Resolving the delta Andromedae spectroscopic binary with direct imaging
Michael Bottom, Jonas Kuhn, Bertrand Mennesson, Dimitri Mawet, Jean C. Shelton, J. Kent Wallace, Eugene Serabyn
RResolving the delta Andromedae spectroscopic binary with direct imaging
Michael Bottom , Jonas Kuhn , , Bertrand Mennesson , Dimitri Mawet , Jean C. Shelton , J.Kent Wallace , Eugene Serabyn [email protected] March 2015
ABSTRACT
We present a direct image of the innermost companion to the red giant δ Andromedaeusing the Stellar Double Coronagraph at the Palomar Observatory. We use a Markov-chain Monte Carlo based algorithm to simultaneously reduce the data and performastrometry and photometry of the companion. We determine that the companion ismost likely a main-sequence K-type star and is certainly not the previously hypothesizedwhite dwarf.
1. Introduction δ Andromedae (K3 III) is red giant with a visual magnitude of 3.28. It has a UV excess whichimplies a hot, high-velocity wind and a 60 and 100 μ m excess (Judge et al. 1987) which is mostlikely due to a debris disk (Decin et al. 2003). It is the brightest star in a quadruple system; of theouter companions (28.7 and 48 arc seconds), the first has been classified as an M2 V star with V =11.3, probably physically associated with the primary as it shares the same proper motion (Bakos1976). The outer component does not share the proper motion of the system and is most likely abackground object (ibid). δ Andromedae is a spectroscopic binary with a rather long period of about 57 years (Massarottiet al. 2008); see Table 1 for a summary of its physical properties. The presence of the secondaryhas been confirmed photocentrically and astrometrically (Gontcharov & Kiyaeva 2002), with bothsources deriving an eccentricity of about 0.5. The companion has been conjectured to be either amain-sequence star later than G-type (Judge et al. 1987) or white dwarf near the Chandrasekharlimit (Gontcharov & Kiyaeva 2002). It has never been directly imaged, however, due to the sec-ondary’s faintness and proximity to the primary. In this work we image the companion for the Cahill Center for Astronomy and Astrophysics , California Institute of Technology, MC 249-17, Pasadena, CA91125, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 91109 USA (current address) Institute for Astronomy, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland a r X i v : . [ a s t r o - ph . S R ] J un δ AndMass (M A +M B ) 2.6 ± (cid:12) Gontcharov & Kiyaeva (2002)a A +a B ± ± ± (cid:12) Piau et al. (2011)Luminosity 68 ± (cid:12) Piau et al. (2011)Surface gravity (log g) 2.0 ± ± v sin i ) 6.5 km/s Massarotti et al. (2008)Age 3.2 Gyr Decin et al. (2003) (v. uncertain)Parallax 0.032 ± δ And b properties (this work)∆M (Bracket- γ ) 6.22 ± λ c = 2.18 µ m, ∆ λ =0.03 µ mAngular Separation 0.357 ± ± ◦ Physical Separation 11.55 ± Hipparcos , as aboveSpectral type K4 ± δ And and newly measured properties of the companion
2. Instrumentation, Observations and Data Analysis2.1. Instrumentation
The Stellar Double Coronagraph (SDC) is a JPL-developed instrument designed for high-contrast imaging of close-in companions to stars, particularly exoplanets. It uses two optical vorticesin series to simultaneously diffract starlight out of the pupil of the instrument and partially correctfor the secondary obscuration of the telescope (Mawet et al. 2011b). It has an inner working angleof approximately 1 λ /D, or 90 mas in K-band (2.2 μ m) behind the 5 m Hale telescope. It is installedbetween the P3K adaptive optics system (Dekany et al. 2013) and the near-IR imager PHARO(Hayward et al. 2001). 3 – We observed δ And on October 8-9 2014 (UTC), during the course of normal science operations.The seeing was 1.2”, with the adaptive optics system delivering a Strehl ratio of about 85% at anairmass of 1.02-1.03. Our observing strategy involved frequently dithering between the target starand a reference star, then using post-processing to subtract the speckle pattern from the targetimages using the reference (see the following section for more detail). A Bracket- γ filter was usedconcurrently with neutral density filters to reduce the flux from the target when off the coronagraphto below detector saturation. Absolute transmissivity of the neutral density filters was measuredseparately, and found to be consistent with Metchev & Hillenbrand (2004). Sky backgrounds wereinterspersed with the target and reference star observations; sky flats were taken five days later. Asummary of the observations is presented in Table 2.2.Observing date: Oct. 9-10 2014, JD 2456939-10Target Images Filters Exposure Time[s] Purpose δ And 29 Br- γ , ND2 9.91 Photometry, Astrometry β And 100 Br- γ , ND2 2.83 Photometry δ And 10 Br- γ , ND3 2.83 Non-coronagraphic, PhotometryTable 2: Summary of observations. One of the main challenges in high contrast imaging is trying to remove speckles due toaberrations in the optics after the wavefront sensor. There are a number of ways to tackle thiscontrast-limiting/quasi-static aberration problem; our strategy is sometimes called “reference dif-ferential imaging” (Mawet et al. 2011a), which involves dithering between the target and a nearbystar of similar visible magnitude, spectral type, and airmass. This leads to a similar AO correctionand gravity vector, ensuring a similar speckle pattern. It is then possible to remove some of thespeckles by either subtracting the reference image or using a more advanced image processing tech-nique such as the Karhunen-Loeve eigenimage decomposition (Soummer et al. 2012). The lattermethod gives better results than the former in terms of contrast, but has the unfortunate side ef-fect of reducing the flux of any nearby companions that might be in the image, therefore renderingaccurate photometry difficult. In this paper, we use a slightly different approach where we forwardmodel the target image as a combination of a scaled reference image and a shifted, attenuatedpoint-spread function image. This method has some advantages that will be explained below.We acquired coronagraphic images of δ Andromedae and the reference star, β Andromedae.We aligned and median combined these images after flat-fielding, background subtraction and bad 4 –pixel removal. We derive a relative magnitude and offset between the star and companion usinga Markov Chain Monte Carlo (MCMC) fitting algorithm (Foreman-Mackey et al. 2013). This issomewhat different than the usual approach to analyzing fluxes and positions, where one prioritizesmaximising the signal to noise ratio of the companion, often performing astrometry and photometryseparately. Here the image reduction, raw photometry, and astrometry are all performed at thesame time by the MCMC algorithm. There are a few advantages to doing everything at once withMCMC. First, one can measure the precision of the reduction algorithm much more accurately:the per-pixel uncertainties are Poissonian and straightforward to propagate in the model above.Furthermore, the MCMC returns marginal likelihoods, which shows the precision in each parameteras well as any correlations. Finally, one does not need an analytic model of the PSF but can useimages of the instrumental point spread function taken off the coronagraph. This reduces thenumber of parameters in the model, decreases degeneracy, and improves accuracy.The generative model for the image data is T [ x, y ] = R a · R [ x, y ] + P a · P [ x − x c , y − y c ] (1)where T is the coronagraphic image of δ And, R a is a constant scale factor, R is the coronagraphicreference image of β And, P a is another constant scale factor, and P is the point-spread function(ie, a unit-intensity normalized, non-coronagraphic image of a point source). Images T , R , and P are all single median images. The indices x , y refer to pixel coordinates, and the factors x c , y c areshifts in point-spread function imaging data (ie, P[x-1, y-0.34] corresponds to a pixel shift of 1,0.34). The constant R a is to correct for the fact that the background speckle field in the scienceimage is of a different mean intensity, due to differing stellar magnitudes. P a is the intensity scalingprefactor of the point spread function of the companion. MCMC is used to solve for x c , y c , P a ,and R a simultaneously; the results are presented in Figure 1. The “reference subtracted” image, T [ x, y ] − R a · R [ x, y ] is shown in Figure 2.In order to determine the relative brightness, we similarly use the unit-intensity PSF model tofit a non-coronagraphic image of δ And, and the derived intensity allows us to establish a relativeintensity in magnitudes. The uncertainty in relative intensity is dominated by the uncertainty onthe neutral density filters’ absolute extinctions. For the companion location, the typical error inthis case for x c and y c was about 0.01 pixels, or less than a milliarcsecond at 0.025”/pixel. However,this is not the true uncertainty in separation because the primary star’s image is suppressed anddistorted by the coronagraph and its true position is not obvious to calculate. In order to locatethe position of the primary, we imposed a waffle pattern on the deformable mirror of the adaptiveoptics during observations. The waffle generates astrometric spots 3.9” away from the primary,which can be used to locate the position of the star, and we verified our result using the Radontransform (Pueyo et al. 2014). The waffle centration has an uncertainty of about 0.1 pixels, whichdominates the total separation uncertainty. 5 – . . . . y c . . . R a .
62 0 .
64 0 .
66 0 . x c P a .
30 3 .
28 3 .
26 3 . y c .
22 4 .
24 4 . R a P a Fig. 1.— Left: a) the background-subtracted target median image, b) the background-subtractedreference star median image, c) the background-subtracted point-spread function image, d) best-fitting model from the MCMC algorithm combining images b) and c) attempting to match a) asexplained above. The stretch is nonlinear to better show the companion and speckles. Right:All the one and two dimensional projections of the posterior probability distributions of the pixelshifts ( x c , y c , the reference background scaling factor ( R a , and the PSF amplitude used to fitthe companion P a . The two-dimensional projections show very little covariance among any twoparameters, and the marginal distribution histograms (along the diagonal) are nicely peaked. 6 – Fig. 2.— The reduced, background-removed coronagraphic image of δ Andromedae. The first Airyring is visible around the companion. The stretch in the image is linear. The colorbar shows therelative intensity (as a fraction) compared to the primary 7 –
3. Results and Conclusions
The results of the above analysis are shown in Table 1. Judge et al. suggest that the secondarycompanion is either a main sequence star later than G type or a white dwarf. Gontcharov andKiyaeva measure a mass fraction m B / ( m A + m B ) = 0.5 ± / L o g [ F l u x ] + c o n s t K giant (T = 4250K, logg = 2, R=13.6 R fl )K0 dwarf (T = 5250K, logg = 4.5, R=0.85 R fl )K5 dwarf (T = 4500K, logg = 4.5, R=0.72 R fl )K7 dwarf (T = 4000K, logg = 4.5, R=0.63 R fl )White dwarf (50000 K blackbody, R=.01 R fl ) Fig. 3.— Comparison of the approximate fluxes of δ And A, three K dwarfs, and a 50000K whitedwarf. The spectral models are from Castelli & Kurucz (2004). The width of the shaded bar is thespan of the Bracket- γ filter.However, assuming that the companion is a white dwarf, its radius is constrained to be about0.01 R (cid:12) , as white dwarfs of 0.5-1.4 M (cid:12) span the radius range of 0.014 to 0.005 R (cid:12) . Comparingthe expected flux levels of a hot white dwarf to that of the primary (see Figure 3), the magnitudedifference through the Bracket- γ filter would be about 12 magnitudes, not the measured 6, adiscrepancy of greater than 100 times our photometric uncertainty. Furthermore, such a hot white 8 –dwarf would have a UV continuum that was not detected in Judge et al., who constrain thewhite dwarf’s temperature to less than 10000K if it exists. This low temperature would make themagnitude difference even more extreme. The white dwarf possibility is thus definitively excluded.On the other hand, the measured flux is consistent with a main-sequence K-type dwarf. Shownin Figure 3 are spectral models of K0, K5, and K7 stars, with our measured flux shown as a blackdot. For the δ And primary, the effective temperature and radius is taken from published results(Table 1; note that the radius is known accurately from interferometry (Piau et al. 2011)). Forthe secondary, the effective temperatures and surface gravities are taken from Castelli & Kurucz(2004) and the radii are taken from Cox (2000). While the formal photometric error is smallerthan the size of the datapoint, lack of knowledge about the companion’s radius and temperaturemake it impossible to give a completely specific spectral classification; the best we can say isthat the companion is most likely a K-type dwarf. Making a more accurate measurement of thesecondary spectral type is possible in principle. The simplest way would likely be a similarlyprecise coronagraphic measurement in J band, as the J - K colors of K dwarfs change by about 200millimags over the spectral type. Alternatively, an AO-fed integral field spectrograph might beable to measure the spectral type from the CO band at approximately 2.3 µ m.The conclusion that the companion is K-type is mostly consistent with previous work. Asmentioned before, Judge et al. concluded that a main sequence companion would have to be a starlater than G-type. A K-dwarf has a mass of between 0.6-0.8 M (cid:12) ; taking values of 1.1 - 1.2M (cid:12) for δ And A gives 0.3-0.4 as the mass fraction, reasonably consistent with the value of Gontcharov &Kiyaeva (2002) of 0.5 ±
4. Acknowledgements
We are pleased to acknowledge the Palomar Observatory staff for their excellent support,particularly Steve Kunsman. We greatly benefited from the expert assistance of Rick Burruss(JPL) with the adaptive optics system. We thank the referee for a useful review, particularly for 9 –pointing out some discrepancies in our analysis and previous work, which improved the paper. Partof this work was carried out at the Jet Propulsion Laboratory, California Institute of Technology,under contract with the National Aeronautics and Space Administration (NASA). Michael Bottomis supported by a NASA Space Technology Research Fellowship, grant NNX13AN42H.
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