The zodiacal light in the ultraviolet, visual and near-infrared region is due to sunlight scattered by the interplanetary dust particles. In the mid- and far-infrared it is dominated by the thermal emission of those particles. Zodiacal light brightness is a function of viewing direction (, ), wavelength, heliocentric distance (R) and position of the observer relative to the symmetry plane of interplanetary dust. Its brightness does not vary with solar cycle to within 1% or at most a few percent (Dumont & Levasseur-Regourd 1978; Leinert & Pitz 1989), except for subtle effects associated with the scattering of sunlight on the electrons of the interplanetary plasma (Richter et al. 1982). However, seasonal variations occur because of the motion of the observer in heliocentric distance and with respect to the symmetry plane of interplanetary dust cloud (by the annual motion of the earth or the orbital motion of the space probe). The colour of the zodiacal light is similar to solar colour from 0.2 m to 2 m, with a moderate amount of reddening with respect to the sun (see Fig. 39 (click here)). Beyond these wavelengths, the thermal emission of interplanetary dust gradually takes over, the emission being about equal to the scattering part at 3.5 m (Berriman et al. 1994). In general the zodiacal light is smoothly distributed, small-scale structures appearing only at the level of a few percent.
At present, the overall brightness distribution and polarisation of zodiacal light have been most completely, with the largest sky coverage determined in the visual. The infrared maps obtained by the DIRBE experiment on satellite COBE (see Sect. 8.5) from 1.25 m to 240 m provide excellent data, with relative accuracies of 1% to 2% at least for the wavelengths between 1.25 m and 100 m. Their absolute accuracy is estimated to 5% for wavelengths 12 m and 10% for the longer wavelengths. But these maps are limited to the range in solar elongations of = 94 30. An impression of the accuracy achieved in the visual is obtained by comparing the best available ground-based map (Levasseur-Regourd & Dumont 1980) with space probe results from Pioneer 10 (Toller & Weinberg 1985) and Helios A/B (Leinert et al. 1982) in Fig. 34 (click here). Among these, e.g. the calibration of the Helios zodiacal light photometers was extensive enough to predict before launch the count rates for bright stars observed in flight to within a few percent, and to propose the same correction to solar U-B and B-V colours (Leinert et al. 1981) as the dedicated solar measurements of Tüg & Schmidt-Kaler (1982). However the deviation between the three zodiacal light data sets is larger than suggested by this precision, typically 10%, and up to 20%. The deviation appears to be more systematic than statistical in nature. We conclude that the zodiacal light in the visual is known to an accuracy of 10% at best, about half of which uncertainty is due to multiplicative errors like calibration (including the definition of what a V = 10 mag solar analog G2V star exactly looks like).
In the ultraviolet, the maps of zodiacal light brightness and polarisation are less complete than in the visual, and the calibration is more difficult. In lack of convincingly better information, we assume the overall distribution of zodiacal light brightness at these wavelengths to be the same as in the visual. This, of course, is only a convenient approximation to hardly better than 20%. Figures 35 (click here) and 36 (click here) show that this assumption nevertheless gives a reasonable description of the IRAS zodiacal light measurements at elongation = 90 (Vrtilek & Hauser 1995) and an acceptable approximation to the 10.9 m and 20.9 m rocket measurements of Murdock & Price (1985) along the ecliptic over most of the elongation range. Therefore, in the infrared, it also may be used in those areas where direct infrared measurements are not available.
In this spirit, we now want to give the reader the information
necessary to get the mentioned estimates of
zodiacal light brightness on the basis of
the brightness table for visual wavelengths.
To this end we write the observed zodiacal light brightness
for a given viewing direction,
position of the observer and wavelength of observation
in acceptable approximation (i.e. more or less
compatible with the uncertainties
of the results) as a product
In the following sections 8.2 - 8.7 we provide the quantitative information needed to use the unifying approximate Eq. (14 (click here)) but also present present individual original results and topics not directly related to it. Section 8.8 discusses the structures present in the zodiacal light on the level of several percent, and Sect. 8.9 indicates how the observed zodiacal light brightness depends on the position of the observer in the solar system.
Figure 34: Comparison of zodiacal light measurements along the bands of constant ecliptic latitude = 16.2 and = 31.0 observed by Helios A and B. The ground-based measurements of Levasseur-Regourd & Dumont (1980) at = 502 nm have been linearly interpolated to these latitude values. The Helios measurements at B and V (Leinert et al. 1981) have been linearly interpolated to = 502 nm. The Pioneer measurements (Toller & Weinberg 1985) have been extrapolated from blue to 502 nm with the values applicable for Helios and from = 10 to = 16 according to the table of Levasseur-Regourd & Dumont (1980). For definition of the unit see Sect. 2 (click here)
Figure 35: Comparison of the out-of-ecliptic decrease of zodiacal light brightness at elongation 90 as measured from ground at 502 nm (Levasseur-Regourd & Dumont 1980) and by IRAS (Vrtilek & Hauser 1995). The IRAS measurements are represented here by their annual average. The squares give the average of the profiles at 12 m, 25 m and 60 m, the bars given with the IRAS measurements show the range covered by the profiles at the different wavelengths, with the measurements at 60 m delineating the lower and the measurements at 12 m the upper envelope
Figure 36: Comparison of zodiacal light brightness profile along the ecliptic as measured by Levasseur-Regourd & Dumont (1980) at 502 nm and by a rocket flight (Murdock & Price 1985) at 10.9 m and 20.9 m. The rocket data for the two wavelength bands have been averaged and normalised to the ground-based measurements at an elongation of 60. For definition of the unit see Sect. 2 (click here)
This section gives information which allows us to estimate the factor
Leinert et al. 1980)
found the visual brightness to increase with decreasing heliocentric distance
for all elongations between 16 and 160 as
In this same range the Helios experiment (Leinert et al. 1982) observed the degree of polarisation to increase with increasing heliocentric distance as
In the outer solar sytem, for 1.0 AU < R < 3.3 AU, Pioneer 10 (Toller & Weinberg 1985, see also Hanner et al. 1976) found a decrease with heliocentric distance which can be summarised as
neglecting the correction for Pioneer 10's changing distance from the symmetry plane (compare Table 33). Such a steepening is expected to result if there is less interplanetary dust outside the asteroid belt than extrapolated from the inner solar system (van Dijk et al. 1988; Hovenier & Bosma 1991).
Similarly simple expressions for the thermal infrared cannot be given, since the thermal emission of interplanetary dust
Value at 1 AU Gradient Range (power law) (in AU) Density 10-19 kg/m3 -0.93
0.07 1.1 - 1.4
Temperature 260 10 K -0.36 0.03 1.1 - 1.4
Albedo 0.08 0.02 -0.32 0.05 1.1 - 1.4 (from IRAS)
Polarisation 0.30 0.03 +0.5 0.1 0.5 - 1.4
(0.5 m, local)
First we give here the values for the zodiacal light at 500 nm (the
possible minute difference to 502 nm, to which the data of
Levasseur-Regourd & Dumont (1980) refer, is neglected).
Brightnesses are expressed in units. At 500 nm ( = 10 nm) we have
The annually averaged brightness and degree of polarisation and the
polarised intensity at the
ecliptic poles at 500 nm result as (Levasseur-Regourd & Dumont
1980; Leinert et al. 1982)
For completeness we note that the polarized intensity appears to be very much agreed upon, while many of the space experiments (Sparrow & Ney 1968; Sparrow & Ney 1972a,b; Levasseur & Blamont 1973; Frey et al. 1974; Weinberg & Hahn 1980) tend to find lower by about 10% and correspondingly higher. But for uniformity of reference within the zodiacal light map below we recommend use of the numbers given above.
Because of the approximate symmetry of the zodiacal light with respect to the ecliptic (resp. symmetry plane) and also with respect to the helioecliptic meridian (sun-ecliptic poles-antisolar point) only one quarter of the celestial sphere has to be shown. We present the groundbased brightness map for 500 nm in three ways:
The zodiacal light tables given here deviate somewhat
from the original earthbound data sets, which were limited
to elongation > 30, because they were subject to
additional smoothing, and because they also give a smooth
two measurements closer to the sun:
the results obtained by Helios A/B (Leinert et al.
1982) and those of a precursor rocket flight (Leinert et al.
1976) for small elongations (). For
interpolation, if the smaller 5 spacing is needed, still
the table in Levasseur-Regourd & Dumont (1980) can be
used. In addition, Table 18 gives a map of zodiacal light
polarisation, structured in the same way as Tables 16 and 17.
For these maps, the errors in polarisation are about 1%. The errors in brightness are 10-15 for low values and for the higher brightnesses.
Figure 37: Annually averaged distribution of the zodiacal light over the sky in differential ecliptic coordinates. Upper half: zodiacal light brightness ), lower half: degree of polarisation of zodiacal light. The circumference represents the ecliptic, the ecliptic pole is in the center, and the coordinates and are drawn in intervals of 10. The "*" indicates a line of lower reliability. From Dumont & Sanchéz (1976)
The wavelength dependence of the zodiacal light generally follows the solar spectrum from 0.2 m to 2 m. However, detailed study shows a reddening of the zodiacal light with respect to the sun. The thermal emission longward of 3 m, as mentioned already in Sect. 8.2, can be approximated by a diluted blackbody radiation. This will bediscussed in more detail in Sect. 8.5. A recent determination of the temperature of this radiation gives the value of 261.5 1.5 K (Reach et al. 1996b).
Figure 38 (click here) gives an impression of the spectral flux distribution of the zodiacal light at elongation in the ecliptic. It emphasises the closeness to the solar spectrum from 0.2 m to 2 m. Note that at wavelengths 200 nm the intensity levels expected for a solar-type zodiacal light spectrum are quite low, therefore difficult to establish (see Sect. 8.6).
Figure 38: Broadband spectrum of the zodiacal light. The shown observations are by Frey et al. (1974, ), Hofmann et al. (1973, +), Nishimura et al. (1973, ) and Lillie (1972, ). From Leinert (1975)
This section gives information which allows us to estimate the factor .
From the ultraviolet to near-infrared, if zodiacal light brightness is given in units and the zodiacal light spectrum were solar-like, then we would have simply = 1.0.
If the zodiacal light brightness again is expressed in units but its reddening is taken into account, we still take = 1.0 and put the reddening into the colour correction factor (see the following section).
If the zodiacal light brightness is given in physical units, gives the factor by which the absolute level of brightness changes from = 500 nm to a given wavelength. Because best defined observationally at an elongation of in the ecliptic, the factors should be used for that viewing direction. Table 19 already implicitly contains these factors, since it gives the wavelength dependent brightnesses (500 nm), for the 90 points in the ecliptic. (Where appropriate, the factor has also been included). For the infrared emission this brightness is taken from the COBE measurements (see Sect. 8.5) and added here for completeness and easy comparability.
|(m)||W m-2 sr-1 m-1||MJy/sr|
|0||.||7 ()||220||2.0 10-6|
|0||.||9 ()||233||1.3 10-6|
|1||.||2 (J)||8.1 10-7||0||.||42|
|2||.||2 (K)||1.7 10-7||0||.||28|
|3||.||5 (L)||5.2 10-8||0||.||21|
|4||.||8 (M)||1.2 10-7||0||.||90|
This section gives information which allows us to estimate the factor . This factor applies to the ultraviolet to near-infrared part of the spectrum only. Since it deviates from unity by less than 20% from 350 nm to 800 nm, neglecting it (i.e. assuming a strictly solar spectrum) may be acceptable in many applications. Otherwise one has to go through the somewhat clumsy colour correction detailed below.
It is convenient to express the colour of zodiacal light
as a colour ratio which
linearly measures the deviation of zodiacal light from the
the solar spectrum:
and which, for , is related to the colour indices (CI) by
We compile in Fig. 39 (click here)
measurements of the colour of the zodiacal light
with respect to the solar spectrum. There is quite some disagreement
in detail, but also a trend for a general reddening which is stronger
at small elongations (). To be specific,
we decide on
the basis of Fig. 39 (click here), on the following reddening relations
(straight lines in this log-linear presentation and giving particular
weight to the Helios measurements):
Here, coresponds to solar colour, while a reddening results in for and in for .
For intermediate values of , can be interpolated. The curves for the assumed colour in Fig. 39 (click here) are made to closely fit the Helios data, where the UBV (363 nm, 425 nm, 529 nm) colours (Leinert et al. 1982), again expressed as colour ratios, were
Obviously the colour ratio factor cannot be very accurate in the ultraviolet (where measurements don't agree too well) nor beyond 1 m (where partly extrapolation is involved). The situation for 220 nm in the ultraviolet and for the emission part of the zodiacal light are described below in separate sections.
Figure 39: Reddening of the zodiacal light according to colour measurements by various space-borne and balloon experiments. Left: at small elongations; right: at large elongations. The quantity plotted is the ratio of zodiacal light brightness at wavelength to zodiacal light brightness at wavelength 500 nm, normalised by the same ratio for the sun (i.e. we plot the colour ratio C(, 500 nm). Reddening corresponds to a value of this ratio of < 1.0 for 500 nm and > 1.0 for 500 nm. The thick solid line represents the adopted reddening (Eq. (22)). The references to the data points are: Leinert et al. (1981) (Helios), Vande Noord (1970) (Balloon), Feldman (1977) (Aerobee rocket), Pitz et al. (1979) (Astro 7 rocket), Cebula & Feldman (1982) (Astrobee rocket), Frey et al. (1977) (Balloon Thisbe), Nishimura (1973) (rocket K-10-4), Sparrow & Ney (1972a,b) (OSO-5), Morgan et al. (1976) (TD-1), Lillie (1972) (OAO-2), Maucherat-Joubert et al. (1979) (D2B), Matsuura et al. (1995) (rocket S-520-11), Tennyson et al. (1988) (Aries rocket)
The available zodiacal light polarisation measurements between 0.25 m and 3.5 m fall in two groups (Fig. 40 (click here)). Most observations in the visual can be represented within their errors by a polarisation constant over this wavelength range. Two quite reliable measurements, on the other hand (by Helios in the visible and by COBE in the near-infrared), show a definite decrease of observed degree of polarisation with wavelength.
In the limited wavelength range from 0.45 m to 0.80 m
it is still an acceptable approximation to assume the polarisation
of the zodiacal light as independent of wavelength. But overall, the
wavelength dependence of polarisation summarised in
Fig. 40 (click here)
has to be taken into account. For an elongation of 90, to
which most of the data in Fig. 40 (click here)
refer, it can be reasonably represented
by the relation (solid line in the figure)
i.e. by a decrease of 3% per factor of two in wavelength. With , this can also be written in the form
which may be applied tentatively also to other viewing directions.
At longer wavelengths, with the transition region occuring between 2.5 m and 5 m, the zodiacal light is dominated by thermal emission and therefore unpolarised. At shorter wavelengths the zodiacal light brightness is very low, and the polarisation is not known (although it may be similar to what we see in the visual spectral range).
Maps of the zodiacal light polarisation at present are available with large spatial coverage for the visual spectral range only. For other wavelength ranges, it is a first approximation to use the same spatial distribution.
Figure 40: Wavelength dependence of polarisation observed at different positions in the zodiacal light. Filled triangles - Skylab at the north celestial pole (Weinberg & Hahn 1979); open circles: rocket Astro 7 at elongation (Pitz et al. 1979); dots: Helios at = 16, = 90 (Leinert et al. 1982); diamonds: COBE measurements (Berriman et al. 1994); stars: an average of three similar results (OSO-5, = 90, Sparrow & Ney 1972; balloon at = 30, Vande Noord 1970; ground-based at = 39, Wolstencroft & Brandt 1967). Note: it is the wavelength dependence within each group which matters. The solid line shows the approximation (24) to the wavelength dependence of p
Extensive space-based measurements of the diffuse infrared sky brightness in the infrared have become available over the past 13 years (e.g., Neugebauer et al. 1984 (IRAS); see Beichman 1987 for a review of IRAS results; Murdock & Price 1985 (ZIP); Boggess et al. 1992 (COBE); Murakami et al. 1996 (IRTS); Kessler et al. 1996 (ISO)). In general, some form of modeling is required to separate the scattered or thermally emitted zodiacal light from other contributions to the measured brightness, though at some wavelengths and in some directions the zodiacal light is dominant. Because the COBE/DIRBE measurements have the most extensive combination of sky, temporal, and wavelength coverage in the infrared, and have been carefully modeled to extract the zodiacal light signal (Reach et al. 1996a; COBE/DIRBE Explanatory Supplement), we largely rely on these results.
The spectral energy distribution of the zodiacal light indicates that the contributions from scattered and thermally emitted radiation from interplanetary dust are about equal near 3.5 m (Spiesman et al. 1995; Matsumoto et al. 1996), where the interplanetary dust (IPD) contribution to the infrared sky brightness is at a local minimum. This turnover is most clearly seen in the data of the near-infrared spectrometer onboard the satellite IRTS (Matsumoto et al. 1996, see Fig. 41 (click here)). Observations in the range 3-5 m are expected to be neither purely scattering not purely thermal. The thermal spectrum peaks near 12 m, and the observed spectral shape for < 100 m approximates that of a blackbody (for a power law emissivity proportional to , spectral index n= 0) with a temperature in the range (Murdock & Price 1985; Hauser et al. 1984; Spiesman et al. 1995), depending in part on the direction of observation. As already mentioned, recent results from ISO (Reach et al. 1996b, Fig. 42 (click here)) fit the 5 - 16.5 m wavelength range with a blackbody of . Using COBE/DIRBE data, Reach et al. (1996a) find a slow roll-off of the emissivity in the far-infrared (spectral index for ).
Except near the Galactic plane, the signal due to interplanetary dust dominates the observed diffuse sky brightness at all infrared wavelengths shortward of 100 m. This is illustrated in Fig. 43 (click here), which presents COBE/DIRBE observations (0.7 deg resolution) of a strip of sky at elongation 90 deg in 10 photometric bands ranging from . The estimated contribution from zodiacal light (based upon the DIRBE model, see below) is also shown at each wavelength in Fig. 43 (click here). Even in the far infrared, the contribution from zodiacal light is not necessarily negliglible: Reach et al. (1996a) estimated the fraction of total sky brightness due to zodiacal light at the NGP as roughly 25% at 240 m. Examination of Fig. 43 (click here) shows that, although the signal due to interplanetary dust peaks near the ecliptic plane at all wavelengths, the detailed shape of the signal is wavelength-dependent. An analytic empirical relation for the brightness in the thermal infrared at 90 elongation (based upon IRAS data) has been described by Vrtilek & Hauser (1995). As already mentioned, the brightness distribution in visual can serve as a first approximation to the brightness distribution in the thermal infrared, if the respective infrared data are not available.
Although the shape of the underlying zodiacal "lower envelope" is clearly visible in the data of Fig. 43 (click here), the determination of the zero-level of the zodiacal light in the infrared is difficult. In addition to calibration uncertainties in the sky brightness measurements themselves, contributions from Galactic sources and possibly extragalactic background make this a challenging problem.
A summary of several techniques which have been used to isolate the zodiacal light from other sky signals is documented by Hauser (1988): many involve filtering the data in either the angular or angular frequency domain, leaving the absolute signal level uncertain. Others accomplish removal of the Galactic component via models, e.g. by using the statistical discrete source model of Wainscoat et al. (1992), or by use of correlations with measurements at other wavelengths (e.g., HI; Boulanger & Perrault 1988). We choose here to quote zodiacal light levels as derived from the DIRBE zodiacal light model, which is based upon a parameterized physical model of the interplanetary dust cloud similar to that used for IRAS (Wheelock et al. 1994, Appendix G). Rather than determining the model parameters by fitting the observed sky brightness, the DIRBE model was derived from a fit to the seasonally-varying component of the brightness in the DIRBE data, since that is a unique signature of the part of the measured brightness arising in the interplanetary dust cloud (Reach et al. 1996a). The model explicitly includes several spatial components (see Sect. 8.8): a large-scale smooth cloud, the dust bands attributed to asteroidal collisions, and the resonantly-trapped dust ring near 1 AU. Zodiacal light levels given here are estimated to be accurate to 10% for wavelengths of 25 m and shortward, and 20% for longer wavelengths. Note that for all DIRBE spectral intensities presented here, the standard DIRBE (and IRAS) convention is used: the calibration is done for a spectrum with = constant, which means in particular that the effective bandwidth of each DIRBE wavelength band is calculated assuming a source spectrum with this shape. In general, and for accurate work, then a colour correction based upon the actual source spectral shape must be applied (see DIRBE Explanatory Supplement for details).
Figure 44 (click here) presents contours of "average" zodiacal light isophotes in geocentric ecliptic coordinates for one quarter of the sky (other quadrants are given by symmetry), as computed from the DIRBE model. Although this average serves as a guideline for the contribution of zodiacal light to the night sky brightness at infrared wavelengths, at no point in time will an Earth-based observer see a zodiacal light foreground exactly resembling these contours. The detailed DIRBE measurements indicate that the individual spatial components of the interplanetary dust cloud possess their own geometry, their own "symmetry plane" and their own temporal variation pattern.
Figure 45 (click here) illustrates, again on the basis of the COBE zodiacal light model, the variation in isophotes at 25 m at four different times during the year, corresponding roughly to the times when the Earth is in the symmetry plane of the main dust cloud [days 89336 and 90162] and when it is 90 further along its orbit [days 90060 and 90250].
Detailed quantitative maps of the DIRBE measurements and zodiacal
light model are available from the NASA National Space Science
Data Center in the DIRBE Sky and Zodiacal Atlas. The COBE/DIRBE data products
and the Explanatory Supplement are accessible through the COBE
Home Page at
http:://www.gsfc.nasa.gov/aas/cobe/cobe-home.html on the World Wide Web.
Figure 41: Near-infrared spectra of the sky brightness measured with the satellite IRTS at low and at high ecliptic latitudes . The solid line gives a solar spectrum, normalised to the measurements at low at 1.83 m. From Matsumoto et al. (1996)
Figure 42: Spectrum of the zodiacal light from 5 m to 16.5 m as measured with the circular variable filter of the infrared camera (CAM) onboard the ISO satellite. Actually, two separate measur4ements are overplotted. "D4" and "D5" are measurements of the DIRBE/COBE exoeriment shown here for comparison, where the horizontal bar indicates the width of the filters. "LW8" and the asterisk refer to independent measurements obtained with CAM. Note the possible broad emission feature between 9 m and 12 m. From Reach et al. (1996b)
Figure 43: Example of total IR sky brightness measured by the COBE/DIRBE instrument and brightness contributed by zodiacal light at 10 infrared wavelengths. At each wavelength, the upper curve shows the sky brightness measured by DIRBE on 1990 Jun 19 at solar elongation 90, ecliptic longitude 179, as a function of geocentric ecliptic latitude. Because of low signal-to-noise ratio at the longest wavelengths, the 140 m and 240 m data have been averaged and smoothed. The lower curve in each plot is the zodiacal light brightness for this epoch obtained from the DIRBE zodiacal light model. DIRBE is a broad-band photometer: flux densities are given in MJy/sr at the nominal wavelengths of the DIRBE bands, assuming an input energy distribution of the form constant
Figure 44: Contour maps of average zodiacal light brightness in the 10 DIRBE wavebands, as derived from the DIRBE zodiacal light model. Contours are labelled in units of MJy/sr. No color corrections for the broad DIRBE bandwidths have been applied (see DIRBE Explanatory Supplement, Sect. 5.5 (click here), for details)
Figure 45: Contour maps of the zodiacal light brightness at 25 m for four different times of the year, based on the DIRBE zodiacal light model. Contours are given in increments of 5 MJy/sr, with the 25 MJy/sr level labelled. Each pair of maps shows contours for both the leading side and trailing side of the Earth's orbit. The epoch for each pair is indicated above the map, in the format yyddd, e.g., 89336 is day 336 (Dec. 2) of 1989. Asymmetries between the two sides, as well as changes with epoch, can be seen in these maps. Again, flux densities are given in MJy/sr at the nominal wavelengths of the DIRBE bands, assuming an input energy distribution of the form = constant. () is given from 70 to 120 in steps of 10
The difficulty with this wavelength range is that here the zodiacal light
contribution appears only as a small fraction of the observed background.
Available measurements therefore have large error bars or only give
upper limits. In addition there is a sharp drop of solar irradiance
below 220 nm, by three orders of magnitude until 150 nm. This can
be seen in Fig. 46 (click here)
which summarises available results. The scatter between
the observations is very large. Whatever the reason for Lillie's
(1972) high values (variation, galactic component, instrumental
effects), his results shortward of = 220 nm no longer are accepted
as originally given. In view of the obvious discrepancies we suggest to
accept the following:
Here, I() refers to the map of the zodiacal light at 500 nm given above in Table 16.
Murthy et al. (1990) from their Space Shuttle experiment found that the colour of the zodiacal light gets bluer with increasing ecliptic latitude between 165 nm and 310 nm. This would mean, that the zodiacal light is less flattened and more symmetrically distributed around the sun at these wavelengths, as also found from OAO-2 (Lillie 1972). This is an important result which should systematically be confirmed. In Eq. (26) we take such an effect qualitatively into account and approximate it by halving the out-of ecliptic decrease with respect to the visible wavelengths (this is what the lengthy fraction does).
At 220 nm there are now two expressions for the brightness of zodiacal light in Eq. (26), with different out-of ecliptic decrease of brightness. They agree at an intermediate latitude (resp. inclination) of . The discontinuity at the other ecliptic latitudes is acceptable, given the large uncertainties of the determination of zodiacal light brightness at these wavelengths.
Figure 46: Ultraviolet zodiacal light measurements at 90 elongation in the ecliptic in absolute fluxes, compared to the solar spectrum. Measurements from smaller elongations have been transformed to the intensity scale of the figure by assuming the same distribution of zodiacal light brightness over the sky as in the visual. The chosen average zodiacal light brightness for 160 nm 220 nm is shown as thick broken line. Differences with respect to Fig. 38 result from what is used as solar spectrum in the ultraviolet and from the way in which visual data are compared to ultraviolet measurements. The references to the data points are: Lillie (1972), Morgan (1978), Morgan et al. (1976), Frey et al. (1977), Feldman (1977), Cebula & Feldman (1982), Pitz et al. (1979) and a reanalysis by Maucherat-Joubert et al. (1979), Maucherat-Joubert et al. (ELZ, 1979), Tennyson et al. (1988). Adapted from Maucherat-Joubert et al. (1979)
The effects to be discussed in this section have been summarised as factor in Eq. (14) above.
Seasonal variations of zodiacal light brightness occur for an observer moving with the earth, on the level of 10%. They result from the orbital motion of the earth through the interplanetary dust cloud, which changes the heliocentric distance (by 2e = 3.3%) and the position of the observer with respect to the symmetry plane of the interplanetary dust distribution (see Fig. 47 (click here)). (The symmetry plane is a useful concept for describing the interplanetary dust distribution, although in detail it is too simplified: the symmetry properties appear to change with heliocentric distance, see Table 20). The change in heliocentric distance of the observer translates into a brightness increase of about 8% from aphelion in July to perihelion in January. Otherwise, the effects are different for high and for low ecliptic latitudes. Since the effects are very similar in the visual spectral range and in the infrared, examples from both wavelength ranges will be used to show the effects.
Figure 47: Geometry of the earth orbit and the symmetry plane of interplanetary dust (with ascending node and inclination i). Numbers give the position of the earth at the beginning of the respective month. Also shown are the orbits of the Helios spaceprobes and the direction to the vernal equinox
At high ecliptic latitudes, the main effect is a yearly sinusoidal variation of the brightness with an amplitude of 10%. This is due to the motion of the earth south and north of the midplane of dust depending on its orbital position. The extrema occur when the earth (the observer) is at maximum elevation above or below the symmetry plane, while the average value is obtained when crossing the nodes. The effect is clearly visible in the broadband optical Helios measurements in the inner solar system (Fig. 48 (click here)), in the D2A satellite observations at 653 nm along the earth's orbit (Fig. 49 (click here)) and in the COBE infrared measurements (Fig. 50 (click here)) . Of these, the Helios measurements have been corrected for the changing heliocentric distance of the instrument, while in the other data the modulation still contains the 8% effect due to the eccentricity of the earth's orbit. The effect of the tilted symmetry plane gradually decreases towards low ecliptic latitudes to 1%. The brightness changes in low ecliptic latitude observations from the earth or from earthbound satellites then are dominated by the effect of changing heliocentric distance.
Figure 48: Change of brightness with ecliptic longitude observed by Helios at the ecliptic poles. The dashed line gives a sinusoidal fit to the data. These observations refer to the inner solar system, from 0.3 AU to 1.0 AU. The perihelia of the Helios space probes are at . From Leinert et al. (1980b)
Figure 49: Yearly variation of zodiacal light brightness at the north ecliptic pole and at 45 ecliptic latitude, observed at 653 nm by the satellite D2A. The dashed line is a prediction for a plane of symmetry coinciding with the invariable plane of the solar system (i = 1.6, = 107), including the effect of changing heliocentric distance. Adapted from Levasseur & Blamont (1975)
Figure 50: Yearly brightness variations in the zodiacal light at the ecliptic poles, observed at 25 m by the DIRBE experiment on infrared satellite COBE. The variation is dominated by the effect of the tilt of the symmetry plane but also includes the variation due to the changing heliocentric distance of the earth. From Dermott et al. (1996b)
At low ecliptic latitudes, the motion of the earth with respect to the symmetry plane of interplanetary dust mainly leads to a sinusoidal variation in the ecliptic latitude of the peak brightness of the zodiacal light by a few degrees. Figure 51 (click here) shows this variation as observed at 25 m from COBE. In these measurements, the remaining yearly peak flux variation of is almost exclusively due to the change in heliocentric distance. Misconi (1977) has used an approximate method to predict the expected position of the brightness maxima in the visible zodiacal light for elongations of (typically, the positions vary by a couple or a few degrees; at elongations 150 the approximation he uses gets unreliable).
Figure 51: Yearly variation of the ecliptic latitude of zodiacal light peak brightness (left) and yearly variation of peak brightness (right) observed at 25 m at elongation = 90 By the DIRBE experiment on infrared satellite COBE. Open circles refer to the leading (apex), filled circles to the trailing (antapex) direction. From Dermott et al. (1996a,b)
The seasonal variations discussed above have repeatedly been used to determine the plane of symmetry of interplanetary dust. This midplane of the interplanetary dust distribution appears to vary with heliocentric distance, as summarised in Table 20, compiled from Reach (1991). For comparison, we give here also inclinations and ascending nodes for Venus, Mars and the invariable plane of the solar system (i = 3.4, = 76; i = 1.8, = 49; i = 1.6, = 107).
0.3 - 1.0
Notwithstanding the variety of sources contributing to the interplanetary dust population, the zodiacal light in general is quite smooth, and it was found to be stable to 1% over more than a decade (Leinert & Pitz 1989). However, there are fine structures on the brightness level of a few percent, most of which have been detected by the IRAS infrared sky survey: asteroidal bands, cometary trails, and a resonant dust ring just outside the Earth's orbit. They are included here because of their physical importance; they also represent upper limits in brightness to any other structures which still might be hidden in the general zodiacal light distribution. The rms brightness fluctuations of the zodiacal light at 25 m have been found by observations from the satellite ISO in a few half-degree fields to be at most 0.2% (Ábráham et al. 1997).
They were seen in the IRAS infrared scans across the ecliptic as bumps in the profile near ecliptic latitude and as shoulders at (Low et al. 1984, see Fig. 52 (click here)). The bands near the ecliptic plane have been called and (counted from ecliptic latitude outwards), the ones around have been called bands. Their peak brightness is of the in-ecliptic zodiacal light brightness, their width at half maximum (Reach 1992, but the detailed values depend on the method actually used to fit the bumps, in this case by Gaussians). They are thought to be the result of major collisions in the asteroid belt, in the Themis and Koronis families for the and bands, in the Eos family for the higher latitude bands (Dermott et al. 1984). The collisional debris then is expected to be mainly distributed along the walls of widely opened, slightly tilted, sun-centered cones. Therefore the ecliptic latitudes at which these bands occur vary both with the annual motion of the observer (the earth in most cases) and, at a given date, with the elongation from the sun. Formulae to predict the position of the maximum with help of a simplified geometrical model are given by Reach (1992). Figure 53 (click here), resulting from an analysis of the IRAS data, gives a good impression of the resulting yearly sinusoidal latitude variation. Table 21 (taken again from Reach 1992) summarises the average observed properties of the asteroidal dust bands in the case Gaussian fitting is used to measure the bumps in the general distribution of zodiacal light. There must be in addition an underlying distribution of asteroidal debris particles of about 10% of the zodiacal light brightness, which cannot be seen separately from the general zodiacal light. Note that Sykes (1988) resolved the and bands also into band pairs, with a FWHM of 0.5 for each of the components. The claim for eight additional, though weaker bands between and (Sykes 1988) should be taken with reservation and can be neglected here.
|Band||12 m||25 m||60 m|
|Peak surface brightness (MJy sr-1)|
|Average geocentric latitude of peak ()|
|Full width at half maximum brightness ()|
Figure 52: Scans through the ecliptic at ecliptic longitude = 1 on June 24, 1983. The approximate galactic coordinates for the point at 30 ecliptic latitude are given. The curves are labelled by the wavelength of measurement in m. A rough calibration is given by the bar at upper left, the length of which corresponds to 12, 30, 10 and 6 MJy/sr in the wavelength bands from 12 m to 100 m. The dashed curve illustrates how a completely smooth zodiacal light distribution might have looked. The arrows indicate the positions of the asteroidal bands. The 100 m profile is strongly distorted by thermal emission from interstellar dust ("cirrus''). Adapted from Low et al. (1984)
Figure 53: Observed ecliptic latitude of the peak brightness of the asteroidal bands as function of the ecliptic longitude of the viewing direction (basically as function of the orbital motion of the earth). The expected sinusoidal variation is evident but distorted, since the elongation of the viewing direction was modulated on an approximately monthly timescale, and because observations both east and west of the sun were contained in the data set. Taken from Reach (1992)
These trails have been seen in the IRAS infrared sky survey stretching along the orbit of a few periodic comets, which were in the perihelion part of their orbit (Sykes et al. 1986). These were the comets Tempel 2, Encke, Kopff, Tempel 1, Gunn, Schwassmann-Wachmann 1, Churyumov-Gerasimenko and Pons-Winnecke, but also nine faint orphan trails without associated comet were found (Sykes & Walker 1992). The trails typically extend 10 behind and 1 ahead of the comet, their brightness decreasing with increasing distance from the comet. They are thought to consist of roughly mm-sized particles ejected from the comet during times of activity over many years (Sykes et al. 1990). The trails are bright enough to be seen above the zodiacal light only when the comets are near perihelion and the dust in the trails is warm. The width of the trails is about one arcminute, for comet Tempel 2 it has been determined to (). Trail brightnesses are of the order of 1% of the zodiacal light brightness near the ecliptic. Examples are given in Table 22, taken in shortened form from Sykes & Walker (1992). Other periodic comets in the perihelion part of their orbit are expected to behave similarly. A new observation of the comet Kopff trail from ISO (Davies et al. 1997) has shown changes in the trail since the observations by IRAS, and measured a trail width of 50''.
|Comet||R(AU)||(AU)||()a)||(12 m)||(25 m)||(60 m)||(100 m)|
The somewhat related brightness enhancements along some meteor streams, seen in the visible from the satellite D2A-Tournesol, have not been confirmed, neither by the photometric experiment on the Helios space probes (Richter et al. 1982) nor from IRAS. They probably are fainter than originally thought and certainly of lower surface brightness in the infrared than cometary trails or asteroidal bands.
A leading/trailing asymmetry, with the zodiacal light at elongation 90 being brighter in the trailing (antapex) direction, has been found in the IRAS observations (Dermott et al. 1988, 1994) and has been confirmed by measurements of the DIRBE experiment on board the COBE spacecraft (Reach et al. 1995b). From the COBE measurements, the excess in the trailing direction in January 1990 was MJy/sr or at 4.9 m, MJy/sr or at 12 m and MJy/sr or at 25 m. The region of enhanced brightness in the trailing direction is at 90 from the sun, extending 30 (FWHM) in latitude and 15 (FWHM) in longitude (see Fig. 54 (click here), taken from Reach et al. 1995b). In the leading direction there is a smaller enhancement around elongation 80.
These are quite extended structures (see Fig. 54 (click here)). They are explained by resonant interaction of the orbiting earth with interplanetary particles drifting closer to the sun under the action of the Poynting-Robertson effect. This interaction leads to an inhomogeneous torus of enhanced dust density just outside the earth's orbit, with the earth sitting in a gap of this torus and the largest enhancement following it at a few tenths of an AU. The resonant ring structure therefore is expected to be a persistent feature of the zodiacal light.
Figure 54: Distribution of excess zodiacal light brightness due to the resonant dust ring outside the earth's orbit according to COBE measurements (Reach et al. 1995b). In this presentation, the position of the sun is at the center, the ecliptic runs horizontally through it, the ecliptic north pole is at top, the black central circle is the region inaccessible to COBE within 60 elongation from the sun, and the two bright spots at 90 from the sun on the ecliptic are at left the trailing (antapex) enhancement due to this dust ring, with a peak brightness of 1.7 MJy/sr at 25 m, and at right the corresponding but weaker enhancement in leading (apex) direction.The S-shaped bright strip crossing the image is due to the Milky Way
The decrease of zodiacal light brightness seen in a given viewing direction, occuring when the observer moves to larger heliocentric distances, has been measured along the ecliptic in the visual out to 3 AU (Pioneer 10, Toller & Weinberg 1985) and can be reasonably predicted also for the infrared. The change to be expected when moving out of the ecliptic plane is less well known, but can be predicted from models fitting the out-of-ecliptic observations obtained from in-ecliptic positions at earth orbit.
For the infrared, Fig. 55 (click here) shows the predicted brightnesses in viewing directions parallel to the ecliptic and towards the ecliptic pole for an observer moving from 1 AU to 3 AU in planes of different height above the ecliptic. The outward decrease is stronger for 12 m than for 25 m. This is because the thermal emission of interplanetary dust is close to black-body radiation, and for black-body radiation with decreasing temperature the shorter wavelengths first enter into the exponential decrease of the Wien part of the emission curve.
For the visual, Fig. 56 (click here) shows the corresponding decrease for the visual zodiacal light brightness when the observer moves from 1 AU to 3 AU in planes of different height above the ecliptic. Only one curve is shown, since any colour dependence is expected to be small.
The careful reader will note that the visual in-ecliptic brightness decreases a little slower with increasing distance than given in Sect. 8.2. This is because Giese (1979) used a slightly different heliocentric radial brightness gradient, I(R) . The decrease as function of height above the ecliptic Z0 is typical for the models of three-dimensional dust distribution being discussed to explain the distribution of zodiacal light brightness (Giese et al. 1986). Since the three-dimensional dust distribution is not very well known, the decreases shown in Figs. 55 (click here) and 56 (click here) cannot be very accurate either.
Figure 55: Decrease of infrared zodiacal light brightness when moving out of the ecliptic plane. Left: for a viewing direction parallel to the ecliptic plane at elongation = 90. Right: for a viewing direction towards the ecliptic pole. The calculations have been done for a position of the observer in the ecliptic (Z0 = 0 AU) and heights above of the ecliptic of 0.5 AU and 1.0 AU, as indicated in the figure. R0 is the heliocentric distance of the observer, projected into the ecliptic plane. The solid and broken lines give the predicted run of brightness with heliocentric distance for a wavelength of 25 m and 12 m, respectively. The calculations have assumed grey emission of the interplanetary particles, and radial decreases of spatial density and of particle temperature (W. Reach, private communication)
Figure 56: Decrease of the visual brightness of the zodiacal light when the observer moves out of the ecliptic. Left: for a viewing direction parallel to the ecliptic plane at elongation = 90. Right: for a viewing direction towards the ecliptic pole. The curves show how the brightness changes with projected heliocentric distance R0 (measured in the ecliptic) for different heights Z0 above the ecliptic plane (interpolated from Giese 1979)
Since the interplanetary dust cloud is optically very thin, the pole-on surface brightness at 1 AU is just twice the polar surface brightness observed from the earth, and the edge-on surface brightness just twice the brightness observed at elongation 90 in the ecliptic. The same type of relations hold for other heliocentric distances.
The brightness in an annulus extending over a range of heliocentric distances has to be obtained by integration. The total brightness as seen from outside very much depends on the distribution of interplanetary dust near the sun, and therefore is strongly model dependent. E.g., at least in the optical wavelength range an annulus of width dr [AU] has a brightness dr over a large region of the inner solar system, making the integrated brightness contribution strongly peaked towards the solar corona. In discussions of future planet-searching spacecraft (called DARWIN (Léger et al. 1996) and Terrestrial Planet Finder (Angel & Woolf 1997)) a value of integrated zodiacal light brightness at 10 m, when seen from a distance of 10 pc, of 70 Jy, 300 to 400 times brighter than the Earth, is assumed ( of the solar brightness).