Galactic Orbits of Hipparcos Stars: Classification of Stars
aa r X i v : . [ a s t r o - ph . GA ] O c t Galactic Orbits of Hipparcos Stars:Classification of Stars
G. A. Gontcharov and A. T. Bajkova
Pulkovo Astronomical Observatory, Russian Academy of Sciences, St.-Petersburg, Russia
Abstract —The Galactic orbits of 27 440 stars of all classes with accurate coordinatesand parallaxes of more than 3 mas from the Hipparcos catalogue, proper motions fromthe Tycho-2 catalogue, and radial velocities from the Pulkovo Compilation of Radial Ve-locities (PCRV) are analyzed. The sample obtained is much more representative thanthe Geneva–Copenhagen survey and other studies of Galactic orbits in the solar neigh-borhood. An estimation of the influence of systematic errors in the velocities on orbitalparameters shows that the errors of the proper motions due to the duplicity of stars aretangible only in the statistics of orbital parameters for very small samples, while the errorsof the radial velocities are noticeable in the statistics of orbital parameters for halo stars.Therefore, previous studies of halo orbits may be erroneous. The distribution of starsin selection-free regions of the multidimensional space of orbital parameters, dereddenedcolors, and absolute magnitudes is considered. Owing to the large number of stars andthe high accuracy of PCRV radial velocities, nonuniformities of this distribution (apartfrom the well-known dynamical streams) have been found. Stars with their peri- andapogalacticons in the disk, perigalacticons in the bulge and apogalacticons in the disk,perigalacticons in the bulge and apogalacticons in the halo, and perigalacticons in thedisk and apogalacticons in the halo have been identified. Thus, the bulge and the haloare inhomogeneous structures, each consisting of at least two populations. The radius ofthe bulge has been determined: 2 kpc.
Using the stellar coordinates α and δ , parallaxes π from the Hipparcos catalogue (vanLeeuwen 2007), proper motions µ from the Tycho-2 catalogue (H¨og et al. 2000), andradial velocities V r allows not only the complete set of coordinates X , Y , Z and velocitycomponents U , V , W , but also the Galactic orbits of stars to be calculated.Because of the small number of stars with accurate V r and because of the distrustin the joint use of µ and V r , the Galactic orbits have been investigated so far only forsmall lists of stars, as a rule, obtained with the same instrument. Since the samples areincomplete, the studies of the orbits for stars that do not belong to the Galactic disk areparticularly poor.The appearance of the Pulkovo Compilation of Radial Velocities for 35 493 Hipparcosstars (PCRV; Gontcharov 2006), in which the systematic errors of V r were taken intoaccount and all the main classes of stars are represented, allows one to set the task ofcomprehensively studying the statistical characteristics of samples of stars based on theirGalactic orbits by invoking their metallicities and ages.The PCRV is still the largest source of V r with included systematic errors. The medianaccuracy of V r from the PCRV is 0.7 km s.1; V r is more accurate than 5 km s.1 for all stars.The PCRV includes the values of V r from 203 catalogues for which the systematic errors1etected in them were taken into account. These include the two largest present-daycatalogues: the Geneva–Copenhagen survey (GCS) of more than 14 000 stars mostly oftypes FV–GV near the Sun (Nordstr . om et al. 2004; Holmberg et al. 2007, 2009) and thekinematic survey of more than 6000 KIII–MIII stars based on CORAVEL observations(Famaey et al. 2005). The velocity components and Galactic orbits for 11 218 starscalculated in the GCS are used in this study to check the results, while the metallicitiesFe/H for 11 615 stars and the ages for 10 249 stars calculated in the GCS will be usedin our subsequent studies of the age–kinematics and metallicity–kinematics relations forvarious groups of stars. The sample considered below is limited in parallax, π > π <
3, leaving most ofthe stars in the sample (28 600, 80.6%), corresponds to a space where the PCRV issufficiently representative. In addition, the accuracy of the components µ α cos δ and µ δ for the overwhelming majority of PCRV stars is higher than 3 mas yr − . This valuecorresponds to the accuracy of V r used (higher than 5 km s − ) at a distance of 333 pc.The limitation of the sample at this distance makes it homogeneous with regard to theaccuracy of the velocity components U , V , W . It is also important that, according toour numerical simulations (see Gontcharov 2012a), the Lutz–Kelker and Malmquist biasesare negligible under the mentioned limitation in π . These are the biases of the sample’sstatistical characteristics, primarily the distances and absolute magnitudes of the starsbeing determined, that arise when the sample is limited in measured parallax and/or inobserved magnitude (Perryman 2009, pp. 208–212).In addition to π > σ ( π ) /π < . σ ( µ α cos δ ) < σ ( µ δ ) < − (37 stars were lost), and the accuracies of the Tycho- 2 photometryare σ ( B T ) < . m and σ ( V T ) < . m (243 stars were lost). The final sample contains 27440 stars.More severe limitations, for example, σ ( π ) /π < . σ ( µ α cos δ ) < σ ( µ δ ) < − , leave 25 082 stars in the sample. In this case, all of the conclusionsreached in this study remain valid and all of the categories of stars found are identifiedwith no lesser confidence. However, a considerable number of bulge and halo stars thatare few anyway are lost under severe limitations. Therefore, here we give preference tothe mentioned mild limitations to exclude only the stars whose data do not allow themto be classified.The dereddened color ( B T − V T ) was calculated for each star:( B T − V T ) = ( B T − V T ) − E ( B T − V T ) , (1)where the reddening E ( B T − V T ) = A V T /R V T ≈ . A V / . R V . The coefficients in thisformula were calculated by taking into account the extinction law from Draine (2003); theextinction A V was calculated from our 3D analytical extinction model (Gontcharov 2009,2012b) as a function of the trigonometric distance r = 1 /π . and Galactic coordinates l and b , while the extinction coefficient R V was calculated from the 3Dmap of its variations2s a function of the same coordinates (Gontcharov 2012a).The absolute magnitude M V T was calculated for each star from the formula M V T = V T + 5 − r − A V T . (2)The positions of our 27 440 sample stars on a Hertzsprung–Russell (H–R) diagramof the form “( B T − V T ) – M V T ” are shown in Fig. 1a. The sample under considerationcontains almost all GCS stars with accurate data and a similar diagram for them is shownin Fig. 1b. It can be seen that, following the PCRV and in contrast to the GCS, allclasses, including the main sequence (MS), the red giant clump and branch, supergiants,subgiants, subdwarfs, red dwarfs, and one white dwarf, are represented in the sample. Theline indicates the theoretical zero-age main sequence (ZAMS) from the Padova databaseof evolutionary tracks and isochrones (http://stev.oapd.inaf.it/cmd; Bressan et al. 2012),which was fitted with an accuracy (about 0.1m) sufficient for the subsequent analysis bythe polynomial Y = 5 . X − . X + 21 . X − . X + 5 . X + 1 . , (3)where X = ( B T − V T ) , Y = M V T . The cross indicates typical errors, σ (( B T − V T ) ) =0 . m and σ ( M V T ) = 0 . m , for an individual star. It can be seen that cloud of points ofMS stars is located mainly to the right and above the ZAMS, as it must be. However, inthe range 0 m < ( B T − V T ) < . m , which roughly corresponds to the spectral type AV,the well-known deviation of the cloud from the shown ZAMS is noticeable. This deviationwill be discussed in a separate study.The Galactic orbits of the stars under consideration were calculated using the Galacticpotential from Fellhauer et al. (2006) and Helmi et al. (2006): Φ = Φ halo + Φ disk + Φ bulge .In this case, • the halo was represented by a potential dependent on the cylindrical Galactic coor-dinates R and Z as Φ halo ( R, Z ) = ν ln(1 + R /d + Z /d ), where ν = 134 km s − and d = 12 kpc; • the disk was represented by the potential from Miyamoto and Nagai (1975) as afunction of the same coordinates: Φ disk ( R, Z ) = − GM d ( R + ( b + ( Z + c ) / ) ) − / ,where the disk mass M d = 9 . · M ⊙ , b = 6 . c = 0 .
26 kpc; • the bulge was represented by the potential from Hernquist (1990): Φ bulge ( R ) = − GM b / ( R + a ), where the bulge M b = 3 . · M ⊙ and a = 0 . r = 8 kpc for the Sun was taken to be 220 km s − .The solar motion relative to the local standard of rest was taken to be ( U = 10, V = 11, W = 7) km s − based on the results by Bobylev and Bajkova (2010) in agreement withthe results by Sch¨ o nrich et al. (2010) and Gontcharov (2012d).The key characteristics of the calculated orbits are the peri- and apogalactic distancesdesignated below as r min and r max , respectively, the orbital eccentricity e , and the largestdistance of the orbit from the Galactic plane Z max . Let us estimate the influence of errors in V r and µ on r min , r max , e and Z max .For double and multiple stars, the observed component or photocenter can move overthe celestial sphere nonlinearly. For visual binary stars (resolved systems), this occurs3ue to the orbital motion of the components or because one of them falls or does notfall within the field of view. For astrometric binaries (unresolved systems), this occursdue to the orbital motion of the system’s photocenter relative to the barycenter. In bothcases, the variability of at least one of the components can also have an effect. AlthoughVityazev et al. (2003) showed an insignificant influence of the orbital motions in starpairs on the stellar kinematics, let us estimate this influence by a different method.The proper motions from catalogues with a large difference of epochs (e.g., more than50 years for Tycho-2), a small difference of epochs (e.g., 3.5 years for Hipparcos), and theorbital motions were compared, for example, by Gontcharov et al. (2001) and Gontcharovand Kiyaeva (2002). It follows from this comparison that precisely the orbital motionsare responsible for the large differences of µ in such catalogues as Hipparcos and Tycho-2and that here it is more appropriate to use µ from Tycho-2. Their replacement by . fromHipparcos when calculating the Galactic orbits just reflects the influence of the orbitalmotions in star pairs. The standard deviation of the differences between . from Tycho-2and Hipparcos for the stars under consideration is 1.8 mas yr − . The values of r min , r max , e and Z max calculated using µ from Tycho-2 and r ′ min , r ′ max , e ′ and Z ′ max calculated using µ from Hipparcos differ insignificantly: the standard deviations of the differences are σ ( r ′ max − r max ) = 0 .
15 kpc, σ ( r ′ min − r min ) = 0 . σ ( e ′ − e ) = 0 . σ ( Z max − Z ′ max ) = 0 . V r on it itself (probably primarily due to the scale error andthe tilt of the focal plane when the distances between spectral lines were measured), onthe ( B − V ) color (probably primarily due to the differences between the measured andcomparison spectra), and on the celestial coordinates α and δ (probably primarily due tothe seasonal correlations between the celestial coordinates, the instrument’s temperature,and the hour angle) in the original catalogues. For the original catalogues produced withsimilar instruments, similar systematical dependences were found in the PCRV. For exam-ple, the GCS and the results by de Medeiros and Mayor (1999) obtained with the identicalCORAVEL spectrometers give coincident (within the accuracy limits) dependences of V r on V r , ( B − V ), and α , as shown in Fig. 1 and Table 3 from Gontcharov (2006).To model the influence of systematic errors in V r , we calculated the orbits using aradial velocity distorted by errors: V ′ r = V r + 2 . B − V ) − . B − V ) + 0 . V r − . α − .
04 cos( α + 0 .
7) + 1 . , (4)where V ′ r and V r are in km s − , ( B − V ) is in magnitudes, and α is in radians. Thisformula reflects the errors found by Gontcharov (2006) in the GCS (an error was madein the text of the paper when the PCRV was published but not in the calculations: thereshould be cos( α + 0 .
7) or cos( α + 40 ◦ ) if the phase is in degrees instead of the publishedcos( α − ◦ )).For the stars under consideration, the difference | V ′ r − V r | from Eq. (4) can reach 2.3km s − , which is approximately triple the median random error of V r in the PCRV.In our analysis, it makes sense to model the errors by Eq. (4) instead of using r min , r max , e and Z max directly from the GCS, because these errors, as follows from our com-parison of the GCS and the results by de Medeiros and Mayor (1999), also extend to thespectral types of stars earlier than F and later than G, which are virtually absent in the4CS. In addition, the GCS results differ from the results of this study due to the differ-ences not only in radial velocities but also in distances and extinction estimates, while wewant to estimate the influence of only the errors in V r .The values of r min , r max , e and Z max calculated using V r and r ′ min , r ′ max , e ′ and Z ′ max rcalculated using V ′ r differ insignificantly for disk stars and markedly for halo stars, i.e., forstars with r max >
20 and Z max >
4. Consequently, the systematic errors of V r affect thestatistical results of analyzing the Galactic orbits of only the halo stars due to the smallnumber of these stars in the sample. Thus, either a careful allowance for the systematicerrors in V r or sample completeness is needed to analyze the Galactic orbits of halo stars.Obviously, both conditions are violated in most of the previous studies of the halo orbits.The mean value of the differences r ′ max − r max , just as of the remaining orbital param-eters, is zero. The standard deviations of the differences are σ ( r ′ max − r max ) = 0 .
44 kpc, σ ( r ′ min − r min ) = 0 .
03 kpc, σ ( e ′ − e ) = 0 . σ ( Z ′ max − Z max ) = 0 .
08 kpc. A direct compari-son of the orbital parameters from the GCS with those obtained here gives the mean valuesof the differences ∆ r max = 0 .
19 kpc, ∆ r min = 0 .
08 kpc, ∆ e = 0 . Z max = − .
05 kpcand their standard deviations σ (∆ r max ) = 0 .
35 kpc, σ (∆ r min ) = 0 .
19 kpc, σ (∆ e ) = 0 . σ (∆ Z max ) = 0 .
15 kpc. The noticeable differences between the modeling and the real GCSfor σ ( r ′ min − r min ) = 0 .
03 versus σ (∆ r min ) = 0 .
19 kpc and σ ( Z ′ max − Z max ) = 0 .
08 versus σ (∆ Z max ) = 0 .
15 kpc are caused by the differences in distance and extinction estimatesin this study compared to the GCS.Here, we considered the main sources of systematic errors and, in addition, can es-timate the random errors of the orbital parameters based on the errors in the observedquantities. In our subsequent analysis of the results, typical total error estimates aremarked in the figures. They are determined mainly not by the random errors of thevelocities but by their systematic errors, which should not be ignored.
Figures 1c and 1d show the positions of the sample and GCS stars, respectively, on the“( B T − V T ) – e ” diagram; Figs. 1e and 1f, 1g and 1h, and 1i and 1j show their positionson the “( B T − V T ) – r max ”, “( B T − V T ) – r min ”, and “( B T − V T ) – Z max ” diagrams,respectively (the orbital parameters in Figs. 1d, 1f, 1h, and 1j were taken directly fromthe GCS).It can be seen that all categories of stars except FV–GV are represented in the GCSmuch more poorly than they are in the sample under consideration, although the distri-bution has the same structure.The dashed lines in Figs. 1c, 1e, 1g, and 1i indicate an approximate separation ofthe stars into six categories by their evolutionary status and membership in Galacticsubsystems. Below, we analyze separately • B T − V T ) < . m , below referred to as the OA subsample), •
12 600 stars with 0 . m < ( B T − V T ) < . m (mostly FV–GV, below referred to asthe FG subsample), • B T − V T ) > . m (mostly K–M with a large fraction of giants,below referred to as the KM subsample).The results for the FG subsample can be compared with those from the GCS. Eachsubsample was divided in the figure by the horizontal dashed line approximately into stars5ith eccentric orbits (halo and bulge stars) and with more circular orbits (disk stars, sofar without any separation into the thin and thick disks, given that this separation hasrecently been called into question (Bovy et al. 2012)).The present-day theory of stellar evolution suggests that hot subdwarfs (evolved starsmainly with reactions in the helium core, i.e., on the horizontal giant branch), cool subd-warfs (unevolved low metallicity dwarfs near the MS) and low-mass branch giants domi-nate among the high-eccentricity stars of the OA, FG, and KM subsamples, respectively.It can be seen that there are much more high-eccentricity stars in the FG subsample thanin the remaining subsamples. This could not be affected by the sample selection in r and V T , because the absolute magnitudes of hot and cool subdwarfs are approximately equal,while giants are seen even at a greater distance. Most of the high-eccentricity stars we ob-serve theoretically have a mass smaller than 0.8 Solar mass. Therefore, the predominanceof cool subdwarfs is explained by the fact that only the oldest and low-mass metal-poorstars have managed to become giants in the lifetime of the Galaxy, while the majorityremain near the MS.For nonsingle stars in Hipparcos, the orbital parameters, π and µ were determinedjointly from directly observed quantities, the abscissas on the reference great circle. Theorbital motion can distort the observed π predominantly in the direction of its increase.When the angular measure is converted to the linear one, the measured µ then turn outto be smaller than the true ones due to the erroneous distance. As a result, the calculatede is larger than the true one and disk stars demonstrate the orbits of halo or bulge stars.This effect should manifest itself irrespective of ( B T − V T ) . However, the significantlynonuniform distribution of halo and bulge stars on ( B T − V T ) seen in Fig. 1 suggeststhat this effect is absent.The following effects are less pronounced in Fig. 1 but important. The small numberof high-eccentricity stars in the range 0 . m < ( B T − V T ) < . m corresponds to thetheory of subdwarfs (Gontcharov et al. 2011). A local minimum in the scatter of orbitalparameters for disk stars is reached at ( B T − V T ) ≈ . m , while this scatter in the range0 . m < ( B T − V T ) < . m increases sharply.Applying the more stringent star selection criteria σ ( π ) /π < . σ ( µ α cos δ ) < σ ( µ δ ) < − , which leave only 25 082 stars in the sample, does not changequalitatively the distribution of stars on the diagrams of Figs. 1a, 1c, 1e, 1g, and 1i. Asan example, Fig. 2 presents the “( B T − V T ) – r min ” (a) and “( B T − V T ) – Z max ” (b)diagrams for 25 082 sample stars with the above stringent selection criteria, which areworth comparing with Figs. 1g and 1i, respectively. Comparison of Orbital Parameters
Figure 3 shows the distribution of stars from the OA subsample on the (a) “ r max – e ”,(b) “ Z max – e ”, (c) “ r min – e ”, (d) “ r min – Z max ”, (e) “ r max – r min ”, and (f) “ r max – Z max ”diagrams. Here, the limitations due to the sample selection by r and V T are noticeable.For example, the selection in Fig. 3c manifests itself in the correlation between r min and e . Despite the selection, some conclusions are possible.As expected, the overwhelming majority of stars from the OA subsample are younglow-eccentricity stars. Indeed, Gontcharov (2012d) found a correlation between the ageand ( B T − V T ) for stars near the MS with ( B T − V T ) < . m : T = 0 . e . B T − V T ) , (5)6hich agrees well with that from the GCS data. According to this formula, the OA-subsample stars near the MS ( >
80% of the subsample) have ages younger than 1.34Gyr and nearly circular orbits ( e < . r max <
10 kpc, r min > Z max < . r min ≈ r max ≈ r min < e > . . < r max < . . < r max < . r max . Consequently, there is a physical cause oftheir absence. The separation of bulge stars into at least two groups should be admitted.However, there are different Z max and F e/H in each of these groups and the stars fromthe groups occupy approximately the same region of the H–R diagram, being known orsuspected hot subdwarfs (the blue part of the horizontal branch). The only detecteddifferences are related to the difference in r max : the group with larger r max has larger ab-solute values of the velocity component | U | >
150 km s − and is in the longitude octantsof the Galactic center and anticenter, while the group with smaller r max has | U | <
150 kms − and is at longitudes far from the center–anticenter line. The distribution of bulge starsin apogalactic distances are possibly subjected to density waves and other dynamical pro-cesses, as are the dynamical, predominantly radial Sirius (Ursa Major), Pleiades, Hyades,Coma Berenices, α Cet/Wolf 630, Hercules, and other steams (Gontcharov 2012c, 2012d).We then see two groups of bulge stars that are dynamically associated with two spiralarms. Judging by the mean r max for the stars from these groups that are not too far fromthe Galactic plane, these arms are at Galactocentric distances of 8.3 (the arm near theSun) and 11.6 kpc, respectively. Obviously, the group of stars with 3 . < r min < . . < e < .
42 is then also isolated in Fig. 3c not by selection but by the dynamicalprocesses that associated it with the arm nearest to us ( r max = 8 . e < . < r min < < r max <
10 kpc, and Z max < . e > . Z max > r max >
15 kpcon the graphs of Fig. 4 is particularly noticeable. Because of the selection effect, not somuch the regions of enhanced star density in the figure as the voids between them thatare surrounded by stars and, therefore, that did not result from selection are important.Judging by the almost complete absence of stars with 2 < Z max < < Z max < e > . r min < . < Z max <
13 kpc,the halo group with 0 . < e < .
75, 7 < r min < < r max < < Z max <
21 kpc,and two more groups are identified with lesser confidence:group 3 with 0 . < e < .
8, 3 . < Z max < . < r min < . . < e < .
55, 3 < Z max < . . < r min < . e , the perigalacticon falls into the bulge). Selection probablyhid the halo stars with approximately circular orbits whose existence is not ruled out.Judging by the absence of intermediate stars with 1 . < r min < r min < Z max < r min < e > .
6, i.e., with the apogalacticons in the disk, is identified among the stars withtheir perigalacticons in the bulge. Thus, we see the separation of the bulge stars intostars with disk and halo kinematics. Of particular importance is the absence of starswith intermediate 2 < Z max < r min ≈ r max ≈ e < . Z max < Z max ≈ r min < Z max < . Z max > Z max = 2 . rbital Parameters and Luminosity Some categories of stars can be revealed by the deviation of their M V T from theZAMS specified by Eq. (3). We will consider this deviation from the ZAMS .MVT tobe negative for high-luminosity stars (e.g., branch giants) and positive for low luminositystars (subdwarfs and white dwarfs).Figure 7 shows the distribution of stars from the OA and KM subsamples on thefollowing diagrams: “∆ M V T – e ” (a) and (b), respectively; “∆ M V T – r max ” (c) and (d),respectively; “∆ M V T – r min ” (e) and (f), respectively; “∆ M V T – Z max ” (g) and (h),respectively. The solid vertical straight line marks .MVT = 0m and the dashed straightline marks .MVT = 1m, which corresponds to a 2. error in calculating M V T .The star HIP 14754 with .MVT = 8.1m is the only white dwarf in the sample and ismarked in the figure by the large circle.The hot subdwarfs known from spectroscopy are marked in Figs. 3a, 3c, 3e, and 3g bythe squares. Those of them that belong to the bulge ( r min < e > .
6) and two starsin the adjacent regions on the graphs (2 < r min < . . < e < .
6) have a highluminosity (∆ M V T < m ). As has been pointed out above, although their perigalacticonsare in the bulge, judging by their kinematics they belong to the disk ( Z max < . Z max > M V T > m ) and belong to the disk ( e < . Z max < . × yr, and a mass of more than 0 . M ⊙ , the horizontal branch appears as aclump of giants at 0 . m < ( B T − V T ) < . m . The horizontal branch becomes bluer withdecreasing metallicity, increasing age, and decreasing mass to the extent that it turns outto be near the MS (blue horizontal branch) or even considerably bluer and lower than theMS(extremely blue horizontal branch) at F e/H < − .
8, an age older than 13 × yr,and a mass of less than 0 . M ⊙ . The corresponding stars are classified as sdA, sdB, andsdO. Thus, the main path of a star’s transformation into a hot subdwarf is a very lowmetallicity or an age older than that of the Galactic disk or very fast evolution due to thelarge mass loss on the giant branch. The less common paths of fast evolution of low-massstars into the region of hot subdwarfs are related to mass transfer in a close star pair orother ways of the addition or removal of stellar material (for references, see Gontcharovet al. 2011). In any case, the existence of hot subdwarfs in the Galactic thin disk is farfrom an unambiguous explanation.The group of thin-disk BV stars exhibiting a low luminosity that stands out in thefigure with ∆ M V T > m , e ≈ . r max ≈ . r min ≈ . Z max ≈ .
05 kpcmay have a bearing on this problem. A detailed analysis of their characteristics fromthe Strasbourg database shows that they are all located in two regions of ongoing starformation, in Orion and near the star ρ Oph at distances 200 < r <
300 pc. Both regionsare known to exhibit small-scale variations in extinction coefficient R V and interstellarextinction. For example, the popular 3D analytical extinction model by Arenou et al.(1992) for a field in Orion at this distance gives A V ≈ m , while the 3D model byGontcharov (2009, 2012b) gives A V ≈ . m . Both values are appreciably higher thanthe typical A V estimates at these distances in other directions. It is the large value of9he adopted A V that gives a very blue dereddened color (( B T − V T ) for the stars underconsideration according to Eq. (1). As a result, the stars turned out to be well belowthe MS in its blue part. It should be noted that the extinction model and the 3D map of R V variations used give E ( B T − V T ) for these stars that are smaller than other sources ofestimates. Consequently, the derived low luminosity of these stars cannot be explained bythe erroneous extinction and R V estimates and should be investigated additionally. Themost plausible explanations are: either the peculiarity of the medium and BV stars on theMS in the star-forming regions causes them to appear as low-luminosity stars on the H–Rdiagram, for example, due to an anomalously high extinction (this explanation appearsmore plausible) or they are actually not BV stars but hot sdB subdwarfs and the mediumof the star-forming regions aids the formation of such stars. Indeed, an especially intensemass loss on the giant branch, including that due to an external stellar wind at smalldistances between the stars, the presence of a close component for mass transfer, and ahigh spatial and physical density of clouds supplying hydrogen into the stellar envelopethat has already used it up contribute to the formation of a hot subdwarf.The subdwarfs from the OA subsample will be studied in detail separately after thecollection of data on their metallicity.In the KM subsample in Figs. 7b, 7d, 7f, and 7h, we see the separation into giants(∆ M V T < − m ) and dwarfs (∆ M V T > − m ). The overwhelming majority of both giantsand dwarfs belong to the disk ( e < . r min > Z max < . r min < M V T > m and, thus, are probably cool low-metallicity subdwarfs in the disk. As expected, the KMsubsample contains almost no cool subdwarfs due to selection. However, the tendencyfor ∆ M V T to increase with increasing e and decreasing r min caused by a drop in meanmetallicity should be noted for both bulge giants and dwarfs ( e > . r min < e < . r min > Z max < M V T > − m ) and giants (∆ M V T < − m ) with their perigalacticons inthe bulge ( r min < Z max > M V T < m , they have alow luminosity (∆ M V T > m ). This makes them similar to the KM subsample stars anddistinguishes them from the hot subdwarfs of the OA subsample.There are five halo stars with their perigalacticons outside the bulge in the FG sub-sample: the previously mentioned halo group. Their small number in the subsample isexplained by the fact that the FG dwarfs have a low luminosity and are not visible fromafar, while the horizontal-branch giants with (( B T − V T ) < . m , i.e., with F e/H < − . F e/H > − . B T − V T ) > . m ,and there are probably no such stars in the halo. Out of these five stars, HIP 103311 is adwarf, while HIP 92 167, 85 855, 71 458, and 62 747 are horizontal-branch low-metallicitygiants. All of their characteristics confirm that they belong to the halo, with the interval10 . m < ∆ M V T < − . m populated by these stars just corresponding to the location ofthe horizontal branch relative to the MS for the F and G types. Therefore, the entireisolated group of stars with − . m < ∆ M V T < − . m , Z max > r max >
12 kpcprobably consists of horizontal-branch low-metallicity giants. It can be seen from Fig. 8that these stars are absent in the GCS and were first detected as an isolated group in thisstudy.Gontcharov et al. (2011) found no cool disk subdwarf (with e < . e < . M V T >
1. The FG subsample contains several suchstars. Analysis of their characteristics from the Strasbourg database shows that they areall young nonsingle and variable stars in starforming regions rather than subdwarfs.
We analyzed the Galactic orbits of 27 440 stars of all classes with accurate α , δ and π > µ from the Tycho-2 catalogue, and V r from thePulkovo Compilation of Radial Velocities (PCRV). The detection of systematic errors in V r when the PCRV was created and the noticeable difference between . from Tycho-2 andHipparcos caused by the orbital motions in star pairs forced us to estimate the influenceof these errors on orbital parameters: the peri- and apogalactic distances r min and r max ,the eccentricity e , and the largest distance of the orbit from the Galactic plane Z max . Wefound that the errors of µ due to the duplicity of stars are tangible only in the statisticsof orbital parameters for very small samples (fewer than 10 stars), while the errors of theradial velocities are noticeable in the statistics of orbital parameters for stars far from theSun, i.e., halo stars. The sample considered here is much more representative than theGeneva–Copenhagen survey with regard to F–G stars that do not belong to the disk andexceeds considerably any other sample for O–A and K–M stars. This allows our study tobe considered as the largest survey of Galactic orbits in the solar neighborhood to date.Note that the derived orbital parameters agree with those from the GCS for the samestars.Here, we analyzed the distribution of stars in the multidimensional space of orbitalparameters, dereddened colors, and absolute magnitudes so far almost without invokingthe stellar metallicities and ages (this will be done in a subsequent paper). Since thesample is limited in parallax and apparent magnitude, many of the groups of stars (forexample, halo stars with circular orbits) cannot appear in it. However, even our analysisof selection-free regions of this multidimensional space allowed us to establish a nonuni-formity of the distribution of stars in it and to identify several groups. First of all, thisstudy allowed the radius of the bulge to be determined (2 kpc) and showed that thebulge and the halo are not homogeneous subsystems of the Galaxy. The stars with theirperigalacticons in the bulge are clearly divided into stars with their apogalacticons in thehalo and the disk, while the stars with their apogalacticons in the halo are divided intostars with their perigalacticons in the bulge and the disk. Thus, instead of the evidencefor the membership of a star in a subsystem, the evidence for which subsystem the peri-galacticon and apogalacticon of its orbit are located in is more informative. Therein maylie the difference in the origin of stars: in the Galaxy or in the accreted satellites.The nonuniformity of the distribution of bulge stars with their apogalacticons in thedisk in apogalactic distances may be explained by the dynamical association of these stars11ith spiral arms.Our investigation showed that using Galactic orbits is promising. In future, they canbe applied to calculate the statistical characteristics of the disk and, by invoking thestellar metallicities and ages, for a detailed analysis of the bulge and the halo. We used resources from the Strasbourg Astronomical Data Center (Centre de Donn´eesastronomiques de Strasbourg). This study was supported by Program P21 of the Presid-ium of the Russian Academy of Sciences and the Ministry of Education and Science ofthe Russian Federation under contract no. 8417.
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