From theoretical stellar spectra to realistic models of the Milky Way : a never ending Odyssey

The last chapter is dedicated to the compilation of the results and the discussion about the success of - but also
about the problems that have arisen during - and in part also survived - this work.
The main goal of this thesis was, firstly, to convert the stellar parameters given by galaxy models into observables,
and then to compare these theoretical stellar distributions in different viewing directions with real observational
data to check, if it is possible to find a best-fitting galaxy model for our MilkyWay.
To do so, we transformed the physical parameters, i.e. the stellar mass, current age and constant chemical
abundance of each star in a certain viewing direction and field size, given by ten different, detailed galaxy models
that were computed with the 3D chemo-dynamical code of Samland, Hensler & Theis (1997) and Samland &
Gerhard (2003) into observable absolute and apparent magnitudes and colours.
For each star, we used its stellar mass, age and chemical abundance to select the corresponding evolutionary
track from the stellar evolutionary track library, Padova 1994, computed by Bressan et al. (1993), Fagotto et
al. (1994a, 1994b, 1994c) and Girardi et al. (1996), to derive the appropriate stellar atmospheric parameters (i.e.,
log g and Te�).
Using stellar metallicity, effective temperature and surface gravity, we interpolate an appropriate spectral energy
distribution provided by synthetic stellar spectral libraries, BaSeL 3.2 or PHOENIX, and in connection with
the response filter functions of various photometric filter systems (e. g., RGU and ugriz) for observable magnitudes
and colours for each star.
By means of the spectrophotometric data we compile synthetic colour-magnitude diagrams, and age- and metallicity
distributions for a number of viewing directions and field sizes. These theoretical data are then compared
to the photometric field star observations from both the Basel and the Sloan Digital Sky Surveys.
Our intention is to first compare the differences between our suite of models and observations, so as to
identify the correlations between the observed data and the input parameters of our models. In a next step we
want to fine-tune the model parameters to fit the Basel and/or SDSS survey data and thereby to find the best-fitting
galaxy model for our MilkyWay.
Unfortunately, the fine-tuning of the model galaxy parameters has not been possible1 - which forced us to
limit our analysis to only 10 different models without any further adjustments.
6.1. Success
Before starting our comparison of theoretical with observational data, we complete the BaSeL 3.1 (Westera
2001; Westera et al. 2002)- and the PHOENIX (Hauschildt & Baron 1999, 2004) stellar spectral libraries by
implementing a grid of theoretical white dwarf stellar spectra covering high surface gravities (log g > 5.0) and
high effective temperatures (50’000 K � Te� � 100’000 K) calculated by Koester (2004). Similarly, we also
include hot central star spectra of planetary nebulae computed by Rauch (2003) that cover a temperature range
of 100’000 � Te� � 1’000’000 K and surface gravities of 5.0 � log g � 9.0.
Finally, we end up with a useful tool for reproducing stellar data of various stellar types on different photometric
systems, such as RGU and SDSS. By means of these theoretical spectral libraries the interpretation of any stellar
data (e.g., SDSS SEGUE proprietary data) in terms of physical stellar parameters is highly warranted.
As mentioned above, for our comparison we only have ten model galaxies available. Out of these ten, we
find the best-fitting model galaxy to be the spiral model galaxy S10, described in detail in Subsection 3.2.2.
During our work of comparison we gained deeper insights into all the different fields of work that are involved
in the conversion of the model data into observables. The major ingredients of this study are highlighted
in blue in the previous paragraph:
stellar evolutionary models, stellar atmosphere models,
photometric system parameters, and last, but not least:
the chemo-dynamical galaxy models themselves .
Beside the fact, that gathering and comprehending the actual knowledge of all of them is a great challenge,
the coin also has another side: each field of work still has some unknown or untested parts and therefore brings
its own, sometimes inestimable, uncertainties with it.
We track down several inconsistencies in the above-mentioned ingredients and discuss them in due detail in the
present work.
In future work, we suggest that appropriate corrections be applied, before making further and unbiased
comparisons. In the next Sections, we enlist the major inconsistencies between the surveys, spectral libraries and
between synthetic and observed SDSS colours and propose possible future scientific projects.
6.2. Problems and uncertainties
6.2.1. Chemo-dynamical galaxy model
Westera et al. (2002) showed that the bulge colours derived from disk galaxy formation models of Samland &
Gerhard (2003) agree very well with Hubble Deep Field North bulge colours. In our case, where we are immersed
in a galaxy model and compare its spatial stellar distributions and luminosity functions with the much
more detailed substructures of our own Galaxy, no such good agreement can be found.
The validity of any galactic model is always questionable, as it describes a smooth and in the case of the Samland
models an axially symmetric galaxy, while in our days we know through observations that inhomogeneities exist
even in the disk or in the halo.
Thanks to the increasing computational power, we are able to simulate the formation and evolution of a disk
galaxy in three-dimensional numerical models, including the most important physical processes. But even in our
days, the computational power has its limits. Therefore, it is not possible to account for all the processes acting
from the atomic to the galactic scales.
In the Samland code, the stellar particles are created and distributed according to the star formation. The restriction
to the fundamental processes, which determine the galactic evolution, may affect the detailed shape of the
star formation history. Too many important details influence the formation and evolution of a model star that
affect the stellar radiative properties and spatial distributions in a crucial way, which exceeds by far the error bars
of the empirical calibrations of the local luminosity functions.
Beside these general problems of simulating complex interactions, the Samland code revealed additional artefacts,
as we have seen for example in Subsection 5.1.2. Unfortunately, the easily implementable adjustments to
the code are not possible anymore, as mentioned above.
6.2.2. Stellar evolutionary tracks and synthetic photometry
Stellar evolutionary tracks
Even though the stellar evolutionary models are increasingly sophisticated, with improved physics, various uncertainties
still lie in the description of the details in the shape of stellar evolutionary tracks, and the evolutionary
lifetimes. Here we just mention some of them: Core convection, mass loss, mixing length, rotation, diffusion,
meridional circulation, and nuclear reactions.
Additionally, the complete set of evolutionary tracks of the Padova94 library does not include the TP-AGB nor
the post-AGB phase. On account of this we adopted the enhancements of Bruzual & Charlot (2003) that consist
only of simplified descriptions of these phases.
Spectral libraries
In addition, we have shown that the two theoretical stellar spectral libraries, BaSeL 3.2 and PHOENIX, do not
provide matching synthetic colours throughout the full parameter ranges. The largest differences between the
two stellar spectral libraries show up in almost all colours at lower effective temperatures (3’500 � Te� ) and
higher surface gravities (2.5 � log g) (see A.1).
Due to the bright limiting apparent magnitudes that we apply to produce model colours under the same conditions
as the observed colours, these uncertainties do not affect our work that much. Still, the (small) contribution of
such stars that are not yet sufficiently tested is difficult to estimate and their impacts on the stellar radiative
properties not yet definitely determined.
Filter functions
The comparison of the SDSS survey- with the model star counts reveals a satisfying agreement in the u-gcolour.
Unfortunately, other colours do not show the same result, and therefore lead us to analyse the SDSS
colours more deeply.
The comparison of theoretical and observed stellar distributions in the i-z versus r-i- plane (see 5.2) demonstrates
impressively, that the observed two-colour distribution can not be reproduced by synthetic colours of any
theoretical stars. Only synthetic colours transformed from the Johnson-Cousins system (Jordi, Grebel & Ammon
2005) follow the i-z versus r-i colour relation of the observed stars correctly.
By contrast, the transformed synthetic model and the observed stars in the g-r versus u-g- plane fit well.
The conclusion appears inevitable that three published SDSS filter functions (r, i and z) do not match the observational
system, and are therefore responsible for this deviation.
6.2.3. Observational data
The comparison of the Basel survey with our model galaxies reveals large inadjustable inconsistencies in star
counts in all the available viewing directions. We therefore include checks on SDSS data and compare the apparent
magnitude histograms of stars in common fields.
A comparison of the Basel- with the Sloan Digital Sky Survey uncovers unexpected large systematic deviations
between the apparent magnitude histograms in the magnitude range that is common to both surveys.
The higher resolution of the SDSS CCD photometry compared with the one of the Basel survey can only partly
explain the differences of these two surveys. By comparing three fields that both surveys have in common, Jordi,
Grebel & Ammon (2005) discovered uncertainties concerning the identification of some of the observed objects:
Some objects recognised by the Sloan Digital Sky Survey as galaxies are treated as stars in the Basel survey. In
other cases, the SDSS detector simply did not observe a star, whereas the Basel survey detected one. Occasionally
the SDSS detected a fainter object within a radius of 1" to 3" of the dominant star, whereas Basel detected
only one single source. Around 10 % of the Basel stars are not identified in the SDSS catalogue as single stars.
In our work we compare (assumed) observed single stars with single model stars. If a survey classifies galaxies
or the like as single stars, the whole stellar spatial distribution gets affected.
Furhermore, the SDSS survey has a saturation cutoff at the apparent magnitude of r ~ 14.0, which means that the
images of all stars brighter than this magnitude contain saturated pixels and that their photometry is questionable.
Another uncertainty of the SDSS DR3 are quasars which have not yet been separated. And, as we showed in
Subsection 5.2, a satisfactory algorithm to unambiguously identify and exclude all quasars from a mixed stellar
sample does not exist. But all this is not a final explanation, why these two surveys end up with different star
numbers.
Of course, such mismatches between the two surveys do not allow a definite validation of the model.
Because of all these still considerable inconsistencies and uncertainties accompanying the use of the major ingredients
(stellar evolutionary models of Padova, stellar atmosphere models of the BaSeL 3.2 and the PHOENIX
library, photometric system parameters, such as the SDSS filter functions, and last but not least: the chemodynamical
model galaxies) mentioned above, we are unable - unfortunately - to draw final conclusions about
the validity of the Samland models, or to find a unique best-fitting solution for the Milky Way.