We model the observed precision differential abundance (PDA) pattern of three G-type dwarfs: HIP 29432, HIP 77052, and HIP 101905. PDAs are from Bedell et al. (2018, ApJ, 865, 68, 2018, BD18). We also model the wide pair HIP 34407 and HIP 34426, where galactic chemical evolution (GCE) corrections are assumed unnecessary using data from Ramirez, et al. (2019, MNRAS, 490, 2448). PDA’s for the pair are taken as HIP 34407 minus HIP 34426. These PDAs are closely correlated with the 50% elemental condensation temperature, Tc. We show how it is possible to match the slope of such trends and the quantitative abundance differences.
We assume planetary or disk material was added to or missing from the stellar convection zone (CZ) with an assumed mass of 0.025 M⊙. The added material has the bulk earth (BE) composition of Wang, et al. (2018, Icarus, 299, 460). The differential abundance changes by a factor p + q*[N(EL)BE/N(EL)CZ], where the ratio in brackets gives the ratio of number of atoms in the BE to those in the assumed CZ, for each element. With the sun as the comparison star, we expect p to be close to unity. If it is negative, the star is slightly metal poor with respect to the sun. All of the BD18 stars have compositions only slightly different from solar. The q parameter measures the number of BE added to the convection zone. The parameters p and q are fit by linear regression to the stellar PDAs corrected for GCE vs. Tc from Wood, et al. (2019, AmMin, 104, 844). Very similar results are obtained with Tc from Lodders (2003, ApJ, 591, 1220). Results are as follows, for star(p,q,sig): HIP 29432 (0.81, -1.42, 0.01), HIP 77052 (0.97, 4.60, 7.5E-5), HIP 101905 (1.07, 5.00, 1.4E-7), and the pair HIP 34407/HIP 34426 (1.28, 7.78, 0.0001). Here, ‘sig’ is the F-test significance level. For HIP 29432, p < 1 and q < 0 indicating that the star is slightly metal poor; for HIP 34407/HIP 34426, the positive value of p indicates HIP 34407 is slightly metal rich with respect to its companion, while q = 7.78 indicates significantly more than one bulk earth mass was added to HIP 34407.