AstrophysicsChemical evolution of the Galactic bulge as traced by microlensed dwarf and subgiant stars , V. Evidence for a wide age distribution and a complex MDF ABSTRACTBased on high-resolution spectra obtained during gravitational microlensing events we present a detailed elemental abundance analysis of 32 dwarf and subgiant stars in the Galactic bulge. Combined with the sample of 26 stars from the previous papers in this series, we now have 58 microlensed bulge dwarfs and subgiants that have been homogeneously analysed. The main characteristics of the sample and the findings that can be drawn are: (i) the metallicity distribution (MDF) is wide and spans all metallicities between [Fe/H] = −1.9 to +0.6; (ii) the dip in the MDF around solar metallicity that was apparent in our previous analysis of a smaller sample (26 microlensed stars) is no longer evident; instead it has a complex structure and indications of multiple components are starting to emerge. A tentative interpretation is that there could be different stellar populations at interplay, each with a different scale height: the thin disk, the thick disk, and a bar population; (iii) the stars with [Fe/H] −0.1 are old with ages between 10 and 12 Gyr; (iv) the metal-rich stars with [Fe/H] −0.1 show a wide variety of ages, ranging from 2 to 12 Gyr with a distribution that has a dominant peak around 4−5 Gyr and a tail towards higher ages; (v) there are indications in the [α/Fe] − [Fe/H] abundance trends that the "knee" occurs around [Fe/H] = −0.3 to −0.2, which is a slightly higher metallicity as compared to the "knee" for the local thick disk. This suggests that the chemical enrichment of the metal-poor bulge has been somewhat faster than what is observed for the local thick disk. The results from the microlensed bulge dwarf stars in combination with other findings in the literature, in particular the evidence that the bulge has cylindrical rotation, indicate that the Milky Way could be an almost pure disk galaxy. The bulge would then just be a conglomerate of the other Galactic stellar populations (thin disk, thick disk, halo, and ...?), residing together in the central parts of the Galaxy, influenced by the Galactic bar.

We present the first measurement of the planet frequency beyond the "snow line," for the planet-to-star mass-ratio interval −4.5 < log q < −2, corresponding to the range of ice giants to gas giants. We find d 2 N pl d log q d log s = (0.36 ± 0.15) dex −2 at the mean mass ratio q = 5 × 10 −4 with no discernible deviation from a flat (Öpik's law) distribution in logprojected separation s. The determination is based on a sample of six planets detected from intensive follow-up observations of high-magnification (A > 200) microlensing events during 2005-2008. The sampled host stars have a typical mass M host ∼ 0.5 M , and detection is sensitive to planets over a range of planet-star-projected separations (s −1 max R E , s max R E), where R E ∼ 3.5 AU (M host /M) 1/2 is the Einstein radius and s max ∼ (q/10 −4.3) 1/3. This corresponds to deprojected separations roughly three times the "snow line." We show that the observations of these events have the properties of a "controlled experiment," which is what permits measurement of absolute planet frequency. High-magnification events are rare, but the survey-plus-follow-up high-magnification channel is very efficient: half of all high-mag events were successfully monitored and half of these yielded planet detections. The extremely high sensitivity of high-mag events leads to a policy of monitoring them as intensively as possible, independent of whether they show evidence of planets. This is what allows us to construct an unbiased sample. The planet frequency derived from microlensing is a factor 8 larger than the one derived from Doppler studies at factor ∼25 smaller star-planet separations (i.e., periods 2-2000 days). However, this difference is basically consistent with the gradient derived from Doppler studies (when extrapolated well beyond the separations from which it is measured). This suggests a universal separation distribution across 2 dex in planet-star separation, 2 dex in mass ratio, and 0.3 dex in host mass. Finally, if all planetary systems were "analogs" of the solar system, our sample would have yielded 18.2 planets (11.4 "Jupiters," 6.4 "Saturns," 0.3 "Uranuses," 0.2 "Neptunes") including 6.1 systems with two or more planet detections. This compares to six planets including one twoplanet system in the actual sample, implying a first estimate of 1/6 for the frequency of solar-like systems.

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Based on high-resolution spectra obtained during gravitational microlensing events we present a detailed elemental abundance analysis of 32 dwarf and subgiant stars in the Galactic bulge. Combined with the sample of 26 stars from the previous papers in this series, we now have 58 microlensed bulge dwarfs and subgiants that have been homogeneously analysed. The main characteristics of the sample and the findings that can be drawn are: (i) The metallicity distribution (MDF) is wide and spans all metallicities between [Fe/H] = −1.9 to +0.6; (ii) The dip in the MDF around solar metallicity that was apparent in our previous analysis of a smaller sample (26 microlensed stars) is no longer evident; instead it has a complex structure and indications of multiple components are starting to emerge. A tentative interpretation is that there could be different stellar populations at interplay, each with a different scale height: the thin disk, the thick disk, and a bar population; (iii) The stars with [Fe/H] −0.1 are old with ages between 10 and 12 Gyr; (iv) The metal-rich stars with [Fe/H] −0.1 show a wide variety of ages, ranging from 2 to 12 Gyr with a distribution that has a dominant peak around 4-5 Gyr and a tail towards higher ages; (v) There are indications in the [α/Fe] − [Fe/H] that the "knee" occurs around [Fe/H] = −0.3 to −0.2, which is a slightly higher metallicity as compared to the "knee" for the local thick disk. This suggests that the chemical enrichment of the metal-poor bulge has been somewhat faster than what is observed for the local thick disk. The results from the microlensed bulge dwarf stars in combination with other findings in the literature, in particular the evidence that the bulge has cylindrical rotation, indicate that the Milky Way could be an almost pure disk galaxy. The bulge would then just be a conglomerate of the other Galactic stellar populations (thin disk, thick disk, halo, and ...?), residing together in the central parts of the Galaxy, influenced by the Galactic bar.

The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a nonanalytic and computationally intensive problem, it is often useful to have analytic approximations for the parameters as well as their uncertainties and covariances. Here, we give such formulae, for the case of an exoplanet transiting a star with a uniform brightness distribution. We also assess the advantages of some relatively uncorrelated parameter sets for fitting actual data. When limb darkening is significant, our parameter sets are still useful, although our analytic formulae underpredict the covariances and uncertainties.