## 6. The resultsIn this section, the fields will be analyzed separately, deriving the reddening along the line of sight and the possible solutions. For the best fitting solutions the simulated CMDs are displayed in Fig. 4. In the simulations of F3 and F4 a young spiral-arm-like population is also included, as described in Sect. 7. After discussing the single results for each field in the following subsections, they will be compared to derive the best fitting solution for all the fields. Since the studied fields are located at low Galactic latitude, we expect them to be more sensitive to the star formation rate and to the scale height than to the scale lenght of the disk components. For the same reason the parameters of the thick disk component would not be strongly constrained.
## 6.1. Discussing the CMD: extinction determinationsNg et al. (1995), Bertelli et al. (1995) proved that the slope of
the main sequence in the CMD of the disk population is mainly governed
by the extinction along the line of sight. At each magnitude
We point out that F2 and F3 show a relatively modest increase of
the interstellar absorption along the line of sight
(A_ Finally, we would like to address the question whether the trends in the extinction versus the distance shown in Fig. 5 are real. It is quite difficult to give an estimate of the uncertainty on these determinations. However, the simulations show that by changing the extinction of mag at a given distance d a significant shift in the location of the main sequence edge at magnitudes fainter than is produced. We can safely assume that the determination of Fig. 5 cannot have an internal error larger than 0.2 mag. We point out that these determinations of extinction are dependent
on the adopted age and metallicity range of the population. To
estimate the uncertainty due to the combined effect of different age
and metallicity distributions, we derive the extinction separately for
the three disk components, namely the young thin, the old thin and the
thick disk described in Sect. 6.1.
The determination of the extinction along the line of sight
turns out to be different from the
adopted values at maximum of 0.2. To further check these results, we
make a comparison with the values derived from reddening maps by
Mendez & van Altena (1998). Taking into account the errors on
Mendez & van Altena determinations (0.23 mag in
, with A When the maximum reddening in each direction is compared with the maps by Schlegel et al. (1998) derived using DIRBE data, the agreement is excellent, in spite of the fact the authors claim their values should not be trusted for . ## 6.2. Discussing the CMD: the star formation rateTo infer the star formation rate (SFR) of the thin disk component, simulated CMD and LF are calculated with constant, increasing or decreasing rate and then compared with observational CMDs using a test. The thick disc is assumed to have a SFR constant from 11 Gyr to 8 Gyr. Due to the low galactic latitude of the observed fields, it is not possible to distinguish between constant or slightly increasing/decreasing rate for this component. From the analysis of the Hipparcos data Bertelli et al. (1999)derive a disk SFR constant from 10 Gyr to 4.5 Gyr, and then increasing by a factor of 1.5-2 from 4.5 Gyr to 0.1 Gyr. However it is not straightforward that the SFR found in the solar neighborhood is representative of the whole disk, as has already been suggested by Bertelli et al. (1999). To assess this point, we simulate the CMDs and luminosity functions of the fields using the parameterization of the SFR derived from the Hipparcos data by Bertelli et al. (1999). While the luminosity functions are not inconsistent with this SFR, the CMDs of F3 and F4 cannot be reproduced, since too many young stars brighter than V=19.5 and bluer than the main sequence observational edge are produced. This is evident comparing the simulated and the observed CMDs of F3 and F4 in Fig. 6 and Fig. 7. The extinction cannot be responsible of this discrepancy: if the extinction along the line of sight at closer distances is increased to match the observational location of the blue edge of the main sequence at brighter magnitudes, then the faint main sequence turns out to be too red.
The case of F1 and F2 is substantially different. In these fields the blue edge of the main sequence is reproduced using the Hipparcos SFR (see Fig. 8 for F2). However, too many evolved stars are expected in F2 (740 stars brighter than V=22) in comparison with the data (80 stars). No additional information is coming from F1. Due to the poor statistic, the observed and the expected number of stars in this field (63 and 74 respectively) are compatible inside the errors.
However, it cannot be excluded that this result is dependent on the adopted parameterization of the solar neighborhood star formation. To make a further check we use the observed Hipparcos population, and we distribute it along the line of sight in the disk. The resulting CMD is presented in Fig. 9 for F3. The previous conclusions are substantially unchanged. Similar result can be reached in the case of F4, not shown for conciseness.
From this investigation we conclude that the solar neighborhood cannot be considered representative of the properties of the whole disk. An analogous discussion can be made at varying SFR. The simulations show that any assumption of an increasing or even constant SFR yields a too high number of young stars on the blue side of the main sequence. Actually, the most convincing result is obtained with a SFR constant from 10 Gyr to 2 Gyr, then declining by a factor of 10 between 2 Gyr and 0.1 Gyr (see Fig. 4). As a final comment, the CMDs of F3 and F4 show an additional sprinkle of stars brighter that V 15.5 mag and bluer than the mean location of the main sequence (see Fig. 3). These stars cannot be reproduced unless a young burst of star formation well confined in distance is assumed. This feature will be proved to be consistent with the presence of a spiral arm (see Sect. 7). ## 6.3. The results for F3Various combinations of the disk parameters, at changing scale
height and scale length of the thick disk, scale length of the thin
disk. Both spatial distributions (sech
For every set of models the most convincing solutions for decreasing stars formation are listed in Table 2 together with the where and are the observed and the expected number of stars per magnitude bin, and is the number of degrees of freedom (which is equal to the number of bins minus 1, since the in the simulations we impose that the total number of model stars is equal to the observed total number of stars) As expected, the scale height of the thick disk
h Imposing a cut of the disk at 14 Kpc, the fit is not substantially improved, as is expected due to the low Galactic latitude. ## 6.4. The results for F4Table 3 presents the solutions and Fig. 11 shows the
comparison of the observational luminosity function with four
simulations. Analogously to F3, the sech
Concerning the scale height of the think disk, the most convincing solutions are for 270 30 pc. Scale lenght values as low as 1.1 Kpc result is a less good fit of the luminosity function, while all the values in the range 1.2-1.5 Kpc are consistent with the data. Analogously to F3, introducing a cut of the disk at 14 Kpc, we do not improve the fit of the luminosity function. ## 6.5. Hunting for common solutionsThe scale height of the thin disk derived for F4 are in the mean
higher than the ones derived for F3. However they are consistent at
the 2- level, if using the best value
of 28030 pc for F4 and
22030 for F3. The most convincing
common solution with decreasing star formation rate is found about
2-4% of thick disk, a scale height around
and the sech Due to the poor statistics, F1 and F2 (see Table 1) do not set further constraints on the determination of the scale height and lenght of the disk. The errors are relatively large and all the solutions, we found for the fields F3 and F4 do also fit the fields F1 and F2. Hence we can only conclude, that F1 and F2 are consistent within the uncertainties with the other fields. ## 6.6. Discussing the mass distributionWe use the value of the central value of the mass distribution (see Eqs. 2 and 3) to derive the local mass density. can be derived for each field imposing the total number of stars in a selected region of the CMD. So, we expect that inhomogeneities of the mass distribution reflect in different constants in different fields. Taking into account all the disk components, there is a slight
evidence that the total mass density might be higher of a factor 1.5-2
in F4 and F1 than in F2 and F3, the main difference residing in the
mass of the component older than 2 Gyr. However it is not clear
whether this effect is real then reflecting inhomogeneities of the
disk on small scale, or it must simply be interpreted as due to the
uncertainty on the mass determination. From this constant, we can
derive the mass density in the local neighborhood in stars more
massive than 0.1 , calculated using
Kroupa (2000) IMF. For the best solutions, we derive a total local
star density of 0.025 pc
© European Southern Observatory (ESO) 2000 Online publication: September 5, 2000 |