Michelson Science Center, California Institute of Technology, 770 South Wilson Avene, MS 100-22, Pasadena, CA 91125. Received 2003 September 2; ...
The Astrophysical Journal, 600:L71–L73, 2004 January 1 䉷 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.
A SUBSTELLAR COMPANION TO VAN MAANEN 2 Valeri V. Makarov Michelson Science Center, California Institute of Technology, 770 South Wilson Avene, MS 100-22, Pasadena, CA 91125 Received 2003 September 2; accepted 2003 November 20; published 2003 December 12
ABSTRACT The Hipparcos data for the nearest white dwarf van Maanen 2 (pHIP 3829; distance of 4.4 pc) indicate astrometric binarity, in that the proper motion has a large first derivative not accounted for as a perspective acceleration due to changing distance. The presence of a companion was suspected, but never demonstrated, from the pre-Hipparcos astrometric measurements of photographic plates. Inspection of a digital position probability chart based on the Hipparcos Intermediate Astrometry Data reveals a pendulum-like motion of the photocenter mostly in the east-west direction with a period of about 1.5 yr. Having this period as an initial constraint, an orbital fit was obtained with the following parameters: a 0 p 27 mas, P p 1.57 yr, i p 89⬚, q p 95⬚, Q p 92⬚, and T0 p 1991.26. Assuming a mass of 0.83 M, for the primary white dwarf, the mass of the secondary is 0.08 M,. Covariance analysis shows, however, that the uncertainty of the semimajor axis estimate and, subsequently, of the mass estimate is great for this nearly edge-on orbit. A more robust estimate is obtained for the semiminor axis, providing a lower bound mass of the companion of 0.06 Ⳳ 0.02 M,. Subject headings: astrometry — binaries: general — stars: individual (van Maanen 2) — stars: low-mass, brown dwarfs — white dwarfs metric precision. This acceleration provides an upper limit for the semimajor axis a as a function of parallax, its error, and the secondary mass M2 (Kaplan & Makarov 2003). For this star, we derive a ≤ 10冑M2 in AU. A substellar companion as small as 0.01 M, can produce a measurable astrometric excursion of the primary of about 2.5 mas. To further investigate the character of the orbital motion of the primary, a digital probability chart is constructed, based on the Hipparcos Intermediate Astrometry Data (HIAD). The HIAD contains, for each Hipparcos star, a list of preprocessed and compressed astrometric observations gathered during the 3.5 yr span of the mission operation. A few individual transits of the star across the main grid of the instrument were combined to produce a single condition equation that links the five basic unknowns (position and proper motion components and parallax) with the measured and weighted residuals. The residuals are computed with respect to a certain reference point, whose position at any time is determined by the five reference astrometric parameters given in the main catalog and in the header record. Even if the actual number of parameters used in the solution was larger than five (as in the case of van Maanen 2), the reference point and the residuals are determined by the five basic parameters only. The first two coefficients of each condition equation can be understood as direction cosines of the scan motion. Since Hipparcos observations were intrinsically one-dimensional, at each transit, the observed position of the star can, with the same probability, be anywhere along a line perpendicular to the scan direction. Thus, the probability that the star is at a given location can be visualized, from a single transit, with a straight stripe whose intensity is constant along its axis and proportional to a Gaussian with the given standard error across. The distance between the center of the stripe and the reference point is equal to the specified residual. Several subsequent transits at different scan angles can be combined (with the given weights) to produce a two-dimensional digital map, somewhat similar to conventional astronomical images. The intensity of light at each point of such a map (called the position probability chart in the following) is pro-
1. INTRODUCTION
The star van Maanen 2 (HIP 3829) is listed in the Hipparcos catalog as a star with acceleration (ESA 1997, Double and Multiple Systems Annex, Acceleration Solutions). The measured acceleration is (m˙ a∗, m˙ d ) p (⫺33.87, 6.41) Ⳳ (9.71, 7.36) mas yr⫺2. Since the star, at a distance of 4.4 pc, is one of the 100 nearest stars, corrections of perspective acceleration due to the changing distance were used in the astrometric reductions (ESA 1997, Vol. 1, pp. 32–33) assuming a radial velocity of ⫺38 km s⫺1. The expected perspective acceleration of the star, with the Hipparcos proper motion (ma∗, md ) p (⫺1233.05, ⫺2710.56) Ⳳ (4.72, 3.67) mas yr⫺1, is just (⫺0.011, 0.024) mas yr⫺2, orders of magnitude smaller than the observed acceleration. It is evident that no error in the assumed radial velocity (which could arise from, e.g., the uncertainty of the gravitational redshift) can account for the observed acceleration of proper motion. Besides, the directions of the observed acceleration and the expected perspective acceleration are mismatched. We conclude that the observed acceleration is a sign of orbital motion caused by the gravitational pull from a companion. Since only the right ascension component of the observed acceleration is statistically significant (at a 0.9995 confidence level), the orbital perturbation mostly takes place in this component. Some problems with the Hipparcos astrometric solution for van Maanen 2 were noted by Dravins, Lindegren, & Madsen (1999), who could not identify the star in the AC 2000 catalog while attempting to determine its perspective acceleration. Dravins et al. (1999) assumed that the Hipparcos proper motion was in error, without giving any supporting evidence. S. Urban (2003, private communication) identified the star in the AC 2000.2, UCAC-2, and a few other ground-based astrometric catalogs and derived a long-term proper motion consistent with the Hipparcos value within a few milliarcsecond per year. He also noted a larger scatter of position residuals in the right ascension component with respect to the extrapolated Hipparcos astrometry. An acceleration can be measured with a given instrument when the corresponding curvature of the observed segment of the orbital path is large enough in comparison with the astroL71
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Fig. 1.—Position probability charts for van Maanen 2 integrated over 0.5 yr periods. North is up, and east is left. Positions calculated from the orbital fit are indicated with dark dots (see text).
portional to the probability that the star was at that location during the selected interval of time. A position probability chart for van Maanen 2, integrated over 0.5 yr periods from the beginning of the mission, is given in Figure 1. Each window is 81 mas on a side, with the reference point at the crosshair. The lighter spots indicate the most probable locations, which may be elongated because of a small range of scan angles and uneven weights. The chart clearly indicates a pendulum-like motion of the star in the west-east direction with a semiamplitude of about 20 mas. Since the star seems to return to the westernmost position every three integration intervals, the period of oscillation is roughly 1.5 yr. By a least-squares method, minimizing the weighted quadratic sum of residuals, the following orbital fit was obtained: astrometric excursion a 0 p 27 mas, eccentricity e p 0.67, period P p 1.57 yr, inclination i p 89⬚, periastron longitude q p 95⬚, node Q p 92⬚, and periastron epoch T0 p J1991.26. The reduced x 2 over 42 accepted observations (out of 46) is 1.02 in the original Hipparcos solution (but without acceleration components), and 0.53 with the orbital solution, a reduction of 48%.1 According to the F-test with (7, 30) degrees of freedom, the formal confidence in this orbital fit is 0.995, that is, the probability that the orbital fit is bogus is 0.005. Adopting a mass of 0.83 M, for the white dwarf component from Bergeron, Leggett, & Ruiz (2001) and a parallax of 227 mas from Hipparcos, the total mass of the system is about 0.9 M,, and the secondary mass is 0.08 Ⳳ 0.03 M,. The expected semiamplitude of the radial velocity of the primary star is 0.5 km s⫺1. Covariance analysis shows, however, that the solution for the astrometric semimajor axis a 0 is quite uncertain for this orbit seen almost edge-on, with the periastron directed toward us. The eccentricity is very poorly determined since the orbit is elongated along the line of sight. In mathematical terms, the uncertainty of a 0 stems from a large correlation of this parameter with the ec1 The expected reduced x2 for a normal, unperturbed solution should be well below unity as a result of the positive correlations between the observations provided by the Northern Data Analysis Consortium (NDAC) and the Fundamental Astrometry by Space Techniques (FAST) consortium.
centricity (0.94) and the indeterminacy of the latter (0.67 Ⳳ 0.51). In other words, we do not know the true eccentricity of the orbit. Similar cases of ill-conditioned orbital fits are discussed in Pourbaix (2002). On the other hand, the observed astrometric excursion is close to the projected semiminor axis. Rewriting the condition equations in terms of the semiminor axis a s, a robust estimate of a s p 20 Ⳳ 4.7 mas was obtained with standard errors and correlations given in Table 1. In computing the covariance matrix, correlations between the NDAC and FAST observations were taken into account, as described in van Leeuwen & Evans (1998). If the true eccentricity is 0, the lower bound mass of the secondary is M2 p 0.06 Ⳳ 0.02 M,. Since eccentricities higher than 0.67 (corresponding to M2 p 0.08 M,) are perhaps unlikely, we conclude that van Maanen 2 has a companion of substellar mass. This 3.67 billion year old substellar companion should be very dim compared with the primary star, so the photocenter effects are negligible. Two of the four images of van Maanen 2, obtained on 1997 October 1 with the Hubble Space Telescope Near-Infrared Camera and Multi-Object Spectrometer, available through the Multimission Archive Space Telescope database, seem to indicate a red companion about 7⬙ northwest of the star, which corresponds to ∼30 AU, but the close and dim astrometric companion, with its maximum separation of only 0⬙. 3, could not be resolved with that instrument. An astrometric companion to van Maanen 2 has long been suspected from photographic measurements. Van de Kamp (1971) reported some perturbation in the standard plate coordinate y (corresponding to the west-east direction) from observations collected from 1937 to 1970 and suggested an orbital motion with a period of about two decades. Gatewood & Russell (1974) also found that the standard error in y was 1.4 times larger than in h from Allegheny plates covering 1917–1922 and 1949–1973 but could not find a periodic motion, possibly because they also were looking for a long-period orbit. More recently, Dahn et al. (1988) discussed this problem but did not notice any orbital motion in their 3.4 yr parallactic measurements at USNO.
TABLE 1 Orbital Parameters, Standard Errors, and Covariances Parameter
Value
Standard Error
Correlations
as (mas) . . . . . . P (yr) . . . . . . . . e .............. T0 (yr) . . . . . . . . q (deg) . . . . . . . Q (deg) . . . . . . . i (deg) . . . . . . .
20 1.57 0.67 1991.26 95 92 89
4.7 0.14 0.51 0.24 10 10 4
… 0.39 0.07 ⫺0.46 ⫺0.22 ⫺0.38 0.09
Note.—a0 p 27 Ⳳ 18 mas.
… 0.56 ⫺0.94 ⫺0.67 ⫺0.06 0.09
… ⫺0.56 ⫺0.80 ⫺0.22 0.20
… 0.75 0.10 ⫺0.10
… 0.18 ⫺0.36
… ⫺0.16
No. 1, 2004
COMPANION TO VAN MAANEN 2
N. Zacharias is thanked for his advice on photographic plate astrometry issues. S. Urban kindly provided identification and
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proper-motion analysis of van Maanen 2 based on a collection of astrometric catalogs at USNO.
REFERENCES Bergeron, P., Leggett, S. K., & Ruiz, M. T. 2001, ApJS, 133, 413 Dahn, C. C., et al. 1988, AJ, 95, 237 Dravins, D., Lindegren, L., & Madsen, S. 1999, A&A, 348, 1040 ESA. 1997, The Hipparcos and Tycho Catalogues, ed. M. A. C. Perryman (SP-1200; Noordwijk: ESA) Gatewood, G., & Russell, J. 1974, AJ, 79, 815
Kaplan, G. H., & Makarov, V. V. 2003, Astron. Nachr., 324, 419 Pourbaix, D. 2002, A&A, 385, 686 van de Kamp, P. 1971, in IAU Symp. 42, White Dwarfs, ed. W. J. Luyten (Dordrecht: Reidel), 32 van Leeuwen, F., & Evans, D. W. 1998, A&AS, 130, 157
