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ISSN 1063-7729, Astronomy Reports, 2023, Vol. 67, No. 3, pp. 288–293. © The Author(s), 2023. This article is an open access publication. Russian Text © The Author(s), 2023, published in Astronomicheskii Zhurnal, 2023, Vol. 100, No. 3, pp. 297–302. O. Yu. Malkov* Institute of Astronomy, Russian Academy of Sciences, Moscow, 119017 Russia *e-mail: malkov@inasan.ru Received December 31, 2022; revised January 14, 2023; accepted January 24, 2023 Abstract—The hypothesis that the Sun is a component of a binary star system has been around for about a hundred years. Assumptions about the nature of the companion continue to be published as new observa- tional data become available. The paper shows that the results of the work of the Gaia space observatory impose certain restrictions on the nature and location of the companion. The fact that the companion is not registered by the observatory leaves the following marginal possibilities: a cool brown dwarf (Y3 and later) in an orbit inside the Oort cloud, or an L/T brown dwarf in a higher orbit (from a ≈ 10 AU). At the same time, the companion is quite likely cataloged in the 2MASS and WISE surveys. We also provided estimates for the absolute G-magnitudes of brown dwarfs of late spectral types. Keywords: binary stars, Solar System, brown dwarfs DOI: 10.1134/S1063772923030046 1. INTRODUCTION 5 companion of the Sun—is about AU, see discus- The question of whether the Sun has a companion sion in Section 3); and was first raised about a hundred years ago [1]. As can- • (iv) features of the orbits of Sedna and other didates for a companion of the Sun, both known trans-Neptunian objects caused by the presence of the objects (46 Tau [1]) and hypothetical ones, whose Sun’s companion [5, 6, 16]. presence could be confirmed by indirect signatures, In a number of papers, attempts were made to indi- were considered: a relativistic object [2], a black dwarf cate the boundaries for the possible values of the com- [3], and a brown dwarf [4]. These works are also panion and orbit parameters or even to estimate them related to studies of the question of whether the Sun [3, 6, 16–18]. Assumptions were made about the pres- has an unknown companion with a planetary mass ence of the desired object in modern large infrared [5‒7]. photometric surveys (IRAS, 2MASS, and WISE) [6, Among the possible indicators of the presence of a 16, 19]. companion near the Sun, the following were consid- With the advent of preliminary results from the ered: Gaia astrometric space observatory, it became possi- • (i) acceleration of the barycenter of the Solar ble to refine the characteristics of this hypothetical System, leading to anomalous changes in the period of object. The fact that the Gaia observatory has not (yet) pulsars located in a certain direction in the sky [8, 9]; discovered the Sun’s companion places certain • (ii) an abundance of comets with hyperbolic restrictions on its nature and location. orbits caused by the gravitational inf luence of a com- This paper investigates the possibility of the exis- pact massive object (neutron star or black hole) [10] or tence and detection of a brown dwarf, a possible com- even a high speed solar mass object [11]. Note that at panion of the Sun. Its limiting parameters, the possi- present, only one comet with a hyperbolic orbit has ble distance from the Sun and the magnitude of its been 100% recorded, namely, comet 2I/Borisov [12, proper motion are estimated. A comparison is made 13] (also known is the interstellar asteroid 1I/’Oumua- both with real wide binary systems and with the esti- mua [14] and moving, with a certainty of 99.999%, mates of other authors investigating this issue. along the perbolic orbit CNEOS meteor 2014-01-08 [15]); 2. OBSERVED WIDE BINARIES • (iii) the presence of a cycle duration of 26 × 10 years in biological mass extinctions, which are First of all, we determine what values of the orbital supposed to be caused by intense comet showers [3] parameters and parameters of the components have (the expected boundary of the Oort cloud—a reservoir the widest of the observed binary systems with known of comets that can be perturbed by a hypothetical orbital elements. The most authoritative source of 288 GAIA ARGUMENTS FOR AND AGAINST A HYPOTHETICAL SUN COMPANION 289 Table 1. Orbital and physical parameters of wide binary Table 2. Absolute magnitudes of cold dwarfs systems Band , Gaia , 2MASS , 2MASS , WISE G H Ks W 1 Parameters WDS 01522–5220 WDS 00524–6930 M9.5 16.40 11.00 10.50 10.15 P, 10 yr 5.607369 5.8 L5 18.50 12.44 11.87 11.19 a, arcsec 76.6 170 ± 11 T4.5 21.0 4 14.49 14.55 12.97 e 0.999 0.74 ± 0.02 Y2 32.2 22.6 23.5 18.1 Spect. type K3V + M9.5 F7 IV–V ϖ , mas 11.5431 ± 0.0122 16.5718 ± 0.0163 The source of the values M for the M9.5 and L5 stars a , AU 6637.78 10 259.5 was Mamajek tables published in [28]. Data on M a , pc 0.0322 0.0 497 and M for brown dwarfs T4.5 and Y2 are taken from Ks d , pc 0.0644 0.0865 max the same tables. To estimate the values M and M for the last two G W 1 information about such systems is the catalog of spectral types, we used the catalog of brown dwarfs orbital binaries ORB6 [20]. About a dozen of the 3310 closest (up to 20 pc) to the Sun 525 L, T, and Y [29]. It stars contained in ORB6 can be called very wide pairs contains data for the WISE photometric system, and to estimate the -values, we identified the cataloged (having a period P >10 years and/or semi-major axis sources with the Gaia DR3 archive. The identif ication a > 100″). was carried out with the identification radius 1″. We Not all of these objects will be considered in this managed to identify 132 objects out of 496. Two study. As shown in works on determining the masses of objects, 2MASS 0915+0422 and 2MASS 1520–4422, the components of orbital binaries [21, 22], the WDS each received two analogues in Gaia DR3, in both 23100+3651 system can be suspected of optical bina- cases the one located closer to the source object was rity, while others (WDS 14396–6050, WDS 07204– recognized as suitable. Further analysis included a 5219) show a discrepancy between the dynamic mass comparison of the proper motions and parallaxes values determined by Kepler’s third law, and photo- found in [29] with the Gaia data, as well as the con- metric masses determined from the brightness of the struction of various photometric relationships components, the distance to the system, and the between the G-value and the photometry presented in mass–luminosity ratio. For the WDS 19464+3344 [29]. As a result, five objects (2MASS 0355+1133, and WDS 00057+4549 systems, ORB6 provides three WISE 0715–1145, WISE 0720–0846B, DENIS 1253– rather different orbital solutions each. 5709, and Gaia 1831–0732) were found to be incor- For our purposes, we can consider double WDS rectly identified and discarded. 00524 6930 and WDS 01522 5220. Their parameters The identif ication results are shown in Fig. 1. It can are given in Table 1. Orbital elements (P , A , and e ) are be seen that objects of spectral types no colder than T6 taken from ORB6, spectral classification from WDS were found in the Gaia archive, and that although the [23] and SIMBAD, parallaxes from Gaia DR3. The limiting magnitude of Gaia objects reaches semi-major axes in linear units and the maximum dis- G ≈ 21.25 , however, the limiting brightness required tance between the components da≈+(1e ) are max estimated here. to determine the parallax is at the G ≈ 20.75 level. The results obtained can be used to obtain at least a rough relationship between the G-value of an object 3. ABSOLUTE MAGNITUDES OF BROWN and its brightness in the infrared bands H (2MASS) DWARFS AND THE POSSIBILITY OF THEIR DETECTION and J (2MASS). Figure 2 shows all identified objects with , , and photometry, as well as the result of G H J This section lists (both published and obtained in linear approximation, this paper) the absolute magnitudes of brown dwarfs. (1) GH = 1.363 + 1.358, To estimate the brightness of the companion at dif- ferent distances from the main component (the Sun), GJ = 1.235 + 1.918, (2) it is necessary to know the absolute magnitude of the object M . Table 2 contains the absolute magnitudes are the correlation coefficients in formulas (1) and in several photometric bands of the Gaia [24, 25], (2)—0.97 and 0.96, respectively. The object 2MASS 2MASS [26], WISE [27] surveys for the case when the 0746+2000 (the brightest in the diagrams) has the companion is a cold red dwarf (M9.5), a hot brown dwarf (L5), a warm brown dwarf (T4.5) and a cool http://www.pas.rochester.edu/emamajek/EEM_dwarf_UBVI- JHK_colors_Teff.txt brown dwarf (Y2). ASTRONOMY REPORTS Vol. 67 No. 3 2023 290 MALKOV 0 0 0 5 10 15 20 25 17 18 19 20 21 Sp type G Fig. 1. Identification of brown dwarfs from the catalog [29] with the Gaia DR3 archive. Left panel: distribution of brown dwarfs by spectral type (red—all stars and green—identif ied with Gaia). The spectral type is def ined as follows: 0—L0, …, 5—L5, …, 10— T0, …, 20—Y0, … . Right panel: distribution of identified objects by brightness (red—all, blue—no parallax value in Gaia). G G 11 12 13 14 12 13 14 15 16 H J Fig. 2. Identif ied brown dwarfs in the HG − (left) and JG − (right) diagrams. Straight lines are the results of linear approximation according to formulas (1) and (2). attribute VARIABLE in the Gaia DR3 archive and did extinction was assumed to be negligible. It can be seen not participate in the approximation. that a brown dwarf later than Y3 will not be detected by the Gaia observatory, even if it is inside the Oort cloud. Extrapolating these ratios to the region of low tem- Here it is considered that the inner boundary of the peratures, it is possible to estimate the absolute G-val- Oort cloud is at a distance of 2–5 thousand AU from ues of T and Y type brown dwarfs (in the Mamajek the Sun, and the outer one is 50–100 thousand AU table, these values are given only for L8 and hotter). This estimate is shown in Fig. 3, left panel. It is note- (see, for example, [30]; see also the site on the NASA worthy that in the region of hot brown dwarfs, our data portal). At the same time, this hypothetical brown are in good agreement with Mamajek data. dwarf will def initely be included in the 2MASS catalog The data obtained make it possible to estimate the (red curve; here we consider that 2MASS is full up to limiting distance at which a brown dwarf of one type or J = 16.5 ) and even more so in WISE. Hotter objects another will be detected by the Gaia observatory (L and T dwarfs) need to be located outside the Oort (Fig. 3, right panel). was used as the limiting G.75 https://solarsystem.nasa.gov/solar-system/oort-cloud/overview/ magnitude for Gaia observation, and interstellar ASTRONOMY REPORTS Vol. 67 No. 3 2023 GAIA ARGUMENTS FOR AND AGAINST A HYPOTHETICAL SUN COMPANION 291 M d, AU 1e7 1e6 1e5 1e4 0 5 10 15 20 0 5 10 15 20 Sp type Sp type Fig. 3. Left panel - absolute magnitudes of brown dwarfs. The red curve is an approximation of values M (2MASS) from the Mamajek table, the green curve is the values M (Gaia) calculated by Eq. (2), and the blue dots are the values M (Gaia) from G G the Mamajek table. The right panel shows the limiting distance for the band 2MASS (red curve) and the band Gaia DR3 J G (green curve), where brown dwarfs can be observed. Objects located below these curves should fall into the corresponding views. The horizontal stripes are the approximate positions of the inner (yellow) and outer (grey) boundaries of the Oort cloud. The principle of encoding the spectral types of brown dwarfs is similar to that given in the caption to Fig. 1. cloud in order not to fall into the Gaia observational and r are expressed in units of ″/year, km/s, and pc, archive. respectively. Such a noticeable proper motion would immedi- ately highlight the object in the astrometric survey, but 4. PROPER MOTION at the same time it would make it extremely diff icult to cross-identify it between photometric surveys, even It seems appropriate to estimate the magnitude of with a small difference in observation epochs. the proper motion of a cold brown dwarf, a satellite of the Sun, located in the region of the inner boundary of the Oort cloud. The orbital velocity at any instant of 5. BLACK DWARFS time can be written as The term “black dwarf” does not have a clear quan- titative definition. Moreover, in the literature, this v=( Gm+− m) . (3) ( ) concept refers to two completely different types of ra objects. Here, the gravitational constant G = 6.6743 × ‒11 3 –2 –1 1. Stars of very low mass (mm <0.08 ), which do 10 m s kg , mm , are the masses of the compo- not pass through the stage of the thermonuclear reac- nents: kg, and the mass of the mm==1.989 ×10 tion of burning hydrogen, become completely degen- component m can be neglected. Let’s take the current 2 erate objects or black dwarfs in a time much shorter distance to the companion r as 2000 AU (= 3 × than the age of the Galaxy [31]. 10 m), and for the semi-major axis a consider 2. Old white dwarfs that have cooled their outer lay- options ra = (circular orbit) and ra =1.9 (compan- ers to several thousand degrees and have a luminosity ion is located in the vicinity of the aphelion of a very −5 of the order of 10 L or less are also called black eccentric orbit). Then the orbital velocities estimated dwarfs [32]. This process is much longer; formulas for from (3) for these two cases will be 665.2 and estimating the parameters of these objects can be 210.4 m/s. Proper motion, found in [33]. Obviously, if the Sun’s companion is a black dwarf, (4) μ=, 4.74r then the probability of its detection is greatly reduced. Note, however, that a black dwarf of the “second type” in these cases it will be equal to 14.5 and 4.6″/year, (former white dwarf), in contrast to a black dwarf of respectively (compare with the proper motion of Bar- the “first type” (former brown dwarf), has a mass that nard’s star, 10.4″/year). In Eq. (4), the values μ, v , should not be neglected when estimating the proper ASTRONOMY REPORTS Vol. 67 No. 3 2023 292 MALKOV motion of such an object. Assuming that the compan- makes its detection by modern astrometric and photo- ion has a mass equal to the Sun, the values given in metric methods practically impossible. The paper also Section 4 should be increased by 40%. obtained an empirical dependence M (SpT) for brown dwarfs. 6. COMPARATIVE ANALYSIS ACKNOWLEDGMENTS Let us compare the estimates made here with those observed and predicted by other authors. The author is grateful to the anonymous reviewer, whose Note that the binary system “Sun–brown dwarf remarks made it possible to significantly improve the con- Y3" discussed at the end of Section 3 would be very tent of the article. We used data from the Gaia DR3 archive similar to the systems WDS 01522–5220 and WDS and from the ADS, SIMBAD, and VizieR databases. This 00524–6930 described in Section 2 and would be even study used TOPCAT, a tool for interactive graphical viewing more compact. and editing of tabular data [34]. The authors of [3] suggest that the Sun has a com- −4 panion, a black dwarf with a mass from 21 × 0 to FUNDING −2 71 × 0 m , in a very eccentric (e ≥ 0.9) orbit with The work was supported by the Ministry of Education and Science of the Russian Federation, project no. 13.2251.21.0177. semi-major axis a≈× 8.8 10 AU. As follows from Fig. 3 (right panel), it is unlikely that such an object could be included in the Gaia archive and existing OPEN ACCESS infrared surveys. This article is licensed under a Creative Commons Attri- In [17], in order to determine the boundaries of the bution 4.0 International License, which permits use, sharing, Solar System, hypothetical satellites of the Sun were adaptation, distribution and reproduction in any medium or considered in a wide mass range, from 0.005 to 0.3 format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Com- in orbits with semi-major axis a ≈× 910 AU. In this mons license, and indicate if changes were made. The images case, obviously, the probability of detection depends or other third party material in this article are included in the on the mass of the object. article’s Creative Commons license, unless indicated other- Finally, in [16], a relationship was proposed wise in a credit line to the material. If material is not included between the mass of a hypothetical object and the in the article’s Creative Commons license and your intended major semiaxis of its orbit: mm / ≈ 5 9000 AU/a . use is not permitted by statutory regulation or exceeds the It can be seen that in these studies, the emphasis permitted use, you will need to obtain permission directly was mainly on high (above the Oort cloud) orbits for from the copyright holder. To view a copy of this license, visit the hypothetical companion of the Sun. In [19], how- http://creativecommons.org/licenses/by/4.0/. ever, lower orbits were also considered, but they dealt with objects of planetary masses, (1–5) m . However, REFERENCES as the analysis performed in this paper shows, under certain conditions, a companion, a brown dwarf, can 1. W. J. Luyten, Harvard College Observ. Bull. 814, 2 also exist in low orbit (below the Oort cloud) and (1925). remain unnoticed by the Gaia observatory and unrec- 2. S. Pineault, Nature (London, U.K.) 275, 727 (1978). ognized (although possibly present) in modern infra- 3. D. P. Whitmire and A. A. Jackson, Nature (London, red photometric surveys. U.K.) 308, 713 (1984). 4. J. J. Matese, in Planetary Systems in the Universe, Pro- ceedings of the IAU Symposium No. 202, Manchester, 7. CONCLUSIONS UK, August 7–11, 2000, Ed. by A. Penny, Proc. IAU The paper considers the restrictions on the nature Symp. 202, 214 (200 4). and characteristics of the hypothetical component of 5. R. S. Gomes, J. J. Matese, and J. 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Astronomy Reports – Springer Journals
Published: Mar 1, 2023
Keywords: binary stars; Solar System; brown dwarfs
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