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2.1. Spectroscopic Data

Spectroscopic data were obtained to determine the mean properties of the night‐sky spectrum of moonless nights at the observatory. In Calar Alto spectrographs are normally mounted in bright and gray nights, while dark nights are more frequently allocated for deep imaging programs. Thus, it is somewhat difficult to find spectroscopic data taken during dark nights. The most frequently mounted spectrographs at the Calar Alto observatory are CAFOS at the 2.2 m (∼50% of the allocated time) and PMAS (Roth et al. 2005) at the 3.5 m telescope (∼30% of the allocated time). PMAS is an integral field unit with two different setups, a lens array with a reduced field of view ( in its largest configuration), and a wide fiber bundle that covers a field of view of with 331 individual fibers of 2.7 diameter each (PPAK; Kelz et al. 2006). This latter configuration is particularly interesting to study the properties of the sky emission, since in a single shot centered on a calibration star (or a science target) a substantial fraction of the field of view samples the sky. Its large aperture, and the possibility of performing self‐calibration, allows one to obtain spectrophotometric calibrated and high signal‐to‐noise ratio (S/N) spectra of the night‐sky emission even with reduced exposure times. Even more, this instrument is frequently mounted with a low‐resolution grating (V300), which covers a wavelength range of ∼3500 Å with a spectral resolution of ∼10 Å (FWHM). This is also very convenient to obtain spectra of the sky emission in the entire optical wavelength range. Restricting ourselves to the same instrument and configuration ensures the homogeneity of the data.

There were 14 clear moonless nights when the instrument was mounted using this configuration in the period between 2005 January and 2006 December. A sample of 23 observations, including night‐sky emission spectra, were selected from the data taken during those nights. The sample was selected by including only observations of calibration stars and/or small‐size and faint targets (e.g., high‐z Lyα emitters; S. F. Sánchez et al. 2007, in preparation), with most of the PPAK field‐of‐view sampling sky emission. In addition, only observations near the zenith, with an air mass lower than 1.5, were included in the sample. In all the cases the observations were taken far away the ecliptic and the Galactic plane. The data were then reduced using R3D (Sánchez 2006), following the standard steps for fiber‐based Integral Field Spectroscopy data. Once reduced, the sky spectra were extracted from the frames using E3D (Sánchez 2004), by selecting areas clean of objects within the field of view. Although the S/N level of each individual sky spectrum is somewhat different, depending on the exposure time and the number of selected fibers to extract the spectra, in all cases they are good enough for the purposes of this study.

Not all the observations during a moonless night are equally dark. The darkness of an observation depends strongly on the time distance of the corresponding night from the full moon, the presence of cirrus, dust, and local contamination when pointing toward highly populated areas (like Almeria, toward the south of the observatory), the zenith distance, and even more the time distance from twilight. Thus, from the original data set we did not consider those spectra whose intensity at 5200 Å were larger than ergs s cm Å ( mag). We were then left with a final sample of 10 individual spectra obtained on seven different nights, representative of the typical dark observation in a moonless dark night at Calar Alto. This sample still comprises a wide range of brightness, and only one (2005 June 2) can be considered completely dark, corresponding to a new moon night. Table 1 shows the final list of nights, together with the wavelength range covered by the spectra each night.

TABLE 1 Log of the Data Set per Night

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2.2. Imaging Data

Multiband imaging data are collected to characterize the sky brightness of moonless nights at the observatory. The search was restricted to CAFOS covering a similar time period of the selected spectroscopic data set, to preserve the homogeneity of the data. Only exposures on calibration fields were selected to perform a self–flux‐calibration, avoiding the possible errors due to changes in the atmospheric condition between calibration and measurement. Although these exposures tend to have short exposure times, from 20 to 200 s, the large field of view of CAFOS CCD (∼ ) and pixel size ( ) allow a good estimation of the sky background. The use of calibration fields, with more than four calibration stars observed per field, guarantees a good estimation of the magnitude zero point per filter and exposure (photometric calibration error <0.1 mag). We focused our search in nights dedicated to a single project, aiming to study the time evolution of the multiband photometry of supernovae (PI: W. Hillebrandt; Pastorello et al. 2007) observed in service mode. The reason for that was that this program uses the same instrument setup, filters, and calibration fields and covers large periods of time. The number of nights totally or partially dedicated to this project were ∼21 along the considered time period. Finally, we selected the darkest possible nights, i.e., moonless nights with a distance of at least 13 days from the full moon. We were then left with five nights. However, only in two of them were the calibration fields observed at least one hour after the beginning of the astronomical night. In the remaining three nights there was still substantial contamination from the twilight, and they are therefore excluded from any further analysis. Table 1 shows the final list of selected nights, including the broadband filters observed each night.

The Landolt calibration fields PG1633 and PG0918 (Landolt 1992) were observed each night, respectively, in the listed filters. The images were reduced following the standard steps, using IRAF routines. First, a master bias frame was created for each night by averaging all the bias frames obtained along the night and smoothing it. All images were then bias‐corrected by subtracting the corresponding master bias. For each band a master flat‐field frame was obtained by averaging the bias‐corrected dome‐flat images and normalizing to the median intensity value. Images were then corrected for pixel‐to‐pixel response variations dividing by their corresponding flat‐field frames. No sky subtraction was performed since the aim of this study is to determine its intensity.

2.3. Extinction Data

The Calar Alto Extinction monitor (CAVEX) is an in‐house developed instrument (PI: U. Thiele), which estimates the monochromatic extinction in the V band continuously along each night. The system is fully automatic, opening half an hour after the beginning of the astronomical night and closing half an hour before its end. It continuously points toward the north (the polar star), taking images of ∼20 s exposure time every ∼76 s covering a field of view of ∼55° with a resolution of 2.3 pixel⁻¹. By tracking the location of 15–20 stars in the field, it estimates the extinction by measuring their apparent magnitudes across a range of 1.1–2.4 air masses. It shares the same limits of humidity and wind speed as the telescopes at the observatory, producing a measurement of the extinction every ∼2 minutes if the night is clear. When the night is cloudy or the extinction has strong fluctuations, the instrument does not produce reliable data, flagging it. Therefore, the fraction of time without precise extinction measurements from the CAVEX is a good estimation of the amount of time lost due to nonastronomical weather conditions in the observatory. We have collected all the available data from the extinction monitor during the last 4 years, from 2003 May to 2007 May. The data comprise 214,193 individual measurements, corresponding to 1044 nights from a total of 1478 nights included in this period.

CAVEX estimates the total extinction in a single band. To characterize the extinction curve it is necessary to measure the extinction at different wavelengths. In the summer of 2006 (2006 July 27–August 15) and the winter of 2006–2007 (2006 December 17–2007 January 13), an instrument built with the sole purpose of estimating this extinction curve was installed, named the Extinction Camera and Luminance Background Register (EXCALIBUR; PI: J. Aceituno). EXCALIBUR is a robotic extinction monitor able to do quasi‐simultaneous photometric observations in eight narrow bands covering the wavelength range between 3400 and 10200 Å, characterizing the extinction curve in this wavelength range (although only six of the bands were operative when installed at Calar Alto). The instrument was built to estimate the aerosol abundance based on the shape of the extinction curve (Pérez‐Rámirez et al. 2007a, 2007b). It estimates ∼16 extinction coefficients for each of the sampled bands per hour and an average of ∼160 extinction coefficients per band for each night. It was operative for a total of six nights in the summer season and 14 nights in the sinter season. We collected all these data for the current study.

2.4. Seeing Data

The night‐sky seeing was measured by a Differential Image Motion Monitor (DIMM; Aceituno 2004) at the Calar Alto observatory since 2004 August, and it is nowadays a fully automatic instrument. It measure the seeing at the wavelengths corresponding to the Johnson V band. This DIMM was calibrated with a previous one installed in the observatory (Vernin & Muñoz‐Tuñon 1995), which, at the same time, was also calibrated with a Generalized Seeing Monitor in 2002 May (Ziad et al. 2005), when they both estimated a median seeing of 0.90 for that time period. To study the possible evolution of the seeing at the observatory and its possible dependencies with other night‐sky parameters, we collected all the available seeing measurements for the time period between 2005 January and 2006 December. Contrary to the CAVEX, the DIMM has more severe limitations to be operative, and it closes automatically when the humidity is larger than 80% or the wind speed is 12 m s , which comprises ∼50% of the time. The DIMM produces an estimation of the transversal and horizontal seeing in each measurements. Whenever there is an occasional large difference between both estimations (not due to a dominant wind component), they most probably are not due to atmospheric effects, but rather to mechanical oscillations. Due to the inherent stability of a DIMM system to this kind of oscillation, these cases comprise a relatively small number (∼5%). They have been excluded from the final data set. We finally collected a total of 213,622 seeing measurements distributed along 335 nights during the considered time period.

3.1. Night‐Sky Spectrum

The data included in the final sample of night‐sky spectra for moonless dark nights described in § 2.1 were combined to create a typical moonless night‐sky spectrum at the observatory. In doing so each spectrum was normalized to the mean intensity (of the sample) at 5200 Å ( ergs s cm Å ). Then the final spectrum was produced by averaging the flux of these normalized spectra at each sampled wavelength. Figure 16 shows the resulting spectrum, covering a wavelength range between 3700 and 7933 Å. This is the first time that a typical night‐sky spectrum is published for the Calar Alto observatory.7 The emission lines clearly identified in the spectrum have been labeled with their corresponding atomic name and wavelength. Several of the distinctive features of the night‐sky spectrum are due to airglow, although a substantial fraction are due to light pollution.

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Fig. 1.— Night‐sky spectrum at the Calar Alto Observatory in the optical wavelength range (3700–7950 Å), obtained after averaging 10 spectra of six moonless nights pointing near the zenith (black solid line). The intensity has been scaled to that of the darkest moonless night in the V band. Several emission lines are indentified in the spectrum. The most relevant ones have been labeled with their corresponding name and wavelength. In addition, the broad‐emission band of Na i centered at ∼5900 Å and the water vapor Meinel bands are clearly identified in the spectrum. For purposes of comparison we included the night‐sky spectrum at the Kitt Peak Observatory derived by Massey & Foltz (2000), obtained from their Web site. (orange dotted line). Note how strong the pollution lines are at Calar Alto, in comparison with Kitt Peak.

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The airglow is emitted by atoms and molecules in the upper atmosphere, which are excited by solar UV radiation during the day and twilight (Ingham 1972). Airglow is the most important component of the light of the night sky. It produces the 5577 and 6300 Å lines from O i (which are stronger near twilight). It contributes to the ubiquitous 5890–5896 Å Na D doublet, although this line is heavily contaminated by light pollution from low‐ and high‐pressure street lamps. Airglow is also responsible for the OH rotation/vibration bands in the red and IR, known as the Meinel bands (Meinel 1950), visible at the redder wavelengths of the spectrum (see Fig. 1). In addition, it produces a pseudocontinuum in the blue from overlapping O₂ bands (2600–3800 Å) and in the green from NO₂ bands (5000–6000 Å). A more detailed description of the effects of the airglow on the night‐sky emission can be found in Benn & Ellison (1998a). An atlas of the airglow from 3100 to 10000 Å was presented by Ingham (1962) and Broadfoot & Kendall (1968).

Other contributions to the night‐sky spectrum are the zodiacal light, the starlight, and the extragalactic light, which increases the background continuum emission (see Benn & Ellison 1998a and references therein for a more detailed explanation on their effects). All of these, including the airglow, comprise the natural processes that produce the night‐sky spectrum in any astronomical site. In addition, the night‐sky spectrum can be affected by the light pollution due mostly to the street lights of populated areas near the observatories. Light pollution arises principally from tropospheric scattering of light emitted by sodium and mercury vapor and incandescent street lamps (McNally 1994; Holmes 1997).

Typical spectra of the three more used types of street lamps were presented by Osterbrock et al. (1976): the sodium low‐pressure lamps, the sodium high‐pressure lamps, and the mercury lamps. The first of the three is the one with the least impact in astronomical observations, since its produces most of its light concentrated in the 5890–5896 and 8183–8195 Å Na D emission lines. Therefore, only a very reduced number of astronomical observations are strongly affected by them. On the other hand, the high‐pressure sodium lamps emit most of their light in a broad Na D line centered in ∼5890 Å, with a FWHM of ∼400 Å, that shows a central reversal. They also show a strong 8183–8195 Å emission line, and fainter emission lines at 4494–4498, 4665–4669, 4758–4752, 4979–4983, 5149–5153, 5683–5688, 6154–6161, and 7665, 7699 Å. The high‐pressure sodium lamps may strongly affect the quality of any astronomical observation. Finally, the mercury lamps produce narrow lines at 3651/63, 4047, 4358, 5461, 5770, and 5791 Å, together with broad features at 6200 and 7200 Å of FWHM ∼ 100 Å, from the phosphor used to convert UV to visible light. They also produce a weak continuum emission over the whole visible range. Some mercury pollution lines can strongly affect certain astronomical studies: (1) The Hg 4358 Å line strongly affects any attempt to measure the emission of the [O iii] 4364 Å line in any object in the Galaxy. This line is fundamental for the estimation of the electron temperature of galactic nebulae. (2) The Hg 5460 Å line lies in the center of the y‐band of the ubvy Strömgren photometric system, which may affect the programs devoted to the study of stellar populations that use this filter set.

Other sources of light pollution are the incandescent lamps and the high‐pressure metal halide lamps. The spectrum of the former consists of continuum emission only, and it is difficult to identify in a night spectrum. The latter are nowadays frequently used in the illumination of sport stadiums and arquitectonical monuments (which can be considerable, since they are normally oriented toward the sky). These high‐pressure metal halide lamps exhibit some scandium, titanium, and litium emission lines that are characterized by a blue edge due to molecular bands (General Electric 1975; Lane & Garrison 1978; Osterbrock et al. 1976).

The night‐sky spectrum shown in Figure 1 shows clear evidence of strong light pollution from all the street lamps described previously. It shows strong mercury lines all over the spectrum, the typical emission lines and features of high‐pressure sodium lamps, with a well‐detected broad emission at ∼5900 Å, and a strong Na i emission line at 5893 Å, indicative of low‐pressure sodium lamps. Even more, it also presents the typical emission lines corresponding to high‐pressure metal halide lamps. All this pollution comes from the populations nearby the observatory, in particular from Almeria (∼250,000 habitants), at 40 km toward the south, and smaller towns at the north (e.g., Baza, ∼21,000 habitants; Macael, ∼6000 habitants). There are well‐established estimations of the contribution of city lighting to dark‐sky brightness (e.g., Treanor 1973; Walker 1973; Yocke et al. 1986; Garstang 1991 and reference therein). However, its contribution to the spectrum is more complex, since it depends on the particular kind of lamps used for street illumination. Most major observatories near by populated areas have some kind of night‐sky protection laws with the aim of reducing the effects of light pollution by controlling the fraction of light that escapes toward the sky and the kind of lamps used (normally, they promote the use of low‐pressure sodium lamps). The Calar Alto Observatory does not yet benefit from any local sky‐protection law that regulates the street illumination, with the corresponding effects that can be appreciated in the night‐sky spectrum.

To estimate the contribution of light pollution to the night‐sky spectrum we derive the flux intensity corresponding to each of the detected emission lines. Each line was fitted with a single Gaussian function using FIT3D (Sánchez et al. 2007b), using the same procedure described in Sánchez et al. (2007a). Table 2 lists the integrated flux for each of the detected emission lines shown in Figure 1, together with the identification of the line and the nominal wavelength. In addition to the emission lines, the flux intensity of the sodium broadband emission at ∼5900 Å was also estimated by fitting the feature with a single broad Gaussian function. The result is also listed in Table 2. All the fluxes were converted to rayleighs following the conversion formulae by Benn & Ellison (1998a).

TABLE 2 Properties of the Detected Emission Lines

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These values can be compared to those obtained for other astronomical sites. For example, Pedani (2005) presented a study of the night‐sky spectrum at the Observatory of the Roque de los Muchachos, La Palma. The intensity of the lines produced by the mercury and low‐pressure sodium lamps found in our spectrum are only comparable to those in La Palma when pointing in the directions toward the most polluting towns in this island. On the other hand, the contribution of the lines produced by the high‐pressure sodium lamps is much lower, being comparable to that of the less polluted areas of the sky in La Palma. This may indicate that most of the street lamps used in Almeria are mercury and low‐pressure sodium lamps, rather than high‐pressure sodium ones, and therefore they only affect specific wavelength ranges (and science programs). Finally, we clearly see lines produced by high‐pressure metal halide lamps, only marginally (and recently) detected in the sky spectrum at La Palma (Pedani 2005).

Once the contribution of each emission line to the night‐sky spectrum is determined, it is possible to decontaminate it by the effect of the pollution lines (ie., all but the O i ones), creating a clean night‐sky spectrum. This can be done directly for the mercury, scandium, titanium, and litium lines, since all its emission is produced by light pollution. However, in the case of the sodium lines there is a natural contribution due to the airglow. We lack a direct measurement of this natural contribution at Calar Alto, which can only be achieved nowadays with a general blackout. However, its natural contribution must not be significantly larger than that at other astronomical sites. Benn & Ellison (1998a) estimated the natural contribution by the broad sodium emission band in ∼0.03 mag in V and ∼0.02 mag in R for La Palma observatory. Similar contributions are expected by the Na i 5893, 5896 Å emission lines. Therefore, the natural contribution by sodium due to the airglow is expected to be of the order of ∼0.04 mag in both bands. Thus, as a first order we can assume that all the detected emission by sodium in our sky‐emission spectrum is due to pollution, and once its contribution is determined we can correct it by the expected contribution of natural emission, if needed.

Table 3 lists the estimated contribution of light pollution to the sky background in different bands. It includes the Johnson B, V, and R filters, and a set of medium‐band filters selected from those used by the ALHAMBRA survey (Moles et al. 2007), a major imaging survey currently ongoing at the Calar Alto observatory. They are included to illustrate the effects of the pollution lines in the background sky when using median/narrowband filters affected by these lines. The contamination from light pollution is clearly stronger in the B band than at other astronomical sites, for example, ∼0.02 mag at La Palma (Benn & Ellison 1998a) and 0.02–0.04 mag at Kitt Peak (Massey et al. 1990), although there are astronomical sites with similar or stronger contaminations, for example, Mount Hopkins (see Massey & Foltz 2000, Fig. 2). This contamination can be reduced by a proper light pollution law that limits the use of mercury street lamps. Strong benefits from such laws have been experienced at different sites (e.g., Benn & Ellison 1998a; Massey & Foltz 2000). The contamination in the V and R bands is slightly stronger than at some other places, like La Palma (0.05–0.10 mag at the V band and 0.07–0.12 mag at the R band; Pedani 2005), but it is similar or smaller than at other astronomical sites, like Kitt Peak (0.19–0.33 mag in the V band; Massey et al. 1990) or Mount Hopkings (0.17 mag in the V band; Massey & Foltz 2000). One of the two recommendations of the IAU for a dark place is that the contribution of the pollution to the sodium emission should not exceed the natural airglow in intensity (Smith 1979). If we consider that the airglow emission is similar at Calar Alto to that at La Palma (or at least of the same order), it is clear that the contribution from the light pollution is much stronger. In these regards Calar Alto does not fulfill the IAU recommendations for a dark place. A proper light‐pollution law that increases the use of low‐pressure sodium lamps rather than high‐pressure ones will not reduce the net effect of the light pollution to the sky‐background in these bands, but it will concentrate it in a more reduced wavelength range, affecting less observing programs.

TABLE 3 Contribution of the Light Pollution Lines to the Sky Brightness

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Most of the lamps that cause light pollution also produce a certain level of continuum emission, in particular, mercury and high‐pressure metal halide lamps. However, their contribution is difficult to estimate. Although we cannot quantify its effect, the reduction of the use of mercury, high‐pressure sodium lamps, and high‐pressure metal halide lamps in the vicinity of the observatory will certainly also reduce the sky‐background continuum.

The lack of previous similar studies of the night‐sky spectrum at the Calar Alto observatory (to our knowledge) does not let us analyze the evolution of light pollution over time.

3.2. Night‐Sky Brightness

The night‐sky brightness was determined by using both the imaging and spectroscopic data described previously. In the case of the imaging data, the calibration fields contain at least five calibration starts per frame. The magnitude zero point for each image was determined by measuring the counts intensity of each of these stars within a fixed aperture of 8 radius, using IMEXAM task of IRAF package, and applying the formula where is the magnitude zero point, is the apparent magnitude of the calibration star in the corresponding band, “ext” is the extinction derived from the corresponding value measured by the CAVEX this night and the air mass of the image, “counts” are the measured counts within the indicated aperture, and is the exposure time. Since the measured seeing of the images (FWHM of the field stars) ranges between 0.9 and 1.3 , this aperture ensures that most of the flux is contained within it, and no aperture correction was applied. The average of the values derived for each calibration star in the field is considered the zero point of the image, and the standard deviation from this mean value is considered the photometric error. This standard deviation ranges between 0.02 and 0.06 mag for each band and each night.

The sky brightness was then determined in each image by measuring the mean counts level in several (>10) square apertures of ∼ , in areas free of targets, using the IMEXAM task of IRAF package. The mean value of these measurements is considered the count level of the sky brightness, and the standard deviation with respect to this mean value is the error in the count level estimation. Finally, the sky surface brightness was determined using the formula where is the surface brightness in magnitudes per square arcsecond, is the zero point described before, is the sky counts level estimated, and scale is the pixel scale in arcseconds (ie., 0.53 for CAFOS). It is noted that the magnitude zero point was corrected by the extinction, but the sky brightness was not, following the convention adopted in most of the recent studies of sky brightness (e.g., Walker 1988b; Krisciunas 1990; Lockwood et al. 1990; Leinert et al. 1995; Mattila et al. 1996; Benn & Ellison 1998a, 1998b). Correcting the sky brightness for extinction would be appropriate only if the extinguishing layer were known to be below all sources of sky brightness, which is not the case (Benn & Ellison 1998a, 1998b).

In addition to the estimations of the sky surface brightness obtained using direct imaging, we also derived the sky surface brightness by using the PPAK spectroscopic information for the only full moonless night of our sample (2005 June 2). The two night‐sky spectra obtained this night cover the wavelength range of the B‐, V‐, and R‐band filters. We derived the sky flux intensity for each of these filters by convolving each spectrum with the corresponding filter transmission curves listed in the Asiago Database on Photometric Systems (Moro & Manuri 2000). Then the fluxes were transformed to magnitudes by using the zero pointings listed in Fukugita et al. (1995). The mean value of the two derived magnitudes in each filter is adopted as the sky surface brightness of that night, and the absolute difference between both magnitudes as the error.

Table 4 lists the sky‐surface brightness obtained from both the imaging and spectroscopic data at the different bands for each moonless night. In addition, it lists previous results on the sky brightness at different astronomical sites, including the results presented by Leinert et al. (1995) for Calar Alto, derived from broadband photometry obtained along three nights in 1990.

TABLE 4 Summary of the Night‐Sky Surface Brightness

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3.3. Extinction Coeffcients

The median V‐band extinction at the Calar Alto observatory for the time period covered by the CAVEX data (§ 2.3) was ∼0.18 mag, with a mean value of ∼ mag. This value is slightly smaller than that previously reported by Hopp & Fernandez (2002), which was based on a much smaller sample of data (comprising 74 nights spanning between 1986 and 2000). They found that there was an increase in the extinction during the summer season that was most probably associated with an increase of the aerosols (i.e., dust) in this period of the year. A similar seasonal pattern has been noted at other major observatories; for example, La Palma observatory is strongly affected by dust extinction in the summer when dust from the Sahara desert (∼400 km away) blows over the Canary Islands (Benn & Ellison 1998a). Although the Calar Alto observatory is nearer to the Sahara desert (∼250 km away) than La Palma, it is normally out of its main wind streams, being shielded by the Atlas mountains. On the other hand, it is located in an arid region near by a much smaller desert, the Tabernas desert (∼15 km away).

Figure 2 shows the evolution of the average V‐band extinction for each night over the period of time sampled by the data set. As already suspected by Hopp & Fernandez (2002), there is a clear seasonal pattern. The typical extinction in the winter nights is mag, being mostly restricted to values lower than mag. In summer time there is a wider range of extinctions, although in most of the cases the extinction is lower than mag. As indicated before, this increase in the extinction is most probably associated with a rise of the aerosols (dust) in the atmosphere. We explore that possibility later.

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Fig. 2.— Distribution of the V‐band extinction along 1044 astronomical useful nights in the period between 2003 March and 2007 May (∼70% of the total nights). The extinction shows a clear seasonal pattern, with a maximum in summer and a minimun in winter. The median value of the extinction is mag, with a typical value of ∼0.15 mag in winter. The fraction of nights with mag, ∼20%, is similar to other observatories (e.g., La Palma), although the peaks of extinction are much lower.

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This seasonal pattern is somewhat similar to the one seen in La Palma. Indeed, the fraction of nights with mag is similar in both observatories, ∼20% of the nights. However, there is a major difference: the fraction of nights with high extinction, mag, at Calar Alto is significantly reduced, ∼3%, while at La Palma this fraction is ∼10% of the nights, with frequent peaks of extinction over mag (Benn & Ellison 1998a, Fig. 3).

Based on the fraction of nights that the CAVEX was operative and derived reliable measurements of the V‐band extinction ( ), it is estimated that ∼70% of the nights were astronomically useful in the period covered by these data (4 complete years). This fraction is remarkably similar to that at many other astronomical sites (e.g., La Palma; Benn & Ellison 1998a). The fraction of fully photometric nights, defined as nights where the V‐band extinction varies less than 20% during all the night, was ∼30%.

3.3.1. Contributions to the Extinction The EXCALIBUR data described in § 2.3 were used to determine the typical extinction curve at Calar Alto. This curve was previously studied by Hopp & Fernandez (2002), using an inhomogenous data set. The extinction coefficients were analyzed separately for the summer and winter seasons due to the observed seasonal pattern. First, the mean extinction coefficients per night was derived by averaging all the measured extinction coefficients per band obtained during each night (∼160 values). Then the mean extinction coefficients per season were determined by averaging all the measured extinction coefficients per band obtained along each season's nights. Table 5 lists the average extinctions coefficients obtained for each season for each of the six bands sampled by the instrument, including their central wavelengths and the standard deviation with respect to these mean values. As expected, the standard deviation in the extinction coefficients is larger for the summer data than for the winter data, in agreement with the results shown in the previous section. The EXCALIBUR results are consistent with the CAVEX results for the wavelength covered by both instruments, i.e., ∼500 nm. This indicates that the extinction coefficients listed in Table 5 are a good representation of the typical values for each season.

TABLE 5 Extinction Coefficients at Calar Alto

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The total extinction is mostly due to three contributions: the Rayleigh scattering at the atmospheric atoms and molecules, the extinction due to aerosol particles (mostly dust), and extinction due to ozone (Walker 1987b). The Rayleigh scattering can be described by where λ is the wavelength and B is a constant that mostly depends on the pressure, the temperature and the normalized refractive index of the air ( , slightly wavelength dependent). In general B can be replaced by its average value for the mean conditions in a certain astronomical site (e.g., Rufener 1986). The aerosol particles produce a similar absorption, which can be described by where b is a parameter that depends mostly on the height of the observatory ( ) and α is a power‐law index that depends on the size of the aerosol grains. Although , derived by Siedentopf (1948), is widely used, we adopted a value of for consistency with the previous study of the extinction curve at Calar Alto (Hopp & Fernandez 2002). The ozone extinction is a selective absorption by molecular bands. It can be approximately described by a broad Gaussian function centered on Å (matching the shape shown in Rufener 1986 and Hopp & Fernandez 2002): Each single contribution to the extinction depends on the wavelength and a particular constant that, in the case of the first two, depends on the height and the average atmospheric conditions in the observatory. We adopted the values listed for Å in Rufener (1986), consistent with those derived by Tüg (1977), obtained at La Silla observatory. A similar approach was followed by Hopp & Fernandez (2002). The height and average weather conditions in this observatory are very similar to those of Calar Alto, which justifies the use of these constants.

Therefore, the total extinction curve is a linear combination of these three contributions: The extinction coefficients for the two seasons were fitted to this linear combination, deriving the relative contribution of each one ( ) to the total extinction. Table 6 lists the results from this fitting analysis, including the relative contribution ( ) derived for each component for each season. For comparison, it also includes the same relative contributions derived for Calar Alto by Hopp & Fernandez (2002) and their compilation of similar results for different astronomical sites.

TABLE 6 Contribution of the Rayleigh Scattering ( ), Aerosol Extinction ( ), and Ozone Absorption ( ) to the Total Extinction

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The contribution of the Rayleigh scattering, like the ozone absorption, seems to be rather constant for the two considered seasons. On the other hand, the aerosol contribution rises considerably in the summer time, being responsible for the increase of the extinction in this season, as it was thought. The estimated contributions of the Rayleigh scattering and the aerosol extinction are very similar to the values reported by Hopp & Fernandez (2002) for the winter season, which may indicate that both contributions have not changed considerably with time (their data correspond to 1986–2000). Both contributions are also similar to the ones derived for other major astronomical sites. On the other hand, the contribution of the ozone absorption seems to be stronger than that in previous measurements and other astronomical sites. Unfortunately, the coverage of EXCALIBUR when mounted at Calar Alto did not allow us to perform an accurate sampling of the wavelength range affected more strongly by the ozone absorption, which did not let us be conclusive in this respect.

Figure 3 shows the distribution of the extinction coefficients along the wavelength for the two season data sets. It also includes the best‐fitted linear combination of the three components to the extinction and each of these components scaled to its relative contribution to the total extinction. Despite the apparent increase of the ozone absorption, its actual contribution to the total extinction at any wavelength is very limited, being negligible in comparison with the other two contributions. Indeed, the fitting process derives equally good results when this contribution is removed. As already indicated, the Rayleigh scattering contribution is very similar for both data sets, being the dominant contribution in the winter season, i.e., in conditions of low extinction. In winter time it is responsible for ∼85% of the extinction in the V band; only ∼11% is due to aerosol extinction and ∼4% to ozone absorption. On the other hand, in summer its contributions drop to ∼63%, with ∼35% due to aerosol extinction and ∼2% due to ozone absorption. Curiously, the contribution of aerosols to the extinction in the conditions of minimum extinction are much more reduced than the one found in other astronomical sites, like La Silla (Burki et al. 1995).

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Fig. 3.— Extinction curves derived for a set of winter (top) and summer nights (right), using the EXCALIBUR extintion curve monitor (red filled circles). The error bars indicate the standard deviation over the mean values. The data were fitted to a linear combination of the three different contributions to the extinction described in Walker (1987a, 1987b): the Rayleigh scattering (dashed line), the aerosol or dust extinction (dash‐dotted line), and the ozone extinction (dotted line), each one scaled to their relative contribution to the extinction. The blue solid line shows the best fit to the data.

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3.4. Atmospheric Seeing

The seeing data described in § 2.4 were used to determine an average seeing for each night comprised in the data set (spanned along ∼2 years). The median atmospheric seeing for all the time period was ∼0.90 , with ∼70% of the nights under subarcsecond seeing (<1 ). Figure 4 shows the nightly averaged seeing distribution along the time. The epochs without data in 2005 April and 2006 March were due to reparations in the hut of the DIMM. There is a mild seasonal pattern in the seeing distribution, with the best seeing concentrated in the summer season. To further investigate this possibility, we created the seeing histogram for all the data comprised in the data set and for two different subsets of data corresponding to the summer season (May–September) and the winter season (the rest of the months). Figure 5 shows the three histograms. The differences in the seeing distribution for the summer (median seeing ∼0.87 ) and winter seasons (median seeing ∼0.96 ) are clearly appreciated. Not only is the median seeing better in the summer season, the chances of having better seeing on a summer night are larger.

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Fig. 4.— Distribution of the seeing along the time for the 335 nights with measurements from the DIMM monitor in the period between 2005 January and 2006 December. There is the suggestion of a seasonal pattern, with a minimun during summer and a maximum during winter.

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Fig. 5.— Normalized histogram of the seeing distribution shown in Fig. 4 (solid line). The median value of the seeing is ∼0.90 , with ∼46% of the nights with a seeing better than this value. The red dashed line shows a similar histogram for the summer values (May to September), when the median seeing drops to ∼0.87 . The blue dash‐dotted line shows a similar histogram for the winter values, comprising the remaining data, when the median seeing rise to ∼0.96 . The seeing distribution is clearly different in both seasons.

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Table 7 lists the median seeing estimated for both the total sample and the two season subsamples. For purposes of comparison it also lists the atmospheric seeing measured at different astronomical sites worldwide, ordered by increasing seeing. Although the median seeing at Calar Alto is larger than that at some major astronomical observatories (Mauna Kea, La Palma), it is actually better than at many other astronomical sites (e.g., Mount Graham, Paranal).

TABLE 7 Median Seeing Compared with Other Astronomical Sites

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