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arXiv:0804.1182v3 [astro-ph] 8 May 2008
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THE AMPLITUDE OF SOLAR OSCILLATIONS USING STELLAR TECHNIQUES
HANS KJELDSEN,
1
TIMOTHY R. BEDDING,
2
TORBEN ARENTOFT,
1
R. PAUL BUTLER,
3
THOMAS H. DALL,
4
CHRISTOFFER KAROFF,
1
LÁSZLÓ L. KISS,
2
C. G. TINNEY
5
AND WILLIAM J. CHAPLIN
6
To appear in ApJ
ABSTRACT
The amplitudes of solar-like oscillations depend on the excitation and damping, both of which are controlled by
convection. Comparing observations with theory should therefore improve our understanding of the underlying
physics. However,theoretical models invariably compute oscillation amplitudes relative to the Sun, and it is there-
fore vital to have a good calibration of the solar amplitude using stellar techniques. We have used daytime spectra
of the Sun, obtained with HARPS and UCLES, to measure the solar oscillations and made a detailed comparison
with observations using the BiSON helioseismology instrument. We find that the mean solar amplitude measured
using stellar techniques, averaged over one full solar cycle, is 18.7 ± 0.7cms
−1
for the strongest radial modes
(l = 0) and 25.2± 0.9cms
−1
for l = 1. In addition, we use simulations to establish an equation that estimates
the uncertainty of amplitude measurements that are made of other stars, given that the mode lifetime is known.
Finally, we also give amplitudes of solar-like oscillations for three stars that we measured from a series of short
observations with HARPS (γ Ser, β Aql andα For), together with revised amplitudes for five other stars for which
we have previously published results (α Cen A, α Cen B, β Hyi, ν Ind and δ Pav).
Subject headings: Sun: helioseismology — stars: oscillations — stars: individual (γ Ser, β Aql, α For, α Cen A,
α Cen B, β Hyi, ν Ind, δ Pav)
1. INTRODUCTION
The list of stars in which solar-like oscillations have
been observed is growing rapidly, thanks to improve-
ments in high-precision velocity measurements (for a re-
cent review see Bedding & Kjeldsen 2007). While most
excitement centres on the frequencies of the oscillations,
there is also considerable interest in the amplitudes (e.g.,
Christensen-Dalsgaard & Frandsen 1983; Kjeldsen & Bedding
1995; Houdek et al. 1999; Houdek & Gough 2002; Houdek
2006; Samadi et al. 2005, 2007a,b, 2008). This is because the
excitation and damping are both controlled by convection and
so the study of oscillation amplitudes will hopefully lead to an
improvement in our understanding of the underlying physics.
Theoretical calculations of oscillation amplitudes, such as
those cited above, are calibrated with reference to the Sun. It
is therefore crucial to establish the amplitudes of the solar os-
cillations. There is an abundance of solar observations from
helioseismology projects such as BiSON (Birmingham Solar
Oscillations Network) and GOLF (Global Oscillations at Low
Frequencies). However, these velocity measurements are made
using a single spectral line, such as sodium (λ5896Å, used by
GOLF) or potassium (λ7699Å, BiSON), and the measured os-
cillation amplitude depends on the height in the solar atmo-
sphere at which the spectral line is formed (e.g., Isaak et al.
1989; Baudin et al. 2005; Houdek 2006). Velocity measure-
ments of other stars, on the other hand, employ a wide wave-
length range that includes many spectral lines, mostly from
neutral iron. The iron lines are formed lower in the atmo-
sphere than sodium and potassium and so we might expect so-
lar amplitudes measured using stellar techniques to be lower
than those from helioseismic measurementssuch as BiSON and
GOLF. On the other hand, BiSON and GOLF measure ve-
locities using a resonance scattering cell, whereas the stellar
technique involves measuring line centroids. These approaches
havedifferentsensitivities as a function of the mode angular de-
gree l (Christensen-Dalsgaard 1989), which must be corrected
for when interpreting measured amplitudes.
We have recently pointed out the importance of establish-
ing the oscillation amplitude of the Sun using stellar techniques
(Kjeldsen et al. 2005). In that paper,we reported a limited set of
observations of the solar oscillations obtained from spectra of
the full moon. The results gave some support to the conclusion
that Fe I measurements give lower amplitudes than both GOLF
and BiSON, but we emphasized the desirability of obtaining
more measurements of the Sun, in order to better calibrate the
relationship between stellar and solar amplitudes. That is the
main purpose of this paper.
2. OBSERVATIONS
We have obtained solar spectra by observing the daytime sky.
Although detailed line profiles of daytime spectra show differ-
ences from the actual solar spectrum (Gray et al. 2000), and the
bisector varies with solar angle (Dall et al. 2006), there is no
reason to suspect any systematic effects on mean velocities on
the timescale of the 5-minute oscillations.
We made the observations in 2005 September during
a dual-site asteroseismology campaign on the star β Hyi
(Bedding et al. 2007). Figure 1 shows the full set of data. At
the European Southern Observatory on La Silla in Chile we
1
Danish AsteroSeismology Centre (DASC), Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark; hans@phys.au.dk,
toar@phys.au.dk, karoff@phys.au.dk
2
School of Physics A28, University of Sydney, NSW 2006, Australia; bedding@physics.usyd.edu.au, laszlo@physics.usyd.edu.au
3
Carnegie Institution of Washington, Department of Terrestrial Magnetism, 5241 Broad Branch Road NW, Washington, DC 20015-1305; paul@dtm.ciw.edu
4
Gemini Observatory, 670 N. Aohoku Pl., Hilo, HI 96720, USA; tdall@gemini.edu
5
School of Physics, University of NSW, 2052, Australia; cgt@phys.unsw.edu.au
6
School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK; wjc@bison.ph.bham.ac.uk
7
Based on observations collected at the European Southern Observatory, La Silla, Chile (ESO Programme 075.D-0760)
1
2 Kjeldsen et al.
used the HARPS spectrograph (High Accuracy Radial velocity
Planet Searcher) with the 3.6-m telescope.
7
. A thorium emis-
sion lamp was used to provide a stable wavelength reference.
We obtained 626 spectra over 9.7hr spread over four consecu-
tive afternoons, with typical exposure times of 25 s and a me-
dian cadence of one exposure every 56s (which corresponds
to a Nyquist frequency of 8.9mHz). The velocities were pro-
cessed using the standard HARPS pipeline.
At Siding Spring Observatory in Australia we used UCLES
(University College London Echelle Spectrograph) with the
3.9-m Anglo-Australian Telescope (AAT). An iodine absorp-
tion cell was used to provide a stable wavelength reference,
with the same setup that we have previously used with this
spectrograph (Butler et al. 2004). With UCLES we obtained
265 spectra of the Sun over about 8.5hr, spread over three non-
consecutive afternoons. Typical exposure times were 45–60s,
with a median cadence of one exposure every 115s (which cor-
responds to a Nyquist frequency of 4.35mHz).
In addition, we have analysed velocities obtained by Bi-
SON (Birmingham Solar Oscillations Network) over the first
10 days of 2005 September, which covers the period in which
the UCLES and HARPS data were taken. We also examined a
14-yeartime series (1992.6 to 2006.9)from the BiSON archive,
which allows us to follow variations in amplitude with the solar
activity cycle (see §3.3). The BiSON data have 40-second sam-
pling. They had also been high-pass filtered by subtracting a
moving mean calculated in a boxcar of length 1000s. We have
corrected for this by dividing the power spectra by the transfer
function of this filter.
2.1. Observations of γ Ser, β Aql and α For
As mentioned above, the night-time target for this asteroseis-
mology campaign was the star β Hyi. However, β Hyi was
not accessible to HARPS for the first part of each night due
to hour-angle restrictions on the ESO 3.6-m telescope. We used
this time to observe two other stars, taken from the list of tar-
gets presented by Bedding et al. (1996). The first was γ Ser
(HR 5933, HD 142860, HIP 78072), which has spectral type
F6IV-V and magnitude V = 3.85, and was observed for about
75 minutes at the start of each of three consecutive nights. The
second star was β Aql (HR 7602, HD 188512, HIP 98036),
spectral type G8IV and magnitude V = 3.71, which was ob-
served on four consecutive nights for periods of 65, 95, 10 and
70 minutes, respectively.
This limited set of observationswas not sufficient to allow us
to measure oscillation frequencies,but we were able to estimate
the amplitudes, in the same way as we have previously done
for the star δ Pav (Kjeldsen et al. 2005). In addition, we also
analysed observations of the star α For (HR 963, HD 20010,
HIP 14879), which has spectral type F8IV and magnitude
V = 3.85. Those observations were taken with HARPS in 2007
January for about 20-30 minutes at the start of each of seven
consecutive nights, during a multi-site campaign on Procyon
(T. Arentoft et al., in prep.). Note that the behaviour of the
line bisectors for these observations of γ Ser and β Aql were
already discussed by Dall et al. (2006).
3. ANALYSIS AND RESULTS
3.1. Time series and power spectra
The first step in the analysis of the solar velocities from
HARPS and UCLES was to remove slow trends from each data
set by a high-pass filter that only affected frequencies below
1mHz. Figure 2 shows a close-up comparison of HARPS and
BiSON for one afternoon of data (160min). There is excellent
agreement and we see that the two data sets are of comparable
quality. The UCLES data have somewhat poorer precision per
data point.
The next step was to calculate the power spectra of the ve-
locities. For HARPS and UCLES, we used the measurement
uncertainties, σ
i
, as weights in calculating the power spectrum
(according to w
i
= 1/σ
2
i
). No uncertainty estimates were avail-
able for the BiSON velocities and so all points were given
equal weight. The power spectrum of the HARPS time series
is shown in the upper panel of Fig. 3, while the lower panel
shows the spectrum of the segment of BiSON data taken at
the same times. We see that the HARPS and BiSON power
spectra are very similar. Figure 4 shows a similar analysis
for the UCLES data and the corresponding BiSON segment.
The UCLES power spectrum has higher noise but, taking this
into account, we again see good agreement between the two.
A comparison of Figures 3 and 4 show that the solar power
spectrum was quite different for the two time series, reflecting
the intrinsic variations in the solar oscillations. Given that the
HARPS data have lower noise than the UCLES data, we do not
show results for UCLES in the remainder of the analysis.
3.2. Calculating smoothed amplitude spectra
The amplitudes of individual modes are affected by the
stochastic nature of the excitation and damping. To mea-
sure the oscillation amplitude in a way that is independent
of these effects, we have followed the method introduced by
Kjeldsen et al. (2005). In brief, this involves the following
steps: (i) heavily smoothing the power spectrum (by an amount
defined in the next paragraph), to produce a single hump of
excess power that is insensitive to the fact that the oscillation
spectrum has discrete peaks; (ii) converting to powerdensity by
multiplying by the effective length of the observing run (which
we calculate as the reciprocal of the area under the spectral
window in power); (iii) fitting and subtracting the background
noise; and (iv) multiplying by ∆ν/c and taking the square root,
in order to convert to amplitude per oscillation mode. Here, ∆ν
is the large frequency separation, which has a value of 135µHz
in the Sun, and c is a factor that measures the effective number
of modes per order.
The amount of smoothing affects the exact height of the
smoothed amplitude spectrum. To establish a standard that al-
lows comparisons, we propose that smoothing be done by con-
volving (in power) with a Gaussian having a full width at half
maximum of 4∆ν. We have adopted this convention for all the
figures and measurements in this paper.
3.2.1. The value of c
In our previous work, we used a value of c = 3.0
(Kjeldsen et al. 2005; Bedding et al. 2006, 2007). However, c
depends on the sensitivity of the observations to the various
low-degree modes, which in turn depends on the method used
to observe the oscillations. We therefore reconsider the calcu-
lation of c, as follows. Let S
l
/S
0
be the spatial response of
the observations to modes with degree l, relative to those with
l = 0. Table 4 of Christensen-Dalsgaard (1989) allows us to
calculate S
l
/S
0
for BiSON velocity observations and these are
shown in Table 1. We have also calculated values for veloc-
ity observations using the stellar technique, using the results
in Bedding et al. (1996) for an adopted mean wavelength of
Amplitudes of solar oscillations 3
550nm. These are also shown in Table 1. The difference from
the BiSON values arises from the way the BiSON resonance
scattering cell measures velocities, as discussed in detail by
Christensen-Dalsgaard (1989). Finally, Table 1 also shows the
response factors for intensity measurements at the three wave-
lengths of the SoHO VIRGO instrument, again derived from
the results in Bedding et al. (1996).
8
The last row of Table 1 shows the value of c, calculated as
c =
4
X
l=0
S
l
/S
0
2
. (1)
These are the values that we will adopt in future. Note that the
value of c = 3.0 that we used previously was based on normal-
izing to the mean of l = 0 and 1, rather than to l = 0, as we now
propose. The l = 0 modes make a sensible reference because
they are not split by rotation, but it is important to remember
that the l = 1 modes are actually stronger than the radial modes.
Note that comparing observed amplitudes with theoreti-
cal calculations requires knowledge of the actual value of
the spatial response function of the observations. For in-
tensity measurements, S
0
= 1 by definition. For BiSON,
Christensen-Dalsgaard (1989) has calculated S
0
= 0.724, while
for stellar velocity measurements we have used the results in
Bedding et al. (1996) to derive S
0
=0.712(again, for an adopted
mean wavelength of 550nm).
3.3. The solar amplitude
The smoothed amplitude spectrum for our solar observations
with HARPS is shown in Fig. 5, together with that from BiSON
from exactly the same observation times. Note that here we did
not use the weights when calculating the HARPS power spec-
trum, since these were not available for BiSON and we wanted
to make the window functions exactly the same. The ampli-
tude of solar oscillations measured using the stellar technique
is slightly lower than that measured by BiSON, by a factor of
1.07± 0.04. The error bar comes from the uncertainty in fitting
the background to the HARPS spectrum. However, we must
keep in mind that our observations of the Sun were made over
only a few hours, and at a single epoch during the 11-year solar
cycle. To correct for this and hence determine the mean am-
plitude of the Sun, we have made use of the full set of BiSON
observations.
We have analysed the 14-year time series from the BiSON
archive, measuring amplitudes in ten-day segments in the way
described above. In practice we chose all segments to have the
same number of data points, which meant that the lengths of
most segments were in the range 8–12d, reflecting variations in
the filling factor of the network. The result is shown in Fig. 6,
where each point represents the peak amplitude in one segment.
We see clearly the variations in amplitude with the solar activ-
ity cycle, as has been well studied from these BiSON data by
Chaplin et al. (2000, 2003).
Note that the scatter in the amplitudes in Fig. 6 is not mea-
surement error, but rather reflects the intrinsic variability of the
modes. We see that both the amplitude and the scatter on the
amplitude are smallest at solar maximum (in 2001), which is
explained by the shorter mode lifetime during periods of high
solar activity. Any changes in the excitation rate during the so-
lar cycle would also contribute to amplitude variability, but no
evidence for such changes has so far been reported.
The mean BiSON amplitude over one 11-year solar cycle,
measured from the data in Fig. 6, is 20.0± 0.1cms
−1
. Com-
bining this with the result in the previous section, we conclude
that the mean amplitude of the radial oscillations in the Sun,
measured using stellar techniques, is 18.7± 0.7cms
−1
. This is
the quantity that we were seeking to measure. It is important
to remember that this is based on the process we used (includ-
ing the 4∆ν-smoothing described in §3.2) and is normalized to
the modes with l = 0. Values for non-radial modes can be cal-
culated from the ratios in column 3 of Table 1. For example,
the mean peak amplitude for l = 1 modes is significantly higher
than for l = 0, and both are given in the first line of Table 2.
Figure 7 shows smoothed amplitude spectra for 10-day seg-
ments of BiSON data for one full year, starting at 2005.0. This
period covers the solar minimum and so the variations are dom-
inated by the stochastic nature of the excitation and damping,
rather than by variations due to the solar cycle. Note that the
curves show less spread at the higher frequencies than at the
lower frequencies, reflecting the fact that the mode lifetimes in
the Sun increase with frequency.
The mean of these curves is shown in Fig. 8 after scaling so
that the peak is 18.7cms
−1
, which is the solar mean as mea-
sured with stellar techniques.
3.4. Amplitudes for other stars
In Figure 8 we show the amplitude curves for the three
stars described in §2.1 (β Aql, α For and γ Ser), together with
five other stars for which we have previously published am-
plitudes: α Cen A, α Cen B and δ Pav (Kjeldsen et al. 2005),
ν Ind (Bedding et al. 2006) and β Hyi (Bedding et al. 2007).
All the curves were calculated using the revised method de-
scribed in §3.2.
Table 2 summarizes our results for the Sun and these eight
stars. Column 2 gives the large frequency separation that we
used in the calculation (there are no measurements of ∆ν for
γ Ser, α For, β Aql and δ Pav and so we estimated a value
from the stellar parameters). Column 3 of Table 2 gives our
measurement of ν
max
, the frequency of the envelope peak, and
column 4 gives the peak height (the amplitude per radial mode,
as plotted in Fig. 8). Column 5 gives the peak amplitude of the
l =1 modes, using the calibration factor of S
1
/S
0
= 1.35 (see Ta-
ble 1), which we include to emphasise that the strongest peaks
will generally be those with l = 1.
3.5. The uncertainty in measuring oscillation amplitudes
Part of the uncertainty in each measured oscillation ampli-
tude arises from the precision with which we can fit and sub-
tract the background. This is a measurement error and is given
in columns 4 and 5 of Table 2.
In addition, stars will presumably have variations with activ-
ity cycle, analogous to the ∼ ±5% variation seen in the Sun,
but for the moment we do not have enough information to es-
timate those effects. However, we can estimate the scatter on
the measured amplitude that is caused by the finite lifetime of
the modes. This arises because a typical stellar observing run
does not last long enough to sample a large number of mode
lifetimes.
For the BiSON data in Fig. 6, the relative scatter of the mea-
sured amplitude about the smoothed curve has an average value
of σ
A
/A = 6.2± 0.2%. This relative scatter σ
A
/A depends on
8
The values in Table 1 are summed over all m values. To calculate response functions for individual m values, as would be observed in rotationally split modes, see
Gizon & Solanki (2003) and references within.
4 Kjeldsen et al.
two parameters. One is T/τ, where T is the duration of the
observations (10d in this case) and τ is the mode lifetime.
The other parameter is N, the number of low-degree oscillation
modes that are excited within the smoothed envelope, which is
about 30 in the Sun. We expect σ
A
/A to vary inversely with
both of these parameters:
σ
A
A
= k
N
1+
T
τ
−0.5
. (2)
We have verifiedthat equation(2) holds, andthat the constant of
proportionality is k = 0.75, by using simulations with different
values of the parameters. We simulated the stochastic nature of
the oscillations using the method described by De Ridder et al.
(2006).
Our decision to adopt a smoothing width of 4∆ν (§3.2)
means that N will be the same for all stars (provided there are
not a large number of additional mixed modes in the power
spectrum). Since we know the mode lifetime of the Sun, we
can calibrate equation (2) using the solar value of σ
A
/A =
6.2 ± 0.2% for the 10-d segments of BiSON data. The av-
erage mode lifetime in the Sun, measured over a solar cycle
from the linewidths in the range 2.8–3.4mHz, is 2.88± 0.07d
(Chaplin et al. 1997). Using this, we get
σ
A
A
= (0.131± 0.004)
1+
T
τ
−0.5
. (3)
Equation 3 can be used to estimate the uncertainty of ampli-
tude measurements that are made on other stars, provided τ is
known (see also Toutain & Appourchaux 1994).
The last column of Table 2 shows σ
A
/A for the observa-
tions. We have used published measurements of mode lifetimes
for α Cen A and B (Kjeldsen et al. 2005), ν Ind (Carrier et al.
2007) and β Hyi (Bedding et al. 2007). There are no measure-
ments available for the other stars (γ Ser, β Aql, α For and
δ Pav) and so we adopted the solar value.
To obtain the total uncertainties for the amplitudes in Ta-
ble 2, the uncertainty from the background subtraction should
be added in quadrature to σ
A
/A (although in practice, the latter
dominates). Finally, we repeat that there is an additional source
of uncertainty in these amplitude measurements, namely any
variations with stellar activity cycle.
4. CONCLUSIONS
We have used daytime spectra of the blue sky, obtained with
the stellar spectrographs HARPS and UCLES, to measure os-
cillations in the Sun. We measured amplitudes by smoothing
in power density and subtracting the background, as previously
described by Kjeldsen et al. (2005). In this paper we propose
two conventions in the use of this method. Firstly, we suggest
the smoothing be done by convolution with a Gaussian having
a FWHM (in power) of 4∆ν. Secondly, we have chosen to re-
port mean amplitudes for the radial modes (l = 0), but stress
that the highest peaks in the amplitude spectrum will generally
correspond to l = 1.
In the daytime sky observationsreported here, the solar oscil-
lation amplitude was slightly lower than that measured simulta-
neously by BiSON, by a factor of 1.07± 0.04. This difference
arises from two factors: (i) the stellar techniques measure a ve-
locity that is dominated by neutral iron lines, which are formed
lower in the solar atmosphere than the potassium line measured
by BiSON; (ii) the two methods have slightly different spatial
response functions.
A single-epoch measurement of the solar amplitude has a
significant uncertainty due to the stochastic nature of the os-
cillations. We find the mean solar amplitude measured by
BiSON over one full solar cycle (for radial modes) to be
20.0± 0.1cms
−1
, implying a mean amplitude measured using
stellar techniques of 18.7± 0.7cms
−1
. The mean peak ampli-
tude for l = 1 modes is 25.2± 0.9cms
−1
.
By using simulations, we have estimated the scatter in the
amplitude measured fromsolar-like oscillations thatarises from
the stochastic nature of the excitation and damping. The result
is given in Equation 3, which matches the scatter that we find
from BiSONobservationsof the Sun. This equation canbe used
to estimate the uncertainty of amplitude measurements that are
made other stars, provided the mode lifetime is known.
Finally, Table 2 gives amplitudes for three stars (γ Ser, β Aql
and α For) that were measured from a series of short observa-
tions with HARPS, together with revised amplitudes for five
other stars for which we have previously published results.
Now that the solar amplitude is established, these measure-
ments should be valuable tests for theoretical models of solar-
like oscillation amplitudes.
We thank Graham Verner for providing the time series of Bi-
SON velocity measurements, and Yvonne Elsworth and Den-
nis Stello for comments on this paper. We thank ESO and
the AAO for supporting the daytime observations. This work
was supported financially by the Danish Natural Science Re-
search Council and the Australian Research Council. We fur-
ther acknowledge support by NSF grant AST-9988087 (RPB),
and by SUN Microsystems. CK acknowledgessupport from the
Danish AsteroSeismology Centre and the Instrument Center for
Danish Astrophysics.
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TABLE 1
SPATIAL RESPONSE FUNCTIONS
BiSON Stellar Intensity
velocities velocities 402 nm 500 nm 862 nm
S
1
/S
0
... 1.37 1.35 1.26 1.25 1.20
S
2
/S
0
... 1.08 1.02 0.81 0.75 0.67
S
3
/S
0
... 0.58 0.47 0.25 0.18 0.10
S
4
/S
0
... 0.22 0.09 −0.03 −0.06 −0.10
c... 4.43 4.09 3.31 3.16 2.91
6 Kjeldsen et al.
TABLE 2
AMPLITUDES OF VELOCITY OSCILLATIONS
∆ν ν
max
v
osc
(cms
−1
)
Star (µHz) (mHz) l = 0 l = 1 σ
A
/A
Sun... 134.8 3.1 18.7± 0.7 25.2± 0.9 0.3%
γ Ser... 90 1.6 34.2± 1.3 46.2± 1.8 10%
α For... 60 1.1 34.8± 0.9 47.0± 1.2 7%
β Aql... 30 0.41 48.8± 1.1 65.9± 1.5 9%
α Cen A... 106.2 2.4 22.5± 0.2 30.4± 0.2 8%
α Cen B... 161.4 4.1 7.2± 0.1 9.7± 0.2 7%
β Hyi... 57.5 1.0 41.9± 0.3 56.6± 0.5 6%
ν Ind... 25.1 0.32 64.7± 0.9 87.4± 1.3 10%
δ Pav... 93 2.3 19.5± 0.4 26.3± 0.5 8%
FIG. 1.— Velocity time series of the Sun measured from the blue sky by HARPS (red squares) and UCLES (black diamonds).
FIG. 2.— Close-up showing 160min of the HARPS (red squares) together with contemporaneous measurements by BiSON (black diamonds).
FIG. 3.— Power spectrum of the HARPS velocities of the Sun (upper), and of the BiSON series taken at the same times (lower).
Amplitudes of solar oscillations 7
FIG. 4.— Same as Fig. 3, but for UCLES and the corresponding BiSON data.
FIG. 5.— Amplitude per mode of oscillations in the Sun, as measured from the power spectra in Fig. 3.
FIG. 6.— Amplitude of solar oscillations measured from BiSON data. The points were measured from independent 10-day segments of data and the thick line is
after smoothing with a boxcar running mean of 50 points (500 days).
8 Kjeldsen et al.
FIG. 7.— Smoothed amplitude spectra of solar oscillations measured from BiSON data in the year 2005. Each curve was measured from an independent 10-day
segment of data.
FIG. 8.— Smoothed amplitude curves for oscillations in the Sun and other stars (see text for details).
