A&A 479, 845-848 (2008)
DOI: 10.1051/0004-6361:20078426
S. V. Marchenko
Department of Physics and Astronomy, Western Kentucky University, 1906 College Heights Blvd., 11077, Bowling Green, KY 42101-1077, USA
Received 6 August 2007 / Accepted 31 December 2007
Abstract
Aims. Procyon A, a bright F5 IV-V Sun-like star, is justifiably regarded as a prime asteroseismological target. This star was repeatedly observed by MOST, a specialized microsatellite providing long-term, non-interrupted broadband photometry of bright targets. So far, the widely anticipated p-modes eluded direct photometric detection, though numerous independent approaches hinted for the presence of signals in the
mHz range.
Methods. Implementation of an alternative approach in data processing, as well as combination of the MOST data from 2004 and 2005 (264 189 measurements in total) helps to reduce the instrumental noise affecting previous reductions, bringing the
detection limit down to
5.5 part-per-million in the
f=0.8-1.2 mHz range.
Results. This enabled us to cross-identifiy 16 p-mode frequencies (though not their degrees) which were previously detected via high-precision radial velocity measurements, and provides an estimate of the large spacing,
mHz at
mHz. The relatively low average amplitude of the detected modes,
ppm, closely matches the amplitudes inferred from the ground-based spectroscopy and upper limits projected from WIRE photometry. This also explains why such low-amplitude signals eluded the direct-detection approach which exclusively relied on the MOST 2004 (or 2005) data processed by a standard pipeline.
Key words: stars: oscillations - stars: individual: Procyon A - techniques: photometric - methods: data analysis
The MOST satellite (Walker et al. 2003) is a 15 cm telescope acquiring high-precision, non-stop CCD photometric data on bright objects through a broad-band, 350-700 nm, optical filter. MOST observed Procyon A in 2004 (32-day, non-stop observations, 231 524 0.9 s exposures: see the results discussed in Matthews et al. 2004), 2005 (taken over 17 sequential days with the general setup of the experiment following the 2004 campaign: Guenther et al. 2007) and 2007 (data are being processed: Matthews 2007, priv. comm.).
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Figure 1:
The upper section
shows the new spectrum (black lines) derived from the stand-alone 2004 data and the previously published (red lines) spectrum derived from the same data. The orbital harmonics and their n*1/d sidelobes are marked by vertical solid-line and dashed-line arrows, respectively.
Middle section: the Fourier amplitude spectrum calculated from the combined 2004-2005 data set processed with the alternative
algorithm (black lines),
compared to the published (Matthews et al. 2004: red lines) spectrum as a reference. Blue arrows mark the identified
p-modes. Bottom section: an artificial spectrum calculated from the shuffled MOST
2004+2005 data with added stochastically-excited sinusoidal signals. Their frequencies
are taken from Table 1. For simplicity, all signals are assigned equal amplitudes a=10 ppm and lifetimes L=7 days
(red lines), and a=15 ppm, L=3 days (black lines). Blue arrows mark the identified
p-modes. In all sections, the
horizontal blue lines denote the 3![]() |
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We took the publicly available
raw data from 2004 and 2005 and processed them using an alternative algorithm
(see the description in Aerts et al. 2006).
While generally conforming to the approach of the standard processing
pipeline applied to the 2004-2005 data,
the alternative algorithm treats the highly variable stray light, the main source of instrumental noise, in a more flexible manner. In addition to the iterative subtraction of scattered light, the algorithm
accounted for less substantial sources of instrumental noise, such as sensitivity drift caused by
slow variations of the CCD temperature. The alternative approach resulted in a lower point-to-point scatter,
s=440 part-per-million (ppm), vs. s=500 ppm (Matthews et al. 2004) (cf. the upper section of Fig. 1). This should be compared to the projected level of the Poisson-dominated instrumental noise
ppm. The
alternative approach also reduces the average (noise-dominated) amplitudes and scatter in the frequency spectrum: e.g., for
f=1.05-1.25 mHz one obtains
ppm in the
older reduction vs.
for the new algorithm (Fig. 1).
The modified
approach, when efficiently combining the two available data streams (SDS1 and SDS2: see the definition in Aerts et al. 2006), proves to be even more effective with the 2005 data where the better planning of experiment
allowed more straightforward suppression of the stray-light component, providing
ppm,
which only moderately exceeds the expected level of
ppm. Predictably, the lower noise level brings down average amplitudes in the frequency domain:
ppm in the
f=1.05-1.25 mHz range, twice lower than in the data from 2004. On the other hand, the standard approach (Guenther et al. 2007), relying uniquely on the SDS2 channel, provides
a noise level comparable to the 2004 set.
During the processing of the 2004 data we kept the time-binning approach similar to the
original scheme (Matthews et al. 2004); this provided a valuable point-to-point comparison between the two different approaches and retained 214 279 flux measurements. For the 2005 data we slightly
changed the approach, by time-binning the SDS1 observations centered on the less frequent SDS2 measurements. On average, taking into account the higher rejection rates,
the SDS1 data were 5.5 times more abundant in the 2005 set. This time-binning
approach resulted in 49 910 flux measurements.
The next step aims at an optimal combination of the data. A host of potential problems stems
from: (a) the different durations of the 2004 and 2005 runs; (b) different planning of the experiments
resulting in different levels of stray light; (c) presumably unstable nature of the signals.
In the time domain we experimented with different lengths of segments derived from the original time series, varying them from 3 days to 2 weeks and producing a weighted combination of the frequency spectra derived from the segments.
This allows us to see that the typical lifetime of signals does not exceed 1 week. However,
the segment-based approach comes at a high price, raising, in the region of interest,
f=0.5-2.0 mHz, the detectability limits to an unacceptably high level, a>10 ppm.
Hence, we finally relied on the simplest and most straightforward approach, by combining the unweighted 2004 and 2005
data into a single set (Fig. 1). Obviously, this results in a further improvement of sensitivity:
considering the 3-sigma level counted from the average amplitude of the noise-dominated signal, one is able to detect coherent oscillations with
ppm (
f=0.7-0.8 mHz),
ppm (
f=0.8-1.2 mHz),
ppm (
f=1.2-1.6 mHz),
ppm (f>1.6 mHz), to be compared to
ppm (
f=0.5-2.0 mHz: Matthews et al. 2004) and
ppm (Guenther et al. 2007). Beyond the overall improvement of sensitivity, such
a straightforward combination of the 2004 and 2005 data should substantially increase the chance of a positive detection which depends on the presumably
short lifetimes of the coherent signals (p-modes) in Procyon A (Leccia et al. 2007) and the stochastic
nature of the mode-excitation events (Kjeldsen & Bedding 1995).
As a first test for the presence of any periodic variations, we derived a Fourier amplitude spectrum (AS) of the combined 2004+2005 data in the
f=0.5-2.0 mHz domain specifically targeted in
numerous observing campaigns. Then we calculated the number of peaks exceeding the detectability levels (see above). We also produced 10 samples via random shuffling of the
real data and calculated the incidence of significant signals in the artificial ASa.
We normalize the real data by the outcomes of simulations and show them in Fig. 2. There is a surplus of
detections around
mHz, which closely matches the spread and location of the power
excess determined from numerous independent spectroscopic runs (see Leccia et al. 2007, and
references therein).
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Figure 2:
The numbers (![]() ![]() ![]() ![]() ![]() |
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Further testing brings even more encouraging results. We select a prominent feature at f=1.072 mHz (Table 1
and Fig. 1) and search for a comb-like pattern
(Kjeldsen et al. 1995) in the immediate vicinity of the peak. Scanning the adjacent region with
mHz steps, we find a maximum response at f=1.0726 mHz (Fig. 3), related to the large
frequency separation of
mHz, in good agreement with
mHz consistently provided by all previous spectroscopic campaigns (Eggenberger et al. 2004; Martic et al. 2004; Leccia et al. 2007).
The clear presence of a regularly-spaced signal in the MOST-2004 data was noted on multiple
occasions:
mHz (Régulo & Roca Cortés 2005),
mHz (Matthews, priv. comm. 2005; see also the detailed simulations by Baudin et al. 2008). Can the regular spacing
of signals be caused by an unaccounted component of the stray light contributing to the
orbital harmonics with 0.0548 mHz separation? Probably not, as the newly derived
is more than sufficiently distanced from the instrumental component. Moreover, we find only a very weak trace of the instrumental signal in the comb-generated response at f=1.0726 mHz and its complete lack at f=1.6424 mHz (Fig. 3: note that f=1.6424 mHz matches an orbital harmonic).
Table 1: Detected p-modes.
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Figure 3:
The comb-response functions obtained for the central frequencies f=1.0726 mHz (full line), f=0.9158 mHz
(dashed line) and f=1.6424 mHz
(dashed line, offset for clarity).
The tallest peak corresponds to a large separation
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The presence of a regular ``comb'' of periodic signals around f=1.072 mHz prompted the final step of the
analysis. We compiled a list of frequencies presumably related to p-modes (Eggenberger et al. 2004; Martic et al. 2004;
Leccia et al. 2007) and searched for corresponding significant peaks in our 2004+2005 AS. We limited our search to the immediate
surroundings of the published frequencies, i.e., to the
mHz intervals, where
is an uncertainty related to frequency resolution
in the AS derived on
1 week-long runs. Note that a formal
frequency resolution in the combined 2004+2005 AS reaches
mHz. We recorded the maxima which were very close to, or above, the corresponding
levels for the given frequencies. Facing the rapidly rising level of instrumental+intrinsic (granulation?) noise,
we disregarded all positive detections with frequencies below f=0.7 mHz.
We also eliminated all positive detections (4 cases) which matched high harmonics
of the orbital period and their 1/d side lobes. We present the results in Table 1,
where in parentheses we retain some prominent signals despite their relatively large
deviations from the published frequencies. As a reference, we provide the
amplitudes of signals in the separate subsets from 2004 and 2005, even if they do not exceed detection limits.
We compare our positive 2004+2005 detections with signals
exceeding (or being reasonably close to) the detectability limits in the previously published MOST-2004 data
(Matthews et al. 2004),
finding
of positive matches, both in frequency and amplitude. On average, one may expect
(
20 in total) noise-generated signals exceeding the imposed
threshold
in an 0.1 mHz-wide bin placed in the region of interest,
f=0.7-1.6 mHz. Hence, the chance for an
accidental match between a noise-generated peak and a pre-determined signal
registered in the previous spectroscopic campaigns (Eggenberger et al. 2004; Martic et al. 2004) is
,
i.e., at least 50% of the frequencies provided in Table 1 should be geniune. The 16 signals identified as
p-modes,
plus 20 noise-generated peaks do not account for all positive detections, 46 signals in the
f=0.7-1.6 mHz range. The origin of the 10 remaining peaks is unclear.
The average amplitude of the recovered signals,
ppm, closely matches the
ppm level inferred from the ground-based spectroscopy (Leccia et al. 2007) and
ppm upper
limit from WIRE photometry (Bruntt et al. 2005). Such low-amplitude signals were inevitably swamped by instrumental noise in the
previous reduction of the stand-alone data from 2004 and 2005. The unusually low level of the
detected signals may be related to the anticipated short life-time of the modes,
d
(Leccia et al. 2007). Indeed, one may re-shuffle the original 2004-2005 MOST data and add
16 sinusoidal signals with the frequencies matching the identified p-modes from Table 1. For simplicity, we assign to the signals the same amplitude
and lifetime L, let the phases of the signals vary randomly, then calculate the resulting ASa and
show them in Fig. 1. In both shown cases,
ppm, L=7 days, and
ppm, L=3 days, one may detect up to
of the artificial signals. The
ppm case provides the
average amplitude
ppm, and
ppm case results in
ppm and a slightly
better detection rate, thus proving the starting assumption about the short lifetime
of the modes. On the other hand, the relative low signal/noise ratio of the data and, presumably,
interaction of the stochastically excited modes affects
the derived frequencies of artificial signals (
):
mHz, to be compared to the formal frequency resolution
mHz in the combined 2004+2005 data.
Recently Bedding (2007, priv. comm.;
see also Kjeldsen & Bedding 1995)
brought to our attention two effects which may influence the estimate of
amplitudes of the detected p-modes. Namely, the [frequency-dependent] instrumental noise may lead to a systematic over-estimate of amplitudes of the real signals. On the other hand, the presumably short life-time of the detected modes (as compared to the length
of the MOST observations)produces Lorentz-broadened profiles, thus leading to under-estimated
amplitudes. These effects can be accurately evaluated (and thus, disentangled) if: (a) the signals are detectable at a high signal-to-noise ratio, ;
(b) the instrumental noise can be treated as [practically] frequency-independent
in any narrow (
0.1 mHz) frequency interval and, more importantly,
such noise can be treated as stationary (time-independent). Neither one applies to the MOST data,
hence we provide uncorrected estimates of amplitudes.
To investigate the impact of these effects, we constructed an average, normalized profile from the signals related
to the positive detections of p-modes (Table 1) and smoothed it
via 2-point binning. One may compare this profile with an average profile of noise-related
signals, which were selected from the immediate
vicinities of the signals related to p-modes. In addition, these noise-related peaks
closely match the amplitudes of the mode-related signals. There is a noticeable
pedestal which is related to the
instrumental noise. There is also
some, rather marginal, [Lorentz-related?] broadening of the p-mode profile, in accordance with
expectations. However, severe blending problems related to low S/N levels
make impractical any precise evaluations of the broadening.
With these effects working in opposite directions,
we conclude that the derived average p-mode amplitude, a=5.8 ppm, may carry a substantial
uncertainty,
1.0-1.5 ppm (i.e. twice the formal,
0.6 ppm, value) and may be considered as an upper limit for mode detection in these data.
Acknowledgements
The author is grateful to the MOST team for making the Procyon data available through the Canadian Astronomy Data Centre (CADC; operated by the Hertzberg Institute of Astrophysics, national Research Council of Canada). Numerous suggestions of the anonymous referee helped to improve presentation of the results.