Zodiacal Light

From Tauwiki

1 Overview
2 On-line Calculator
3 Implementation
4 References

[edit] Overview

This is a brief introduction to the Zodiacal light as implemented in the TAUVEX ETC. For a more detailed description of the zodiacal light, please see the references cited below.

The zodiacal light in the TAUVEX spectral range is due to sunlight scattered by interplanetary dust grains. Because the Sun is a cool star, there will not be much contribution from the zodiacal light in the UV, particularly in the FUV.

The zodiacal light will effectively be a smooth background over the image plane. The level of the zodiacal light will be dependent on the helioecliptic longitude and β, the angle from the ecliptic.

[edit] On-line Calculator

The on-line calculator is a front end to the C program. The only inputs required are the date and the observing direction. The output is the zodiacal light spectrum in units of photons cm^-2 s^-1 sr^-1 Å^-1 plotted as a function of wavelength. This can be integrated with the filter response function to give a count rate in each of the TAUVEX filters. The spectrum itself can be downloaded by clicking on the image.

[edit] Implementation

[edit] Problem Statement

In order to calculate the zodiacal light, we need:

Sun position
Zodiacal light spectrum
Zodiacal distribution

[edit] Sun Position

I have used the algorithm from the Solar position calculator of Bjørn Håkon Granslo. There was a mistake in equation 14 where R_S should be replaced by L_S. I have coded this program as a C function which can be downloaded from the TAUVEX CVS area as: SUN_RA_DEC. The inputs are time of year and the output is celestial coordinates.

[edit] Spatial Dependence

The spatial dependence of the zodiacal light has been tabulated by Leinert et al. and is reproduced here. The heliocentric longitude increases with row number and the β angle increases with column number. The units of the zodiacal light are 10^-8 W m^-2 sr^-1 μm^-1 m^-1 at a wavelength of 500 nm. The scale factor to convert these units into photons cm^-2 s^-1 sr^-1 Å^-1 is 252 at 5000 Å; ie, the numbers in the table have to be multiplied by 252.

Zodiacal light as a function of ecliptic coordinates
β	0	5	10	15	20	25	30	45	60	75	90
0				3140	1610	985	640	275	150	100	77
5				2940	1540	945	625	271	150	100	77
10			4740	2470	1370	865	590	264	148	100	77
15	11500	6780	3440	1860	1110	755	525	251	146	100	77
20	6400	4480	2410	1410	910	635	454	237	141	99	77
25	3840	2830	1730	1100	749	545	410	223	136	97	77
30	2480	1870	1220	845	615	467	365	207	131	95	77
35	1650	1270	910	680	510	397	320	193	125	93	77
40	1180	940	700	530	416	338	282	179	120	92	77
45	910	730	555	442	356	292	250	166	116	90	77
60	505	442	352	292	243	209	183	134	104	86	77
75	338	317	269	227	196	172	151	116	93	82	77
90	259	251	225	193	166	147	132	104	86	79	77
105	212	210	197	170	150	133	119	96	82	77	77
120	188	186	177	154	138	125	113	90	77	74	77
135	179	178	166	147	134	122	110	90	77	73	77
150	179	178	165	148	137	127	116	96	79	72	77
165	196	192	179	165	151	141	131	104	82	72	77
180	230	212	195	178	163	148	134	105	83	72	77

[edit] Spectral Effects

The zodiacal light is reddened but by not more than 20% so a first approximation is to simply use the solar spectrum from Colina et al. This spectrum is shown in Fig. 1 with a normalization described below.

Fig.1 Zodiacal light from UV to IR

Although there are indications that the colour (the brightness relative to the Sun) of the zodiacal light is dependent on both wavelength and position, I have assumed that the colour is unity. The Colina et al. [spectrum] has been scaled such that the value at 5000 Å is 252, corresponding to 10^-8 W m^-2 sr^-1 μm^-1 m^-1 at 5000 Å. Thus the spectrum simply has to be multiplied by the appropriate scale factor from the Table, with a colour correction if desired.

[edit] Coordinate Transformation

The natural coordinate system for the zodiacal light is ecliptic coordinates or, rather, helioecliptic coordinates, while astronomers use celestial or galactic coordinates. I have used the coordinate conversion cannibalized from the [Skyview] routines. The code may be downloaded from our CVS area.

[edit] Input/Output

The input of the program is

hour day month year look_ra look_dec

thus:

12.0 30 9 2007 254.5 -12.6

The output of the program is the zodiacal light at the specified coordinates and date in units of photons cm^-2 s^-1 sr^-1 Å^-1 and should be good to within 20%. More accurate values could be obtained by adding a colour to the spectrum.