Interpretation of results in terms of physical models (Zodiacal Dust Cloud) Part 5

Further analysis of the data by comparison with new radial velocity data and model theory available in 2007

As discussed in topic 1, there have been long periods of inactivity in Doppler studies of the ZL since 1974. Nevertheless, some interesting results have now been added to the data in this field, and it is very informative to study these for the first time in relation to the complete HMR observations. I present them here in chronological order.

Observations of Fried 1977

Figure 4.14 Shows the results of Fried (1977). It is immediately apparent that there is little or no agreement here between the two sets of measurements. Reference to Figure 4.5 suggests that Reay’s model with p = 2 is a fairly good fit to Fried’s points, which paints a picture of large numbers of large dust particles rotating in prograde orbits, at speeds close to the orbital speed of the Earth in the case of particles at around 1 AU, giving those very low wavelength shifts around 90 degrees elongation. Indeed Fried himself deduced an ensemble of dust particles in hyperbolic orbits, with a size dependence on orbital radius r given by


If these data had come to my attention in 1977, I would doubtless have felt depressed, since they do not in any way support our results. It is therefore something of a comfort that as time went on, no other observers’ findings conformed with these of Fried. This is not, of course, to say that there is anything wrong with these observations. There is still, as we have discussed, debate about the variability of the ZL, and it may well be that, since no-one else was observing its Doppler signature in 1977, Fried saw a temporal effect.

East and Reay (1984)

Figure 4.15 shows the points published by East and Reay (1984) on the single wavelength shift versus elongation graph, plotted in direct comparison with the HMR data.

These data have an improved signal-to-noise over ours - the product of a more stable, servo-controlled Fabry-Perot etalon, and a greater number of observations to average. Overall they show a remarkable congruency with the HMR data, with the qualifications that the wavelength shifts are slightly smaller in the range 60° East to 60° West, and the morning-evening asymmetry is even more pronounced. East and Reay, from a polynomial curve fitted to these results, reported a confirmation of a predominantly prograde orbiting Zodiacal Cloud, with no evidence of retrograde component, in elliptical orbits, rather than hyperbolic, and a recession of the Gegenschein of about 2.5 km/s. The Gegenschein results were supported by an extra body of data specifically amassed to reduce errors.

Wavelength shift vs. elongation: the results of East and Reay (1984), compared with the Hicks and Reay data.

Figure 4.15 Wavelength shift vs. elongation: the results of East and Reay (1984), compared with the Hicks and Reay data.

The WHAM observations, and theoretical model predictions

In 2004, Reynolds, Madsen and Moseley published some new data, collected using the WHAM spectrometer, designed for H Alpha mapping, at Kitt Peak, Arizona. The spectrometer itself was a dual Fabry-Perot, 15 cm in diameter, of superior resolution (0.2 A) and high throughput. The results were published in Reynolds et al (2004), and analysed with reference to models by Ipatov et al (2006) in Madsen et al (2006). A great improvement of signal-to-noise ratio over our measurements was achieved by feeding the spectrometer from a 0.6 m telescope, the whole assembly being remotely controlled from Madison, Wisconsin.

The observations were obtained quickly, on just two nights in November 2002. Because of the higher resolution, the WHAM team were able to identify, and subtract, non-MgI emission lines from the atmosphere, contaminating the MgI absorption line, again improving the reliability of the data. It is possible that these unseen emissions had an influence on our data points – perhaps even producing the morning asymmetry and the red shift of the Gegenschein, though this would be hard to prove.

Wavelength shift data and theoretical curves from Madsen et al (2006), plotted in comparison with HMR data.

Figure 4.16 Wavelength shift data and theoretical curves from Madsen et al (2006), plotted in comparison with HMR data.

The WHAM results, shown in Figure 4.16, are shown plotted alongside the HMR data. The general agreement between the two sets of observations is quite good, although there is a tendency for the HMR data to present higher shift at intermediate longitudes, and the WHAM data does not show any morning-evening asymmetry, or any shift at 180° for the Gegenschein.

In 2006, Ipatov et al published their model of a Zodiacal Cloud, starting from the erosion of comets and asteroids, as mentioned in topic 1, and developing orbital velocity elements by simulating their dynamical behaviour with time. Some of the resulting curves are shown in Figure 4.16, and it can be seen that they fit the WHAM observations well. I decided to see how the HMR radial velocity data would look, as compared to the Madsen et al (2006) curves, if they were binned into larger groups of averaged scans (next section).

Comparison of East and Reay (1984) with WHAM data.

Figure 4.17 Comparison of East and Reay (1984) with WHAM data.

We have already seen the WHAM line-width data in Figure 4.4, and remarked that there was some similarity with HMR in the grouping of the points. Certainly the disagreement in the wavelength shift data between HMR and WHAM is not very big, perhaps within the probable errors of the HMR data; but reconciling WHAM with the East and Reay data, with its smaller error bars, is not so easy (Figure 4.17).

The evidence is clearly conflicting here; East and Reay’s data shows a distinct divergence from WHAM at all elongations which is not inside the predictions of probable error. Since our HMR data conforms more closely to East and Reay than WHAM, there is still evidently a need for a new set of data, to determine if the differences are a conflict, or the result of seasonal or other variations. The East and Reay results, in almost every case, show a shift towards the red as compared with Madsen et al (2006). As we saw earlier, the only model which has a chance of explaining such asymmetries between morning and evening, or Spring to Autumn, is my continuous flow, interstellar dust model. Could it be that we are seeing a combination of rotating and free-flowing dust in the ZL? If the difference between Spring and Autumn radial velocities suggested by our data is real, it is possible that the WHAM experiment, a snapshot in time at the November configuration, was simply fortunate in catching the radial velocities in a neat, symmetrical pattern, perhaps in a period of low density in the interstellar dust component. Perhaps only time and still higher resolution and signal-to-noise will tell, but there would clearly be good reason to try to monitor the radial velocity versus elongation curve all the year round. There is one more piece of reductive analysis on the HMR data which can be done: binning.

The result of binning the HMR data in wavelength intervals of 20°.

Figure 4.18 The result of binning the HMR data in wavelength intervals of 20°.

‘Binning’ of the HMR data

Bins of 20-degree spans in wavelength were chosen, and the mean shifts in each 20-degree interval were calculated. The results are shown in Figure 4.18.

This figure shows only elongations from zero to 180°, because the plotted points for evening and morning have been ‘folded’ together, reversing the sign of the evening observations, as many previous authors have done, assuming the shifts to be symmetrical about the antisolar point. The ‘ghost’ points are the original HMR data.

Binned folded HMR data, averaged in wavelength intervals of 20°, compared with folded WHAM data.

Figure 4.19 Binned folded HMR data, averaged in wavelength intervals of 20°, compared with folded WHAM data.

Three sets of binning averages are shown, the results for 1971 only, for 1972 only, and for both sets averaged together. Except for the region 110°-130°, the HMR observations consistently show a shift about 5 km/s larger than the Madsen/Ipatov curves. Again the fit seems quite good for a Reay curve in which p = 5. The separate binned HMR points underline the view that there is a real difference between morning and evening radial velocities, and a time dependence.

Finally, Figure 4.19 shows a direct comparison between the consolidated HMR data and the WHAM data, both folded about the antisolar point. The folding reveals that there actually is a morning-evening asymmetry in the WHAM points – not immediately apparent in the un-folded figures. The morning points seem to cross the zero line at about 30° elongation, and the evening points at about 50° – a discrepancy well outside the limits of the predicted uncertainties in the data. The HMR data shows a crossing at about 40°, but is lacking in enough low elongation data to be sure. Elsewhere the agreement between the two sets of data is good except between 60° and 110° – where our radial velocities are almost twice that indicated by the WHAM data. It has to be emphasised that all the information on time variation, if there is any, has been eliminated from this graph.

Variations with time

I did not expect to find evidence of short-term changes in the parameters of the Zodiacal Cloud. But the differences between our two periods of observation (at opposite ends of the Earth’s orbit) are so pronounced that it is plainly worth checking in the future to see if the differences can be reproduced. Throughout the history of the observation of the ZL there have been reports of seasonal and other variations in intensity of both morning and evening ZL. But there has not been a consensus on what these variations are, or the magnitude of the changes, and since very few truly long-term projects have been undertaken, it has not been established whether the fluctuations are cyclic or not with the season, or due to unique events, such as solar flares or visits from comets, or indeed, as discussed later in this topic, due to influences beyond the Solar System.

Variations in intensity were recorded by naked-eye observations as long ago as 1856, by G. Jones in his voyage from the USA to Japan and back on a boat, which I mentioned in topic 1 (Figure 1.1). Jones’s meticulously drawn nightly contour maps of the Zodiacal Band show what he thought was a dependence of the ecliptic latitude of the cones on the latitude of the observer. Jones interpreted this dependence as an indication that most of the Zodiacal Cloud was attendant on the Earth, rather than the Sun. Though this became an unfashionable view in the second half of the 20th Century, the existence of a component of ‘local’ light-scattering dust can still not be ruled out, especially since the discovery (Reach et al 1995) of the ‘Earth Tail’ of dust, gravitationally channelled by the passage of the Earth on its journey around the Sun. It is also possible, however, that the variation Jones saw was not latitudinal, but seasonal, and this might turn out to be the earliest observed manifestation of the departure of the ZC from the invariable plane, which has been documented in recent satellite experiments (Hauser et al 1984).

E. O. Hulbert (1930), in a much later analysis of the Jones observations, wrote that Jones had witnessed 23 unusually bright periods of the ZL, 16 of which took place 3 days after a magnetic storm. Hulbert also noted other enhancements preceded by magnetic activity. He notes, however, that some of the variations might be interpreted as overall sky brightness changes, as a true separation of ZL component does not seem to have been made. It seems likely to me that Jones himself would have placed more significance in his observations of the variations shape of the ZL than those of overall intensity.

In more recent times, seasonal oscillations in brightness, of magnitude about 20 per cent, were reported by Elvey and Roach (1937) using photoelectric measurements.

In the evening ZL they found a maximum in April-May, and a minimum in January-February; and an opposite effect in the morning ZL. These conclusions were supported by their reduction of visual Japanese observers.

Divari (1955), found seasonal variations in which the morning ZL intensity increased in September to November, and the evening intensity decreased from January to March. These results clearly do not concur with Elvey and Roach’s. As noted in topic 1, Sanchez (1974) found a correlation between ZL brightness and solar activity.

The question of variability of the ZL seems central to interpretation of the Doppler data so far gathered in 2007, to account for the discrepancies revealed in this thesis between all currently available sets of results.

Summary of the implications of the 1970-4 work, and pointers for the future

It is clear that a reasonable fit to our data can be obtained using a model of the Zodiacal Cloud comprising dust particles, some in orbit around the Sun, and some drifting through the Solar System, possibly to be identified with interstellar dust. The differences between the two periods of observations, if they are real, may be attributed either to a seasonal effect, corresponding to an asymmetry of the dust cloud with respect to the Earth’s orbit, or to short-term fluctuations of the orbiting or drifting component. Such short term variations in the former might be due to the visits of comets, or variations in Solar Wind. In the latter, the differential would indicate either that there are short-range inhomogeneities in the interstellar medium, or that, in its passage through the Solar System, the flow of such material is disrupted, for instance by the planets themselves.

In future work the data from high elongations may be the most useful, since a pure rotating model can account for the shape in all cases for which e > 70 (degrees of elongation from the Sun). Our results are consistent with the theory that a higher percentage of drifting dust was present in September-October 1971 than in the April period the following year.

More data is still required, critical for distinguishing between models, and hence for belief in the conclusions we are drawing, and more precise determinations of the actual spectrum profiles, rather than simply averaged shifts, will in the future yield better mapping of the motions of the interplanetary dust cloud.

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