A revised comparison of distant and nearby solar twins

Properties of solar twins reported by Lehmann et al. (2023) at kiloparsec distances from the local standard of rest (LSR) are compared to solar twins within 100 pc of the Sun. These have velocity distributions closely similar to those of the nearby twins in addition to closely matching $T_{\rm eff}$, $\log{(g)}$ and $[Fe/H]$. The new twins are at slightly higher galactic latitudes, and are somewhat closer to the Galactic center. Additionally, they may be significantly older than nearby solar twins.

Solar twins have been discussed extensively in the literature (see Bedell, et al. 2018, henceforth, BD18). The BD18 stars are all within 100 pc of the Sun. In this note we discuss potential distant twins or analogues as investigated by Lehmann et al. (2022Lehmann et al. ( , 2023 and Liu et al. (2022). The authors designate their work SDST (Survey for Distant Solar Twins). Twins and analogues are defined in their work by limits on effective temperature, surface gravity, and [Fe/H], 1 with kiloparsec distances-far greater than for twins previously investigated.
A goal of SDST was to provide observations that might detect variations in the fine structure constant over kiloparsec distances.  give an introduction to the problem of fine structure variation and the proposed investigation method using sunlike spectra.
SDST explored one sharply limited direction of the Galaxy, an area of only 3.02 square degrees, in the direction of Galactic longitude 330.0 deg, latitude 16.55 deg. The survey yielded 877 candidate stars with Gaia DR3 1 We use the notation [Y /X] = log(Y /X)star − log(Y /X) Sun distances 483 ≤ d ≤ 5425 (mean=1933) pc. Twenty of the 877 stars were designated as twins and 299 as solar analogues. Figure 1 is a plot of Z-values of the 877 SDST stars vs. ρ = (X 2 + Y 2 ), where the origin of the coordinates is located at the mean sun position. The line of sight is out of the plane, the most distant of the 877 stars is Z = 1495 pc. The ρ values of the 20 solar twins are indicated by the blue arrows. This sightline encroaches on the so-called thick disk. The idea of a thick galactic disk was proposed by Abadi et al. (2003) -see also Prantzos et al. (2023) -to describe 'accretion debris' from galactic mergers. A scale height of 1.5 kpc would be seen at a distance of 4.5 kpc, for objects observed at galactic latitude 16 degrees. The Lehmann sample includes a few objects between 4.5 and 5.5 kpc distance and thus, could include thick disk components with potentially altered composition.

SIGHTLINE
The vertical scatter in Figure 1 is partially due to small differences in the line of sight to the SDST stars, and partially due to errors in the Gaia parallaxes (ϖ and ∆ϖ). It is beyond the (X 2 + Y 2 ) for 877 SDST stars (black filled circles). The red clump in the lower left corner are the 79 BD18 stars, mostly with velocities less than 63 km/sec. The orange line through the SDST points shows their allignment which departs very slightly for the most distant stars. See text for further discussion.
scope of this paper to explore the latter in detail (see Luri et al. 2018). A naive interpretation of the distance errors, however, between 1/(ϖ + ∆ϖ) and 1/(ϖ -∆ϖ) would lead to far greater scatter than is seen in Figure 1.

KINEMATICS: VELOCITIES
We have computed the velocities of the 20 twins and all 877 of the SDST stars, and compared them with the kinematical properties of sets of solar twins discussed by Cowley & Yüce (2022, henceforth, CY22) notably, 79 stars with precision differential abundances from BD18, which we consider definitive twins for the local solar neighborhood. Because the SDST twins are in a different region of the Galaxy, and at significantly greater distances than those of the BD18 sample, we focus on the velocities relative to the LSR; the distribution of stars in physical space is distinct by definition (see Figure 2).
We also consider the velocities in the Zdirection with the help of Figure 3.
Finally, it is of interest to examine the distributions of velocity in the phase space of kinetic energy (per unit mass) vs. L Z , the Z-component of the angular momentum (per unit mass). The solid line is part of a parabola that describes the locus of circular orbits near the Sun. Both the  BD18 and SDST points adhere closely to that line.
We conclude that the velocity kinematics of the 20 SDST distant twins are closely similar to BD18 objects.

AGES
Both the BD18 and SDST ages were computed using the q2 algorithm of Ramírez et al. (2014). The mean age differences are of interest. For 12 twins from the BD18 stars, CY22 found a mean age of 4.86 Gyr (see their Table  2). In CY22, four other sources of 12 twins were  ) 4.78 (Brewer et al. 2016, and 3.96 Gyr (Nissen 2015). The average of these five means is 4.41 Gyr. We take 1.5 Gyr as a working, conservative uncertainty of an individual twin's age-roughly a standard deviation (see Delgado Mena et al. (2019) and CY22). Dividing these N -1 values by (11) = 3.32, these give an uncertainty of 0.45 Gyr for the mean. Altogether, we may say that solar twins in the solar neighborhood have a mean age of 4.43 ± 0.45 Gyr.
The mean distance of the 20 distant twins from the Galactic center is 6.72±0.65 kpc. They have a mean age of 8.35 Gyr and if we again use 1.5 Gyr as a typical uncertainty, the uncertainty of this mean is 1.5 (19) = 0.34 Gyr. So the distant twins have a mean age of 8.35 ± 0.34 Gyr. The mean age of the near twins plus 2 sigma is 5.25 Gyr while the mean age of the distant twins minus 2 sigma is 7.69, leaving a substantial gap.
Judging by conservative estimates for the random errors, the distant twins are significantly (> 2σ) older than the nearby ones. However, the typically larger systematic errors could change that conclusion.

SUMMARY
The distant solar twins of the SDST studies have very similar velocity distributions to those of the classic BD18 stars in the solar neighborhood, supporting their validity as solar twins, and supporting their use in the investigation of possible variations in the fine structure constant. An age difference in the near and distant twins is of interest because of a possible connection with galactic chemical evolution, and/or violation of the Vogt-Russell theorem (Russell 1931).