Interpretation of results in terms of physical models (Zodiacal Dust Cloud) Part 4

Comparison of continuous flow model with experiment

The model gives a good fit to the experimental values for the September-October 1971 period for the high elongations where the rotating model failed to provide a satisfactory fit. At low elongations in the morning the rotating model gives a better agreement, and at low evening elongations there is little to choose between the two models anyway. The April 1972 data show some signs of higher shifts at intermediate elongations which cannot be accounted for by the rotating model, and these could be explained if some of the dust were in uniform linear flow; it would make sense that in these elongations we are looking at a much reduced density of orbiting particles, as assumed in all the models, and a constant density of interstellar immigrants, giving them a relatively higher percentage of the total in this region. Again, the rotating model satisfactorily predicts the low elongations. The assumption of the presence of a greater percentage of flowing dust in September-October 1971 than in April 1972 could account for the lack of consistency in fit to the rotating dust model. The Autumn continuous flow curve in Figure 4.11 has another interesting feature: apart from giving a creditable visual fit to the HMR data, it gives the right kind of morning-evening asymmetry, and a crossover well into the morning side, giving a recessional speed for the Gegenschein. These features were both to be confirmed later by East and Reay (1984), as will be discussed in section 4.13.2.


It seems, then, that a combination of the rotating and continuous flow models might give the best fit to these data. A ten per cent contribution of continuously flowing dust produces an effect similar to that seen in our results, but higher quality data, over a longer period, would be needed, to put any certainty into this estimate.

Showing the Doppler shift from light emitted by distant sources, observed from the Earth,in the ecliptic plane only.

Figure 4.12 Showing the Doppler shift from light emitted by distant sources, observed from the Earth,in the ecliptic plane only.

Estimation of the effect of a contribution to the Zodiacal Light from sources distant from the Solar System

Computation

Supposing that the continuum spectrum from background starlight contains some kind of absorption feature at 5183.6 A, it is possible to estimate the ‘shift versus elongation’ curve which would arise from such radiation as observed from the Earth. The shift of the line, corresponding to a relative radial velocity, depends on the combination of the Sun’s proper motion in the local stellar group, and the Earth’s orbital motion. Since all the emission takes place at a large distance, no line-of-sight integration is needed, and a further simplification is introduced if we are interested only in the plane of the ecliptic. Only components of velocity in the ecliptic plane are considered here.

We require the apparent radial velocity of distant matter as a function of elongation, which is simply the negative of the ecliptic plane component of the Earth’s total motion in the direction specified by this elongation.

The geometry is a simpler version of the continuous flow model, and is shown in Figure 4.12.If the Sun’s proper motion is S km/s and the direction of the apex of this motion has ecliptic latitude B, the numeric velocity component in the ecliptic plane is S cos B, directed towards ecliptic longitude A. Coordinate conversions from Right Ascension and Declination to ecliptic longitude and latitude were made using tables. For any day in the year the ecliptic longitude of the Sun, C degrees, is given in the Astronomical Ephemeris. The ecliptic latitude is, of course, zero. From this, the direction of the Earth’s motion, at speed E km/s relative to the Sun, is C — 90 (degrees ecliptic longitude). These velocities are shown as vectors in Figure 4.12 in which the angles A and C are measured relative to 0 degrees ecliptic longitude.

The angle, a degrees, between the two components of velocity is

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Using the cosine rule for the component triangle, since its obtuse angle is 180- a, the magnitude R, of the component in the ecliptic plane of the Earth’s total velocity, is given by

tmp69274_thumb52[2]

This is directed towards ecliptic longitude L where

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obtained using the cosine rule in the same triangle.

The elongation of this vector from the Sun

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and so

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Values of E and S were taken from Astrophysical Quantities and R and £r were calculated for October and April. The apparent component of velocity of distant matter at an elongation £ from the Sun is evidently

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The wavelength shifttmp69279_thumb52[2]for a given radial velocity is found by the usual formula for optical Doppler shift at a wavelengthtmp69280_thumb52[2]

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where v is the radial velocity and c is the speed of light. Thus we have

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This function is shown plotted in Figure 4.13 for the two periods of observation. The figures are

Time

tmp69-285 tmp69-286

October 30th

0.3

73 W

April 15th

0.6

97 W

The Earth’s velocity - approximately 30 km/s – is the dominant factor in the Doppler shift since S cos B is only about 12 km/s. This means that the maximum blue shift is always on the morning side within about 15 degrees of the 90 elongation position. The Sun’s velocity adds in the case of the April position, which gives near maximum amplitude of the curve. October is near the minimum case and shows a small amplitude.

Comparison of distant emitting model with the data

Comparison of the curves with our experimental points shows that the rough general shape of the experimental curves can be produced by such a theory, so it is certainly worth finding out if galactic starlight does contribute to the spectrum observed, and in what proportion.

In the October case, the curve is quite similar to that predicted by the rotating dust cloud model but, like the latter, does not satisfactorily fit the data, predicting a cross-over point nearly 60 in error, and a maximum blue shift at an elongation where the experimental points are at around zero shift. The contribution of galactic light in the October observations must thus be small.

Showing all the wavelength shift data available in 1974, compared with predicted curves for distant emitting matter.

Figure 4.13 Showing all the wavelength shift data available in 1974, compared with predicted curves for distant emitting matter.

Comparison of our data with that of Fried 1977.

Figure 4.14 Comparison of our data with that of Fried 1977.

In the April case, this theory predicts very large maxima, not commensurate with most of the data. A few points are, in fact, found with shifts up to 0.6 A, and it is possible that the spectra for these points were measured when the direction was in line with a region of strong starlight background. The outskirts of the Milky Way may have been responsible. Overall, however, the curves fitted to the data do not on the whole agree well with the predictions of this theory. This, added to the fact that considerable care was taken to avoid making measurements in areas of the sky contaminated by other sources, leads me to believe that the contribution of a background starlight absorption line is small enough is most cases to be ignored in our analysis.

This opinion is strongly reinforced by the experimental appearance of line shapes. These are very near to the theoretical predictions of the program CONVOL, which simulates the output when a pure ZL spectrum is input to the system. Diffuse starlight is by no means entirely composed of light from stars with pronounced Fraunhofer features in their spectra. Even if it were, in a particular direction, the lines should be smeared by the combination of proper motions; and so an absorption line, if it exists at all in the spectrum of distant aggregate starlight, would be expected to be shallow and wide. The very fact that our observed shapes are not significantly shallower than the predictions from local dust particle models suggests again that background contributions are, on the whole, small. It is worth noting here that for the future it would be useful to confirm this view of the spectral content of distant starlight, both in theory, in different populations of stars and regions of nebulosity, and in practice, by direct spectroscopy of such regions, without the interference of the ZL. Of course, this requires a viewpoint outside the Solar System.

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