Master Thesis Abstract
Galactic Helium-to-Metals enrichment ratio
(∆Y /∆Z) from the analysis of local main sequence
stars observed by HIPPARCOS
Candidate: Advisor:
Mario Gennaro Prof. Scilla Degl’Innocenti
Co-Advisor:
Dr. Pier Giorgio Prada Moroni
Helium (4He) is the second most abundant element in the Universe after
Hydrogen. The greatest part of 4He nuclei has been produced in the Pri-mordial Nucleosynthesis, during the very first minutes after the Big Bang; from the end of this initial phase, and before stars were formed, the Uni-verse was made of about 75% Hydrogen and 25% Helium, with traces of other elements.
The following chemical evolution of the interstellar medium (ISM) in galaxies was driven by thermonuclear processes that take place in stellar interiors. Stars first convert Hydrogen into Helium then, in the following evolutionary phases, if the temperature is high enough, they synthesize heav-ier elements with higher binding energies and thus more stable, ending with the most stable element: Iron. Elements of the periodic table heavier than Iron can be produced in the final phases of the life of stars by neutron or proton captures. During this phases stars can lose mass to the surrounding enviroment for example by winds or also explosions. The ISM then becomes richer in Helium and all other elements heavier than Helium (metals); con-sequently the cycle can start again with the formation of new stars with greater Helium and metal abundances than the previous generation.
An estimate of the original 4He abundance is of primary importance to
predict the evolution of a star. For example, it influences stellar interior temperatures which control nuclear burning rates and hence the lifetimes of stars. Unfortunately the Helium abundance in stars (called Y1) cannot be determined directly from stellar spectra observations, at least not in most cases. Only stars with surface temperatures higher than about 15000 K show
4He absorption lines in their spectra; in cooler stars, the medium kinetic
energy per particle is not enough to excite Helium to its first excited state and so it is impossible to observe any absorption feature of this element.
However, it is possible to estimate Helium abundance in an indirect way, using other features. As said before4He abundance directly influences tem-peratures and luminosities of stellar structures; if we have observations for these two quantities (which observationally translates in colors and magni-tudes) together with estimates of metallicities2 we can try to reproduce the observations in the Color-Magnitude diagram. This can be done by varying the Helium abundance of the models until we find the best agreement with the data. Since the position in the CM diagram depends, at fixed mass and age, both on Y and Z, it is possible to find a relation between these two quantities or rather between their relative differences respect to primordial abundances.
For my master thesis work I developed a method to determine this rela-tion, more precisely the value of the so called Helium-to-metals enrichment ratio, ∆Y /∆Z. I selected a set of nearby stars for which precise parallaxes were available from the HIPPARCOS 3 mission, and thus for these stars
absolute magnitudes could be obtained. For the same stars I also looked for high quality photometry and metallicity estimates. Among this sample I only selected the less bright stars (MV ≥ 6) which, as I showed, can be
considered as unevolved.
So the position of these stars in the CM diagram doesn’t depend on age, but only on their mass and composition. If we reasonably suppose that the values of Y and Z are related, we can say that the locus described by the stars in the CM diagram is determined by this relation, while the mass of the single star determines where it is placed on the locus. Usually, for the sake of simplicity a linear relation is assumed between Y and Z:
Y = YP +
∆Y ∆ZZ ,
where YP is the primordial Helium abundance, soon after the Big Bang.
Comparing the position in the CM diagram of the stellar data set with that of stellar models on the Zero Age Main Sequence (ZAMS), calculated for different ∆Y /∆Z values, it is possible to estimate this quantity.
1
Y indicates the fractional mass abundance of Helium with respect to all other elements
2Relative mass abundances of elements heavier than Helium, called Z 3
ESA (1997). The Hipparcos and Tycho Catalogues (ESA 1997). VizieR Online Data Catalog, 1239
Clearly, to the obtained value an uncertainty is related, due both to observational errors in the data set and to theoretical uncertainties in the models. The first is mainly due to uncertainties on the spectroscopic de-termination of the [Fe/H] values4, while errors on colors and magnitudes are less important; the second is due to uncertainties both in physical in-puts used in the evolutionary codes and in the treatment of macroscopic mechanisms such as convection in the outer layers of stars.
To evaluate uncertainties on ∆Y /∆Z due to errors on [Fe/H] estimates I developed a Montecarlo simulation in order to vary the measured values in the range determined by their own error. Theoretical uncertainties on the treatment of convection have been evaluated by constructing models with different values of αM LT; uncertainties on ∆Y /∆Z due to the input physics
have been evaluated by estimating the shift of single ZAMS due to different inputs5 and then using shifted ZAMS in the simulations.
The stellar models used in this work have been calculated with the FRANEC6 evolutionary code, using up-to-date physical inputs. In the first part of my thesis, mainly Chapter 1, I describe the update I performed on the part of the code regarding the opacity calculation; the effects of this update have been discussed in detail also building a new Solar Standard Model.
To compare the results obtained using the code with observational data, there was the need to convert the results of the calculations from the HR theoretical diagram (log Te, log L/L ) to the CM diagram. To do this I used
synthetic spectra calculated with both ATLAS9 7 and PHOENIX (version GAIA v2.6.1) 8 model atmospheres. In Chapter 2 I described the prin-cipal characteristics of these models and some of the differences between them. Moreover I described the methods of synthetic photometry and the appropriate programs I developed to convert FRANEC calculations from the theoretical to the observational plane. In particular in this work I used B and V Johnson’s passbands.
In Chapter 3 theoretical models have been compared with the CM di-agram of the Hyades cluster as observed from the HIPPARCOS satellite. For this cluster values for distances, and hence absolute magnitudes, of the single stars are known with good precision, from HIPPARCOS parallaxes; moreover this cluster shows very low (practically zero) reddening values and
4 [Fe/H]∗= log NNF e H ∗− log NF e NH 5
Prof. Degl’Innocenti private communication
6Frascati Raphson Newton Evolutionary Code, see e.g. Chieffi A.; Straniero O. (1989).
ApJS, 71, 47
7
See Castelli F.; Kurucz R. L. (2003). New Grids of ATLAS9 Model Atmospheres, In Modeling of Stellar Atmospheres. Edited by Piskunov N., Weiss W. W., Gray D. F., IAU Symposium volume 210, p. 20.
8Brott I.; Hauschildt P. H. (2005). A PHOENIX Model Atmosphere Grid for Gaia,
In The ThreeDimensional Universe with Gaia. Edited by Turon C., O’Flaherty K. S., Perryman M. A. C., ESA Special Publication volume 576, p. 565.
so also the colors are known with good precision. Hence this cluster is a very valid test bench for evolutionary models. The uncertainties of this comparison are qualitatively discussed.
In Chapter 4 I described the characteristics of the sample of nearby field stars I selected for my work.
In Chapter 5 I described the characteristics of stellar the models calcu-lated for my analysis also showing a first, qualitative comparison between models and data.
In Chapter 6 I described in detail the analysis performed to estimate the ∆Y /∆Z value. The final result is ∆Y /∆Z ∈ [3.0, 5.0]. As said before, the range of uncertainty for this value was derived taking into account ob-servational uncertainties on metallicity (using a Montecarlo simulation) and theoretical uncertainties on the input physics and the external convection treatment. This analysis was followed by a check of the results; the ∆Y /∆Z value found for nearby stars was used, together with [Fe/H] estimates, to determine Y and Z for Hyades and Pleiades clusters; whith those chemical composition values isochrones were built to be compared with the observa-tional data. A very good agreement between models and observations was found for both the two clusters.
