Download Development of Iodine Cells for the Subaru HDS and the Okayama

PASJ: Publ. Astron. Soc. Japan 54, 873–882, 2002 December 25
c 2002. Astronomical Society of Japan.
Development of Iodine Cells for the Subaru HDS and the Okayama HIDES:
II. New Software for Precise Radial Velocity Measurements
Bun’ei S ATO,1,2 Eiji K AMBE,3 Yoichi TAKEDA,4 Hideyuki I ZUMIURA,2
and
Hiroyasu A NDO2
1
Department of Astronomy, School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033
[email protected]
2
National Astronomical Observatory, Mitaka, Tokyo 181-8588
3
National Defense Academy, Yokosuka, Kanagawa 239-8686
4
Komazawa University, Komazawa, Setagaya, Tokyo 154-8525
(Received 2002 September 3; accepted 2002 October 15)
Abstract
We have developed a computer code for precise measurements of stellar radial velocity variations with iodine (I2 )
cells attached to the High Dispersion Spectrograph (HDS) on Subaru Telescope and the HIgh Dispersion Echelle
Spectrograph (HIDES) on Okayama 188 cm reflector. Our modeling technique for I2 data is similar to those described by Butler et al. (1996, AAA 65.036.447) and Valenti et al. (1995, AAA 64.036.209) concerning the point
that the stellar spectrum taken through the I2 cell (star + I2 spectrum) is modeled as the product of high-resolution
stellar and I2 template spectra convolved with the modeled instrumental profile (IP) of the spectrograph. In order
to generate a template stellar spectrum, we have devised a new method to extract an intrinsic stellar spectrum from
observed star + I2 spectra. This enables us to obtain a well-established template stellar spectrum even in cases when
the IP and the wavelength scale are apt to vary with time and the observational conditions, and the existing method
which reconstructs the IP from a B-star + I2 spectrum (Butler et al. 1996; Endl et al. 2000, A&A, 362, 585) fails. We
here report on the results of our Doppler measurements of three solar-type stars, 16 Cyg B, τ Cet, and υ And, based
on data collected with HDS and HIDES for about one year. These results show that we have achieved a precision of
about 5–6 m s−1 over a time span of one year with our current analysis package with both spectrographs.
Key words: instrumentation: spectrographs — stars: individual (16 Cyg B, τ Cet, υ And) — stars: oscillations
— stars: planetary systems — techniques: radial velocities
1. Introduction
Since the discovery of the first extrasolar planet (Mayor,
Queloz 1995), more than 100 planetary candidates have been
identified so far by detecting a tiny wobble of a star in radial velocity due to the reflex motion caused by the gravitational pull of unseen companions. Today, many groups around
the world are searching for extrasolar planets extensively, and
they regularly monitor the radial velocities of a total sample
of 3000 F–M dwarfs (Fischer et al. 2002; Vogt et al. 2002;
Jones et al. 2002; Udry et al. 2002; Zucker et al. 2002; Noyes
et al. 1997; Cochran et al. 1997; Kürster et al. 2000). Precise
Doppler measurements of stars have also turned out to be a very
efficient technique to detect solar-type oscillations (Bedding
et al. 2001; Queloz, Mayor 2001). These variations in the
radial velocity (Jupiter imparts a velocity of 12.4 m s−1 on the
Sun and the 5-min solar oscillation has a radial velocity amplitude of a few ten cm s−1 ) are very much smaller than the
precision achieved by conventional techniques, such as determining a wavelength scale by other exposures of a reference
lamp, which is at best several hundred m s−1 . Therefore, to detect such tiny signals from stars, it is essential to minimize any
instrumental measurement errors in the wavelength calibration.
For this purpose, iodine absorption cells (I2 cell) are widely
used as a gas filter, through which pre-dispersed stellar light
passes and a reference I2 spectrum is superposed directly onto
the stellar spectra. Because the I2 and the stellar lines experience the same instrumental shifts and distortions of the
telescope and the spectrograph, we can use I2 lines both as
a wavelength standard and as a reference to correct for the
instrumental profile (IP) of the spectrograph at each position
on the detector for every exposure. The Doppler precision of
3 m s−1 has been attained using this technique by the Lick,
Keck, and AAT groups (Butler et al. 1996; Vogt et al. 2000;
Butler et al. 2001).
We started a pilot project of precise measurements of
stellar radial-velocity variations at Okayama Astrophysical
Observatory (OAO) in 1998, using the C10 spectrograph on the
188 cm reflector and a proto-type I2 cell (Takeda et al. 2002),
but at that time the measurement precision was at best
50–60 m s−1 because of its poor wavelength resolution (R ∼
30000) and narrow wavelength coverage (a few ten to hundred Å). In 2000, motivated by the development of a new
echelle-type High Dispersion Spectrograph for Subaru telescope (HDS, Noguchi et al. 1998, 2002) and of a new HIgh
Dispersion Echelle Spectrograph for the Okayama 188 cm
reflector (HIDES, Izumiura 1999), we developed new I2 cells
optimized for both spectrographs. We can potentially measure the radial-velocity variation of solar-type stars with an
accuracy of 1–2 m s−1 (Kambe et al. 2002, hereafter Paper I)
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using these systems.
In analyzing I2 data, it is essential to eliminate as many
instrumental errors as possible by sophisticated modeling of a
stellar spectrum observed through the I2 cell (star + I2 spectrum). Correct reconstruction of IP’s is indispensable since
its asymmetry introduces apparent Doppler shifts in the stellar absorption lines. In fact, the precision of our radial velocity measurement was limited to 20 m s−1 or so without such
corrections (Takeda et al. 2002). Butler et al. (1996) first outlined such a modeling technique that a star + I2 spectrum is
expressed as the product of high-resolution stellar and I2 template spectra convolved with a modeled IP. As an IP modeling technique, multiple Gaussian fitting is used most successfully at present (Valenti et al. 1995; Butler et al. 1996; Endl
et al. 2000). This procedure is widely adopted by many groups,
and we follow a similar one in this paper.
To achieve long-term precision in radial velocity, it is also
important to obtain a well-established template stellar spectrum, whose wavelength scale should be precisely determined
and which has high resolution and a high S/N ratio, and
which should not be influenced by any particular observations.
However, it is hard to obtain such a spectrum directly from
observations without a large telescope and an extremely highdispersion spectrograph. Instead, a template spectrum is often
generated from an observed stellar spectrum, which is deconvolved with the IP reconstructed from a B-star + I2 spectrum
(Butler et al. 1996; Endl et al. 2000). It turns out not to produce
a good template spectrum in the cases of HDS and HIDES,
due to the fact that their IP’s and their wavelength scales easily
vary with the observational conditions or by inserting the I2
cell in the telescope beam, we have devised a new method
to extract a high-resolution template stellar spectrum from the
observed star + I2 spectra.
In the present work, we developed a new computer code for
sophisticated I2 data analysis, and report on the Doppler precisions currently being achieved with HDS and HIDES. In
section 2, we describe our data-modeling techniques in detail.
IP’s of both spectrographs and examples of template stellar
spectra obtained by our newly developed method are presented
in section 3. The results of Doppler tests of some solar-type
stars are also shown in this section. Lastly, in section 4, current limitations and future improvements of our data analysis
software are discussed.
2.
Method of Analysis
2.1. Outline of the Data Modeling Technique
In order to determine the radial velocity of a star, we construct a parameterized model for a star + I2 spectrum. Our
modeling technique is conceptually similar to that described
by Butler et al. (1996).
A spectrum taken through the I2 cell, I (λ), can be modeled
using two functions, the intrinsic stellar spectrum, S(λ), and
the transmission function of the I2 cell, A(λ), as
I (λ) = k[A(λ)S(λ + ∆λ)] ∗ IP,
(1)
where k, ∆λ (= λv/c), and IP denote a normalization factor,
the stellar Doppler shift, and the instrumental profile of the
spectrograph, respectively, and “∗” represents convolution.
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The S(λ) and A(λ) are normalized with respect to their continuum levels.
As the I2 cell transmission function, A(λ), we use the
Lick-Hamilton I2 cell spectrum of extremely high spectral
resolution (R ∼ 400000), which was obtained by the Fourier
Transform Spectrometer of Kitt Peak National Observatory
(kindly provided by Dr. G. W. Marcy). In using this spectrum,
we assume the Menzel–Minnaert–Unsöld interpolation formula [see, e.g., equation (3.47) in Pagel 1997] as the relation
between the line-depth (R) and the line-to-continuum opticaldepth ratio η (≡ l/κ) while introducing a parameter, α (≡ η/η0 )
(“0” represents the Lick-Hamilton cell), corresponding to the
ratio of the optical thickness of I2 lines between our cells and
theirs (Takeda et al. 2002).
The intrinsic stellar spectrum, S(λ), is hard to obtain directly
from our observations, since it is required to have high resolution and a high S/N ratio and not to contain any systematic
errors. Thus, we have developed a new method to reconstruct
a pure stellar spectrum from star + I2 spectra. Details of this
method are described in subsection 2.2.
For modeling the IP, we adopt a technique described by
Valenti et al. (1995). The IP is modeled with a combination of a
central and several satellite Gaussian profiles which are placed
at appropriate intervals and have suitable widths, depending on
the properties of the spectrograph. We use ten and six Gaussian
satellites for HDS and HIDES, respectively, and determine
their heights relative to that of the central Gaussian profile as
free parameters, while the widths of all Gaussian ones and
the intervals between them are fixed to 0.9 pixels. Since the
wing of IP of HDS is broader than that of HIDES, the number
of satellites for HDS needs to be larger than that for HIDES.
The accuracy of radial-velocity measurements depends on how
we can reconstruct the IP of the spectrograph well. Thus, we
examine the characteristics of the IP in detail in section 3.
We divide the entire echelle spectrum into several hundred
5 Å (typically 300 pixels for HDS and 200 pixels for HIDES)
segments, and apply a Doppler analysis to each segment. We
adopt a linear form (k1 λ + k0 ) instead of a constant k, considering the slope of the observed spectrum after being divided
by the echelle blaze profile (derived from data for flatfielding).
The model spectrum is calculated five-times more densely than
the observed sampling in wavelength to make use of the high
resolution of the I2 cell transmission function, and its wavelength scale is described by a 6th-order Legendre polynomial.
These parameters, the polynomial coefficients, the ratio of the
optical thickness of I2 cells, the IP, and the Doppler shift (v),
are simultaneously determined by comparing the model with
the observation using a least-squares fitting. Two examples of
the modeling process are shown in figure 1.
To determine the Doppler shift of each observation, we
take the average of the radial velocities of individual segments
weighted according to their uncertainties, including systematic
errors caused by inaccuracy of the modeling of the IP or the
template stellar spectrum in addition to the random errors
estimated from the photon-shot noise. For example, the IP
is reconstructed less accurately in extremely line-crowded
regions, such as the bandheads of the I2 molecular spectra.
The deviation in the shape of an absorption line in the generated template stellar spectrum from the intrinsic spectrum
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and the systematic errors. We found that such weighting is effective when and only when spectra are taken with a not so
good focus of the spectrograph that the IP varies considerably,
depending on the position on the CCD detector.
The derived velocity is finally corrected to the Solar System
barycenter. This correction is calculated by the TEMPO program (Taylor et al. 2000), which is a barycentric transformation code using pulsar timing data. A high regularity of pulse
periods of pulsars can be used as an excellent clock and its observed variation enables us to estimate the velocity correction
due to the orbital motion of the Earth and relativistic time transformations, etc., to a very high precision. McCarthy (1995)
claimed that the algorithm developed by him for the barycentric correction using the JPL ephemeris and the theory of relativity has a precision of 0.01 m s−1 , and the result agrees with
that calculated by TEMPO to machine precision. We calculate
a photon-weighted mid-exposure time, using output of the photon monitor, which records the number of photons coming into
the entrance slits of the spectrographs at every second within an
accuracy of 1% at least (Paper I). We can typically determine
the exposure center to a precision of ∼ 3 s, while it depends
on the observational conditions, such as the seeing size and the
guiding error.
2.2. How to Obtain a Template Stellar Spectrum
Fig. 1. Examples of modeling the star + I2 spectrum for HDS (16
Cyg B, upper) and HIDES (τ Cet, lower). From top to bottom, I2
template spectrum, stellar template spectrum, observed spectrum taken
through the I2 cell (dots) overlaid with the model (solid line), and the
residuals (5 times the difference between the model and the observation). The observation is modeled as the product of the I2 and stellar
template spectra convolved with the derived instrumental profile of the
spectrograph.
also affects the radial-velocity analysis. The possible imperfect
modeling of the I2 cell transmission function of our cell, that
is, the difference between our cell and the Lick’s cell, might as
well cause some errors in the obtained stellar radial velocity.
Such errors would depend on which parts of the I2 and the stellar lines are included in the segment, that is, how to divide the
spectrum into segments. We investigated how it influences the
resulting radial velocity by shifting the wavelength center of
the segment back and forth by about 0.3 Å (15 pixels for HDS
and 10 pixels for HIDES) with its span of 5 Å being unchanged.
The mean of the differences of the derived velocities between
the shifted and the initial segments is taken and considered to
be the systematic error for each segment. The radial velocity
of the spectrum is obtained by averaging those of individual
segments weighted by the inverse squares of the random errors
A template stellar spectrum should have high resolution and
not be smeared by the IP of the spectrograph. One of the methods to obtain such a spectrum is to deconvolve an observed
stellar spectrum (taken without I2 cell) with an IP reconstructed
from a B-star + I2 spectrum obtained by observing a rapidly
rotating B star just before and/or after the stellar reference observation (Butler et al. 1996; Endl et al. 2000). Since the spectrum of the B star is essentially featureless, it is thought to convey the absorption spectrum of the I2 molecule. A B-star + I2
spectrum can also provide a wavelength standard with which to
determine the wavelength scale of a generated template spectrum. It should be determined precisely for achieving a longterm radial-velocity precision.
However, the IP’s and the wavelength scales of these spectra, even if they are obtained with similar observing configurations, are not exactly the same. The paths of the stellar light
beam entering the spectrograph may slightly differ, depending
on the telescope orientations. Differences in seeing size and
guiding errors may cause different illumination patterns of the
stellar beam on the spectrograph slit. Thermal variations of the
spectrograph, which cannot be completely suppressed during
observations, will also cause changes of the IP and the wavelength scales between the stellar reference spectrum and the
B-star + I2 spectrum. In fact, upon applying this method to
HIDES data, a systematic dependence upon the position on the
detector emerges in the derived radial velocities. It is possibly
due to the fact that the IP and the wavelength scale of HIDES
data are apt to be influenced by the observational conditions
(see also section 3). In the case of HDS, the I2 cell is located
behind the entrance slit and the wavelength scale of a spectrum
slightly shifts and is distorted when the I2 cell is inserted in
the telescope beam. Thus, we can’t determine the wavelength
scale of a pure star spectrum using any I2 spectra.
In order to avoid these problems, we have developed a
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method to extract a template stellar spectrum from star + I2
spectra. This method is based on the concept that we use such a
template that is best suited for existing data rather than the ideal
intrinsic one that might be different from the obtained template. The basic procedure of the method is as follows. First,
we model the observed star + I2 spectrum expressed in equation (1), using the initial guess of the intrinsic stellar spectrum,
S 0 (λ). The wavelength scale and IP are determined by fitting
this model spectrum, I 0 (λ), to the observed spectrum, I (λ), in
the same manner as described in the previous subsection. Next,
we take the difference of these two spectra, as
δS(λ) = I (λ) − I 0 (λ).
(2)
Since this difference is considered to be due to an imperfection
of the initial guess of the stellar spectrum [the I2 cell transmission spectrum, A(λ), is known beforehand], we revise S 0 (λ), as
S (λ) = S (λ) + δS(λ).
1
0
(3)
We use this new guess of S 1 (λ) for the next iteration to obtain
a revised I 1 (λ) and the IP. We repeat this process until reduced
χ 2 becomes less than 1.0 or the number of iteration reaches
maximal time. As a result, we obtain a template stellar spectrum, whose wavelength scale is very accurately determined
by the I2 lines, and out of which the IP is deconvolved simultaneously. The algorithm of the deconvolution adopted here is
called Iterative/Recursive Deconvolution described by Coggins
et al. (1994) in detail. As an initial guess of the intrinsic stellar
spectrum, S 0 (λ), we use a theoretically synthesized spectrum
calculated by us, which is normalized with respect to the continuum level.
The template stellar spectrum determined above is still
affected by particular features of the star + I2 spectrum, such
as the relative positions of the stellar and I2 absorption lines in
the spectrum and its IP. To remove such effects from the final
template spectrum as well as to increase its S/N ratio, we use
several star + I2 spectra. The procedure described above is applied to each observing frame to obtain a set of new guesses
of the intrinsic stellar spectrum. Then, we take their average
after the barycentric velocity correction and adopt it as the new
guess of the next iteration for all frames. The iteration is repeated until the reduced χ 2 of all spectra become less than 1.0,
or the number of iteration reaches the maximal time, which is
usually set to ten. Examples of thus-determined template stellar spectra are shown in the next section.
3.
Results
To evaluate the radial velocity precision that can be achieved
with our current systems and analysis package, we have
observed several solar-type stars with known radial-velocity
variations. We here show the results of 16 Cyg B observed
with both HDS and HIDES, and τ Cet and υ And observed
with HIDES.
3.1. Observation Using I2 Cell with HDS and HIDES
As the standard setup of observations using I2 cell with
HDS, we usually set the wavelength region to cover 4900–
7600 Å (StdI2a) or 3500–6200 Å (StdI2b). The region of
5000–5800 Å, where many deep and sharp I2 absorption lines
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exist, spans 24 echelle orders without crossing a gap between
the two mosaic CCD’s. The slit width is set to 150 µm (0. 3)
corresponding to a spectral resolution of R ∼ 110000 by about
3.0 pixels sampling.
In the case of HIDES, the slit width is set to 200 µm (0. 76),
which enables us to obtain spectra with a resolution of R ∼
65000 by about 3.5 pixels sampling, and the wavelength region
is set to cover 4800–5900 Å. The region of 5000–5800 Å used
for the radial velocity analysis spans 15 echelle orders.
The reduction of echelle data (i.e. bias subtraction, flatfielding, scattered-light subtraction, and spectrum extraction)
was performed by using the IRAF software package in the standard manner.
3.2. Instrumental Profile of HDS and HIDES
It was reported in our previous paper that the IP of HDS is
rather close to the Gaussian profile, while that of HIDES is
more or less box-like shape, when a spectrum is taken with
a typical slit width corresponding to three pixels (Paper I). In
figure 2, we show examples of the modeling of a flat + I2 spectrum (flat-field spectrum taken through the I2 cell, which is flatfielded with the flat spectrum without the I2 cell) for HDS and
HIDES. The relative difference, that is the ratio between the
model and the observation, is 0.3–0.5% rms, corresponding to
the S/N ratio of 200–300, though the S/N ratio in the observed
spectrum is higher than 500 in each case. The residual is apparently not randomly distributed along wavelength, which is
possibly due to the incompleteness of our modeling technique
and/or the difference between our cells and the Lick’s cell, but
we can not distinguish them at this stage.
In figure 3, we show a set of examples of IP’s from several
consecutive star + I2 observations. The interval of each exposure is about 4–7 min. We can see that the shape of IP varies
from exposure to exposure, so it is indispensable to make a
correction for IP even for such short time scales.
The IP of HIDES is box-shaped if the slit is uniformly illuminated. This always happens, since the average seeing size
at OAO is around 1. 5, while the typical slit width corresponds
to 0. 76. However, under a good sky condition with a seeing
size of less than one arcsec and almost all the stellar image fall
into the slit, it is no longer illuminated evenly, especially for
a short exposure. In figure 4, we show how the IP of HIDES
varies with the seeing size. These are reconstructed from three
spectra of τ Cet observed at nearly the same time on three consecutive nights. The IP is not box-shaped for the seeing size of
0. 9 and is rather asymmetric, in contrast to the IP’s for the seeing size of 1. 3 or 2. 0. Since a box-shaped IP is easily affected
by a change of conditions in an observation like this, careful
modeling of it is very important to measure the Doppler shifts
of stars precisely.
3.3. Template Stellar Spectrum
To obtain a template stellar spectrum by the method described in section 2, we tried to model the template stellar
spectrum, the I2 spectrum, and the IP from observed star + I2
spectra as independently as possible. This is important since
in our method any residuals between the model and the observation are attributed to the incompleteness of the guess of the
template stellar spectrum [see equations (2) and (3)]. We set
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Fig. 2. Examples of modeling the pure I2 (flat + I2 ) spectrum for HDS
(upper) and HIDES (lower). The bottom plot of each panel is 5-times
the difference between the model and the observation.
the width of each segment to be 5 Å for HIDES, which is wide
enough to estimate the IP and the I2 depth parameter α sufficiently well. Star + I2 spectra with high S/N ratios (≥ 200)
from different nights and/or seasons, which have various relative positions between stellar and I2 absorption lines, are used
to derive the template stellar spectrum. This helps to prevent
any I2 lines from appearing in the final template stellar spectrum.
Figure 5 shows examples of the thus-determined template
stellar spectra. We generate the template spectrum of 16
Cyg B using five star + I2 spectra and that of τ Cet using
ten star + I2 spectra observed with HIDES on different nights.
As shown in this figure, the template spectrum of 16 Cyg B
generated from HIDES spectra successfully reproduces the
high resolution (R ∼ 100000) spectrum obtained by HDS
(upper panel) without significant contamination of I2 lines or
distortion of stellar absorption lines. The difference between
the model (the template spectrum broadened by an appropriate
single Gaussian profile so as to be best fitted to the stellar
observation) and the observation is 0.61% rms, which is
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Fig. 3. Upper: The IP of HDS derived from 16 Cyg B + I2 spectra
observed in 2000 August 21 (solid, dashed, and dash-dot-dash-dotted
lines, slit width 180 µm) and 2001 October 10 (dotted and
dash-dot-dot-dotted lines, slit width 150 µm). The interval of each exposure is 4–7 min. Lower: The IP of HIDES derived from τ Cet + I2
spectra observed in 2001 September 24 (all lines, slit width 200 µm).
The interval of each exposure is about 7 min.
larger than the value expected solely from the photon-shot
noise in the observation of S/N ∼ 500, and the residual is
apparently not randomly distributed along wavelength. In the
case of τ Cet (lower panel), we also obtain a good fit of the
model (the template spectrum broadened by a single Gaussian
profile in the same manner as in the case of 16 Cyg B) to the
observation with HIDES with 0.3% rms, while the expected
photon-limited value is 0.2% rms. One possible cause of
the differences between models and observations resides in
using a single Gaussian profile as a broadening function of the
template spectrum, which can not be accurately determined
unless I2 spectrum is superposed. Another possibility is that
smearing by the IP may not be completely removed from the
extracted template spectrum. It is possibly more significant
for 16 Cyg B, comparing the HIDES template with the HDS
observation, whose IP’s have quite different shapes. The
accuracy of radial-velocity measurements using these template
spectra is discussed in the following sections.
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Fig. 4. Variation of the HIDES IP according to the seeing size.
The IP is estimated from the spectrum of τ Cet + I2 observed in
2001 September 22 (solid line, 2. 0), 23 (dashed line, 0. 9) and 24
(dash-dot-dash-dotted line, 1. 3). The slit width was set to be 0. 76 on
every night.
With regard to the initial guess of the template spectrum, the
differences in the atmospheric parameters and the abundances
between the synthesized and observed spectra do not seem to
be a problem as long as a spectrum similar in spectral type is
used. However, strong lines in the synthesized spectrum, which
are not present at all in the observed one, can not completely
be removed from the extracted template stellar spectrum. In
such a case, the abundance of corresponding element should
be adjusted to reproduce the observed spectrum.
3.4. Distribution of Velocities on the Detector
In Takeda et al. (2002), we reported that the derived velocities showed a systematic dependence upon the position on the
detector without correcting for the difference in the wavelength
scale between a template stellar spectrum and a star + I2 spectrum. Such an effect also appears when the method using a
B-star + I2 spectrum is applied to data of HDS and HIDES.
Figure 6 shows distributions of the derived radial velocities
on the detector for HDS and HIDES using a template spectrum obtained by our method described in this paper. The
template stellar spectra generated from HIDES data are used
for the analyses in both cases, because we have not obtained
enough HDS data to make a template spectrum. We can see
no position-dependent pattern over the detector for both spectrographs, which means that the difference in the dispersion
relation between the template stellar spectrum and the star + I2
spectrum is properly corrected at this noise level. The internal
measurement error of 6.2 m s−1 for 16 Cyg B (upper panel)
is larger than the value of 2.8 m s−1 estimated from purely
photon-shot noise in this observation. The mean velocity of
τ Cet (lower panel) is determined with an internal precision of
4.4 m s−1 , while a value of 2.0 m s−1 is expected for a photonlimited error.
Fig. 5. Examples of the template stellar spectra (solid line) extracted
from the HIDES spectra. The spectrum of 16 Cyg B is compared with
the high resolution spectrum (R ∼ 100000) observed with HDS (upper), and the spectrum of τ Cet is compared with the HIDES spectrum
(lower). The bottom plot of each panel is 5-times the difference between the observation and the template stellar spectrum broadened by
the Gaussian profile (dotted line).
3.5. Radial Velocity Precision Tests
3.5.1. 16 Cyg B
16 Cyg B (G3 V) is orbited by an extrasolar planet in an
about 800-day eccentric (e = 0.68) orbit, showing radial velocity variation with an amplitude of 50 ms−1 (Cochran et al. 1997
with the updating from http://exoplanets.org/). This star is
chromospherically inactive and the chromospheric activity in
dicator, RHK
, has log RHK
= −5.04 (Henry et al. 2000). From
the calibration of Saar et al. (1998) based on chromospheric
activity indicators, its expected photospheric velocity jitter is
∼ 3ms−1 . Fischer et al. (2001) reported that the velocity residuals of the Keplerian fit exhibited a rms scatter of ∼ 7 m s−1 ,
consistent with their measurement errors. We observed this
star on 2000 August 21 (JD 2451778.9) and 2001 October 10
(JD 2452193.7) with HDS and on five different nights from
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Fig. 7. Radial velocity variation of 16 Cyg B observed with HDS (triangle) and HIDES (circle). The solid line represents the known orbital
solution (from http://exoplanets.org/).
Fig. 6. Distributions of the radial velocities determined for each segment of a HDS spectrum of 16 Cyg B (180 segments, upper) and a
HIDES spectrum of τ Cet (260 segments, lower). The segments further off than 3 σ from the mean are rejected.
2001 July to 2002 April with HIDES. For HDS, the wavelength
region was set to StdI2a in 2000 August, while it was set to
StdYc covering 4400–7050 Å in 2001 October. The slit width
was set to 180 µm (0. 36) and 150 µm (0. 3), respectively. A
total of five spectra were taken with the I2 cell, and the typical S/N ratios were 300 with exposure times of 2–4 min. For
HIDES, we collected six star + I2 spectra whose S/N ratios
were 100–200 with exposure times of 15–20 min, five of which
observed on different nights were used to make a template stellar spectrum. We could not make a good template from HDS
data alone because they were obtained only on two nights, so
the one reconstructed from HIDES data was used to analyze
the data from both spectrographs.
Figure 7 shows the combined HDS and HIDES radial velocities of 16 Cyg B. We can see that our observational plots are
in reasonable agreement with the predicted curve, and the internal measurement errors are about 6–8 m s−1 for all observations. The first two points of HIDES data (JD 2452111.16 and
JD 2452111.17) may contain more systematic errors than other
points, because the focus of the spectrograph was not completely adjusted at that time, and those IP’s turned out to vary
largely over the detector, for which we couldn’t entirely make
Fig. 8. Radial velocities of τ Cet observed with HIDES for seven
months.
corrections. Excluding these two points, the scatter around the
known orbit is about 8 m s−1 , consistent with our measurement
errors and the result by Fischer et al. (2001).
3.5.2. τ Cet
τ Cet (G8 V) has been known to be one of the most stable
stars in radial velocity, and was measured by the Lick and the
AAT Planet Search survey (Butler et al. 1996, 2001) as constant
at a level of of 5ms−1 . Its intrinsic velocity jitter is expected to
be ∼ 4ms−1 , estimated from its chromospheric activity indica
tor, log RHK
= −4.96 (Henry et al. 1996). We collected a total
of 58 spectra of τ Cet with HIDES on 24 separate nights from
2001 July to 2002 February. Typical S/N ratios were 200–300
with exposure times of 5 min. The template stellar spectrum
was reconstructed from ten star + I2 spectra selected from every observing run equally.
As shown in figure 8, our resulting rms scatter for the measured radial velocities is 5.9 m s−1 over a seven-month period
of time, which confirms the previous results by other groups,
and is consistent with our measurement errors of 5–7 m s−1 .
880
B. Sato et al.
[Vol. 54,
Fig. 9. Radial velocity variation of υ And observed with HIDES. The solid line represents the known orbital solution (from http://exoplanets.org/).
Upper: Observed velocity variation due to all three companions. Lower left: Residual velocities after the Doppler velocities attributed to companions c
and d were subtracted from the observed velocities, plotted as a function of orbital phase for companion b. Lower right: Residual velocities after the
Doppler velocities attributed to companion b were subtracted from the observed velocities.
3.5.3. υ And
υ And (F8 V) is one of the brightest stars among planetharboring stars. It is known to have three planets with the
main variation (due to the innermost companion b) showing
a velocity amplitude of 73 m s−1 with a period of 4.62 d, and
the other two companions, c and d, have periods of 241 and
1308 d, respectively (Butler et al. 1999 with the updating from
http://exoplanets.org/). We observed υ And with HIDES on
30 separate nights between 2000 October and 2001 December
and obtained a total of 46 spectra. Typical S/N ratios were
300–400 with exposure times of 10–15 min. We generate a
template stellar spectrum from ten star + I2 spectra obtained on
different nights.
In figure 9, we show our results of analysis for one-year-long
observations, with a total rms scatter of 16.0 m s−1 around the
known orbit, though some systematic errors are left depending
on the observing runs. The internal measurement error is typically 10 m s−1 , larger than that for τ Cet with a similar S/N ratio, due to its relatively larger rotational velocity, which broadens the spectral lines and lowers the measurement precision
of radial velocity. From the value of log RHK
= −4.93 (Henry
et al. 2000) for this star, we can estimate that υ And is subject
to an intrinsic photospheric velocity scatter, ∼ 10 m s−1 . When
added in quadrature of these two errors, the overall uncertainty
is 15 m s−1 , which is consistent with the rms scatter of our observations.
4.
Summary and Discussion
We have developed a computer code for precise measurements of the stellar radial-velocity variations using the I2
cells on HDS and HIDES. Our technique is similar to those
described by Butler et al. (1996) and Valenti et al. (1995); that
is, the observed star + I2 spectrum is modeled as the product of
high-resolution stellar and I2 template spectra convolved with
the spectrograph IP which is reconstructed by combining several Gaussian profiles. To generate a template stellar spectrum,
we have devised a new method in extracting a template stellar spectrum from star + I2 spectra, whose wavelength scale
can be accurately determined by the I2 lines superposed on the
star + I2 spectra, and out of which the IP is deconvolved simultaneously. This enables us to obtain a well-established template
spectrum even when the IP and the wavelength scale are apt to
be influenced by observational conditions and are subject to
vary with time.
For testing the Doppler precision using our I2 cells and current analysis package, we have observed several solar-type
stars with HDS and HIDES. For HIDES, the rms scatter in
No. 6]
Iodine Cells for Subaru and Okayama Spectrographs
the measured radial velocities of τ Cet is 5.9 m s−1 over a time
span of seven months. The average internal measurement error is about the same number, which is slightly larger than
the photon-limited error of 2–3 m s−1 for the observations of
S/N ∼ 200. We have also observed υ And for about one year
with HIDES, and the derived radial velocities reproduce the
known orbit with a rms scatter of 16.0 m s−1 , which is consistent with the measurement uncertainty from the combination
of the measurement error and the expected stellar jitter. For
HDS, it is also considered that a year-long precision of about
5–6 m s−1 has already been achieved based on the results of
16 Cyg B. However, we have not obtained enough data to evaluate its accuracy of radial velocity measurements correctly, so
we have been continuing test observations of this star.
The IP of HIDES is influenced by observational conditions.
It shows Gaussian-like or box-like shape depending on the seeing size at Okayama varying from about 0. 8 to 3. 0, while
that of HDS is always close to Gaussian profile. The box-like
IP can not be reproduced completely by our present modeling
procedure with the multiple Gaussian fitting, especially when
it is asymmetric. Improvements of the IP modeling technique
are necessary to increase our radial velocity precision further.
Using many stellar spectra in different seasons and nights
to derive the template stellar spectrum, systematic errors attributed to particular features of the individual spectra can be
removed from the template spectrum, and also its S/N ratio is
increased. We have succeeded in obtaining a high-resolution
(R ∼ 100000) pure stellar spectrum from the HIDES spectra
(R ∼ 65000). However, compared with the HDS spectrum,
the residual is apparently not randomly distributed along the
wavelength. The derived template may still contain smearing
from the IP, and be slightly broadened by the process of averaging many spectra. An improvement of the technique for IP
reconstruction is required again from this point of view, and the
881
algorithm of the deconvolution should also be refined further.
The difference between our cells and the Lick’s cell is possibly one of the causes of the imperfect modeling of our I2 cell
transmission function, which is about 0.3% or so at its largest.
For an analysis with a precision of 5 m s−1 or so, the difference is probably not serious, since with our I2 cell the relative
position of our I2 spectra can be determined with an accuracy
of 1 m s−1 or less (Paper I). But, it may finally limit our radial
velocity precision at a much more higher level of 1–2ms−1 , so
we plan to obtain a high resolution template spectrum of our
cell and examine it.
Finally, our modeling procedure described in this paper
requires significant CPU time. Approximately 1 CPU hour on
a Alpha 700 MHz class machine is required to derive the radial
velocity of each observation, and 30 CPU hr are required to
generate a template stellar spectrum from ten star + I2 spectra.
An improvement of the algorithm of the deconvolution will enable us to obtain a more precise template spectrum from many
more star + I2 observations.
In 2001 July, we started a Doppler survey of intermediatemass stars in their evolved stage as late-G giants, searching for
planets around them. Current searches for extrasolar planets
around these stars are less extensive than those around solartype stars, but to reveal that the properties of planets around
various types of stars may give us a hint on the formation mechanism of planetary systems. The first results of this project are
presented in Sato et al. (2002), and will be discussed in our
forth-coming paper.
We thank all of the staffs at the Okayama Astrophysical
Observatory and the Subaru Telescope for their support during the observations. We especially thank Seiji Masuda for his
kind help for every observation at Okayama.
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