Extended envelopes around Galactic Cepheids III. Y Oph and
α Per from near-infrared interferometry with CHARA/FLUOR
Antoine Mérand
Center for High Angular Resolution Astronomy, Georgia State University, PO Box 3965,
Atlanta, Georgia 30302-3965, USA
antoine@chara-array.org
Jason P. Aufdenberg
Embry-Riddle Aeronautical University, Physical Sciences Department, 600 S. Clyde Morris
Blvd, Daytona Beach, FL 32114, USA
Pierre Kervella and Vincent Coudé du Foresto
LESIA, UMR 8109, Observatoire de Paris, 5 place Jules Janssen, 92195 Meudon, France
Theo A. ten Brummelaar, Harold A. McAlister, Laszlo Sturmann, Judit Sturmann and
Nils H. Turner
Center for High Angular Resolution Astronomy, Georgia State University, PO Box 3965,
Atlanta, Georgia 30302-3965, USA
ABSTRACT
Unbiased angular diameter measurements are required for accurate distances
to Cepheids using the interferometric Baade Wesselink method (IBWM). The
precision of this technique is currently limited by interferometric measurements at
the 1.5% level. At this level, the center-to-limb darkening (CLD) and the presence
of circumstellar envelopes (CSE) seem to be the two main sources of bias. The
observations we performed aim at improving our knowledge of the interferometric
visibility profile of Cepheids. In particular, we assess the systematic presence of
CSE around Cepheids in order determine accurate distances with the IBWM
free from CSE biased angular diameters. We observed a Cepheid (Y Oph) for
which the pulsation is well resolved and a non-pulsating yellow supergiant (α Per)
using long-baseline near-infrared interferometry. We interpreted these data using
a simple CSE model we previously developed. We found that our observations
of α Per do not provide evidence for a CSE. The measured CLD is explained by
an hydrostatic photospheric model. Our observations of Y Oph, when compared
http://arxiv.org/abs/0704.1825v1
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to smaller baseline measurements, suggest that it is surrounded by a CSE with
similar characteristics to CSE found previously around other Cepheids. We have
determined the distance to Y Oph to be d = 491 ± 18 pc. Additional evidence
points toward the conclusion that most Cepheids are surrounded by faint CSE,
detected by near infrared interferometry: after observing four Cepheids, all show
evidence for a CSE. Our CSE non-detection around a non-pulsating supergiant
in the instability strip, α Per, provides confidence in the detection technique and
suggests a pulsation driven mass-loss mechanism for the Cepheids.
Subject headings: stars: variables: Cepheid - stars: circumstellar matter - stars:
individual (Y Oph) - stars: individual (α Per) - techniques: interferometric
1. Introduction
In our two previous papers, (Kervella et al. 2006; Mérand et al. 2006b), hereafter Paper I
and Paper II, we reported the discovery of faint circumstellar envelops (CSE) around Galactic
classical Cepheids. Interestingly, all the Cepheids we observed (ℓ Car in Paper I, α UMi,
and δ Cep in Paper II) were found to harbor CSE with similar characteristics: a CSE 3 to 4
times larger than the star which accounts for a few percent of the total flux in the infrared
K band. The presence of CSE was discovered in our attempt to improve our knowledge of
Cepheids in the context of distance determination via the interferometric Baade-Wesselink
method (IBWM). Part of the method requires the measurement of the angular diameter
variation of the star during its pulsation. The determination of the angular diameters from
sparse interferometric measurements is not straightforward because optical interferometers
gather high angular resolution data only at a few baselines at a time, thus good phase and
angular resolution coverage cannot be achieved in a short time. For Cepheids, the main
uncertainty in the IBWM was thought to be the center-to-limb darkening (CLD), which
biases the interferometric angular diameter measurements (Marengo et al. 2004).
The direct measurement of CLD is possible using an optical interferometer, given suffi-
cient angular resolution and precision. Among current optical interferometers, CHARA/FLUOR
(ten Brummelaar et al. 2005; Mérand et al. 2006a) is one of the few capable of such a mea-
surement for Cepheids. The only Cepheid accessible to CHARA/FLUOR, i.e. large enough
in angular diameter, for such a measurement is Polaris (α UMi), which we observed and
found to have a CLD compatible with hydrostatic photospheric models, though surrounded
by a CSE (Paper II). Polaris, however, is a very low amplitude pulsation Cepheid: 0.4%
in diameter, compared to 15 to 20% for type I Cepheids (Moskalik & Gorynya 2005), thus
the agreement is not necessarily expected for large amplitude Cepheids, whose photospheres
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are more out of equilibrium. The direct measurement of CLD of a high amplitude Cepheid
during its pulsation phase remains to be performed.
Hydrodynamic simulations (Marengo et al. 2003) suggest that the CLD variations dur-
ing the pulsation do not account for more than a 0.2% bias in distance determination in the
near infrared using the IBWM, where most of the IBWM observing work has been done in
recent years: the best formal distance determination to date using the IBWM is of the order
of 1.5% (Mérand et al. 2005b).
Whereas the near infrared IBWM seems to be relatively immune to bias from CLD, the
recent discovery of CSEs raises the issue of possible bias in angular diameter measurements,
hence bias in distance estimations at the 10% level (Paper II). It is therefore important
to continue the study of CSE around Cepheids. We present here interferometric observa-
tions of the non-pulsating supergiant α Per and the low amplitude Cepheid Y Oph. We
obtained these results in the near infrared K-band, using the Fiber Linked Unit for Optical
Recombination — FLUOR — (Mérand et al. 2006a), installed at Georgia State University’s
Center for High Angular Resolution Astronomy (CHARA) Array located on Mount Wilson,
California (ten Brummelaar et al. 2005).
2. The low amplitude Cepheid Y Oph
In the General Catalog of Variable Stars (Kholopov et al. 1998), Y Oph is classified in
the DCEPS category, i.e. low amplitude Cepheids with almost symmetrical light curves and
with periods less than 7 days. The GCVS definition adds that DCEPS are first overtone and/or
crossing the instability strip for the first time. A decrease in photometric variation amplitude
over time has been measured, as well as a period change (Fernie et al. 1995b). Using this
period change rate, 7.2± 1.5 syr−1 and the period of 17.1207 days, the star can be identified
as crossing the instability strip for the third time, according to models (Turner et al. 2006).
The fact that Y Oph belongs to the DCEPS category is questionable: its period is longer
than 7 days, by almost three times, though its light curve is quasi-symmetric and with a low
amplitude compared to other type I Cepheids of similar periods (Vinko et al. 1998). Indeed,
Y Oph is almost equally referred to in publications as being a fundamental-mode Cepheid
or a first overtone.
In this context, a direct determination of the linear diameter can settle whether Y Oph
belongs to the fundamental mode group or not. This is of prime importance: because of its
brightness and the large amount of observational data available, Y Oph is often used to cali-
brate the Period-Luminosity (PL) or the Period-Radius (PR) relations. The interferometric
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Baade-Wesselink method offers this opportunity to geometrically measure the average linear
radius of pulsating stars: if Y Oph is not a fundamental pulsator, its average linear diameter
should depart from the classical PR relation.
2.1. Interferometric observations
The direct detection of angular diameter variations of a pulsating star has been achieved
for many stars now using optical interferometers (Lane et al. 2000; Kervella et al. 2004a;
Mérand et al. 2005b). We showed (Mérand et al. 2006b) that for a given average diameter,
one should use a baseline that maximizes the amplification factor between the variation in
angular diameter and observed squared visibility. This baseline provides an angular resolu-
tion of the order of Bθ/λ ≈ 1, in other words in the first lobe, just before the first minimum
(Bθ/λ ≈ 1.22 for a uniform disk model), where B is the baseline (in meters), θ the angular
diameter (in radians) and λ the wavelength of observation (in meters). According to pre-
vious interferometric measurements (Kervella et al. 2004a), the average angular diameter of
Y Oph is of the order of 1.45 mas (milli arcsecond).
Ideally, that would mean using a baseline of the order of 300 m, which is available at
the CHARA Array. Because of a trade we made with other observing programs, we used
only a 250 m baseline provided by telescopes S1 and E2.
The fringes squared visibility is estimated using the integration of the fringes power
spectrum. A full description of the algorithm can be found in Coude Du Foresto et al. (1997)
and Mérand et al. (2006a).
The raw squared visibilities have been calibrated using resolved calibrator stars, chosen
from a specific catalog (Mérand et al. 2005a) using criteria defined to minimize the calibra-
tion bias and maximize signal to noise. The error introduced by the uncertainty on each
calibrator’s estimated angular diameter has been properly propagated. Among the three
main calibrators (Tab. 1), one, HR 6639, turned out to be inconsistent with the others. The
raw visibilility of this star was found to vary too much to be consistent with the expected
statistical dispersion. The quantity to calibrate, the interferometric efficiency (also called
instrument visibility), is very stable for an instrument using single mode fibers, such as
FLUOR. If this quantity is assumed to be constant over a long period of time, and if obser-
vations of a given simple star are performed several times during this period, one can check
whether or not the variation of the raw visibilities with respect to the projected baseline
is consistent with a uniform disk model. Doing so, HR 6639 was found inconsistent with
the over stars observed during the same night (Fig 1). The unconsistency may be explained
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by the presence of a faint companion with a magnitude difference of 3 or 4 with respect
to the primary. Two over calibrators, from another program, were also used as check stars:
HR 7809 and ρ Aql (Tab. 1). This latter calibrator is not part of the catalog by Mérand et al.
(2005a). Its angular diameter has been determined using the Kervella et al. (2004b) surface
brightness calibration applied to published photometric data in the visible and near infrared.
For each night we observed Y Oph, we determined a uniform disk diameter (Tab. 3)
based on several squared visibility measurements (Tab. 2). Each night was assigned a
unique pulsation phase established using the average date of observation and the Fernie et al.
(1995b) ephemeris, including the measured period change:
D = JD − 2440007.720 (1)
E = 0.05839D − 3.865× 10−10D2 (2)
P = 17.12507 + 3.88× 10−6E (3)
where E is the epoch is the epoch of maximum light (the fractional part is the pulsation
phase) and P the period at this epoch.
2.2. Pulsation
2.2.1. Radial Velocity integration
In order to measure the distance to a pulsating star, the IBWM makes use of radial
velocities and angular diameters. The latter is the integral other time of the former. The
radial velocities, which have been acquired at irregular intervals during the pulsation phase,
must be numerically integrated. This process is highly sensitive to noisy data and the best
way to achieve a robust integration is to interpolate the data before integration. For this
purpose, we use a periodic cubic spline function, defined by floating nodes (Fig. 2). The
coordinates of these nodes are adjusted such that the cubic spline function going through
these nodes provides the best fit to the data points. The phase positions φi of these nodes
are forced to be between 0 and 1, but they are replicated every φi+n, where n is an integer,
in order to obtain a periodic function of period 1.
Among published Y Oph radial velocities data, we chose Gorynya et al. (1998) because
of the uniform phase coverage and the algorithm used to extract radial velocities: the cross-
correlation method. As shown by Nardetto et al. (2004), the method used can influence
the distance determination via the choice of the so-called projection factor, which we shall
introduce in the following section. The pulsation phases have been also determined using
Eq. 2.
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The data presented by Gorynya et al. (1998) were acquired between June 1996 and
August 1997. As we already mentioned, Y Oph is known for its changing period and photo-
metric amplitude. Based on Fernie et al. (1995b), the decrease in amplitude observed for the
photometric B and V bands does not have a measurable counterpart in radial velocity. This
is why we did not apply any correction in amplitude to the radial velocity data in order to
take into account the ten years between the spectroscopic and interferometric measurements.
2.2.2. Distance determination method
Once radial velocities vrad are interpolated (Fig. 2) and integrated, the distance d is
determined by fitting the radial displacement to the measured angular diameters (Fig. 3):
θUD(T )− θUD(0) = −2
vrad(t)dt (4)
where θUD is the interferometric uniform disk diameter, and k is defined as the ratio between
θUD and the true stellar angular diameter. The projection factor, p, is the ratio between the
pulsation velocity and the spectroscopically measured radial velocity. The actual parameters
of the fit are the average angular diameter θUD(0) and the biased distance
This formalism assumes that both k and p do not vary during the pulsation. There is
evidence that this might be true for k, based on hydrodynamic simulation (Marengo et al.
2003), at the 0.2% level. Observational evidence exists as well: when we measured the p-
factor of δ Cep (Mérand et al. 2005b) we did not find any difference between the shapes of
the left and right parts of Eq. 4, therefore kp is probably constant other a pulsation period,
at least at the level of precision we have available.
For this work, we will adopt the value for p we determined observationally for near
infrared interferometry/ cross correlation radial velocity: p = 1.27. This result has been
established for δ Cep (Mérand et al. 2005b). This is also the latest value computed from
hydrodynamical photospheric models (Nardetto et al. 2004). The IBWM fit yields a biased
distance d/k = 480± 18 pc and an average angular uniform disk diameter θUD(0) = 1.314±
0.005 mas. Note that we had to allow a phase shift between interferometric and radial
velocity observations: −0.074 ± 0.005 (Fig. 3). The final reduced χ2 is of the order of 3,
mostly due to one data point (φ = 0.887).
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2.2.3. Choice of k
Usually, the choice of k is made assuming the star is a limb-darkened disk. The strength
of the CLD is computed using photospheric models, then a value of k is computed. This
approach is sometimes confusing because, even for a simple limb darkened disk, there is no
unique value of k, in the sense that this value varies with respect to angular resolution. The
uniform disk angular size depends upon which portion of the visibility curve is measured.
However, it is mostly unambiguous in the first lobe of visibility, i.e. at moderate angular
resolution: Bθ/λ ≤ 1.
However, as shown in Paper II, the presence of a faint CSE around Cepheids biases k
up to 10%, particularly when the angular resolution is moderate and the star is not well
resolved (V 2 ∼ 0.5). Under these conditions, the CSE is largely resolved, leading to a strong
bias if the CSE is omitted. On the other hand, at greater angular resolution (Bθ/λ ∼ 1), the
star is fully resolved (V 2 approaches it first null) and the bias from the CSE is minimized.
In any cases, it is critical to determine whether or not Y Oph is surrounded by a CSE if an
accurate distance is to be derived.
2.3. Interferometric evidence of a CSE around Y Oph
We propose here to compare the uniform disk diameters obtained by VLTI/VINCI
(Kervella et al. 2004a) and CHARA/FLUOR (this work). This makes sense because these
two instruments are very similar. Both observe in the near infrared K-band. Moreover, both
instruments observed Y Oph in the first lobe of the visibility profile, though at different
baselines.
If Y Oph is truly a uniform disk, or even a limb-darkened disk, the two instruments
should give similar results. That is because the star’s first lobe of squared visibility is insen-
sitive to the CLD and only dependent the on the size. Conversely, if Y Oph is surrounded
by a CSE, we expect a visibility deficit at smaller baseline (VLTI/VINCI), hence a larger
apparent uniform disk diameter (see Fig. 5). This is because the CSE is fully resolved at
baselines which barely resolve the star.
This is indeed the case, as seen on Fig. 4: VLTI/VINCI UD diameters are larger than
CHARA/FLUOR’s. Even if the angular resolution of VLTI/VINCI is smaller than for
CHARA/FLUOR, leading to less precise angular diameter estimations, the disagreement
is still statistically significant, of the order of 3 sigmas. Using the CSE model we can predict
the correct differential UD size between the two instruments, consistant with the presence
of a CSE around Y Oph. The amount of discrepancy can be used to estimate the flux ra-
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tio between the CSE and the star. In the case of Y Oph, we find that the CSE amounts
for 5 ± 2% of the stellar flux. Note that for this comparison, we recomputed the phase of
VLTI/VINCI data using Fernie et al. (1995b) ephemeris presented in Eq. 2.
In Fig. 5, we plot k as a function of the observed squared visibility for different models:
hydrostatic CLD, 2% CSE and 5% CSE (K-Band flux ratio). For the hydrostatic model
we have k = 0.983. For the 5% CSE models, for CHARA/FLUOR (0.20 < V 2 < 0.35),
θUD/θ⋆ = 1.023. This is the value we shall adopt. If we ignore the presence of the CSE, the
bias introduced is 1.023/0.983 ≈ 1.04, or 4%.
2.4. Unbiased distance and linear radius
This presence of a 5% CSE leads to an unbiased distance of d = 491 ± 18 pc, which
corresponds to a 3.5% uncertainty on the distance. This is to be compared with the bias we
corrected for if one omits the CSE, of the order of 4%. Ignoring the CSE leads to a distance
of d = 472± 18 pc
We note that k biases only the distance, so one can form the following quantity:
[θUD(0)]× [d/k], which is the product of the two adjusted parameters in the fit, both biased.
This quantity is by definition the linear diameter of the star, and does not depend on the
factor k, even if it is still biased by the choice of p. If θ is in mas and d in parsecs, then
the average linear radius in solar radii is: R = 0.1075θd. In the case of Y Oph, this leads to
R = 67.8± 2.5 R⊙.
2.5. Conclusion
YOph appears larger (over 2 sigma) in the infrared K-band at a 140 m baseline comapred
to a 230 m baseline. Using a model of a star surrounded by a CSE we developed based
on observations of other Cepheids, this disagreement is explained both qualitatively and
quantitatively by a CSE accounting of 5% of the stellar flux in the near infrared K-Band.
This model allows us to unbias the distance estimate: d = 491 ± 18 pc. The linear radius
estimate is not biased by the presence of CSE and we found R = 67.8± 2.5 R⊙.
Our distance is not consistent with the estimation using the Barnes-Evans method:
Barnes et al. (2005) found d = 590 ± 42 pc (Bayesian) and d = 573 ± 8 pc (least squares).
For this work, they used the same set of radial velocities we used. Our estimate is even more
inconsistent with the other available interferometric estimate, by Kervella et al. (2004a): d =
690±50 pc. This later result has been established using an hybrid version of the BWmethod:
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a value of the linear radius is estimated using the Period-Radius relation calibrated using
classical Cepheids, not measured from the data. This assumption is questionable, as we noted
before, since Y Oph is a low amplitude Cepheid. Kervella et al. (2004a) deduced R = 100±
8 R⊙ from PR relation, whereas we measured R = 67.8±2.5 R⊙. Because Y Oph’s measured
linear radius is not consistent with the PR relation for classical, fundamental mode Cepheids,
it is probably safe to exclude it from further calibrations. Interestingly, Barnes et al. (2005)
observationally determined Y Oph’s linear radius to be also slightly larger (2.5 sigma) than
what we find: R = 92.1±6.6 R⊙ (Bayesian) and R = 89.5±1.2 R⊙ (least squares). They use
a surface brightness technique using a visible-near infrared color, such as V-K. This method is
biased if the reddening is not well known. If the star is reddened, V magnitudes are increased
more than K-band magnitudes. This leads to an underestimated surface brightness, because
the star appears redder, thus cooler than it is. The total brightness (estimated from V) is also
underestimated. These two underestimates have opposing effects on the estimated angular
diameter: an underestimated surface brigthness leads to an overestimated angular diameter,
whereas an underestimated luminosity leads to an underestimated angular diameter. In the
case of a reddening law, the two effects combine and give rise to a larger angular diameter: the
surface brightness effect wins over the total luminosity. Based on their angular diameter, θ ≈
1.45 mas, it appears that Barnes et al. (2005) overestimated Y Oph’s angular size. Among
Cepheids brighter than mV = 6.0, Y Oph has the strongest B-V color excess, E(B − V ) =
0.645 (Fernie et al. 1995a) and one of the highest fraction of polarized light, p = 1.34±0.12 %
(Heiles 2000). Indeed, Y Oph is within the galactic plane: this means that it has a probably
a large extinction due to the interstellar medium.
3. The non-pulsating yellow super giant α Per
α Per (HR 1017, HD 20902, F5Ib) is among the most luminous non-pulsating stars
inside the Cepheids’ instability strip. The Doppler velocity variability has been found to be
very weak, of the order of 100 m/s in amplitude (Butler 1998). This amplitude is ten times
less than what is observed for the very low amplitude Cepheid Polaris (Hatzes & Cochran
2000).
α Per’s apparent angular size, approximately 3 mas (Nordgren et al. 2001), makes it
a perfect candidate for direct center-to-limb darkening detection with CHARA/FLUOR.
Following the approach we used for Polaris (Paper II), we observed α Per using three different
baselines, including one sampling the second lobe, in order to measure its CLD strength, but
also in order to be able to assess the possible presence of a CSE around this star.
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3.1. Interferometric observations
If the star is purely a CLD disk, then only two baselines are required to measure the
angular diameter and the CLD strength. Observations must take place in the first lobe of the
squared visibility profile, in order to set the star’s angular diameter θ. The first lobe is defined
by BθUD/λ < 1.22. Additional observations should taken in the second lobe, in particular
near the local maximum (Bθ/λ ∼ 3/2), because the strength of the CLD is directly linked
to the height of the second lobe. To address the presence of a CSE, observations should be
made at a small baseline. Because the CSEs that were found around Cepheids are roughly 3
times larger that the star itself (Paper I and II), we chose a small baseline where Bθ/λ ∼ 1/3.
As demonstrated by our Polaris measurements, the presence of CSE is expected to weaken
the second lobe of visibility curve, mimicking stronger CLD.
FLUOR operates in the near infrared K-band, with a mean wavelength of λ0 ≈ 2.13 µm.
This sets the small, first-lobe and second-lobe baselines at approximatively 50, 150 and 220
meters, which are well-matched to CHARA baselines W1-W2 (∼ 100 m), E2-W2 (∼ 150 m)
and E2-W1 (∼ 250 m). See Fig. 6 for a graphical representation of the baseline coverage.
The data reduction was performed using the same pipeline as for Y Oph. Squared
visibilities were calibrated using a similar strategy we adopted for Y Oph. We used two sets
of calibrators: one for the shorter baselines, W1-W2 and E2-W2, and one for the longest
baseline, E2-W1 (Tab. 4).
3.2. Simple Model
3.2.1. Limb darkened disk
To probe the shape of the measured visibility profile, we first used an analytical model
which includes the stellar diameter and a CLD law. Because of its versatility, we adopt
here a power law (Hestroffer 1997): I(µ)/I(0) = µα, with µ = cos(θ), where θ is the angle
between the stellar surface and the line of sight. The uniform disk diameter case corresponds
to α = 0.0, whereas an increasing value of α corresponds to a stronger CLD.
All visibility models for this work have been computed taking into account instrumental
bandwidth smearing (Aufdenberg et al. 2006). From this two-parameter fit, we deduce a
stellar diameter of θα = 3.130 ± 0.007 mas and a power law coefficient α = 0.119 ± 0.016.
The fit yields a reduced χ2 = 1.0. There is a strong correlation between the diameter and
CLD coefficent: 0.9. This is a well known effect, that a change in CLD induces a change in
apparent diameter.
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This fit is entirely satisfactory, as the reduced χ2 is of the order unity and the residuals
of the fit do not show any trend (Fig. 7). We note that this is not the case for Polaris (Paper
II). Polaris, with very similar u-v coverage to α Per, does not follow a simple LD disk model
because it is surrounded by a faint CSE.
3.2.2. Hydrostatic models
We computed a small grid of models which consists of six one-dimensional, spherical,
hydrostatic models using the PHOENIX general-purpose stellar and planetary atmosphere
code version 13.11; for a description see Hauschildt et al. (1999) and Hauschildt & Baron
(1999). The range of effective temperatures and surface gravities is based on a summary of
α Per’s parameters by Evans et al. (1996):
• effective temperatures, Teff = 6150 K, 6270 K, 6390 K;
• log(g) = 1.4, 1.7;
• radius, R = 3.92× 1012 cm;
• depth-independent micro-turbulence, ξ = 4.0 km s−1;
• mixing-length to pressure scale ratio, 1.5;
• solar elemental abundance LTE atomic and molecular line blanketing, typically 106
atomic lines and 3× 105 molecular lines dynamically selected at run time;
• non-LTE line blanketing of H I (30 levels, 435 bound-bound transitions), He I (19 levels,
171 bound-bound transitions), and He II (10 levels, 45 bound-bound transitions);
• boundary conditions: outer pressure, 10−4 dynes cm−2, extinction optical depth at
1.2 µm: outer 10−10, inner 102.
For this grid of models the atmospheric structure is computed at 50 radial shells (depths)
and the radiative transfer is computed along 50 rays tangent to these shells and 14 additional
rays which impact the innermost shell, the so-called core-intersecting rays. The intersection
of the rays with the outermost radial shell describes a center-to-limb intensity profile with
64 angular points.
Power law fits to the hydrostatic model visibilities range from α = 0.132 to α = 0.137
(Tab. 6), which correspond to 0.8 to 1.1 sigma above the value we measured. Our measured
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CLD is below that predicted by the the models, or in other words the predicted darkening
is slightly overestimated.
3.3. Possible presence of CSE
Firstly, we employ the CSE model used for Cepheids (Paper I, Paper II). This model is
purely geometrical and it consists of a limb darkened disk surrounded by a faint CSE whose
two-dimensional geometric projection (on the sky) is modeled by a ring. The ring parameters
consist of the angular diameter, width and flux ratio with respect to the star (Fs/F⋆). We
adopt the same geometry found for Cepheids: a ring with a diameter equal to 2.6 times the
stellar diameter (Paper II) with no dependency with respect to the width (fixed to a small
fraction of the CSE angular diameter, say 1/5).
This model restriction is justified because testing the agreement between a generic CSE
model and interferometric data requires a complete angular resolution coverage, from very
short to very large baselines. Though our α Per data set is diverse regarding the baseline
coverage, we lack a very short baseline (B ∼ 50m) which was not available at that time at
the CHARA Array.
The simplest fit consists in adjusting the geometrical scale: the angular size ratio be-
tween the CSE and the star is fixed. This yields a reduced χ2 of 3, compared to 1.1 for a
hydrostatic LD and 1.0 for an adjusted CLD law (Tab. 7).
We can force the data to fit a CSE model by relaxing the CLD of the star or the CSE
flux ratio. A fit of the size of the star and the brightness of the CSE leads to a reduced χ2 of
1.4 and results in a very small flux ratio between the CSE and the star of 0.0006± 0.0026,
which provides an upper limit for the CSE flux of 0.26% (compared to 1.5% for Polaris and
δ Cep for example, and 5% for Y Oph). On the other hand, forcing the flux ratio to match
that for Cepheids with CSEs and leaving the CLD free leads to a reduced χ2 of 1.4 but also
to a highly unrealistic α = 0.066± 0.004 (Tab. 7 and Fig. 7).
This leads to the conclusion that the presence of a CSE around α Per similar to the
measured Cepheid CSE is highly improbable. As shown above, the measured CLD is slightly
weaker (1 sigma) than one predicted by model atmospheres. A compatible CSE model exists
if the CLD is actually even weaker but in unrealistic proportions.
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3.4. Conclusion
The observed α Per visibilities are not compatible with the presence of a CSE similar to
that detected around Cepheids. The data are well explained by an adjusted center-to-limb
darkening. The strength of this CLD is compatible with the hydrostatic model within one
sigma.
4. Discussion
Using the interferometric Baade-Wesselink method, we determined the distance to the
low amplitude Cepheid Y Oph to be d = 491± 18 pc. This distance has been unbiased from
the presence of the circumstellar envelope. This bias was found to be of the order of 4% for
our particular angular resolution and the amount of CSE we measured. Y Oph’s average
linear diameter has also been estimated to be R = 67.8 ± 2.5 R⊙. This latter quantity
in intrinsically unbiased by the center-to-limb darkening or the presence of a circumstellar
envelope. This value is found to be substantially lower, almost 4 sigmas, than the Period-
Radius relation prediction: R = 100 ± 8 R⊙. Among other peculiarities, we found a very
large phase shift between radial velocity measurements and interferometric measurements:
∆φ = −0.074 ± 0.005, which corresponds to more that one day. For these reasons, we
think Y Oph should be excluded from future calibrations of popular relations for classical
Cepheids, such as Period-Radius, Period-Luminosity relations.
So far, the four Cepheids we looked at have a CSE: ℓ Car (Paper I), Polaris, δ Cep
(Paper II) and Y Oph (this work). On the other hand, we have presented here similar
observations of α Per, a non-pulsating supergiant inside the instability strip, which provides
no evidence for a circumstellar envelope. This non detection reinforces the confidence we
have in our CSE detection technique and draws more attention to a pulsation driven mass
loss mechanism.
Interestingly, there seems to be a correlation between the period and the CSE flux ratio
in theK-Band: short-period Cepheids seem to have a fainter CSE compared to longer-period
Cepheids (Tab. 8). Cepheids with long periods have higher masses and larger radii, thus, if
we assume that the CSE K-Band brightness is an indicator of the mass loss rate, this would
mean that heavier stars experience higher mass loss rates. This is of prime importance in the
context of calibrating relations between Cepheids’ fundamental parameters with respect to
their pulsation periods. If CSEs have some effects on the observational estimation of these
fundamental parameters (luminosity, mass, radius, etc.), a correlation between the period
and the relative flux of the CSE can lead to a biased calibration.
– 14 –
Research conducted at the CHARA Array is supported at Georgia State University
by the offices of the Dean of the College of Arts and Sciences and the Vice President for
Research. Additional support for this work has been provided by the National Science
Foundation through grants AST 03-07562 and 06-06958. We also wish to acknowledge the
support received from the W.M. Keck Foundation. This research has made use of SIMBAD
database and the VizieR catalogue access tool, operated at CDS, Strasbourg, France.
– 15 –
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– 17 –
This preprint was prepared with the AAS LATEX macros v5.2.
– 18 –
 230  240  250  260
Y Oph
B (m)
 230  240  250  260
B (m)
HR 6639
Fig. 1.— Evidence that calibrator HR 6639 is probably a binary star. Calibrated squared
visibility as a function of baseline for UT 2006/07/10. Left is Y Oph and right is HR 6639.
The interferometric efficiency was supposed constant during the night and established using
HR 7809 and ρ Aql with a reduced χ2 of 1.3. A UD fit, shown as a continuous line, works for
Y Oph (χ2r = 0.6) whereas it fails for HR 6639 (χ
r = 7.2). This could the sign that HR 6639
has a faint companion: the visibility variation has a 3-5% amplitude, which corresponds to
a magnitude difference of 3 to 4 between the main star and its companion.
– 19 –
0.0 0.5 1.0
0.0 0.5 1.0
Fig. 2.— Y Oph: Radial velocities from Gorynya et al. (1998). The continuous line is the
periodic spline function defined by 3 adjustable floating nodes (large filled circles). The
systematic velocity, Vγ = −7.9 ± 0.1 kms
−1, has been evaluated using the interpolation
function and removed. The lower panel displays the residuals of the fit.
– 20 –
0.0 0.5 1.0
0.0 0.5 1.0
−0.02
Fig. 3.— Y Oph: angular diameter variations. Upper panel: CHARA/FLUOR uniform disk
angular diameters as a function of phase. Each data point corresponds to a given night,
which contains several individual squared visibility measurements (Tab. 3). The solid line
is the integration of the radial velocity (Fig. 2) with distance, average angular diameter and
phase shift adjusted. The dashed line has a phase shift set to zero. The lower panel shows
the residuals to the continuous line.
– 21 –
CSE 2%
CSE 5%
0.0 0.5 1.0
Fig. 4.— Y Oph: Comparison between CHARA/FLUOR and VLTI/VINCI observations.
Uniform disk angular diameter as a function of phase. Small data points (with small error
bars) and lower continuous line: CHARA/FLUOR observations and distance fit. Large open
squares: VLTI/VINCI observations. The distance fit and it uncertainty are reprensenteb by
the shaded band. Dashed and dotted lines: VLTI/VINCI expected biased observations based
on CHARA/FLUOR and our CSE model with a flux ratio of 2% (dashed) and 5% (dotted).
– 22 –
CSE 5%
CSE 2%
0.0 0.2 0.4 0.6 0.8
squared visibility
Fig. 5.— Y Oph: angular diameter correction factor. We plot here θUD/θ⋆ for three different
Cepheid models as a function of observed squared visibility (first lobe): the dashed line is
a simple limb darkened disk with the appropriate CLD strength; the continuous line is a
similar LD disk surrounded by a CSE with a 2% K-band flux (short period: Polaris and
δ Cep, see Paper II) and 5% (long period: ℓ Car, see paper I). Note that, in the presence of
CSE, the bias is stronger at large visibilities (hence smaller angular resolution). The shaded
regions represents near infrared Y Oph observations: from CHARA (this work) and the
VLTI (Kervella et al. 2004a).
– 23 –
−200  0  200
u (m)
Fig. 6.— α Per. Projected baselines, in meters. North is up East is right. The shaded area
corresponds to the squared visibility’s second lobe. The baselines are W1-W2, E2-W2 and
E2-W1, from the shortest to the longest.
– 24 –
adjusted CLD
CSE "Polaris"
CSE (1)
 50  100  150  200  250
B (m)
Fig. 7.— α Per squared visibility models: UD, adjusted CLD, PHOENIX and 2 different
CSE models are plotted here as the residuals to the PHOENIX CLD with respect to baseline.
The common point at B ≈ 175 m is the first minimum of the visibility function. The top
of the second lobe is reached for B ≈ 230 m. See Tab. 7 for parameters and reduced χ2 of
each model.
– 25 –
α UMi δ Cep
Y Oph
l Car
α Per
 0  10  20  30  40
Period (days)
Fig. 8.— measured relative K-band CSE fluxes (in percent) around Cepheids, as a function
of the pulsation period (in days). The non-pulsating yellow supergiant α Per is plotted with
– 26 –
Table 1. Y Oph calibrators.
Star S.T. UD Diam. Notes
(mas)
HD 153033 K5III 1.100± 0.015
HD 175583 K2III 1.021± 0.014
HR 6639 K0III 0.904± 0.012 rejected
HR 7809 K1III 1.055± 0.015
ρ Aql A2V 0.370± 0.005 not in M05
Note. — “S.T.” stands for spectral type. Uniform Disk diameters, given in mas, are only
intended for computing the expected squared visibility in the K-band. All stars but ρ Aql
are from M05 catalog (Mérand et al. 2005a). Refer to text for an explanation why HR 6639
has been rejected.
– 27 –
Table 2. Journal of observations: Y Oph.
MJD-53900 B P.A. V 2
(m) (deg)
18.260 229.808 63.540 0.2348± 0.0061
18.296 215.049 71.242 0.2823± 0.0065
18.321 207.247 77.913 0.3030± 0.0075
21.245 232.792 62.353 0.2511± 0.0065
21.283 216.576 70.243 0.2954± 0.0085
21.309 208.313 76.765 0.3194± 0.0085
22.212 245.894 58.023 0.2092± 0.0071
22.234 236.338 61.050 0.2352± 0.0078
22.251 228.941 63.902 0.2615± 0.0085
24.188 253.988 55.914 0.2108± 0.0062
24.212 243.641 58.680 0.2427± 0.0060
24.231 235.388 61.389 0.2634± 0.0065
26.168 259.377 54.714 0.2185± 0.0041
26.194 249.210 57.113 0.2526± 0.0039
26.224 235.772 61.251 0.2983± 0.0034
26.242 227.859 64.367 0.3171± 0.0035
27.194 247.788 57.495 0.2650± 0.0040
27.211 240.340 59.704 0.2854± 0.0038
27.228 232.806 62.348 0.3177± 0.0045
27.250 223.415 66.429 0.3385± 0.0045
28.241 225.978 65.207 0.3332± 0.0045
28.257 219.413 68.547 0.3629± 0.0061
29.219 234.329 61.775 0.2857± 0.0049
29.237 226.405 65.012 0.3148± 0.0053
29.253 219.709 68.380 0.3320± 0.0054
30.192 245.267 58.203 0.2510± 0.0035
30.216 234.738 61.624 0.2893± 0.0041
30.235 226.418 65.007 0.3112± 0.0044
30.244 222.544 66.866 0.3226± 0.0046
30.261 215.937 70.653 0.3462± 0.0048
– 28 –
Table 2—Continued
MJD-53900 B P.A. V 2
(m) (deg)
Note. — Date of observation (modified julian day), telescope projected separation (m),
baseline projection angle (degrees) and squared visibility
– 29 –
Table 3. Y Oph angular diameters.
MJD-53900 φ Nobs. B θUD χ
(m) (mas)
18.292 0.248 3 207-230 1.3912± 0.0067 0.55
21.279 0.423 3 208-233 1.3516± 0.0074 1.06
22.232 0.478 3 229-246 1.3387± 0.0077 0.05
24.210 0.594 3 235-254 1.2929± 0.0059 0.19
26.207 0.710 4 228-259 1.2488± 0.0029 0.61
27.221 0.770 4 223-248 1.2374± 0.0032 0.76
28.249 0.830 2 219-226 1.2394± 0.0055 0.30
29.237 0.887 3 220-234 1.2728± 0.0047 0.26
30.229 0.945 5 216-245 1.2715± 0.0030 0.56
Note. — Data points have been reduced to one uniform disk diameter per night. Avger-
age date of observation (modified julian day), pulsation phase, number of calibrated V 2,
projected baseline range, uniform disk angular diameter and reduced χ2.
– 30 –
Table 4. α Per calibrators.
Name S.T. UD Diam. Baselines
(mas)
HD 18970 G9.5III 1.551± 0.021 W1-W2, E2-W2
HD 20762 K0II-III 0.881± 0.012 E2-W1
HD 22427 K2III-IV 0.913± 0.013 E2-W1
HD 31579 K3III 1.517± 0.021 W1-W2, E2-W2
HD 214995 K0III 0.947± 0.013 W1-W2
Note. — “S.T.” stands for spectral type. Uniform Disk diameters, given in mas, are only
intended for computing the expected squared visibility in the K-band. These stars come
from our catalog of interferometric calibrators (Mérand et al. 2005a)
– 31 –
Table 5. Journal of observations: α Per.
MJD-54000 B P.A. V 2
(m) (deg)
46.281 147.82 79.37 0.02350± 0.00075
46.321 153.87 69.04 0.01368± 0.00067
46.347 155.79 62.17 0.01093± 0.00060
46.372 156.27 55.30 0.01134± 0.00039
46.398 155.65 48.10 0.01197± 0.00051
46.421 154.41 41.32 0.01367± 0.00052
46.442 152.94 34.84 0.01581± 0.00045
46.466 151.13 27.03 0.01824± 0.00064
46.488 149.58 19.40 0.02167± 0.00071
46.510 148.49 12.06 0.02250± 0.00058
46.539 147.77 1.53 0.02370± 0.00070
47.225 96.66 -44.51 0.27974± 0.00282
47.233 97.75 -47.34 0.27321± 0.00274
47.252 100.37 -53.97 0.24858± 0.00258
47.274 103.03 -60.91 0.23529± 0.00242
47.327 249.17 81.65 0.01363± 0.00032
47.352 251.22 74.84 0.01340± 0.00032
47.374 251.04 68.91 0.01330± 0.00035
47.380 250.67 67.10 0.01316± 0.00035
Note. — Date of observation (modified julian day), telescope projected separation, base-
line projection angle and squared visibility
– 32 –
Table 6. α Per PHOENIX models.
Teff log g = 1.4 log g = 1.7
6150 0.137 0.136
6270 0.135 0.134
6390 0.133 0.132
Note. — Models tabulated for different effective temperatures and surface gravities. The
K-band CLD is condensed into a power law coefficient α: I(µ) ∝ µα.
– 33 –
Table 7. Models for α Per.
Model θ⋆ α Fs/F⋆ χ
(mas) (%)
UD 3.080±0.004 0.000 - 5.9
PHOENIX CLD 3.137±0.004 0.135 - 1.1
adjusted CLD 3.130±0.007 0.119±0.016 - 1.0
CSE “Polaris” 3.086±0.007 0.135 1.5 3.0
CSE (1) 3.048±0.007 0.066±0.004 1.5 1.4
CSE (2) 3.095±0.010 0.135 0.06±0.26 1.4
Note. — The parameters are: θ⋆ the stellar angular diameter, the CLD power law coef-
ficient α and, if relevant, the brightness ratio between the CSE and the star Fs/F⋆. The
first line is the uniform disk diameter, the second one expected CLD from the PHOENIX
model, the third one is the adjusted CLD. The fourth line is a scaled Polaris CSE model
(Paper II). The last two lines are attempts to force a CSE model to the data. Lower script
are uncertainties, the absence of lower script means that the parameter is fixed
– 34 –
Table 8. Relative flux in K-Band for the CSE discovered around Cepheids and the non
pulsating α Per.
Star Period CSE flux
(d) (%)
α UMi 3.97 1.5± 0.4
δ Cep 5.37 1.5± 0.4
Y Oph 17.13 5.0± 2.0
ℓ Car 35.55 4.2± 0.2
α Per - < 0.26
	Introduction
	The low amplitude Cepheid Y Oph
	Interferometric observations
	Pulsation
	Radial Velocity integration
	Distance determination method
	Choice of k
	Interferometric evidence of a CSE around Y Oph
	Unbiased distance and linear radius
	Conclusion
	The non-pulsating yellow super giant  Per
	Interferometric observations
	Simple Model
	Limb darkened disk
	Hydrostatic models
	Possible presence of CSE
	Conclusion
	Discussion

  Unbiased angular diameter measurements are required for accurate distances to
Cepheids using the interferometric Baade Wesselink method (IBWM). The precision
of this technique is currently limited by interferometric measurements at the
1.5% level. At this level, the center-to-limb darkening (CLD) and the presence
of circumstellar envelopes (CSE) seem to be the two main sources of bias. The
observations we performed aim at improving our knowledge of the interferometric
visibility profile of Cepheids. In particular, we assess the systematic
presence of CSE around Cepheids in order determine accurate distances with the
IBWM free from CSE biased angular diameters. We observed a Cepheid (Y Oph) for
which the pulsation is well resolved and a non-pulsating yellow supergiant
(alpha Per) using long-baseline near-infrared interferometry. We interpreted
these data using a simple CSE model we previously developed. We found that our
observations of alpha Per do not provide evidence for a CSE. The measured CLD
is explained by an hydrostatic photospheric model. Our observations of Y Oph,
when compared to smaller baseline measurements, suggest that it is surrounded
by a CSE with similar characteristics to CSE found previously around other
Cepheids. We have determined the distance to Y Oph to be d=491+/-18 pc.
Additional evidence points toward the conclusion that most Cepheids are
surrounded by faint CSE, detected by near infrared interferometry: after
observing four Cepheids, all show evidence for a CSE. Our CSE non-detection
around a non-pulsating supergiant in the instability strip, alpha Per, provides
confidence in the detection technique and suggests a pulsation driven mass-loss
mechanism for the Cepheids.

Introduction
In our two previous papers, (Kervella et al. 2006; Mérand et al. 2006b), hereafter Paper I
and Paper II, we reported the discovery of faint circumstellar envelops (CSE) around Galactic
classical Cepheids. Interestingly, all the Cepheids we observed (ℓ Car in Paper I, α UMi,
and δ Cep in Paper II) were found to harbor CSE with similar characteristics: a CSE 3 to 4
times larger than the star which accounts for a few percent of the total flux in the infrared
K band. The presence of CSE was discovered in our attempt to improve our knowledge of
Cepheids in the context of distance determination via the interferometric Baade-Wesselink
method (IBWM). Part of the method requires the measurement of the angular diameter
variation of the star during its pulsation. The determination of the angular diameters from
sparse interferometric measurements is not straightforward because optical interferometers
gather high angular resolution data only at a few baselines at a time, thus good phase and
angular resolution coverage cannot be achieved in a short time. For Cepheids, the main
uncertainty in the IBWM was thought to be the center-to-limb darkening (CLD), which
biases the interferometric angular diameter measurements (Marengo et al. 2004).
The direct measurement of CLD is possible using an optical interferometer, given suffi-
cient angular resolution and precision. Among current optical interferometers, CHARA/FLUOR
(ten Brummelaar et al. 2005; Mérand et al. 2006a) is one of the few capable of such a mea-
surement for Cepheids. The only Cepheid accessible to CHARA/FLUOR, i.e. large enough
in angular diameter, for such a measurement is Polaris (α UMi), which we observed and
found to have a CLD compatible with hydrostatic photospheric models, though surrounded
by a CSE (Paper II). Polaris, however, is a very low amplitude pulsation Cepheid: 0.4%
in diameter, compared to 15 to 20% for type I Cepheids (Moskalik & Gorynya 2005), thus
the agreement is not necessarily expected for large amplitude Cepheids, whose photospheres
– 3 –
are more out of equilibrium. The direct measurement of CLD of a high amplitude Cepheid
during its pulsation phase remains to be performed.
Hydrodynamic simulations (Marengo et al. 2003) suggest that the CLD variations dur-
ing the pulsation do not account for more than a 0.2% bias in distance determination in the
near infrared using the IBWM, where most of the IBWM observing work has been done in
recent years: the best formal distance determination to date using the IBWM is of the order
of 1.5% (Mérand et al. 2005b).
Whereas the near infrared IBWM seems to be relatively immune to bias from CLD, the
recent discovery of CSEs raises the issue of possible bias in angular diameter measurements,
hence bias in distance estimations at the 10% level (Paper II). It is therefore important
to continue the study of CSE around Cepheids. We present here interferometric observa-
tions of the non-pulsating supergiant α Per and the low amplitude Cepheid Y Oph. We
obtained these results in the near infrared K-band, using the Fiber Linked Unit for Optical
Recombination — FLUOR — (Mérand et al. 2006a), installed at Georgia State University’s
Center for High Angular Resolution Astronomy (CHARA) Array located on Mount Wilson,
California (ten Brummelaar et al. 2005).
2. The low amplitude Cepheid Y Oph
In the General Catalog of Variable Stars (Kholopov et al. 1998), Y Oph is classified in
the DCEPS category, i.e. low amplitude Cepheids with almost symmetrical light curves and
with periods less than 7 days. The GCVS definition adds that DCEPS are first overtone and/or
crossing the instability strip for the first time. A decrease in photometric variation amplitude
over time has been measured, as well as a period change (Fernie et al. 1995b). Using this
period change rate, 7.2± 1.5 syr−1 and the period of 17.1207 days, the star can be identified
as crossing the instability strip for the third time, according to models (Turner et al. 2006).
The fact that Y Oph belongs to the DCEPS category is questionable: its period is longer
than 7 days, by almost three times, though its light curve is quasi-symmetric and with a low
amplitude compared to other type I Cepheids of similar periods (Vinko et al. 1998). Indeed,
Y Oph is almost equally referred to in publications as being a fundamental-mode Cepheid
or a first overtone.
In this context, a direct determination of the linear diameter can settle whether Y Oph
belongs to the fundamental mode group or not. This is of prime importance: because of its
brightness and the large amount of observational data available, Y Oph is often used to cali-
brate the Period-Luminosity (PL) or the Period-Radius (PR) relations. The interferometric
– 4 –
Baade-Wesselink method offers this opportunity to geometrically measure the average linear
radius of pulsating stars: if Y Oph is not a fundamental pulsator, its average linear diameter
should depart from the classical PR relation.
2.1. Interferometric observations
The direct detection of angular diameter variations of a pulsating star has been achieved
for many stars now using optical interferometers (Lane et al. 2000; Kervella et al. 2004a;
Mérand et al. 2005b). We showed (Mérand et al. 2006b) that for a given average diameter,
one should use a baseline that maximizes the amplification factor between the variation in
angular diameter and observed squared visibility. This baseline provides an angular resolu-
tion of the order of Bθ/λ ≈ 1, in other words in the first lobe, just before the first minimum
(Bθ/λ ≈ 1.22 for a uniform disk model), where B is the baseline (in meters), θ the angular
diameter (in radians) and λ the wavelength of observation (in meters). According to pre-
vious interferometric measurements (Kervella et al. 2004a), the average angular diameter of
Y Oph is of the order of 1.45 mas (milli arcsecond).
Ideally, that would mean using a baseline of the order of 300 m, which is available at
the CHARA Array. Because of a trade we made with other observing programs, we used
only a 250 m baseline provided by telescopes S1 and E2.
The fringes squared visibility is estimated using the integration of the fringes power
spectrum. A full description of the algorithm can be found in Coude Du Foresto et al. (1997)
and Mérand et al. (2006a).
The raw squared visibilities have been calibrated using resolved calibrator stars, chosen
from a specific catalog (Mérand et al. 2005a) using criteria defined to minimize the calibra-
tion bias and maximize signal to noise. The error introduced by the uncertainty on each
calibrator’s estimated angular diameter has been properly propagated. Among the three
main calibrators (Tab. 1), one, HR 6639, turned out to be inconsistent with the others. The
raw visibilility of this star was found to vary too much to be consistent with the expected
statistical dispersion. The quantity to calibrate, the interferometric efficiency (also called
instrument visibility), is very stable for an instrument using single mode fibers, such as
FLUOR. If this quantity is assumed to be constant over a long period of time, and if obser-
vations of a given simple star are performed several times during this period, one can check
whether or not the variation of the raw visibilities with respect to the projected baseline
is consistent with a uniform disk model. Doing so, HR 6639 was found inconsistent with
the over stars observed during the same night (Fig 1). The unconsistency may be explained
– 5 –
by the presence of a faint companion with a magnitude difference of 3 or 4 with respect
to the primary. Two over calibrators, from another program, were also used as check stars:
HR 7809 and ρ Aql (Tab. 1). This latter calibrator is not part of the catalog by Mérand et al.
(2005a). Its angular diameter has been determined using the Kervella et al. (2004b) surface
brightness calibration applied to published photometric data in the visible and near infrared.
For each night we observed Y Oph, we determined a uniform disk diameter (Tab. 3)
based on several squared visibility measurements (Tab. 2). Each night was assigned a
unique pulsation phase established using the average date of observation and the Fernie et al.
(1995b) ephemeris, including the measured period change:
D = JD − 2440007.720 (1)
E = 0.05839D − 3.865× 10−10D2 (2)
P = 17.12507 + 3.88× 10−6E (3)
where E is the epoch is the epoch of maximum light (the fractional part is the pulsation
phase) and P the period at this epoch.
2.2. Pulsation
2.2.1. Radial Velocity integration
In order to measure the distance to a pulsating star, the IBWM makes use of radial
velocities and angular diameters. The latter is the integral other time of the former. The
radial velocities, which have been acquired at irregular intervals during the pulsation phase,
must be numerically integrated. This process is highly sensitive to noisy data and the best
way to achieve a robust integration is to interpolate the data before integration. For this
purpose, we use a periodic cubic spline function, defined by floating nodes (Fig. 2). The
coordinates of these nodes are adjusted such that the cubic spline function going through
these nodes provides the best fit to the data points. The phase positions φi of these nodes
are forced to be between 0 and 1, but they are replicated every φi+n, where n is an integer,
in order to obtain a periodic function of period 1.
Among published Y Oph radial velocities data, we chose Gorynya et al. (1998) because
of the uniform phase coverage and the algorithm used to extract radial velocities: the cross-
correlation method. As shown by Nardetto et al. (2004), the method used can influence
the distance determination via the choice of the so-called projection factor, which we shall
introduce in the following section. The pulsation phases have been also determined using
Eq. 2.
– 6 –
The data presented by Gorynya et al. (1998) were acquired between June 1996 and
August 1997. As we already mentioned, Y Oph is known for its changing period and photo-
metric amplitude. Based on Fernie et al. (1995b), the decrease in amplitude observed for the
photometric B and V bands does not have a measurable counterpart in radial velocity. This
is why we did not apply any correction in amplitude to the radial velocity data in order to
take into account the ten years between the spectroscopic and interferometric measurements.
2.2.2. Distance determination method
Once radial velocities vrad are interpolated (Fig. 2) and integrated, the distance d is
determined by fitting the radial displacement to the measured angular diameters (Fig. 3):
θUD(T )− θUD(0) = −2
vrad(t)dt (4)
where θUD is the interferometric uniform disk diameter, and k is defined as the ratio between
θUD and the true stellar angular diameter. The projection factor, p, is the ratio between the
pulsation velocity and the spectroscopically measured radial velocity. The actual parameters
of the fit are the average angular diameter θUD(0) and the biased distance
This formalism assumes that both k and p do not vary during the pulsation. There is
evidence that this might be true for k, based on hydrodynamic simulation (Marengo et al.
2003), at the 0.2% level. Observational evidence exists as well: when we measured the p-
factor of δ Cep (Mérand et al. 2005b) we did not find any difference between the shapes of
the left and right parts of Eq. 4, therefore kp is probably constant other a pulsation period,
at least at the level of precision we have available.
For this work, we will adopt the value for p we determined observationally for near
infrared interferometry/ cross correlation radial velocity: p = 1.27. This result has been
established for δ Cep (Mérand et al. 2005b). This is also the latest value computed from
hydrodynamical photospheric models (Nardetto et al. 2004). The IBWM fit yields a biased
distance d/k = 480± 18 pc and an average angular uniform disk diameter θUD(0) = 1.314±
0.005 mas. Note that we had to allow a phase shift between interferometric and radial
velocity observations: −0.074 ± 0.005 (Fig. 3). The final reduced χ2 is of the order of 3,
mostly due to one data point (φ = 0.887).
– 7 –
2.2.3. Choice of k
Usually, the choice of k is made assuming the star is a limb-darkened disk. The strength
of the CLD is computed using photospheric models, then a value of k is computed. This
approach is sometimes confusing because, even for a simple limb darkened disk, there is no
unique value of k, in the sense that this value varies with respect to angular resolution. The
uniform disk angular size depends upon which portion of the visibility curve is measured.
However, it is mostly unambiguous in the first lobe of visibility, i.e. at moderate angular
resolution: Bθ/λ ≤ 1.
However, as shown in Paper II, the presence of a faint CSE around Cepheids biases k
up to 10%, particularly when the angular resolution is moderate and the star is not well
resolved (V 2 ∼ 0.5). Under these conditions, the CSE is largely resolved, leading to a strong
bias if the CSE is omitted. On the other hand, at greater angular resolution (Bθ/λ ∼ 1), the
star is fully resolved (V 2 approaches it first null) and the bias from the CSE is minimized.
In any cases, it is critical to determine whether or not Y Oph is surrounded by a CSE if an
accurate distance is to be derived.
2.3. Interferometric evidence of a CSE around Y Oph
We propose here to compare the uniform disk diameters obtained by VLTI/VINCI
(Kervella et al. 2004a) and CHARA/FLUOR (this work). This makes sense because these
two instruments are very similar. Both observe in the near infrared K-band. Moreover, both
instruments observed Y Oph in the first lobe of the visibility profile, though at different
baselines.
If Y Oph is truly a uniform disk, or even a limb-darkened disk, the two instruments
should give similar results. That is because the star’s first lobe of squared visibility is insen-
sitive to the CLD and only dependent the on the size. Conversely, if Y Oph is surrounded
by a CSE, we expect a visibility deficit at smaller baseline (VLTI/VINCI), hence a larger
apparent uniform disk diameter (see Fig. 5). This is because the CSE is fully resolved at
baselines which barely resolve the star.
This is indeed the case, as seen on Fig. 4: VLTI/VINCI UD diameters are larger than
CHARA/FLUOR’s. Even if the angular resolution of VLTI/VINCI is smaller than for
CHARA/FLUOR, leading to less precise angular diameter estimations, the disagreement
is still statistically significant, of the order of 3 sigmas. Using the CSE model we can predict
the correct differential UD size between the two instruments, consistant with the presence
of a CSE around Y Oph. The amount of discrepancy can be used to estimate the flux ra-
– 8 –
tio between the CSE and the star. In the case of Y Oph, we find that the CSE amounts
for 5 ± 2% of the stellar flux. Note that for this comparison, we recomputed the phase of
VLTI/VINCI data using Fernie et al. (1995b) ephemeris presented in Eq. 2.
In Fig. 5, we plot k as a function of the observed squared visibility for different models:
hydrostatic CLD, 2% CSE and 5% CSE (K-Band flux ratio). For the hydrostatic model
we have k = 0.983. For the 5% CSE models, for CHARA/FLUOR (0.20 < V 2 < 0.35),
θUD/θ⋆ = 1.023. This is the value we shall adopt. If we ignore the presence of the CSE, the
bias introduced is 1.023/0.983 ≈ 1.04, or 4%.
2.4. Unbiased distance and linear radius
This presence of a 5% CSE leads to an unbiased distance of d = 491 ± 18 pc, which
corresponds to a 3.5% uncertainty on the distance. This is to be compared with the bias we
corrected for if one omits the CSE, of the order of 4%. Ignoring the CSE leads to a distance
of d = 472± 18 pc
We note that k biases only the distance, so one can form the following quantity:
[θUD(0)]× [d/k], which is the product of the two adjusted parameters in the fit, both biased.
This quantity is by definition the linear diameter of the star, and does not depend on the
factor k, even if it is still biased by the choice of p. If θ is in mas and d in parsecs, then
the average linear radius in solar radii is: R = 0.1075θd. In the case of Y Oph, this leads to
R = 67.8± 2.5 R⊙.
2.5. Conclusion
YOph appears larger (over 2 sigma) in the infrared K-band at a 140 m baseline comapred
to a 230 m baseline. Using a model of a star surrounded by a CSE we developed based
on observations of other Cepheids, this disagreement is explained both qualitatively and
quantitatively by a CSE accounting of 5% of the stellar flux in the near infrared K-Band.
This model allows us to unbias the distance estimate: d = 491 ± 18 pc. The linear radius
estimate is not biased by the presence of CSE and we found R = 67.8± 2.5 R⊙.
Our distance is not consistent with the estimation using the Barnes-Evans method:
Barnes et al. (2005) found d = 590 ± 42 pc (Bayesian) and d = 573 ± 8 pc (least squares).
For this work, they used the same set of radial velocities we used. Our estimate is even more
inconsistent with the other available interferometric estimate, by Kervella et al. (2004a): d =
690±50 pc. This later result has been established using an hybrid version of the BWmethod:
– 9 –
a value of the linear radius is estimated using the Period-Radius relation calibrated using
classical Cepheids, not measured from the data. This assumption is questionable, as we noted
before, since Y Oph is a low amplitude Cepheid. Kervella et al. (2004a) deduced R = 100±
8 R⊙ from PR relation, whereas we measured R = 67.8±2.5 R⊙. Because Y Oph’s measured
linear radius is not consistent with the PR relation for classical, fundamental mode Cepheids,
it is probably safe to exclude it from further calibrations. Interestingly, Barnes et al. (2005)
observationally determined Y Oph’s linear radius to be also slightly larger (2.5 sigma) than
what we find: R = 92.1±6.6 R⊙ (Bayesian) and R = 89.5±1.2 R⊙ (least squares). They use
a surface brightness technique using a visible-near infrared color, such as V-K. This method is
biased if the reddening is not well known. If the star is reddened, V magnitudes are increased
more than K-band magnitudes. This leads to an underestimated surface brightness, because
the star appears redder, thus cooler than it is. The total brightness (estimated from V) is also
underestimated. These two underestimates have opposing effects on the estimated angular
diameter: an underestimated surface brigthness leads to an overestimated angular diameter,
whereas an underestimated luminosity leads to an underestimated angular diameter. In the
case of a reddening law, the two effects combine and give rise to a larger angular diameter: the
surface brightness effect wins over the total luminosity. Based on their angular diameter, θ ≈
1.45 mas, it appears that Barnes et al. (2005) overestimated Y Oph’s angular size. Among
Cepheids brighter than mV = 6.0, Y Oph has the strongest B-V color excess, E(B − V ) =
0.645 (Fernie et al. 1995a) and one of the highest fraction of polarized light, p = 1.34±0.12 %
(Heiles 2000). Indeed, Y Oph is within the galactic plane: this means that it has a probably
a large extinction due to the interstellar medium.
3. The non-pulsating yellow super giant α Per
α Per (HR 1017, HD 20902, F5Ib) is among the most luminous non-pulsating stars
inside the Cepheids’ instability strip. The Doppler velocity variability has been found to be
very weak, of the order of 100 m/s in amplitude (Butler 1998). This amplitude is ten times
less than what is observed for the very low amplitude Cepheid Polaris (Hatzes & Cochran
2000).
α Per’s apparent angular size, approximately 3 mas (Nordgren et al. 2001), makes it
a perfect candidate for direct center-to-limb darkening detection with CHARA/FLUOR.
Following the approach we used for Polaris (Paper II), we observed α Per using three different
baselines, including one sampling the second lobe, in order to measure its CLD strength, but
also in order to be able to assess the possible presence of a CSE around this star.
– 10 –
3.1. Interferometric observations
If the star is purely a CLD disk, then only two baselines are required to measure the
angular diameter and the CLD strength. Observations must take place in the first lobe of the
squared visibility profile, in order to set the star’s angular diameter θ. The first lobe is defined
by BθUD/λ < 1.22. Additional observations should taken in the second lobe, in particular
near the local maximum (Bθ/λ ∼ 3/2), because the strength of the CLD is directly linked
to the height of the second lobe. To address the presence of a CSE, observations should be
made at a small baseline. Because the CSEs that were found around Cepheids are roughly 3
times larger that the star itself (Paper I and II), we chose a small baseline where Bθ/λ ∼ 1/3.
As demonstrated by our Polaris measurements, the presence of CSE is expected to weaken
the second lobe of visibility curve, mimicking stronger CLD.
FLUOR operates in the near infrared K-band, with a mean wavelength of λ0 ≈ 2.13 µm.
This sets the small, first-lobe and second-lobe baselines at approximatively 50, 150 and 220
meters, which are well-matched to CHARA baselines W1-W2 (∼ 100 m), E2-W2 (∼ 150 m)
and E2-W1 (∼ 250 m). See Fig. 6 for a graphical representation of the baseline coverage.
The data reduction was performed using the same pipeline as for Y Oph. Squared
visibilities were calibrated using a similar strategy we adopted for Y Oph. We used two sets
of calibrators: one for the shorter baselines, W1-W2 and E2-W2, and one for the longest
baseline, E2-W1 (Tab. 4).
3.2. Simple Model
3.2.1. Limb darkened disk
To probe the shape of the measured visibility profile, we first used an analytical model
which includes the stellar diameter and a CLD law. Because of its versatility, we adopt
here a power law (Hestroffer 1997): I(µ)/I(0) = µα, with µ = cos(θ), where θ is the angle
between the stellar surface and the line of sight. The uniform disk diameter case corresponds
to α = 0.0, whereas an increasing value of α corresponds to a stronger CLD.
All visibility models for this work have been computed taking into account instrumental
bandwidth smearing (Aufdenberg et al. 2006). From this two-parameter fit, we deduce a
stellar diameter of θα = 3.130 ± 0.007 mas and a power law coefficient α = 0.119 ± 0.016.
The fit yields a reduced χ2 = 1.0. There is a strong correlation between the diameter and
CLD coefficent: 0.9. This is a well known effect, that a change in CLD induces a change in
apparent diameter.
– 11 –
This fit is entirely satisfactory, as the reduced χ2 is of the order unity and the residuals
of the fit do not show any trend (Fig. 7). We note that this is not the case for Polaris (Paper
II). Polaris, with very similar u-v coverage to α Per, does not follow a simple LD disk model
because it is surrounded by a faint CSE.
3.2.2. Hydrostatic models
We computed a small grid of models which consists of six one-dimensional, spherical,
hydrostatic models using the PHOENIX general-purpose stellar and planetary atmosphere
code version 13.11; for a description see Hauschildt et al. (1999) and Hauschildt & Baron
(1999). The range of effective temperatures and surface gravities is based on a summary of
α Per’s parameters by Evans et al. (1996):
• effective temperatures, Teff = 6150 K, 6270 K, 6390 K;
• log(g) = 1.4, 1.7;
• radius, R = 3.92× 1012 cm;
• depth-independent micro-turbulence, ξ = 4.0 km s−1;
• mixing-length to pressure scale ratio, 1.5;
• solar elemental abundance LTE atomic and molecular line blanketing, typically 106
atomic lines and 3× 105 molecular lines dynamically selected at run time;
• non-LTE line blanketing of H I (30 levels, 435 bound-bound transitions), He I (19 levels,
171 bound-bound transitions), and He II (10 levels, 45 bound-bound transitions);
• boundary conditions: outer pressure, 10−4 dynes cm−2, extinction optical depth at
1.2 µm: outer 10−10, inner 102.
For this grid of models the atmospheric structure is computed at 50 radial shells (depths)
and the radiative transfer is computed along 50 rays tangent to these shells and 14 additional
rays which impact the innermost shell, the so-called core-intersecting rays. The intersection
of the rays with the outermost radial shell describes a center-to-limb intensity profile with
64 angular points.
Power law fits to the hydrostatic model visibilities range from α = 0.132 to α = 0.137
(Tab. 6), which correspond to 0.8 to 1.1 sigma above the value we measured. Our measured
– 12 –
CLD is below that predicted by the the models, or in other words the predicted darkening
is slightly overestimated.
3.3. Possible presence of CSE
Firstly, we employ the CSE model used for Cepheids (Paper I, Paper II). This model is
purely geometrical and it consists of a limb darkened disk surrounded by a faint CSE whose
two-dimensional geometric projection (on the sky) is modeled by a ring. The ring parameters
consist of the angular diameter, width and flux ratio with respect to the star (Fs/F⋆). We
adopt the same geometry found for Cepheids: a ring with a diameter equal to 2.6 times the
stellar diameter (Paper II) with no dependency with respect to the width (fixed to a small
fraction of the CSE angular diameter, say 1/5).
This model restriction is justified because testing the agreement between a generic CSE
model and interferometric data requires a complete angular resolution coverage, from very
short to very large baselines. Though our α Per data set is diverse regarding the baseline
coverage, we lack a very short baseline (B ∼ 50m) which was not available at that time at
the CHARA Array.
The simplest fit consists in adjusting the geometrical scale: the angular size ratio be-
tween the CSE and the star is fixed. This yields a reduced χ2 of 3, compared to 1.1 for a
hydrostatic LD and 1.0 for an adjusted CLD law (Tab. 7).
We can force the data to fit a CSE model by relaxing the CLD of the star or the CSE
flux ratio. A fit of the size of the star and the brightness of the CSE leads to a reduced χ2 of
1.4 and results in a very small flux ratio between the CSE and the star of 0.0006± 0.0026,
which provides an upper limit for the CSE flux of 0.26% (compared to 1.5% for Polaris and
δ Cep for example, and 5% for Y Oph). On the other hand, forcing the flux ratio to match
that for Cepheids with CSEs and leaving the CLD free leads to a reduced χ2 of 1.4 but also
to a highly unrealistic α = 0.066± 0.004 (Tab. 7 and Fig. 7).
This leads to the conclusion that the presence of a CSE around α Per similar to the
measured Cepheid CSE is highly improbable. As shown above, the measured CLD is slightly
weaker (1 sigma) than one predicted by model atmospheres. A compatible CSE model exists
if the CLD is actually even weaker but in unrealistic proportions.
– 13 –
3.4. Conclusion
The observed α Per visibilities are not compatible with the presence of a CSE similar to
that detected around Cepheids. The data are well explained by an adjusted center-to-limb
darkening. The strength of this CLD is compatible with the hydrostatic model within one
sigma.
4. Discussion
Using the interferometric Baade-Wesselink method, we determined the distance to the
low amplitude Cepheid Y Oph to be d = 491± 18 pc. This distance has been unbiased from
the presence of the circumstellar envelope. This bias was found to be of the order of 4% for
our particular angular resolution and the amount of CSE we measured. Y Oph’s average
linear diameter has also been estimated to be R = 67.8 ± 2.5 R⊙. This latter quantity
in intrinsically unbiased by the center-to-limb darkening or the presence of a circumstellar
envelope. This value is found to be substantially lower, almost 4 sigmas, than the Period-
Radius relation prediction: R = 100 ± 8 R⊙. Among other peculiarities, we found a very
large phase shift between radial velocity measurements and interferometric measurements:
∆φ = −0.074 ± 0.005, which corresponds to more that one day. For these reasons, we
think Y Oph should be excluded from future calibrations of popular relations for classical
Cepheids, such as Period-Radius, Period-Luminosity relations.
So far, the four Cepheids we looked at have a CSE: ℓ Car (Paper I), Polaris, δ Cep
(Paper II) and Y Oph (this work). On the other hand, we have presented here similar
observations of α Per, a non-pulsating supergiant inside the instability strip, which provides
no evidence for a circumstellar envelope. This non detection reinforces the confidence we
have in our CSE detection technique and draws more attention to a pulsation driven mass
loss mechanism.
Interestingly, there seems to be a correlation between the period and the CSE flux ratio
in theK-Band: short-period Cepheids seem to have a fainter CSE compared to longer-period
Cepheids (Tab. 8). Cepheids with long periods have higher masses and larger radii, thus, if
we assume that the CSE K-Band brightness is an indicator of the mass loss rate, this would
mean that heavier stars experience higher mass loss rates. This is of prime importance in the
context of calibrating relations between Cepheids’ fundamental parameters with respect to
their pulsation periods. If CSEs have some effects on the observational estimation of these
fundamental parameters (luminosity, mass, radius, etc.), a correlation between the period
and the relative flux of the CSE can lead to a biased calibration.
– 14 –
Research conducted at the CHARA Array is supported at Georgia State University
by the offices of the Dean of the College of Arts and Sciences and the Vice President for
Research. Additional support for this work has been provided by the National Science
Foundation through grants AST 03-07562 and 06-06958. We also wish to acknowledge the
support received from the W.M. Keck Foundation. This research has made use of SIMBAD
database and the VizieR catalogue access tool, operated at CDS, Strasbourg, France.
– 15 –
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This preprint was prepared with the AAS LATEX macros v5.2.
– 18 –
 230  240  250  260
Y Oph
B (m)
 230  240  250  260
B (m)
HR 6639
Fig. 1.— Evidence that calibrator HR 6639 is probably a binary star. Calibrated squared
visibility as a function of baseline for UT 2006/07/10. Left is Y Oph and right is HR 6639.
The interferometric efficiency was supposed constant during the night and established using
HR 7809 and ρ Aql with a reduced χ2 of 1.3. A UD fit, shown as a continuous line, works for
Y Oph (χ2r = 0.6) whereas it fails for HR 6639 (χ
r = 7.2). This could the sign that HR 6639
has a faint companion: the visibility variation has a 3-5% amplitude, which corresponds to
a magnitude difference of 3 to 4 between the main star and its companion.
– 19 –
0.0 0.5 1.0
0.0 0.5 1.0
Fig. 2.— Y Oph: Radial velocities from Gorynya et al. (1998). The continuous line is the
periodic spline function defined by 3 adjustable floating nodes (large filled circles). The
systematic velocity, Vγ = −7.9 ± 0.1 kms
−1, has been evaluated using the interpolation
function and removed. The lower panel displays the residuals of the fit.
– 20 –
0.0 0.5 1.0
0.0 0.5 1.0
−0.02
Fig. 3.— Y Oph: angular diameter variations. Upper panel: CHARA/FLUOR uniform disk
angular diameters as a function of phase. Each data point corresponds to a given night,
which contains several individual squared visibility measurements (Tab. 3). The solid line
is the integration of the radial velocity (Fig. 2) with distance, average angular diameter and
phase shift adjusted. The dashed line has a phase shift set to zero. The lower panel shows
the residuals to the continuous line.
– 21 –
CSE 2%
CSE 5%
0.0 0.5 1.0
Fig. 4.— Y Oph: Comparison between CHARA/FLUOR and VLTI/VINCI observations.
Uniform disk angular diameter as a function of phase. Small data points (with small error
bars) and lower continuous line: CHARA/FLUOR observations and distance fit. Large open
squares: VLTI/VINCI observations. The distance fit and it uncertainty are reprensenteb by
the shaded band. Dashed and dotted lines: VLTI/VINCI expected biased observations based
on CHARA/FLUOR and our CSE model with a flux ratio of 2% (dashed) and 5% (dotted).
– 22 –
CSE 5%
CSE 2%
0.0 0.2 0.4 0.6 0.8
squared visibility
Fig. 5.— Y Oph: angular diameter correction factor. We plot here θUD/θ⋆ for three different
Cepheid models as a function of observed squared visibility (first lobe): the dashed line is
a simple limb darkened disk with the appropriate CLD strength; the continuous line is a
similar LD disk surrounded by a CSE with a 2% K-band flux (short period: Polaris and
δ Cep, see Paper II) and 5% (long period: ℓ Car, see paper I). Note that, in the presence of
CSE, the bias is stronger at large visibilities (hence smaller angular resolution). The shaded
regions represents near infrared Y Oph observations: from CHARA (this work) and the
VLTI (Kervella et al. 2004a).
– 23 –
−200  0  200
u (m)
Fig. 6.— α Per. Projected baselines, in meters. North is up East is right. The shaded area
corresponds to the squared visibility’s second lobe. The baselines are W1-W2, E2-W2 and
E2-W1, from the shortest to the longest.
– 24 –
adjusted CLD
CSE "Polaris"
CSE (1)
 50  100  150  200  250
B (m)
Fig. 7.— α Per squared visibility models: UD, adjusted CLD, PHOENIX and 2 different
CSE models are plotted here as the residuals to the PHOENIX CLD with respect to baseline.
The common point at B ≈ 175 m is the first minimum of the visibility function. The top
of the second lobe is reached for B ≈ 230 m. See Tab. 7 for parameters and reduced χ2 of
each model.
– 25 –
α UMi δ Cep
Y Oph
l Car
α Per
 0  10  20  30  40
Period (days)
Fig. 8.— measured relative K-band CSE fluxes (in percent) around Cepheids, as a function
of the pulsation period (in days). The non-pulsating yellow supergiant α Per is plotted with
– 26 –
Table 1. Y Oph calibrators.
Star S.T. UD Diam. Notes
(mas)
HD 153033 K5III 1.100± 0.015
HD 175583 K2III 1.021± 0.014
HR 6639 K0III 0.904± 0.012 rejected
HR 7809 K1III 1.055± 0.015
ρ Aql A2V 0.370± 0.005 not in M05
Note. — “S.T.” stands for spectral type. Uniform Disk diameters, given in mas, are only
intended for computing the expected squared visibility in the K-band. All stars but ρ Aql
are from M05 catalog (Mérand et al. 2005a). Refer to text for an explanation why HR 6639
has been rejected.
– 27 –
Table 2. Journal of observations: Y Oph.
MJD-53900 B P.A. V 2
(m) (deg)
18.260 229.808 63.540 0.2348± 0.0061
18.296 215.049 71.242 0.2823± 0.0065
18.321 207.247 77.913 0.3030± 0.0075
21.245 232.792 62.353 0.2511± 0.0065
21.283 216.576 70.243 0.2954± 0.0085
21.309 208.313 76.765 0.3194± 0.0085
22.212 245.894 58.023 0.2092± 0.0071
22.234 236.338 61.050 0.2352± 0.0078
22.251 228.941 63.902 0.2615± 0.0085
24.188 253.988 55.914 0.2108± 0.0062
24.212 243.641 58.680 0.2427± 0.0060
24.231 235.388 61.389 0.2634± 0.0065
26.168 259.377 54.714 0.2185± 0.0041
26.194 249.210 57.113 0.2526± 0.0039
26.224 235.772 61.251 0.2983± 0.0034
26.242 227.859 64.367 0.3171± 0.0035
27.194 247.788 57.495 0.2650± 0.0040
27.211 240.340 59.704 0.2854± 0.0038
27.228 232.806 62.348 0.3177± 0.0045
27.250 223.415 66.429 0.3385± 0.0045
28.241 225.978 65.207 0.3332± 0.0045
28.257 219.413 68.547 0.3629± 0.0061
29.219 234.329 61.775 0.2857± 0.0049
29.237 226.405 65.012 0.3148± 0.0053
29.253 219.709 68.380 0.3320± 0.0054
30.192 245.267 58.203 0.2510± 0.0035
30.216 234.738 61.624 0.2893± 0.0041
30.235 226.418 65.007 0.3112± 0.0044
30.244 222.544 66.866 0.3226± 0.0046
30.261 215.937 70.653 0.3462± 0.0048
– 28 –
Table 2—Continued
MJD-53900 B P.A. V 2
(m) (deg)
Note. — Date of observation (modified julian day), telescope projected separation (m),
baseline projection angle (degrees) and squared visibility
– 29 –
Table 3. Y Oph angular diameters.
MJD-53900 φ Nobs. B θUD χ
(m) (mas)
18.292 0.248 3 207-230 1.3912± 0.0067 0.55
21.279 0.423 3 208-233 1.3516± 0.0074 1.06
22.232 0.478 3 229-246 1.3387± 0.0077 0.05
24.210 0.594 3 235-254 1.2929± 0.0059 0.19
26.207 0.710 4 228-259 1.2488± 0.0029 0.61
27.221 0.770 4 223-248 1.2374± 0.0032 0.76
28.249 0.830 2 219-226 1.2394± 0.0055 0.30
29.237 0.887 3 220-234 1.2728± 0.0047 0.26
30.229 0.945 5 216-245 1.2715± 0.0030 0.56
Note. — Data points have been reduced to one uniform disk diameter per night. Avger-
age date of observation (modified julian day), pulsation phase, number of calibrated V 2,
projected baseline range, uniform disk angular diameter and reduced χ2.
– 30 –
Table 4. α Per calibrators.
Name S.T. UD Diam. Baselines
(mas)
HD 18970 G9.5III 1.551± 0.021 W1-W2, E2-W2
HD 20762 K0II-III 0.881± 0.012 E2-W1
HD 22427 K2III-IV 0.913± 0.013 E2-W1
HD 31579 K3III 1.517± 0.021 W1-W2, E2-W2
HD 214995 K0III 0.947± 0.013 W1-W2
Note. — “S.T.” stands for spectral type. Uniform Disk diameters, given in mas, are only
intended for computing the expected squared visibility in the K-band. These stars come
from our catalog of interferometric calibrators (Mérand et al. 2005a)
– 31 –
Table 5. Journal of observations: α Per.
MJD-54000 B P.A. V 2
(m) (deg)
46.281 147.82 79.37 0.02350± 0.00075
46.321 153.87 69.04 0.01368± 0.00067
46.347 155.79 62.17 0.01093± 0.00060
46.372 156.27 55.30 0.01134± 0.00039
46.398 155.65 48.10 0.01197± 0.00051
46.421 154.41 41.32 0.01367± 0.00052
46.442 152.94 34.84 0.01581± 0.00045
46.466 151.13 27.03 0.01824± 0.00064
46.488 149.58 19.40 0.02167± 0.00071
46.510 148.49 12.06 0.02250± 0.00058
46.539 147.77 1.53 0.02370± 0.00070
47.225 96.66 -44.51 0.27974± 0.00282
47.233 97.75 -47.34 0.27321± 0.00274
47.252 100.37 -53.97 0.24858± 0.00258
47.274 103.03 -60.91 0.23529± 0.00242
47.327 249.17 81.65 0.01363± 0.00032
47.352 251.22 74.84 0.01340± 0.00032
47.374 251.04 68.91 0.01330± 0.00035
47.380 250.67 67.10 0.01316± 0.00035
Note. — Date of observation (modified julian day), telescope projected separation, base-
line projection angle and squared visibility
– 32 –
Table 6. α Per PHOENIX models.
Teff log g = 1.4 log g = 1.7
6150 0.137 0.136
6270 0.135 0.134
6390 0.133 0.132
Note. — Models tabulated for different effective temperatures and surface gravities. The
K-band CLD is condensed into a power law coefficient α: I(µ) ∝ µα.
– 33 –
Table 7. Models for α Per.
Model θ⋆ α Fs/F⋆ χ
(mas) (%)
UD 3.080±0.004 0.000 - 5.9
PHOENIX CLD 3.137±0.004 0.135 - 1.1
adjusted CLD 3.130±0.007 0.119±0.016 - 1.0
CSE “Polaris” 3.086±0.007 0.135 1.5 3.0
CSE (1) 3.048±0.007 0.066±0.004 1.5 1.4
CSE (2) 3.095±0.010 0.135 0.06±0.26 1.4
Note. — The parameters are: θ⋆ the stellar angular diameter, the CLD power law coef-
ficient α and, if relevant, the brightness ratio between the CSE and the star Fs/F⋆. The
first line is the uniform disk diameter, the second one expected CLD from the PHOENIX
model, the third one is the adjusted CLD. The fourth line is a scaled Polaris CSE model
(Paper II). The last two lines are attempts to force a CSE model to the data. Lower script
are uncertainties, the absence of lower script means that the parameter is fixed
– 34 –
Table 8. Relative flux in K-Band for the CSE discovered around Cepheids and the non
pulsating α Per.
Star Period CSE flux
(d) (%)
α UMi 3.97 1.5± 0.4
δ Cep 5.37 1.5± 0.4
Y Oph 17.13 5.0± 2.0
ℓ Car 35.55 4.2± 0.2
α Per - < 0.26
	Introduction
	The low amplitude Cepheid Y Oph
	Interferometric observations
	Pulsation
	Radial Velocity integration
	Distance determination method
	Choice of k
	Interferometric evidence of a CSE around Y Oph
	Unbiased distance and linear radius
	Conclusion
	The non-pulsating yellow super giant  Per
	Interferometric observations
	Simple Model
	Limb darkened disk
	Hydrostatic models
	Possible presence of CSE
	Conclusion
	Discussion
