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Astron. Astrophys. 348, 627-635 (1999)

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4. Results and discussion

The GOLF signal and the MDI LOI-proxy velocity signals with and without spatial masking are compared in the following subsections. The comparison is for a continuous sequence of 759 days for the period of May 25, 1996 through June 22, 1998.

4.1. Power spectra comparison

The power spectra of LOI-proxy and GOLF-sim are very similar. The ratio of the two power spectra are shown in Fig. 4, which exhibits an enhancement of the GOLF-sim signal in the 5-minute band. The power spectra for the GOLF and the spatially masked MDI velocity signals are shown in Fig. 5. For the LOI-proxy, north-south and GOLF-sim signals the power in the 5-minute band is below that observed from GOLF. This power difference is expected since velocity scales with atmospheric height and GOLF observes at an altitude above MDI. The MDI central region signals have additional power from higher degree modes, which accounts for the increased power observed from these signals compared to GOLF in the 5-minute band.

[FIGURE] Fig. 4. Ratio of the velocity power spectra of GOLF-sim relative to LOI-proxy for a 759 day period: May 25, 1996 through June 22, 1998. The power spectra are averaged for 100 bins evenly spaced in log frequency over the range shown above.

[FIGURE] Fig. 5. Comparison of the GOLF power spectra and the MDI LOI-proxy velocity power spectra with and without spatial masking for a 759 day period: May 25, 1996 through June 22, 1998. Each power spectrum is averaged for 100 bins evenly spaced in log frequency over the range shown above.

For frequencies above the 5-minute band, the differences between the power spectra are quite noticeable. Between the MDI signals, the overall reduction in instrumental noise for the zero-sum masked signals is readily evident in the north-south and the central zero-sum signals shown in Fig. 5. The source of this instrumental full-disk signal is believed to be due to variations in the shutter effective open duration when a major frame pulse occurs during exposure (Scherrer 1997).

In addition to the reduction of the shutter background noise, the zero-sum masked signals have nearly no contribution from the [FORMULA] modes. The power spectra of the north-south signal is further reduced relative to the other signals since the spatial masking filters out the sectoral modes.

The difference between the GOLF and MDI power spectra for frequencies below the 5-minute band, near 1500 µHz, is also quite noticeable in Fig. 5. The MDI zero-sum masked signals have the lowest background power in this region. The MDI LOI-proxy and GOLF-sim power is above the zero-sum signals due to the shutter background noise. The power in the GOLF and central region signals is higher near 1100 µHz which is most likely due to contribution from granulation.

In Fig. 6 the ratio of the power spectra illustrates the differences in the background power as observed by MDI and GOLF. Most of the variation between the MDI signals shown in Fig. 6 is a result of the shutter noise background. The GOLF signal relative to the MDI signals with a zero-sum spatial mask exhibits a broad band excess centered near 1000 µHz ([FORMULA]16 minutes) and a strong broad band excess centered near 5700 µHz ([FORMULA]3 minutes). These two power bands in the GOLF signal relative to MDI are similar to the ratio of the GOLF spectra reduced from one-wing data relative to two-wing data during the period when GOLF observed both wings of the Na D lines (e.g. Gabriel et al. 1997 and Henney et al. 1998b). In earlier comparisons between GOLF and MDI velocity power spectra, the 16-minute and 3-minute broad band power difference were reported by Scherrer (1997), García (1997) and Henney et al. (1998b). The substantial difference shown in the power ratio near 5700 µHz in Fig. 6 is most likely the result of intensity-like contributions from chromospheric oscillations (e.g. Noyes 1966). In Fig. 6, the GOLF power spectra bulge centered near 1000 µHz may be the result of velocity and intensity contributions from granulation overshoot (e.g. Harvey et al., 1993). Notice in Fig. 6 that within the frequency band of 1800 to 4000 µHz, the power spectra ratio of GOLF relative to the zero-sum signals along with the central region signal are at a local minimum.

[FIGURE] Fig. 6. The log of the power spectra ratio of the GOLF and MDI signals for a 759 day period: May 25, 1996 through June 22, 1998. Each power spectrum is averaged for 100 bins evenly spaced in log frequency over the range shown above.

In the frequency range of interest for g-modes, below 500 µHz, the power of the GOLF signal is at least twice the power of the MDI signals, except for the central zero-sum signal. Although the nature of this difference is currently uncertain, it may be produced by a combination of the altitude difference in the solar atmosphere observed by the two instruments and intensity contribution from supergranulation. In addition, the lack of an absolute calibration for the signals investigated in this work may play an important role in this comparison. The closer agreement between GOLF and MDI signal is achieved when the central zero-sum spatial mask is used, in particular at frequencies below 300 µHz. A cross analysis of these two signals may be useful for verification of future g-mode candidates.

4.2. Signal-to-background comparison

A detailed comparison of the GOLF and the MDI power spectra for low degree modes ([FORMULA]) is shown in Fig. 7. Notice the enhanced signal amplitude for the [FORMULA] acoustic mode between the GOLF and the MDI north-south and central region masked data in Fig. 7. As a relative measure of merit for each time series, the signal-to-background ratio, [FORMULA], for modes within the frequency range 1200-2100 µHz are compared here. The signal is defined as the sum of the mode multiplet amplitude, [FORMULA], and the background, c, from the fit of the power spectra using Eq. (5). For each power spectrum, except the north-south masked signal, the multiplet pairs for the sectoral modes of degree [FORMULA] are compared in Fig. 8. The north-south signal is not compared here since it is primarily comprised of zonal and tesseral modes (see Fig. 7). The [FORMULA] results shown in Fig. 8 are obtained from the power spectra fitting procedure described in Sect. 3.3.

[FIGURE] Fig. 7. The GOLF power spectra along with the MDI LOI-proxy velocity power spectra with and without spatial masking for a 759 day period: May 25, 1996 through June 22, 1998. The clearly noticeable acoustic modes in the central region panel, from left to right, are: [FORMULA] and [FORMULA]. Note that the north-south signal is predominately comprised of [FORMULA] odd modes. In addition, note that a [FORMULA] mode is detectable visible near 1685 µHz in the bottom three panels.

[FIGURE] Fig. 8. Comparison of low frequency acoustic mode signal-to-background ratios ([FORMULA]) for different MDI masked signals with the GOLF signal. The [FORMULA] are compared for the sectoral acoustic modes of [FORMULA] (top left ), [FORMULA] (top right ), [FORMULA] (bottom left ) and [FORMULA] (bottom right ). The [FORMULA] values for LOI-proxy (solid), GOLF-sim (dot), GOLF (dash), central region (dot-dash), and central zero-sum (three dots-dash) are shown. The signal is defined as the mode multiplet amplitude plus the background from the model fit. The error bars are 1[FORMULA] and are only shown for the central region signal for visual clarity and are representive of the estimated errors for the other signals.

For the frequency range and the signals compared in this work, the GOLF signal has the highest [FORMULA] for [FORMULA] acoustic modes. Also illustrated in Fig. 8 is that the [FORMULA] of the GOLF and central region data are both good for detecting [FORMULA] acoustic modes. For [FORMULA] modes, the central region masked signals have the highest [FORMULA] values compared to GOLF, LOI-proxy and GOLF-sim. Between the MDI signals, the GOLF-sim [FORMULA] is found to be slightly systematically higher than the MDI LOI-proxy signal without spatial masking (see Fig. 8). In addition, the GOLF-sim signal has the highest [FORMULA] on average relative to the other MDI signals compared for the l=0 modes shown in Fig. 8.

The [FORMULA] for a given mode may be improved by averaging the GOLF spectra with a corresponding MDI masked spectra. In addition, cross spectral analysis may be useful for the time series with similar signals but different backgrounds due to the different spatial weighting of supergranules. Further [FORMULA] improvements may come from future additions to the GOLF-simulated signal which account for active region effects. Intensity fluctuations associated with magnetic activity produce velocity signal amplitudes as large as [FORMULA]7 m/s with periods on the order of a few days for measurements such as done by GOLF (e.g. Ulrich et al. 1993). To estimate these effects for the observed GOLF signal, the GOLF-simulated signal will incorporate the MDI line-depth images, as a magnetic proxy, along with MDI line-continuum images (e.g. Ulrich et al. 1999). In this way we hope to model and understand the low frequency background power in the GOLF signal associated with magnetic activity. Ultimately we want to match frequencies of agreed signals between the two instruments regardless of predicted mode frequencies.

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© European Southern Observatory (ESO) 1999

Online publication: July 26, 1999