Specifying the Appropriate Background¶

There are several potential types of background and noise that can affect the observations; the main contributors being:

Earthshine
Zodiacal light
Geo-coronal emission Lines (UV)
Atmospheric helium (IR)
Thermal background (IR)
Dark current
Read noise (CCDs and NICMOS)

The sum of the External Background components is presented on the Results page. Note that each of the components of External Background can be switched off (set to None or No airglow) so that one of the components can be selected for display on the Results page. All components should be included when simulating observations, as artificially turning off the sky does not represent actual observing conditions.

External Background¶

Earthshine¶

Earthshine can vary strongly depending on the limb angle, on the fraction of the earth that is sun-lit, and on the fraction of cloud cover. At low limb angles, it can dominate the zodiacal light, which varies by only a factor of ~3 throughout the sky available to HST (See Giavalisco et al. WFC3 ISR 2002-12).

The table below lists the relative levels of Earthshine selectable in the ETC.

Table 1: Earthshine Background Contributions Relative to “High”

Level:	None	Average	High	Extremely High
Earthshine	0%	50%	100%	200%
Limb angle	N/A	50 deg	38 deg	24 deg

The phase II special requirement LOW-SKY ensures that the limb angle will be greater than 40 degrees, i.e. that it will avoid the limb angle of the High Earthshine case by at least 2 deg. This requirement greatly reduces scheduling opportunities, so should be requested only when critical to the science and should be well justified in the phase I proposal.

Zodiacal Light¶

The Zodiacal light values given in Table 2 are in ecliptic co-ordinates $\beta$ (ecliptic latitude) and $\lambda-\lambda_{\odot}$ (helio-ecliptic longitude or elongation). See the following figure.

When a user request to calculate the contribution of the Zodiacal light with position, first the Equatorial coordinates are converted to Ecliptic coordinates. The relation between these set of coordinates is:

$\sin(\beta) = \sin(\delta) \cos(\epsilon) - \cos(\delta) \sin(\epsilon) \sin(\alpha) \ \ (i) \\ \cos(\lambda) = \cos(\alpha) \cos(\delta) / \cos(\beta) \ \ (ii) \\ \sin(\lambda) = [\sin(\delta) \sin(\epsilon) + \cos(\delta) \sin(\alpha) \cos(\epsilon) ] / \cos(\beta) \ \ (iii)$

or

$\sin(\beta) = \sin(\delta) \cos(\epsilon) - \cos(\delta) \sin(\epsilon) \sin(\alpha) \ \ (iv) \\ \tan(\lambda) = [\tan(\delta) \sin(\epsilon) + \cos(\epsilon) \sin(\alpha) ] / \cos(\alpha) \ \ (v)$

where:: $\alpha$ = right ascension

$\delta$ = declination

$\epsilon$ = obliquity of the ecliptic with $\epsilon = 23.446^o$ for equinox 1950.

Since we know $\epsilon$ we can then use (i) and (ii) to calculate $\beta$ and $\lambda$ .

To solve for the ambiguity of the sign you should calculate the equations (iii) and (v) and

if $\lambda_1 < 0$ and $\lambda_2 > 0$ and $\lambda_3 > 0$ then $\lambda = \lambda_1 + 180$
if $\lambda_1 > 0$ and $\lambda_2 < 0$ and $\lambda_3 > 0$ then $\lambda = \lambda_1 + 180$
if $\lambda_1 < 0$ and $\lambda_2 < 0$ and $\lambda_3 > 0$ then $\lambda = \lambda_1 + 360$

where:: $\lambda_1 = \tan^{-1}(\tan(\lambda))$

$\lambda_2 = \sin^{-1}(\sin(\lambda))$

$\lambda_3 = \cos^{-1}(\cos(\lambda))$

The ETC then calculates the helio-ecliptic logitude or elongation (sun angle between sun-earth and earth particle) to determine the brightness along the line of sight:

$\lambda' = \lambda - \lambda_{\odot}$

where:: $\lambda_{\odot}$ is the equatorial longitude of the Earth

$\lambda_{\odot}$ is derived as follows:

$\lambda_{\odot} = 360 \times \Delta / 365.25 \ \ (vi)$

where:: $\Delta$ is the number of days from the Vernal Equinox of the selected year (March 20).

Once the Helioeclipic coordinates are calculated, the ETC performs a bilinear interpolation using the values in Table 2 in order to derive the Johnson V magnitude for the Zodiacal contribution. The result is then fed to the pysynphot task renorm to renormalize the Zodiacal light spectrum model (currently zodiacal_model_001.fits) to the derived V magnitude.

Table 2 provides the approximate values of the Zodiacal light background ( $V_{mag} / arcsec^2$ ) in ecliptic latitude ( $\beta$ ) and helio-ecliptic longitude ( $\lambda' = \lambda - \lambda_{\odot}$ ). The SE values correspond to the solar exclusion zone. This table has been updated for cycle 24 using a finer grid to provide better estimates of the zodiacal light as a target approaches the 50 degree HST-to-target limiting angle. It was again modified for ETC 29.1 to correct typos in a few positions (marked with ‘*’).

Table 2: Zodiacal Light Background Contributions

$\lambda'$ (degrees)	$\beta$ (degrees)
$\lambda'$ (degrees)	0	5	10	15	20	25	30	35	45	50	60	75	90
0	SE	SE	SE	SE	SE	SE	SE	SE	SE	22.0708	22.5136	22.9538	23.2298
5	SE	SE	SE	SE	SE	SE	SE	SE	SE	22.0816	22.5136	22.9538	23.2298
10	SE	SE	SE	SE	SE	SE	SE	SE	SE	22.1033	22.5210	22.9538	23.2298
15	SE	SE	SE	SE	SE	SE	SE	SE	SE	22.1454	22.5360	22.9538	23.2298
20	SE	SE	SE	SE	SE	SE	SE	SE	SE	22.2004	22.5743	22.9649	23.2298
25	SE	SE	SE	SE	SE	SE	SE	SE	22.0808	22.2586	22.6141	22.9762	23.2298
30	SE	SE	SE	SE	SE	SE	SE	SE	22.1578	22.3237	22.6554	23.0107	23.2298
35	SE	SE	SE	SE	SE	SE	SE	21.9203	22.2350	22.3924	22.7071	23.0224	23.2298
40	SE	SE	SE	SE	SE	SE	21.8257	22.0287	22.3181	22.4628	22.7522	23.0343	23.2298
45	SE	SE	21.0810	21.3356	21.5717	21.7872	21.9545	22.1379	22.3948	22.5232	22.7801	23.0707	23.2298
50	20.8432	21.0663	21.3194	21.5397	21.7408	21.9486	22.0833	22.2472	22.4715	22.5837	22.8080	23.1071	23.2298
60	21.1844	21.3356	21.5842	21.7872	21.9859	22.1525	22.2937	22.4437	22.6304	22.7237	22.9104	23.1212	23.2298
75	21.6258	21.6965	21.8737	22.0611	22.2180	22.3621	22.4989	22.6319	22.7801	22.8542	23.0024	23.1607	23.2298
90	21.9155	21.9768	22.0660	22.2350	22.3948	22.5284	22.6470	22.7699	22.9104	22.9807	23.1212	23.2016	23.2298
105	22.1315	22.1419	22.2124	22.3686	22.5136	22.6387	22.7614	22.8912	22.9990	23.0529	23.1607	23.2298*	23.2298
120	22.2639	22.2757	22.3305	22.4844	22.5980	22.7071	22.8186	22.9646	23.0707	23.1237	23.2298	23.2736	23.2298
135	22.3181	22.3243	22.3948	22.5284	22.6304	22.7339	22.8483	22.9224*	23.0707	23.1237*	23.2298*	23.2885	23.2298
150	22.3181	22.3243	22.4014	22.5210	22.6060	22.6896	22.7801	22.8639	22.9990	23.0665	23.2016	23.3037	23.2298
165	22.2180	22.2407	22.3181	22.4014	22.4989	22.5743	22.6554*	22.7435	22.9104	22.9938	23.1607	23.3037	23.2298
180	22.0418	22.1315	22.2236	22.3243	22.4216	22.5210	22.6304	22.7348	22.8998	22.9823	23.1473	23.3037	23.2298

Derived from Leinert, et al. (1998), Table 17.

This is used to normalize the Zodiacal Light spectra used by the ETC and shown in the figure below.

Geo-Coronal Emission Lines¶

Table 3: Geo-Coronal Emission Line Properties

Line		Low		Average		High
	Wavelength Angstrom	Flux(erg cm^-2 s^-1)	FWHM Angstrom	Flux(erg cm^-2 s^-1)	FWHM Angstrom	Flux(erg cm^-2 s^-1)	FWHM Angstrom
Lyman_Alpha	1215.7	6.1e-14	0.04	3.05e-13	0.04	6.1e-13	0.04
O_I	1302	3.8e-16	0.013	2.85e-14	0.013	5.7e-14	0.013
O_I	1356	3.0e-17	0.013	2.5e-15	0.013	5.0e-15	0.013
O_II	2471	1.5e-17	0.023	1.5e-15	0.023	3.0e-15	0.023

The strength of the geo-coronal Lyman alpha varies between about 2 and 20 kilo Rayleighs, depending on the time of observations and the position of the target relative to the Sun, and can be kept low by the special requirement “SHADOW”. For more details, see the corresponding Instrument Handbook.

Atmospheric Helium¶

Short-wavelength WFC3/IR imaging filters (F105W and F110W) and WFC3/IR grisms (G102 and G141) are subject to excess background emission caused by metastable Helium atoms in the solar-illuminated upper atmosphere. The background is due to He I emission at 10830 Angstrom. Its contribution is negligible in Earth’s shadow but increases sharply when the telescope is outside of shadow (up to 5 e-/s/pix in extreme cases). The He background also increases with decreasing limb angle, but can still be significant as high as 40 degrees above the Earth limb. For more information on this background component, see WFC3/ISR 2014-03 (Brammer et al.)

The contribution of atmospheric helium to the WFC3 background is negligible in Earth’s shadow, corresponding to the “None” default ETC setting. The “Average”, “High” and “Very High” values implemented in the ETC correspond to 0.1, 0.5, and 1.5 e-/sec/pix in F105W and are the 50, 75, and 95 percentile fluxes of the excess flux, per exposure, from the Helium line determined from archival observations. The ETC model of this emission is a gaussian source at 10830 Angstrom with FWHM = 2 Angstrom.

Thermal Background and Noise¶

The thermal background is negligible below about 8000 Angstrom and increases slowly towards longer wavelengths. For WFC3/IR, the thermal count rate (per unbinned pixel) is calculated by an algorithm that is described in detail in “Thermal Background Limitations for IR Instrumentation Onboard HST”, Sosey, M., Wheeler, T., Sivaramakrishnan, A., 2003, NICMOS ISR 2003-007.

Detector dark current is an intrinsic source of background counts. The dark current rate is dependent upon the detector design and temperature. It is measured in counts per unbinned pixel per second. For CCDs, 1 count = 1 e^-; for MAMAs, 1 count results from each charge cloud detected.

CCD detectors and the WFC3 IR detector are subject to noise caused by the process of reading out the charge accumulated by the pixels. The amount of read noise varies by detector and as a function of gain. CCD read noise is measured per binned pixel, per read. WFC3/IR read noise per pixel is measured by a linear fit to a complete sequence of 15 reads. Fewer reads (smaller NSAMP) result in greater read noise, not taken into account in the computation. (See WFC3 ISR 2009-21).

Table 4: Dark Current and Read Noise Values

Instrument	Detector	Dark Current	Read Noise
		(counts $\cdot$ s^-1 $\cdot$ pixel^-1)	(counts $\cdot$ pixel^-1)
ACS	HRC	0.058	4.7 (for gain=2.0)
	SBC	8.52e-6	N/A
	WFC	0.0168	4.45 (for gain=2.0)
COS	FUVB	9.20e-6 (target acquisition)	N/A
	FUVA	8.92e-6 (target acquisition)	`"`
	FUVB	5.49e-6 (spectroscopic)	`"`
	FUVA	4.81e-6 (spectroscopic)	`"`
	NUV	1.18e-3	N/A
STIS	CCD	0.027 (low; top of detector)	6.5 (for gain=1); 8.9 (for gain=4)
		0.033 (medium; middle of detector)	`"`
		0.039 (high; bottom of detector)	`"`
	FUV	3.0e-5 (no glow component)	N/A
		7.5e-5 (low glow component) [1]	`"`
		1.5e-4 (medium glow component)	`"`
		4.0e-4 (high glow component)	`"`
	NUV	0.0011	N/A
WFC3	IR	0.02	14.6 (for gain=2.5)
	UVIS1	0.00213 ADU/s/pix = 0.00319 counts/s/pix	3.0 (for gain=1.5)
	UVIS2	0.00222 ADU/s/pix = 0.00333 counts/s/pix	3.0 (for gain=1.5)

Specifying the Appropriate Background¶

External Background¶

Earthshine¶

Zodiacal Light¶

Geo-Coronal Emission Lines¶

Atmospheric Helium¶

Thermal Background and Noise¶

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Specifying the Appropriate Background¶

External Background¶

Earthshine¶

Zodiacal Light¶

Geo-Coronal Emission Lines¶

Atmospheric Helium¶

Thermal Background and Noise¶

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