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TO APPEAR IN THE ASTROPHYSICAL JOURNALPreprint typeset using LATEX style emulateapj v. 8/13/10 ELEMENTAL ABUNDANCES OF SOLAR SIBLING CANDIDATES I. RAM´IREZ1 , A. T. BAJKOVA2 , V. V. BOBYLEV2,3 , I. U. ROEDERER4 , D. L. LAMBERT1 , M. ENDL1 , W. D. COCHRAN1 , P. J. MACQUEEN1 , AND R. A. WITTENMYER5,6 To appear in the Astrophysical Journal Dynamical information along with survey data on metallicity and in some cases age have been used recently by some authors to search for candidates of stars that were born in the cluster where the Sun formed. We haveacquired high resolution, high signal-to-noise ratio spectra for 30 of these objects to determine, using detailedelemental abundance analysis, if they could be true solar siblings. Only two of the candidates are found tohave solar chemical composition. Updated modeling of the stars' past orbits in a realistic Galactic potentialreveals that one of them, HD 162826, satisfies both chemical and dynamical conditions for being a sibling of theSun. Measurements of rare-element abundances for this star further confirm its solar composition, with the onlypossible exception of Sm. Analysis of long-term high-precision radial velocity data rules out the presence of hotJupiters and confirms that this star is not in a binary system. We find that chemical tagging does not necessarilybenefit from studying as many elements as possible, but instead from identifying and carefully measuring theabundances of those elements which show large star-to-star scatter at a given metallicity. Future searchesemploying data products from ongoing massive astrometric and spectroscopic surveys can be optimized byacknowledging this fact.
Subject headings: stars: abundances — stars: kinematics and dynamics — stars: fundamental parameters — stars: general — stars: individual (HD 162826) system planets' orbits must be stable and that the early UV Infrared surveys and observations of young stars made over radiation fields were not strong enough to evaporate the so- the past two decades suggest that most stars (80–90 %) are lar nebula. ) argues that the Sun most likely born in rich clusters of more than 100 members inside gi- formed in an environment resembling an OB association (as ant molecular clouds ; opposed to a starburst cluster), where star densities are not . Although it has been pointed out that, de- sufficient for the destruction of protoplanetary disks due to pending on the definition of cluster, the fraction of stars born stellar encounters.
in them could be as low as 45 % ), there The mean lifetime of open clusters in the Galactic disk is is convincing evidence that the Sun was born in a moderately estimated to be about 100 Myr . Consid- large stellar system.
ering the solar system age of 4.57 Gyr Daughter products of short-lived (< 10 Myr) radioactive ), it is not surprising that the solar cluster is now fully species have been found in meteorites, suggesting that the ra- dissipated and its members scattered throughout the Galaxy.
dioactive isotopes themselves were present in the early solar The hypothesis that the Sun was born in the solar-age, solar- metallicity open cluster M67 ). A nearby supernova explosion could have injected ; , which hosts some these isotopes into the solar nebula (e.g., of the most Sun-like stars known an event that has a high probability in a dense stellar environ- , has been refuted by ment (e.g., . Additional evidence ) using dynamical arguments. These authors even con- that the Sun was born in such an environment is provided clude that the Sun and M67 could not have been born in the by the dynamics of outer solar system objects like Sedna same giant molecular cloud.
), which has large eccentricity (e ∼ 0.8) Stars that were born together with the Sun are re- and perihelion (∼ 75 AU). Numerical simulations show that ferred to as "solar siblings." They should not to be con- these extreme orbital properties can arise from close encoun- fused with "solar twins," which are stars with high res- ters with other stars (e.g., .
olution, high signal-to-noise ratio spectra nearly indistin- In his review of "The Birth Environment of the Solar Sys- guishable from the solar spectrum, regardless of their ori- tem," concludes that the Sun was born in a cluster of 103 − 104 stars. The probability of close stellar en- ; ; ). By defini- counters and nearby supernova pollution is high in a bound tion, the siblings of the Sun must have solar age and solar cluster with more than ∼ 103 members. On the other hand, chemical composition because they formed essentially at the the upper limit of ∼ 104 is set by the conditions that the solar same time from the same gas cloud. They do not need to be"Sun-like" with respect to their fundamental parameters such 1 McDonald Observatory and Dept. of Astronomy, Univ. of Texas, Austin as effective temperature, mass, luminosity, or surface gravity.
2 Pulkovo Astronomical Observatory, St. Petersburg, Russia In principle, the siblings of the Sun could be found by mea- 3 Sobolev Astronomical Institute, St. Petersburg State University, Russia suring accurately and with high precision the ages and de- 4 Department of Astronomy, University of Michigan tailed chemical compositions of large samples of stars, an ap- School of Physics, UNSW, Sydney, Australia 6 Australian Centre for Astrobiology, UNSW, Sydney, Australia proach that is obviously impractical. Fortunately, analytical RAM´IREZ ET AL.
models of the Galactic potential can be used to predict their proposed as candidate) could all well be true solar siblings.
present-day dynamical properties.
Alternatively, the same The problem of searching for solar siblings in the solar models can be employed to determine in retrospect if a given neighborhood using existing survey data was tackled also by star could have possibly originated within the solar cluster.
They suggested a different method Thus, by applying dynamical constraints, manageable sam- for finding them.
First, targets were searched using the ples of solar sibling candidates can be constructed to be later stars' Galactic space velocities U,V,W (their data set is de- examined carefully using more expensive methods such as scribed in by excluding those whose total speeds relative to the solar one are significantly dif- ferent ( U 2 +V 2 +W 2 > 8 km s−1).
Then, the orbits of the remaining objects (162 FGK stars with parallax errors was used by to reverse the orbit of lower than 15 %) were simulated backwards in time using the Sun and calculate its birth-place in the Galaxy.
the ) Galactic potential perturbed by orbits of simulated solar clusters with 2048 members were spiral density waves (as suggested by then computed to determine the fraction of solar siblings to ) to determine parameters of encounter with the solar or- be found today in the solar neighborhood. bit such as relative distance and velocity difference over a concludes that 10–60 of them should be found within 100 pc period of time comparable to the Sun's age. Finally, these from the Sun.
This somewhat optimistic view was chal- parameters were examined to calculate the probability that lenged by ), who employed the any of these objects was born together with the Sun. Their Galactic potential by ) and perturbed calculations rule out HD 28676 and HD 192324, both solar it with both quasi-stationary ) and transient sibling candidates according to . On the ) spiral density waves to show that other hand, list as their best candidates the stars the orbits of solar siblings strongly deviate from being nearly HD 83423 and HD 162826. Note that the former is also a good find that only a few solar candidate according to . Further- siblings may be found within 100 pc from the Sun if the solar more, the calculated dynamic properties of this star seem to cluster had ∼ 103 members. The situation might be worse be very robust under different model parameters.
if scattering by molecular clouds or close stellar encounters In this work, we perform chemical analysis using newly ac- were to be taken into consideration, but "less hopeless" if the quired high resolution, high signal-to-noise ratio spectra to solar cluster contained ∼ 104 stars instead.
establish if any of the stars discussed above can be consid- Following the modeling by , ered a true solar sibling. Finding these objects could shed ) pointed out that one could use the regions light onto our origins. For example, knowledge of the spatial of phase-space occupied by the simulated stars to narrow- distribution of solar siblings can help determining the Sun's down the search for the siblings of the Sun. Their calculations birthplace and understand the importance of radial mixing in suggest that these stars should have proper motions lower than shaping the properties of disk galaxies 6.5 mas yr−1 and parallaxes larger than 10 mas. Then, by ). It will also enable us to better constrain the physical employing data from the Hipparcos catalog characteristics of the environment in which our star was born ), in its revised version , they were . Furthermore, theoretical calculations show able to find the 87 stars satisfying these conditions, after that large impacts of rocks into planets produce fragments imposing an additional constraint of 10 % for the precision where primitive life can survive as they travel to other planets of the parallaxes. Their list of candidates was further nar- or even other nearby planetary systems, a mechanism known rowed down by excluding stars with (B − V ) < 0.5, which as "lithopanspermia" are bluer than the solar-age isochrone turn-off. Finally, they ; ). For example, employed the stellar ages given in the Geneva-Copenhagen estimate that about 5 % of impact remains from Earth have escaped the solar system. A similar value is obtained for the ) to find the 6 stars with solar age within the errors. Based case of Mars. ) point out that the pos- on the radial velocities and metallicities given in the GCS, sibility of contamination of solar siblings by "spores of life" conclude that only one star (HD 28676) may be from our planet should make the siblings of the Sun prime a true solar sibling. Five other candidates with (B −V ) > 1.0 targets in the search for extraterrestrial life.
were not found in the GCS.
As we enter the era of massive, far-reaching astromet- A procedure similar to the one described above was ric/photometric surveys led by Gaia ) as adopted by , but employing well as comparably large high-resolution spectroscopic sur- in addition to the GCS other metallicity data sets veys such as Gaia-ESO ) and GALAH ), a thorough investigation of the available and ). By selecting stars with −0.1 < data, albeit relatively small in the context of solar sibling re- [Fe/H] < +0.1 and using the same proper motion and paral- search, must be made to guide the more statistically signifi- lax constraints described above, they created a list of 21 can- cant search strategies of the near future.
didates for siblings of the Sun. Then, they used the previouslypublished stellar atmospheric parameters and the PARAMcode by )7 to estimate isochrone ages forthose stars and thus find the nine objects with solar age within 2. SAMPLE AND SPECTROSCOPIC ANALYSIS the errors. Further examination of the available data led themto conclude that the stars HD 28676 (already suggested by 2.1. The Solar Sibling Candidates ), HD 83423, and HD 175740 (the first giant Our target list consists of all interesting objects discussed in the previous exploratory searches by , hereafter Br10), hereafter Bo11), and SOLAR SIBLING CANDIDATES Solar Sibling Candidates McD – Dec. 2012 McD – Dec. 2012 McD – Dec. 2012 McD – Dec. 2012 McD – Dec. 2012 LCO – Apr. 2013 McD – Dec. 2012 McD – Dec. 2012 McD – Dec. 2012 McD – Dec. 2012 LCO – Apr. 2013 LCO – Apr. 2013 McD – Dec. 2012 McD – Dec. 2012 McD – Dec. 2012 McD – Mar. 2013 McD – Mar. 2013 McD – Mar. 2013 LCO – Apr. 2013 McD – Dec. 2012 McD – Dec. 2012 LCO – Apr. 2013 McD – Dec. 2012 LCO – Apr. 2013 LCO – Apr. 2013 McD – Dec. 2012 McD – Dec. 2012 McD – Dec. 2012 McD – Dec. 2012 McD – Dec. 2012 a Spectral type from SIMBAD.
b Distance derived from Hipparcos parallax.
c McD: Tull spectrograph on the 2.7 m Harlan J. Smith Telescope at McDonald Observatory. LCO: Mikespectrograph on the 6.5 m Magellan/Clay Telescope at Las Campanas Observatory.
d Br10: ), Bo11: , Ba12: ).
hereafter Ba12).8 In addition to The Tull/McDonald spectra were reduced in the stan- the six candidates listed in Table 1 of Br10, i.e., those they dard manner using the echelle package in IRAF9 while the found in the GCS catalog, we also observed the five stars MIKE/Magellan data were reduced using the CarnegiePython with (B −V ) > 1.0 that satisfied all other criteria for solar sib- pipeline.10 After correcting for the Earth's motion using the ling candidate in that work. The two stars discussed in detail rvcorrect task in IRAF, the radial velocities (RV s) of our tar- in Bo11 were also included. Finally, all 21 stars in the ex- get stars were measured by cross-correlation with the spectra tended list by Ba12 (see their Table A) were observed. Note of stars in our sample with known stable radial velocities. For that Ba12's list includes one object from Bo11 and three from the McDonald data we used as radial velocity standards the Br11. Thus, a total of 30 targets were observed for this work stars HD 196676 (RV = −0.5 km s−1) and HD 219828 (RV = −24.1 km s−1). Their radial velocities are from Three of the stars observed from Las Campanas 2.2. Spectroscopic Observations have radial velocities in the GCS catalog (HD 46100, RV =21.0 ± 0.2 km s−1; HD 183140, RV = −29.3 ± 0.1 km s−1, We used the Tull coud´e spectrograph on the 2.7 m Har- and HD 192324, RV = −4.4 ± 0.2). In all cases, regardless of lan J. Smith Telescope at McDonald Observatory which star(s) is(are) used as standards, the resulting RV val- ) to observe most of our targets (23). All but three of ues are robust. They are given in Table Formal, internal er- them were observed in December 2012; the others were ob- rors on our RV values are typically around 0.2 km s−1. These served in March 2013. The rest of our targets (7) have too errors are due to the order-to-order cross-correlation velocity low declinations to be observed from McDonald Observa- scatter and the uncertainties in the velocities of the standard tory. Instead, they were observed using the MIKE spectro- stars. Systematic uncertainties will increase these errors by at graph on the 6.5 m Telescope at Las Campanas Observatory least 0.5 km s−1.
in April 2013. Slit sizes were chosenso that the spectral resolution of the data is about 60 000 in the 9 IRAF is distributed by the National Optical Astronomy Observatory, visible part of the spectrum. We targeted a signal-to-noise ra- which is operated by the Association of Universities for Research in Astron- tio (S/N) per pixel of at least 200 at 6 000 ˚ A. Only one of our omy (AURA) under cooperative agreement with the National Science Foun- targets (HD 46100) has a significantly lower S/N spectrum.
8 Very recently, ) employed the detailed elemental abun- dance analysis of one of the largest exoplanet host star samples to find anothersolar sibling candidate: HD 186302. We did not include this star in our work.
RAM´IREZ ET AL.
Figure 1. Spectra of high V sin i stars. Our solar (Vesta) spectrum is shown
Figure 2. Spectra of double-lined spectroscopic binary (SB2) stars. Our
in the top panel for comparison.
solar (Vesta) spectrum is shown in the top panel for comparison.
with wavelength persists, suggesting that the line strengths 2.3. Moderately Fast Rotators and Double-lined have been affected by the contribution to the continuum of the nearby, and probably very cool companion.
The methods that we employ to derive atmospheric param- All moderately fast rotators and SB2s were excluded from eters and to measure elemental abundances (see Sections further analysis. Therefore, hereafter our sample is reduced and are not suited for stars with high projected rota- to 18 stars.
tional velocity (V sin i) or double-lined spectroscopic binaries(SB2s). The spectral lines in the former are either severely 2.4. Stellar Parameter Determination blended or they cannot be identified due to the extreme ro- tational broadening. SB2s, on the other hand, require spe- tion/ionization balance of iron lines to determine the cial treatment because even in cases where both sets of spec- stars' atmospheric parameters Teff (effective temperature), tral lines can be identified and measured independently, the log g (surface gravity), [Fe/H] (iron abundance), and vt blended continuum flux must be first estimated from previous The details of this method have been knowledge of the two stars, making the problem somewhat described multiple times, for example in degenerate and the results not as accurate as those that can be , ). Basically, the equivalent widths of a achieved for single spectra stars. More importantly, in most large number of non-blended, unsaturated Fe I and Fe II lines cases these stars have been selected because their photome- are measured using Gaussian line profile fits. In our case, try suggests a solar metallicity. Photometric calibrations of this was done using IRAF's splot task.
metallicity should only be applied to single stars.
curve-of-growth approach is employed to determine the iron Figures and show the small spectral region of our spec- abundance from each line for a given set of guess stellar troscopic data containing the 5853.7 ˚ A Ba II line for our target stars with very high V sin i and targets which are SB2s, respec- We used the spectrum synthesis code MOOG tively. For reference, our solar (Vesta) spectrum is shown in )11 and MARCS model atmospheres with standard the top panel of these figures. The SB2 nature of HD 101197, chemical composition )12 for our iron and specially HD 183140 is obvious. The spectra of HD 7735 abundance calculations. The initial guess stellar parameters and HD 35317 show excess absorption on the blue wings of all were iteratively modified until the correlations between iron spectral lines. The latter in fact has a very high V sin i compan- abundance and excitation potential and reduced equivalent ion, which was not analyzed in this work (hence the "nw" flag, width of the line disappear while simultaneously enforcing which stands for North-West component). HD 168442 has a agreement between the mean iron abundances inferred from spectrum that is irreproducible with single star models. It ap- Fe I and Fe II lines separately. For these calculations, we pears to be a blend of a Sun-like star and an M-type dwarf.
employed relative iron abundances, i.e., the iron abundances HD 192324 has a very nearby companion which appears to were measured differentially with respect to the Sun, on a have contaminated our spectrum. Even though this star canbe analyzed and stellar parameters were determined as de- scribed in Section a very clear trend of iron abundance 12 Available online at SOLAR SIBLING CANDIDATES 0.2 GCS (H09) − TW 0.2 GCS (C11) − TW The number to the left of the decimal point indicates the atomic number. The number to Figure 3. Comparison of iron abundances. Top panel: [Fe/H] values from
the right of the decimal point indicates the the GCS , H09) minus those derived in this work (TW) ionization state, where "0" is neutral and "1" as a function of [Fe/H] (TW). Bottom panel: as in the top panel for the im- is singly ionized.
proved GCS values by C11).
line-by-line basis, and using the reflected sunlight spectrum photometric metallicity calibration. The average difference of the asteroid Vesta, taken from McDonald Observatory in in [Fe/H] values between those given by December 2012.
) and ours is −0.02 ± 0.11.
Formal errors for our spectroscopically derived stellar pa- The discussion above regarding Figure shows that the rameters were calculated as described in Appendix B of ) GCS metallicities should be the pre- ) and in Section 3.2 of ferred set for the purpose of constraining a stellar sample . These errors are small given the high-quality of our based on the stars' [Fe/H] values. Moreover, although the 1- data (hence highly-precise EW values) and the strict differ- σ errors of the photometric metallicities are quoted typically ential nature of our work which minimizes the impact of un- as 0.1 dex, one should keep in mind that this number corre- certainties in the atomic data. Indeed, the average errors in sponds to a sample and not to individual stars. By definition, Teff, log g, and [Fe/H] are 30 K, 0.07 dex, and 0.02 dex, re- at least 30 % of stars with real [Fe/H] < 0.1 have photomet- spectively. However, we note that these values are not rep- ric [Fe/H] values outside of that "solar" range. Thus, a metal- resentative of the real errors in these parameters, which are licity constraint of 0.1 dex already excludes a good number of dominated by systematic uncertainties, as will be discussed in potentially good candidates. Given that in the case of a search for nearby siblings of the Sun it is crucial not to discard a sin- Our iron line list and adopted atomic data are given in gle potentially interesting candidate, perhaps the safer choice Table The stellar parameters derived as described above should be [Fe/H] < 0.2, which would exclude only about (hereafter referred to as the "spectroscopic" parameters Teff, 5 % of real solar-metallicity stars. Indeed, none of the 5 key log g, [Fe/H]) are listed in Table The other set of parame- solar sibling candidates that will be discussed in Section ters listed in Table T ′ , log g′, [Fe/H]′ will be described in would have survived a [Fe/H] < −0.1 cut had we used the ) GCE metallicities.
2.5. Reliability of Photometric Metallicities 2.6. Elemental Abundance Determination A comparison of our spectroscopically-derived [Fe/H] val- We employed equivalent width measurements and standard ues with those inferred from photometric calibrations, as curve-of-growth analysis to derive the abundances of 14 ele- given in the GCS catalog, is presented in Figure This com- ments other than iron: O, Na, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Co, parison is relevant because solar sibling searches can bene- Ni, Y, and Ba. As in the case of iron, equivalent widths were fit from a reasonable [Fe/H] constraint, and large catalogs measured using IRAF's splot task while the curve-of-growth like the GCS have been found convenient for that purpose.
analysis was made using MOOG and MARCS model atmo- The top panel in Figure shows that the GCS [Fe/H] val- spheres. Oxygen abundances were inferred from the 777 nm ues, as given in , are systematically O I triplet lines and corrected for departures from local ther- low by about 0.1 dex relative to ours (the mean difference is modynamical equilibrium (LTE) using the grid of non-LTE −0.13 ± 0.07; the error bar here corresponds to the 1-σ star- corrections by .13 Hyperfine structure to-star scatter). This, combined with the fact that most previ- was taken into account for lines due to V, Mn, Co, Y, and ous exploratory searches of solar siblings have employed the Ba using the wavelengths and relative log g f values from the original GCS catalog, is the reason why our sample centers Kurucz atomic line database.14 Our adopted linelist for ele- around [Fe/H] ∼ +0.1 and not [Fe/H] = 0.
ments other than iron is given in Table Our derived abun- The bottom panel of Figure shows that the improved GCS dances are listed in Tables and Errors listed in these tables metallicities given in ) are consistent correspond to the 1-σ line-to-line scatter and do not include with our spectroscopic solutions. have discussed at length the systematic offset required for the 13 An online tool to calculate these non-LTE corrections is available at original GCS [Fe/H] values, which essentially stems from a better and more consistent set of T eff values in the underlying RAM´IREZ ET AL.
Stellar Parameters Line List For Elements Other Than Iron a The number to the left of the decimal pointindicates the atomic number. The number tothe right of the decimal point indicates the ionization state, where "0" is neutral and "1" is singly ionized.
Figure 4. Effective temperature versus surface gravity. Various theoretical
isochrones of solar age and solar metallicity have been overplotted. The
systematic uncertainties. The latter will be discussed in Sec- three stars whose parameters are not compatible with the solar-age, solar- metallicity isochrone are labeled.
In addition to Fe, lines due to neutral and singly-ionized ical isochrones of solar age ( Ti and Cr are available in the spectra of our stars. Thus, ∼ 4.5 Gyr) and solar metallicity.
Although different isochrones have different definitions of so- we derived Ti and Cr abundances using Ti I and Ti II as lar metallicity, the differences are small and not important for well as Cr I and Cr II lines separately in each case.
our purposes. Isochrones computed by the following groups mean differences in Ti and Cr abundances inferred from the are shown in Figure ordered by their hottest isochrone point two types of lines are [Ti I/H]−[Ti II/H]= −0.03 ± 0.06 and (coolest is last in this list): ; [Cr I/H]−[Cr II/H]= +0.02 ± 0.05, i.e., consistent with zero within the observational uncertainties, but not exactly zero, ). There are important differences between them, but as one would expect if true ionization balance had been collectively they can help us discard a few stars based on a achieved. The latter reflects our limitations in the modeling zeroth-order age estimate.
of stellar atmospheres and spectral line formation. Neverthe- Determining ages of individual stars is a very difficult task, less, given the opposite signs of the Ti and Cr differences, we particularly for stars on the main-sequence, but a quick in- do not expect improved models to be significantly different spection of Figure clearly shows that three of our sample from the ones employed in this work.
stars cannot have solar age within any reasonable uncertain- 3. LOOKING FOR THE SUN'S SIBLINGS ties. HD 199881 and HD 207164 are too warm given the turn-off Teff of the solar-age, solar-metallicity isochrone, which is 3.1. The Solar-Age, Solar-Metallicity Isochrone at most ∼ 6300 K. HD 199951, on the other hand, appears to Figure shows one version of the theoretical Hertzprung- be a giant star of younger age than solar. All of our other Russell diagram using our derived stellar parameters effective targets have stellar parameters reasonably consistent with the temperature and surface gravity. It also shows several theoret- solar-age, solar-metallicity isochrone.
SOLAR SIBLING CANDIDATES Abundances of "M" Elements: O, Si, Ca, Sc, Ti, Cr, Mn, Co, and Ni Abundances of "not M" Elements: Na, Al, V, Y, and Ba 3.2. Chemical Tagging like Si, Mg, Ca, Mn, Zr, and Ni have almost indistinguish- Although [Fe/H] values are an excellent starting point to able [X/Fe] abundance ratios at any given [Fe/H]. Although search for stars with similar composition, strict "chemical tag- some elements such as Ni present very small cluster-to-cluster ging," i.e., the association of groups of field stars according scatter, the larger scatter in the other cases can be reasonably to their common composition which would suggest a com- explained by dissimilar measurement errors (not all elements mon site of formation , in are equally easy or difficult to analyze). One open cluster of principle requires a precise knowledge of abundances of sev- sub-solar metallicity has a very low Zr abundance, but being eral other elements. Nevertheless, it is well known that the a single and extreme outlier, that seems to be a very special behavior of most elements often analyzed in solar-type stars case and not the rule among these objects. Element Na does is such that their abundances scale very well with [Fe/H] re- seem to have a scatter larger than the expected observational gardless of the place of origin of the star, making them use- errors, indicating that its abundance is more useful to disen- less in the search for common chemical abundance patterns.
tangle stars born in different clusters. A much more obvious A few species, however, are known to show large star-to-star case is that of Ba, which for nearly solar-metallicity clusters scatter at constant [Fe/H], and those should be preferentially can vary by almost one order of magnitude. Thus, this study employed in the search for groups of stars with a common clearly indicates that only Ba, and to some extent Na could be origin, particularly solar siblings.
used in practice given the level of uncertainty in these mea- In ), the mean abundance ratios [X/Fe] of a number of elements in fifteen Galactic open clusters were Here we should acknowledge the potential impact of stars plotted against the mean [Fe/H] of each cluster (their Fig- with peculiar abundances such as the so-called Ba stars ures 11–15). The [Fe/H] range covered by these clusters goes on our work. These are objects from −0.6 to +0.3, but five of them have nearly solar [Fe/H] that have prominent Ba II features in their spectra, which are (i.e., −0.1 . [Fe/H] . +0.1). With rare outliers, elements attributed to close binary interactions, namely mass transferfrom an intermediate-mass star that has now evolved into a RAM´IREZ ET AL.
−0.1 0.0 0.1 0.2 0.3 −0.1 0.0 0.1 0.2 0.3 −0.1 0.0 0.1 0.2 0.3 −0.1 0.0 0.1 0.2 0.3 Figure 5. Elemental abundance ratios relative to iron as a function of [Fe/H]. Evolved stars are shown with open squares; dwarfs and sub-giants are represented
by filled circles. The dashed lines intersect at the solar values.
white dwarf (e.g., ; ; very small observational errors at any given metallicity in the ; ). Quantitatively, their [Ba/Fe] abun- −0.2 < [Fe/H] < +0.2 range. This is in good agreement with dance ratios can be as high as 1 dex at [Fe/H] ≃ 0 (e.g., the open cluster work. Also consistent ; . This type of metal pollution by with that work is the fact that ) find a very a close companion could certainly be problematic for a solar large star-to-star scatter for Zn, Y, Zr, and Ba. Thus, those ele- sibling search, although it is possible that the frequency of ments are key for our purposes. The few available lines due to these events is low enough to have a relatively minor impact.
Zn and Zr are blended in the majority of our sample stars. Al- Indeed, the star-to-star scatter of the [Ba/Fe] abundance ratio though we are able to measure precise Zn and Zr abundances observed in individual open clusters is low and can be ex- in the most Sun-like stars in our sample, we excluded these plained purely by observational errors .
elements from our work in order to maintain homogeneity in Detailed chemical composition studies of large numbers of the analysis.
field stars (e.g., ; ; The reason α- and iron group element abundance ratios [X/Fe] show little or no star-to-star scatter at a given [Fe/H] ; can also guide us is that they are produced together in supernovae and their pro- in our search. The problem with these large samples, however, duction ratios are set by nuclear properties. The differences in is that systematic errors will produce large star-to-star scatter abundance ratio scatter with other elements can be understood at similar [Fe/H] that may prevent us from finding other useful in terms of the different nucleosynthesis sites and timescales chemical elements. In this context, the work by (see for a recent overview of Galactic is highly relevant. They measured abundance ratios of chemical evolution). In particular, in material of roughly solar 20 elements in an important number of so-called solar analog metallicity, most barium has been produced by s-process nu- stars. All these objects have spectra very similar to the solar cleosynthesis, which does not occur in the supernovae respon- spectrum. Therefore, their atmospheric parameters Teff and sible for the production of the α- and iron-group elements.
log g are very similar. This means that systematic errors in the Barium is produced mostly by low-mass AGB (asymptotic gi- chemical analysis can be almost fully removed by employing ant branch) stars, where the Ba yields are sensitive to the phys- a strict differential analysis relative to the Sun. Indeed, their ical conditions at the time of nucleosynthesis and the stellar [X/Fe] versus [Fe/H] trends show very little star-to-star scat- parameters; Ba production is thus decoupled from Fe produc- ter relative to other works using less strict sample selections.
By examining Figure 1 in it is clear were among the first to point out that elements such as Si, Ca, Sc, Ti, V, Cr, Mn, and Ni a significant correlation between Ba abundance and stellar are useless in the search for solar siblings. The star-to-star age at a given [Fe/H]. Later investigations of open clusters scatter of their abundance ratios is fully consistent with the SOLAR SIBLING CANDIDATES Fe <M> Na Al Fe <M> Na Al Fe <M> Na Al HD28676 (5942,4.32) HD44821 (5727,4.52) HD46100 (5543,4.58) HD83423 (6096,4.48) HD91320 (6146,4.23) HD95915 (6414,4.22) HD100382 (4751,2.69) HD102928 (4796,2.84) HD148317 (6041,3.87) HD154747 (5322,3.87) HD162826 (6210,4.41) HD168769 (5355,4.42) HD175740 (4890,2.91) HD196676 (4841,3.1) HD199881 (6691,4.35) HD199951 (5218,3.09) HD207164 (6886,4.47) HD219828 (5886,4.18) Fe <M> Na Al Fe <M> Na Al Fe <M> Na Al Figure 6. Chemical composition of solar sibling candidates. < M > represents the average of elemental abundances for O, Si, Ca, Sc, Ti, Cr, Mn, Co, and Ni.
Teff in K and log g values are given between parenthesis next to the stars' names.
) as well as surveys of field stars ; dwarfs and sub-giants. The reason for this is that it is known ; have confirmed that that large systematic errors are introduced when comparing result, which holds true also for Y.15 This implies that the these two types of stars.
Their extremely different atmo- scatter in the [Ba/Fe] versus [Fe/H] and [Y/Fe] versus [Fe/H] spheric structures prevent us from deriving highly accurate relations is at least in part due to an age effect. Younger abundances for both sets of stars simultaneously. Differen- stars tend to exhibit higher barium and yttrium abundances.
tial analysis reduces the errors somewhat, but since the refer- have shown that these trends can be re- ence object (the Sun) is a dwarf, the analysis of giant stars is produced in Galactic chemical evolution models if AGB nu- more suspect. One should therefore be careful when inspect- cleosynthesis of M < 1.5 M⊙ stars is such that the neutron ing these trends, because the giant stars may introduce artifi- source is enhanced by a factor of four relative to that of more cial scatter. Indeed, the [Na/Fe], [Al/Fe], [Si/Fe], and [Y/Fe] massive AGB stars.
versus [Fe/H] plots clearly show that the giant star sampleis shifted upwards with respect to the dwarf stars. Thus, the 3.3. Elemental Abundances of Solar Sibling Candidates magnitude of the star-to-star scatter of those elements is am- The abundance ratios relative to iron as a function of [Fe/H] plified by the fact that the analysis of dwarfs and giants is not for the elements that we measured are shown in Figure fully compatible. By examining the [Si/Fe] trends for giants Evolved stars, in our particular case defined as objects with and dwarfs separately, it is clear that the star-to-star scatter is log g < 3.5 (see Figure are shown separately from the in fact zero within the uncertainties. Therefore, Si is not auseful element in our context, but one could have been mis- 15 Note, however, that find only a weak Ba-age correla- led by the data if dwarfs and giants had not been examined tion in their study of open clusters.
RAM´IREZ ET AL.
In good agreement with the open cluster and solar analog studies, we find that most elements present a star-to-star scat- ter that is fully compatible with the measurement errors. The exceptions are the following species: Na, Al, V, Y, and Ba.
Hereafter, all other elements are combined into a single indi- In Figure we show elemental abundances, relative to H, on a star-by-star basis, separating the important elements in our context (Na, Al, V, Y, and Ba) from M (the combination of all other elements: O, Si, Ca, Sc, Ti, Cr, Mn, Co, and Ni).
A star with the same composition as the Sun must have all values in Figure around zero within the errors. Two stars stand out in this context: HD 154747 and HD 162826. Both have solar abundances within the errors, although the latter appears to have a slightly super-solar Ba abundance. Another interesting object is HD 28676, which appears to have a +0.1 offset in the abundances of all elements while retaining almost Figure 7. Physical minus spectroscopic parameters.
perfectly solar [X/Fe] abundance ratios. A similar pattern isexhibited by HD 93210, with the exception of its V abundance Figure shows the difference between physical and spec- that appears very high. The latter, however, could be due to an troscopic parameters for our sample stars. On average, they uncertain effective temperature (see below). From the chemi- are −97 ± 60 K for Teff, −0.12 ± 0.11 for log g, and −0.03 ± cal standpoint, these four objects are key solar sibling candi- 0.05 for [Fe/H] (physical minus spectroscopic). Although there are non-negligible systematic offsets in Teff and log g,the [Fe/H] values appear relatively robust, particularly for 3.4. Accounting for Systematic Errors stars with Teff . 6000 K. Depending on the spectral features In Section we described our method for deriving at- used, certain elements can be more sensitive to systematic er- mospheric parameters using only measurements of iron line rors in the stellar parameters. Thus, we re-examined Figure strength on our high resolution, high signal-to-noise ratio for the case of elemental abundances determined using phys- Stellar properties derived in this manner are of- ical parameters. None of the stars previously discarded as ten referred to as "spectroscopic parameters." Another com- solar sibling candidates, i.e., all but the four key targets men- mon approach to derive the fundamental stellar parameters tioned in the last paragraph of Section has its chemical Teff and log g involves the use of photometric data (colors) composition affected in such a way that it would resemble the and measured trigonometric parallaxes. The former allow solar abundances had we employed only physical parameters.
us to constrain Teff from color calibrations based on less There are in some cases important variations of the elemen- model-dependent techniques such as the infrared flux method tal abundances, but generally they are not larger than 0.1 dex.
(IRFM) or even temperatures measured directly from known Thus we conclude that systematic errors in the stellar param- stellar angular diameters and bolometric fluxes. Parallaxes, eters are important only for those objects which already have on the other hand, allow us to calculate absolute magnitudes near solar abundances (or at least near solar abundance ratios), of stars, which can then be employed along with theoretical but are not large enough to force us to re-consider the other isochrones to compute the stellar masses and thus have an- targets in our sample as potentially true solar siblings.
other way of estimating log g. The stellar parameters thus de- In addition to the potential systematic errors introduced by rived are sometimes referred to as "physical parameters." model parameter uncertainties, it is worth mentioning the pos- In order to assess the impact of systematic errors in our el- sibility that the photospheric composition of stars may be af- emental abundance measurements, we re-derived them using fected by planet formation processes. physical parameters, which were determined using the pro- have found that, relative to the majority of solar twin stars, cedure outlined in ). Briefly, Teff was the Sun is deficient in refractory elements by about 0.08 dex.
measured using as many photometric colors as available and They attribute this deficiency to the fact that the Sun formed the IRFM Teff-color calibrations by .
rocky planets, which retained those metals during the forma- Surface gravities were then inferred using the stars' Hippar- tion of the solar system. Similarly, have cos parallaxes and the Yonsei-Yale isochrone grid found that the secondary star in the 16 Cyg binary system, ; . All four physical parameters, here- which hosts a gas giant planet, is metal-poor relative to the pri- after referred to as T ′ , log g′, [Fe/H]′, and v′ mary, which does not appear to have sub-stellar mass compan- t , were de- termined iteratively until a final self-consistent solution was ions ). The observed metallicity differ- achieved, i.e., [Fe/H]′ and v′t were re-computed by forcing ence of about 0.04 dex (volatiles and refractories are equally the iron abundances to be independent of reduced equivalent depleted in this case) is also attributed to the formation of the width, but the excitation and ionization balance conditions planet, in this case a gas giant.
were relaxed. Errors in T ′ correspond to the color-to-color It is important to point out that other authors have found scatter, but weighted by the uncertainty of each color-Teff cal- conflicting results to the ones described above. In particu- ibration. The error in log g′ was estimated from the width of lar, based on an analysis of a stellar sample with a known the isochrone log g probability distribution (see Section 3.2 planet population, in for details). Finally, the uncertainty in argue that the connection to planet formation processes is [Fe/H]′ was computed by propagating the T ′ and log g′ errors weak, although their exoplanet host sample is admittedly bi- into the iron abundance calculations.
ased towards massive planets whereas the hy- SOLAR SIBLING CANDIDATES Fe <M> Na Al Fe <M> Na Al Fe <M> Na Al Teff, logg (spec.) = 5942K ,4.32 Teff, logg (phys.) = 5845K ,4.22 Teff, logg (spec.) = 6096K ,4.48 Teff, logg (phys.) = 6090K ,4.43 Teff, logg (spec.) = 6146K ,4.23 Teff, logg (phys.) = 5975K ,4.11 Teff, logg (spec.) = 5322K ,3.87 Teff, logg (phys.) = 5268K ,3.86 Teff, logg (spec.) = 6210K ,4.41 Teff, logg (phys.) = 6101K ,4.25 Fe <M> Na Al Fe <M> Na Al Fe <M> Na Al Figure 8. Chemical composition of our 5 key solar sibling candidates. Each row corresponds to one star, whose name is provided in the right-most panel. Left
panels: as in Figure i.e., elemental abundances obtained using spectroscopic parameters. Middle panels: as in the left panels, but for elemental abundances
derived using physical parameters. Right panels: average of "spectroscopic" and "physical" abundances. < M > represents the average of elemental abundances
for O, Si, Ca, Sc, Ti, Cr, Mn, Co, and Ni. An error bar of 0.1 dex, which we estimate as a conservative uncertainty for our abundances, including systematics, is
also shown in these panels.
pothesis concerns rocky bodies.
In any case, one should to the solar abundances. They are: HD 28676, HD 91320, keep in mind that the chemical abundance anomalies are still HD 154747, and HD 162826. As will be explained in Section present, and that regardless of their interpretation, they do HD 83423 is another interesting candidate, but purely on introduce systematic uncertainties in our context. Similarly, a dynamical basis. We add this star to our list of key targets ) have found no differences in chemical to emphasize certain points of our discussion.
composition between the two components of the 16 Cyg bi- The chemical compositions of our 5 key solar sibling can- nary system. While this discrepancy with the didates are re-examined in Figure The left panels show the results remains unresolved, another study, which employed same data plotted in Figure The middle panels correspond much higher quality data for these stars and independent mea- to the elemental abundances derived using physical parame- surements of the spectral features, has confirmed the slightly ters. The average values of "spectroscopic" and "physical" dissimilar chemical composition of the 16 Cyg stars (Tucci- chemical composition are shown in the right panels, along Maia et al., in preparation).
with our representative and conservative error bar of 0.1 dex.
From the discussion above, a conservative estimate of our The lower physical Teff values tend to shift the [X/H] [X/Fe] errors, including model systematics and the poten- abundances downwards, thus making the compositions of tial impact of planet formation on the surface composition of HD 28676 and HD 91320 more solar, as anticipated. Nev- stars, is ≃ 0.1 dex. The line-to-line scatter values listed in Ta- ertheless, the former has still a slightly super-solar overall bles and are not the dominant source of uncertainty for metallicity while the Na and V abundances of the latter still most elements.
depart from the other elements' nearly constant [X/H] value.
As explained above, HD 83423 is only included in our list 3.5. Key Targets of key targets due to its dynamical properties. Figure clearly In Section we listed four key targets for siblings of the shows that the composition of this object is very far from Sun based on the similarity of their metal abundance ratios solar, regardless of which set of atmospheric parameters is RAM´IREZ ET AL.
employed. Note that this is true even though the [Fe/H] and [M/H] parameters for this star can be considered fully consis- 0)2 fr0 tan i tent with the solar values. This finding stresses the importance of identifying and subsequently studying key elements as op- posed to simply measuring abundances of "as many elements χ(R) = − as possible" when it comes to the practical search of stars with common chemical abundance patterns.
Our adopted spiral wave parameters are: pitch angle i = The chemical composition of HD 154747 is solar for both −12◦, number of arms m = 4, phase of Sun χ0 = −120◦, sets of stellar parameters. The only marginally super-solar strength fr0 = 0.05, and velocity of spiral pattern Ωp = abundance is that of V, if derived with spectroscopic param- 20 km s−1 kpc−1. The circular speed at the solar radius (R⊙ = eters, but it becomes perfectly solar if physical parameters 8.0 kpc) is 220 km s−1 and the peculiar solar velocities are are employed instead. HD 162826 has a slightly super-solar (U⊙,V⊙,W⊙ = 10, 11, 7) km s−1 overall metallicity if the abundances are derived using spec- troscopic parameters, and a slightly sub-solar metallicity for The model described above allows us to compute encounter abundances inferred using its physical parameters.
parameters between the stellar and solar orbit in the past. In within the systematic (and observational) uncertainties, this particular, we can find the relative distance d and velocity dif- star also has a chemical composition that very closely resem- ference dV for the two orbits as a function of time in the past bles that of the Sun.
over a 4.5 Gyr age interval, i.e., the lifetime of the Sun. The Thus, from further examination of chemical abundances results for our five key targets are shown in Figures and and the potential impact of systematic errors, only two of our A quick inspection of Figures and clearly reveals that, key targets can be considered real solar sibling candidates: according to our model, the orbits of HD 28676, HD 91320, HD 154747 and HD 162826.
and HD 154747 have taken these stars far away from the Sunin the past. In general, the distance between these stars and 3.6. Dynamical Considerations the Sun has been shortening considerably. If these objects Our target list consists of stars previously suggested by were born also 4.5 Gyr ago, they may have formed 5–15 kpc other authors as solar sibling candidates based on their dy- away from the solar cluster. At that time, their velocities rela- namical properties and, in some cases, additional informa- tive to the solar motion would have been 30–50 km s−1. Thus, tion regarding age and metallicity. The criteria and associated the dynamics rule out these three stars as siblings of the Sun.
models employed by these authors are somewhat different.
Of these three objects, only HD 154747 passed our chemi- Also, the input radial velocities generally differ from those cal composition constraint. Not surprisingly, these findings derived in our work using our high-quality spectra. Thus, demonstrate that elemental abundance analysis alone is not it is important to re-assess the dynamical properties of our sufficient, and neither is the dynamical argument by itself.
targets in the context of a solar sibling search, in particular Both are required to make a proper solar sibling identifica- those of our five key solar sibling candidates, using a consis- tent model. In this work, we use the model by It is also not surprising that of all stars in our sample only , which is described below. The parallaxes and proper HD 83423 and HD 162826 passed the dynamical constraint, motions of stars were taken from the revised version of the at least in the sense that their d and dV parameters do not Hipparcos catalog .
diverge or oscillate with large amplitudes as time recedes.
Stellar and solar orbits were computed using the following They were the two best solar sibling candidates identified by Galactic potential: , whose model is employed in this work.
This shows that relatively small changes to the input radial ve- Φ = Φhalo + Φdisk + Φbulge + Φsp .
locities (we used those measured in our high-resolution, high The first three components are constructed as follows (e.g., signal-to-noise spectra, and not those previously published ): the halo is represented by and found in large RV compilations) have a minor impact on a logarithmic potential: these calculations.
As discussed in Section our chemical analysis quickly Φhalo = v20 ln 1+R2/d2 +z2/d2
, ruled out HD 83423 as a solar composition star. Its [Fe/H]value is certainly solar, as is its combined "M" abundance (i.e.
with v0 = 134 km s−1 and d = 12 kpc (R and z are cylindrical the average of O, Si, Ca, Sc, Ti, Cr, Mn, Co, and Ni) as well coordinates); the disk is represented by a Miyamoto-Nagai as its V abundance (see Figure . However, the star has a somewhat low (high) Na (Y) abundance, and a definitely too low (high) Al (Ba) abundance. The latter are irreconcilable R2 + (b + z2 + c2)2 with the solar values within any acceptable uncertainties instellar parameters.
This leaves us with only one true solar sibling candidate: d = 9.3 × 1010 M⊙, b = 6.5 kpc, and c = 0.26 kpc; and the bulge is modeled as a Hemquist potential: HD 162826. Its chemical composition is solar within the er-rors and its past orbit includes a number of close encounters r + a ≃ 10 pc) with the Sun which happened with relative ve- locities of about 10 km s−1 or less. The encounter parameters with Mb = 3.4 × 1010 M⊙ and a = 0.7 kpc.
are particularly favorable around t = −4 Gyr, i.e., at an epoch The following spiral wave component makes this Galactic when the solar cluster may have not fully dissipated yet.
gravitational potential model more realistic We did not consider the impact of interactions with field stars and/or giant molecular clouds in our model. Also, we ne- Φsp = Acos[m(Ωpt −θ)+ χ(R)] , glected the gravitational interaction between stars in the solar SOLAR SIBLING CANDIDATES Figure 9. Relative distance between the stellar and solar orbits as a function
Figure 10. Velocity difference between the stellar and solar orbits as a func-
of time in the past.
tion of time in the past.
proto-cluster. According to ), the and 4 arms, varying the pitch angle from −10 to −14 degrees Hipparcos data suggests a frequency of 2 stellar encounters for the 4-arm model and from −5 to −7 for the 2-arm model.
within one parsec for each 106 yr (1 Myr). After correcting The phase of the Sun relative to the spiral arm was varied from for incompleteness, this rate increases to about 12 per Myr.
−90 to −140 degrees, and the pattern speed was varied from One should keep in mind, however, that the orbit of a star 10 to 24 km s−1 kpc−1. The total number of models computed can change significantly only in very close encounters with is 900 for each star.
massive stars, which are rare and short-lived. The latter leads For HD 162826 we obtained past close encounters (d < to a significantly lower rate of encounters compared to M- 100 pc, ∆V < 50 km s−1, t < −3 Gyr) in 64 % of the mod- dwarfs. Indeed, the results from (cf.
els. On the other hand, HD 154747 shows this type of en- their Table 8) imply that for a period of 4 Gyr the Sun may counters in only 1.3 % of the models. Thus, within reason- have encountered, within 0.1 pc, only 1 or 2 B-type stars.
able model uncertainty, HD 162826 remains a good dynam- The theoretical calculations by are even ical solar sibling candidate, while it remains highly unlikely more reassuring; to change the velocity of a star by more than that HD 154747 was born near the Sun.
20 km s−1 in an encounter within 40 AU, the required timeperiod (∼ 1013 yr) is longer than the lifetime of our Galaxy.
3.7. Abundances of Trace Elements in HD 162826 Giant molecular clouds, on the other hand, affect the orbits of We use several of the rare earth elements to further test the Sun and nearby stars, including any potential siblings, at whether HD 162826 meets our chemical criteria for being a the same time. Therefore, in this case it is the differential (sig- solar sibling. In solar-type stars, these elements owe their ori- nificantly smaller) impact of such encounters that one would gin to both r-process and s-process neutron-capture reactions, need to take into consideration.
which reflect a different set of chemical evolution clocks than Our dynamical model has a number of input parameters, the lighter elements. We identify 17 lines of 4 species that are particularly those related to the spiral arms, which can be var- unblended in our spectra of the Sun and HD 162826. These ied within reasonable uncertainties to establish the degree of lines are listed in Table Abundances of La II, Ce II, Nd II, model dependency of our results. Given the demanding nature and Sm II are derived from spectrum synthesis using MOOG.
of these computations, we restricted them to two of our stars: Linelists were constructed using the HD 154747 and HD 162826, i.e., the two stars that have solar lists, using updated log g f values from recent laboratory stud- chemical composition. Orbit calculations were made with 2 ies when possible. We adjust the line strengths to reproduce RAM´IREZ ET AL.
Rare Earth Element Abundances References. — (1) (2) (3) (4)
; (5) ; (6) a Spectroscopic model parametersb Physical model parameters Mean Line-by-Line Rare Earth Element Abundance Differences HD 162826a − Sun HD 162826b − Sun a Spectroscopic model parametersb Physical model parameters the solar spectrum and then use these lists without change for 3.8. High-precision Radial Velocity Data for HD 162826 the analysis of HD 162826. Table lists the wavelength, exci- HD 162826 is included in the target sample of 250 F, G, tation potential (EP), and log g f value for each transition, al- K, and M-type stars of the McDonald Observatory planet though the transition probabilities cancel out in a differential search program at the Harlan J. Smith 2.7 m Telescope (e.g., analysis. Our syntheses account for hyperfine splitting (hfs) and isotope shifts (IS) for several of these lines. We adopt the This long-term radial velocity (RV) survey is designed to solar isotopic fractions given by for the Sun probe the population of gas giant planets beyond the ice line and HD 162826. The derived abundances are listed in Table at several AU. Such planets presumably have not migrated in- Table lists the mean line-by-line differential abundances be- wards from the location of their formation. Figure displays tween the Sun and HD 162826. Two sets of values are given, the 15 years of precise RV measurements of HD 162826. The one using the set of spectroscopic model atmosphere parame- 50 RV data points have an overall rms-scatter of 6.0 m s−1 ters for HD 162826 and one using the set of physical values.
and an average error of 5.4 m s−1. The star is constant at the Using spectroscopic parameters, the La, Ce, and Nd are 6 m s−1 level and does not seem to have a massive planetary very similar to the Ba abundance, i.e., slightly supersolar companion with a period of < 15 years. Also, there is no clear (≃ +0.08). However, using physical parameters, all these el- evidence of binarity.
ements have solar abundances in HD 162826 within the in- We computed the upper limits on detectable planets in the ternal error. The Sm abundance is also solar within the er- RV data for HD 162826. The detection limit was determined rors if we employ the physical parameters, but super-solar at by adding a fictitious Keplerian signal to the data, then at- +0.14 dex using spectroscopic parameters. The average of tempting to recover it via a generalized Lomb-Scargle peri- these abundances (excluding Sm), as derived using both sets odogram . Here, we have as- of parameters, is about +0.02 dex, i.e., solar within both sys- sumed circular orbits; for each combination of period P and tematic and internal errors. Of all elements studied in this RV semi-amplitude K, we tried 30 values of orbital phase.
work for HD 162826, only Sm appears to depart from the so- A planet is deemed detectable if 99% of orbital configura- lar abundances, with a spectroscopic/physical average value tions at a given P and K are recovered with a false-alarm of +0.09. However, considering our conservative estimate of probability ) of less than 1%. This 0.1 dex of systematic error, this value may be marginally con- approach is essentially identical to that used in the work by sistent with the solar Sm abundance.
. The resulting mass SOLAR SIBLING CANDIDATES Only the star HD 162826 (HR 6669, HIP 87382) satisfies both our dynamical and chemical criteria for being a true sib- ling of the Sun. This object, a late F-type dwarf star located at about 34 pc (∼ 110 light years) from the Sun in the con- stellation Hercules, is bright (V = 6.7) and easily observable with small and medium-sized telescopes. High-precision ra-dial velocity observations carried out over a period of time longer than 15 years rule out the presence of hot-Jupiter plan- ets. These data also suggest a 2/3 chance that a Jupiter ana-log is not present either. Smaller terrestrial planets cannot beruled out at this moment.
The mass of HD 162826, estimated from the location of the star on the HR diagram compared to Yonsei-Yale isochrones JD - 2400000 (days) (as in ), is 1.15 M⊙. If this star were the Figure 11.
Relative radial velocity as a function of Julian Date for only solar sibling in the 1.1 to 1.2 M⊙ range, the HD 162826. The radial velocities in this plot are given with respect to the ) initial mass function would suggest the existence of weighted mean of all observed values.
another ∼ 400 solar siblings of mass greater than 0.1 M⊙ dis- persed throughout the Galaxy. Since the number of stars in the solar cluster is estimated to be 103 − 104, this implies that there should be just a few other solar siblings of ∼ 1 M⊙ present in the solar neighborhood. On the other hand, this means that there are a few hundred M-dwarfs that are also siblings of the Sun within 100 pc. Unfortunately, the detailed chemical composition analysis of M-dwarfs that would be re- quired to identify them is currently beyond our capabilities.
The combination of astrometric data from the ongoing Gaia Mission and spectroscopic data from surveys of comparable large size such as the ESO-Gaia survey, APOGEE, and/orGALAH will allow us to discover many more solar siblingsin a very near future. We expect that the analysis presented in this paper will guide future endeavors in this field and allow us to perform these searches more efficiently.
Figure 12.
Mass limits for single planets in circular orbits around HD 162826. Planets with parameters in the region above the solid line wouldhave been recovered with 99 % probability at a false-alarm-probability of less I.R. acknowledges support from NASA's Sagan Fellowship Pro- gram to conduct most of the observations presented in this paper.
limits are shown in Figure Clearly, hot Jupiters, i.e., plan- A.T.B and V.V.B.'s work is supported by the "Nonstationary Phe- ets with masses comparable to that of Jupiter in short-period nomena in Objects of the Universe" Programme of the Presidium of orbits, can be ruled out.
the Russian Academy of Sciences and the "Multiwavelength Astro- To determine the probability that an undetected Jupiter- physical Research" grant no. NSh-16245.2012.2 from the President mass planet orbits HD 162826, we repeated the detectabil- of the Russian Federation. D.L.L. thanks the Robert A. Welch Foun- ity simulations described above for a range of recovery rates dation of Houston, Texas for support through grant F-634. The Mc- (10%.90%) as in . For a Jupiter- Donald Observatory exoplanet survey is currently supported by the mass planet in a Jupiter-like (12 yr) circular orbit, we estimate National Science Foundation under grant AST #1313075. Previous a 35 % probability that such a planet is present based on the support for this project was given by the National Aeronautics and non-detection from our RV data.
Space Agency through the Origins of Solar Systems Program grantsNNX07AL70G, NNX09AB30G and NNX10AL60G.
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