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Astron. Astrophys. 328, 702-705 (1997)

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3. Results and discussion

Not unexpectedly, the results of our measurements shown in Table 2 confirm the general smoothness of zodiacal light. However, we consider the average residual fluctuation of [FORMULA] 0.2% ([FORMULA] 25 mJy per beam at high ecliptic latitudes, [FORMULA] 80 mJy in the ecliptic) only as an upper limit for possible true variations on [FORMULA] scales. First, we note that the absolute values of the fluctuations appear to increase with the total brightness in the field. This could be the signature of real zodiacal light fluctuations, but would also be the signature of variations in instrument sensitivity. Now, among the time series of the observations in the five fields at least one showed a clear event of a fluctuation in the detector sensitivity, as they typically occur after particle hits, corresponding on the sky to a quite untypical striplike depression. Therefore we assume that less conspicuous instrumental instabilities still contribute a significant amount to the observed fluctuations. Since at the level of fractions of a percent the instrument behaviour is not really known, we cannot quantify this contribution, and therefore take the full observed fluctuations as given in Table 2 as upper limits. This only emphasizes again the general smoothness of zodiacal light. Although the area covered is small (1.6 degree2 or [FORMULA] 640 individual measurements), we consider the result as representative and do not expect that larger samples to be accumulated during the ISO mission will lead to a different result.

We do not anticipate an important contribution to the observed fluctuations from other astronomical sources. The regions mapped were selected for low cirrus emission, [FORMULA] 2 MJy/sr at 100 [FORMULA] m, which corresponds to 0.09 MJy/sr at 25 [FORMULA] m (Désert et al. 1990), and for which a brightness fluctuation of [FORMULA] 0.001 MJy/sr is predicted for a [FORMULA] diameter field-of-view at 25 [FORMULA] m (Helou and Beichman 1990). This is well below the limits on brightness fluctuation derived from our measurement. Stars also were avoided in our fields, down to magnitudes of R = 12. Even a rather red star of this brightness, spectral type M4, with a typical colour index of R-N [FORMULA] 4.5-5, would have an estimated 25 [FORMULA] m flux of only 6-10 mJy (corresponding to 0.010 MJy/sr - 0.017 MJy/sr), again small compared to the measured fluctuations. Also, one or two sources from the IRAS faint source catalogue, with upper flux limits of between 40 mJy and 140 mJy, fall into our fields, but they are not causing a signal at their position which obviously exceeds the general level of fluctuation. Anyway, the method of histogram fitting is not very sensitive to the existence of a few point sources in the field. The observed fluctuations therefore appear not to be due to background sources. Rather they have to be attributed, as assumed above, mostly to a combination of intrinsic zodiacal light brightness fluctuations and the present instrumental noise limit. Our values give upper limits to both of these effects.

As far as the zodiacal light is concerned, this relative smoothness of the brightness distribution does not mean that the cloud of interplanetary dust has to be homogeneous. Rather it emphasizes the efficiency of mixing to which the interplanetary dust is subject by gravitational, electromagnetic and mechanical forces. The few known structures in the zodiacal light are the exceptions from the rule: cometary trails and asteroidal bands show dust close to the locus of production respectively in a region of enhanced production, while the dust ring outside the earth's orbit (Dermott et al. 1994) is caused by a special, resonant interaction.

The observed limit on zodiacal light fluctuations has also to be considered for deep source counts, since such small-scale fluctuations may degrade the detection limit or introduce systematic uncertainties. The structure function of the fluctuations shown in Figure 4 is flat, indicating a statistical behaviour like for white noise. We therefore assume that this is the behaviour of the fluctuations also at the smaller separations not observable in our data. The fluctuations then simply scale with the diameter of the aperture (pixel size), like in the photon noise limit. An extrapolation to other beam sizes is therefore not so problematic and can be extended to the longer wavelengths of 60 [FORMULA] m or 90 [FORMULA] m , where the Airy disks and the pixel sizes (at least for ISO) are still comparable to our diaphragm size. Using the average zodiacal light spectrum as measured by COBE at [FORMULA] from the sun in the ecliptic, and the pixel sizes of [FORMULA] used on ISO, and assuming that the fluctuations are proportional to observed zodiacal light brightness, we then predict fluctuations of less than 2 mJy at 60 [FORMULA] m and smaller than 1 mJy at 90 [FORMULA] m. This is far below the cutoff of 50 mJy reached in the deep IRAS source counts at 60 [FORMULA] m (Hacking and Houck 1987). It indicates that the above limits on zodiacal light fluctuations should not compromise faint source counts going to ten times fainter brightness limits. Of course, there are usually more restrictive limits due to cirrus fluctuations or instrumental effects.

[FIGURE] Fig. 4. Structure function [FORMULA] calculated from the measured single-pixel brightnesses in the map at the North Galactic Pole. The smallest separation is the pixel separation of [FORMULA], the largest separation is determined by the size of the map.

At the wavelengths short of 25 [FORMULA] m much smaller pixel sizes are used ([FORMULA] 12 [FORMULA] in the infrared camera ISOCAM onboard ISO). Nevertheless, we note for information and comparison that the above assumptions (flat power spectrum for the fluctuations, proportionality to total zodiacal light brightness) lead to an upper limit to 1 [FORMULA] fluctuations for a pixel size of 6 [FORMULA] of [FORMULA] 0.06 mJy at 7 [FORMULA] m and [FORMULA] 0.45 mJy at 15 [FORMULA] m.

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© European Southern Observatory (ESO) 1997

Online publication: March 26, 1998