HD 181068: a red giant in a triply eclipsing compact hierarchical triple system.
ABSTRACT Hierarchical triple systems comprise a close binary and a more distant component. They are important for testing theories of star formation and of stellar evolution in the presence of nearby companions. We obtained 218 days of Kepler photometry of HD 181068 (magnitude of 7.1), supplemented by ground-based spectroscopy and interferometry, which show it to be a hierarchical triple with two types of mutual eclipses. The primary is a red giant that is in a 45-day orbit with a pair of red dwarfs in a close 0.9-day orbit. The red giant shows evidence for tidally induced oscillations that are driven by the orbital motion of the close pair. HD 181068 is an ideal target for studies of dynamical evolution and testing tidal friction theories in hierarchical triple systems.
, 216 (2011);
, et al.A. Derekas
HD 181068: A Red Giant in a Triply Eclipsing Compact Hierarchical
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Space Agency–European Southern Observatory (ESA-ESO)
Working Group Report no. 4, Paris, 2008].
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36. Kepler is a NASA discovery class mission, which was
launched in March 2009 and whose funding is provided
by NASA’s Science Mission Directorate. The authors
thank the entire Kepler team, without whom these results
would not be possible. The asteroseismology program
of Kepler is being conducted by the Kepler Asteroseismic
Supporting Online Material
Materials and Methods
Figs. S1 to S3
16 December 2010; accepted 22 February 2011
HD 181068: A Red Giant in a
Triply Eclipsing Compact
Hierarchical Triple System
A. Derekas,1,2* L. L. Kiss,2,3T. Borkovits,4,5D. Huber,3H. Lehmann,6J. Southworth,7
T. R. Bedding,3D. Balam,8M. Hartmann,6M. Hrudkova,6M. J. Ireland,3J. Kovács,9Gy. Mező,2
A. Moór,2E. Niemczura,10G. E. Sarty,11Gy. M. Szabó,2R. Szabó,2J. H. Telting,12A. Tkachenko,6
K. Uytterhoeven,13,14J. M. Benkő,2S. T. Bryson,15V. Maestro,3A. E. Simon,2D. Stello,3
G. Schaefer,16C. Aerts,17,18T. A. ten Brummelaar,16P. De Cat,19H. A. McAlister,16
C. Maceroni,20A. Mérand,21M. Still,15J. Sturmann,16L. Sturmann,16N. Turner,16
P. G. Tuthill,3J. Christensen-Dalsgaard,22R. L. Gilliland,23H. Kjeldsen,22E. V. Quintana,24
P. Tenenbaum,24J. D. Twicken24
Hierarchical triple systems comprise a close binary and a more distant component. They are important
for testing theories of star formation and of stellar evolution in the presence of nearby companions.
We obtained 218 days of Kepler photometry of HD 181068 (magnitude of 7.1), supplemented by
ground-based spectroscopy and interferometry, which show it to be a hierarchical triple with two types
of mutual eclipses. The primary is a red giant that is in a 45-day orbit with a pair of red dwarfs in a
close 0.9-day orbit. The red giant shows evidence for tidally induced oscillations that are driven by the
orbital motion of the close pair. HD 181068 is an ideal target for studies of dynamical evolution and
testing tidal friction theories in hierarchical triple systems.
able sample of Earth-like planets around main-
photometry (2–4) of HD 181068 [also Kepler
Input Catalog (KIC) 5952403], a star with mag-
nitude V = 7.1 and a distance of about 250 pc. It
had been previously identified as a single-lined
spectroscopic binary (5), but there have been no
reports of eclipses.
The data were obtained in long-cadence (LC)
mode (one point every 29.4 min) over 218 days
using quarters 1, 2, and 3. Our observations re-
veal a very distinctive light curve. It shows
eclipses every ∼22.7 days and slow variations
in the upper envelope (Fig. 1A) that are likely
caused by ellipsoidal distortion of the primary
narrower eclipses (Fig. 1B). These minima have
alternating depths, corresponding to a close pair
22.7-day eclipses all have similar depths, but
there are subtle differences between consecutive
of (6)]showthatthe true orbitalperiodoftheBC
pair around the A component is 45.5 days. The
ing both types of the deep minima, implying that
the three stars have very similar surface bright-
he Kepler space mission is designed to
observe continuously more than 105stars,
with the ultimate goal of detecting a siz-
nesses, so that when the BC pair is in front of A,
of light coming from the system (in accordance
with the nearly equal depths of the two deep
minima). When the BC pair is in front of A, the
BC’s secondary eclipses appear as tiny bright-
enings (Fig. 1, D and F), showing that the surface
brightness of B is almost equal to that of A,
whereas C is a bit fainter,so thatits disappearance
The observed changes in the eclipses of the
BC pair and the radial velocity variations of the
A component confirm that the A and BC sys-
tems are physically associated and not a chance
alignment. Their periods are PBC= 0.90567(2)
day and PA-BC= 45.5178(20) days (numbers in
parentheses refer to the standard error in the last
digits).Giventheshallowdepthsof the eclipses,
star A must be the most luminous object in the
system. In addition to the eclipses, there are
brightness fluctuations during the long-period
minima that imply that component A is also an
intrinsic variable star with a mean cycle length
close to half the shorter orbital period, possibly
indicating tidally induced oscillations.
in the light curve that usually lasted about 6 to
8 hours. We checked the Kepler Data Release
Notes (7) for documented instrumental effects in
the vicinity of the “flares” but found none.More-
over, almost all flares appear right after the
shallower minimum of the BC pair, suggesting
that this activity might be related to the close
with a 1-m telescope [section 1.1 of (6)] but
found none. We also obtained 38 high-resolution
optical spectra to measure the orbital reflex mo-
tion of the A component (6) (fig. S1). The orbital
parameters for the wider system (Table 1) reveal
that star A revolves on a circular orbit, which has
an orbital period twice the separation of the two
consecutive flat-bottomed minima in the light
PAVO (Precision Astronomical Visible Observa-
tions) beam combiner (8) at the CHARA [Cen-
terfor High Angular ResolutionAstronomy(9)]
Array show that the angular diameter of HD
1Department of Astronomy, Eötvös University, Budapest, Hun-
gary.2Konkoly Observatory, Hungarian Academy of Sciences,
H-1525 Budapest, Post Office Box 67, Hungary.3Sydney In-
stitute for Astronomy, School of Physics, University of Sydney,
H-6500 Baja, Szegedi út, Kt. 766, Hungary.5Eötvös József
07778 Tautenburg, Germany.7Astrophysics Group, Keele Uni-
West Saanich Road, Victoria, BC V9E 2E7, Canada.9Gothard
Observatory, Eötvös University, H-9704 Szombathely, Szent
University, Kopernika 11, 51-622 Wroclaw, Poland.11Depart-
ment of Physics and Engineering Physics, University of Sas-
katchewan, 9 Campus Drive, Saskatoon, Saskatchewan S7N
Santa Cruz de La Palma, Spain.13Laboratoire Astrophysique,
Instrumentation, et Modélisation, Commissariat à l’Energie
Atomique (CEA)/Direction des Sciences de la Matière–CNRS–
fondamentales de l’Univers, Service d’Astrophysique, Saclay,
91191, Gif-sur-Yvette, France.14Kiepenheuer-Institut für Son-
tional Aeronautics and Space Administration (NASA) Ames
Research Center, Moffett Field, CA 94035, USA.16Center for
ty, Post Office Box 3969, Atlanta, GA 30302–3969, USA.17In-
stituut voor Sterrenkunde, Katholieke Universiteit Leuven,
Celestijnenlaan 200 D, 3001 Leuven, Belgium.18Institutefor
Mathematics, Astrophysics, and Particle Physics (IMAPP), De-
partment of Astrophysics, Radboud University Nijmegen, Post
Office Box 9010, NL-6500 GL Nijmegen, Netherlands.19Royal
Observatory of Belgium, Ringlaan 3, 1180 Brussel, Belgium.
20Istituto Nazionale di Astrofisica (INAF), Osservatorio astro-
21European Southern Observatory, Alonso de Córdova 3107,
Astronomy, Building 1520, Aarhus University, 8000 Aarhus C,
CA 94035, USA.
*To whom correspondence should be addressed. E-mail:
8 APRIL 2011VOL 332
on April 8, 2011
181068 A, corrected for limb darkening (10), is
qLD= 0.461 T 0.011 milli–arc sec (mas) (Fig. 2)
[see (6) for details].
Combining the measured angular diameter
we find the linear radius of the primary
component to be R = 12.4 T1.3 R◉(where R◉is
the radius of the Sun). With use of the spec-
troscopically determined Teff= 5100 T 200 K,
that found from the Hipparcos parallax and the
apparent magnitude. We also estimated the ab-
the Wilson-Bappu effect (12), which correlates
the width of the chromospheric Ca II K emission
line at 3934 Å with the V-band absolute magni-
nitude, which matches the parallax and the inter-
We estimated the mass of HD 181068 A by
comparing the effective temperature and the lu-
database (14). We obtained MA∼ 3.0 T 0.4 M◉
(where M◉is the mass of the Sun), corresponding
to a red giant, possibly in the He-core burning
phase of its evolution (15). The full spectral en-
broad-band optical magnitudes and infrared flux
values (6) does not show any excess in compar-
ison to a 5200-K photospheric model, indicat-
Fig. 1. Kepler-band light
curves of HD 181068from
observations in LC mode:
(A) the full 218 days and
ing two consecutive deep
minima. Time is expressed
in barycentric Julian date.
(C to F) Close-ups of two
day eclipses. The dashed
and dotted linesmarkthe
primary and the second-
eclipses, respectively. The
discontinuities in (A) cor-
respond to the telescope
rolls at the end of each
Table 1. Orbital elements for the wider system
derived from the A component’s radial velocity
curve (fig. S1). K2, the velocity amplitude of com-
ponent A; vg, the center-of-mass velocity of the
system; e2, the eccentricity of the wide pair; f(m),
the mass function.
45.5178 days (fixed)
2,455,454.573 T 0.095 (fixed)
37.195 T 0.053 km s−1
6.993 T 0.011 km s−1
0.24 T 0.02 M◉
Fig. 2. Squaredvisibilityversusspatialfrequency(projectedbaselinelengthoverwavelength)fromPAVO
on CHARA. Gray points show all collected measurements; black symbols show the average of each scan
over all wavelength channels; the error bars show the standard error of the mean. Each symbol type
of the observations at the longer baselines.
VOL 332 8 APRIL 2011
on April 8, 2011
We have constrained the parameters of the
BC pair by modeling the short-period eclipses in
the Kepler band using the jktebop code (16, 17).
The ratio of the radii of the B and C components
the low sampling rate of the Kepler LC data. The
A component contributes 99.29% of the system
light in the Kepler passband, and the BC pair
contribute 0.44% and 0.27%, respectively. Taking
the V-band absolute magnitude of HD 181068 A
for the Kepler passband are representative of the
V band, we find MV(B) = 5.6 and MV(C) = 6.1.
Such absolute magnitudes indicate spectral types
of G8 Vand K1 V for stars B and C,respectively
(18). Because we do not have independent mea-
surements of Tefffor the BC pair, we can only es-
timate their masses based on their spectral types.
This indicates that their masses are about 0.7 T
0.1 M◉each (6).
One puzzling feature of the system is the
short-period fluctuations that have the largest
amplitudes when the BC pair is behind star A,
amplitude in all the other phases of the wide
orbit. We have investigated this variability of HD
181068 Awith a detailed frequency analysis and
a comparison to other red giant stars that have
similar properties (6). The frequency content of
the light curve suggests an intimate link to tidal
effects in the triple system, with the first four
dominant peaks in the power spectrum identifi-
able as simple linear combinations of the two
orbital frequencies. On the other hand, solarlike
oscillations (meaning those excited by near-
surface convection, as in the Sun but also ob-
served in red giants) that are expected to produce
an equidistant series of peaks in the power
spectrum are not visible, even though all stars
words, the convectively driven solarlike oscil-
lations that we would expect to see in a giant of
this type seem to have been suppressed (6).
In a recent compilation of 724 triple stars
(19), there is only one system with an outer or-
for which Pout= 33.03 days). Carter et al. (20)
short outer period (Pout= 33.92 days). Extremely
compact hierarchical triple systems form a very
small minority of hierarchical triplets, with only 7
of the catalogized 724 systems having outer pe-
riods shorter than 150 days. Furthermore, HD
181068 and KOI-126 have the highest outer
mass ratios [∼ 2.1 and 3, defined as mA/(mB+
mC)] among the known systems. In 97% of the
known hierarchical triplets before the Kepler era,
the mass of the close binary exceeded that of
the wider companion, and even the largest outer
observationalselection effect or has an underlying
stellar evolutionary or dynamical explanation.
and its massive primary, we can expect short-
term orbital element variations on two different
time scales of 46 days (i.e., with period of PA-BC)
and about 6 years (PA-BC2/PBC), the time scale of
the classical apsidal motion and nodal regression
(21), which for the triply eclipsing nature could
be observed relatively easily.
References and Notes
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5. P. Guillout et al., Astron. Astrophys. 504, 829 (2009).
6. Materials and methods are available as supporting
material on Science Online.
7. Available at http://archive.stsci.edu/kepler/.
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Astrophys. J. 612, 168 (2004).
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Mon. Not. R. Astron. Soc. 355, 986 (2004).
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P. B. Etzel, Mon. Not. R. Astron. Soc. 363, 529 (2005).
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19. A. A. Tokovinin, Mon. Not. R. Astron. Soc. 389, 925 (2008).
20. J. A. Carter et al., Science 331, 562 (2011);
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22. A.D. is a Magyary Zoltán Postdoctoral Research Fellow.
Funding for this Discovery mission is provided by NASA’s
Science Mission Directorate. The authors gratefully
acknowledge the entire Kepler team, whose outstanding
efforts have made these results possible. This project
has been supported by Hungarian Scientific Research
Fund (OTKA) grants K76816, K83790, and MB08C
81013; the “Lendület” Program of the Hungarian
Academy of Sciences; and the Magyary Zoltán Higher
Educational Public Foundation. The DAO observations
were supported by an American Astronomical Society
Small Research Grant. The CHARA Array is owned by
Georgia State University. Additional funding for the
CHARA Array is provided by NSF under grant
AST09-08253, the W. M. Keck Foundation, and the
NASA Exoplanet Science Center. TLS observations were
done as a part of the Deutsche Forschungsgemeinschaft
grant HA 3279/5-1. For her research, C.A. received
funding from the European Research Council (ERC)
under the European Community’s Seventh Framework
Programme (FP7/2007-2013)/ERC grant agreement
no. 227224 (Prosperity).
Supporting Online Material
Materials and Methods
Figs. S1 to S3
Tables S1 to S3
15 December 2010; accepted 3 March 2011
Surface-Plasmon Holography with
Miyu Ozaki,1,2Jun-ichi Kato,1Satoshi Kawata1,3*
The recently emerging three-dimensional (3D) displays in the electronic shops imitate depth illusion by
overlapping two parallax 2D images through either polarized glasses that viewers are required to wear or
lenticular lenses fixed directly on the display. Holography, on the other hand, provides real 3D imaging,
on credit cards—are also produced from parallax images that change color with viewing angle. We report
on a holographic technique based on surface plasmons that can reconstruct true 3D color images, where
the colors are reconstructed by satisfying resonance conditions of surface plasmon polaritons for individual
wavelengths. Such real 3D color images can be viewed from any angle, just like the original object.
oble metal films, such as silver and gold
ly oscillate and propagate as the surface
wave in optical frequency region. The quantum
of this surface wave is called surface plasmon
erated by SPP can be enhanced and strongly con-
fined spatially in the near field (with the distance
less than the wavelength) from the metal surface
as a nonirradiative evanescent field (2, 3). The
ability to confine and enhance the optical field to
the vicinity of the metal surface or nanometal par-
ticle has been applied to immuno-sensor (4), fluo-
and photodynamic cancer cell treatment (13).
We report an application of SPP to three-
dimensional (3D) color holography with white-
1RIKEN, Wako, Saitama 351-0198, Japan.2Department of Ro-
botics and Mechatronics, Tokyo Denki University, Chiyoda-ku,
Tokyo 101-8457, Japan.3Department of Applied Physics and
Photonics Advanced Research Center, Osaka University, Suita,
Osaka, 565-0871, Japan.
*To whom correspondence should be addressed. E-mail:
8 APRIL 2011 VOL 332
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