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The Astronomical Journal, 145:41 (12pp), 2013 February C 2013.

doi:10.1088/0004-6256/145/2/41

The American Astronomical Society. All rights reserved. Printed in the U.S.A.

DETERMINATION OF ORBITAL ELEMENTS OF SPECTROSCOPIC BINARIES USING HIGH-DISPERSION SPECTROSCOPY 1

Noriyuki Katoh1 , Yoichi Itoh2 , Eri Toyota3 , and Bun’ei Sato4

Graduate School of Science, Kobe University, 1-1 Rokkoudai, Nada-ku, Kobe, Hyogo 657-8501, Japan 2 Nishi-Harima Astronomical Observatory, Center for Astronomy, University of Hyogo, 407-2 Nishigaichi, Sayo, Sayo, Hyogo 679-5313, Japan 3 Kobe Science Museum, 7-7-6 Minatojimanakacho, Chou-ku, Kobe, Hyogo 650-0046, Japan 4 Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan Received 2012 May 2; accepted 2012 December 3; published 2013 January 11

ABSTRACT Orbital elements of 37 single-lined spectroscopic binary systems (SB1s) and 5 double-lined spectroscopic binary systems (SB2s) were determined using high-dispersion spectroscopy. To determine the orbital elements accurately, we carried out precise Doppler shift measurements using the HIgh Dispersion Echelle Spectrograph mounted on the Okayama Astrophysical Observatory 1.88 m telescope. We achieved a radial-velocity precision of ∼10 m s−1 over seven years of observations. The targeted binaries have spectral types between F5 and K3, and are brighter than the 7th magnitude in the V band. The orbital elements of 28 SB1s and 5 SB2s were determined at least 10 times more precisely than previous measurements. Among the remaining nine SB1s, five objects were found to be single stars, and the orbital elements of four objects were not determined because our observations did not cover the entire orbital period. We checked the absorption lines from the secondary star for 28 SB1s and found that three objects were in fact SB2s. Key words: binaries: spectroscopic – stars: solar-type – techniques: radial velocities Online-only material: extended figure, machine-readable and VO tables

that radial-velocity precision is less than 300 m s−1 . However, few studies have reexamined previous measurements of radial velocities of binary systems using the new techniques. In this study, we redetermined the orbital elements of 37 single-lined spectroscopic binaries (SB1s) and 5 double-lined spectroscopic binaries (SB2s) using high-precision measurements of their radial velocities. The radial velocities were measured with the 1.88 m telescope at the Okayama Astrophysical Observatory (OAO) using the HIgh Dispersion Echelle Spectrograph (HIDES; Izumiura 1999). We achieved a radial-velocity precision of ∼10 m s−1 using an iodine cell. In Section 2, we present the targets of our radial-velocity measurements. We describe the observations and data analysis in Section 3. In Section 4, we redetermine the orbital elements of our targets and estimate the masses of the primary and secondary stars. Finally, we discuss individual objects and the period–eccentricity distribution of the sample in Section 5.

1. INTRODUCTION More than half of the solar-like stars in the solar neighborhood are generally accepted to exist in binary systems (Duquennoy & Mayor 1991; Raghavan et al. 2010). The accurate value of binary system mass ratios and orbital elements is important for understanding the formation and evolution of binary systems. Several observations have revealed the distinctive aspects of binary systems. Duquennoy & Mayor (1991) pointed out that the mean eccentricities for disk population stars and halo population stars are similar, indicating that the mean eccentricity of binaries is independent of system age. However, for the short-period binaries, tidal interactions circularize the orbit of the secondary star (Burki & Mayor 1986; Duquennoy & Mayor 1991). The cutoff period is defined as the longest orbital period of a circularized binary system. All binaries with periods shorter than the cutoff period have circular orbits. The cutoff period is ∼6 days in the Hyades and Praesepe clusters (Mayor & Mermilliod 1984). In the M67 cluster, this period is as long as 10 days (Mathieu & Mazeh 1988). Meibom & Mathieu (2005) suggested the cutoff period as an increasing function of population age. The cutoff period indicates the amount of dissipation of the orbital angular momentum of the secondary star. Several characteristics are also predicted by theory. On the topic of orbital evolution, Koch & Hrivnak (1981), Mathieu & Mazeh (1988), and Zahn & Bouchet (1989) estimated the circularization timescales of binary orbits. To determine the orbital elements accurately, precise radialvelocity measurements are required. Until 1980, the precision of radial-velocity measurements was as large as 1000 m s−1 because only 10–100 stellar lines were used to determine the radial velocities. These measurements might miss binaries with radial-velocity amplitudes of less than 2.0 km s−1 . Since the 1980s, radial-velocity measurement techniques have improved through new methods such as cross-correlation spectroscopy, so

2. TARGET STARS We selected 48 SB1s and 22 SB2s from the Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Systems (Batten et al. 1989) and the Ninth Catalogue of Spectroscopic Binary Orbits (Pourbaix et al. 2004). The targets are mainsequence stars whose spectral types are between F5 and K3. Early-type and late-type main-sequence stars are not included in the sample due to their large rotational velocities and low apparent magnitudes. The targets had to be brighter than the 7th magnitude in the V band to achieve a Doppler shift measurement precision of better than 10 m s−1 . The separations of the targeted binaries are not over 10 AU. We selected targets whose declinations were larger than −16◦ to observe them at OAO. Among these targets, 37 SB1s and 5 SB2s have sufficient radial velocity measurements to calculate their orbital elements (Table 1). 1

The Astronomical Journal, 145:41 (12pp), 2013 February

Katoh et al.

Table 1 Targets of the Radial Velocity Measurements

object was observed an average of 20 times. We also observed 70 Vir, β Vir, and ι Per as radial-velocity standard stars. 70 Vir is known to have one planet (Marcy & Butler 1996). β Vir and ι Per are stable in radial velocity. We measured the radial velocities using an iodine absorption cell (I2 cell; Kambe et al. 2002). The I2 cell is a glass case filled with I2 gas. The iodine absorption lines are appended to the stellar spectra through the I2 cell. We also derived a photonweighted central exposure time using a photon monitor, which records the intensity of the object in the HIDES slit every 3 s. We used the program TEMPO (Taylor et al. 2000) to calculate and correct for an apparent radial velocity caused by Earth’s movement.

HD 5015 9312 9939 11613 12923 14214 15814 35956 36859 43587 43821 46588 54563 77247 79028 82328 82674 92000 105982 109358 112048 122742 124570 131511 137052 139461 143333 150680 153597 160346 162596 163840 170829 172831 178428 203345 210763 213428 213429 219420 219834 220007

HIP

R.A. (J2000)

Decl. (J2000)

V (mag)

Plx (mas)

Sp. Type

4151 7143 7564 8922 9827 10723 11843 25662 26291 29860 29982 32439 34608 44464 45333 46853 46893 52032 59459 61317 62915 68682 69536 72848 75379 76603 78400 81693 82860 86400 87428 87895 90729 91751 93966 105431 109647 111171 111170 114834 115126 115187

00 53 04.197 01 32 03.127 01 37 25.094 01 54 53.784 02 06 29.308 02 18 01.440 02 32 54.141 05 28 51.629 05 35 55.499 06 17 16.138 06 18 40.354 06 46 14.151 07 10 06.679 09 03 32.272 09 14 20.541 09 32 51.434 09 33 19.906 10 37 52.265 12 11 46.071 12 33 44.545 12 53 38.123 14 03 32.351 14 14 05.180 14 53 23.766 15 24 11.890 15 38 40.082 16 00 19.592 16 41 17.160 16 56 01.690 17 39 16.916 17 51 59.446 17 57 14.326 18 30 41.651 18 42 36.117 19 07 57.322 21 21 21.585 22 12 43.869 22 31 18.419 22 31 18.312 23 15 40.268 23 19 06.668 23 19 49.875

+61 07 26.29 +16 56 50.03 +25 10 03.97 +40 42 07.32 +00 02 07.38 +01 45 28.09 +15 02 04.40 +12 33 02.96 +27 39 44.45 +05 06 00.40 +09 02 49.86 +79 33 53.32 +21 14 49.15 +53 06 29.82 +61 25 23.94 +51 40 38.28 −07 11 24.74 +34 04 43.04 +23 19 21.00 +41 21 26.93 −04 13 28.78 +10 47 12.40 +12 57 34.00 +19 09 10.07 −10 19 20.16 −08 47 29.36 −16 32 00.06 +31 36 09.81 +65 08 05.26 +03 33 18.86 −01 14 12.50 +23 59 45.20 +20 48 54.17 −07 04 25.16 +16 51 12.19 +10 19 56.20 −04 43 14.45 −02 54 40.59 −06 33 18.54 +01 18 29.71 −13 27 30.79 +57 14 37.07

4.80 6.78 6.99 6.25 6.29 5.60 6.00 6.71 6.27 5.70 6.24 5.44 6.43 6.87 5.18 3.17 6.25 6.42 6.73 4.24 6.45 6.27 5.53 6.00 4.92 6.45 5.47 2.81 4.88 6.53 6.33 6.32 6.49 6.13 6.08 6.72 6.39 6.15 6.15 6.76 5.20 6.89

53.85 17.15 23.80 9.45 5.98 40.04 34.84 34.55 4.08 51.76 9.42 56.02 21.67 2.86 51.12 74.15 7.75 2.75 5.19 119.46 9.61 60.24 30.06 86.69 30.90 40.19 30.49 92.63 66.28 93.36 7.33 35.02 27.92 13.43 47.72 21.54 10.68 6.89 39.18 22.51 48.22 3.74

F8V G5 K0IV K2 K0 G0.5IV F8V G0V K0 G0.5Vb K0 F8V G9V K0 F9V F6IV K0 K0 K2 G0V K0 G8V F6IV K2V F5IV F6V F7V F9IV F6Vvar K3V K0 G2V G8IV K0.5III G5V F5 F7V K0 F7V F5 G6/G8IV K2

3.2. Data Reduction Reduction of the spectral data was performed using the IRAF software package in the standard manner. We reduced the data using a 5000–6000 Å spectral range until 2007 November, and a 5000–6600 Å spectral range after 2007 December. To calculate the radial velocity, iodine lines superposed on the stellar spectra were used as wavelength references. We calculated the radial velocity over the 5000–6000 Å spectral range. Over this range, the spectra contain many deep and sharp iodine lines as well as hundreds of stellar absorption lines. We used an analysis code for HIDES data (Sato et al. 2002), which was based on Butler et al. (1996). This code divided the spectra into 5 Å segments. In every segment, the spectrum was modeled as I (λ) = k[A(λ)S(λ + Δλ)] ∗ IP,

(1)

where A(λ) is an iodine template spectrum, S(λ) is an intrinsic stellar spectrum, and Δλ = λv/c. λ represents the wavelength, v represents the radial velocity of the star, c is the speed of light, the * sign indicates the convolution, and IP represents the instrumental profile. We reconstructed S(λ) from the observed spectrum using the iodine spectrum, following the method of Sato et al. (2002). The intrinsic stellar spectrum was still affected by the differences in wavelength scale and IP between the stellar and iodine spectra. To remove these effects, and to increase the S/N ratio, we averaged several intrinsic stellar spectra. These intrinsic stellar spectra were selected as the observation dates, which were distributed throughout the entire observational term. The resulting averaged spectrum was treated as the final intrinsic-stellar spectrum, S(λ). The radial velocity and IP were simultaneously determined by fitting the model spectrum developed above to the observed spectrum. An average of the radial velocities of the individual segments was regarded as the radial velocity of the star. The radial velocities of the individual segments were weighted by their uncertainties, including systematic errors caused by inaccuracy of the modeling of the IP or the template stellar spectrum in addition to the random errors estimated from the photon-shot noise. The systematic errors would depend on which parts of the I2 and the stellar lines are included in the segment, that is, how to divide the spectrum into segments. To estimate these errors, we calculated the radial velocities by shifting the wavelength center of the segment back and forth by 0.3 Å, keeping the segment span of 5 Å fixed. We derived the differences in radial velocities between the shifted and initial segments. The mean of the differences is considered to be the systematic error for each segment. The weight of the radial velocity of the individual segments is obtained to the inverse squares of the random errors and the systematic errors.

References. The Hipparcos and Tycho catalogs (Perryman & ESA 1997).

3. OBSERVATIONS AND DATA REDUCTION 3.1. Observations We observed 37 SB1s and 5 SB2s using precise Doppler shift (radial velocity) measurements every one or two months since 2003. In total, observations were taken over about 100 nights. We used the 1.88 m telescope and HIDES at OAO. Until 2007 November, HIDES was equipped with a single 2 K × 4 K CCD and the observational wavelengths ranged from 5000 Å to 6100 Å. Since 2007 December, when HIDES was upgraded to three CCDs, the observational range expanded to 3750–7500 Å with a RED cross-disperser. The spectral resolution (R = λ/Δλ) was ∼60,000 with a 200 μm (0. 76) width slit. Exposure times were 120–1800 s depending on the target luminosity and weather conditions. We obtained typical signal-to-noise ratios of 100–200 for a sixth magnitude star with an exposure time of less than 1800 s. We observed, on average, 20 stars per night. Each 2


Katoh et al.

Table 2 Radial Velocities of 33 Samples BJD-UTC∗ (−2400000)

Radial Velocity (m s−1 )

Uncertainty (m s−1 )

O−C (m s−1 )

HD9312 53721.00939 53723.93661 53969.26562 54017.27272 54048.21179 54126.01144 54142.94948 54341.30912 54350.26276 54408.19403 54767.14600 54824.07572

−8287.9 −24567.8 25604.6 −29993.9 −13.8 −26334.1 29626.2 −5288.7 −33776.3 23380.8 33888.0 −35644.0

8.5 11.3 8.4 10.5 8.8 10.5 9.7 13.7 8.8 9.9 9.8 9.6

2.2 −14.3 −4.2 −19.1 10.3 12.1 −10.5 9.2 −7.6 −17.2 21.6 16.9 Figure 1. Radial velocity of β Vir. The vertical and horizontal axes represent the radial velocity and Julian date, respectively. The typical uncertainty of the measurements is 7.3 m s−1 . The standard deviation of the radial velocity is 7.7 m s−1 .

Notes. ∗ We converted HJD to BJD-UTC with a calculation code of Eastman et al. (2010). † The previous velocities corrected with the offsets. (This table is available in its entirety in machine-readable and Virtual Observatory (VO) forms in the online journal. A portion is shown here for guidance regarding its form and content.)

25 SB1s did not include their errors, the orbital elements for these 25 SB1s were determined only from our data. The uncertainty in each orbital element was estimated using Monte Carlo methods. The mean uncertainties of the radialvelocity measurements are systematically smaller than the corresponding O−C values (Table 3). We consider this discrepancy to be caused by relatively low signal-to-noise ratio of the spectra, and/or an orbital motion of a third body and stellar activity, if any. Thus, the uncertainties of the binary orbital elements were estimated using the mean of the O−C absolute values. For each observed radial velocity, we generated 10,000 fake data sets by adding random noise corresponding to the O−C values. We determined the best-fit Keplerian parameters for each fake data set and adopted the standard deviation of each parameter as the uncertainty in each orbital element.

The uncertainties of the radial velocities are the standard deviations between the mean velocity derived from all the segments and velocities of the individual segments. New orbital elements were determined by least-squares fitting. We used the orbital elements from the Ninth Catalogue of Spectroscopic Binary Orbits (Pourbaix et al. 2004) and the Eighth Catalogue of the Orbital Elements of Spectroscopic Binary systems (Batten et al. 1989) for the initial values. We weighted the radial velocities according to their errors and sought the best-fit Keplerian elements. We estimated the offset between the HIDES velocities and the published ones with the following manner. First, we determined orbital parameters by using only HIDES data. Next, we fitted the orbital curve thus determined to the HIDES velocities and the published ones simultaneously without any offset between them (case 1). In this case, the curve is practically fitted to the HIDES velocities because their errors are dozens of times smaller than those of the published velocities. Then, we fitted the orbital curve only to the published velocities (case 2). The difference in resulting published velocities between cases 1 and 2 corresponds to the offset that should be corrected relative to the HIDES velocities. For example, the offset of HD35956 is +1.6133 km s−1 . We list the previous velocities corrected with the offsets in Table 2. We also show the offsets in Table 3. For HD9939, HD79028, HD153597, HD163840, HD170829, and HD178428, the precisions of the orbital elements determined with the HIDES velocities are not different from those of the orbital elements determined with the HIDES velocities and the published velocities. New orbital elements for these six objects were determined by us using the HIDES data. For the other 11 binaries, the precisions of the orbital periods and/or orbital eccentricities determined with both data taken in this study and data from the previous works are 10 times precise than those of the orbital elements determined with only HIDES data. We derived the orbital elements of these 11 objects from the HIDES velocities and the published velocities. Since the previous radial-velocity measurements for the remaining

4. RESULTS 4.1. Radial-velocity Precision We observed three radial-velocity standard stars. β Vir is known to have only small variations in its radial velocity (σ = 7.6 m s−1 ; Wittenmyer et al. 2006). ι Per is also stable in radial velocity (σ = 10.2 m s−1 ; Wittenmyer et al. 2006). The observed radial velocities of β Vir are shown in Figure 1. The typical uncertainty in the measurements is 7.3 m s−1 and the standard deviation of the radial velocities is 7.7 m s−1 . This indicates the long-term stability of the measurements. Figure 2 shows the radial velocities of 70 Vir. This star has a radial-velocity variation with a period of 116.7 days and an amplitude of 315 m s−1 , induced by one planet (Marcy & Butler 1996). Our measurements of 70 Vir are consistent with the orbital motion of the known planet. 4.2. New Orbital Elements We succeeded in determining the orbital elements for 28 SB1s and 5 SB2s out of a sample of 42 targets. The radial velocities of these 33 binaries are shown in Figure 3 and listed in Table 2. Their new orbital elements are listed in Table 3. The uncertainties in the new orbital elements are, for the most cases, 10 times smaller than those previous studies. For HD9312, the previous orbital eccentricity and semi-amplitude of the radial 3


Katoh et al.

Table 3 Orbital Elements Determined for 33 Binaries HD 9312 9939 11613 14214 15814 35956 36859 43587 43821 54563 77247 79028 82674 92000 105982 112048 131511 137052 139461 143333 150680 153597 160346 162596 163840 170829 172831 178428 210763 213429 219420

P (days)

T0 (−2450000)

e

ω (deg)

K (km s−1 )

36.51907 ±0.00015 25.20890 ±0.00006 836.88261 ±0.48647 93.28281 ±0.00118 19.41612 ±0.00047 1426.71012 ±0.09079 381.77598 ±0.02991 12489.96477 ±85.32950 1320.22128 ±0.31213 113.23143 ±0.00048 80.53888 ±0.00173 16.23966 ±0.00001 820.84720 ±0.47900 1500.35387 ±0.24788 1448.20574 ±7.27819 1016.89580 ±2.21963 125.03910 ±0.00030 226.94370 ±0.00248 844.52277 ±0.08439 1144.18513 ±0.42605 12408.96935 ±43.80751 52.10905 ±0.00021 83.72696 ±0.00084 467.53899 ±0.11832 882.23739 ±0.60476 26.38466 ±0.00005 485.20579 ±0.02259 21.95544 ±0.00003 42.38181 ±0.00678 632.60590 ±0.09084 468.84602 ±0.08247

4094.819 ±0.008 3400.192 ±0.008 3733.258 ±1.348 4084.667 ±0.007 4101.914 ±0.018 3649.768 ±0.153 4121.815 ±0.109 832.574 ±0.471 4097.653 ±0.202 3356.310 ±0.006 4108.609 ±0.087 3400.081 ±0.003 3875.204 ±2.638 4405.731 ±1.389 3842.542 ±7.490 3477.606 ±3.222 3463.458 ±0.012 3593.022 ±0.041 3555.014 ±0.078 3576.217 ±5.661 2401.026 ±60.875 3427.869 ±0.009 3334.363 ±0.040 4500.184 ±24.661 3886.654 ±0.325 4108.968 ±0.004 4084.266 ±0.188 3408.758 ±0.008 3428.422 ±0.223 3476.901 ±1.563 3950.642 ±0.527

0.1432 ±0.0003 0.1022 ±0.0003 0.1285 ±0.0014 0.5241 ±0.0003 0.4096 ±0.0033 0.6159 ±0.0004 0.5017 ±0.0009 0.8045 ±0.0009 0.4358 ±0.0005 0.3870 ±0.0001 0.1087 ±0.0007 0.1055 ±0.0001 0.0990 ±0.0018 0.5811 ±0.0051 0.2586 ±0.0047 0.2812 ±0.0037 0.5087 ±0.0003 0.6649 ±0.0014 0.8332 ±0.0013 0.1054 ±0.0025 0.3609 ±0.0278 0.2223 ±0.0002 0.2056 ±0.0007 0.0044 ±0.0010 0.4121 ±0.0015 0.2223 ±0.0002 0.2019 ±0.0006 0.0918 ±0.0002 0.6058 ±0.0095 0.3830 ±0.0060 0.0999 ±0.0006

203.26 ±0.07 312.20 ±0.11 63.61 ±0.67 104.03 ±0.03 179.09 ±0.44 326.55 ±0.06 126.91 ±0.22 75.21 ±0.15 39.95 ±0.08 100.53 ±0.03 38.40 ±0.37 137.41 ±0.07 289.56 ±1.18 58.59 ±0.67 242.25 ±0.74 183.14 ±0.60 219.11 ±0.15 339.84 ±0.15 106.32 ±0.18 61.50 ±1.63 131.64 ±4.33 338.42 ±0.06 139.46 ±0.19 253.54 ±19.02 135.46 ±0.20 223.69 ±0.06 75.50 ±0.16 64.56 ±0.13 290.53 ±1.15 169.88 ±0.92 202.28 ±0.43

34.954 ±0.005 35.080 ±0.008 4.635 ±0.005 19.264 ±0.006 23.365 ±0.090 3.798 ±0.002 12.667 ±0.014 4.321 ±0.003 11.007 ±0.007 21.242 ±0.004 8.499 ±0.006 35.305 ±0.005 6.047 ±0.008 8.372 ±0.082 5.500 ±0.013 2.264 ±0.006 19.039 ±0.036 14.175 ±0.036 10.448 ±0.057 3.805 ±0.008 3.583 ±0.116 17.160 ±0.004 5.679 ±0.004 3.513 ±0.004 11.363 ±0.020 12.817 ±0.003 9.648 ±0.006 13.335 ±0.003 47.244 ±1.054 11.860 ±0.145 10.815 ±0.005

4

a σHIDES (m s−1 )

b σall (m s−1 )

Measurements (offsetc (km s−1 ))

Mean O−C (m s−1 )

14.0

14.0

1

12.1

25.4

25.4

1

19.1

23.9

23.9

1

18.1

24.0

24.0

1

16.4

392.0

392.0

1

204.9

10.6

12.2

1, 2(+1.6133)

12.5

56.8

56.8

1

45.6

20.1

1170.0

1, 2(−5.2550), 3(−14.2000)

13.1

31.1

31.1

1

22.1

14.5

14.5

1

11.3

29.7

29.7

1

23.7

34.6

34.6

1

24.4

13.3

13.3

1

11.0

62.8

669.7

1, 4(−13.7876)

111.4

38.6

38.6

1

26.6

31.5

31.5

1

19.0

26.1

35.0

1, 5(+27.4836)

31.9

78.0

1829.0

1, 6(+9.3673)

77.6

20.7

489.0

1, 7(−0.8019), 8(−0.8019)

15.1

28.6

684.0

1, 6(+23.7718)

24.5

51.9

635.9

1, 6(+68.9355), 9(+68.9355)

40.7

26.4

26.4

1

20.3

11.4

545.4

1, 10(−19.8368)

9.9

17.7

17.7

1

13.5

50.7

50.7

1

41.1

12.1

12.1

1

9.8

11.2

11.2

1

9.1

17.0

17.0

1

12.8

855.9

855.9

1

564.6

89.5

1175.2

1, 11(+9.1265)

60.0

18.4

18.4

1

15.9


Katoh et al. Table 3 (Continued)

HD 219834 220007

P (days)

T0 (−2450000)

e

ω (deg)

K (km s−1 )

2298.15845 ±2.51609 1599.79091 ±28.56126

3748.271 ±2.978 2818.667 ±29.085

0.1620 ±0.0020 0.5396 ±0.0179

212.13 ±0.43 236.95 ±1.78

6.025 ±0.008 4.689 ±0.072

a σHIDES (m s−1 )

b σall (m s−1 )

Measurements (offsetc (km s−1 ))

Mean O−C (m s−1 )

20.7

219.3

1, 12(−11.4800)

14.5

203.1

203.1

1

160.8

Notes. Measurements: (1) this work; (2) Vogt et al. (2002); (3) Beavers & Eitter (1986); (4) Batten et al. (1983); (5) Nidever et al. (2002); (6) Abt & Levy (1976); (7) Tokovinin & Gorynya (2007); (8) Struve & Zebergs (1959); (9) Duquennoy et al. (1991); (10) Tokovinin (1991); (11) Pourbaix (2000); (12) Sarma (1962). a Standard deviation of the radial velocities measured by HIDES. b Standard deviation of the radial velocities measured in this study and previous studies. c Offset between the HIDES velocity and the published velocity.

newly determined orbital elements of the remaining 27 binaries show little change from those derived by the previous works. Discrepancies in the period are typically less than 1%, those in the eccentricity are less than 0.01, and those in the semiamplitude are less than 0.5 km s−1 . For the five SB2s, the standard deviations in radial velocity were larger than the typical uncertainties in the radial-velocity measurements. We note also that HD15814 and HD210763 are equal-mass binaries whose standard deviations in radial velocity were significantly larger than the typical measurement uncertainties. We suggest that the analysis code of Sato et al. (2002) may not precisely derive the radial velocities of SB2s. HD220007 shows obvious variations in radial velocity in addition to the binary orbital motion (Figure 3). The amplitude of the variations is 203.1 m s−1 . On the other hand, the typical measurement uncertainty is only 40 m s−1 . If the variations are generated by a third object in the binary system, the object has a mass of ∼0.01 M and a semimajor axis of 1.7 AU. Otherwise, photospheric activity in HD220007 may be responsible for the variations. Bakos (1974) indicated that the spectral type of HD220007 is M3III. If the radial-velocity variations were produced by photospheric activity, the line profiles of the HD220007 spectra would vary. To identify the cause of the radial-velocity variations, we will investigate the line profiles in the HD220007 spectra. We did not determine the new orbital elements for the remaining nine targets. The periods of four objects were longer than the observational term, and five objects turned out to be single stars. Abt & Levy (1976) argued that these five objects (HD5015, HD46588, HD82328, HD109358, and HD124570) had radial-velocity amplitudes of 1.6, 1.7, 4.3, 2.6, and 2.9 km s−1 , respectively. However, Morbey & Griffin (1987) indicated that these five objects are not spectroscopic binaries. In this study, the radial velocities of these five objects do not show large variation, as previously indicated. As an example, the radial velocity of HD124570 is shown in Figure 5.

Figure 2. Phased radial velocity of 70 Vir. The solid line represents the orbital motion induced by an extrasolar planet (Marcy & Butler 1996).

velocity are 0.20 ± 0.03 and 30.0 ± 0.9 km s−1 (Heard 1940). We derived new eccentricity of 0.1432 ± 0.0002 and semiamplitude of 34.954 ± 0.004 km s−1 . The orbital eccentricity of HD11613 is 0.0 (fixed; Griffin 1981) or 0.129 ± 0.001 (this work). The orbital period and eccentricity of HD105982 are 1355 ± 5 days and 0.30 ± 0.03 in Griffin (1985). In this work, the period and eccentricity are derived to be 1448 ± 3 days and 0.259 ± 0.002. For HD143333, Abt & Levy (1976) indicated a periodic velocity variation with a period of 3100 ± 9 days, an eccentricity of 0.13 ± 0.09, and an amplitude of 9.0 ± 0.9 km s−1 . They used radial-velocity data obtained between 1915 and 1921 with a precision of 1–8 km s−1 (Abt 1973) and data obtained between 1968 and 1971 with a precision of 0.2–0.8 km s−1 (Abt & Levy 1976). In contrast, Morbey & Griffin (1987) argued that the velocities of HD143333 do not vary periodically. Our measurements indicate a periodic variation with a period of 1144.2 ± 0.4 days and an amplitude of 3.805 ± 0.008 km s−1 . This periodic variation does not match the orbital solution derived by Abt & Levy (1976) (Figure 4). The variation follows the measurements during 1968–1971 but does not follow the measurements taken in 1915–1921. Duquennoy & Mayor (1991) derived the orbital period of 2441 ± 87 days and the orbital eccentricity of 0.205 ± 0.036 for HD219834. However, we derived the period of 2298 ± 2 days and the eccentricity of 0.162 ± 0.001. For HD220007, the previous orbital period and eccentricity are 1520 ± 5 days and 0.51 ± 0.02 (Griffin 1979). In contrast, the period and eccentricity in this work are 1600 ± 7 days and 0.540 ± 0.004. The

4.3. Resolved Masses of Primary and Secondary Stars We calculated the mass of the primary star, M1 , and that of the secondary star, M2 , for each binary (Table 4). First, we calculated M1 using the mass–temperature relationship for main-sequence stars. We used the following expression: log

M1 = 1.471 log T1 − 5.545. M

(2)

This expression is derived from the formulae in Allen’s astrophysical quantities (Cox 2000). By comparing with previously 5


Katoh et al.

Figure 3. Phased radial velocities of HD9312, HD9939, HD11613, HD14214, HD15814, HD35956, HD36859, and HD43587. Our measurements are indicated by the filled circles. The open circles indicate the radial velocities from previous work. The solid lines are radial-velocity variations calculated from the newly determined orbital elements. (An extended version of this figure is available in the online journal.)

6


Katoh et al.

Table 4 Physical Parameters of the Binaries Obtained from the New Orbital Elements HD 9312 9939 11613 14214 15814 35956 36859 43587 43821 54563 77247 79028 82674 92000 105982 112048 131511 137052 139461 143333 150680 153597 160346 162596 163840 170829 172831 178428 210763 213429 219420

†

a1 sin i (109 m)

a† (AU)

v† (km s−1 )

f(m) (M )

T1 (K)

M1 (M )

M2,min (M )

q†

17.372 ±0.003 12.097 ±0.003 52.897 ±0.097 21.045 ±0.011 5.691 ±0.031 58.702 ±0.058 57.525 ±0.103 440.789 ±4.222 179.851 ±0.205 30.498 ±0.007 9.357 ±0.008 7.840 ±0.001 67.920 ±0.142 140.570 ±2.029 105.803 ±0.920 30.381 ±0.181 28.184 ±0.059 33.041 ±0.139 67.094 ±0.610 59.533 ±0.163 570.183 ±27.044 11.988 ±0.003 6.399 ±0.006 22.585 ±0.032 125.602 ±0.401 4.534 ±0.001 63.046 ±0.050 4.009 ±0.001 21.906 ±0.691 95.303 ±1.435 69.377 ±0.048

0.24373 ±0.00005 0.19163 ±0.00005 1.61644 ±0.00298 0.46040 ±0.00025 0.15692 ±0.00086 2.70063 ±0.00267 1.07118 ±0.00191 11.61266 ±0.11123 2.63346 ±0.00301 0.52746 ±0.00013 0.36039 ±0.00029 0.14599 ±0.00002 1.64880 ±0.00344 2.71258 ±0.03915 2.61873 ±0.02276 1.89544 ±0.01130 0.53728 ±0.00113 0.85192 ±0.00359 1.99502 ±0.01815 2.38773 ±0.00655 12.28129 ±0.58250 0.31583 ±0.00009 0.34829 ±0.00030 1.09456 ±0.00153 2.13129 ±0.00680 0.17463 ±0.00005 1.47504 ±0.00117 0.16079 ±0.00004 0.30735 ±0.00970 1.73544 ±0.02614 1.39126 ±0.00097

72.61 ±0.01 82.70 ±0.02 21.01 ±0.05 53.69 ±0.03 87.92 ±0.49 20.59 ±0.02 30.52 ±0.06 10.11 ±0.17 21.70 ±0.03 50.68 ±0.01 48.68 ±0.04 97.80 ±0.02 21.85 ±0.06 19.67 ±0.29 19.67 ±0.27 20.28 ±0.17 46.75 ±0.10 40.84 ±0.17 25.70 ±0.24 22.70 ±0.07 10.77 ±0.55 65.94 ±0.02 45.26 ±0.04 25.47 ±0.04 26.28 ±0.10 72.00 ±0.02 33.07 ±0.03 79.67 ±0.02 78.89 ±2.50 29.84 ±0.45 32.28 ±0.03

0.15664 ±0.00009 0.11099 ±0.00009 0.00842 ±0.00004 0.04268 ±0.00007 0.01948 ±0.00032 0.00396 ±0.00001 0.05204 ±0.00027 0.02187 ±0.00033 0.13299 ±0.00039 0.08815 ±0.00006 0.00503 ±0.00001 0.07281 ±0.00003 0.01853 ±0.00009 0.04917 ±0.00211 0.02250 ±0.00036 0.00108 ±0.00001 0.05705 ±0.00036 0.02791 ±0.00035 0.01687 ±0.00046 0.00642 ±0.00005 0.04797 ±0.00649 0.02528 ±0.00002 0.00149 ±0.00000 0.00210 ±0.00001 0.10144 ±0.00083 0.00533 ±0.00001 0.04241 ±0.00010 0.00533 ±0.00001 0.23319 ±0.02202 0.08618 ±0.00387 0.06053 ±0.00011

4898a ±98 5050b ±100 4420c (*) 6099d ±80 6063d ±114 5946d ±80 4750c (*) 5926d ±80 5030e ±321 5590c (*) 5150c (*) 5971d ±80 4492e ±239 4750c (*) 4770e ±172 4751f ±48 5224d ±80 6552d ±80 6375d ±80 6348d ±80 6026a ±121 6298d ±80 4841d ±80 4750c (*) 5888a ±136 5248a ±105 4786a ±111 5684d ±80 6388d ±91 6060d ±100 6188d ±80

0.76 ±0.02 0.80 ±0.02 0.66

0.690 ±0.021 0.583 ±0.014 0.182 ±0.001 0.460 ±0.006 0.337 ±0.003 0.178 ±0.001 0.409 ±0.008 0.342 ±0.003 0.665 ±0.018 0.581 ±0.012 0.170 ±0.001 0.567 ±0.010 0.252 ±0.003 0.388 ±0.008 0.272 ±0.005 0.089 ±0.001 0.460 ±0.008 0.410 ±0.004 0.331 ±0.003 0.227 ±0.001 0.465 ±0.011 0.384 ±0.003 0.103 ±0.001 0.114 ±0.001 0.648 ±0.026 0.179 ±0.001 0.294 ±0.005 0.191 ±0.001 1.027 ±0.034 0.598 ±0.015 0.545 ±0.009

0.91 ±0.05 0.73 ±0.04 0.28

7

1.05 ±0.02 1.05 ±0.03 1.02 ±0.02 0.73 1.01 ±0.02 0.79 ±0.07 0.92 0.82 1.02 ±0.02 0.67 ±0.05 0.73 0.73 ±0.04 0.73 ±0.01 0.84 ±0.02 1.17 ±0.02 1.13 ±0.02 1.12 ±0.02 1.04 ±0.03 1.11 ±0.02 0.75 ±0.02 0.73 1.00 ±0.03 0.85 ±0.02 0.74 ±0.03 0.95 ±0.02 1.13 ±0.02 1.04 ±0.02 1.08 ±0.02

0.44 ±0.01 0.32 ±0.01 0.17 ±0.01 0.56 0.34 ±0.01 0.84 ±0.10 0.63 0.21 0.56 ±0.02 0.38 ±0.03 0.53 0.37 ±0.02 0.12 ±0.01 0.54 ±0.02 0.35 ±0.01 0.29 ±0.01 0.20 ±0.01 0.45 ±0.02 0.34 ±0.01 0.14 ±0.01 0.16 0.65 ±0.05 0.21 ±0.01 0.40 ±0.02 0.20 ±0.01 0.91 ±0.05 0.58 ±0.03 0.50 ±0.02


Katoh et al. Table 4 (Continued) †

HD

a1 sin i (109 m)

a† (AU)

v† (km s−1 )

f(m) (M )

T1 (K)

M1 (M )

M2,min (M )

q†

219834

187.887 ±0.518 86.846 ±4.067

3.71858 ±0.01025 2.58235 ±0.12094

17.60 ±0.07 17.56 ±1.14

0.05004 ±0.00030 0.01020 ±0.00107

5370a ±124 5016e ±882

0.87 ±0.03 0.79 ±0.20

0.441 ±0.007 0.232 ±0.003

0.51 ±0.03 0.29 ±0.08

220007

References. (a) Allende Prieto & Lambert (1999); (b) Torres et al. (2010); (c) Wright et al. (2003); (d) Casagrande et al. (2011); (e) Ammons et al. (2006); (f) Valentini & Munari (2010). (∗) Uncertainties of the temperatures are not listed in the previous study. † a, v, M2,min , and q include the uncertainty in inclination.

function, f(m): f (m) =

K 3P M1 sin3 iq 3 (1 − e2 )3/2 , = (1 + q)2 2π G

(3)

where q = M2 /M1 is the mass ratio of the binary and G is the gravitational constant. M2 was determined to be the minimum mass, M2,min because the inclination was not obtained by our observations. The mean uncertainty of the derived M2,min from the new orbital elements was ∼0.007 M . 4.4. Semimajor Axis We calculated the semimajor axis of the primary star, a1 , for each binary (Table 4). The semimajor axis is expressed by a1 =

Figure 4. Phased radial velocities of HD143333 folded by the previously determined orbital period. The filled circles indicate the radial velocities obtained in the present study. The open circles indicate the radial velocities measured by Abt & Levy (1976). The cross marks indicate the radial velocities obtained between 1915 and 1921 at Mount Wilson Observatory (Abt 1973). The solid line represents the orbital solution derived from the radial velocities of the open circles and cross marks (Abt & Levy 1976). The filled circles do not follow the previous orbital solution.

KP (1 − e2 )1/2 , 2π sin i

(4)

where K is the amplitude of the radial velocity, P is the period, e is the eccentricity, and i is the inclination. Since the inclination was not obtained from the observations, we described the semimajor axis of the primary star as a1 sin i. We also derived the mean distance between the primary star and the secondary star, a. This distance is expressed by the following equation: 1 , (5) a = a1 + a2 = a1 1 + q where a2 is the semimajor axis of the secondary star. The mean distance also has an uncertainty due to the absence of a value for the inclination. 5. DISCUSSION 5.1. SB2 Identification For the 28 SB1s and 5 SB2s whose orbital elements were newly determined, we checked the absorption lines from the secondary component in the binary spectra. An SB2, a doublelined spectroscopic binary, shows spectral features of both the primary and secondary stars. In the Ninth Catalogue of Spectroscopic Binary Orbits (Pourbaix et al. 2004), 5 objects (HD9939, HD15814, HD163840, HD210763, and HD213429) among the 33 targets were identified as SB2s. HD15814 and HD210763 were also classified as SB2s in the Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Systems (Batten et al. 1989). The other 28 objects were identified as SB1s in these catalogs. We examined the absorption lines from the secondary star in the 6300–6600 Å spectral range for each of the 33 targets. In this

Figure 5. Phased radial velocity of HD124570. The filled circles indicate the radial velocities obtained in this work. The open circles indicate the radial velocities measured by Abt & Levy (1976). The solid line represents the orbital solution obtained by Abt & Levy (1976). The object appears to be a single star.

determined spectral types (Table 1), we were convinced that the uncertainty in the primary mass was less than 0.05 M . Next, we estimated M2 using the mass of the primary star and the mass function. We used the following expression for the mass 8


Katoh et al. Table 5 Stellar Parameters of Five SB2s

2

Oct. 2, 2008 1.8 1.6

HD (B) (A)

(B)

9939 (A)

15814

(A) 1.2

163840

Nov. 22, 2009

1

210763 0.8

(B)

0.6 0.4 6430

(B)

(B)

(A)

213429

(A)

q

M2 (M )

T2 (K)

i (deg)

44.2 ±4.3 28.7 ±1.7 15.5 ±1.6 56.3 ±3.8 19.4 ±4.5

0.79 ±0.08 0.81 ±0.05 0.73 ±0.09 0.84 ±0.06 0.61 ±0.15

0.63 ±0.05 0.85 ±0.04 0.73 ±0.07 0.95 ±0.05 0.63 ±0.14

4300 ±230 5270 ±170 4750 ±360 5680 ±200 4300 ±650

71 29 66

73

(A) 6435

6440

Wavelength [

6445

diagrams using the Padova evolutionary track (Marigo et al. 2008). The evolutionary track calculates the isochrones from the zero-age main sequence (ZAMS) up to 13.5 Gyr. The V-band absolute magnitudes of the primary and secondary stars are calculated from the V-band apparent magnitude of the binary, the distance to the system, and the luminosity ratio. We use the V-band apparent magnitudes for the five systems listed in the Hipparcos–Tycho catalog (Perryman & ESA 1997). We also calculate the distances of the five systems from their parallaxes measured by Hipparcos. The luminosity ratio between the primary and secondary stars was estimated from the mass ratio derived in the previous section. We used following expression:

6450

[

Relative Flux

1.4

K2 (km s−1 )

Figure 6. Observed spectra of HD15814 between 6430 and 6450 Å on 2008 October 2 and 2009 November 22, respectively. (A) and (B) represent the absorption lines of the primary star and the secondary star, respectively. We clearly identify the absorption lines of the secondary star. Thus, HD15814 is an SB2.

spectral range, the stellar spectrum is not heavily contaminated by the iodine and telluric spectra. Moreover, the secondary continuum emission in this range is expected to be stronger than the emission at shorter wavelengths because the secondary star is expected to have a small mass, and thus, a low effective temperature. We compared two observed spectra taken at different orbital phases. As an example, two spectra of HD15814 are shown in Figure 6. We found the secondary absorption lines in the spectra of the five objects previously identified as SB2s. Moreover, three objects (HD153597, HD170829, and HD178428) in the 28 SB1s were newly identified as SB2s. These three SB2s have radial-velocity amplitudes of 13–17 km s−1 . For HD9939, HD15814, HD163840, HD210763, and HD213429 among the eight objects identified as SB2 systems, we derived the radial velocities and their amplitudes of the secondary stars, K2 , following the method of Section 3.2. The typical uncertainty of the velocities is as large as 1 km s−1 because the absorption lines of the secondary star are weak and the spectra are contaminated by the primary lines. The secondary amplitude K2 is a free parameter, while the values of the other orbital elements were fixed at those of the primary star newly determined by this study. The mass ratio of binary, q, was calculated from comparing the K2 with the primary amplitude. The mass of the secondary star, M2 , was estimated with the mass ratio and the primary mass. For HD9939, HD15814, HD163840, and HD213429, the values of M2 were larger than M2,min derived from the orbital motions. We calculated the inclination, i, for the four SB2s by comparing M2 with M2,min . We did not calculated the inclination of HD210763 because its M2 is smaller than M2,min . If the primary mass of HD210763 is 1.738 ± 0.042 M (Takeda et al. 2007), the values of M2,min and the M2 are 1.287 M and 1.46 M . In that case, we estimated the inclination of 66◦ . We also estimated the effective temperature of the secondary star, T2 , using Equation (2). We listed K2 , q, M2 , T2 , and i in Table 5. For newly identified SB2 systems, HD153597, HD170829, and HD178428, we did not calculate the velocities of the secondary star due to the weakness of the secondary lines.

log

L2 = 3.8 log q, L1

(6)

where L1 and L2 are the luminosities of the primary and secondary stars. This expression is derived from the mass–luminosity relation in Allen’s astrophysical quantities (2000). The uncertainty in the V-band absolute magnitude is derived from the uncertainty in the luminosity ratio and distance. We do not include the photometric error in the uncertainty of the V-band absolute magnitude. The photometric uncertainty is much smaller than that of the luminosity ratio and distance. HR diagrams for the five SB2s are shown in Figure 7. HD9939. The temperature of the primary star is 5050 K (Torres et al. 2010) and that of the secondary star is 4300 K. The distance to the binary system is 42.0 ± 1.5 pc. The absolute magnitudes of the primary and secondary stars in the V band are 4.4 mag and 5.3 mag, respectively. The locus of the primary star is coincident with the 13.5 Gyr isochrone. On the other hand, the secondary star does not appear on any isochrone, even if the uncertainty is taken into account. Wright et al. (2004) calculated the age of HD9939 as 4.6 ± 2.6 Gyr from the relationship between chromospheric emission and stellar age (Donahue 1993). We did not determine the age of HD9939 from their HR diagrams. HD15814. The temperatures of the primary and secondary stars are 6063 K (Casagrande et al. 2011) and 5270 K, respectively. The distance to the system is 28.7 ± 0.7 pc. Given a distance of 28.7 pc, the V-band absolute magnitudes of the primary and secondary stars are 4.2 mag and 5.0 mag, respectively. The locus of the primary star is coincident with the 2.0–4.0 Gyr isochrones, but the position of the secondary star does not fit any isochrone. Wright et al. (2004) derived the system age of 3.0 ± 1.8 Gyr. HD163840. T1 is 5888 K (Allende Prieto & Lambert 1999) and we derived T2 = 4750 K. The distance to HD163840 is 28.6 ± 0.5 pc. The absolute magnitudes of the primary and

5.2. Ages of the SB2 Binaries For five SB2s whose primary and secondary masses were determined, we estimate the ages of the binaries on the HR 9


Katoh et al. 2.0 Gyrs

3.2 Gyrs 4.0 Gyrs

ZAMS

13.5 Gyrs

ZAMS

5.0 Gyrs

7.9 Gyrs 1.6 Gyrs 2.0 Gyrs

2.5 Gyrs

ZAMS

3.2 Gyrs

4.0 Gyrs

2.5 Gyrs

5.0 Gyrs

1.0 Gyrs

Figure 7. H-R diagrams of HD9939, HD15814,HD163840, HD210763, and HD213429. The vertical axes represent the absolute magnitude in the V band. The horizontal axes represent the effective temperatures on a logarithmic scale. The primary and secondary stars are plotted with filled circles and triangles, respectively. The uncertainty in the V-band magnitudes is derived from the uncertainties in the luminosity ratio and distance. The solid lines indicate the isochrones derived by Marigo et al. (2008).

10


Katoh et al.

than 0.62, yet they are not SB2s. Their secondary stars may be white dwarfs. 5.3.1. HD9312

We calculated the mass of the secondary companion as M2,min = 0.690 M . If the secondary star is a white dwarf, its mass in the main-sequence phase would be 3.7 M , as derived from the initial-mass–final-mass relationship (Weidemann 2000). The main-sequence lifetime of the secondary star is ∼3.8 × 108 yr, which is considerably shorter than that of the primary star (∼1.3 × 1010 yr). The white dwarf cooling model (Richer et al. 2000) indicates that the apparent visual magnitude of the secondary star in the white dwarf phase would decrease from 15.4 mag to 22.1 mag, while the primary star remained on the main sequence. As the apparent magnitude of the primary star is 6.8 mag, the luminosity of the secondary star is at least ∼103 times fainter than that of the primary star. If the secondary star of HD9312 is a white dwarf, its absorption lines are undetected, resulting in a classification of SB1. 5.3.2. HD43821

The calculated mass of the secondary star is M2,min = 0.665 M . We assumed that the secondary star was a white dwarf whose mass in the main-sequence phase was 3.1 M , derived from the initial mass–final mass relationship (Weidemann 2000). The lifetimes of the primary and secondary stars in the main-sequence phase are ∼1.4 × 1010 yr and ∼5.9 × 108 yr, respectively. The white dwarf evolutionary track (Richer et al. 2000) indicates that the apparent visual magnitude of the secondary star in the white dwarf phase would decrease from 16.4 mag to 23.1 mag, while the primary star remained on the main sequence. As the primary magnitude is 6.2 mag, the luminosity of the secondary star is at least ∼104 times fainter than that of the primary star. We think that the secondary star of HD43821 is also a white dwarf.

Figure 8. Primary-mass–secondary-mass relationship. The filled circles represent the masses of the 25 SB1s and those of the 3 SB2s in which velocities of the secondary star were not measured. The open circles represent the masses of the five SB2s. The dashed line represents the equal-mass binaries. The solid line indicates a mass ratio of 0.62, corresponding to the boundary between the SB1s and SB2s in our sample.

secondary stars in the V band are 4.4 mag and 5.7 mag, respectively. The location of the secondary star on the H-R diagram is not consistent with any isochrone. In contrast, that of the primary star is consistent with the isochrones of ZAMS—7.9 Gyr. The previously estimated age is 7.4+1.1 −1.2 Gyr (Holmberg et al. 2009). HD210763. The primary and secondary star temperatures are 6388 K (Casagrande et al. 2011) and 5680 K, respectively. The distance to HD210763 is 93.6 ± 8.1 pc. The V-band absolute magnitudes of the primary and secondary stars are 2.1 mag and 2.8 mag, respectively. In that case, the locations of the primary and secondary star are coincident with the 2.5 Gyr isochrone. This age is comparable to that of 2.86 ± 0.43 Gyr derived by Marsakov & Shevelev (1995). HD213429. Casagrande et al. (2011) derived T1 = 6060 K and we estimated T2 = 4300 K. We calculated the distance to HD213429 of 25.5 ± 1.2 pc. Given a distance of 25.5 pc, the V-band absolute magnitudes of the primary and secondary stars are 4.4 mag and 6.4 mag, respectively. The isochrones allow us to estimate the age of the system as 1.0–5.0 Gyr, which is comparable to the previously estimated age of 3.7+1.3 −2.0 Gyr (Holmberg et al. 2009).

5.4. Period–Eccentricity Relationship In a close binary, tidal forces circularize the orbit of the secondary at the periastron (Burki & Mayor 1986; Duquennoy & Mayor 1991). Numerical simulations indicate that the possible longest orbital period of the circularization, Pb , is between 7.2 and 8.5 days for an equal-mass binary system with an initial eccentricity of 0.3 (Zahn & Bouchet 1989). Most of the orbital circularization occurs during the pre-main-sequence stage, and the orbit is rather stable during the main-sequence phase (Zahn & Bouchet 1989). Observations indicated that Pb is 12 days, within which the tidal force circularizes the orbits for nearby G-dwarf binaries (Raghavan et al. 2010). For the 33 binaries in our sample, the period–eccentricity relationships are shown in Figure 9. The 33 binaries cover a wide range in eccentricity values, between 0 and 0.9. In the sample, HD15814 has the smallest periastron, ∼0.08 AU with an eccentricity of 0.410. Several studies indicated a tendency for longer cutoff periods in older binary populations (e.g., Mazeh 2008). Meibom & Mathieu (2005) suggested the Pb for the eight coeval samples as an increasing function of their age. Koch & Hrivnak (1981) claimed that the tidal force circularizes a close binary system orbit even during the main-sequence phase. Their calculation indicated that, for a binary with an initial period of 17 days, the circularization does not begin before 4 × 109 yr for any eccentricity. HD15814 has an eccentricity of 0.410, a period of 19.416 days, and an age of 3.4 × 109 yr (Holmberg et al.

5.3. Mass Ratios of the Binaries The primary-mass–secondary-mass relationship for the 33 binaries in our sample is shown in Figure 8. The secondary masses of the SB2s were estimated from the mass ratios and primary masses. For the SB1s, we determined the minimum mass of the secondary star from the orbital motion. Most binaries with large mass ratios are SB2s. SB2s in our sample have a mass ratio larger than 0.62 dominantly. We regarded a mass ratio of 0.62 as the boundary between the SB1s and SB2s. This boundary corresponds to a magnitude difference of 2.0 mag. The estimated mass ratios of HD9312 and HD43821 are larger 11


Katoh et al.

Astronomical Observatory of Japan (NAOJ). We thank all of the staff members at OAO for their support during the observations. This study was supported by “The Global COE Program: Foundation of International Center for Planetary Science” of the Ministry of Education, Culture, Sports, Science and Technology, Japan. This research has made use of the SIMBAD database and the VizieR Service, operated at CDS, Strasbourg, France. REFERENCES Abt, H. A. 1973, ApJS, 26, 365 Abt, H. A., & Levy, S. G. 1976, ApJS, 30, 273 Allende Prieto, C., & Lambert, D. L. 1999, A&A, 352, 555 Ammons, S. M., Robinson, S. E., Strader, J., et al. 2006, ApJ, 638, 1004 Bakos, G. A. 1974, AJ, 79, 866 Batten, A. H., Fletcher, J. M., & MacCarthy, D. G. 1989, PDAO, 17, 1 Batten, A. H., Fletcher, J. M., & McClure, R. D. 1983, JRASC, 77, 241 Beavers, W. I., & Eitter, J. J. 1986, ApJS, 62, 147 Burki, G., & Mayor, M. 1986, in IAU Symp. 118, Instrumentation and Research Programmes for Small Telescopes, ed. J. B. Hearnshaw & P. L. Cottrell (Dordrecht: Reidel), 385 Butler, R. P., Marcy, G. W., & McCarthy, C. 1996, PASP, 108, 500 Casagrande, L., Sch¨onrich, R., Asplund, M., et al. 2011, A&A, 530, 138 Cox, A. N. 2000, Allen’s Astrophysical Quantities (4th ed.; New York: AIP), 382 Donahue, R. A. 1993, PhD thesis, New Mexico State Univ. Duquennoy, A., & Mayor, M. 1991, A&A, 248, 485 Duquennoy, A., Mayor, M., & Halbwachs, J.-L. 1991, A&AS, 88, 281 Eastman, J., Siverd, R., & Gaudi, S. 2010, PASP, 122, 935 Goldman, I., & Mazeh, T. 1991, ApJ, 376, 260 Griffin, R. F. 1979, Obs, 99, 198 Griffin, R. F. 1981, Obs, 101, 175 Griffin, R. F. 1985, JApA, 6, 71 Heard, J. F. 1940, PDDO, 1, 194 Holmberg, J., Nordstrom, B., & Andersen, J. 2009, A&A, 501, 941 Izumiura, H. 1999, in Proc. 4th East Asian Meeting on Astronomy, ed. P. S. Chen (Kunming: Yunnan Observatory), 77 Kambe, E., Sato, B., Takeda, Y., et al. 2002, PASJ, 54, 865 Koch, R. H., & Hrivnak, B. J. 1981, AJ, 86, 438 Marcy, G. W., & Butler, R. P. 1996, AJ, 464, 147 Marigo, P., Girardi, L., Bressan, A., et al. 2008, A&A, 482, 883 Marsakov, V. A., & Shevelev, Yu. G. 1995, BICDS, 47, 13 Mathieu, R. D., & Mazeh, T. 1988, ApJ, 326, 256 Mayor, M., & Mermilliod, J. C. 1984, in IAU Symp. 105, Observational Tests of the Stellar Evolution Theory, ed. A. Maeder & A. Renzini (Dordrecht: Reidel), 411 Mazeh, T. 2008, in Tidal Effects in Stars, Planets and Disks, ed. M.-J. Goupil & J.-P. Zahn (EAS Publ. Ser. 29; Les Ulis: EDP Sciences), 1 Meibom, S., & Mathieu, R. D. 2005, ApJ, 620, 970 Morbey, C. L., & Griffin, R. F. 1987, ApJ, 317, 343 Nidever, D. L., Marcy, G. W., Butler, R. P., Fischer, D. A., & Vogt, S. S. 2002, ApJS, 141, 503 Perryman, M. A. C., & ESA 1997, in ESA Publ. Ser. 1200, The Hipparcos and Tycho Catalogues, (Noordwijk: ESA), 0 Pourbaix, D. 2000, A&AS, 145, 215 Pourbaix, D., Tokovinin, A. A., Batten, A. H., Fekel, F. C., & Hartkopf, W. I. 2004, A&A, 424, 727 Raghavan, D., McAlister, H. A., Henry, T. J., et al. 2010, ApJS, 190, 1 Richer, H. B., Hansen, B., Limongi, M., & Chieffi, A. 2000, ApJ, 529, 318 Sarma, M. B. K. 1962, ApJ, 135, 301 Sato, B., Kambe, E., Takeda, Y., Izumiura, H., & Ando, H. 2002, PASJ, 54, 873 Struve, O., & Zebergs, V. 1959, AJ, 64, 219 Takeda, G., Ford, E. B., Sills, A., et al. 2007, ApJS, 168, 297 Taylor, J. H., et al. 2000, http://pulsar.princeton.edu/tempo Tokovinin, A. A. 1991, A&AS, 91, 497 Tokovinin, A. A., & Gorynya, N. A. 2007, A&A, 465, 257 Torres, G., Andersen, J., & Gime’nez, A. 2010, A&ARv, 18, 67 Valentini, M., & Munari, U. 2010, A&A, 522, 79 Vogt, S. S., Buteler, R. P., Marcy, G. W., Fischer, D. A., & Pourbaix, D. 2002, ApJ, 568, 352 Weidemann, V. 2000, A&A, 363, 647 Wittenmyer, R. A., Endl, M., Cochran, W. D., et al. 2006, AJ, 132, 177 Wright, C. O., Egan, M. P., Kraemer, K. E., & Price, S. D. 2003, AJ, 125, 359 Wright, J. T., Marcy, G. W., Butler, R. P., & Vogt, S. S. 2004, ApJS, 152, 261 Zahn, J.-P., & Bouchet, L. 1989, A&A, 223, 112

Figure 9. Period–eccentricity relationship. The filled circles represent the 25 SB1s and 8 SB2s. The solid and dashed lines indicate the period–eccentricity relationships of binaries with periastrons of 0.10 AU and 0.15 AU, respectively. The 33 binaries cover a wide range in eccentricities of between 0 and 0.9.

2009). We consider that the eccentricity of HD15814 has not yet been altered by tidal interaction. Goldman & Mazeh (1991) calculated that circularization begins before 1 × 1010 yr for a binary system with a periastron