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The Astronomical Journal, 128:1265–1272, 2004 September
# 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.

John Asher Johnson,2 Geoffrey W. Marcy,2 Catrina M. Hamilton,3, 4 William Herbst,5 and Christopher M. Johns-Krull3, 4
Received 2004 March 3; accepted 2004 May 19

We present the results of a high-resolution spectroscopic monitoring program of the eclipsing pre–mainsequence star KH 15D that reveal it to be a single-lined spectroscopic binary. We find that the best-fit Keplerian
model has a period P ¼ 48:38 days, which is nearly identical to the photometric period. Thus, we find the best
explanation for the periodic dimming of KH 15D is that the binary motion carries the currently visible star
alternately above and behind the edge of an obscuring cloud. The data are consistent with the models involving
an inclined circumstellar disk, as recently proposed by Winn et al. and Chiang & Murray-Clay. We show that
the mass ratio expected from models of pre–main-sequence evolution, together with the mass constraints for
the visible star, restrict the orbital eccentricity to 0:68  e  0:80 and the mass function to 0:125 M 
FM =sin3 i  0:5 M.
Key words: binaries: spectroscopic — circumstellar matter — stars: individual (KH 15D) —
stars: pre–main-sequence — techniques: radial velocities


alternately above and behind the edge of an opaque screen,
causing the eclipses. The long-term evolution of the light
curve is reproduced by allowing the screen to move slowly
across the binary orbit—a feature of the model that led the
authors to envision the screen as a precessing, circumbinary
disk. A similar model is proposed by Chiang & Murray-Clay
(2004, hereafter CM04), who also envision the opaque screen
as an inclined, precessing circumbinary disk, or ‘‘ring,’’ with
an inner edge truncated by tidal interactions with the binary
and an outer edge possibly shepherded by a planetary companion. Both models provide explanations of the unique
features of KH 15D’s light curve. The W04 model makes
quantitative predictions about the orbital parameters of the
binary system, while the CM04 model provides a physical
description of the circumbinary ring.
A fundamental question that has not yet been answered is
whether KH 15D is a single or multiple stellar system. He02
(see also Hamilton et al. 2003, hereafter Ha03) first searched
for evidence of orbital companions using high-resolution VLT
spectra and reported a radial velocity change of þ3:3 
0:6 km s1 over two widely spaced epochs. However, one of
the measurements was made during egress, when there was a
strong possibility of contamination from scattered light or line
profile distortions from a sharp-edged cloud only partially
occulting the stellar disk.
Over the past 2 years, we have conducted a high-resolution,
multisite spectroscopic monitoring campaign to determine
whether or not KH 15D exhibits orbital motion indicative of a
multiple system. Here we present the results of our study,
which show that KH 15D undergoes significant radial velocity
variations. The variations are consistent with a binary companion with an orbital period equal to the 48 day photometric
period. In x 2, we summarize our observations and reduction
procedures. The radial velocity measurements and best-fit
Keplerian orbital parameters are presented in x 3. We conclude
in x 4 with a discussion of our findings and implications for
existing models of the KH 15D eclipse mechanism.

KH 15D is a K6–K7 pre–main-sequence star that exhibits
dramatic photometric variability ( Kearns & Herbst 1998).
Every 48.35 days, the star’s brightness dims by 3.5 mag and
remains in this faint state for nearly half of the photometric
period. These deep brightness minima are accompanied by a
slight blueing of the star’s color indexes ( Herbst et al. 2002,
hereafter He02), little or no change in spectral type ( Hamilton
et al. 2001), and an increase in linear polarization (Agol et al.
2004). This implies that the star is completely eclipsed by an
optically thick, extended collection of dust grains, possibly in
the form of a circumstellar disk. If this is the case, the serendipitous alignment of the KH 15D star-disk system may
provide insights into the evolution of young stars and their
interactions with their circumstellar environments.
While KH 15D has periodic eclipses, it cannot be an ordinary eclipsing binary, because of the long duration of minimum light. Recent theories postulate that there is, nonetheless,
a currently unseen binary companion to the visible star. In a
study of archival photographic plates, Johnson & Winn (2004,
hereafter JW04) discovered that the historical light curve of
KH 15D is similar to the modern light curve but appears to be
diluted by light from a second star. Motivated by these findings, Winn et al. (2004, hereafter W04) constructed a model
composed of a binary system with the orbital plane inclined
with respect to the edge of an optically thick screen. As the
two stars orbit one another, the reflex motion carries one star
Based on observations obtained at the W. M. Keck Observatory, which
is operated as a scientific partnership among the California Institute of Technology, the University of California, and the Naional Aeronautics and Space
Administration; at Las Campanas Observatory of the Carnegie Institution with
the Magellan II Clay Telescope; and at McDonald Observatory of the University of Texas at Austin.
Department of Astronomy, University of California at Berkeley, Berkeley,
CA 94720-3411;,
Visiting Astronomer, McDonald Observatory, which is operated by the
University of Texas at Austin.
Department of Physics and Astronomy, Rice University, 6100 Main
Street, Houston, TX 77005;,
Van Vleck Observatory, Wesleyan University, Middletown, CT 06459;

During the 2002–2003 and 2003–2004 observing seasons,
we made 16 observations of KH 15D at maximum light,



Vol. 128

Spectroscopic Observations of KH 15D

UT Date

Oct 25 .........
Oct 28 .........
Dec 16 ........
Jan 14..........
Feb 8...........
Feb 9...........
Mar 9 ..........
Nov 3 ..........
Nov 4 ..........
Jan 4............
Jan 5............
Jan 10..........

2004 Jan 11..........
2004 Feb 9...........
2004 Feb 10.........

Telescope and




Keck / HIRES
Keck / HIRES
Magellan / MIKE
Keck / HIRES
Keck / HIRES
Keck / HIRES
Magellan / MIKE
Keck / HIRES
Keck / HIRES
McDonald /CE
McDonald /CE
Keck / HIRES
McDonald /CE
Keck / HIRES
Keck / HIRES
Keck / HIRES




(km s1)


Multiple reference stars were used to calculate the radial velocity. The reported velocity is the mean velocity
measured from the various target-reference star pairs. The estimated uncertainty is the standard deviation of the
mean velocity. See Table 2 for a listing of individual reference stars and radial velocity measurements for each
target-reference star pair.
b Only one reference star was used in the radial velocity measurement. The reported velocity is the mean velocity
from all echelle orders. The estimated uncertainty is the standard deviation of the mean velocity.

including 11 spectra with the 10 m Keck I Telescope and
HIRES echelle spectrometer, two spectra with the 6.5 m
Magellan II (Clay) telescope and the MIKE echelle spectrometer, and three spectra with the 2.1 m Otto Struve Telescope
at McDonald Observatory with the Sandiford Cassegrain
Echelle Spectrometer (CE). The observations are summarized
in Table 1. Additional Keck HIRES spectra were obtained
during minimum light. However, since it is unlikely that the
star’s photosphere is visible through the obscuring material,
we decided to exclude from our analysis spectra that were
obtained within 10 days of mid-eclipse. In addition to our own
measurements, we also include the out-of-eclipse radial velocity measurement, vr ¼ 9:0  0:2 km s1, reported by Ha03
based on their observations with the VLT UV-Visual Echelle
Most of the HIRES observations were made as part of the
California and Carnegie Planet Search.6 For these observations,
the relatively faint apparent magnitude of KH 15D (V ¼ 16) at
maximum light precluded the use of the iodine cell to establish
a wavelength scale. The cell was therefore removed from the
light path during observations of KH 15D to increase the
throughput of the spectrometer. The raw CCD frames from all
telescopes were reduced using reduction packages written in
IDL. The details of the reduction procedures are fundamentally identical to the algorithm presented by Valenti (1994).
After bias subtraction, each echelle frame is divided by a
normalized median flat-field image. Order definition is performed using a bright star or flat-field exposure, and scattered
light is removed by fitting a two-dimensional B-spline to the
interorder regions and interpolating across each spectral order.
After the scattered light is subtracted, each order is rectified,
sky-subtracted, and summed in the cross-dispersion direction
to form the final one-dimensional spectrum.
Instead of a summation in the cross-dispersion direction,
the rectified orders of the McDonald spectra are reduced to


one-dimensional spectra using the optimal extraction algorithm described by Hinkle et al. (2000). In the case of the
MIKE reductions, the standard code is modified to correct for
the tilt of the spectrometer entrance slit with respect to the
CCD columns. The correction of the slit tilt is necessary because the sky subtraction algorithm we employ requires that
the projected slit image lie parallel to the detector columns.
The radial velocity of KH 15D relative to the solar system
barycenter is measured from each spectral observation by
means of a cross-correlation analysis. For the spectra of
KH 15D obtained as part of the Planet Search observing
program, the program stars observed on each night provided
an extensive selection of reference stars with known barycentric radial velocities, listed in Nidever et al. (2002). We
selected reference stars that were observed within 30 minutes
of KH 15D and with spectral types ranging from M0 to G5.
Since the Planet Search target stars are observed through an
iodine cell, orders containing iodine absorption lines are
avoided in the analysis. For KH 15D observations obtained as
part of programs other than the Planet Search, a single K-type
reference star observed either before or after KH 15D is used
as the reference star.
The cross-correlation of each KH 15D spectrum with
respect to the reference spectra is performed using custom
routines written in IDL. The procedure involves first rebinning
each one-dimensional spectral order onto a new wavelength
scale that is linear in log k. This ensures that each pixel in the
rebinned spectrum represents a velocity interval that is uniform over the entire spectral order ( Tonry & Davis 1979).
Regions containing telluric lines, strong emission features,
and CCD defects are masked out, and each spectral order is
cross-correlated with respect to the corresponding order of
the reference spectrum. Each spectral order thus yields an
independent measurement of the radial velocity of KH 15D
relative to the reference star. The average of the ensemble set
of velocities from all orders is then adopted as the relative
radial velocity of KH 15D for a given epoch.

No. 3, 2004


Absolute Radial Velocity Measurements of
KH 15D from Each Reference Star

Reference Star
HD No.

v ra
(km s1)



1.6  0.1
2.1  0.1
2.1  0.08
1.3  0.09
1.2  0.2
2.9  0.2
4.0  0.08
3.2  0.2
2.2  0.1
2.7  0.3
3.1  0.2
3.6  0.1
2.7  0.1
3.1  0.07
3.6  0.09
3.4  0.1
9.0  0.5
11.5  0.5
0.8  0.2
1.2  0.4
1.8  0.3
1.4  0.6
1.7  0.4
5.1  0.2
5.6  0.3
5.8  0.4
7.0  0.2
2.0  0.2
1.7  0.1
1.8  0.2
1.9  0.2
1.6  0.1
1.3  0.1
0.9  0.1
1.2  0.1





estimation typically yields a larger value than the order-toorder scatter seen for an individual observation (0.2 km s1 
v  0.6 km s1 compared with 0:1  v  0:3). The larger
scatter in velocity measurements among the target-reference
star combinations is likely due to external systematic effects
such as small shifts in the position of the CCD throughout the
night caused by thermal relaxation of the detector mount.
Thus, the standard deviation measured from the echelle orders
in a single observation likely underestimates the true uncertainty by approximately a factor of 2.
Figure 1 illustrates how the radial velocity of KH 15D
varies temporally out of eclipse over a range of 10.7 km s1.
These data indicate that there must be an unseen star in the
system, as had previously been inferred from the analysis of
the historical light curve (JW04). Hereafter we will adopt the
naming convention of W04 and refer to the currently visible
star as A and the hidden companion as B.
3.1. Orbit Solution


Velocities are the mean value from all echelle
orders used in the cross-correlation analysis. Estimated
uncertainties are the standard deviation of the mean
velocity from all echelle orders.

The relative radial velocities from each night are converted
into absolute barycentric radial velocities using the relation
vrad ¼ v þ (BCkh  BCref ) þ vref :



In equation (1), v is the relative velocity from the crosscorrelation analysis; BCkh and BCref are the barycentric corrections for KH 15D and the reference star, respectively; and
vref is the absolute barycentric radial velocity of the reference
star as listed in Nidever et al. (2002). The mean measured
velocities from each epoch are listed in the final column of
Table 1. Table 2 lists the velocities obtained from our crosscorrelation analysis for each individual reference star on each
For nights when only one reference spectrum is available,
the uncertainty is estimated using the standard deviation of
the mean radial velocity measured from all echelle orders.
For nights with multiple reference spectra, the standard deviation of the velocities computed from each target-reference
pair is adopted as the uncertainty. This latter method of error

Using a nonlinear least-squares algorithm, we found a bestfit model orbit with a period P ¼ 48:38 days, eccentricity
e  0:27, and velocity semiamplitude K  8:15 km s1. The
other orbit parameters are listed in Table 3. Figure 2 shows a
plot of radial velocity versus orbital phase for P ¼ 48:38 days.
The rms p
ffiffiffiffiffiffi of the fit residuals is 0.38 km s and the
2 ¼ 1:5. The vertical lines at  ¼ 0:33 and
 ¼ 0:73 denote the approximate phases of ingress and egress,
respectively, based on the He02 ephemeris. We have no radial
velocity measurements between these phases because of the
eclipse of star A.
We find that the orbit solution is not well constrained as a
consequence of the lack of data near periapse, which allows
the velocity semiamplitude of the orbit solution to compensate
for changes in the eccentricity. As such, we were able to obtain reasonable fits by fixing the eccentricity at values e >
0:27, with each solution p
different values of the orbit
parameters and values of 2 that are equivalent at the 97.5%
confidence level (based on
ffiffiffiffiffiffi 9 degrees of freedom in the fit).
Figure 3 shows how 2 and the orbit parameters vary
as a function of eccentricity. While the period varies little
over a wide range of eccentricities, it is apparent that the
radial velocity data alone provide poor constraints for the
other orbit parameters. However, the implied mass ratio from
other KH 15D observations, together with the measured mass
limits of star A, can be used to place limits on the orbital
eccentricity, as we now show.
3.2. Orbit Parameter Constraints
JW04 determined from photometric measurements of archival plates that the out-of-eclipse magnitude of KH 15D was
0.9 mag brighter (at I band ) 40 years ago compared with the
modern bright state. The two most probable explanations for
the brighter apparent magnitude in the past are that either
both stars were visible or star B alone was visible. If both stars
were visible, then LB =LA ¼ 1:3. If only B were visible, then
LB =LA ¼ 2:3. In either case, the condition LB =LA > 1 must
Multicolor photometric measurements obtained during
minimum light show a slight blueing of the color indexes
( Ha03) compared with the colors at maximum light. Similarly,
Agol et al. (2004) measure slightly bluer colors during eclipse



Vol. 128

Fig. 1.—Radial velocity of KH 15D as a function of time. The dashed curve is the best-fit Keplerian orbit with the eccentricity fixed at e ¼ 0:74, the mean value
allowed by our orbit constraints (see x 3.2).

from their low-resolution spectropolarimetric observations
compared with their out-of-eclipse observations. One possibility for the bluer color indexes during eclipse is that the
scattered light is dominated by Rayleigh scattering. However,
He02 show that there is no reddening of the light from star A

during ingress and egress. This suggests that the opacity of the
occulting material is wavelength independent and that the
bluer colors are due to a bluer object. Therefore the temperature of B must be hotter than the temperature of A, assuming
both stars contribute nearly equally to the scattered component

Optimized Model Parameters


Acceptable Fit
to Velocitiesa

Acceptable Fit
with e = 0.74

P (days)......................
! (deg) .......................
 b ( km s1)................
a sin i (AU) ...............
K ( km s1).................
FM /sin3 i.....................
Tpc (JD) ......................
Fit rms ( km
Reduced 2 ............

48.38 to 48.40
20 to 1
+6.9 to +22.5
2.4 ; 103 to 2.2

48.38 (0.01)
0.74 (Bfixed)
2 (1)
+14.7 (0.9)
0.21 (0.5)
53 (4)
0.24 (0.05)
2,452,251.0 (0.6)

Model 1

48.35 (Bfi
3.8 ; 102
The limits on the fit parameters correspond to the 97.5% confidence upper limit on 2
(see Fig. 3) and the condition e < 1.
Radial velocity of the binary center of mass with respect to the solar system barycenter.
Time of periastron passage.

No. 3, 2004



Fig. 2.—Radial velocity of KH 15D as a function of orbital phase. The solid curve
ffi the best-fit Keplerian orbit with the eccentricity fixed at e ¼ 0:74, the mean
value allowed by our orbit constraints (see x 3.2). The fit has reduced chi-square 2 ¼ 1:5. The vertical dotted lines represent the approximate phases of ingress
(left) and egress (right) based on the He02 ephemeris. The bottom panel shows the 2001–2002 I-band light curve. The phased photometric measurements have been
binned for clarity using phase intervals of  ¼ 0:015.

of the light observed during the eclipse of A. However, since
the colors are only 0.1 mag bluer at minimum light ( He02),
TB cannot be much larger than TA.
For most low-mass (M < 1:0 M) pre–main-sequence evolutionary models (e.g., Chabrier & Baraffe 1997; D’Antona &
Mazzitelli 1997), the stellar mass is monotonic with both luminosity and temperature. For coeval stars on their Hayashi
tracks, TB k TA and LB =LA > 1 imply that MB k MA or, in
terms of the mass ratio, MA =MB P 1.
The mass function of a Keplerian orbit can be expressed as
FM (e; K; P) ¼

K 3 P(1  e2 )3=2 sin3 i
MB3 sin3 i
(MA þ MB )2


where P is the orbital period and K is the velocity semiamplitude. Solving equation (2) for MA yields
MA (e; MA =MB ) ¼

MA 2 FM (e; K; P)
sin3 i


The mass function FM =sin3 i in equation (3) is calculated from
the parameters of the best-fit orbit to the radial velocity data
with the value of e fixed in the fitting procedure. Figure 4
/MB 0.8, 0.9 and 1.0.
shows plots of MA versus e for MA =MB M
Also shown is the value of MA =MB ¼ 1:6 obtained by W04

based on their model fit to the KH 15D light curve (see x 4).
Since the mass of the visible star is known to fall within the
limits 0:5 M  MA  1:0 M (Flaccomio et al. 1999; Park
et al. 2000), it can be seen by inspection of Figure 4 that
acceptable choices of the eccentricity fall within the range
0:68  e  0:80.
The resulting range of acceptable orbit parameter values is
shown in Figure 3 between the solid vertical lines in each
panel. The third column of Table 3 lists the best-fit parameter
values obtained using the mean acceptable value of the eccentricity, e ¼ 0:74 (see also Fig. 2). The uncertainties in the
fit parameters were estimated using a Monte Carlo simulation.
We generated 103 statistical realizations of the velocity time
series assuming the errors are normally distributed with
standard deviations equal to the measurement uncertainties.
The estimated uncertainties are also displayed in Figure 3, as
error bars on the points located at e ¼ 0:74.
3.3. Periodicity
As discussed in x 3.1, we find the best-fit Keplerian has an
orbital period of P ¼ 48:38  0:01 days. He02 report a period
of P ¼ 48:35  0:02 days from their photometric monitoring,
and JW04 report P ¼ 48:42  0:02 days from a periodogram
analysis of archival photographic plates photometry. Thus, our
measured orbital period differs by 1.5  and 2  from the
modern and historical photometric periods, respectively. Since



Vol. 128

Fig. 3.—Dependence of the best-fit orbit parameters (top five panels) and reduced 2 (bottom) on the orbital eccentricity. The ordinate values are generated by
fixing the orbital eccentricity in thepleast-squares
fit to the radial velocity data. The vertical dashed line indicates the lower limits placed on the fit parameters based
on the 97.5% confidence level for 2 with 9 degrees of freedom. The solid vertical lines denote the upper and lower limits placed on the eccentricity as discussed
in x 3.2 (see also Fig. 4), and the fits generated for e ¼ 0:74 are denoted by circles with error bars.

the evolving shape of the light curve may complicate the accurate determination of the photometric period, we conclude
that the orbital period and photometric period of KH 15D are
indistinguishable within measurement errors.
He02 noted that the shape of the light curve varies from
eclipse to eclipse in such a way as to suggest a 96 day period
for the system, with each cycle containing two brightness
minima. In order to investigate this alternative periodicity,
we fixedp
in our fit at P ¼ 96:76 days and obtained a
reduced 2 of 47.5. Based on this poor quality of fit, we find
that a 96 day period is incompatible with our radial velocity
The results of our spectroscopic monitoring campaign show
that KH 15D is a spectroscopic binary system. The observed

radial velocities are consonant with a stellar companion with
an orbital period equal to the photometric period. We now
discuss the implications of the binarity of KH 15D for current
models of the photometric variability mechanism.
Existing models of the KH 15D eclipse mechanism fall into
two classes differentiated by whether it is the orbital motion of
the star or a feature of a circumstellar disk that causes the
photometric variability. The first class of models posits the
existence of a single star surrounded by a circumstellar disk
containing a nonaxisymmetric density enhancement or, alternatively, a warp. As the disk feature orbits the star with a
48 day period, it periodically blocks the line of sight to the
stellar surface. Based on their spectropolarimetric observations, which showed an increase in polarization during minimum light, Agol et al. (2004) developed a model of a warped
disk with an extended atmosphere and obtained a reasonable

No. 3, 2004


Fig. 4.—Mass of the visible component of KH 15D, MA, vs. orbital eclines show that
centricity for five choices of the mass ratio MA =MB .MThe
for 0:5 M < MA < 1:0 M and MA =MB P 1:0, acceptable values of the eccentricity fall within the range 0:68  e  0:80. The inclination is assumed to
be i ¼ 90 (sin3 i ¼ 0).

fit to the 2001–2002 light curve. A similar analysis was performed by Barge & Viton (2003) using a model involving a
large dusty vortex.
While these single-star models are able to match the light
curve of KH 15D at one point in time, they do not adequately
explain the temporal changes in the observed light curve. Perhaps more importantly, it is not clear if a binary companion to
KH 15D is compatible with an eclipsing disk feature. If a
density enhancement in a circumstellar disk is responsible for
the 48 day photometric period, the feature must orbit the central
star at a distance of 0.22 AU, assuming a Keplerian orbit. This
geometry would restrict the stellar companion to orbit either at a
distance less than 0.22 AU or beyond the outer extent of the
circumstellar disk. However, since our best-fit orbit yields a
period of 48:38  0:01 days and a sin i ¼ 0:21 AU (assuming
e ¼ 0:74; see x 3.2) for the binary companion, neither of these
scenarios seems plausible. Thus, it does not seem possible for
both an eclipsing disk feature and a stellar-mass companion to
coexist with the same orbital period.
In the second class of models, proposed by W04 and CM04,
there exists an unseen binary companion of comparable mass to
the visible K-type star seen today. Surrounding the two stars is a
circumbinary disk viewed nearly edge-on. The orbital plane of
the two stars is tilted at a small angle with respect to the disk
plane and the present-day light curve is produced as the reflex
motion of star A carries it above and behind the disk plane.
Independent evidence for the binary nature of KH 15D has
emerged from studies of archival photographic plates. In a
study of photographic plates obtained from Asiago Observatory, JW04 show that the apparent magnitude of KH 15D was
variable from 1968 to 1983 but the light curve from this epoch
was markedly different from the one observed today. The
bright state was nearly a factor of 2 brighter in the past and the
eclipse depth was a factor of 5 shallower. These findings can
be explained by invoking the presence of a second star that
was visible in the past but is unseen today (JW04).
Motivated by these findings, W04 constructed a model of
an eccentric binary with a fraction of the orbital plane obscured by an opaque screen (or circumbinary disk) and found
a quantitative orbital solution by fitting simultaneously to the


2001–2002 photometry of He02, the historical photometry of
JW04 and the radial velocity measurements of Ha03. Based on
a preliminary investigation of the radial velocities presented
here, CM04 independently used physical arguments to propose a similar model of an eccentric binary surrounded by a
nodally precessing circumbinary ring. As the ring precesses,
the light curve gradually changes from the one recovered from
the archival plates to the shape seen today. Perhaps the
greatest advantage of the two-star models is their ability to
explain not only the present-day light curve, but also its
evolution over the past half-century.
In addition to explaining the photometric phenomenology
of KH 15D, the two-star models make predictions about the
nature of the binary orbit. Both CM04 and W04 predict that
(1) periastron passage occurs during minimum light, (2) the
orbital companion has a mass comparable to the currently
visible star, and (3) the binary orbit is highly eccentric. These
predictions are precisely what we find from our orbit solution.
The W04 model makes additional, quantitative predictions
about the orbital parameters of the binary. For an assumed
fixed period of 48.35 days, the model produces a velocity
semiamplitude of 27.5 km s1, eccentricity e ¼ 0:7, a mass
ratio MA =MB ¼ 1:6, argument of pericenter ! ¼ 7N2, and a
center-of-mass radial velocity  ¼ þ15:5 km s1. As can be
seen in Table 3, the predictions of W04 model 1 agree well
with our orbital solution with fixed eccentricity, e ¼ 0:74 (see
x 3.2). We note here that our center-of-mass velocity for the
binary system of  ¼ þ14:7  0:9 km s1 clearly rules out
W04 model 2, which predicts  ¼ þ5:7 km s1 and negative
velocity at periapse.
The W04 model also predicts the inclination of the binary
orbit, a property of the system that our radial velocities do not.
W04 model 1 predicts i ¼ 84N6, or sin i ¼ 0:996. Similarly,
using the geometry of the circumbinary ring proposed by
CM04, an upper limit on the inclination of i < 80 can be
assigned to the binary orbit based on the time lag between
periastron passage and mid-eclipse (E. Chiang 2004, private
We note that the W04 model has the peculiar feature that the
less massive star is the more luminous. Using equation (3), the
values of P, K, and e produced by the W04 model lead to a
mass function FM ¼ 0:038 M and MA ¼ 0:41 M. This mass
is significantly less than the lower limit of 0.5 M measured
by Park et al. (2000) and the value of 0.6 M measured by
Flaccomio et al. (1999). Figure 4 shows a plot of MA as a
function of e for the W04 mass ratio MB =MA ¼ 1:6. For our
best-fitting model parameters, only eccentricities between 0.58
and 0.65 yield a mass of A between 0.5 and 1.0 M. Therefore, for a mass ratio of 1.6, the eccentricity reported by W04
(e ¼ 0:7) is larger than the value allowed by our radial velocity
measurements, assuming 0:5 M  MA  1:0 M . However,
this discrepancy is not too surprising, since the W04 model
used only two radial velocity measurements. It is also important to note that the mass limits on star A are derived by
placing KH 15D on a theoretical H-R diagram and are
therefore subject to the accuracy of the pre–main-sequence
evolutionary model employed. In all other features of the
KH 15D binary system, there is a remarkable agreement between the W04 model and the orbital solution calculated from
the radial velocities. Because of the strong evidence of a
second star from our radial velocity measurements and the
historical photometry, we find the two-star class of model to
be the most compelling explanation of the KH 15D photometric variability mechanism.



However, the case of the ‘‘winking star’’ is still far from
closed. A key missing aspect of the two-star models is direct
detection of a circumbinary disk around KH 15D. He02 report a
lack of near-infrared excess and a null detection at millimeter
wavelengths. CM04 state that such findings are consistent with
a circumbinary ring having an inner radius of 1 AU that is
tidally truncated by the central binary, and an outer radius of
5 AU that is possibly shepherded by an as yet unseen planet.
They predict mid-infrared fluxes that are observable with the
Spitzer Space Telescope. Clearly such observations will be vital
in further development of models of the KH 15D system.

We would like to thank Gibor Basri, Paul Butler, Debra
Fischer, and Subanjoy Mohanty for generously lending portions of their observing time for our project. Many thanks to
Eugene Chiang, Ruth Murray-Clay, Steve Dawson, and Josh
Winn for their helpful conversations and suggestions. We
acknowledge support by NASA grant NAG 5-8299 and NSF
grant AST 95-20443 (to G. W. M.), NASA grant NAG
5-12502 (to W. H.), and Sun Microsystems. We thank the
NASA, University of California, and McDonald Observatory
telescope assignment committees for allocations of telescope

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