THE κ ANDROMEDAE SYSTEM: NEW CONSTRAINTS ON THE COMPANION MASS, SYSTEM AGE, AND FURTHER MULTIPLICITY

We imaged the κ And system on UT 2012 December 23 using "Project 1640" (Hinkley et al. 2011c; Oppenheimer et al. 2012) on the 200 in Hale Telescope at Palomar Observatory. Project 1640 is a coronagraph integrated with an integral field spectrograph (IFS; Hinkley et al. 2008) covering the YJH bands. This instrument ensemble is mounted on the Palomar "PALM-3000" adaptive optics (AO) system (Dekany et al. 1998; Roberts et al. 2012a), which in turn is mounted at the Cassegrain focus of the Hale Telescope. In addition, the system uses an internal wave front calibration interferometer (e.g., Wallace et al. 2004; Zhai et al. 2012) for reducing non-common path wave front errors internal to the instrument ensemble, thereby boosting performance at small angular separations.

Starting at an airmass of 1.02, 16 Project 1640 multi-spectral images were obtained, each with exposure time of 183 s. The star was placed behind the coronagraphic mask, the PALM-3000 AO control loops were locked, and additional corrective wave front sensor offsets were applied to the PALM-3000 AO system from the wave front calibration interferometer, thus minimizing the halo of correlated speckle noise. To alleviate the inherent uncertainty in the position of the occulted star in coronagraphic images (e.g., Digby et al. 2006), the position of the star was determined by using a set of fiducial reference spots created by a physical pupil plane grid in the Project 1640 coronagraph (Sivaramakrishnan & Oppenheimer 2006; Marois et al. 2006b).

The Project 1640 data reduction pipeline is described in Zimmerman et al. (2011). To convert the image data counts obtained by the spectrograph to physically meaningful quantities, the counts in a Project 1640 pupil plane image of the κ And system were measured with the star moved off the coronagraphic mask obtained shortly after the science observations. In this configuration, the entire field of view of the pupil plane is uniformly illuminated. Comparing the counts measured in each channel in the data cube with the actual flux value from an empirical spectrum for a B9 star from the Pickles Stellar Spectral flux library (Pickles 1998) provides a relation of data counts in the science camera to physical units of flux density.

Extracting a spectrum of an object such as κ And B is challenging due to the ∼10⁴ contrast ratio between it and the host star at only 1''. The single largest hindrance to extraction of high signal-to-noise spectra is the quasi-static speckle noise in the image focal plane (Racine et al. 1999; Marois et al. 2000; Hinkley et al. 2007). For objects with brightness greater than or comparable to the speckle noise halo (e.g., Hinkley et al. 2010, 2011b, 2013; Zimmerman et al. 2010; Pueyo et al. 2012b), evaluation of companion spectra can be performed with conventional aperture photometry. However, for objects with higher contrast such as κ And B or HR 8799 (Oppenheimer et al. 2013), an IFS can improve sensitivity through the suppression of this quasi-static speckle noise in the image (Crepp et al. 2011; Pueyo et al. 2012a).

To reduce the effects of quasi-static speckle noise in our multi-spectral images, we use speckle suppression techniques based on the principle component analysis algorithm outlined in Soummer et al. (2012). This method uses a basis of eigenimages created by a Karhunen–Loève transform of point spread function (PSF) reference images to perform the PSF subtraction, and it is amenable to point source forward modeling (L. Pueyo et al., in preparation). Applications of this method have been demonstrated for the directly imaged planets in the HR 8799 system (Oppenheimer et al. 2013). Figure 1 shows three images from the Project 1640 IFS subsequent to our speckle suppression post-processing corresponding the Y-, J-, and H-band central wavelengths.

Zoom In Zoom Out Reset image size

As with any form of PSF subtraction (e.g., classical ADI, LOCI; Marois et al. 2006a; Lafrenière et al. 2007), the performance of the algorithm centers on robust co-alignment of the PSF reference images. To align our reference images, we perform an initial alignment based on the fiducial astrometric reference spots in the data and perform a subsequent sub-pixel cross-correlation using the image speckles. To verify that the extraction of spectra is robust and that flux is not significantly depleted from the κ And B source, we execute a parameter space search as follows: we use 16 different geometries near the location of the companion (which includes varying the size of the search zone and the radial exclusion parameter necessary to mitigate cross talk between nearby spectral channels) and vary the number of eigenmodes in the PSF subtraction from 1 to 130. This parameter search results in ∼2000 spectra for the κ And B companion. From these ∼2000 spectra, we discard any spectra in which (1) the astrometric position of the companion is not consistent between wavelength channels or (2) a sharp flux drop is detected with a small change in the number of modes. Eliminating reduced spectra in case (1) ensures that the extraction is not biased by residual speckle noise (should a speckle have some overlap with the companion then it will yield a wavelength-dependent astrometric bias). A sharp drop in flux over a small number of modes indicates that too many eigenmodes are being used, thus in case (2) we eliminate spectra corresponding to overly aggressive PSF subtractions. Finally, we further trim this subset by only keeping the spectra that exhibit a local signal-to-noise ratio > 3 for all wavelengths in the band of interest (either Y+J or H). This procedure leads to ∼40 high-quality spectra for the companion. The mean of these values comprises the spectral points plotted in Figures 2 and 3 (green individual points), and the error bars denote the standard deviation of these ∼40 spectra plus the uncertainty associated with the pupil-plane spectral calibration added in quadrature.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Figure 2 shows the YJH-band spectrophotometry from Project 1640 for κ And B. Overlaid with the spectra in Figure 2 are empirical spectra for field-age "standard" objects taken from Kirkpatrick et al. (2010), ranging from spectral type L0 to L8. The empirical spectra are normalized such that they match the Project 1640 flux at 1.28 μm, and the figure identifies three regions near 1.1, 1.4, and 1.8 μm where telluric water absorption is particularly strong. Assuming a surface gravity value appropriate for dwarf-like objects, the Palomar data show a best match to the mid-L spectral types. Specifically, as demonstrated in Table 2, a χ² goodness-of-fit metric reveals a best-fit to the L4 field object 2MASS J21580457−1550098.

However, as we discuss in Section 3.2, the κ And system likely has an age of 220 ± 100 Myr, which is significantly younger than typical field ages (∼few Gyr). Thus, comparison with spectra of L-dwarfs with known indicators of youth may be more appropriate. Figure 3 shows our YJH-band spectrophotometry along with several young and intermediate age substellar objects ranging from the very young (∼10 Myr) object 2MASS J12073346−3932539b (hereafter 2M1207b; Patience et al. 2010) to the mid–late young L-dwarf 2M0959 (∼150 Myr; J. K. Faherty et al. in preparation) to LP 944-20, a ∼300 Myr late-M dwarf (Burgasser et al. 2008). Several of these objects are discussed in Section 2.4 and shown in Figure 8 as well. Among the young objects, the best-fitting (χ² = 0.76) synthetic spectrum to our data is 2MASS J01174748−3403258 (hereafter 2M0117-3403), a L1 ± 1 "β" intermediate-gravity brown dwarf (Allers & Liu 2013). Indeed, the best-fit template spectrum of the L1 object 2M0117 to our κ And B spectra has a (J − H) = 0.97 ± 0.05 well matched to that of κ And B. Thus, comparison to objects with ages more appropriate to κ And implies a slightly earlier spectral type object (L1: 2000 ± 200 K; e.g., Kirkpatrick 2005) than would be inferred for a later type field age L4 object (1700–1900 K).

The comparable quality of fits to empirical spectra of the intermediate-gravity L1 object and the L4 field object prevents us from placing extremely strong constraints on the spectral type of κ And B. Given the relatively low spectral resolution and finite wavelength coverage (YJH bands) of Project 1640 data, these data may only be able to discern a range of spectral types for this companion (e.g., ∼L1–L4). Further, discerning gravity-sensitive features from these data may be challenging, especially at high contrast, when heavy contamination from speckle noise is present. Observations of targets with well known gravity features may be needed to calibrate the strength of gravity effects in the data. Nonetheless, our best match to the low-gravity young object 2M0117 is likely a point of consistency with our revised 220 Myr age of the primary (Section 3.2). We thus adopt a conservative estimate of L1 ± 1 for κ And B. As we show below, fitting synthetic models to our spectra give temperatures consistent with an L1 ± 1 object (Section 2.3), and color–magnitude diagram analysis supports the L1 ± 1 identification (Section 2.4, Figure 7).

To directly constrain the physical properties of this object, we compare (e.g., Roberts et al. 2012b; E. Rice et al. in preparation) the observed P1640 spectrum to a grid of synthetic spectra from the PHOENIX models (Hauschildt et al. 1997; Barman et al. 2001; Allard et al. 2001). The model atmospheres cover T_eff = 1400–4500 K and log(g) = 3.0–6.0 in intervals of 50 K and 0.1 dex at solar metallicity using the dusty version of dust treatment and are described in more detail by Rice et al. (2010) and Roberts et al. (2012b). The adopted best-fit parameters are the 50% quantile values of the 10⁶ link posterior distribution functions from a Markov chain Monte Carlo (MCMC) analysis that interpolates between calculated synthetic spectra, creating an effectively continuous grid of models.

We use three different spectral ranges: 0.9–1.32 μm (YJ bands), 1.47–1.78 μm (H-band), and the full range 0.9–1.78 μm (YJH-bands) for the spectral comparison. We exclude the four points occupying the water band separating the J and H bands (∼1.4 μm) as well as the final H-band point near 1.8 μm, but we include the two points in the water band between the Y and J bands since their uncertainties are comparable with points in the bandpasses. Figure 5 shows the three best-fit synthetic spectra and their input physical parameters for each spectral region plotted over the entire observed spectrum. The fit to the full set of data (YJH bands) is the best overall and has similar parameters (2040$^{+58}_{-64}$ K, log(g) = 4.33$^{+0.88}_{-0.79}$, ±68% confidence intervals) as the YJ-band-only fit (2096$^{+103}_{-106}$ K, log(g) = 4.65$^{+1.20}_{-0.89}$). As Figure 5 shows, the fit to only the H-band data significantly underpredicts several flux points in YJ bands, producing a temperature of ∼1550 K, and we regard this as physically unreasonable. Figure 4 shows the posterior distributions for fits for each of the three cases along with the marginalized one-dimensional posterior distributions for each fitting parameter.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In Figure 6, we compare the best-fit T_eff and log(g) values to parameters predicted by DUSTY00 models from Chabrier et al. (2000) and Baraffe et al. (2002) for ages ranging from 1 Myr to 5 Gyr and masses ranging from 8 M_Jup to 75 M_Jup. The uncertainties on the best-fit physical parameters for κ And B represent the width of the distribution of the 10⁶-link Markov chain values marginalized over the other parameter, as described in Roberts et al. (2012b; E. Rice et al. in preparation). Also shown are the locations in log(g) versus T_eff space of several young M and L-type objects taken from Bonnefoy et al. (2013a) and Bowler et al. (2013).

Zoom In Zoom Out Reset image size

The locations of the YJ-band and YJH-band best-fit T_eff values (2000–2100 K) and their uncertainties are consistent with an L1 ± 1 spectral type (e.g., Kirkpatrick 2005; Stephens et al. 2009). However, the constraints on the surface gravity for κ And B still permit a wide range of ages, from very young to several hundred Myr. However, the range still includes our revised age of 220 ± 100 Myr. Indeed, low-resolution spectral fits to known young very low mass objects presented in E. Rice et al. (in preparation) also suggest surface gravities higher than would be expected for the ∼10–100 Myr ages, possibly indicating the inadequacy of the simplified dust treatment of the dusty PHOENIX model atmospheres in recreating the emergent spectra of young, very low-mass objects.

Combining luminosity with NIR color has emerged as a potentially powerful lever for deciphering age properties of brown dwarfs and giant planets. For example, normal field L-dwarfs typically have (J − K_s) = 1.3–1.8, while the γ low-gravity sources are ∼0.3–0.6 mag redder than the median for their respective spectral types (Figure 8). When one combines the absolute JHK magnitudes of the γ sources and compares them to equivalent spectral type targets, one finds they are not just redward but also up to 1.0 mag underluminous (Faherty et al. 2012, 2013; Liu et al. 2013) in the NIR. The same trend has been cited in directly imaged giant exoplanet studies (e.g., 2M1207b and HR 8799b; Chauvin et al. 2004; Marois et al. 2010). Figures 7 and 8 show the properties of κ And B compared to field brown dwarfs as well as five well-studied, young L-dwarfs: AB Pic B, CD-35 2722 B, 2M0355+1133, 2M0122−2439, and 2M1207 B (Chauvin et al. 2004, 2005; Wahhaj et al. 2011; Faherty et al. 2013; Bowler et al. 2013). Several of these young L-dwarfs are used for comparison in Figure 3 (Section 2.1).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

As shown in Figure 7, κ And B has a comparable absolute magnitude to L0–L4 dwarfs, including the planetary-mass object AB Pic B (SpT L1; Bonnefoy et al. 2013a). However, AB Pic B is redder than the "main sequence" of L and T dwarfs as well as κ And B, and forms a sequence with comparably young sources 2M1207b and 2M0355. Indeed, Figure 8 shows that κ And B is consistent with the median (J − K_s) colors of field L-dwarfs and is marginally inconsistent with the young γ low-gravity objects. The luminosity alone rules out ∼mid to late spectral types, as the lower temperatures would make κ And B significantly overluminous. This suggests an earlier spectral type, consistent with the L1 ± 1 spectral type derived in Section 2.2.

We list the key Stellar parameters for κ And A in Table 3. κ And A is a V = 4.138 ± 0.003 mag (Mermilliod 1997) B9IVn (Cowley et al. 1969; Garrison & Gray 1994) star at a distance of 51.6 ± 0.5 pc (ϖ = 19.37 ± 0.19 mas; van Leeuwen 2007). The "n" in the spectral type signifies that it is a fast rotator, however, its vsin i (150 km s⁻¹; Abt et al. 2002) is not unusual for field B9 stars (Kraft 1967). At this distance, results from reddening surveys suggest that the star should be negligibly reddened (E(b − y) < 0.02 mag; Reis et al. 2011).

Table 3. Stellar Parameters

(1)	(2)	(3)	(4)
Parameter	Value	Units	Ref.
Parallax(ϖ)	19.37 ± 0.19	mas	1
Distance(1/ϖ)	51.63 ± 0.51	pc	1
μα*	80.73 ± 0.14	mas yr−1	1
μδ	−18.70 ± 0.15	mas yr−1	1
vR	−12.7 ± 0.8	km s−1	2
U	−11.5 ± 0.3	km s−1	This work
V	−20.1 ± 0.5	km s−1	This work
W	−5.9 ± 0.6	km s−1	This work
mV	4.138 ± 0.003	mag	3
MV	0.574 ± 0.037	mag	4
Teff,	11361 ± 66	K	5
vsin i	150	km s−1	6
log (L/L☉)	1.895 ± 0.024	dex	7
Radius	2.29 ± 0.06	R☉	7
Mass	2.8$^{+0.1}_{-0.2}$	M☉	This work
Age	220 ± 100	Myr	This work

References. (1) van Leeuwen 2007; (2) Gontcharov 2006; (3) Mermilliod 1997; (4) this paper, calculated using data in this table; (5) Fitzpatrick & Massa 2005; (6) Abt et al. 2002; (7) calculated using values from Fitzpatrick & Massa (2005) and updated using the new Hipparcos parallax from van Leeuwen (2007).

Download table as:  ASCIITypeset image

Several lines of evidence point to a lower surface gravity for κ And A compared to what would be expected of a ∼30 Myr old star. Early indications of a luminosity class different than the dwarf categorization were presented by Cowley et al. (1969) and Cucchiaro et al. (1977), whose ultraviolet line analysis led to classification of κ And A as "gB9," indicating a surface gravity more indicative of giants rather than dwarf stars. Thereafter, the fitting of atmospheric models to ultraviolet photometry by Malagnini et al. (1983) derived a surface gravity of log(g) = 3.69—lower than the log(g) ≃ 4.2–4.5 value typical for luminosity class V stars. Furthermore, surface gravity estimates of log(g) = 4.17, 4.10, 3.97, 3.87, and 3.78 were estimated by Allende Prieto & Lambert (1999), Fitzpatrick & Massa (2005), Prugniel et al. (2007), Wu et al. (2011), and Bonnefoy et al. (2013b), respectively. Taken as a group, these values are more commensurate with luminosity class IV than typical class V dwarf stars.

As a demonstration of this, Figure 9 shows these values from the literature in a log(g) versus T_eff diagram. This figure also shows a region of log(g) space (shaded band) spanned by a compendium of spectroscopic surface gravity measurements for subgiant standard stars from the PASTEL database (Soubiran et al. 2010).²⁰ An assessment of the quality of the spectroscopic standards was made: those that showed the most consistency in the literature and/or had the best pedigrees were used. This band has a width of ±0.19 dex, as determined by the 1σ variation of the log(g) measurements from the subgiant standards. This scatter reflects a mix of differences among spectroscopic log(g) values published for a single subgiant standard star as well as standard-to-standard differences. Given the heterogeneity of the data, we do not attempt to disentangle which effects dominate, but the data seem to suggest that ±0.2 dex rms accuracy in log(g) is a reasonable lower limit on the predictive power of luminosity class IV to predict surface gravity. Fitting a fifth-order polynomial to the log(g) measurements (spanning spectral types B0 to K1) predicts a log(g) = 3.75 ± 0.19 for a B9IV star.

Zoom In Zoom Out Reset image size

κ And's effective temperature (T_eff) has been estimated as 10594 K (Prugniel et al. 2007), 10733 ± 247 K (Wu et al. 2011), 10839 ± 200 K (Zorec & Royer 2012), 10965 K (Allende Prieto & Lambert 1999), 11246 K (Grosbol 1978), 11240 K (Malagnini et al. 1983; Morossi & Malagnini 1985), 11310 K (Napiwotzki et al. 1993), 11361 ± 66 K (Fitzpatrick & Massa 2005), and 11535 K (Westin 1985). Arguably the most comprehensive analysis is by Fitzpatrick & Massa (2005), who fit the Kurucz ATLAS9 model synthetic spectra to optical/infrared photometry and IUE ultraviolet spectra. Fitzpatrick & Massa (2005) derived extremely well-constrained stellar parameters of T_eff  = 11361 ± 66 K, [Fe/H] = −0.36 ± 0.09 dex, radius 2.31 ± 0.09 R_☉, and spectroscopic surface gravity log(g) = 4.10 ± 0.03 dex. Given their adopted distance based on the original Hipparcos catalog (d = 52.0 ± 1.6 pc), their parameters imply an angular diameter of 413 ± 16 μas (of which ±13 μas is due to the distance error, with presumably ±10 μas coming from the uncertainty in the bolometric flux). Using the revised Hipparcos parallax of ϖ = 19.37 ± 0.19 mas (d = 51.63 ± 0.51 pc; 1%  error), we update the luminosity estimate from Fitzpatrick & Massa (2005) to log(L/L_☉) = 1.895 ± 0.024 dex.

More accurate determinations of luminosity and T_eff could easily be made if the inclination of κ And were to be determined through interferometry (e.g., Monnier et al. 2012), enabling stellar parameters to be computed that are not biased by our unknown viewing angle of this rapid rotator. We discuss aspects of the star's inclination in greater detail in Section 3.4.

3.2.1. Chemical Composition

3.2.2. log(g) versus T_eff Analysis

3.2.3. Luminosity versus T_eff Analysis

In Figure 10, we plot the H-R diagram position for κ And—adopting the T_eff  from Fitzpatrick & Massa (2005)—with the revised luminosity from Section 3.1 along with evolutionary tracks and isochrones from Bertelli et al. (2009) assuming approximately protosolar composition (Y = 0.27, Z = 0.017). Sampling within the T_eff and luminosity uncertainties using Gaussian deviates, we find that the H-R diagram position is consistent with an age of 140 ± 17 Myr and a mass of 2.89 ± 0.03 M_☉. Adopting the Bertelli et al. (2009) tracks for a slightly lower (yet plausible) helium mass fraction (Y = 0.26, Z = 0.017), the H-R diagram point is consistent with age 139 ± 17 Myr (2.90 ± 0.03 M_☉). If we decrease the metal fraction by ΔZ = 0.001 (Y = 0.27, Z = 0.016), this shifts the age slightly upwards to 152 ± 16 Myr (2.84 ± 0.03 M_☉). Lowering the metal fraction to levels suggested for the proto-Sun informed by recent observations using three-dimensional solar atmosphere models (e.g., Asplund et al. 2009) (Y = 0.27, Z = 0.014), one would derive 177 ± 15 Myr (2.79 ± 0.03 M_☉). We can also estimate an isochronal age that assumes that the measured photospheric metallicity is indicative of the star's bulk composition ([Fe/H ∼−0.36]). We scale the star's chemical composition by assuming a linear trend in ΔY/ΔZ = 1.57, which connects the Big Bang primordial abundances (Y = 0.248, Z = 0.00; Steigman 2010) with the solar photospheric ratio (X/Z) and protosolar Y estimated by Asplund et al. (2009). Adopting the metallicity from Fitzpatrick & Massa (2005) ([Fe/H] = −0.36), we interpolate an approximate chemical composition of Y = 0.26, Z = 0.006. Using this subsolar chemical composition, we infer that the H-R diagram position of κ And would be consistent with an age of 317 ± 10 Myr and a mass of 2.52 ± 0.03 M_☉. Note that this chemical composition almost certainly represents a strong lower limit to the plausible helium and metal mass fractions, and hence defines an upper limit on the star's age and a lower limit on its mass.

Zoom In Zoom Out Reset image size

As a check, we evaluate the H-R diagram position of κ And A using other sets of tracks. Using the Girardi et al. (2000) evolutionary tracks for [Fe/H] = 0.0 ± 0.1 via the online isochrone interpolator PARAM 1.1,²¹ we find that κ And's H-R diagram position²² corresponds to an age of 252 ± 33 Myr and a mass of 2.60 ± 0.06 M_☉, with surface gravity log(g)  = 4.12 ± 0.02. Assuming [Fe/H] = 0, the same tracks yield an age of 121 Myr, a mass of 2.85 M_☉ , and a log(g)  = 4.17. Using the rotating evolutionary tracks from Georgy et al. (2013) for their assumed solar composition (Z = 0.014) and given that v_rot/v_crit = 0.3, κ And's age is approximately 250 Myr for mass 2.75 M_☉. Combining our estimate of the mass of κ And A (∼2.8 M_☉) with our updated radius estimate in Table 2 (2.29 R_☉) leads to an estimate of the star's critical rotational velocity of ∼480 km s⁻¹, hence for vsin i  = 150 km s⁻¹(Abt et al. 2002), v_eq/v_crit > 0.3. Hence, the evolutionary tracks that include rotations that show slightly older (∼10%) ages are probably to be favored.

If the star's bulk composition is similar to that of solar (Z ≃ 0.015–0.017), the age is likely to be ∼180 ± 70 Myr. If the star's bulk composition reflects its photospheric abundances (Z ≃ 0.006), then the star may be on the order of ∼250 ± 70 Myr. Hence, there is a systematic uncertainty in the age at the ∼40%  level due to the uncertainty in the bulk metal fraction of the star. Uncertainties due to the helium fraction, observational uncertainties, rotation, and other differences between the input physics of the different stellar evolutionary models, each contribute to the age uncertainty at the ∼10%  level. We conclude that the H-R diagram position for the star is consistent with an approximate age of 220 ± 100 Myr and a mass of 2.8$^{+0.1}_{-0.2}$M_☉. The derived isochronal age range from the H-R diagram analysis is commensurate with that from the T_eff  versus log(g)  analysis in Section 3.2.2.

Our new estimate of 220 ± 100 Myr is ∼7× older than the age estimate presented by Carson et al. (2013). Based on the combination of T_eff, log(g), and luminosity, an age for κ And A younger than 120 Myr or older than 320 Myr seems extremely unlikely. If the bulk composition of κ And is truly as metal-poor as the photosphere ([Fe/H] ≃ −0.3), then not only is κ And ∼10× older than the 30 Myr old Columba association, but its chemical composition contains less than half the metals of other Columba members.

With this revised age in hand, we use the DUSTY models of Chabrier et al. (2000) to estimate the mass of κ And B. Using the L-band photometry from Bonnefoy et al. (2013b) with our revised age of 220 ± 100 Myr, we find a revised mass of 50$^{+16}_{-13}$ M_Jup, where the uncertainty is driven almost entirely by our derived uncertainty in the age of κ And A.

High-mass stars show a high degree of multiplicity (e.g., Duchêne & Kraus 2013 and references therein), and characterizing the multiplicity of the κ And system, and hence the contributions to the observed system luminosity, has significant implications for its age (Section 3.2). An equal-flux binary companion would significantly bias the inferred luminosity (Section 3.1), lowering the log (L/L_☉) value in Figure 10 by 0.3 dex, placing it near the 30 Myr age track. Hence, understanding the multiplicity of this system is crucial for a correct interpretation of Figure 10. Further, low-mass binary companions could be useful as additional age indicators. There have been numerous observations of κ And with various techniques, but they have not been synthesized into a single set of limits. We therefore present new observations with non-redundant aperture-mask interferometry, as well as interpret existing radial velocity and imaging data in the Appendix, and compile a comprehensive limit on the existence of binary companions at all semimajor axes (from 10⁻² AU to 10⁴ AU).

3.3.1. New Limits from Non-redundant Mask Interferometry

3.3.2. Limits on Stellar Binary Companions

Utilizing the information on wide binary companions contained in the Appendix, as well as archival radial velocities also listed there, we have combined all of the above data in a unified Monte Carlo simulation that computes detection rates as a function of companion mass and semimajor axis. We computed 10³ randomly generated orbits across a grid with bins of 0.1 M_☉ in M_secondary (spanning 0.1–2.8 M_☉) and 0.1 dex in log (a) (spanning 10⁻² to 10 AU); we did not test wider separations because the aperture masking and Subaru coronagraphic observations published in Carson et al. (2013) rule out all stellar companions, and the radial velocity data is not useful for substellar companions. For each randomly generated orbit in the Monte Carlo, we tested the χ² goodness of fit for the radial velocity time series while also verifying that the companion would not have been detected in any of the direct imaging epochs. We regarded a companion to be "ruled out" if the χ² statistic is larger than the 95% confidence limit (i.e., the orbit would have produced a signal at >95% confidence). We present the resulting limits on stellar binary companions in Figure 11, which shows the percentage of stellar binary companions as a function of companion mass and semimajor axis that would have been detected by the radial velocity, aperture masking, and direct imaging observations. Nearly all stellar companions with a ≳ 0.6–0.7 AU are ruled out by the aperture masking observations, while radial velocities rule out the majority of short-period stellar companions with M ≳ 0.5 M_☉.

Zoom In Zoom Out Reset image size

We note that there exists a region in which nearly equal mass (2–3 M_☉) binary companions are not completely ruled out. However, in their work reporting observations with the Palomar Testbed Interferometer (PTI), van Belle et al. (2008) did not find this system to be resolved. Further, given the resolution and field-of-view of PTI, this work should have reported a similar-brightness binary companion in their data. They claimed that even given the poor fit to a single point source, the noise in the visibilities would have been consistent with a companion showing 4 mag of K-band contrast or more, rather than 0 or 1 mag of contrast. Thus, we can appeal to their results to argue that nothing lies in the regime that is not formally ruled out by our analysis.

Our analysis suggests that the luminosity of the κ And system is not biased in any meaningful way by binarity of any kind and the calculated luminosity plotted in Figure 10 is due solely to a single host star: κ And A, reinforcing our isochronal 220 ± 100 Myr age estimate.

In this section, we investigate the likelihood that κ And A is a nearly pole-on fast rotator. Such a configuration could account for the position of κ And in the H-R diagram (Figure 10), while still possessing the previously reported age of 30 Myr. Though effects induced by rapid rotation and inclined viewing angles can lead to scatter in diagrams such as Figure 9 and color–magnitude diagrams, thereby confusing the age analysis, such effects are less important for κ And, as we show below. Specifically, an extreme pole-on orientation is not possible for κ And due to its high observed rotational velocity. However, even very low-inclination models would not change the modeled age noticeably: these models cause the star to become not just more luminous but also hotter. Thus, on an H-R diagram, the effect of rotation and inclination is mostly to shift the star along, not across, an isochrone.

Nonetheless, the observed properties of κ And allow us to place some constraints on its inclination. With a projected rotational velocity of vsin i = 150 km s⁻¹ (Abt et al. 2002) and taking the approximate mass and radius of κ And listed in Table 3, the formulae of Townsend et al. (2004) predict that the critical rotational velocity for κ And to be 394 km s⁻¹, which is indeed typical for B9 stars (Table 1 of Townsend et al. 2004). Since we do not know the ratio of the star's equatorial to polar radii, we have adopted the radius inferred from the luminosity and effective temperature as the star's polar radius in the formula presented in Townsend et al. (2004). A lower limit to the aspect ratio r_eq/r_polar can be estimated via the Roche approximation formula from Townsend et al. (2004), where vsin i = 150 km s⁻¹ places a lower limit on the equatorial velocity of the star. We estimate r_eq/r_polar > 1.05. The combination of vsin i and the predicted critical velocity lead to a constraint on the inclination of the star: i > 224. Hence the star cannot be within 22° of pole-on in orientation.

As Townsend et al. (2004) demonstrate, a fast-rotating B star can get a boost in absolute magnitude and/or reddening in optical color due to the effects of gravity darkening and viewing angles. Figure 3 of Townsend et al. (2004) is instructive for testing whether κ And could be interpreted as a young, extremely fast rotator seen at high inclination. In Figure 3 of Townsend et al. (2004), the authors take non-rotating B-type stars (conveniently including a fiducial B9 dwarf) and calculate the effects of gravity darkening and viewing angle on B−V color and absolute V magnitude for a range of rotation velocities (ranging from non-rotating to near critical v_eq/v_crit = 0.95) and at three different inclination angles (0°, 45°, 90°). As discussed previously, the vsin i constraints are consistent with v_eq/v_crit > 0.38 and i > 22°. So we can already rule out κ And being a near face-on star rotating near v_crit. For Townsend et al.'s models, it is the face-on orientation (i = 0°) that produces the greatest brightening in absolute magnitude, approximately 0.6 mag in M_V for their most optimistic model (i = 0°, v_eq/v_crit = 0.95). The absolute magnitude of κ And is similar to that of late B-type Pleiades (∼120 Myr) and approximately 0.4 mag brighter than the ZAMS of Schmidt-Kaler (1982), which is a reasonable approximation for the sequence of ∼30 Myr late B-type stars. While the i = 45° and 90° models of Townsend et al. (2004) are plausible for κ And, the i = 0° is not. Interpolating among the predicted differences in absolute magnitude and color for the fiducial B9 model of Townsend et al. (2004), it appears that it is extremely difficult to get a plausible model that can provide a ∼0.4 mag boost in absolute magnitude. For i ≃ 22° (roughly halfway between the i = 0° and 45° models), κ And would have to be rotating at or near critical velocity, i.e., v_eq/v_crit ≃ 0.95. More modest inclinations of i = 45° and 90° cannot provide sufficient brightening of the star's real absolute magnitude to the observed value.

Measurement of a photometric rotation period for the star could provide a measure of the star's rotation, as well as interferometric diameter measurements to test whether the star is consistent with an extreme aspect ratio. While included as a suspected variable star in the General Catalogue of Variable Stars catalog (Samus et al. 2007), the Hipparcos survey found the star to be remarkably photometrically quiet (classified "C" = constant), with scatter in Hp magnitudes of only 0.004 mag, and hence measuring a photometric period may be challenging.

Given the evidence presented that the κ And system is ≳220 Myr, it is worthwhile to revisit the original suggestion by Zuckerman et al. (2011) that this system may be a member of the 30 Myr Columba association. Using the position, proper motion, and parallax from van Leeuwen (2007) and mean radial velocity from Gontcharov (2006), we estimate the velocity of κ And to be (U, V, W) = (−11.5 ± 0.3, −20.1 ± 0.5, −5.9 ± 0.6) and (X, Y, Z) = (−16.7, 46.5, −14.8). As noted in Carson et al. (2013), the space velocity and position of κ And yield >95% probability of Columba membership according to the moving group prediction method (Malo et al. 2013). However, this 95% probability was only for an additional hypothesis in which a 0.75 mag shift was applied to the photometric sequence for the association to account for possible unresolved binarity, which is a case we rule out in Section 3.3. The probability for a non-binary case carries a lower probability, although this value was not tabulated in Malo et al. (2013). Additionally, further investigation reveals that κ And was included as a bona fide member of the collection of stars comprising the Columba group kinematics in this work. This fact automatically increases its derived probability for membership in Columba.

Figure 12 shows the UVWXYZ velocities and positions for the 21 bona fide Columba members listed in Malo et al. (2013), with the κ And system highlighted. Figure 12 shows that the UVW velocities for κ And are consistent with the 20 other bona fide members of Columba. However, it is a 2.7σ outlier in galactic Y position, which is the largest Y position of the entire Columba ensemble. Even further, Zuckerman et al. (2011) do not use the galactic Y position as part of their criteria for moving group membership.

Zoom In Zoom Out Reset image size

The strong agreement between the UVW velocity of κ And B and the Columba association make a full kinematic "traceback" analysis challenging. Despite the fact that this object is a significant positional outlier in the Y-direction, any discussion of the star's past position, velocity relative to the centroid of the Columba association, and so forth is weakened due to the similarities in velocities of the star and the Columba group discussed above. Further, the errors in velocities for κ And A and Columba are sizeable (∼0.5 km s⁻¹ and ∼1 km s⁻¹, respectively). Nonetheless, adopting the centroid position and UVW velocity for Columba listed in Malo et al. (2013) and the UVW for κ And A listed in Table 3, the star is currently 80 pc away from the centroid of Columba, and its velocity differs by 1.5 km s⁻¹. Using an epicycle orbit approximation code, it appears that κ And was only slightly closer to the Columba centroid in the past: 18 Myr ago it was 60 pc from Columba, and 30 Myr ago it was 74 pc away.

However, the outlying Y position of κ And (46.5 pc) raises questions about the likelihood of its formation near the Columba groups centroid (Y = −31.3). Notably, for κ And to have formed near Columba's centroid 30 Myr ago, it would have had to have inherited a peculiar V velocity of ΔV = (46.5 + 31.3pc)/(30 Myr) = 2.59 pc Myr⁻¹ ∼ 2.6 km s⁻¹. Given Columba's current V velocity of V = −21.3, a "runaway" star would have velocity V + ΔV ≃ −18.7 km s⁻¹. However, this is still within ∼1σ of what is observed for κ And.

The primary star κ And A has been observed by numerous radial velocity surveys over the past century; we list those radial velocity observations that we could recover in Table 5. Palmer et al. (1968) reported 11 radial velocity measurements for κ And that were taken between 1960 October 4 and 1961 November 4 (UT) and found a mean radial velocity of v = −15 km s⁻¹ with a standard deviation of σ = 10.5 km s⁻¹ and a standard deviation of the mean of σ_μ = 3 km s⁻¹. Harper (1937) reported three radial velocity measurements that were taken between 1923 September 13 and 1926 December 14 (UT) and found a mean radial velocity of v = −19 km s⁻¹ with a standard deviation of σ = 5 km s⁻¹ and a standard deviation of the mean of σ_μ = 3 km s⁻¹. Since there are only three epochs and we must be concerned with zero point shifts, we do not use these data. Wilson (1953) reported that κ And had a mean radial velocity of v = −9.0 km s⁻¹ for 10 observations, but the author did not report an uncertainty or the individual measurements, so we cannot use these measurements either. Finally, we also note that Huang & Gies (2008) reported that κ And is a relatively fast rotator (v_rot = 169 km s⁻¹), and so even if it is a low-amplitude double-lined spectroscopic binary, radial velocity measurements might not resolve the individual components. Our analysis therefore must consider the shift in spectral line centroids in placing constraints on the presence of a double-lined spectroscopic binary.

Even before the discovery of κ And "b," κ And was considered a binary (ADS 16916, WDS 23404+4420, HJ 1898). J.F.W. Herschel reported (Herschel 1831) possible companions to κ And at ρ = 35''  ("B") in epoch 1828 and ρ = 98''  ("C") in epoch 1836 (Smyth 1844; Mason et al. 2001). The nearest Two Micron All Sky Survey (2MASS) counterparts for these stars are 2MASS J23402285+4419177 (ρ = 48'') and 2MASS J23401480+4420469 (ρ = 113''). If these (or any other) stars were indeed associated, then they would offer a valuable check on the age of the system. To test the association of these candidates and to search for other potential comoving companions, we have investigated the nature of all identifiable sources within <5'  (<15000 AU) of κ And.

We queried the 2MASS Point Source Catalog (which has the highest image fidelity) to identify 38 candidate companions with K < 14.3 and ρ < 5'. The PSC clearly detected a source with K = 13.9 at ρ = 27'', and the background flux is similar down to ρ = 20''. We therefore estimate that any source brighter than the 2MASS detection limit (K = 14.3 at 10σ) would have been detected at ρ > 20''. We also compiled proper motions for most of these sources from UCAC4 (for nine sources; Zacharias et al. 2012) and from PPMXL (for 25; Roeser et al. 2010). Four candidate companions did not have proper motions in either catalog, but in all cases, visual inspection of the raw images showed that they moved by <1''  (≲20 mas yr⁻¹) between the POSS-I epoch (1952) and the 2MASS epoch (1998).

In Figure 13 (left), we show a (J−K,K) color–magnitude diagram for the 38 sources with K < 14.3 identified by 2MASS. Figure 13 also shows the main sequence for stars located at the distance of κ And. Only 7 sources are located within Δ(J − K) < 0.3 mag of the main sequence; the remaining 31 sources (including the "B" companion from 1831, as well as 3 of the 4 sources with visually estimated proper motions) appear to be unassociated background stars. In Figure 13 (right), we show a proper motion diagram for the 34 sources with measured proper motions. None agree with the Hipparcos proper motion for κ And to within 3σ (including both "B" and "C" objects from 1831), and hence all (including the fourth star with a visually estimated proper motion limit) appear to be unassociated background sources. We therefore conclude that there are no comoving companions (including the purported "B" and "C" companions) with K < 14.3 (M_lim > 15 M_Jup, for the null hypothesis of τ = 30 Myr) located within ρ =20''–300''  (ρ = 1000–15,000 AU) of κ And.