A&A 401, 781-796 (2003)
DOI: 10.1051/0004-6361:20030075

The Asiago Database on Photometric Systems (ADPS)[*],[*]

II. Band and reddening parameters

M. Fiorucci1,2 - U. Munari1,2

1 - Osservatorio Astronomico di Padova - INAF, Sede di Asiago, 36012 Asiago (VI), Italy
2 - CISAS, Centro Interdipartimentale Studi ed Attività Spaziali "Giuseppe Colombo", Università di Padova, Italy

Received 18 August 2002 / Accepted 14 January 2003

The Asiago Database on Photometric Systems (ADPS) is a compilation of basic information and reference data on 201 photometric systems (both ground-based and space-born), available in printed form (Moro & Munari 2000, hereafter Paper I) and electronically (http://ulisse.pd.astro.it/ADPS). Seventeen new systems have been added to ADPS since its publication, bringing the total to 218. In this Paper II, band and reddening parameters are homogeneously computed via synthetic photometry for the censed photometric systems with known band transmission profiles (179 systems). Band parameters include various types of wavelengths (mean, peak, Gaussian, and effective according to a series of representative spectral types), widths (width at half maximum, at 80% and 10% of transmission's peak, FWHM of the fitting Gaussian, equivalent, and effective for representative spectral types), moment of the 2nd order, skewness and kurtosis indices, and polynomial expressions for the behavior of effective wavelength and effective width as function of black-body temperature. Reddening parameters include $A(\lambda )/A(V)$ for three reddening laws (characterized by RV=5.0, 3.1 and 2.1) and its range of variability over the HR diagram, the Cardelli et al. (1989) a(x) and b(x) coefficients, second order fits to $A(\lambda )/E_{B-V}$ for three representative spectral types, and polynomial expressions for the behavior of effective wavelength and effective width as function of reddening (for the RV=3.1 law).

Key words: techniques: photometric - astronomical data bases: miscellaneous - catalogs

1 Introduction

The first paper of this series (Moro & Munari 2000, Paper I), devoted to the Asiago Database on Photometric Systems (ADPS), presented a compilation of basic information and reference data for ultraviolet, optical and infrared photometric systems, for both the ground-based and space varieties. In Paper I, 167 photometric systems were censed in extenso and other 34 were briefly noted. Only data from the literature were used, with all information traceable back to the original source.

The literature survey in Paper I proved how poorly documented the majority of the systems was and, even when data were provided, it was usually difficult to interpret unambiguously their meaning, or to inter-compare them, because of the highly heterogeneous methods and conventions adopted by different authors. Even basic concepts such as wavelength and width of a band came in so many varieties that common grounds could be established, from literature data, only for a thin minority of the systems (see discussion under System Description in Sect. 2 of Paper I). The situation with band and reddening parameters is worth some statistics. Out of 201 censed systems, (a) 24% had no wavelength or width information or they were in clear conflict with published band transmission curves, (b) 28% had poor information, typically just the mean or peak wavelength, (c) 44% had decent information (mainly systems with square bands or interference filters), and only for (e) 4% the available information included effective wavelengths for more than one spectral type (just 2% in the case of effective widths). The situation with reddening parameters is even more depressing. Again, out of the 201 censed systems, reddening information was (i) completely missing for 78% of them, (ii) poorly known for 15% (typically $A(\lambda )/E_{B-V}$ for just one or two bands), (iii) satisfactory for 4%, and (iv) complete for only 3% of them.

It appears therefore mandatory to establish a common set of parameters for all photometric systems, and to calibrate them via homogeneous synthetic photometry algorithms and a common sample of input spectra. The availability of the same extensive set of homogeneous parameters would support a proper use of the systems, an easier inter-comparison among them and the appreciation of their legacy when attempting the design of a new one.

A first step in such an homogeneous documentation of existing photometric systems is the derivation of band and reddening parameters for all the photometric systems with known transmission curves. The band parameters derived in this paper include various types of wavelengths, widths and moments for a set of normal and peculiar input spectra, as well as polynomial fits of their behavior with blackbody temperature. Reddening parameters include the Cardelli et al. (1989) a(x) and b(x) coefficients, $A(\lambda )/A(V)$ and $A(\lambda )/E_{B-V}$ for various types of source spectra and extinction laws (RV=5.0, 3.1 and 2.1), and polynomial fits to the behavior of effective wavelength and width.

All our work is based on synthetic photometry. It is by far the only viable mean to document so many systems on homogeneous grounds. However, it cannot entirely substitute detailed individual characterization of photometric systems based on careful analysis of published observations (when available in large enough number and accuracy). Such individual analysis, by iteratively working on the color differences recorded between known stars, can even lead to a revision of published band profiles (cf. Bessell 2000 revision of the Hipparcos/Tycho band profiles published in the ESA's Hipparcos Catalogue). A detailed characterization based on actual observations has been so far successfully attempted only for very few systems and its application to the >200 censed in the ADPS is vastly out of the scope and possibilities of the present series of papers.

Finally, when compiling Paper I we tried to be as complete as possible for the optical and ultraviolet regions ( $\lambda \leq 1~\mu$m). In the infrared the completeness was known to be lower. To improve the completeness of ADPS, further 12 infrared and additional 5 optical systems are now included, bringing the total number of photometric systems censed by ADPS to 218. The new 17 systems are briefly noted in Sect. 4.

\par\includegraphics[width=8.8cm,clip]{fig_001.ps} \end{figure} Figure 1: The set of spectra of normal stars used in the computations of this paper.
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\par\includegraphics[width=8.8cm,clip]{fig_002.ps} \end{figure} Figure 2: The set of peculiar spectra used in the computation of equivalent wavelengths and widths. Note the logarithmic scale for the ordinates, used to expand the dynamical range of the plot so to emphasize visibility of weak features. Some guidance to line identification is provided.
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2 Input spectra for synthetic photometry

A set of input spectra for the synthetic photometry to be carried out in this Paper II has been assembled. It includes normal and peculiar stars. Both sets can be downloaded from the ADPS web site, where further information on them is available.

Normal stars include synthetic spectra of $\iota$ Her (B3 IV), Vega (A0 V), Sun (G2 V), Arcturus (K2 III) and Betelgeuse (M2 Iab) as representative of the range of stars over the HR diagram. The spectrum of a carbon star characterized by  $T_{\rm eff}=3000$ K, $\lg g=0.0$, solar metallicity and ${\rm C/O}=1.1$ is added to the set of normal stars. Vega and the Sun are among the stellar sources more frequently used in literature in the computation of effective wavelengths. The spectrum of $\iota$ Her is taken from Castelli et al. (1997), the carbon star spectrum is from Ya. Pavlenko (private communication), and the others were downloaded from Kurucz's web site (http://kurucz.harvard.edu/), who computed them. Figure 1 presents the 3000 Å-6 $\mu $m portion of these spectra in a linear flux scale and logarithmic wavelength scale.

Peculiar stars include observed spectra of a sample of peculiar objects representative of those affected by emission lines. The spectra, absolutely fluxed, come from the spectral survey of Munari & Zwitter (2002) and cover the wavelength range 3200-9100 Å at a dispersion of $\sim$2.5 Å/pix. The spectra of the peculiar stars are used only with the optical photometric systems. For those bands which outer wings extended outside the 3200-9100 Å interval, the spectra of peculiar stars have been expanded by blackbody approximations of their continua to cover the whole profile band. Figure 2 displays the spectra in a logarithmic flux scale and linear wavelength scale, suitable to expand the dynamical range of the plot and to emphasize visibility of weak features. The peculiar objects are:

average spectrum of the two Wolf-Rayet stars of nitrogen type HD 50896 and HD 96548;

average spectrum of the two Wolf-Rayet stars of carbon type HD 136488 and HD 165763;

PN$_{\rm Ne}$:   
spectrum of the compact planetary nebula M1-13, that is given as representative of low electron density conditions (strong forbidden emission lines);

PN$^{\rm Ne}$:
spectrum of the compact planetary nebula M1-12, that is given as representative of high electron density conditions (hydrogen emission lines dominating);

average spectrum of the three novae Nova Lup 1993, Nova Cir 1995 and Nova Cen 1995 during their nebular phases;

average spectrum of the white dwarfs of type A (hydrogen dominated spectra) EG 274, LTT 7987 and LTT 4816.

3 The database

The database is organized as a series of figures, one for each of the systems with known transmission curves (179 in all). Given their large number, these figures are available in electronic form only, with Fig. 1 given here as an example. Each figure plots in a compressed, normalized format the band transmission profiles (for a finer view and a tabular version see Paper I or the ADPS web site), and reports for each band the computed data following the scheme outlined in Fig. 4 and discussed in detail later in this section. Table 1 lists the photometric systems considered in this paper and gives the number of the corresponding figure. The photometric systems are grouped in Table 1 in four distinct categories (ultraviolet, optical, infrared, and mixed systems) because of their slightly different figure layout scheme and input spectra (see detailed description in Sects. 3.1 and 3.2 below). Within each category the chronological order is followed. The names of the photometric systems are the same as used in Paper I. For reader's convenience, the number of the corresponding figure in Paper I is given too.

Actual transmission profiles were presented in Paper I for slightly more than half of the censed systems (105 out of 201). This number is expanded here (179 out of 218) in several ways, and Table 1 summarizes the source for band transmission profiles for all the systems included in this paper. First, transmission profiles have been located in literature for some more systems. Second, transmission profiles have been reconstructed for other systems by combining filter, atmospheric and telescope transmissions with detector response. Details and tabular versions of these new transmission profiles are available via the web interface to ADPS. Third, bands that were reported by the authors as obtained with interference filters, but for which the transmission profiles have never been published, are assumed to have a symmetric Gaussian profile. Symmetric Gaussians are generally found to give a satisfactory representation of the actual profiles of interference filters. For example, the v, b, y bands of the uvbyH$\beta$ - Strömgren and Crawford - 1956 system[*] (see Fig. 16) are realized with interference filters. If the band and reddening parameters obtained using their actual profiles are compared with those derived using a Gaussian approximation, a mean difference of $\sim$5.1 Å ($\sim$0.1%) is found for the various types of wavelengths and 3.9 Å ($\sim$2.0%) for the equivalent widths. Similar figures are obtained for interference filters of other photometric systems. It may be than assumed that approximating with symmetric Gaussians the unknown transmission profiles of bands realized with interference filters is an acceptable procedure, suitable to provide results accurate to better than 5% for band wavelengths and better than 10% for band widths. For those interference filters that are particularly wide, the accuracy could be lower.

The data contained in Fig. 3 (and those of the other ones available in electronic form only) are described in the subsections below, following the scheme numbered in Fig. 4. The band parameters (areas \begin{figure}{\large\ding{182}}\end{figure}   \begin{figure}{\large\ding{183}}\end{figure}   \begin{figure}{\large\ding{184}}\end{figure} and \begin{figure}{\large\ding{185}}\end{figure}) are discussed first, followed by the reddening parameters (areas \begin{figure}{\large\ding{186}}\end{figure}   \begin{figure}{\large\ding{187}}\end{figure}  \begin{figure}{\large\ding{188}}\end{figure}  \begin{figure}{\large\ding{189}}\end{figure} and \begin{figure}{\large\ding{190}}\end{figure}). In this paper $F(\lambda)$is the transmission profile of the band, $f(\lambda$) the same normalized to 1.0 at its maximum, $S(\lambda)$ the energy distribution of a source spectrum and ${\cal B}(T,\lambda)$ the Planck function for the temperature T. In the figures, quantities for ultraviolet and optical systems are expressed in Å, in $\mu $m for the infrared ones.

3.1 Data scheme for band parameters

3.1.1 Area \begin{figure}{\large\ding{182}}\end{figure}

The information contained within this area pertains to the pure band transmission profile, without convolution with a source spectrum. Figure 5 provides a graphical representation for some of the quantities here considered.

Table 1: List of the 179 photometric systems considered in this paper (all those with known transmission curves among the 218 so far censed by the ADPS project). The names of the systems are the same as in Paper I. Columns 4-6 give respectively the number of the electronic figure devoted to the given system, the number of photometric bands considered in this paper and the type of source for their transmission profiles, while Col. 7 lists the number of the corresponding figure in Paper I ( bn: systems only briefly noted in Paper I, Sect. 3). The sources for the transmission profiles are coded as follow. Tabular: as tabulated by the author(s); graph: derived by us from plots of the transmission profiles published by the author(s); rectangl: rectangular profiles as prescribed by the author(s); reconstr: reconstructed for this paper by combining the detector sensitivity with filter and atmospheric transmission; Gaussian: a Gaussian profile is assumed for the narrow bands obtained with interference filters and for which no other information is available.
\par\includegraphics[width=13cm,clip]{tab_1_A.ps} \end{table}

Table 1: continued.
\begin{table}{\includegraphics[width=13.5cm,clip]{tab_1_B.ps} }

Table 1: continued.
\begin{table}{\includegraphics[width=14.cm,clip]{tab_1_C.ps} }

{\includegraphics[width=18.1cm,clip]{fig_003.ps} }
\end{figure} Figure 3: The figure relative to the Sloan DSS - Fukugita et al. - 1996 photometric system is presented as an example of Figs. 9-187 only available in electronic form at the CDS.
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\par\begin{tabular}{crrrr\vert cccccc\vert}
\end{tabular} \end{figure} Figure 4: Scheme for the organization of numerical data in the figures devoted to the documentation of the photometric systems (see also Fig. 3). The areas in which data are organized are labelled in the same order as they are described in the text in Sects. 3.1.1 to 3.2.5.
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\par {\includegraphics[width=8.8cm,clip]{fig_005.ps} }
\end{figure} Figure 5: Graphical representation of some of the wavelength and width quantities described in Sects. 3.1.1 and 3.1.2. The band is $K_{\rm s}$ from the DENIS - Epchtein et al. - 1994 system (cf. Fig. 172). The shadowed area is the band equivalent width $W_\circ $.
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\fbox{$\lambda_c$ }  is the wavelength halfway between the points where the band transmission profile reaches half of the maximum value. In some cases the bands have complicated shapes, with the band transmission profile crossing several times the 50%-line, like the N band of the NQ - Low and Rieke - 1974 system in Fig. 159. In all such cases the most external 50% points are taken in computing $\lambda_{\rm c}$.

\fbox{$\lambda_\circ$ }  is the mean wavelength of the band:

\begin{displaymath}\lambda_\circ = \frac{\int \lambda~F(\lambda)~{\rm d}\lambda}{\int F(\lambda)~{\rm d}\lambda}\cdot
\end{displaymath} (1)

\fbox{$\lambda_{\rm peak}$ }  is the wavelength at which the band transmission profile reaches its maximum.

\fbox{$\lambda_{\rm gauss}$ }  is the central wavelength of the approximating Gaussian with an area equal to that of the actual band transmission profile. If both the band and the Gaussian are normalized to 1.0 at peak response, and ${\cal A}$ is the area of the band, the equal-area fitting Gaussian is then:

\begin{displaymath}g(\lambda) = \exp{\left[-\pi \frac{(\lambda-\lambda_{\rm gauss})^2}{{\cal A}^2}\right]}\cdot
\end{displaymath} (2)

The value of $\lambda_{\rm gauss}$ has been computed using the Levenberg-Marquardt method (Press et al. 1988).

\fbox{{\it WHM}}  is the the full wavelength span between the points where the band transmission profile reaches half of the maximum value. As for $\lambda_{\rm c}$, in the case of complicated band profiles the most external 50% points are taken when computing WHM.

\fbox{{\it W}10\%}  is the wavelength span between the points where the band transmission profile reaches 10% of the maximum value. In the case of complicated band profiles the most external 10% points are taken in computing W10%. It is worth noticing that for a Gaussian profile of area ${\cal A}$, dispersion $\sigma$ and 1.00 peak transmission it is:

                       $\displaystyle W10\%$ = $\displaystyle 2{\cal A}\sqrt{(\ln 10)/\pi}\ =\ 1.712\ {\cal A}$ (3)
  = $\displaystyle 2\sigma\sqrt{2\ln 10}\ =\ 4.292\ \sigma.$  

\fbox{{\it W}80\%}  is the wavelength span between the points where the band transmission profile reaches 80% of the maximum value. Again, in the case of complicated band profiles, the most external 80% points are taken in computing W80%. It is worth noticing that for a Gaussian profile of area ${\cal A}$, dispersion $\sigma$ and 1.00 peak transmission it is:

                         $\displaystyle W80\%$ = $\displaystyle 2{\cal A}\sqrt{(\ln 1.25)/\pi}\ =\ 0.533\ {\cal A}$ (4)
  = $\displaystyle 2\sigma\sqrt{2\ln 1.25}\ =\ 1.336\ \sigma.$  

\fbox{$FWHM$ }  is the full width at half maximum of the approximating Gaussian with an area equal to that of the actual band transmission profile. If both the band and the Gaussian are normalized to 1.0 at peak response, and ${\cal A}$ is the area of the band, then:

                        FWHM = $\displaystyle 2 {\cal A} \sqrt{(\ln 2)/\pi}\ =\ 0.939\ {\cal A}$ (5)
  = $\displaystyle 2\sigma\sqrt{2\ln 2}\ =\ 2.355\ \sigma.$  

\fbox{$W_\circ$ }  is the equivalent width of the band transmission profile:

\begin{displaymath}W_{\circ}\ =\ \int f(\lambda)~{\rm d}\lambda\ =\ \frac{1}{C} \int F(\lambda)~{\rm d}\lambda
\end{displaymath} (6)

where $C= [ F(\lambda)/f(\lambda)]$ is the normalization factor. $W_\circ $ is the area shadowed in Fig. 5.

\fbox{$\mu$ }  is the 2nd order momentum of the band transmission profile (for a discussion see Golay 1974, pp. 41-43), i.e. the square root of the expression:

\begin{displaymath}\mu^2\ =\ \frac{\int (\lambda-\lambda_\circ)^2 ~F(\lambda)~{\rm d}\lambda}
{\int F(\lambda)~{\rm d}\lambda}\cdot
\end{displaymath} (7)

For a Gaussian profile it is $\mu\ =\ \sigma$, while for a rectangular band of width W it is $\mu\ =\ \sqrt{3}/6\ W$.

\fbox{$I_{\rm asym}$ }  is the skewness index and it closely resembles the 3rd order moment (the only difference lies in the presence of $\mu^3$):

\begin{displaymath}I_{\rm asym}\ =\ \frac{\int (\lambda-\lambda_\circ)^3 ~F(\lambda)~{\rm d}\lambda}
{\mu^3 \int F(\lambda)~{\rm d}\lambda}
\end{displaymath} (8)

with $\mu $ being given by Eq. (7). An $I_{\rm asym}<0.0$ pertains to a band with an extended blue wing (as the band i of the ri - Argue - 1967 system in Fig. 45 that has $I_{\rm asym} = -1.32$), and $I_{\rm asym}>0.0$ to a band with an extended red wing (as the band R of the WBVR - Straizys - #Straiz<#494 system in Fig. 81 that has $I_{\rm asym} = +0.66$). Symmetric profiles are characterized by $I_{\rm asym}= 0.0$ (as the band 35 of the system DDO - McClure and Van den Bergh - 1968 in Fig. 51a for which it is $I_{\rm asym}= 0.06$).

\fbox{$I_{\rm kurt}$ }  is the kurtosis index and it closely resembles the 4rd order moment (the only difference lies in the presence of $\mu^4$. For the normalization constant -3 see below):

\begin{displaymath}I_{\rm kurt}\ =\ \frac{\int (\lambda-\lambda_0)^4 ~F(\lambda)~{\rm d}\lambda}
{\mu^4 \int F(\lambda)~{\rm d}\lambda} - 3.
\end{displaymath} (9)

The kurtosis index gives an indication of the balance between the core and the wings of a profile. The -3 is inserted to have $I_{\rm kurt}~=~0.0$ for a Gaussian profile. A $I_{\rm kurt}>0.0$ indicates a band transmission profile more sharply peaked than a Gaussian, i.e. with more wings than core (as the band Pfor the KLMNPQR - Borgman - 1960 system in Fig. 21a that has $I_{\rm kurt} =+1.66$). A $I_{\rm kurt}<0.0$ pertains instead to a band with more core than wings (as the band T2 for the photoelectric version of the Washington - Canterna - 1976 system in Fig. 94a that has $I_{\rm kurt} =
-1.08$). The kurtosis index for a rectangular band is $I_{\rm kurt}=-6/5$, for an equilateral triangular band it is $I_{\rm kurt}=-3/5$, and for an ${\rm e}^{-\vert x\vert}$ profile it is $I_{\rm kurt}=3$.

\par {\includegraphics[width=8.7cm,clip]{fig_006.ps} }
\end{figure} Figure 6: Values of the 2nd order moment ($\mu $), the skewness and the kurtosis indices for some sample profiles.
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Figure 6 provides a graphical representation of $\mu $, $I_{\rm asym}$ and  $I_{\rm kurt}$ for some reference profiles.

Several systems contain rectangular or Gaussian bands. In the corresponding figures only non-redundant data are provided. It is therefore appropriate to summarize here for these two types of profiles the values of the above described parameters. For a rectangular band with 1.00 peak transmission and width W it is:

                                        $\displaystyle \lambda_c \equiv \lambda_\circ \equiv \lambda_{\rm peak} \equiv \lambda_{\rm gauss}$ (10)
    $\displaystyle WHM \equiv W10\% \equiv W80\% \equiv W \equiv W_\circ$ (11)
    $\displaystyle FWHM = 2 W_\circ \sqrt{(\ln{2})/\pi}\ =\ 0.939\ W_\circ$ (12)
    $\displaystyle \mu = \sqrt{3}/6\ W_\circ\ =\ 0.289\ W_\circ$ (13)
    $\displaystyle I_{{\rm asym}} = 0$ (14)
    $\displaystyle I_{{\rm kurt}} = - \frac{6}{5}$ (15)

and for a Gaussian profiles of peak transmission 1.00 it is:
                                                $\displaystyle \lambda_c \equiv \lambda_\circ \equiv \lambda_{\rm peak} \equiv \lambda_{\rm gauss}$ (16)
    $\displaystyle W_\circ = \frac{1}{2} \sqrt{\pi/\ln 2}\ FWHM\ =\ 1.064\ FWHM$ (17)
    $\displaystyle W10\% = \sqrt{\frac{\ln~ 10 }{\ln~ 2 }} FWHM\ =\ 1.823\ FWHM$ (18)
    $\displaystyle W80\% = \sqrt{\frac{\ln~ 1.25 }{\ln~ 2 }} FWHM\ =\ 0.567\ FWHM$ (19)
    FWHM = WHM (20)
    $\displaystyle \mu = \sigma \ =\ 0.425\ FWHM$ (21)
    $\displaystyle I_{{\rm asym}} = 0$ (22)
    $\displaystyle I_{\rm kurt} = 0.$ (23)

3.1.2 Area \begin{figure}{\large\ding{183}}\end{figure}

This area documents how effective wavelengths (upper rows) and widths (in square bracketts) change with the source spectra  $S(\lambda)$ described in Sect. 2. The effective wavelength is:

\begin{displaymath}\lambda_{\rm eff}\ =\ \frac{\int \lambda~F(\lambda)~S(\lambda...
... d}\lambda}
{\int F(\lambda)~S(\lambda)~{\rm d}\lambda}\cdot
\end{displaymath} (24)

The effective width $W_{\rm eff}$ is the width of a rectangular bandpass of height 1.0, centered at $\lambda_{\rm eff}$, that collects from a source $S(\lambda)$ the same amount of energy going through the filter $f(\lambda)$:

\begin{displaymath}\int f(\lambda)~S(\lambda)~{\rm d}\lambda\ =\
...{\lambda_{\rm eff} + W_{\rm eff}/2} S(\lambda)~{\rm d}\lambda
\end{displaymath} (25)

$W_{\rm eff}$ is the amount by which to multiply the flux per unit wavelength (normally expressed, for example, is erg cm2 s-1 Å-1 at $\lambda_{\rm eff}$) to obtain the flux through the whole band (normally expressed, for example, in erg cm2 s-1).

Different data schemes are adopted for optical, ultraviolet and infrared systems:

optical systems. All normal and peculiar spectra discussed in Sect. 2 are considered. For normal spectra, both the effective wavelength and width are given, while for peculiar spectra only the effective wavelength is listed;

ultraviolet systems. For UV systems the effective wavelength and width are computed for the Sun ( $T_{\rm eff}=5770$ K), Vega ( $T_{\rm eff}=9550$ K) and $\iota$ Her ( $T_{\rm eff}=17~100$ K), and for three Kurucz's models completing the sequence toward higher temperatures: $T_{\rm eff}= 20~000$, 30 000 and 40 000 with $[Z/Z_\odot]=0.0$ and $\lg g = 5.0$;

near-IR systems. For bands between 1 and 8 $\mu $m the effective wavelength and width are computed for the same set of normal stars used with optical photometric systems;

far-IR systems. For bands longward of 8 $\mu $m the effective wavelength and effective width are computed for blackbody energy distributions characterized by the temperatures $T_{\rm eff}=3000$, 1500, 800, 400, 200 and 100 K.

3.1.3 Area \begin{figure}{\large\ding{184}}\end{figure}

The effective wavelength of a blackbody energy distribution is:

\begin{displaymath}\lambda_{\rm eff}\ =\ \frac{\int \lambda~F(\lambda)~{\cal B}(...
{\int F(\lambda)~{\cal B}(T,\lambda)~{\rm d}\lambda}
\end{displaymath} (26)

where ${\cal B}(T,\lambda)$ is the Planck function. In this area it is reported a third order polynomial fit to the behaviour of $\lambda_{\rm eff}$ with blackbody temperature:

\begin{displaymath}\lambda_{\rm eff}(T)\ =\ a\ +\ b T_{\rm eff} +\ c T_{\rm eff}^2\ +\ d T_{\rm eff}^3 .

To limit the number of significant digits of the polynomial coefficients to three (for a compact writing of the expressions), the temperature must be parametrized. For ultraviolet and optical systems, the temperature is expressed as:

\begin{displaymath}\theta\ =\ \frac{2500}{T {\rm (K)}}
\end{displaymath} (27)

and the polynomial fit

\begin{displaymath}\lambda_{\rm eff}(T)\ =\ a_\theta\ +\ b_\theta \theta\ +\
c_\theta \theta^2\ +\ {\rm d}_\theta \theta^3
\end{displaymath} (28)

is computed over the interval $50~000\leq T \leq 2500$ K. Within this range of temperatures the polynomial fits provide $\lambda_{\rm eff}(T)$ accurate to better than 3 Å for essentially all systems. For near-IR systems, the temperature is expressed as :

\begin{displaymath}\Phi\ =\ \frac{500}{T {\rm (K)}}
\end{displaymath} (29)

and the polynomial fit

\begin{displaymath}\lambda_{\rm eff}(T)\ =\ a_\Phi\ +\ b_\Phi \Phi\ +\
c_\Phi \Phi^2\ +\ d_\Phi \Phi^3
\end{displaymath} (30)

extends over the range $10~000\leq T \leq500$ K. Within it, the fit provides $\lambda_{\rm eff}(T)$ accurate to better than 0.01 $\mu $m for most systems. Finally, for far-IR systems, the temperature is expressed as:

\begin{displaymath}\Psi\ =\ \frac{100}{T {\rm (K)}}
\end{displaymath} (31)

and the polynomial fit

\begin{displaymath}\lambda_{\rm eff}(T)\ =\ a_\Psi\ +\ b_\Psi \Psi\ +\
c_\Psi \Psi^2\ +\ d_\Psi \Psi^3
\end{displaymath} (32)

is computed over the interval $3000\leq T \leq100$ K, where it provides results accurate to 0.02 $\mu $m for nearly all systems.

The coefficients in the polynomial fits are given explicitely even when null: for example, writing 0.00 for $c_\Psi$ means that the actual coefficient of $\Psi^2$ is $\vert c_\Psi\vert < 0.005$ (0.005 being rounded to 0.01). The same applies to all other coefficients used in this paper (Sects. 3.1.4, 3.2.4 and 3.2.5).

3.1.4 Area \begin{figure}{\large\ding{185}}\end{figure}

The effective width $W_{\rm eff}$, in the case of a blackbody energy distribution, is the width of a rectangular bandpass of height 1.0, centered at $\lambda_{\rm eff}$, that collects from a blackbody ${\cal B}(T,\lambda)$ the same amount of energy going through the filter $f(\lambda)$:

\begin{displaymath}\int f(\lambda)~{\cal B}(T,\lambda)~{\rm d}\lambda\ =\
...\rm eff} + W_{\rm eff}/2} {\cal B}(T,\lambda)~{\rm d}\lambda.
\end{displaymath} (33)

Here it is provided a third order polynomial fit to the behaviour of $W_{\rm eff}$ with the blackbody temperature. The same parametrization of temperature ($\theta$, $\Phi$ and $\Psi$) and ranges of applicability adopted for $\lambda_{\rm eff}(T)$ are mantained for $W_{\rm eff}(T)$ too.

The third order polynomial fits to $W_{\rm eff}(T)$ tipically provide results accurate to 5 Å for UV and optical systems, 0.01 $\mu $m for near-IR systems and 0.02 $\mu $m for far-IR ones.

3.2 Data scheme for reddening parameters

The behaviour with different reddening laws and amount of extinction is investigated in the remaining areas numbered in Fig. 4 for all photometric bands at $\lambda \leq 8~\mu$m. The amount of extinction in a given band is :

\begin{displaymath}A(\lambda)\ =\ -2.5 \lg \frac{ \int F(\lambda)~S(\lambda)~\ta...
...a)~{\rm d}\lambda}{ \int F(\lambda)~S(\lambda)~{\rm d}\lambda}
\end{displaymath} (34)

where $\tau(\lambda)$ is the transmission coefficient of the interstellar medium and $\eta$ in the relative mass of the medium. The latter is taken so that a unit amount of medium ($\eta=1$) causes a reddening EB-V = 1.0 for O-type stars (Straizys #Straiz<#649, p. 10, 100 and 136). In such a case the corresponding hydrogen column density is $N_{\rm H}({\rm HI}+{\rm H}_2)=5.8 \times 10^{21}$atoms cm-2 (Savage & Mathis 1979) for the average interstellar medium characterized by the standard RV=3.1 law.

Three extinction laws are considered, labelled according to their RV = A(V)/EB-V ratio, as representative of the continuum of extinction laws encountered in Nature (from Fitzpatrick 1999). Their shapes are compared in Fig. 7. Their tabular version can be downloaded via anonymous ftp from astro2.astro.vill.edu (directory pub/fitz/Extinction/FMRCURVE.pro) or from the ADPS web site.

\par {\includegraphics[width=8.8cm,clip]{fig_007.ps} }
\end{figure} Figure 7: The three extinction laws considered (from Fitzpatrick 1999). The dot marks the V band from the UBV - Johnson and Morgan - 1953 system.
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The quantities normally employed in characterizing the effects of reddening and extinction in a given photometric system are color excess ratios $E(\lambda_4 -\lambda_3)/E(\lambda^{\rm ref}_{2} -\lambda^{\rm ref}_{1})$, ratios of total to selective extinction $A(\lambda)/E(\lambda^{\rm ref}_{2}-\lambda^{\rm ref}_{1})$, and absolute extinction ratios $A(\lambda)/A(\lambda^{\rm ref})$. Historically, the adopted $\lambda^{\rm ref}_{i}$ are the B and V bands of the UBV - Johnson and Morgan - 1953 system. Such a choice may not be the optimal one because these bands are rather wide, they embrace a lot of fine structure features of the interstellar extinction and they are not on the RV-independent part of the extinction curve at $\lambda \geq 8500$ Å. However, we will adopt B and V as $\lambda^{\rm ref}_{i}$ in this paper both for historical reasons and commonality with existing literature. In all computations we explicitely integrate over the whole and exact B and V profiles, and we do not limit ourselves to simply compute at the characteristic wavelength of the band.

Before to proceede, the B and V reference bands must be accurately defined. Throughout this paper we adopt for B and V the so called Vilnius reconstruction (Azusienis & Straizys 1969) of the original UBV - Johnson and Morgan - 1953 system (hereafter VILNIUS-REC-UBV; see Azusienis & Straizys 1969 for details on which Bband to use in combination with U and V bands). The effect of choosing one or another band profile for the reference B and V bands has non-negligible effects. Table 2 (built from data in Figs. 12, 61 and 131, for the RV=3.1 extinction law and the B3 spectral type) shows the differences between the USA, Vilnius, photographic, Buser (1978), Bessell (1990) and Landolt (1983) versions of the same UBV - Johnson and Morgan - 1953 system. It is evident how the differences cannot be ignored when an accurate analysis is required.

Table 2: Values of the reddening parameters $A(\lambda )/A(V)$ and $A(\lambda )/E_{B-V}$ for different reconstructions of the V band of the UBV - Johnson and Morgan - 1953 photometric system. The reference B and V bands are those of the Vilnius reconstruction. The reconstruction by Buser (1978) adopts the same reconstruction as Vilnius for the V band, which explains the identical numbers for the two.
{\includegraphics[width=8.8cm,clip]{tab_2.ps} }

It has to be noted that the reddening expressions depend on the spectral type of the star and the amount of reddening because both change the band effective wavelengths. An example illustrates the effect of the stellar spectral type. For VILNIUS-REC-UBV in Fig. 12b, RV=3.1 law and $\eta=1$ in Eq. (34), the effective wavelengths of the A(V)/EB-Vratio for a B3 star are:

\begin{displaymath}\frac{A(V)}{E_{B-V}}\ \longrightarrow\ \frac{A (5429\ {\rm\AA})}{E(4336{-} 5429\ {\rm\AA})}

while for a M2 star they become:

\begin{displaymath}\frac{A(V)}{E_{B-V}}\ \longrightarrow\ \frac{A (5595\ {\rm\AA})}{E(4666{-} 5595\ {\rm\AA})}\cdot

Going from spectral type B3 to M2, the $\lambda_{\rm eff}$ of the Bband changes by 330 Å while for the V band the change is only 166 Å. The lever arm (i.e. the distance in $\lambda_{\rm eff}$ between B and V bands) reduces toward redder spectral types, therefore requiring a higher A(V) extinction to match the EB-V = 1.0 condition. From data in Fig. 12b it is in fact:

\begin{eqnarray*}\frac{A(V)}{E_{B-V}} & = & 3.13\ {\rm for\ early\ type\ stars} ...
...\rm for\ Sun-like\ stars} \\
& = & 3.69\ {\rm for\ M\ stars}.

The effect of the reddening is also quite strong. Again from Fig. 12b for VILNIUS-REC-UBV, a $\bigtriangleup E_{B-V} = 1.0$ changes the effective wavelength of the B band by 133 Å, and that of the V band by 113 Å.

The net effect is that the reddening does not translate rigidly the main-sequence over the color-magnitude diagram: the shape of the main-sequence modifies according to the amount of reddening (with obvious implications for classical reddening estimates of clusters). How much the main-sequence shape modifies for different amounts of reddening is grafically represented in Fig. 8 for the UBVRI - Landolt - 1983 system (the curves are available in electronic form from the ADPS web site).

\par {\includegraphics[width=8.8cm,clip]{fig_008.ps} }
\end{figure} Figure 8: Modification of the main-sequence on the MV, $(B-V)_\circ $ plane of the UBVRI - Landolt - 1983 system for the RV=3.1 extinction law and different reddenings (EB-V=0,1,2) . The curves are shifted so that the solar positions for them coincide (dot). Nearly identical modifications apply for the RV=5.0 and RV=2.1 cases. The unreddened main-sequence is from Drilling & Landolt (2000, their Table 15.7).
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3.2.1 Area \begin{figure}{\large\ding{186}}\end{figure}

The $A(\lambda )/A(V)$ absolute extinction ratio

\begin{displaymath}\frac{A(\lambda)}{A(V)}\left\vert \begin{array}{l}\\ R_V \end{array} = X.XX
\begin{array}{c}Q_1 \\ Q_2 \end{array} \right.
\end{displaymath} (35)

is reported in this area for the pure band transmission profile, without covolution with a source spectrum and for $\eta=1$ (cf. Eq. (34)). The ratio is computed for the three different extinction laws labelled by their RV values.

The covolution with a source spectrum modifies however the value of the ratio: the extremes reached over the sources considered in area \begin{figure}{\large\ding{183}}\end{figure} are listed as values Q1 and Q2 in the equation scheme above. For optical systems only spectra of normal stars (cf. Sect. 2) are considered.

3.2.2 Area \begin{figure}{\large\ding{187}}\end{figure}

The shape of the extinction law $A(\lambda )/A(V)$ can be conveniently and accurately parametrized in term of RV as :

\begin{displaymath}\frac{A(\lambda)}{A(V)}\ =\ a(x)\ +\ \frac{b(x)}{R_V}
\end{displaymath} (36)

where $x=1/\lambda$ (in $\mu $m-1). The analytical expressions of a(x) and b(x) coefficients are given by Cardelli et al. (1989). They offer a powerful way to derive the extinction at any wavelength for any extinction law parametrized by RV.

The a(x) and b(x) coefficients can be profitably used to parametrize in terms of RV the reddening relations normally used :

\begin{displaymath}\frac{E(\lambda_2-\lambda_1)}{A(V)} = (a_2 - a_1) + \frac{(b_2-b_1)}{R_V}
\end{displaymath} (37)

\begin{displaymath}\frac{A(\lambda)}{E_{B-V}} = \frac{A(\lambda)}{A(V)} R_V\
=\ a R_V + b
\end{displaymath} (38)

\begin{displaymath}\frac{E(\lambda-V)}{E_{B-V}} = \frac{A(\lambda)}{E_{B-V}} - R_V\ =\ (a-1) R_V + b
\end{displaymath} (39)

\begin{displaymath}\frac{E(\lambda_2-\lambda_1)}{E_{B-V}} = (a_2 - a_1) R_V + (b_2 - b_1).
\end{displaymath} (40)

These relations show that expressing the extinction in terms of $A(\lambda )/A(V)$ or $E(\lambda-V)/E_{B-V}$ is equivalent, provided that RV is known. If the extinction law is unknown, $A(\lambda )/A(V)$ and $E(\lambda-V)/E_{B-V}$ cease to be equivalent ways to describe the extinction.

The values of a(x) and b(x) depend on the source spectrum and the amount of reddening because both change the $\lambda_{\rm eff}$ at which the coefficients are computed. For example, for the R band of the UBVRI - Landolt - 1983 system, it is $\bigtriangleup \lambda_{\rm eff} =124$ Å when moving from B3 to Sun spectral type, and $\bigtriangleup
\lambda_{\rm eff} =264$ Å when changing from EB-V = 0.0 to EB-V = 1.0. Such variations are too large to be ignored, and therefore we have computed the a(x) and b(x) coefficients for the B3 and Sun spectral types (representative of the hotter and cooler regions of the HR diagram, respectively) for both EB-V = 0.0 and EB-V = 1.0 conditions. They are given in area \begin{figure}{\large\ding{187}}\end{figure} in the following format:

\begin{displaymath}\begin{tabular}{r\vert rl\vert}
...sl Sun}\\

The a(x) and b(x) coefficients are useful also in deriving Q or reddening-free parameters for any extinction law characterized by RV. A reddening-free parameter is a combination of colors that is independent from interstellar reddening. Given four photometric bands A, B, C and D, the reddening-free parameter and its expression in terms of a(x) and b(x) coefficients are:
                                 QABCD = $\displaystyle (A\ -\ B)\ -\ \frac{E_{A-B}}{E_{C-D}}(C\
-\ D)$ (41)
  = $\displaystyle (A\ -\ B)\ -\ \frac{(a_A - a_B)R_V +
(b_A - b_B)}{(a_C - a_D)R_V
+ (b_C - b_D)}(C\ -\ D) .$  

Because a(x) and b(x) depend upon the effective wavelength, the QABCD so derived will be most accurate only in the neighborhood of a given spectral type and for a given amount of reddening.

The best known reddening-free parameter is perhaps that for the UBV - Johnson and Morgan - 1953 system, given by Hiltner & Johnson (1956) as $Q_{UBV}=(U-B) - \Upsilon (B-V)$ where $\Upsilon = 0.72 + 0.05E_{B-V}$ for O-type stars suffering from a standard RV=3.1 extinction law. Using the values of a(x) and b(x) from Fig. 12b ( VILNIUS-REC-UBV) for the B3 spectral type, Eq. (49) provides $\Upsilon = 0.71$ for EB-V = 0.0 and $\Upsilon = 0.78$ for EB-V = 1.0, in excellent agreement with Hiltner and Johson's values. The corresponding figures for a Sun-like source spectrum would be instead $\Upsilon = 0.88$ for EB-V = 0.0 and $\Upsilon = 1.06$for EB-V = 1.0.

3.2.3 Area \begin{figure}{\large\ding{188}}\end{figure}

In this area it is given the second order polynomial fit to extinction versus reddening for the RV=3.1 extinction law and three different spectral types according to the wavelength region: B3, Sun and M2 for optical and infrared systems, and $\iota$ Her (B3), Sun and a Kurucz's 40 000 K, $[Z/Z_\odot]=0.0$, $\lg g = 5.0$ spectrum for ultraviolet systems. The coefficients are given in the form:

\begin{displaymath}\frac{A(\lambda)}{E_{B-V}}\ =\ \alpha\ +\ \beta~E_{B-V}\
=\ (\alpha,\ \beta) %
_{\rm spectrum}.%
\end{displaymath} (42)

The expression provides an exact solution, in the sense that the absorption in the three bands B, V and $\lambda$ is computed for each incremental value of x in Eq. (34). The regression coefficient rgives as an indication of the accuracy of the fit (generally pretty high with |r| close to 1.0).

The $\alpha$ and $\beta$ coefficients can be used to derive the reddening-free parameter QABCD in a direct way (for the RV=3.1 law, while for others it is necessary to use Eq. (49) above):

                                  QABCD = $\displaystyle (A\ -\ B)\ -\ \frac{E_{A-B}}{E_{C-D}}(C\
-\ D)$ (43)
  = $\displaystyle (A\ -\ B)\ -\ \frac{\alpha_A - \alpha_B + (\beta_A -
\beta_B)E_{B-V}}{\alpha_C - \alpha_D + (\beta_C -
\beta_D)E_{B-V}}(C\ -\ D).$  

From the $\alpha$ and $\beta$ coefficients in Fig. 12b in the VILNIUS-REC-UBV case and B3 spectral type, it is found $\Upsilon =
0.70 + 0.05E_{B-V}$ for $Q_{UBV}=(U-B) - \Upsilon (B-V)$, again in excellent agreement with Hiltner & Johnson (1956) value for O-type stars.

3.2.4 Area \begin{figure}{\large\ding{189}}\end{figure}

In this area it is reported the first order polynomial fit to the behaviour of $\lambda_{\rm eff}$ with EB-V for the pure band transmission profile and the RV=3.1 extinction law:

\begin{displaymath}\lambda_{\rm eff}\ =\ \delta\ +\ \gamma\ E_{B-V}.
\end{displaymath} (44)

The regression coefficient r is given as an indication of the accuracy of the fit.

3.2.5 Area \begin{figure}{\large\ding{190}}\end{figure}

Similarly, a first order polynomial fit to the behaviour of $W_{\rm eff}$ with EB-V for the pure band transmission profile and the RV=3.1 extinction law is given:

\begin{displaymath}W_{\rm eff}\ =\ \varepsilon\ +\ \zeta\ E_{B-V}.
\end{displaymath} (45)

Again, the regression coefficient r is given as an indication of the accuracy of the fit.

4 Additional photometric systems

The 17 new photometric systems added to the ADPS are here briefly noted. The wavelength and width of the bands listed in this section (including terminology and number of decimal figures) are those given in the original papers, while wavelengths and widths given in the rest of this paper (electronic Figs. 9-187) come from our computations based on the actual band profiles. The new systems with available band transmission profiles are:

Strömgren and Gyldenkerne - 1955 (Fig. 15). From a series of 25 interference filters with transmission peaks in the range 3800-5500 Å  used to measure 110 MKK standard stars at the Observatoire de Haute-Provence, a first group of four filters was isolated and used by Strömgren (1956) to define his uvby system aiming to study F stars (and later extended to A and B types). A second group of five filters was selected by Strömgren & Gyldenkerne (1955) to become the base of a system designed to measure G and K stars, in particular the CaII-K line, the discontinuity at the G-band and CN intensity. The adopted bands have widths at half maximum of 100 Å and central wavelengths at 3910, 4030, 4170, 4240 and 4360 Å.

Bahner - 1963 (Fig. 31). A system composed by 16 square bands in the range 3200-6400 Å aimed to investigate B and A stars. Four bands are devoted to the measurement of the Balmer continuum, and ten bands to the optical continuum away from strong absorption features.

Mould and Wallis - 1977 (Fig. 103). In ADPS I we briefly mentioned it as a modification of the Mould - 1976 system. Actually, the differences are large enough to justify its inclusion in ADPS II as a separate photometric system. It is aimed to the measurement of CaH and TiO bands in M stars and T Tau stars of the M spectral type. Five bands, realized with interference filters, have their central wavelengths (and widths at half maximum) at 5450 (200), 6940 (140), 7140 (140), 7520 (140) and 8500 (400) Å.

Malyuto et al. - 1997 (Fig. 142). This is a system with six sets of bands, each one composed by three square bands, aimed to quantitatively classify K and M stars via the strengh of FeI (+TiO $\alpha_1$) around 5013, Mgb (+TiO $\alpha_0$) at 5235, NaI D (+TiO  $\gamma_{1}^{\prime}$) at 5930, TiO  $\gamma_{0}$ at 7235, TiO  $\gamma_{0}^{\prime}$ 6250 and TiO  $\gamma_{1}$ 6723 Å bands. The bands are realized on spectra and are found to be insensitive to differences in data reduction procedures, reddening and resolution of the spectral catalogues to which they are applied. The system is claimed to provide an average accuracy of 0.6 spectral subtype and 0.8 luminosity class in the classification of K and M stars.

Hickson and Mulrooney - 1998 (Fig. 145). A survey of 20 deg2 in 33 narrow bands complete to mag $\sim$20 has been conducted with the 3-m liquid mirror telescope of the NASA Orbital Debris Observatory. The filters have central wavelengths ranging from 4545 to 9477 Å, at intervals of $\sim$0.01 in $\lg \lambda$, and give a resolving power of $\lambda/\Delta\lambda \sim44$. The survey aims to provide photometric redshifts of $\sim$104 galaxies and QSOs and accurate photometry and spectral classification for $\sim$104 field stars. Central wavelengths (and bandwidths) of the photometric bands (in Å) are: 4545 (177), 4659 (185), 4756 (193), 4860 (202), 4981 (219), 5102 (224), 5190 (227), 5327 (228), 5451 (210), 5570 (214), 5711 (217), 5856 (231), 5976 (243), 6137 (236), 6287 (264), 6411 (240), 6546 (280), 6713 (291), 6880 (292), 7044 (299), 7187 (306), 7347 (322), 7524 (332), 7696 (319), 7875 (333), 8059 (346), 8248 (337), 8438 (356), 8679 (351), 8831 (413), 9063 (353), 9245 (400) and 9477 (391).

JHK KPNO - Manduca and Bell - 1979 (Fig. 162). The transmission of the JHK filters in use at KPNO are given together with local Earth's atmosphere transmission. KAO far-IR - Harvey - 1979 (Fig. 163). This is the five bands, far-IR photometric system for the He-cooled bolometer attached to the 0.91 m telescope on board the Kuiper Airborne Observatory airplane. The bolometer explores the range of wavelengths blocked by the Earth's atmosphere longward of 35 $\mu $m. The $\lambda_{\rm eff}$ and widths at half maximum (for a Sun-like energy distribution as reflected by a planetary surface) of the five bands are (in $\mu $m): 40 and 31-49 (band KAO-40); 52 and 44-59 (KAO-52); 100 and 80-130 (KAO-100N); 110 and 80-155 (KAO-100B); 160 and 125-250 (KAO-160).

IRTS FIRP - Lange et al. - 1994 (Fig. 173). The Far-IR Photometer (FIRP) on the IR Telescope in Space (IRTS) provided absolute photometry in four bands, whose central wavelengths (and widths at half maximum) are: 150 (68), 250 (135), 400 (130) and 700 (370) $\mu $m. S-520-15 FIR - Matsuhara et al. - 1994 (Fig. 174). A five bands, far-IR photometer was placed aboard a S-520-15 rocket launched on Feb. 2, 1992 by ISAS (Japan) from the Kagoshima Space Center. The He-cooled telescope aimed to the detection of diffuse far-IR emission at high galactic latitudes during the 350 s flight outside the atmosphere. It carried both wide bands (BC1, BC2 and BC3) and narrow ones, the latter's goal being the detection of diffuse emission in the [CII] line at 157.7 $\mu $m (a narrow LC band at the line nominal wavelength, and an associated control CC band on the adjacent continuum). The central wavelengths and widths at half maximum of the bands are (in $\mu $m): 95 and 19 (band BC1); 134 and 13 (BC2); 186 and 23 (BC3); 157.9 and 1.3 (LC); 153.7 and 1.5 (CC).

iz, iJ, iH, iK, iL, iL$^\prime$, iM, in, iN, iQ - Young et al. - 1994 (Fig. 177). It is the optimization of infrared bands by Young et al. (1994) in response to recommendations made by the Working Group on Infrared Extinction and Standardization of IAU Commission 25. The optimization aims to enhance reproducibility and trasformability and to allow the use of linear extinction curves by reducing the effect of molecular absorption at the edges of the photometric bands. Peak weavelengths and widths at half maximum are (in $\mu $m): 1.032 and 0.073 (band iz); 1.240 and 0.079 (iJ); 1.628 and 0.152 (iH); 2.196 and 0.188 (iK); 3.620 and 0.274 (iL); 3.900 and 0.274 ($iL^\prime$); 4.675 and 0.114 (iM); 9.030 and 0.323 (in); 11.10 and 2.00 (iN); 17.90 and 1.61 (iQ).

ABU SPIREX - 1998 (Fig. 181). A six band photometric system is available at the 60-cm telescope of the SPIREX facility at the South Pole, operated by the Center for Astrophysical Research in Antartica (CARA) and NOAO (Fowler et al. 1998 and http://www.noao.edu/scopes/south_pole/). The bands have their central wavelength and width at half-maximum as follow (in $\mu $m): 2.4245 and 2.4076-2.4414 (band H2Q(3)); 3.299 and 3.262-3.336 (PAH); 3.514 and 3.205-3.823 (L); 3.821 and 3.520-4.122 (L$^\prime$); 4.051 and 4.024-4.078 (Br$\alpha$); 4.668 and 4.586-4.749 (MN).

JHK$^\prime$KsKL$^\prime$M$^\prime$   MKO - Tokunaga et al. - 2002 (Fig. 182). The new set of near-IR filters for the Mauna Kea Observatories (MKO) is designed to avoid as much as possible the detrimental effects of telluric absorption bands, to the aim of reducing background noise, improving photometric transformations between Observatories, providing greater accuracy in extrapolating to zero airmass, and reducing the color dependence of extinction coefficients. The central wavelengths and widths at half maximum (in $\mu $m) for the seven bands are (Tokunaga et al. 2002): 1.250 and 1.170-1.330 (band J); 1.635 and 1.490-1.780 (H); 2.120 and 1.950-2.290 ($K^\prime$); 2.150 and 1.990-2.310 ($K_{\rm s}$); 2.200 and 2.030-2.370 (K); 3.770 and 3.420-4.120 ($L^\prime$); 4.680 and 4.570-4.790 ($M^\prime$).

The new systems censed in the ADPS that have no documentation about their band transmission profiles (and that are therefore not further considered in this paper) are:

Aerobee IR-65 - 1965. An Aerobee rocket carrying a N2-cooled telescope was launched on Oct 29, 1965 for a scan of the sky during a $\sim$300 s ballistic flight outside the atmosphere. Two photometric bands were realized: InAs with a band-pass from 1 to 3 $\mu $m and AuGe with a band-pass from 3 to 7 $\mu $m (McNutt et al. 1966; Harwit et al. 1966).

DIRBE COBE - Kelsall et al. - 1990. DIRBE is an absolute photometer on COBE (COsmic Background Explorer). It is internally stabilized to 1% repeatibility and it is equipped with 10 infrared bands. They are the J(1.25 $\mu $m), K(2.3), L(3.5) and M(4.5) bands, plus the IRAS bands nominally at 12, 25, 60 and 100 $\mu $m, and two additional bands at 160 and 240 $\mu $m.

SpaceLab IRT - Kent et al. - 1992. Survey scans of the sky at six infrared wavelengths were obtained with IRT (infrared telescope experiment), as part of the SpaceLab-2 mission on the Space Shuttle 51-F. The six bands have width at half maximum (in $\mu $m) of 1.7-3.0, 4.5-9.5, 6.1-7.1, 8.5-14, 18-30 and 70-120. Data collected at $\lambda > 3~\mu$m were corrupted by the high background radiation generated by the Shuttle environment. Data from the shortest band were instead useful in producing a map of the Galaxy emission at 2.4 $\mu $m. The single-band photometric system is defined by the flux of three reference stars (g Her, $\alpha$ Her and $\mu $ Cep).

MSX - Egan and Price - 1996. The infrared telescope radiometer (SPIRIT III) aboard the Ballistic Missile Defense Organization (BMDO) Mid-course Space Experiment (MSX) has been used to pinpoint infrared astrometric reference stars (177 860 sources cataloged, Egan & Price 1996). The radiometer includes six photometric bands whose mean wavelengths and widths at half maximum are (in $\mu $m): 4.29 and 4.22-4.36 (band B1); 4.35 and 4.24-4.46 (B2); 8.26 and 6.0-10.9 (A); 12.1 and 11.1-13.2 (C); 14.7 and 13.5-16.0 (D); 21.4 and 18.1-26.0 (E).

TIRCAM 2 - Persi et al. - 2002. Mid-IR photometric system for the TIRGO Infrared Observatory, defined by the flux at 1.0 airmass of six reference stars ($\alpha$ Lyr, $\beta$ Gem, $\alpha$ Boo, $\beta$ And, $\beta$ Peg and $\alpha$ Tau) as given in Persi et al. (2002). $\lambda_{\rm eff}$ and widths at half maximum are (in $\mu $m): 8.81 and 8.4-9.2 (band F[8.8]); 9.80 and 9.3-10.3 (F[9.8]); 10.27 and 9.8-10.8 (F[10.3]); 11.69 and 11.1-12.3 (F[11.7]); 12.49 and 11.9-13.1 ([F12.5]). The TIRCAM 2 is an upgrade of a previous TIRCAM 1 (Persi et al. 1996) version.

5 Notes on individual photometric systems

UBV - Johnson and Morgan - 1953 (Fig. 12). Compared to Paper I, a fourth system reconstruction has been considered (Buser 1978; Buser & Kurucz 1978), while Vilnius one for the B band is now properly splitted into the B and $B_{\rm p}$ variants (cf. Strayzis 1992).

PV - Eggen - 1955 (Fig. 14). The wavelength and width of the V filter as given in Paper I are inaccurate.

Vilnius - Straizys et al. - 1965 (Fig. 38). The transmission curves for S and T filters are taken from Straizys (1992).

27 colors - Wing - 1967 (Fig. 49). In accordance to Paper I, we consider here only the bands for which $\lambda_{\rm c}$ is specified in the source paper.

H $\beta,\gamma$ - Sinnerstad et al. - 1968 (Fig. 52) The overall shape of the H$\beta$-wide filters is taken equivalent to H$\gamma$-wide as specified in the source paper.

Spinrad and Taylor - 1969 (Fig. 56). The widths of the bands (16 Å shortward of 5360 Å and 32 longward) as revised by Spinrad & Taylor (1971) are adopted here.

nh - Landolt - 1970 (Fig. 61). Only the Oct 14, 1965 filter set is considered.

H$\gamma$ - Häggkvist - 1971 (Fig. 64). The source paper reports about aging effects on wavelengths and widths of the adopted interference filters. Mean values are considered here.

Wawrukiewicz - 1971 (Fig. 68). Actual FWHM of TiO bands are twice the values reported in Paper I.

Caplan - 1973 (Fig. 76). Bands 6548 and 6577 given in Paper I are actually a single band extending from 6536 to 6589 Å. 10 colors - Faber - 1973 (Fig. 79). Band transmission profiles are taken from Fig. 1 of the source paper.

H$\alpha$ - Vidal - 1974 (Fig. 89). Paper I reports right values for band FWHM, but plots and tabulates them twice as large.

uvgr 39B 39N - Zinn - 1980 (Fig. 109). The uvgr bands are the same as those of the uvgr - Thuan and Gunn - 1976 system (see Fig. 100), and therefore only the 39B and 39N interference filter bands are considered here.

eight-colors - Tedesco et al. - 1982 (Fig. 116). Band transmission profiles are taken from Fig. 1 of the source paper.

Kenyon and Fernandez-Castro - 1987 (Fig. 125). Differently from Paper I, here we consider also the two bands at 8190 and 8400 Å described in the source paper.

g4r4i4z4 - Schneider et al. - 1989 (Fig. 129). Paper I reports erroneous transmission curves, that have been replaced by the correct ones in the ADPS web site and in this paper.

Hipparcos - 1989 (Fig. 130). Besides the original ESA's transmission curves (as published in the Hipparcos Catalogue, ESA SP-1200), here we consider also the revised profiles by Bessell (2000).

POSS II - Reid et al. - 1991 (Fig. 133). Paper I reports erroneous transmission curves, that have been replaced by the correct ones in the ADPS web site and in this paper.

TNG - Marchetti et al. - 1997 (Fig. 143). Band transmission curves are derived from Fig. 1 of the source paper.

UWTAT - Strassmeier et al. - 1997 (Fig. 144). The photometric system combines bands from other systems (uvby H$\beta$ - Strömgren and Crawford - 1956, UBV - Johnson and Morgan - 1953, R$_{\rm c}$I$_{\rm c}$ - Cousins - 1976, H $\alpha,\beta$ - Guinan and McCook - 1974). Here we adopt the band transmission curves derived from Fig. 4 of the source paper.

Geneva GAIA - Grenon et al. - 1999 (Fig. 148). The provisional band profiles adopted in Paper I are here replaced by the proper ones (C. Jordi, private communication).

OAO2 WEP - 1970 (Fig. 151). Filter names have been revised according to post-lunch documentation (Wende 1974). Filters 213, 256, 297, 333 are here ignored because associated to the nebular photometer that failed shortly after launch.

UIT - 1990 (Fig. 156). Paper I reports erroneous transmission curves, that have been replaced by the correct ones in the ADPS web site and in this paper.

Pilachowski - 1978 (Fig. 161). We have neglected the wide band at 2.2 $\mu $m because it is a standard K band.

M.F. has been financially supported by ASI via contract CISAS 10/2001 to P. L. Bernacca. Dina Moro is kindly acknowledged for her careful documentation of all references used in Paper I, without which the preparation of this Paper II would have been even more laborious. The anonymous referee is thanked for constructive and detailed comments and close scrutiny of the paper.



Copyright ESO 2003