Planetary cartography in the Galaxy

The ultimate goal of these statistical analyses is to answer a simple question: How many stars in the Galaxy are likely to have associated planetary systems? While we are still far from being able to construct a reliable detailed model for the stellar populations in the Milky Way, there have been some initial studies, notably by Gonzalez, Brownlee, & Ward (2001). Here, we briefly consider those models.

4.1. Abundance gradients and the Galactic Habitable Zone

Planetary habitability is likely to depend on many factors: distance from the parent star; the stellar luminosity, activity and lifetime; (perhaps) planetary mass, which may depend on the metallicity of the system; (perhaps) the presence of a massive satellite; the existence of plate tectonics; and (perhaps) the space motion of the system. In contrast, from the perspective of planet formation, the correlation between planetary frequency and metallicity is the only significant factor that has emerged from statistical analysis of the known ESP systems. Extending the present results beyond the Solar Neighborhood requires modeling of both the radial abundance gradient and the age-metallicity relation of the Galactic disk.

Most studies assume a logarithmic radial abundance gradient; for example, Gonzalez et al. (2001) adopt a gradient,

of -0.07 dex kpc-1. More recent analyses of intermediate-age Cepheids (Andrievsky et al. 2002) suggest a more complex radial distribution, with a flatter gradient in the vicinity of the Solar Radius, but steeper gradients outwith these limits. Figure 5a matches both distributions against [O/H] abundances for H ii regions (from Shaver et al. 1983); we also show current estimates for the Sun, and for the Hyades, Pleiades and Praesepe clusters. By and large, the data favor the complex gradient, but one should note that extrapolating the inner gradient implies unreasonably high metallicities at R < 4 kpc. It is probably more reasonable to infer that we require more observations of metallicity tracers in the inner Galaxy.

The metallicity gradients plotted in the upper panel of Figure 6 are based on young objects—even the Cepheids are less the 109 years old. Thus, the distributions are characteristic of the average metallicity of stars forming in the present-day Galaxy. Clearly, there is a substantial distribution of metallicity among the stars in the Solar Neighborhood, and one would expect comparable dispersions at other radii. Gonzalez et al. (2001) address this issue by assuming an age-metallicity relation,

8 10

8 10

Age (Gyrs) VF05

Figure 6. The upper panel plots oxygen abundance data for H II regions as a function of Galactic radius (open squares, data from Shaver et al. 1983). We also show the oxygen abundances for the Sun (solid square) and for the three nearest open clusters, the Hyades, Pleiades and Praesepe (solid triangles). The dotted line plots the abundance gradient adopted by Gonzalez et al. (2001); the solid line marks the composite gradient derived by Andrievsky et al. (2002) from Cepheid data. The lower panel plots the age-metallicity distribution derived by Valenti & Fischer (2005) for stars in the Berkeley/Carnegie radial velocity survey; solid points mark stars known to be ESP hosts. The pentagon marks the Sun.

Age (Gyrs) VF05

Figure 6. The upper panel plots oxygen abundance data for H II regions as a function of Galactic radius (open squares, data from Shaver et al. 1983). We also show the oxygen abundances for the Sun (solid square) and for the three nearest open clusters, the Hyades, Pleiades and Praesepe (solid triangles). The dotted line plots the abundance gradient adopted by Gonzalez et al. (2001); the solid line marks the composite gradient derived by Andrievsky et al. (2002) from Cepheid data. The lower panel plots the age-metallicity distribution derived by Valenti & Fischer (2005) for stars in the Berkeley/Carnegie radial velocity survey; solid points mark stars known to be ESP hosts. The pentagon marks the Sun.

they assume a small dispersion in metallicity (<0.08 dex). Note that this type of relation corresponds to a constant fractional increase in metallicity with time; that, in turn, requires either an increasing yield with increasing metallicity or an increasing star formation rate at a constant yield.

The lower panel of Figure 6 matches the Gonzalez et al. age-metallicity relation against empirical results from Valenti & Fischer's (2005) analysis of stars in the Berkeley/Carnegie survey; both ESP hosts and the Sun are separately identified. Unlike the classic Edvardsson et al. (1993) analysis, there is a trend in mean abundance with age. Overall, the observations indicate a much broader dispersion in metallicity, at all ages, than assumed by Gonzalez et al. (2001).| As with the radial abundance gradient, further analysis is required before settling on reliable values of these parameters.

4.2. Planetary statistics in the Solar Circle

Given all the caveats, what can we say about the likely distribution of planetary systems in the Milky Way? For the moment, any calculations must be restricted to regions rela-

f Note that the Sun, which lies at the mode of the local abundance distribution, appears somewhat metal poor for its age, as compared with VF05 data.

R (kpc)

Figure 7. The upper panel plots the expected numbers of ESP hosts as a function of Galacto-centric distance for 6 < R < 10 kpc; the lower panel plots the corresponding predicted metallicity distribution.

Figure 7. The upper panel plots the expected numbers of ESP hosts as a function of Galacto-centric distance for 6 < R < 10 kpc; the lower panel plots the corresponding predicted metallicity distribution.

tively close to the Sun. However, Figure 6 suggests that the local metallicity distribution may well be representative of stars with Galactic radii between 6 and 10 kiloparsecs. Taking this as a working assumption, we can calculate a back-of-the-envelope estimate of how many solar-type stars in this annulus might have planetary companions.

In making this calculation, we identify solar-type stars as stars with luminosities 4 < Mv < 6; we assumed a density law p(R) = poe(R-Ro)/h e-z/z0 , (4.1)

where p0 = 4.4 x 10-3 stars pc-3, with 90% of the stars assigned to the disk and 10% to the thick disk; h = 2500 pc; and z0 = 300 pc for the disk, and z0 = 1000 pc for the thick disk. We assume an overall planetary frequency of 6%.

Given those starting assumptions, Figure 7 shows the expected radial density distribution and the metallicity distribution of ESP hosts. In total, we predict that ^3.5 x 107 solar-type stars are likely to have gas giant planetary companions with a < 4 AU. The space density increases with decreasing Galactocentric radius (density wins over surface area), and the metallicity distribution is approximately flat for -0.1 < [m/H] < 0.3. ESP hosts are not uncommon in the Solar Circle.

Was this article helpful?

0 0

Post a comment