periodic solar euv flux monitored near venus

P E R I O D I C S O L A R E U V F L U X M O N I T O R E D N E A R V E N U S

CHARLES L. W O L F F and W A L T E R R. HOEGY

NASA Goddard Space Flight Center, Greenbelt, MD 20771, U.S.A.

(Received 8 September, 1988; in revised form 21 March, 1989)

Abstract. A detector sharing the orbital rate of Venus has a unique perspective on solar periodicities. Fourier analysis of the 8.6 year record of solar EUV output gathered by the Langmuir probe on Pioneer Venus Orbiter shows the influences of global oscillation modes located in the convective envelope and in the radiative interior. Seven of the eight lowest angular harmonic r-mode families are detected by their rotation rates which differ almost unmeasurably from ideal theoretical values. This determines a mean sidereal rotation rate for the envelope of 457.9 + 2.0 nHz which corresponds to a period of 25.3 days. Many frequencies are aliased at + 106 nHz by modulation from the lowest angular harmonic r-mode in the envelope. The rotation of this mode seems slightly retrograde, - 1.5 + 2.0 nHz, but small positive values are not excluded. We confirm that the rotation of the radiative interior, 381 nHz, is slower than the envelope by detecting g-mode frequencies for angular harmonics, 2 < l < 6, and a possible first detection of the rotation rate for the l = 1 case. Solar EUV lacks the sudden darkenings (dips) shown by visible irradiance; vortex cores in the photosphere and below are again suggested as a possible explanation.

1. I n t r o d u c t i o n

An earthbound observer cannot always separate intrinsic changes happening on the Sun

from signal modulation caused by its rotation. The rotation is complex, varying with

latitude and containing oscillation modes that rotate slower than the solar material. A

signal intrinsic to the Sun and recurring at the rate, vs, is modulated by any significant

solar rotation, Vrot, and by alias frequencies such as v, + Vrot. A detector sharing the

orbital motion of Venus can help resolve ambiguities in data gathered from Earth

because vrot appears different from planet to planet while vs is the same for every

observer. The apparent rate is Vrot = vin - vp, where vi~ is the solar feature's rotation

relative to inertial space and the planet's orbital rate is vp (= 31.7 nHz for Earth and

51.5 nHz for Venus). We will exploit this difference by analyzing data from the Pioneer

Venus Orbiter (PVO) spacecraft which monitors solar EUV flux from an orbit around

Venus (see Section 2).

The various global oscillation modes of the Sun define a series of rotation rates and

periodicities (months and years) which have been found in sunspot activity (Wolff, 1983)

and in the total solar irradiance measured from Nimbus 7 (Wolff and Hickey, 1987a, b;

hereafter called Papers I and II, respectively). The close numerical agreement between

theoretical oscillation periodicities and those seen in sunspots and irradiance strongly supports a causal connection but independent confirmations are still needed. It seems that the global modes act through their differing rotation rates to produce both intrinsic

and rotational modulations of the Sun's surface. The intrinsic changes consist of the brightening or darkening of surface regions when the prime longitudes of several modes rotate past each other and interact. The rotational changes are merely geometric; bright or dark areas pass in or out of the observer's view. Separating intrinsic and rotational

Solar Physics 123: 7-20, 1989. �9 1989 Kluwer Academic Publishers. Printed in Belgium.

8 CHARLES L. WOLFF AND WALTER R. HOEGY

effects, so that the modes can be identified has been a challenging task, worked on now and then by one of us (CLW). A long continuous data set is required to resolve the closely spaced frequencies. The results are sufficiently complex that analysis is desirable of many data sets covering different intervals of time and having different physical origins.

The oscillation model of solar variability obtains its periods from the basic mechanics of linear standing waves in a sphere, plus an assumption of some nonlinear coupling among those modes whose free rotation rates are very similar. The properties of linear oscillation modes in a star have been known since Cowling (1941) derived the spheroidal oscillations (p-modes and g-modes) and Papaloizou and Pringle (1978) derived the toroidal oscillations (r-modes) whose existence was implied by work in spherical stars (Chandrasekhar and Lebovitz, 1962; Aizenman and Smeyers, 1977). Ledoux (1974) and Cox (1976) gave good reviews of the spheroidal modes. The toroidal modes were worked out by Provost et al. (1981), Smeyers et al. (1981), Saio (1982), and applied to a solar model by Wolff and Blizard (1986). Most work in the field assumes either that the star rotates rigidly or, if differentially rotating, that all oscillation modes sample the same average rotation rate. Rather good agreement with solar observations has been obtained using these approximations.

In this paper, we utilize the unique record gathered from Venus orbit to confirm that the Sun is a complex, multiperiodic system. The data to be analyzed has new information content because of the Venus orbital rate and the EUV source. In Section 2, the data and its physical origins are described and two diagrams of periodic or nonrandom behavior are shown. In Section 3, Fourier analysis is used to detect individual global modes, directly and in two aliases, strengthening earlier detections and extending the list of discovered modes.

2. Whole-Sun Observations

We will show data from two experiments, each integrating into one measurement light from the entire solar hemisphere facing the instrument. One experiment responds only to EUV wavelengths and is in orbit around Venus, the other accepts all wavelengths and orbits the Earth.

2.1. PVO

The data set that will be analyzed in detail was obtained by a Langmuir probe instrument (Krehbiel et aL, 1980) on the Pioneer Venus Orbiter (PVO). Once each earth day (which is also the PVO orbital period), the spacecraft is outside of the Venus ionosphere where the probe produces a photoelectric current, Ipe, driven almost entirely by EUV flux at wavelengths between 30 and 130 nm; thus we can u s e Ipe as a proxy for these solar emissions. Brace, Hoegy, and Theis (1988) describe this use of the instrument and state that about 50~ of Ice comes from the Le line. A more detailed breakdown has now been found in a preliminary measurement of the quantum efficiency of the probe material, Rhenium, performed at the National Bureau of Standards (Canfield et al., 1988, private

PERIODIC SOLAR EUV FLUX MONITORED NEAR VENUS 9

communication). The contributions to the measured photoelectric current are: 56~o (from H Le, 121.6 nm), 28~o from the continuum between 30 and 110 nm, 4~o (from Hell at 30.4 rim), 2~o (HeI, 58.4nm), 2~o (Ov, 62.9nm), 4~o (CItI, 97.7nm), 2~o (H Lfl, 102.6 nm), and 2~o (OvI, 103.2 nm). The data begins in December 1978 and extends to July 1987. These 3145 days (8.6 years) contain 2660 days of data with five data gaps of 2 to 4 weeks duration, spaced 584 days apart when Venus was at superior conjunction. The data was gathered in Venus orbit, above the Venus atmosphere and ionosphere, and outside of the bow shock. This insures that almost all the measured current is due to photoelectrons driven from the probe by the Solar EUV irradiance. The data continues to be gathered.

2.2. NIMBUS 7

Data from the Nimbus 7 satellite will be discussed here but not analyzed in detail. It comes from a cavity pyrheliometer which has been monitoring solar irradiance since November 1978 (Hickey et al., 1980; Hiekey, Major, and Kyle, 1984). This is a black- body device that captures solar energy at all wavelengths and records a voltage propor- tional to the power per unit area received from the Sun. The data has been used to detect a sequence of global oscillation modes, called r-modes, in the Sun's convective envelope (Papers I and II). The four lowest harmonic modes were detected and that was sufficient to determine a mean rotation rate for the outer envelope.

2.3. P H Y S I C A L O R I G I N S

Figure 1 compares the above two data sets for the same 1000 days starting on 1979 June 27. The PVO data was divided by its 400-day running mean to remove long term trends and emphasize the fluctuations. For the first three figures only, the fluctuations were smoothed with a triangular weighting function of five day half width for clarity. Two main differences with the detrended Nimbus data (Hickey, private commun.) are apparent. Every 1.6 years, the PVO experiment views that half of the Sun is not immediately visible at Earth. Near these times, maximums and minimums in the PVO data are often two weeks out of phase with those seen by the earth-orbiting experiment. The other difference has to do with the shape of a fluctuation, disregarding phase. The full solar output at all wavelengths (Nimbus 7) has deep narrow minimums ('dips') and broader, less prominent maximums. In contrast, the EUV curve (PVO) is more symme- trical, departing equally far above and below its mean trend. The difference is confirmed by others: Willson (1982) also sees dips in full solar output while Rottman (1985) sees none in La. We conclude that the presence or absence of dips is no error but originates in differing physical conditions at the sources of the light.

The great majority of the Nimbus input signal is visible and infrared emission from the solar surface, which is a convectively turbulent medium. The EUV flux driving the other instrument originates well above the surface in the chromosphere which is largely stable against convection. L~ is typically emitted more than 2000 km above the surface (Vernazza, Avrett, and Loeser, 1973) and much of the other EUV of interest is also emitted in the upper chromosphere (Lean, 1987). We suggest that the highly nonlinear


(a)

(b)

I I I I I .I o . 2 8 0 . , ~ 0 0 . 6 0 0 . 8 o 0 . J. o o o .

Time (days)

Fig. 1. Smoothed solar irradiance fluctuations from their long term trends. One thousand days are shown, from 1979 June 27 to 1982 March 25. (a)The PVO record is due to Lc~ emission and nearby EUV wavelengths. (b) The Nimbus 7 record from channel 10 c is due to all wavelengths and contains deep dips (minimums). Comparison of the curves sugests that a nonlinear mechanism affects solar output in the visible

or near infrared but is not effective in the EUV.

motion to be expected from convection at the surface and below, is the basic reason why

only the Nimbus signal has deep dips. When a large-scale convective flow creates a

descending vortex, its intense core should temporarily reduce solar output in the visible

and infrared by dragging down the smaller convection cells which carry the bulk of solar luminosity to the surface. For some time, Wolff (1974, 1984) has been suggesting large scale flow patterns and the consequent vortexes as the underlying cause of solar activity (sunspots, flares, etc.) and fluctuations in irradiance.

2.4. PVO PERIODICITY VISUALIZED

Before doing a Fourier analysis, it is instructive to inspect several periodicities on superposed epoch graphs. For these displays only, effects of the 11-year cycle were removed to allow all parts of the 8.6-year data set to be seen about equally. The method chosen was to separate the PVO irradiance data into 500-day intervals and divide each by that constant which converts the largest fluctuation to unit height. This preserves


relative information; the more important peaks within a 500-day interval will still be displayed large and the lesser ones small. Then, superposed epochs of period P were produced by chopping the time axis into segments of length P and plotting each segment above the preceding one.

Figure 2 shows the result for P = 29.45 days, a recurrence frequency of 393 nHz ( _- p - 1). Only the positive fluctuations are plotted and all lie between phase values of 0 and 1. Redundant information is given between phases 1 and 2 to make periodicity more easily visible. The labelled frequency and period are what a detector orbiting Venus would record. The figure shows three nearly vertical features, each lasting between 1.2

100

80

�9 ~ 6O (9

O

Z 4o

f = 393 n H z , P = 29.45 d

- Z -

A

-- 1986

A A

- - - - - 1982

20 -.--- ~

~ ...~.~ 1980

0 1 2 P h a s e

Fig. 2. Superposed epochs of 8.6 years of PVO solar fluctuations beginning at the bottom in December 1978. Events lying on a vertical line recur at the plotted epoch, 29.45 days (frequency, 393 nHz). The band of large fluctuations near phase 1.0 is interrupted several times but maintains its phase. If this periodicity represents a rotation, it would appear as 26.0 days (445 nHz) in an inertial system and as 28.0 days from

Earth.

12 C H A R L E S L . W O L F F A N D W A L T E R R . H O E G Y

and 1.5 years. Within each, solar brightening recurs almost every month. Then, recurrence ceases or drifts out of phase, possibly following another clock. But the phase is remembered each time the pattern reemerges, as if driven by a longer-lasting structure. Similar linear trends appear on Mclntosh's ten year mapping of gross solar surface features (Mclntosh and Wilson, 1985) and it was suggested in Paper I that they might be caused by the rotation of global oscillation modes in the Sun.

If the 393 nHz recurrence at Venus were simply due to some solar rotation period, it would appear in an inertial frame as 444.5 nHz (or 26.0 days) and appear to Earth as 28.0 d. It would be reasonable to identify this with 28 a synodic periods seen in earth-gathered data for some bright features in the 530.3 nm coronal green line emission

1 5

1 0

O9

�9

f = 5 3 n H z ,

I I I I I I I

t J i l .L

i . t i~

P = 2 1 8 d

I i I i I I I I t

i l i l ~ i

I i i . I il i . , . i

I I i . , . , . i ii. l i

I i l l l . , I I i . l i l

ii ,i , i li

i.l il II 1 i. i , i l

~ A l l J . , i l l IA , . . , . I , | i,.,.,,iilii ,.,i

~ "',, .i,., . i A,.. i ~ iii,,. ,i,. ,,i '"i' tiiili ' ' .i ,.,

' '"i' llill i J i 1 .

o , , , , , , . . . . . . . J~l , , I , ,

/

0 1 2

P h a s e

Fig. 3. Superposed epochs of 218 days (frequency, 53 nHz). No single periodicity is proven but there is obvious clustering of the larger maximums and some vertical alignment of the clusters, hinting that at least several long term eoherenees may exist in the data. If rotation caused recurrence at the plotted frequency, it would appear as - 1.5 nHz in an inertial frame-close to that expected for the lowest angular harmonic

r-mode.

I I I

- 1986

i - 1984

l . J m

_ ~

- - 1982

-- 1980


(S)kora, 1971 ; Wagner, 1976) and long lived chromospheric features in the CalI K 3 line at most latitudes (Antonucci et aL, 1979). Under this interpretation of Figure 2, the EUV output of the chromosphere and corona is being enhanced at one band of longitudes (or reduced at another) and the asymmetry rotates into view every 28 days at Earth or 29.5 days at Venus. After a year or so, the special longitudes return to normal brightness, causing the periodicity to disappear from our data. Eventually, a new area erupts at the same longitude and does about the same thing. This idea that some longitude, or band of longitudes, is special has been known throughout this century to observers of sunspots such as Maunder and Losh whose works are discussed by Chapman and Bartels (1940) and Kiepenheuer (1953). Sunspots tend to occur near some preferred longitude and this activity often persists for 6 months to several years. But the fact that no longitude seemed to remain active forever allowed succeeding generations of theorists - all too conveniently - to assume the effect was not real. This attitude avoided a major challenge to the old models of stars, which were not predicting special longitudes, and it considerably delayed the day when enough people were facing the problem of persistent longitudes to begin understanding them.

Not all periodicity in the PVO signal is near the main solar rotation period. A loose organization on much longer time-scales can be seen on Figure 3 which is plotted for a frequency of 53 nHz (P = 218 days). It does not show a single clear periodicity but there is obvious clustering of the highest maximums into groups of two to five successive high peaks. This means that high activity lives roughly two to five months. It tends to recur after hundreds of days. Note the slight tendency for the stronger groups of maximums to align vertically at about phase 1.1, indicating that 218 days may be one of the true underlying periods. Since this is close to the 225 day orbital period of Venus, it suggests that the lowest harmonic r-mode (l = 1) might be partly responsible (see Sections 3.1 and 3.3). Clearly, more long period events are needed on a chart like Figure 3 before drawing conclusions, but the hint of long term coherences is consistent with the solar oscillation model which provides a number of long periodicities, acting simultaneously.

3. Modulation by Global Oscillation Modes

3.1. A L 1 A S I N G D U E T O R O T A T I O N

When strictly periodic pulses are emitted from a point on a rotating body, a distant detector introduces aliases caused by missing information when the source is out of view. Since aliasing is widely understood, we need only state the result for our case. Let vs be the rate at which a signal is emitted from a point on the solar surface and let v~ be the rate at which that point becomes most visible to the detector. Both frequencies are assumed constant and the signal location need not be fixed relative to the rotating solar material. To a first approximation, one expects to see five frequencies and their negative values: 0, vs, vv, and

v~ + v v . (1)


Higher approximations give more frequencies; they are not entirely negligible but will

be omitted from this analysis. Since rotational aliasing of periodic sources produces a

complex observed spectrum, we should not be surprised to encounter spectral graphs cluttered with lines.

Figure 4 shows the rich Fourier spectrum of the PVO fluctuations which were shown,

in part, on Figure 1. Amplitude is in an arbitrary unit. Peaks between 300 and 500 nHz

300 .

250 .

200 .

150.

100.

50 .

O.

2 PERIOD (DAYS) O0 1100 50 80 20 14 20

0 �9 200 �9 400 �9 S00. 800 , 1000 , 1200.

FREQUENCY (NHZ)

Fig. 4. The Fourier spectrum of solar EUV irradiance from 8.6 years of PVO data. The resolution is 3.7 nHz. The broad peak in power at 400 + 100 nHz (central period 29 days if seen from Venus, 26 days inertial) may be partly due to resonances with the solar rotation period. The increasing amplitude below 130 nHz is thought to be due to beat frequencies of oscillation modes in the solar interior. Observed peaks

near F and 2F are attributed to the lowest degree (l = 1) global r-mode oscillation.

seem to be larger the closer they get to the center which corresponds to a period of

29 days, apparent from Venus. This looks like the unresolved effect of aliases between

the rotation frequency and the many very small beat frequencies in the system. The

low-frequency power can also be seen directly in the steep increase of spectral amplitudes

below about 130 nHz. A spectrum of the raw data would show this rise continuing to increase to zero frequency but the data used for Figure 4 was divided by a 400-day

running mean (see Section 2.3) which suppresses amplitudes below 30 nHz. The increase toward low frequencies is due to oscillations in the solar interior which impose on the Sun's output a dense array of recurrence frequencies < 131 nHz (Wolff, 1983).

They are mostly unresolvable by the present data set but two effects of their combined power seem to provide the dominant overall character of the PVO spectrum.

The frequencies, F ( = 53 nHz) and 2F, are marked on the figure. We will identify these with an r-mode (Section 3.3) and use 2F for the visibility rate, v v. There are several reasons why: Many lines in the spectrum seem to have satellites at + 2F. The rate F lies close to the apparent rotation rate, 51.5 nHz, that would be expected at Venus for the lowest angular harmonic r-mode, l = 1. The large angular extent of an l = 1 mode allows it to contribute more than any other mode of equal amplitude to a detector, such as PVO, which integrates the output of an entire solar hemisphere. The interpolated amplitudes at F and 2F are within a factor of two of each other as they stand, or with the local backgrounds removed, or with the 400 day smoothing omitted. This indicates


that there are two sectors of active longitudes, 180 ~ apart and of comparable but

unequal effectiveness. Physically, the use of 2F for the visibility rate assumes that two

active longitudes f)f the l = 1 r-mode act as valves, nonlinearly enhancing other modes when their active longitudes rotate past those of l = 1. This would not be the only pair of valves operating, but it is the obvious one to try first with the PVO data.

3.2. THE INTERIOR MODES (g-MODES)

We start with the g-modes thought to be oscillating deep in the solar interior, underneath

the convective envelope. The envelope is an acoustically reflecting layer for these modes, causing their amplitudes to decline exponentially toward the surface. Their rotation

depends on the solar rotation and on l, the principal index of the spherical harmonics

making up each mode. The best evidence of their existence is about 24 intrinsic

frequencies in the sunspot record from which Wolff (1983) deduced the rotation rates

of 11 nonlinearly coupled g-modes. Some of these rates are listed in Table I relative to

an inertial coordinate system. Except for l = 1 which was fixed by the PVO data, the g-mode rates were measured with an uncertainty of about 0.4 ~ in the sunspot analysis.

TABLE I

Observed sidereal rotation rates affecting solar UV irradiance

Interior modes Envelope modes Deviation of r-modes (g-modes) (r-modes) from Equation (4) (nHz) (nHz) (nHz)

1 ( 1 7 6 ) - 1 . 5 - 1.5 2 314.7 305.3 a - 3 351.9 381.3 -0.3 4 362.0 412.2 0.1 5 368.3 427.1 - 0.3 6 371.9 436.7 0.6 7 441.6 0.1 8 445.3 0.1

a Not measured; expected value given.

The g-modes have two bright or dark longitudes per rotation. Interaction with the

nearly stationary r-mode for l = 1 gives rise to intrinsic frequencies at the surface, causing the observational record to be influenced by twice the rates shown in Table I with aliases (sidebands) at + 2F. (In the sunspot analysis, Wolffleft open the possibility

of symmetry, S = 1, in case there were predominantly only one bright or dark longitude per rotation. But S = 2 was stated as 'somewhat preferable'; it was later adopted in Papers I and II and is used herein.) Twice the rates from Table I are marked and labelled on Figure 5 and then shifted by + v~ ( = 2F) as called for by Equation (1). The theoretical series limit, l = Go, is marked by a tic in each case. The 18 theoretical lines for l < 6 register remarkably well with the expanded view of the PVO spectrum. Only the frequency of the l = 1 was not previously measured. Setting it at 352 nHz gives perfect


180.

150,

u~ 120.

90 , J

<: 6 o .

80.

0 .

: 2 0 0 , 8 0 0 , 4 0 0 . 5 0 0 . 6 0 0 . 7 0 0 , 8 0 0 , 8 0 0 ,

FREQUENCY (NHZ)

Fig. 5. Expanded view of spectrum on Figure 4 with g-mode frequencies marked above. Rates for the first six angular harmonics are labelled as well as the series limit at l = oo. The g-mode spectrum is seen at least three times, shifted by 106 nHz increments, presumably due to aliasing from the lowest degree mode in the

solar envelope.

registration with strong peaks at its prime aliases, 246 and 458 nHz. Higher/-values are expected to cause weaker lines in the PVO spectrum. The close spacing of theoretical lines for l > 6 makes them impossible to observe with certainty in a spectrum whose points are only 3.7 nHz apart. Of the 18 lines, only two (at 618 and 724 nHz) do not fall close to a maximum in the observed spectrum.

It is easy to show the high statistical significance of the above match. For simplicity, assume a probability, p = 0.5, that any theoretical line will lie nearest a maximum in the observed spectrum. The chance C of accidentally finding k successful lines out of a total sample of n is given by the standard binomial expression,

C = n! [k! (n - k)!]- lpk(1 --p)n-k.

TWO successful theoretical lines will be discarded since two could always be fitted by the free parameters that were available (the choice of v v and the rotation rate of l = 1). This leaves k = 14 and n = 16 for which C = 0.0018, exceeding a 30" significance. Note that this test is valid no matter how weak are the observed lines. In a highly multiperiodic system like ours with lots of strong aliases, most real spectral lines are necessarily of average height, creating the illusion of a high noise level with little signal. This characteristic is not appreciated by some critics of this model. Figure 5 is strong confirmation of the g-mode rotational frequencies which were found to even higher significance by Wolff (1983) and seen again in Paper II. The figure shows for the first time that g-modes cause some of the variability in the EUV output of the Sun.

3.3. T H E ENVELOPE M ODE S ( r - M O D E S )

The Sun's convective envelope occupies perhaps the outer third of the solar radius. Here, r-modes can oscillate in toroidal motions similar to that of Rossby waves. Theoretical properties of linear r-modes in the Sun were summarized by Wolff and Blizard (1986). Section 1 cited earlier work. Each mode rotates at a rate (Saio, 1982)

v, = v ~ [ 1 - 2 / l ( l + 1)] (2)


which depends only on the spherical harmonic index, l, and the mean rotation, v~, in a nonrotating coordinate system of the solar material occupied by the mode. Total solar irradiance data has shown that vo~ = 455 + 5 nHz (Paper I) and 459 _+ 4 nHz (Paper II). Within this small range, we searched for the value of %0 for which rates from Equation (2) aligned best with lines observed by PVO. We found that v~ = 457.9 + 2 nHz and the uncertainty (rounded to 2) is half the 3.7 nHz spacing in a Fourier spectrum of 8.6 year extent. As with g-modes, the r-modes have two active longitudes per rotation. The motivation for this and some sketches were given in Paper II. But the strongest proof in print so far is the resulting agreement with observed frequencies (in earlier work and in this paper). With two active longitudes, an r-mode family should cause solar irradiance to vary at the frequency

]"ob . . . . . d = 2 ( ] ) l - l,'p) (3)

where Vp ( = 51.5 nHz for Venus) is the mean orbital rate of the planet where the detector is located. Nonlinear beat frequencies between the r-modes are neglected here since EUV data is more linear (see Figure 1) than that used in Papers I and II to detect beats.

All but one of the central frequencies from Equation (3) for the cases 1 < l < 8 correspond to enhanced power in the PVO spectrum. Most aliases at + 2F also appear except for l = 1 which cannot alias itself. Of the 22 lines expected, only 3 were at low points in the spectrum. But many peaks were not strong and 7 were too wide to test the model rates strictly enough. To sharpen and enhance the expected peaks, the power in each central frequency and its two aliases was collected at one place by averaging the observed spectrum with two other versions of i tself- one shifted in frequency by + 2F and the other by - 2F. (The nearest step available in the Fourier spectrum was 106.7 nHz which was used for 2F in the averaging.) This technique should strengthen any line with satellites at the expected locations. But it also creates a bewildering array of false lines, so the method is only useful, statistically, on a large group of theoretical frequencies whose values are already known. The resulting processed spectrum appears on Figure 6. As would be expected from Figure 5, each central frequency of the g-mode

80.

H

:E

<: 30 .

G-MODES

R-MODEU

I ' v,vv ' , iV', v v V t lV ' tv o , ~ r r P I F 300 . 400 . 5 0 0 . 8 0 0 ,

3 56

Sla 78 -7

p I i I 7 0 0 . 8 0 0 , 8 5 0 ,

FREQUENCY (NHZ)

Fig. 6. Processed spectrum, derived from Figure 4, to emphasize lines with prominent aliases at _+ 2F (see text). Except for the line at 502 nHz, the entire sequence of interior and envelope modes listed in Table I is detected either here or (for the l = 1 r-mode) on Figure 4. The observed peaks match the expected

frequencies within the observational resolution.


sequence is detected again. For the r-modes, ideal values from Equation (3) are shown. It appears that r-modes up to ! = 8 are resolvable and observed except for I = 2 which suffers interference from two tall lines near 400 nHz (see Figure 4). Their great height may be due partly to unresolved aliases with the solar rotation period as mentioned. The l = 1 mode was detected at 106 nHz and through the strong aliasing of other lines by + 106 nHz. To appear as 106 to Venus, the mode has to rotate at a sidereal rate of - 1.5 nHz by Equation (3). This slightly retrograde motion is close to the ideal value, zero. Hoegy and Wolff (1989) looked closer at the peaks near 55 and 75 nHz. The high point in the processed spectrum was used as the observed value except for three wide lines (l = 3, 5, and 6) which were fitted to a quadratic between the nearest minimum points in the spectrum. These readings were converted to inertial rotation rates by inverting expression (3) and are listed in Table I. The last column shows that the observed rates deviate very little from ideal ones calculated from Equation (2) using v~ = 457.9nHz. The value of vo~ was chosen to minimize these deviations. The statistical significance of the agreement shown with g- and r-modes on this figure is less than that proved for Figure 5 because of the additional free parameter v~ but the chance, C, of accidental agreement is still < 1~o. In summary, the r-modes for l < 4 were detected in Papers I and II and are found here to higher accuracy. Those for / > 4 are seen here for the first time.

Finally, to confirm our belief that two active longitudes are predominantly seen by whole-Sun detectors, we inspected the frequencies from Equation (3) divided by two. They would correspond to r-mode families with only one active longitude per rotation. As expected, these frequencies and their aliases agreed poorly with the PVO spectrum except, perhaps, near 400 nHz where they may be amplified by resonance with the Sun's surface rotation.

4 . D i s c u s s i o n

The lowest angular harmonic mode in the envelope stands out in the EUV data and splits other lines into triplets, v and v + 2F. The aliasing arises from a multiplicative interaction (automatically nonlinear) and would not happen if irradiance fluctuations were merely the linear sum of the individual effects of each mode. In Equation (1), the main aliasing was modelled as a visibility effect in which extra brightness at some longitude is enhanced nonlinearly when rotating past an active longitude of the l = 1 mode. Aliasing from higher harmonic modes was ignored, partly because the resolution of the PVO spectrum may not justify searching for more complexity and weaker lines.

The central frequency of a triplet is the irradiance fluctuation rate that a mode would cause if it were the predominant mode in the Sun. The rates have different origins for envelope modes, which exist at the surface, and interior modes which are detected here indirectly. For a family of envelope r-modes, the central frequency has to be twice the synodic rotation period of the mode (Equation (3)). But a lone interior mode affects the surface more when its two active longitudes are rotating past those of the lowest harmonic envelope mode which helps transport its energy to the surface. Because of this,


the actual rotation rate of an interior mode differs slightly from that listed in Table I -

half the observed intrinsic frequency. For example, the interior mode for I = 4 actually rotates at a sidereal rate, v = 362 - 1.5 nHz; its beats with the l = 1 r-mode produce the intrinsic rate, 362 nHz, whose effect was seen on the last two figures. This small shift in g-mode rotation rates will be of interest some day, but is ignored here since it is comparable to the observational uncertainties in this paper and in the sunspot analysis of Wolff (1983).

Finally, we urge caution with the rate 176 nHz listed for the g-mode of l = 1 until confirmed by another method. Even though this rate and its two aliases fit perfectly to three strong lines on Figure 5, the central frequency is almost 8 ~o below the ideal theoretical value for that mode. That might not sound too bad, but Wolff (1983) found that none of the other ten g-modes for I _< 11 deviated more than 1% from the ideal.

5. Summary

The more linear behavior of solar irradiance in the EUV compared with the visible (Figure 1) has permitted a more direct detection of solar oscillation modes by their rotation rates. The EUV de-emphasizes the nonlinear beats between r-modes that were detected previously, better revealing the simpler sequence of rotation frequencies them- selves (Figure 6).

Observing from Venus shifts the frequencies of rotational lines but not those of the beats, giving a spectrum different from one gathered near Earth. Lines that are confused or unresolved in one spectrum may stand out clearly in the other. From the vantage point of Venus, we detected seven of the eight (1 < l < 8) slowest rotating r-modes and the six slowest g-modes. Five are first detections. This analysis gives the most accurate measure yet of the mean rotation rate (as averaged by r-modes) of the Sun's convective envelope: 457.9 + 2.0 nHz in an inertial frame. It corresponds to a period of 25.3 days (27.2 days, viewed from Earth) and applies to the interval 1978 December through 1987 July.

We confirm that the Sun rotates more slowly in the deep interior, 381 nHz, than it does in the convective envelope. This rate was discovered by Wolff (1983) in sunspot records and was seen again in irradiance (Paper II). All these results from g-modes are based on the hypothesis that they populate the deep interior and experience sufficient nonlinear coupling to obey a simple rotation law similar to Equation (2). The three g-modes which penetrate closest to the center of the Sun are the only ones that show any measurable departure from their ideal rotation law.

Acknowledgement

We thank the referee for many helpful comments that improved the organization, clarity, and content of this manuscript.


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periodic solar euv flux monitored near venus

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