TAUVEX bandpasses and wavelengths

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1 Central (or mean) wavelength
2 Effective wavelength
3 Bandwidths

[edit] Central (or mean) wavelength

By the accepted general definition, the central (or mean) wavelength of a filter is equal to:

$\lambda_0=\frac{\int \lambda T(\lambda) d\lambda}{\int T(\lambda) d\lambda} ,$

where $T (λ)$ is the normalized transmission of a filter as a function of wavelength. We assume for the TAUVEX the normalized effective area curves instead of a plain transmission curves. Thus, TAUVEX filters central (or mean) wavelengths are given by:

$\lambda_0=\frac{\int \lambda A(\lambda) d\lambda}{ \int A(\lambda) d\lambda} ,$

where $A (λ)$ is the normalized effective area as a function of a wavelength.

Below are given the central wavelengths for TAUVEX filters


NBF3	SF1	SF2	SF3	BBF
2193.7	1759.5	2230.5	2563.6	2496

However, while $λ 0$ does not depend on the spectrum of the source, it is precisely representative only where the filter bandwidth is negligible in comparison to that. The effect of the source power distribution over a given broadband filter is included in its effective wavelength $λ e f f$ .

[edit] Effective wavelength

Effective wavelength for TAUVEX filters is defined as

$\lambda_{eff}=\frac{\int \lambda A(\lambda) F(\lambda) d\lambda}{\int A(\lambda) F(\lambda)d\lambda}\,,$

where $F (λ)$ is the source spectrum.

Below are given the effective wavelengths for objects of several basic spectral types and 2 standard white dwarfs. Stellar spectra were obtained from TAUVEX oline flux calculator and white dwarfs spectra were obtained from the CALSPEC database.


Filter	Vega	O0V	B0V	A0V	F0V	G0V	G191B2B WD	GD71 WD
NBF3	2186.6	2182.8	2186.1	2186.58	2196.38	2220.7	2181.3	2182.9
SF1	1768. 0	1707.7	1716.87	1768.0	1935.8	2050.6	1701.8	1703.7
SF2	2205.1	2166.9	2177.98	2205.08	2290.7	2445.55	2166.3	2167.3
SF3	2553.2	2471.0	2483.7	2553.2	2646.75	2726.6	2470.2	2473.4
BBF	2466.4	2338.8	2355.7	2466.4	2664.8	2867.2	2339.03	2342.5

[edit] Bandwidths

The bandwidths of the filters are defined as the integrals of their normalized transmissions. We estimate the effective bandwidth of purely filters and effective wavelengths of TAUVEX (based on the total throughput of the system). However, we shall keep in mind that effective bandwidth may be dependent on the radiation wavelength. If radiation is on the falling part of the filter/system throughput curve, where the transmission is much lower than at peak, the effective bandwidths have to be calculated by integrating over wavelength the filter/system throughput curves and dividing by the throughput at the redshifted wavelengths of the lines for each source. [``An Ultraviolet through Infrared Look at Star Formation and Super Star Clusters in Two Circumnuclear Starburst Rings", Dan Maoz, et al. http://arxiv.org/pdf/astro-ph/0103213.]