New Limit on the P-Mode Oscillations of Procyon
by Fourier Transform Seismometry

J.P. Maillard, B. Mosser

IAP (CNRS, UPR 341) 98bis blvd Arago, F-75014 Paris
Electronic-mail: maillard@iap.fr

and

D. Mekarnia, J. Gay

Département Fresnel (CNRS, UMR 6528)
Observatoire de la Côte d'Azur BP 4229
F-06304 Nice cedex 4

Abstract:

The Fourier transform spectrometer (FTS) has been used as a stellar accelerometer in a new seismometric mode. One fringe at a selected path difference of the interferogram, produced by the flux of a star through a bandpass chosen in the near infrared, is continuously scanned. The phase is measured and translated directly into velocity. Observation of Procyon at CFHT in February 1998 in this mode led to a seismological spectrum with a 1-$\sigma$ noise beyond 0.8 mHz as low as 12 cm.s$^{-1}.\mu\hbox{Hz}^{-1/2}$. Even with this noise level, in a single site observation, no firm detection of p-modes can be reported. A limit of 1 m.s^-1 on the amplitude of the modes can be deduced, consistent with models. The signature of a significant regular pattern in the spectrum with a splitting of 53 $\mu$Hz was extracted, interpreted as the large splitting between modes, indication that a signal of stellar origin has been likely detected.

Introduction

  Claims of a positive detection of p-mode oscillations of solar-like stars, and in particular on Procyon, a bright F5 IV-V star, have been already made by Gelly et al. (1986), Brown et al. (1991) and Innis et al. (1991), but none of them is convincing. This challenge justifies the test of a new observational method which is described in Section 2. Observations and data analysis are given in Section 3. Section 4 is devoted to the presentation of results which are discussed in section 5, in comparison with previous results and with theoretical predictions.

Principle of the Observational Method

  The principle of Fourier Transform seismometry, already presented in Mosser et al. (1993) and generalized by Maillard (1996) consists of searching for the Doppler signal not directly in the spectrum of an object, but in its interferogram produced by the FTS. Then, working in the Fourier space makes it possible to benefit of a multiplex advantage, which in this case means, to add in a measurement the contribution of several lines simultaneously. In practice, a fringe of the interferogram generated by all the lines contained within the bandpass of a filter placed in front of the detectors is selected. This fringe will be shifted by the changes of frequency of the lines induced by a Doppler effect. The measurement consists of determining accurately this shift which can be expressed as a phase variation. The advantage of the method rests on the stability of a metrologic laser, that allows to control the path difference between the two arms of the FTS with a precision better than a few nanometers. The phase of a given fringe of the interferogram relative to a fixed sinusoidal reference is simply defined by :  

$${\varphi\over2\pi}\ =\ \sigma_0 \delta\ {v \over c}$$ (1)

with $\varphi$ the phase, v the velocity, $\sigma_0$ the mean wavenumber (cm^-1) of the incoming spectral range and $\delta$ (cm) the working path difference. The advantages of this methods are mainly:

• the determination of the phase is independent of the fringe amplitude. Then, the phase measurement is to a large extent not affected by photometric changes of the source intensity,
• the detection sensitivity is constant and not affected by additional low frequency drifts,
• the velocity signal is directly calibrated as all the factors between the phase and the velocity are perfectly determined.

This new seismometric method was applied on Procyon with the CFHT-FTS (Mosser et al. 1998).

Observations and Data Reduction

A set of 4.5 consecutive nights of observation was obtained in the first half of February 1998, so that a total of 38 hours of observations was reached over a time span of $\sim$ 100 hours, translating into a temporal resolution of 2.8 $\mu$Hz. A filter with a FWHM of $\sim$ 100 cm^-1 isolating a dozen of stellar lines (mostly SiI lines), around 1.072 $\mu$m was placed in front of the InGaAs diodes, as they offer the best quantum efficiency in the very near-infrared. The tank housing the FTS was put under vacuum, in order to cancel any turbulence on the interferometric light path. The selection of the fringe is made by looking in the interferogram for a fringe with a high contrast and a large path difference to increase the interferometric gain $\sigma_0 \delta$. As the fringe contrast tends to decrease with $\delta$, an optimum value does exist which was of the order of 1 cm for the Procyon observations. The data acquisition consists of scanning step-by-step the selected fringe back and forth and recording repeatedly a sample of 16 points along it. The integration time $\delta t$ was chosen equal to 1 s. This tight sampling is obtained by using the elementary step of the FTS, namely $\lambda_{\mathrm{ref}} / 8$, with $\lambda_{\mathrm{ref}}$ the red wavelength in vacuum of the helium-neon metrologic laser. The amplitude and the phase of the fringes are determined by using a least square fit method on each recorded fringe.

Results

The final Fourier power spectrum (Fig. 1) obtained from the concatenation of all the series of data is composed of two parts : The low frequency domain, up to 0.7 mHz, dominated by a noise component varying as $1/\nu^{2.9}$ and the high frequency part which corresponds to a white noise with an equivalent velocity of 12 cm.s$^{-1}.\mu\hbox{Hz}^{-1/2}$. The highest peaks reach the 0.4 m.s^-1 level. There is no evidence for any obvious excess power in the frequency range around 1 mHz, where p-modes are expected from Kjeldsen and Bedding (1995) and where detections were claimed by Brown et al. (1991) and Bedford et al. (1995). We also made use of the search for a ``comb response'', a method proposed by Kjeldsen et al. (1995) in order to search for regularity in the power spectrum, namely to search for a comb-like pattern around the greatest peaks identified in the power spectrum. This method was successful and gave a recurrent signature with a splitting of 53 $\mu$Hz in the frequency range [0.8, 1.2 mHz] where the seismological signal is expected. No response was found outside.

 

Figure 1:   The spectrum in a log-log scale of the raw data, prior to any filtering of the low frequencies. Only an apodisation of each time series by a Hanning function was applied to avoid steps at the beginning and the end of each night.

In order to infer a maximum value for a possible oscillation pattern from the data a simulation was made with an artificial signal corresponding to a plausible oscillation spectrum of Procyon based on an asymptotic development, with an amplitude dependence function of the frequency and the degrees $\ell$ scaled to the solar one: $\nu_{n,\ell} \propto [n+\ell /2]\ \Delta\nu +2\hbox{nd}$ order term. A level of 1 m.s^-1, taking into account the window function which divides by $\sim$ 3 the observed amplitude of the peaks, is necessary to be compatible with the power detected in the frequency range [0.8, 1.2 mHz].

Discussion

The upper limit on the mode intensity we obtain is in agreement with the expected amplitudes of 1.11$\pm$0.17 m.s^-1 theoretically predicted by Kjeldsen and Bedding (1995). If this new limit does not put an additional constraint on the excitation model it can be considered as reliable from the accurate velocity calibration of the method. This amplitude can be compared to previous results. Levels as low as 0.5 m.s^-1 have been proposed by Brown et al. (1991), based on fiber-fed échelle spectrograph measurements which cannot be ruled out, but the detection reported by Bedford et al. (1995), with amplitudes higher than 3 m.s^-1 can be totally rulled out. We should have seen unambiguously the signature of such high-amplitude p-modes.

The signature at 53 $\mu$Hz is quite compatible with the theoretical value of the large splitting computed by Kjeldsen and Bedding (1995) who give for Procyon value of $\Delta\nu \simeq$ 54 or 59 $\mu$Hz, depending on the stellar mass introduced in the model. These results are in contradiction with Gelly et al. (1986) and Brown et al. (1991), as we do not see any signature for the large splitting neither at 79 $\mu$Hz nor at 71 $\mu$Hz. In any case, the detection of this signature is currently the best indication that a signal of stellar origin has likely been detected.

Conclusions

From the above results it seems that a gain of a factor 2 or 3 in sensitivity should lead to a final detection of the oscillation spectrum of Procyon. A factor of 3 is simply lost due to single site observation. A network which is not an easy operation to realize is required. On top of that, a gain of a factor 2 is possible if working with the FTS in the visible. Changes in the data acquisition parameters could also improve the signal-to-noise ratio of the fringes. Therefore, this long-awaited detection of Procyon's oscillations is no longer out of reach.