of SBs, other data of R F Griffin, and the Hipparcos catalogue (for distances and to refer numbers of objects to fractions of the local stellar population as a whole). We use the better-known group of double-lined SBs (SB2s) to calibrate a refined Monte-Carlo approach to modelling the q distribution of the single-lined SBs (SB1s) from their mass function f(m) and primary mass m1. The total q distribution is then found by adding the observed SB2 q distribution to the Monte Carlo SB1 q distribution. By comparing subsamples of different ranges in parameter space, we also address the important questions of completeness and parameter-specific biases. Our results confirm a clear peak in the q distribution of field binaries near unity. We also note a substantial fraction of systems with intermediate to long periods. These are objects that will interact when the primary evolves onto the RGB or AGB, with statistically significant consequences for the mass distribution of white dwarfs.

Galactic archaeology: initial mass function and depletion in the ‘thin disc’

We determine the initial mass function (IMF) of the ‘thin disc’ in the range of, approximately, 1.1 to 4 M⊙ by means of a direct comparison between synthetic stellar samples [for different matching choices of IMF, star formation rate (SFR) and depletion] and a complete (volume-limited) sample of single stars near the Galactic plane (|z| < 25 pc), selected from the Hipparcos catalogue (d < 100 pc, MV < +4.0). Our synthetic samples are computed from first principles: stars are created with a random distribution of mass M* and age t*, which follow a given (genuine) IMF and SFR(t*). They are then placed on the Hertzsprung–Russell (HR) diagram by means of a grid of empirically well-tested evolution tracks. The quality of the match (synthetic versus observed sample) is assessed by means of star counts in specific regions in the HR diagram. Seven regions are located along the main sequence (MS, mass sensitive), while four regions represent different evolved (age-sensitive) stages of the stars. We find a bent slope of the IMF (using the Scalo notation, i.e. a power law on a logarithmic mass scale), with Γ1=−1.70 ± 0.15 (for ≈1.1 < M* < 1.6 M⊙) and Γ2=−2.1 ± 0.15 (for 1.6 < M*≲ 4 M⊙). In addition, comparison of the observed MS star counts with those of synthetic samples with a different prescription of the MS core overshooting reveals sensitively that the right overshoot onset is at M*= 1.50 M⊙. The counts of evolved stars, in particular, give valuable evidence of the history of the ‘thin-disc’ (apparent) star formation and lift the ambiguities in models restricted to MS star counts. The actual counts of evolved stars yield a stellar depletion, when compared with counts created by a constant SFR0 in the sample volume. This depletion becomes more pronounced with age. A very good match of all observed star counts is achieved with a simplistic diffusion approximation, with an age-independent diffusion time-scale of τdif= 6.3 × 109 yr and a (local) SFR0= 2.0 ± 0.15 stars (with M* > 0.9 M⊙) formed per 1000 yr and (kpc)3. We also discuss this ‘thin-disc’ depletion in terms of a geometrical dilution of the expanding stellar ‘gas’, with Hz(t*) ∝σW(t*). This model applies to all stars old enough to have reached thermalization, i.e. for t* > 7 × 108 yr and Hz > 230 pc. It yields a column-integrated (non-local) ‘thin-disc’ SFRcol, which has not changed much over time ( 0.9 M⊙).

The basal chromospheric Mg ii h+k flux of evolved stars: probing the energy dissipation of giant chromospheres

Of a total of 177 cool G, K and M giants and supergiants, we measured the Mg II h + k line emission of extended chromospheres in high-resolution (LWR) International Ultraviolet Explorer (IUE) spectra by using the IUE final data archive at the Space Telescope Science Institute (STScI) and derived the respective stellar surface fluxes. They represent the chromospheric radiative energy losses presumably related to basal heating by the dissipation of acoustic waves, plus a highly variable contribution due to magnetic activity. Thanks to the large sample size, we find a very well defined lower limit, the basal chromospheric Mg II h + k line flux of cool giant chromospheres, as a function of T eff. A total of 16 giants were observed several times, over a period of up to 20 yr. Their respective minimal Mg II h + k line fluxes confirm the basal flux limit very well because none of their emissions dips beneath the empirically deduced basal flux line representative for the overall sample. Based on a total of 15–22 objects with very low Mg II h + k emission, we find as limit log FMg IIhk = 7.33 log Teff − 21.75 (cgs units; based on the B − V relation). Within its uncertainties, this is almost the same relation as has been found in the past for the geometrically much thinner chromospheres of main-sequence stars. But any residual dependence of the basal flux on the surface gravity is difficult to determine, since especially among the G-type giants there is a large spread of the individual chromospheric Mg II fluxes, apparently due to revived magnetic activity. However, it can be stated that over a gravity range of more than 4 orders of magnitude (main-sequence stars to supergiants), the basal flux does not appear to vary by more than a factor of 2. These findings are in good agreement with the predictions by previous hydrodynamic models of acoustic wave propagation and energy dissipation, as well as with earlier empirical determinations. Finally, we also discuss the idea that the ample energy flux of the chromospheric acoustic waves in a cool giant may yield, as a by-product, the energy flux required by its cool wind (i.e. non-dust-driven, ‘Reimers-type’ mass-loss), provided a dissipation mechanism of a sufficiently long range is operating.

Ca II H+K fluxes from S-indices of large samples: a reliable and consistent conversion based on PHOENIX model atmospheres

Context. Historic stellar activity data based on chromospheric line emission using O.C. Wilson’s S-index reach back to the 1960ies and represent a very valuable data resource both in terms of quantity and time-coverage. However, these data are not flux-calibrated and are therefore difficult to compare with modern spectroscopy and to relate to quantitative physics. Aims. In order to make use of the rich archives of Mount Wilson and many other S-index measurements of thousands of main sequence stars, subgiants and giants in terms of physical Ca ii H+K line chromospheric surface fluxes and the related R-index, we seek a new, simple but reliable conversion method of the S-indices. A first application aims to obtain the (empirical) basal chromospheric surface flux to better characterise stars with minimal activity levels. Methods. We collect 6024 S-indices from six large catalogues from a total of 2530 stars with well-defined parallaxes (as given by the Hipparcos catalogue) in order to distinguish between main sequence stars (2133), subgiants (252) and giants (145), based on their positions in the Hertzsprung-Russell diagram. We use the spectra of a grid of PHOENIX model atmospheres to obtain the photospheric contributions to the S-index. To convert the latter into absolute Ca ii H+K chromospheric line flux, we first derive new, colour-dependent photospheric flux relations for, each, main sequence, subgiant and giant stars, and then obtain the chromospheric flux component. In this process, the PHOENIX models also provide a very reliable scale for the physical surface flux. Results. For very large samples of main sequence stars, giants and subgiants, we obtain the chromospheric Ca ii H+K line surface fluxes in the colour range of 0.44 < B −V < 1.6 and the related R-indices. We determine and parametrize the lower envelopes, which we find to well coincide with historic work on the basal chromospheric flux. There is good agreement in the apparently simpler cases of inactive giants and subgiants, and distinguishing different luminosity classes proves important. Main sequence stars, surprisingly, show a remarkable lack of inactive chromospheres in the B − V range of 1.1 to 1.5. Finally, we intoduce a new, “pure” and universal activity indicator: a derivative of the R-index based on the non-basal, purely activity-related Ca ii H+K line surface flux, which puts different luminosity classes on the same scale. Conclusions. The here presented conversion method can be used to directly compare historical S-indices with modern chromospheric Ca ii H+K line flux measurements, in order to derive activity records over long periods of time or to establish the long-term variability of marginally active stars, for example. The numerical simplicity of this conversion allows for its application to very large stellar samples.

Direct detection of a magnetic field in the photosphere of the single M giant EK Bootis: How common is magnetic activity among M giants?

Aims. We study the fast rotating M 5 giant EK Boo by means of spectropolarimetry to obtain direct and simultaneous measurements of both the magnetic field and activity indicators, in order to infer the origin of the activity in this fairly evolved giant. Methods. We used the new spectropolarimeter NARVAL at the Bernard Lyot Telescope (Observatoire du Pic du Midi, France) to obtain a series of Stokes I and Stokes V profiles for EK Boo. Using the least square deconvolution (LSD) technique we were able to detect the Zeeman signature of the magnetic field. We measured its longitudinal component by means of the averaged Stokes V and Stokes I profiles. The spectra also permitted us to monitor the Ca ii K&H chromospheric emission lines, which are well known as indicators of stellar magnetic activity.

The galactic mass injection from cool stellar winds of the 1 to 2.5

We have computed synthetic stellar samples and HR diagrams on the basis of a ne-meshed, consistent grid of evolution tracks for given IMF and SFR(t). In order to model the galactic disk stellar component (single stars only) and to derive its IMF and apparent SFR(t), we selected the synthetic sample which is the best t to the observed distribution of single stars in the solar neighbourhood HR diagram (complete for d< 50 pc, MV 4, based on Hipparcos data). Most giants of this synthetic sample fall in the range of Mi = 1 to 2.5 M.S tellar evolution on the tip-AGB has been computed by adopting, time-step by time-step, the mass-loss rates predicted by very detailed dust-driven, pulsating wind models for carbon-rich stars. This mass-loss description causes the natural development of superwinds. Their properties are in agreement with the range of measured masses and expansion velocities of PNe, i.e. a total mass of between 0.25 M and 0.65 M has been ejected over the nal 30 thousand years. For the preceeding mass-loss on the AGB and RGB, we use a semi-empirical approach, i.e., a re-calibrated Reimers mass-loss which yields an RGB mass-loss (for M < 1 M) consistent with the formation of horizontal branch stars. Combining these approaches, we obtain a consistent grid of mass-loss histories in the mass range of Mi = 1 to 2:5 M. By increasing the number of stars in our synthetic solar neighbourhood stellar sample by a factor of thousand, we have been able to compute a detailed, present-day, synthetic reference sample of galactic disk RGB and AGB giant stars, together with their mass-loss. The results are in good agreement with observations of cool giant stellar mass-loss, as well as with the estimated space density of carbon stars. Finally, we discuss the relative collective yields of the RGB, AGB and tip-AGB stellar mass-loss as contributions to the galactic disk mass re-injection.