Lockheed-Martin Advanced Technology Center, 3251 Hanover Street, Palo Alto, CA 94304. Received 1998 September 3 ; accepted 1998 December 15.
THE ASTROPHYSICAL JOURNAL, 516 : 939È945, 1999 May 10 ( 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.
OBSERVATIONAL CONSTRAINTS ON MODELS OF THE SOLAR BACKGROUND SPECTRUM TH. STRAUS AND G. SEVERINO Osservatorio Astronomico di Capodimonte, V• a Moiarello 16, I-80131, Napoli, Italy
F.-L. DEUBNER Astronomisches Institut, Am Hubland, D-97074, Wurzburg, Germany
B. FLECK ESA Space Science Department, NASA/GSFC, Greenbelt, MD 20771
S. M. JEFFERIES National Solar Observatory, P.O. Box 26732, Tucson, AZ 85726
AND T. TARBELL Lockheed-Martin Advanced Technology Center, 3251 Hanover Street, Palo Alto, CA 94304 Received 1998 September 3 ; accepted 1998 December 15
ABSTRACT We discuss the properties of the solar background signal as observed in high-quality, l [ l power and phase di†erence spectra of the continuum (C), velocity (V), and line intensity (I) Ñuctuations of the Ni I 6768 A line. These spectra were generated from high-resolution images acquired by the Michelson Doppler Imager on board SOHO. We conÐrm that the background signal in the velocity power spectra can be reproduced by a composite model with two quasi-stationary components, describing large-scale and small-scale convective motions, and a periodic component. The line and continuum intensity power spectra require additional quasi-stationary and periodic components. The extra quasi-stationary component dominates the intensity and continuum background signals over the spectral region where the I[V phase di†erence spectra show essentially constant negative phase di†erence : i.e., below and in between the p-mode ridges (called the plateau-interridge regime by Deubner et al.). Since the I[V phase between the p-mode ridges is not random, the solar background beneath the p-modes must be considered as coherent. We thus speculate that the negative phase regime may be the manifestation of a correlated background. Such a background has been proposed to explain the opposite sense of the asymmetries of the p-mode line proÐles in velocity and brightness oscillations. Subject headings : convection È Sun : atmosphere È Sun : granulation È Sun : oscillations 1.
INTRODUCTION
types of investigation are complementary and should be combined to provide a model for the solar background that includes both amplitude and phase information. In doing so, we will attain a better understanding of the nature of the solar background signal and its interaction with the pmodes. The present study is a Ðrst step in this direction.
The concept of a ““ background ÏÏ component in solar oscillation spectra was Ðrst used by Harvey in 1985 to estimate detection limits for the low-frequency, low-degree, pand g-modes. HarveyÏs background modelÈwhich empirically describes the oscillation power spectrum at frequencies below and between the p-modes in terms of contributions from quasi-stationary and periodic perturbationsÈwas originally used with unimaged, fulldisk data. The model has since been successfully applied to the power spectra of intensity and velocity signals originating at di†erent heights in the atmosphere, both for unimaged and full-disk resolved data (see e.g., Harvey et al. 1998 ; Palle` et al. 1995 and references therein). In addition to helioseismic studies, high-spatial resolution observations are frequently used to study the dynamics of the solar atmosphere. One of the foundations of this latter type of research, is the use of the phase relations between di†erent simultaneously measured parameters. In particular, phase di†erence spectra in the k [ u domain have especially contributed to improving our knowledge of the solar atmosphere (e.g., Cram 1978 ; Kneer & Von Uexkull 1985 ; Deubner et al. 1992 ; Deubner, Waldschik, & Ste†ens 1996). Obviously, phase relations can provide information on the background signal that is not available in a power spectrum analysis. We therefore propose that the above two
2.
OBSERVATIONS AND DATA REDUCTION
A 15 hr time series of simultaneous spectroscopic measurements of the continuum intensity, Doppler shift, and line depth in the Ni I 6768 A line, at disk center of the quiet sun has been obtained during a guest investigator campaign with the Michelson Doppler Imager (MDI, see Scherrer et al. 1995). The overall duty cycles of the observations are 98% for the velocity and line depth, and 99% for the continuum intensity data. In addition to the directly measured parameters, the line intensity has been calculated as the di†erence of continuum intensity and line depth. Due to telemetry limitations, the Ðeld of view of the detector is restricted to 400@@ ] 400@@. MDI is programmed to follow a region by shifting the CCD readout area by 1 pixel every 4 minutes. Small residual shifts left by this raw compensation of solar rotation have been removed during the data analysis. Due to the shift of the CCD readout area, we Ðnd artifacts in the Fourier transforms of the continuum and line intensity which are sensitive to Ñat-Ðeld errors. These artifacts are limited to a diagonal line in the l [ l diagram, 939
940
STRAUS ET AL.
which corresponds approximately to a ““ virtual ÏÏ horizontal velocity of the Ñat-Ðeld errors of 1/4 pixel/frame. The longterm contributions of the line-of-sight component of solar rotation to the velocity signal, and the center-to-limb variation for the intensity signals were removed by (1) Ðtting a second-order surface to each frame, (2) lowpass Ðltering the Ðt parameters, and (3) removing the lowpass Ðltered time series of the surface Ðts from each parameter set. The cleaned continuum intensity (C), line intensity (I), and velocity (V ) time series were then subjected to a threedimensional Fourier transform, to produce l [ l power, cross power, phase di†erence, and coherence spectra. 3.
RESULTS AND DISCUSSION
3.1. T he Background in Power Spectra In order to describe the temporal power spectra at low frequencies and to approximate the background beneath the p-modes, a composite model with components of type 1 (1) 1 ] [2nq(l [ l )]a 0 is commonly used (e.g., Harvey et al. 1993). This model was initially intended to predict the power of the solar background from estimates of the componentÏs lifetimes q and rms contributions. It has since been used to Ðt observed power spectra and to determine the properties of each component (e.g., Jimenez et al. 1988). Among the contributions of type (1), one can distinguish oscillatory signals, for which we hereafter Ðx the exponent a to 2, and quasi-stationary signals, for which the frequency l is deÐned to be zero. 0 properties of the backWe have investigated the spatial ground by applying the Harvey model to a wide range of l-values ; from l B 150 up to very high values (l B 4000), where essentially only the background signal is observed. The spatial behavior of the background, in addition to its timescales, which are described by the Harvey model, is as important for the interpretation of the di†erent components as their variation over di†erent heights in the atmosphere. We shall not discuss the variation of the background with height, as the MDI data contain information only on the heights where the continuum and the Ni line are formed. Using the Harvey model, we succeed in describing the high-resolution MDI velocity data over the entire range of l-values covered by the observations. The temporal velocity power spectra can be reproduced by a three-component model (two convective and one oscillatory components), varying with spherical harmonic degree l as shown in Figure 1. The Ðt parameters are summarized in Table 1. The highest l spectra (above l B 4000) show only one convective component and a very weak oscillatory signal at l B 4.2 mHz. A second nonperiodic component rises at very low frequencies and lower l-values. According to their spatial and temporal behavior the three components in the velocity data can be identiÐed as : (1) small-scale convective motions with a time constant q B 400 s and a rms contribution peaking around l B 1500, (2) large-scale convective motions with a time constant q up to approximately 4 hr, and a rms contribution peaking below l B 150, and (3) a power ““ bump ÏÏ centered around l B 4 mHz. Several interpretations of the power bump below the p-modes can be given, including oscillatory signals (e.g., resonant and nonresonant oscillations of the atmosphere), coherent downward scattered oscillations (Deubner et al. 1992 ; Marmolino et P(l) D
Vol. 516
al. 1993), the e†ects of the spatial leakage (*l B 15 in our case), the merging of the p-mode wings in frequency, or a combination of these. Further investigations are necessary to clarify the nature of the bump. It is important to note that the oscillatory contribution changes strongly in width and drifts slightly in frequency with varying l (the lowest central frequency of approximately 3 mHz occurs at l B 500). It may also be asymmetric about its maximum. The background behaves quite di†erently in the brightness (C, I) oscillations (see Fig. 1). In fact, in addition to the three components present in the velocity power spectra, a further low-frequency component and a second higher frequency oscillatory signal are needed to describe the C and I power spectra. Both are most prominent at low l-values, whereas the high l continuum power spectra scale almost like velocity (see Fig. 1). The central frequency of approximately 5 mHz identiÐes the oscillatory component as the atmosphereÏs characteristic response at 3 minutes. Its absence in the continuum (C) signal further supports this interpretation. The low-frequency component, on the other hand, called hereafter ““ plain, ÏÏ is present in both I and C and dominates the background in the lower l spectra at frequencies between the Lamb mode and approximately 3 mHz. It can be described by a nonperiodic signal, but due to its poor deÐnition and the uncertainty about its physical origin, a periodic function can not be fully excluded. The plain component is clearly visible as the spreading of the contours of equal intensity power into the p-mode area in the l [ l plane (see Fig. 2). A similar component is not observed in velocity. 3.2. T he Background in Phase Spectra In the previous section we discussed the di†erence of the background behavior in the velocity and intensity power spectra. Obviously, the phase behavior of the background signal contains additional information that should be used in any model for the solar background. Spatiotemporal phase di†erence spectra in the k [ u diagram have already been exploited to identify phenomena in the solar atmosphere by their dynamical behavior. The general appearance of these phase di†erence spectra between the intensity and the velocity Ñuctuations (hereafter called I[V 1) is now conÐrmed by the MDI data (see Fig. 3). Detailed interpretation of the phase spectra is still awaiting predictions based on a fully compressible treatment of the convective and wave phenomena in a realistic solar atmosphere. We give only a short summary of the various phase regimes evident in Figure 3, helpful for further reading (refer to the labels in the Ðgure) ; a more detailed discussion of this diagnostic can be found in Straus et al. (1998b and references therein) : (1) the ridges of the p-modes showing positive I[V phase values ; their pseudo mode counterparts can be followed up to the Nyquist frequency of 8.3 mHz ; (2) the intermediate, low-power ““ plateau ÏÏ regime (Deubner et al. 1990), which shows negative I[V phase and extends from above the Lamb mode to the region between the ridges ; (3) a regime of positive I[V phase below the Lamb1 The opposite convention V [I has often been used in the past, but the convention used here might be preferred (see Masiello, Marmolino, & Straus 1998) Velocity is considered positive if directed upward, i.e., a phase di†erence I[V \ 90¡ corresponds to a maximum intensity signal a quarter of the period before maximum upward velocity.
SOLAR BACKGROUND SPECTRUM OBSERVATIONS
a)
= 500
100.00
10-6
V power [m2 s-2]
10.00
941
I
convection large sc. small sc.
10-7
"plain"
1.00
10-8
0.10
10-9
power [%2]
No. 2, 1999
"bump" 10-10
0.01 0.1
1.0 ν [mHz]
b)
0.1
1.0 ν [mHz]
V
C
I
log power [arb. unit]
150 200 300
x 10
500
1000 1500
2000 3000
2
3800 0
2
4 6 ν [mHz]
80
2
4 6 ν [mHz]
8
FIG. 1.ÈSolar background in temporal power spectra : (a) Observed power and components of the Harvey model for the spherical harmonic degree l B 500 determined in velocity (left panel ) and line intensity oscillations (right panel ). (b) Observed power of the velocity (left panel ) and brightness oscillations in the continuum and line intensity (right panel ) as a function of l. The approximate l-values are given on the right side (the resolution of our data corresponds to *l B 15). The diagonal lines mark the approximate frequency of the f-mode as a function of l. The solid lines in the left panel represent the background Ðts obtained with the Harvey model. The lighter lines, which mark each component of the Ðts, have been truncated for easier reading of the Ðgure. The total velocity Ðts have been copied into the right panel (dashed lines) using an unique scaling factor, in order to demonstrate the di†erences of the solar background observed in velocity and brightness oscillation. While at the highest spherical harmonic degrees the power spectra of velocity and continuum match quite well, at lower l-values the background beneath the p-modes is ““ Ðlled up ÏÏ more and more by the plain component (see text for a detailed discussion).
mode that has been attributed to internal gravity waves in the atmosphere (Deubner et al. 1992 ; Straus & Bonaccini 1997) ; (4) a nearly zero I[V phase regime dominated by the slow convective motions ; this regime is limited to
spatial wavenumbers less than 5.5 Mm~1. Two other regimes (labeled ““ 5 ÏÏ and ““ 6 ÏÏ in Fig. 3), which show anticorrelation between V and I and merit further attention, have been attributed to the magnetic network dynamics
942
STRAUS ET AL.
Vol. 516
TABLE 1 FIT PARAMETERS OF THE HARVEY MODEL (SEE EQ. [1]) VELOCITY V
l 150 . . . . . . .
200 . . . . . . .
300 . . . . . . .
500 . . . . . . .
1000 . . . . . .
1500 . . . . . .
2000 . . . . . . 3000 . . . . . . 3800 . . . . . .
CONTRIBUTION SSCMa LSCMb plain bump 3 minute SSCMa LSCMb plain bump 3 minute SSCMa LSCMb plain bump 3 minute SSCMa LSCMb plain bump 3 minute SSCMa LSCMb plain bump 3 minute SSCMa LSCMb plain bump 3 minute SSCMa LSCMb SSCMa LSCMb SSCMa LSCMb bump
CONTINUUM C
INTENSITY I
q (s)
l 0 (mHz)
a
rms (m s~1)
q (s)
l 0 (mHz)
a
rms (%)
3.9 ] 102 9.9 ] 103 ... 4.3 ] 102 ... 3.8 ] 102 1.2 ] 104 ... 2.7 ] 102 ... 5.7 ] 102 1.5 ] 104 ... 1.6 ] 102 ... 4.5 ] 102 2.7 ] 103 ... 1.1 ] 102 ... 4.8 ] 102 1.9 ] 103 ... 1.3 ] 102 ... 4.0 ] 102 1.9 ] 103 ... 1.5 ] 102 ... 3.1 ] 102 1.9 ] 103 2.6 ] 102 ... 1.9 ] 102 ... 1.2 ] 102
... ... ... 3.32 ... ... ... ... 3.23 ... ... ... ... 3.13 ... ... ... ... 3.04 ... ... ... ... 3.50 ... ... ... ... 4.15 ... ... ... ... ... ... ... 4.18
2.75 3.00 ... 2.00 ... 2.75 3.00 ... 2.00 ... 2.75 3.00 ... 2.00 ... 2.75 3.00 ... 2.00 ... 2.75 3.00 ... 2.00 ... 2.75 3.00 ... 2.00 ... 2.75 3.00 2.75 ... 3.00 ... 2.00
2.38 10.9 ... 10.3 ... 3.16 7.80 ... 10.4 ... 3.57 6.25 ... 8.50 ... 5.19 4.40 ... 8.02 ... 8.98 2.47 ... 5.55 ... 9.17 2.18 ... 3.46 ... 7.62 1.60 5.89 ... 3.83 ... 0.928
2.5 ] 102 1.9 ] 103 75. 1.6 ] 102 ... 2.5 ] 102 1.9 ] 103 78. 1.6 ] 102 ... 2.5 ] 102 1.9 ] 103 75. 1.4 ] 102 ... 2.5 ] 102 1.9 ] 103 75. 1.4 ] 102 ... 3.9 ] 102 1.9 ] 103 75. 1.4 ] 102 ... 4.5 ] 102 1.9 ] 103 75. 1.7 ] 102 ... 4.6 ] 102 ... 2.6 ] 102 ... 1.9 ] 102 ... 1.7 ] 102
... ... ... 3.32 ... ... ... ... 3.32 ... ... ... ... 3.69 ... ... ... ... 3.69 ... ... ... ... 3.69 ... ... ... ... 4.18 ... ... ... ... ... ... ... 4.18
3.00 3.00 5.00 2.00 ... 3.00 3.00 5.00 2.00 ... 3.00 3.00 5.00 2.00 ... 3.00 3.00 5.00 2.00 ... 2.75 3.00 5.00 2.00 ... 2.75 3.00 5.00 2.00 ... 2.20 ... 2.75 ... 3.00 ... 2.00
0.0625 0.0350 0.0628 0.0241 ... 0.0708 0.0350 0.0689 0.0241 ... 0.0807 0.0350 0.0753 0.0222 ... 0.100 0.0350 0.0929 0.0222 ... 0.106 0.0247 0.0785 0.0222 ... 0.0989 0.0564 0.0566 0.0165 ... 0.0877 ... 0.0649 ... 0.0426 ... 0.00823
q (s) 2.3 7.3 86. 3.1 1.6 2.3 7.3 86. 3.1 1.4 2.3 7.3 83. 3.1 1.2 2.2 1.6 78. 3.1 1.2
] 102 ] 104 ] ] ] ]
102 102 102 104
] ] ] ]
102 102 102 104
] ] ] ]
102 102 102 104
] ] ... 8.6 ] 86. 1.6 ] 1.6 ] ... 2.7 ] 69. ... 1.2 ] ... 6.0 ] ... 3.4 ] ... 2.7 ] 61.
102 102 103 102 102 103
102 102 102 102
l 0 (mHz)
a
rms (%)
... ... ... 3.32 4.89 ... ... ... 3.32 5.16 ... ... ... 3.32 5.35 ... ... ... 3.32 5.53 ... ... ... 2.95 5.90 ... ... ... ... 5.90 ... ... ... ... ... ... 3.87
4.00 1.40 6.00 2.00 2.00 4.00 1.40 6.00 2.00 2.00 4.00 1.40 5.00 2.00 2.00 4.00 2.50 5.00 2.00 2.00 ... 1.40 4.00 2.00 2.00 ... 1.40 4.00 ... 2.00 ... 1.40 ... 1.40 ... 1.40 2.00
0.0822 0.136 0.0795 0.0442 0.0451 0.0919 0.126 0.0917 0.0338 0.0477 0.101 0.114 0.106 0.0202 0.0497 0.108 0.192 0.129 0.0181 0.0495 ... 0.0576 0.116 0.0268 0.0336 ... 0.0553 0.0800 ... 0.0262 ... 0.0542 ... 0.0398 ... 0.0240 0.0207
a Small-scale convective motions. b Large-scale convective motions.
(Deubner et al. 1992) and to Ðne scale magnetic structures (Straus et al. 1998a), respectively. The present work concentrates on regimes 1 and 2, which are of most relevance to helioseismology studies. Hereafter, we use the term ““ coherent ÏÏ for a signal with a well-deÐned I[V phase. Further, signals that are linked to the p-mode oscillations will be called ““ correlated. ÏÏ Our spectra conÐrm that the p-mode signal is embedded in a region of a di†erent, but constant phase (Deubner et al. 1990 ; Deubner et al. 1992)Èat least at frequencies lower than 3.5 mHz. The phase observed on the p-modes depends strongly on frequency as shown in Figure 2, with the exception of the f-mode. We should stress that the p-mode I[V phase is calculated at the very positions of the power maxima along the ridges. This p-mode I[V phase reaches and exceeds 90¡ (the value theoretically expected in an adiabatic atmosphere) at frequencies above 4 mHz and drops slowly to the value of 0¡ expected for running acoustic waves above the acoustic cuto† frequency. Other than progressive admixture of the plateau regime to the p-mode phases
(Deubner et al. 1990), the drop of the I[V phase at low frequencies has no explanation yet, especially since e†ects of nonadiabaticity should even raise the values of I[V above 90¡. This behavior at low frequencies might also be discussed in relation to the long-standing puzzle of the decreasing p-mode I[V -values with decreasing height in the atmosphere (Tanenbaum et al. 1969 ; Fig. 18 of Hill et al. 1991 and references therein). The l-dependent, well-deÐned phase of the plateau regime (approximately [60¡ above 1 mHz in the case of l B 300 of Fig. 4) returns repeatedly in the interridge space. This return to negative I[V -values, missing only at higher frequencies, makes an interpretation of the velocity power bump mentioned in the previous section unlikely to be totally due to unresolved or merged p-mode power. It must be stressed that the location of the plateau regime, where the I background is dominated by the plain component mentioned in the previous section, supports the hypothesis of a link between the p-mode background and this atmospherical phenomenon. Furthermore, its coherent I[V phase
No. 2, 1999
SOLAR BACKGROUND SPECTRUM OBSERVATIONS
943
FIG. 2.ÈL eft panel : the contours of the background power in the l [ l plane clearly reveal the di†erent behavior in the line intensity (black contours) and the velocity signal (light gray contours). The contours above the Lamb line are the result of an interpolation of the total power spectra based only on the points where the I[V phase di†erence is less than [20¡ (i.e., the plateau regime ; see ° 3.2), and on the positions of local minima of the power above 4 mHz. In this way, the power on the p-modes, whose locations are marked for continuum (blue), line intensities (red), and velocity (green), does not show up in the contours. In addition to the convective signals at high l, the plain component (A), the bump (B), and the 3 minute oscillations (C) can be identiÐed as the main components of the background beneath the p-modes. Furthermore, the p-modes show a deviation at the acoustic cuto† from the extrapolation of their low-frequency trends (solid lines). This bend is strongest in continuum and has nearly the same strength in line intensity and velocity. Right panel : I[V phase values on the f-mode and the low radial order p-modes (the same symbols are used as in the left panel to identify each mode) with respect to the whole range of values (light dots) observed above the Lamb mode. The low-frequency p-mode phases remain below the theoretically expected value (90¡ in an adiabatic atmosphere, or more than 90¡ else). In particular, the f-mode never exceeds phase values of 60¡.
together with the general shape of the transitions from the plateau to the p-mode phase, which looks similar to the shape of the p-mode proÐles (see Fig. 4), strongly indicate the plateau or plain regime as the best candidate for a background correlated to the p-mode signal, like the one that seems to be necessary to explain the asymmetry of the p-modes (Roxburgh & Vorontsov 1997 ; Nigam et al. 1998). We should underline at this point the importance of considering the background as a function of both frequency and degree l for the discussion of several observational facts. It has to be stressed, that the background signal is not necessarily small in respect to the power of the resonant modes. Rather, the background signal becomes the dominant signal for the lower l, low-frequency modes, in particular in intensity. This fact might be a hint to a solution of the above mentioned problem of the p-mode phase values at low frequencies, as they will not reÑect in this case the expected value of a pure evanescent wave but will be reduced as observed by the mixing of background signal with a di†erent phase (see Severino, Straus, & Je†eries 1998 for a quantitative example). The di†erent background levels in intensity and velocity have also to be taken into account for the explanation of a frequency shift of the pseudo modes above the acoustic cuto† frequency as observed in the
medium-l MDI data (Nigam et al. 1998). Nigam et al. again attribute the shift of the pseudo modes in continuum intensity with respect to those in velocity to the presence of a correlated background. We note that this relative shift is observable in our high-resolution data only in the continuum intensity (see Fig. 2). There is no apparent frequency shift between the peaks measured in velocity and line intensity pseudo modes. Nevertheless, the ridges show a bend in all three parameters (see Fig. 2), identically in velocity and intensity, and stronger in the continuum intensity. Hints of a ridge bending have been reported previously for the case of the Na D line (Ste†ens et al. 1995). 1 4.
CONCLUSIONS
We discuss the properties of the solar background, based on high-resolution data obtained from the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO). The background properties are investigated through l [ l power and phase di†erence spectra of the continuum, velocity, and line intensity Ñuctuations in the Ni I 6768 A line. The background in the velocity power spectra can be reproduced by a composite model including two quasi-stationary components describing large-scale and small-scale convective motions, and a periodic com-
FIG. 3.Èl [ l phase di†erence spectra between line intensity and velocity signals (upper left panel ), and between line intensity and continuum (lower left panel ), and the relative coherences. The labeled regions are discussed in the text. The origin of the artifacts, which are most prominent at high l, is discussed in ° 2.
SOLAR BACKGROUND SPECTRUM OBSERVATIONS
100 V
10-2
10-2
I
10-4
(I) power [arb. units]
(V) power [arb. units]
102
C
≅ 300
phase I-V
0.5 100 50
0.0
0
coherence I-V
1.0
-50 0
2
4 ν [mHz]
6
8
FIG. 4.ÈDetailed example of observed power (upper panel ), phase and coherence (lower panel ) as a function of frequency at l B 300.
ponent. However, the line and continuum intensity power spectra cannot be adequately described by this threecomponent model. Here another periodic component (““ plain component ÏÏ) dominates the background beneath the p-modes where the plateau regime with negative I[V
945
phase emerges below and in between the ridges. Further, a second periodic component with a period of 3 minutes is present chieÑy in the line intensity. The general appearance of the I[V phase diagrams measured from ground is conÐrmed by the MDI data, thus negating concerns over phase distortion by e†ects of the EarthÏs atmosphere. We conclude, that the solar background beneath the p-modes must be considered coherent. Any correlated background has necessarily to be coherent, as the p-mode oscillations themselves show a coherent I[V phase. A correlated background has recently been discussed (Roxburgh & Vorontsov 1997 ; Nigam et al. 1998) as a possible solution to the puzzle of the opposite p-mode line proÐle asymmetries found in velocity and intensity (Duvall et al. 1993 ; Abrams & Kumar 1996 ; Gabriel 1998 ; Rast & Bogdan 1998). The background is particularly signiÐcant in intensity where it exceeds the amplitude of the lowfrequency f- and p-modes. Models for the p-mode asymmetries need to account for the I[V phase behavior in the transition between modes and background. A correlated background is probably responsible for the observed I[V phase below 90¡ of the low-frequency p-modes. Furthermore, the bend of the ridges observed above the acoustic cuto† frequency might be discussed in the context of a solar background. The latter e†ect is strongest in the continuum intensity, which leads to a frequency shift between highfrequency pseudo modes in velocity and continuum intensity (Nigam et al. 1998). Under these circumstances, the nature of the plain component is of great interest, and the exact deÐnition of the background level beneath the p-modes is paramount to a series of problems in helioseismology. We gratefully acknowledge the discussions with Ciro Marmolino and his helpful comments on a previous version of this paper. SOHO is a project of international cooperation between ESA and NASA. This work has been partially funded by ASI contract ASI ARS 96-146. Writing of this work has been greatly facilitated by the use of NASAÏs Astrophysics Data System Abstract Service.
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