SEEDS DIRECT IMAGING OF THE RV-DETECTED COMPANION TO V450 ANDROMEDAE, AND CHARACTERIZATION OF THE SYSTEM

We observed V450 And as part of the SEEDS (Tamura 2009) survey, which has searched for exoplanets and imaged circumstellar disks around hundreds of nearby stars (e.g., Thalmann et al. 2011; Hashimoto et al. 2012; Janson et al. 2013). One category of SEEDS targets consists of young nearby stars that can be age-dated using their rotation periods or chromospheric activities as clocks (see Kuzuhara et al. 2013), and V450 And is included in this category (we discuss the star's age in Sections 6.2 and 6.3). Its science case, however, also resembles the category of targets which are known to have inner planets or a long-term RV trend (Narita et al. 2010, 2012; Ryu et al. 2016).

We observed V450 And with the HiCIAO camera (Suzuki et al. 2010), a high-contrast imaging instrument on the Subaru telescope. The adaptive optics system AO188 (Hayano et al. 2010) was used to reduce the image degradation caused by atmospheric turbulence and improve the Strehl ratio. AO188's atmospheric dispersion corrector (ADC; Egner et al. 2010) removed the chromaticity of atmospheric refraction. None of our observations used a focal plane mask, but all were performed with a Lyot stop in the pupil plane. HiCIAO's original Lyot stop was replaced in 2013 September with a larger, circular pupil stop (in other words, smaller pupil-plane mask) to increase throughput and improve angular resolution.

We observed the star at four epochs, controlling the image rotator to fix the pupil rotation relative to the camera (angular differential imaging, or ADI, mode, Marois et al. 2006). Each observing sequence consisted of longer sequences of frames in which the central star's point-spread function (PSF) was saturated, and shorter sequences using neutral density filters to avoid saturation. The unsaturated images were taken sparsely during one visit. The saturated images were used to search for faint companions (M. Kuzuhara et al. 2016, in preparation) while the unsaturated images were used for image registration and flux calibration. We discovered one companion candidate, about 40 times fainter than V450 And in the H-band; follow-up observations confirmed it as a low-mass stellar companion. Figure 1 shows the pair V450 And AB. Because of the modest contrast between the primary and secondary, we used only unsaturated images in each observing sequence to measure the astrometry of the system and to track its orbital motion. Table 1 summarizes the unsaturated data used in our analysis of the V450 And system; our analysis makes no use of saturated imaging. The next section discusses the measurement and calibration of the astrometry in each observing sequence.

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Table 1.  Observing Log for Unsaturated Data

Obs. Date	${N}_{\exp }$	${t}_{\mathrm{tot}}$	Filter	Mean Airmass	Field Rotation (degree)		${\rm{\Delta }}\mathrm{mag}$
(UT)		(s)			Total	Average
2012 Nov 05	10	100	J	1.09	1.0	0.12	4.23 ± 0.07
⋯	25	125	H	1.13	24	0.054	4.10 ± 0.05
⋯	10	50	${K}_{{\rm{s}}}$	1.09	0.66	0.073	3.85 ± 0.07
2013 Jan 02	16	40	J	1.39	0.96	0.024	4.18 ± 0.08
⋯	7	62	H	1.43	0.60	0.044	3.95 ± 0.06
⋯	16	24	${K}_{{\rm{s}}}$	1.42	0.74	0.020	3.82 ± 0.08
2013 Oct 16	13	195	H	2.19	1.0	0.062	4.05 ± 0.04
2015 Jan 08	50	575	H	1.08	51	0.10	4.03 ± 0.03

Note. The data sets shown in this table were obtained without a focal-plane mask but with a Lyot stop in a pupil plane (see Section 3). The average field rotation corresponds to the average of each rotation angle during an exposure. Sequences of unsaturated images were taken alternately with saturated frames.

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At an H-band contrast of only ∼40, V450 And B is bright enough to be detected in the unsaturated short-exposure data sets. This enables us to simultaneously obtain very accurate positions and photometry of both stars: our simultaneous relative photometry is unaffected by temporal variations in the Strehl ratio. We used the ACORNS pipeline (Brandt et al. 2013) to correct bad pixels, remove correlated read noise, and to correct the field distortion. We did not, however, apply any algorithms to subtract the primary star's PSF, apart from our removal of an azimuthally symmetric halo. This ensures that there is almost no self-subtraction of the companion's PSF. Our goal is to obtain precise relative astrometry and photometry, not to search for very faint companions.

We use only the H-band observations listed in Table 1 to measure relative astrometry, as HiCIAO's distortion correction is best characterized in this band. We compute the distortion correction of the HiCIAO camera using images of the dense cores of the globular clusters M5 and M15 (Brandt et al. 2013). We then compare the HiCIAO images of M5 or M15 with the archival M5 or M15 images obtained by the Hubble Space Telescope and Advanced Camera for Surveys (ACS). The distortion, plate scale, and true north of the ACS have been well calibrated (see Anderson & King 2004; Anderson 2006; van der Marel et al. 2007). With good seeing, the fractional uncertainties on the distortion are ∼10⁻⁴ near the center of the field. The nonlinear component of the distortion is extremely stable between observing runs, with nearly all of the variation confined to the plate scale. We therefore adopt our nonlinear distortion corrections from runs with good observing conditions.

In the case of 2012 November 5, the seeing was poor, so we used observations of M15 from that date to compute the plate scale and use the high-quality 2011 May distortion map for nonlinear-distortion correction. Likewise, for the 2013 January run, we corrected for only the plate scale based on the M5 data that were acquired in the same run, and the nonlinear distortions were corrected using the 2011 May distortion map. HiCIAO's Lyot stop was replaced before the 2013 October run to improve throughput and angular resolution, necessitating a new measurement of the distortion correction. In the 2013 October and 2015 January runs, we observed globular clusters for the distortion corrections. High-quality data of M5 are available for 2015 January run. Unfortunately, the observing conditions for the 2013 October M15 calibrations were too poor to permit a good measurement of the plate scale and the other distortion components. For this data set we instead used observations of M15 taken in 2013 November, and added an additional uncertainty of 0.25% to the plate scale, corresponding to the measured run-to-run scatter. We found that the new Lyot stop, installed in 2013 September, significantly affected HiCIAO's PSF but had a negligible impact on distortion correction.

After correcting for field distortion, we measured the PSF centroids of the primary star on each individual frame by fitting elliptical Gaussians. Then, all the frames from a given observing night were shifted to a common center. Next, the radial profile of the primary star's PSF was subtracted from each data frame to remove the PSF halo. Failing to remove the PSF halo would bias our measurements both of the companion's flux and position, as the halo's mean and gradient are both nonzero at the location of V450 And B. We injected artificial point sources to determine any loss of companion flux due to halo subtraction. We applied these correction factors, though they are mostly very small (≪10%). Spatial variations in the Strehl ratio are negligible at the $0\buildrel{\prime\prime}\over{.} 5$ separation of the binary, while HiCIAO's flat-field images are stable to ∼2% over a period of years (Brandt et al. 2013), smaller than all of our derived photometric uncertainties. Because our data were obtained with the image rotator maintaining the orientation of the PSF (ADI mode), the PSF-subtracted frames were de-rotated to align their y axes to celestial north. Finally, the de-rotated frames were combined into a single final frame. We fit an elliptical Gaussian to measure the centroid of V450 And B in this final, halo-subtracted frame; Table 2 lists the relative astrometry for each epoch. Figure 1 shows the final image for the observations at 2015-01-08 without subtracting the radial profile of V450 And A. Note that our analyses for the companion V450 And B are all based on the images with subtracted PSF halos.

Table 2.  Astrometric Measurements

Obs. Date	MJD	Separation Angle	Position Angle
(UT)	(days)	(mas)	(°)
2012 Nov 05	56236.342	437.87 ± 0.38	73.095 ± 0.062
2013 Jan 02	56294.375	437.5 ± 1.2	71.76 ± 0.17
2013 Oct 16	56581.652	432.7a ± 1.2	65.512a ± 0.089
2015 Jan 08	57030.244	422.93 ± 0.43	55.61 ± 0.055

Note.

^aCorrected for the effect of atmospheric refraction. The separation and position angle before the correction are 432.3 mas and 65520, respectively.

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To derive the flux ratio between the components, we compare the photometry of the central star and the companion in the same final, combined image. As described above, we measure the companion flux after subtracting the central star's halo and applying a small correction for flux loss. In order to estimate the error in our measured contrasts, the final image is first convolved with a circular aperture having a radius equal to the full width at half maximum (FWHM) of the PSF. As in Brandt et al. (2013), we use the convolved image and compute the standard deviation of residual signals in an annulus surrounding the central star at the same separation as the companion. This scatter is much larger than the companion's photon noise.

Our four data sets obtained over three nights contain a small number of pixels with significant (>3%) nonlinearity. Removing frames with one or more pixels above this nonlinearity threshold has a negligible effect on our results, apart from a 0.04 mag difference in photometry for the 2013 January H-band observations. We do not exclude these frames when deriving our final photometry (Table 1) and astrometry (Table 2).

Our error budget for astrometry is dominated by errors in fitting elliptical Gaussians and in determining the plate scale, with lesser contributions from uncertainties in the nonlinear image distortion and from differential atmospheric refraction. We evaluate the uncertainties in the distortion correction using a Markov Chain Monte Carlo (MCMC) method to sample the space of coefficients in the distortion correction polynomial (see Brandt et al. 2013). Where good images of a dense star cluster are available (as for the 2015 January run), the resulting separation errors are negligible ($\lesssim 0.1$ mas). For some runs, however, simultaneous calibration data are unavailable or are of poor quality. In these cases, we use the 2011 May calibration for the nonlinear distortion and for the orientation of true north. We estimate the resulting uncertainty using the scatter among other runs with good calibration data. The scatter due to the nonlinear distortion is negligible along the vertical axis of the detector, but ranges from $\lesssim 0.1$ mas up to ∼0.3 mas along the horizontal axis depending on the location in the image where the star is observed. The scatter in the angle of true north is negligible, 0031 ($5\times {10}^{-4}$ rad).

For all but the 2013 October run, we measured the plate scale and its uncertainty using MCMC on simultaneous calibration images. The resulting uncertainties are very small, $\lesssim 0.16$ mas at a separation 05. The 2013 October run lacks simultaneous calibration data, so we used the full distortion correction measured in 2013 November. We note that a plate scale variation between each run contributes to an astrometric uncertainty. We estimate the resulting astrometric uncertainty from the plate scale to be a non-negligible ∼1.1 mas by computing the plate scale scatter among 15 other runs with identical instrument configurations (see above for an uncertainty due to the variation of nonlinear distortions).

Finally, we determine the centroid error by calculating the scatter of star–companion separations among sets of frames in an imaging sequence. Before calculating the scatter, all the individual PSF-subtracted frames for a run were divided into several groups and the data in each group were combined. We omitted this step for 2013 January 2 since we had just seven frames, and directly calculated the scatter of separations among those seven frames. The scatter in astrometry among groups of frames ranges from 0.03 to 0.12 pixels (0.3–1.1 mas). This is larger than the field distortion errors for all but the 2013 October run, for which simultaneous distortion data were unavailable. We do not independently incorporate an error of the primary star's centroid into the total error budget. Instead this error is inserted into the astrometry error by computing a scatter of separation measurements between the primary and secondary. This flows from the fact that scatter of the primary star's centroids result in a scatter of measurements of the primary–secondary separations.

We took all our data with the ADC (Egner et al. 2010) in place. This set of prisms corrects the dependence of the PSF center on wavelength, removing the systematic shift in centroid due to difference in spectral type. Atmospheric refraction also shifts PSF centroids over the field of view. This effect is negligible ($\lt 0.1$ mas) for all but the 2013 October observations, which were conducted at airmass 2.19. In that case, we computed the index of refraction as in Mathar (2004, 2007), taking into account the weather conditions during observations: outside atmospheric pressure of 616.3 hPa, outside temperature of 273.19 K, and humidity of 46%, as given in the CFHT weather archive.³² We then corrected the astrometry using a somewhat simplified version of the approach described in Hełminiak (2009). A correction of ∼0.4 mas was applied to the relative separation, while −0008 was applied to the position angle. We added these offsets to our astrometry, but note that they are smaller than the astrometric uncertainties. The error bar for each astrometry in Table 2 includes the uncertainties of centroiding, plate scale, angle of true north, and nonlinear distortions.

The complete set of archival spectra and RV measurements consists of 80 observations coming from three instruments. The total time span of the data is over 18 years, which nearly covers the full orbital period. We present them in Table 7 in the Appendix.

3.4.1. ELODIE

3.4.2. SOPHIE

3.4.3. Hamilton

V450 And is a BY Dra-type variable, and the photometric variability is likely related to the presence of spots on the rotating disk of the star, so its period represents the period of rotation. Unfortunately, the value of 7.6 day given in Strassmeier et al. (2000) is marked as uncertain. A value of 7 day can also be found in the literature (Isaacson & Fischer 2010), but it was found from period–activity relations, not measured directly, and we also find it unreliable.

In order to assess the rotation period we took the Hipparcos time-series photometry (Perryman et al. 1997) and ran a Lomb–Scargle periodogram.³⁵ We focused on periods between 2 and 50 days, and set the constant step in frequency of $1/10W\simeq 9.13\times {10}^{-5}$ day⁻¹, where $W\simeq 1096$ day is the time span of the Hipparcos data. The most distinct peak is found at $P=5.743\pm 0.003$ day or $f=0.17411(91)$ day⁻¹. The periodogram and Hipparcos data phase-folded with this period are shown in Figure 2.

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As a BY Dra type variable, V450 And has been known to show some level of activity. Emission in Ca ii H and K lines has been noted (Strassmeier et al. 2000; Gray et al. 2003; Wright et al. 2004; Isaacson & Fischer 2010), and a photometric variability of 0.02 mag has also been reported (Strassmeier et al. 2000). In Section 3.5 we described how the period of rotation (5.743 day) has been found. The same period can be seen in SOPHIE radial velocities, i.e., in the residuals $(O-C)$ of the orbital fit. In Figure 7 we present them as a function of the rotation phase, and the bisector span bis. The correlation between bis and $(O-C)$ proves the activity origin of the observed RV modulation. The activity of V450 And A mimics a 0.14 M_J planet on an eccentric orbit—a pseudo-orbital fit to all the residuals is also shown, with an rms of only ∼8 m s⁻¹. We would like to note that we did not model the activity-related RV variations together with the orbital motion for two reasons. First, only the SOPHIE data are precise enough to see it clearly, and they do not cover a substantial part of the orbit. Second, we suspect that the pattern of spots (and thus the RV modulation they produce) evolves in time. When making the pseudo-orbital fit to residuals from only one season, one can lower the rms to 2–3 m s⁻¹, and for each season obtain different parameters (shape) of the pseudo-orbit (different $e,K,\omega$, etc.).

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In the further analysis we thus assumed 5.743 day to be the period of rotation. Taking the best-fitting dynamical mass of the star, and $\mathrm{log}(g)$ from the spectral analysis, we can estimate the radius of V450 And A to be 1.09${}_{-0.11}^{+0.09}$ ${R}_{\odot }$. This value of radius, the estimated rotational period, and projected velocity of rotation $v\sin (i)$ lead to the rotation inclination angle of 24.8 or 1552 ± 55, which is in agreement with the orbital inclination. Due to a long orbital period and young age (see the next section), we posit that the system formed in this way, rather than was aligned by tidal forces. A nearly pole-on orientation of the component A may also partially explain why the amplitude of photometric variability is only 0.02 mag—if spots are present near the star's pole, their visibility does not change much with the phase of rotation. Such polar or high-latitude spots have been observed on stars of similar mass, spectral type, and rotation period (e.g., Strassmeier & Rice 1998; Sanchis-Ojeda et al. 2013). In addition, theoretical models support this tendency (e.g., Granzer et al. 2000; Yadav et al. 2015). Hence, it is likely that we observed spots near the star's pole, systematically affecting our luminosity and temperature estimates for V450 And A (see Section 6.3).

Stars with convective envelopes generate magnetic fields that couple them to their stellar winds. The stars shed angular momentum, spinning down and becoming less active with time (Skumanich 1972). This spin-down, either measured directly through a rotation period or indirectly through coronal and chromospheric activity, can be used to date cool main sequence stars (Barnes 2003). The decline of rotation and activity has been calibrated using clusters and binaries to enable gyrochronology (Barnes 2007; Mamajek & Hillenbrand 2008).

V450 And A's B − V was measured by Tycho-2 (Høg et al. 2000) and we convert that to the Johnson B − V ($=0.690\pm 0.015$), which is adopted in the following analysis. V450 And has well-measured rotation and activity indicators, including the period of 5.7 days derived in the preceding section, a ROSAT X-ray flux (Voges et al. 1999), and Ca ii HK chromospheric activity measurements. We use the bolometric corrections of Flower (1996) as corrected by Torres (2010) to convert the measured X-ray flux into R_X, the ratio of X-ray to bolometric flux; we obtain $\,{\mathrm{log}}_{10}\,{R}_{{\rm{X}}}=-4.65$. From Pace (2013), there are 29 literature measurements of the Ca ii HK S index, ranging from 0.235 to 0.348. The lowest measured value, from White et al. (2007), is a clear outlier, while the single measurement from Strassmeier et al. (2000) must be calibrated to the Mount Wilson system. The remaining 27 measurements, from Gray et al. (2003), Wright et al. (2004), and Isaacson & Fischer (2010), have a mean of 0.324 and a standard deviation of 0.013. The median of all literature measurements is an indistinguishable 0.322; we adopt this value as our Ca ii HK index and convert it to $\,{\mathrm{log}}_{10}\,R{^{\prime} }_{\mathrm{HK}}=-4.48$ using the formulae given in Noyes et al. (1984).

We adopt the approach of Brandt et al. (2014) to obtain a posterior probability distribution on the age of V450 And from its rotation and activity. Brandt et al. (2014) used the calibrated relations of Mamajek & Hillenbrand (2008), but also accounted for the fact that stars spend a variable amount of time as rapid rotators before they begin to spin down in earnest (Barnes 2007). For a ∼1 ${M}_{\odot }$ star, Brandt et al. (2014) assumed an additional spin-down time uniformly distributed between 0 and ∼150 Myr, effectively broadening the posterior probability distributions.

Figure 8 shows the ages as inferred from the method of Brandt et al. (2014) using the rotation and activity indicators individually, and by combining all age indicators. We obtain a final age estimate of ${380}_{-100}^{+220}$ Myr, (at 90% confidence). There is a mild tension between the age preferred by chromospheric activity (300–1800 Myr) and that favored by our measured rotation period, which dominates our posterior probability distribution. Following Brandt et al. (2014), we include a 5% probability that the star's rotation and activity do not reflect its true age and that the star could be at any point on its main sequence evolution.

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In order to estimate the age of the system on the basis of theoretical stellar evolution models, we compared our results with the Baraffe et al. (2015, hereafter BHAC15) and PAdova-TRieste Stellar Evolution Code (PARSEC; Bressan et al. 2012; Chen et al. 2014) isochrones. The former set is calculated only for the solar composition, but our iSpec analysis gives metallicity very similar to solar. For PARSEC we used our value of $[M/H$], which translates into Z = 0.0166 in this set. We checked and confirmed that using the solar composition (Z = 0.0152) does not change the final results significantly, so the usage of [M/H] = 0.0 BHAC15 models is justified.

For the comparison we used our estimates of dynamical masses and absolute ${{JHK}}_{{\rm{s}}}$ magnitudes, as they are the most robust parameters we can obtain from our observations for both components. To compute the absolute magnitudes, we assumed the Hipparcos distance to the system, and took the total apparent brightnesses of the system and our magnitude differences from HiCIAO. We list the absolute magnitudes in Table 6. The results are shown in Figure 9. Errors of the values for both components come mainly from the parallax uncertainty, with a small contribution from the uncertainties of the observed magnitudes. For the secondary only, the second dominant source of errors is the differential photometry from Table 1.

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Table 6.  Absolute JHK Magnitudes of V450 And

	Primary	Secondary
MJ (mag)	3.822 ± 0.037	8.002 ± 0.086
MH (mag)	3.530 ± 0.041	7.581 ± 0.044
${M}_{{K}_{{\rm{s}}}}$ (mag)	3.455 ± 0.039	7.275 ± 0.088

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Both sets of models give quite consistent results. The resulting ages are ${400}_{-250}^{+2600}$ Myr ($\mathrm{log}(\tau )={8.60}_{-0.43}^{+0.88}$) for BHAC15, and ${220}_{-90}^{+2120}$ Myr ($\mathrm{log}(\tau )={8.34}_{-0.22}^{+1.03}$) for PARSEC. We adopt the latter because of the smaller error bars. The best-fitting age values are tightly constrained by the best-fitting value of m₂, as found in the orbital fit. The lower limits are defined by the 95% confidence level of the parameters of the secondary, while the primary analogously defines the upper limits. In other words, isochrones of the given range of ages reside within mass versus absolute (${{JHK}}_{{\rm{s}}}$) magnitude planes that are defined by 95% confidence levels (corresponding to ∼2σ for symmetrical posteriors), as derived from both components. The large positive uncertainty is strictly related to the fact that stars do not change much during the main sequence phase, and isochrones for much older years still reside within the error bars shown in Figure 9.

The primary tends to be systematically too faint for its mass. The PARSEC model, for $\tau =220\,\mathrm{Myr}$ and $[M/H]$ = 0.038, predicts absolute magnitudes lower by 0.92 in U, 0.65 in V, and 0.30 mag in K with respect to observed values—5.94 (Myers et al. 2015), 5.74 (Høg et al. 2000), and 3.46 mag (Cutri et al. 2003), respectively, as derived from literature data and distance. This is mainly because the effective temperature at the age of ∼220 Myr is ∼450 K higher in models than what we found with iSpec. This can be at least partially explained by the presence of polar spots, seen in photometry, which decrease the observed T_eff and brightness.

Our analysis also shows that the secondary has just reached the main sequence, but spots may also hamper its results, making it appear fainter. In such a case the true absolute magnitude would be different, and the secondary would move up on Figure 9.

Ages derived from comparison with both sets of models are in good agreement with results from Section 6.2. In Figure 9 we also plot isochrones for ages of 280 and 600 Myr, which are the 90% confidence limits of the Brandt et al. (2014) method. With a little higher temperature of the primary, the agreement would be even better. Additionally, our m₁ determination may be slightly overestimated, due to uncertainties in parallax or astrometry, for example. Note also that the median of the m₁ posterior distribution is smaller. Because, as discussed in Section 4, the sum of two masses is fairly well constrained, this would mean that m₂ is higher. Including the possible effect of spots on component B, described above, the secondary would then move on Figure 9 almost exactly along the isochrone. The resulting age would thus be intact. This issue would be fixed if radial velocities of the secondary were measured directly.

Overall, we obtained a consistent image of the V450 And binary. It is a fairly young, few hundred Myr old system, but with both components already on the main sequence. Probably both stars are active (primary for certain), and possibly their mass ratio is slightly closer to 1, as compared with the best-fitting value we obtained. Our age estimates, especially from Section 6.2, agree well with one of the two mostly accepted determinations of the age of the Castor moving group: 440 ± 40 Myr (Mamajek 2012). The less-agreeing one is ${700}_{-75}^{+150}$ Myr (Monnier et al. 2012). However, it was recently suggested by Mamajek et al. (2013) and Zuckerman et al. (2013) that this moving group is actually a collection of kinematically similar stars showing a spread of ages, rather than a well-defined kinematic structure.