E. Solheim 1. INTRODUCTION Atmospheric Extinction

Home , Air mass (astronomy), Extinction (astronomy)

Baltic Astronomy, vol. 12, 221–242, 2003.

ATMOSPHERIC EXTINCTION CORRECTIONS FOR WET OBSERVATIONS

E. Pakˇstien˙e1 and J.-E. Solheim2 1 Institute of Theoretical Physics and Astronomy, Vilnius University, Goˇstauto 12, Vilnius LT-2600, Lithuania 2 Institutt for Fyzikk, Universitat Tromsø, N-9037, Tromsø, Norway, present: Wilh Wilhelmsen vei 71, N-1362 Hosle, Norway Received December 2, 2002, revised January 13, 2003

Abstract. Account of the extinction in the Earth’s atmosphere is an important part of the WET light curve reduction procedures. Usually, WET observations are not corrected for the second order extinction effects: the dependence of the extinction coefficient on spectral type and on air mass (the Forbes effect). The ignorance of these effects does not change seriously the derived pulsation amplitudes at the frequencies higher than 200 μHz but the increase of the noise at lower frequencies takes place. For obtaining the true extra-atmospheric magnitudes of stars, a modification of the extinction correction procedure is proposed. For photometry with the R647 phototube we recommend to use a filter cutting out the region below 310 nm, in order to decrease and stabilize the extinction coefficient. A method for estimation of spectral type of the comparison star from WET observations is proposed. Key words: methods: data analysis – atmospheric effects – tech- niques: photometric: WET

1. INTRODUCTION Atmospheric extinction is a phenomenon which takes place in the Earth’s atmosphere. Due to extinction the observed stars seem fainter and redder than they are in reality. The amount of the extinction in heterochromatic photometry is different for various types of stars even in the case when they are observed at the same zenith distance (air mass) because of the second order extinction effects. The Forbes effect, which will be explained below, is also significant, especially at large zenith distances, and it can give additional errors in stellar parameters. These effects are especially significant when 222 E. Pakˇstien˙e, J.-E. Solheim super-broad photometric passbands are used in observations (as in WET observations, with no filter). However, in the standard WET reduction procedure, the second order extinction effect and the Forbes effect are not taken into account. This means that the WET data reduced by the standard programs cannot be used to obtain the true extra-atmospheric magnitudes of the investigated stars. For a precise atmospheric extinction correction we have to consider the characteristics and nature of the atmospheric extinction.

2. THE NATURE OF ATMOSPHERIC EXTINCTION AND MONOCHROMATIC EXTINCTION COEFFICIENTS Atmospheric extinction in the Earth’s atmosphere is quite variable, usually it changes even during a night. These changes are dependent on the site and on the light wavelength. There are three main sources of the extinction in the atmosphere: (1) The Rayleigh scattering of light by molecules with diameters smaller than the wavelength of the scattered light. The Rayleigh extinction αR(λ, h) in magnitudes at zenith can be calculated by the equation (Hayes & Latham 1975): −4 2 − h αR(λ, h)=0.0094977 · λ · ns(λ) · e 7.996 ,(1) where λ is the wavelength in μm, h is the altitude of the observatory above sea level in km and ns(λ) is the refraction index: 107.6 0.93161 ns(λ)=0.23465 + 146−λ−2 + 41−λ−2 .(2) (2) The ozone extinction αoz(λ) can be calculated from αoz(λ)=1.09 · T · k(λ),(3) where T is the total thickness of the ozone layer at the standard temperature 0◦C and pressure (1 atm) above the observatory, k(λ) is the ozone absorption coeﬃcient. We took its values from the Handbook of Geophysics (1965). (3) The aerosol extinction by scattering and absorption by particles with diameters of the order of the wavelength or larger. The wavelength dependence of the aerosol extinction can be represented by the empirical equation: −b αaer(λ)=A · λ (4) where: αaer(λ) is the aerosol extinction in magnitudes at zenith for a given wavelength λ in μm, A is the same extinction for λ =1μm and b is a coeﬃcient dependent on the size of aerosol particles and their size distribution (Forbes et al. 1996, Pakˇstien˙e 2001) . Atmospheric extinction correction for WET observations 223

The aerosol extinction can be subdivided into two parts: (1) the neutral aerosol extinction αn which does not depend on the wavelength and (2) the selective aerosol extinction αs described by Equa- tion (4). The combined aerosol extinction coefficient can be written as: −bs αaer(λ)=αn + As · λ .(5) A method for determination of the aerosol extinction parameters are has been described in some of our earlier papers (Zdanaviˇcius & Pakˇstien˙e 1997, Pakˇstien˙e et al. 2001). We have determined that the dependence of aerosol extinction on wavelength in many cases is different in the ’blue’ and ’red’ spectral regions. This dependence changes its character at λ ≈ 465 nm. In rare cases, even in such places as the Mol˙etai Observatory (Lithuania) or Mt. Maidanak Observatory (Uzbekistan), the aerosol extinction can be assumed equal to zero (the atmosphere is almost aerosol-free). Figure 1 shows how all the components of the atmospheric extinction depend on the wavelength. Here the atmospheric extinction at zenith is calculated using the atmospheric extinction parameters typical for the Mol˙etai Observatory (h = 220 m, T = 3 mm, αn =0and the mean weighted values of bs Fig. 1. Dependence of the monochromatic extinction coefficients on and As are 1.35 and 0.14, respec- wavelength for different atmospheric tively) (Zdanaviˇcius & Pakˇstien˙e extinction components. Atmosphe- 1997). Figure 1 shows that ric extinction at zenith is calculated the Rayleigh extinction and the using the typical atmospheric extinc- ozone absorption are most selection parameters for the Mol˙etai Ob- tive. The ozone absorption influ- servatory (see the text). ences the radiation in the Hug- gins (ultraviolet) and Chappuis (red) bands. The dependence of the Rayleigh extinction on the wavelength is steep in the ultraviolet and becomes flatter at longer wavelengths. The aerosol extinction decreases slowly with increasing wavelength.

3. DESCRIPTION OF THE AEROSOL EXTINCTION The aerosol extinction is the most variable and problematic. It depends on the nature, size and the size distribution of aerosol parti- 224 E. Pakˇstien˙e, J.-E. Solheim cles, which again depend on the location of the observatory and the prevailing winds from the sources of aerosol particles. Aerosols can be formed by the water and solution drops, dust, pollen and soot. All these particles can be of different sizes and can have different distributions by sizes. During a particular night the condensation of water vapor can take place, and the dust can be transported by wind, which change the aerosol types and sizes. With increase of the number of small aerosol particles, the dependence of the aerosol extinction on wavelength becomes stronger, and the selective aerosol extinction increases. The amplitude of the selective aerosol extinction in most cases in smaller than of the neutral extinction (Pakˇstien˙e 2001). The most common sources of the variable neutral extinction are thin clouds. When observations are carried out through clouds, and the two- or three-channel photometers are used for continuous photometry, the Channel 1 counts are being divided by the Channel 2 counts for removal of the cloud effects. However, in this case the final light curve is obtained with somewhat larger scatter of points than in the case when the sky is absolutely clear. This happens because we add the noise from two stars, instead of only one; the effect is even more significant, if Channel 2 contains a fainter star than Channel 1, which is often the case. Neutrally scattering aerosol particles make the stars fainter and the sky brighter. Especially strong brightening of the sky takes place during observations with the Moon or if a bright star is close to the program star. In the case of clouds, the sky subtraction is compli- cated, but this is not the result of atmospheric extinction although the effect is caused by the same particles. Onemoreremarkabouttheskysubtraction:theratioofthe sky values between different channels can vary with time even during one night. This can be caused by additional lights and their position with respect to the telescope tube. Additional lights can be the daybreak or evening-glow, moonlight, city lights, auroras, etc. These additional light sources can be reflected by the telescope parts or the dome. The dependence of the ratio of the sky values on the telescope position can be investigated by observing the sky in different directions during several adjacent nights with the moonlight or some glows. Also some photometers record the sky values in a fixed direction relative to the main target, as is the case for Channel 3 in the standard WET photometer (Kleinman et al. 1995) and in the Vilnius design classical WET photometer (Aliˇsauskas et al. 2000). Atmospheric extinction correction for WET observations 225

4. THE SYNTHETIC HETEROCHROMATIC EXTINCTION COEFFICIENTS The synthetic extinction coefficients of a heterochromatic photometric system are calculated by the integral equation: F x − · p (λ)·τ (λ)·I(λ)·ϕ(λ)·dλ α = 2.5 log τ x(λ)·I(λ)·ϕ(λ)·dλ ,(6) where p(λ) is the atmospheric transmittance, F is the air-mass of the Earth’s atmosphere, τ(λ) is the transmittance of interstellar matter, x is the number of the mass units of interstellar matter, I(λ) is the energy distribution in the spectrum of the observed star, ϕ(λ) is the response function of the photometric system. Transmittance of the unit mass of interstellar matter τ(λ) is taken from Straiˇzys (1992), energy distribution in the spectra of stars of various spectral types I(λ) are from Straiˇzys & Sviderskien˙e (1972) and Sviderskien˙e (1980), with extrapolation to UV by Sviderskien˙e (1988). The response curve of the WET passband is the sensitivity of the phototube or other detector multiplied by the reflection efficiency of the aluminum surfaces of the telescope mirrors. Usually, two types of photometers are used for WET observations: (1) a three-channel photometer with the Hamamatsu R647 phototubes and (2) a CCD camera with the “sky” filter (NOT Fil- ter #92) cutting out the red and infrared. Figure 2 shows the response functions of the Tromsø three-channel photometer and the CCD photometer (or TCP), both with and without the filter. The mean wavelengths λ0 and the half-widths (FWHM) of the three response functions are: 388 nm and 190 nm for WET R647, 598 nm and 460 nm for the TCP with no filter, and 545 nm and 265 nm for the TCP with the filter. The atmospheric transmittance curve for a given site can be calculated using five atmospheric extinction parameters (h, T, αn,As,bs). Figure 2 shows the transmittance curve of the atmosphere for the Mol˙etai Observatory calculated with the typical atmospheric extinction parameters listed in Section 2. The WET R647 passband covers a spectral region with the ozone absorption bands and strong Rayleigh scattering. This causes a strong influence of the extinction by these factors on WET observations in this passband. The TCP band is cut at the wavelength ∼300 nm and is less affected by the strong ozone absorption in UV. That is why all the extinction effects are much weaker for the TCP passband than for the R647 passband. In the following we investigate the atmospheric extinction effects only for the R647 passband, for which more precise extinction corrections are necessary. 226 E. Pakˇstien˙e, J.-E. Solheim

Fig. 2. The atmospheric transmittance curve for the Mol˙etai Ob- servatory (solid line) and the response functions for the Tromsø WET photometers. The dashed line – the WET R647 photometer + two aluminum surfaces, the dotted line – the TromsøCCD photometer: TE1051 detector + two aluminum surfaces, the dash-dotted line – TE1051 detector +ﬁlter#92+twoaluminumsurfaces.

Fig. 3. Dependence of the extinction coeﬃcient α on color indices U–B (a) and B–V (b) in the UBV photometric system for unreddened (x =0) and reddened (x = 6) stars. Arrows show the moving direction of stars when the mass of interstellar dust x increases from 0 to 6. Atmospheric extinction correction for WET observations 227

Table 1. Second order extinction coefficients γ and g for WET R647, TCP with no filter and TCP with the filter #92 passbands for the Mol˙etai Ob- servatory, when h = 220 m, T = 3 mm, As =0.2 and bs =0.8. γ g(O V) g(M0 III)

αR647, (U − B)0 –0.2680 –0.5565 –0.0772 αR647, (U − V )0 –0.1526 –0.2405 –0.0415 αR647, (B − V )0 –0.3352 –0.4236 –0.0896 αTCP, (U − B)0 –0.1495 –0.3410 –0.0583 αTCP, (U − V )0 –0.0878 –0.1469 –0.0313 αTCP, (B − V )0 –0.2006 –0.2582 –0.0676 αTCP+filter, (U − B)0 –0.0260 –0.0552 –0.0279 αTCP+filter, (U − V )0 –0.0156 –0.0238 –0.0150 αTCP+filter, (B − V )0 –0.0365 –0.0419 –0.0324

5. THE DEPENDENCE OF EXTINCTION ON SPECTRAL TYPE OF STARS AND INTERSTELLAR REDDENING The dependence of WET extinction coefficients on color indices of the UBV photometric system is shown in Figure 3. The arrows in- dicate the tracks of stars when they are affected by different amounts of interstellar reddening. It is evident that the dependence of atmospheric extinction on color indices is nonlinear. As a first approxi- mation, they are usually described by a linear equation: ∗ α = αe + γ · ΔC,(7) ∗ where α is the extinction coefficient of the target star, αe is the extinction coefficient of the extinction star, ΔC is the difference of color indices of both stars, γ is the second order extinction coefficient: dαC γ = dC .(8) The second order extinction coefficient γ is the gradient of the α(C) dependence. The dependence of extinction on interstellar reddening is almost linear and is shown in Figure 3 by arrows. The slope of this arrow- line is the second order extinction coefficient g. It can be calculated similarly to the extinction coefficient γ: dαE g = dE ,(9) where E is the color excess. Some values of the second order extinction coefficients for WET R647, TCP with no filter and TCP with filter #92 are given in 228 E. Pakˇstien˙e, J.-E. Solheim

Table 1. They are small compared with the errors in the standard reduction process for WET observations. We will describe the causes of these errors in Section 7.

6. DEPENDENCE OF EXTINCTION ON AIR MASS – THE FORBES EFFECT The method of extinction correction when the linear dependence of the extinction on the air mass is supposed, is called the Bouguer method. However, in broad-band photometry, especially in the UV and blue passbands, the extinction increases slower with increasing air mass, because at large air masses the spectral composition of light changes when it crosses the atmosphere. Due to this, the star becomes redder, and it is less affected by extinction in the remaining layers of the atmosphere. Sometimes, when the photometric passband is in the spectral region where the atmosphere has no strong absorption bands, we can use a second order polynomial equation to describe the Forbes effect. When the photometric passband covers a spectral region where the atmospheric transmittance curve has a large slope due to ozone absorption, Fig. 4. Dependence of observed mag- the second order polyno- nitudes on air mass, when the extra- mial equation can be used atmospheric magnitude is 0.0 mag, the only for larger air masses transmittance of the atmosphere is calcu- than 1.0, but cannot be lated for the Mol˙etai Observatory with al- used to calculate the extra- titude h = 220 m and a mean thickness of the ozone layer of T =3mm. The atmospheric parameters of atmosphere is without aerosols and a star stars. Figure 4 shows of the O V spectral type is observed with the dependence of observed in the WET R647 passband. The differ- magnitudes of a star on ence Δα0 = α01 − α12 gives the error of air mass, when the extra- the extra-atmospheric magnitude when it is estimated by the Bouguer method us- atmospheric magnitude of ing the observed magnitudes at 1 and 2 air this star is m =0mag. We masses. tried to fit to the Bouguer Atmospheric extinction correction for WET observations 229 line and the second order polynomial the observations at 1, 2 and 3 air masses, but no method gives the correct extra-atmospheric value m =0mag. In this case the short wavelength side of the passband is defined by the atmospheric ozone absorption band. At the UV wavelengths, shorter than 300 nm, the radiation is cut out by the ozone absorption, but such natural “filter” is not stable because the thickness of the ozone layer changes with time and site. This is not critical in case of differential photometry, especially when both stars are at the same air mass, and their spectral types and interstellar reddening are close. The Forbes effect causes the extinction between 0 and 1 air masses to be larger than that between 1 and 2. The effect can be expressed as Δα0 =(α1 − α0) − (α2 − α1)=α01 − α12, (10) where α0 =0is the extinction coefficient extrapolated to outside the atmosphere; α1 is the extinction coefficient at 1 air mass (zenith distance z =0), α2 is the extinction coefficient at 2 air masses (zenith distance z =60◦)(seeFigure4). If the extinction coefficient does not depend on air mass, then the parameter Δα0 is 0. The parameter Δα0 shows how much extinction for 1 air mass is larger than the difference of extinction between 1 and 2 air masses. This difference is used as the parameter of the Forbes effect. When the Forbes effect is taken into account, the extra-atmospheric magnitudes are slightly brighter than in the case of the linear extrapolation. Cousins & Caldwell (2001) confirm that we can ignore a small curvature of the Bouguer lines for the U–B color index between air masses 1 and 2, but the effect is relevant in the context of comparison between the ground-based and satellite photometric observations. This is valid also for the magnitudes. The dependence of extinction on air masses makes it possible to estimate the error of extra-atmospheric magnitudes Δα, when the Bouguer lines are used for the reduction: αmax−αmin Δα = αmax − Fmax , (11) Fmax−Fmin where: αmax and αmin are the observed extinctions at Fmax and Fmin air masses. For this have to measure the extinction for a standard star at least at two different air masses, when the zero point of the instru- mental system is known. This error is valid only in the case when the extinction is constant during a night. This error can also be calculated by simultaneous observations of two standard stars of the same spectral type at different zenith distances. 230 E. Pakˇstien˙e, J.-E. Solheim

7. THE QED EXTINCTION CORRECTION METHOD AND ITS ERRORS In this section we will analyze the reduction of WET observations with the QED program (Clemens 1993). For this purpose synthetic photometry will be used to avoid the influence of secondary effects and to concentrate on the extinction correction. Synthetic WET observations were modeled in the following way. Fig. 5. Synthetic light curve, calculated (1) Synthetic light cur- as the function: lc =20sin2πt·0.00130+ ve of the program star 25 cos 2πt · 0.00143. (Figure 5) was constructed as a sum of two time-variable functions with the frequencies: 0.0013 μHz with an amplitude of 20 mma, and 0.00143 μHz with an amplitude of 25 mma: lc =20sin2πt · 0.00130 + 25 cos 2πt · 0.00143. (12) (2) Extra-atmospheric synthetic counts for the program and the comparison star I◦ were calculated assuming the mean count of I¯ = 10000. The counts for the program star were modulated by the light curve: I◦ =(1− lc · 0.001) · I¯. (13) (3) Synthetic observed fluxes were calculated by including the atmospheric extinction given by Equation (6). The program star was taken to be of spectral type O V and the comparison star – of spectral type G0 V: ◦ − α(OV) IOV = I · 10 2.5 (14) for the program star and − α(G0V) IG0V = 10000 · 10 2.5 (15) for the comparison star. These synthetic observations were calculated for several moments of observations corresponding to different zenith distances. The synthetic observations can be also modulated by clouds. Examples of cloud modulations are shown in Figure 6. Equations for the modulation of observations through the clouds are the following: Atmospheric extinction correction for WET observations 231

Cloud 1: Δα = −1.142 + 1.78 · 10−3 · i − 5.9 · 10−7 · i2, where i is between 1000 and 2000; Cloud 2: Δα = −10.04 + 5.11 · 10−3 · i − 6.38 · 10−7 · i2, where i is between 3500 and 4500; Cloud 3: Δα = −56.45 + 2.161 · 10−2 · i − 2.06 · 10−6 · i2, where i is between 5000 and 5500. Here i is time in seconds. After that the synthetic observations were reduced using two different options of the usual reduction procedure with the QED program. The third case was a new extinction correction method. Case I. The extinc- Fig. 6. Synthetic observations of a vari- tion coefficient was de- able (Channel 1) and a comparison (Channel termined by the QED 2) stars, when the atmospheric extinction is extinction correction me- calculated for the atmospheric transmittance thod, i.e., the extinction curves shown in Figure 2 with additional ex- coefficient was chosen to tinction values due to clouds, which are defined by polynomials given in the text. produce a flat line of the reduced data. It is known that usually the extinction for the variable star is larger than for the comparison star. That is because the variable stars observed by WET mostly are hot stars of O, B or A spectral types, and the comparison stars in most cases are redder than the variable star. The extinction coefficients for hot stars are always larger than for cooler stars. Case II. We have used the same QED program for reduction of the observations, but with the real extinction coefficients both for the variable and the comparison star. The coefficients determined in this way are much larger than in Case I. Using these real extinction coefficients we get not a very attractive view – the reduced shape of the light curve looks like a “happy smile”. Case III. We have used a new method, when the extinction was calculated for every point of synthetic observations according to the 232 E. Pakˇstien˙e, J.-E. Solheim

Fig. 7. The reduced synthetic observations of the program star O V (a) and of the comparison star G0 V (b). For the reduction the following extinction coefficients are used: the solid curve – the extinction coefficients are determined by the QED program methods (Case I), taking α(OV) = 0.98 mag and α(G0V) = 0.645 mag; the dashed curve – real extinction coefficients are determined by the QED program (Case II), taking α(OV) = 1.607 mag and α(G0V) = 0.915 mag; the dotted curve – the extinction coefficients are calculated by the new method using synthetic photometry (Case III). synthetic extinction coefficient (Equation 6) for each air mass and spectral type of stars. Using this method we are able to correct for the Forbes effect and the difference of spectral types. Figure 7 shows the reduced data using these three methods. We can see, that the best reduction is in Case III, and they look like the initial synthetic data with a mean count number of 10000. In Case I we get a much smaller number of counts: by 40% smaller for the O-type star and by 20% smaller for the G-type star. In Case II we get the correct extra-atmospheric count number only when the star is at culmination; when the air mass is larger than 1, the counts of the reduced data get too large due to the increased value of the used extinction coefficient. It happens because the Forbes effect is ignored. Figure 8 explains how this “happy smile” effect in Figure 7 appears. The solid line shows how the extinction depends on air mass between 1 and 3 air masses. Two straight dashed lines show the Bouguer lines with two different extinction coefficients. These lines connect the zero extra-atmospheric extinction and the two different observations at 1 air mass: the upper line corresponds to the real extinction coefficient at 1 air mass and the lower line represents the standard QED extinction correction in Case I. We can see, that the Bouguer line moves away from the real dependence of extinction for Atmospheric extinction correction for WET observations 233 observations at larger air masses. As a result, the used extinction gets larger than the real extinction. We can see that the straight Bouguer line will never fit exactly to the observed dependence of extinction on air mass. The best case is when the straight line crosses the real dependence over some mean value of air masses. However, in this case we cannot get an absolutely flat line of the reduced data either. We get a curve where the middle part corresponds to the culmination of the star, which looks like it is reduced with too small extinction coefficient, and the ends are turned up like they are reduced with too large extinction coefficients. Such waves in the reduced curve after the Fourier transform Fig. 8. Explanation, why we get (FT) give an additional the curved reduced observations after the noise at low frequencies. Bouguer extinction correction with the QED program: the upper panel shows the In case of the real ob- observations reduced by the standard QED servations of a fast variable extinction correction procedure (Case I), star these slow modula- the lower panel explains the cause of the tions may be hidden in the wrong reduction. light curve, but they give the low frequency noise in the FT. In many cases when the reduced light curves are bent, a polynomial fitting is used for flatting of the curve. When we use a fourth order polynomial fitting for such type of the curve with “waves” caused by the wrong extinction correction, we get a flatter but still a waved curve (see Figure 9) (later we will show results of FT after the polynomial fitting). In addition, if we divide counts of Channel 1 by Channel 2, this curvature for the program star par- tially disappears. How well this curvature will be removed depends 234 E. Pakˇstien˙e, J.-E. Solheim on the selection of extinction coefficients for both stars. When we use the real dependence of the extinction coefficient on air mass and the extinction is calculated for every observation (Case III), we do not get any additional waves. The dependence of extinction on air mass can be estimated by Equation (6) for every moment of observation (for every air mass), or the extinction can be calculated only for some air masses between 1 and the largest air mass, and inter- polated by a second order polynomial. When observations are carried out through thin Fig. 9. The light curve of a comparison clouds and their thickness after extinction correction by the standard changes with time, divi- QED procedure (Case I) without a poly- sion by the light curve of nomial fit and with a 4th order polynomial the comparison star has to fit. be used for removal of the cloud effects. Clouds add gray extinction for observations and division of Channel 1 by Channel 2 can easily remove them. In this case it is important to know spectral types of the stars observed in both channels.

8. FOURIER TRANSFORM OF SYNTHETIC LIGHT CURVES Figure 10 shows FTs of the reduced data shown in Figure 7. We can see that the largest noise is in Case II of extinction correction because the light curve is not flat. Even the difference in amplitudes from the true-values is seen (panel b). Some low frequencies are also found in Case I (panel c). These frequencies appear due to the bent light curve after the linear extinction correction (as mentioned above), but the amplitudes at higher frequencies are not affected by these reduction faults. So, we get the correct amplitudes in Case I even if the extinction correction is wrong. Figure 11 shows FT for the Case I light curve when Channel 1 was divided by Channel 2 (panel a, dashed line). We get a larger noise in the FT because of adding noises from both channels. The dotted line shows the FT of the light curve in Case I, fitted by a Atmospheric extinction correction for WET observations 235

μ Fig. 10. FT for synthetic observations when the extinction is constant all the time, but the extinction correction methods are diﬀerent: (a) – for frequencies between 0 and 1800 μHz; (b) – for frequencies between 1200 and 1600 μHz; (c) – for frequencies between 0 and 500 μHz. The power spectra after use of the QED method and of the new method are close and overlap at higher frequencies. fourth order polynomial equation. This ﬁtting has decreased the amplitudes of the noise at low frequencies (panel a). In all these FTs the amplitudes at our frequencies of interest are constant and equal to the real values (panel b). Figure 12 shows the FTs of synthetic light curves observed through thin clouds when the reduction Case I was used. The solid 236 E. Pakˇstien˙e, J.-E. Solheim

μ Fig. 11. FT for synthetic light curve when extinction is constant all the time, but the extinction correction methods are diﬀerent: (a) – for frequencies between 0 and 500 μHz; (b) – for frequencies between 1200 and 1600 μHz. line shows FT for Channel 1 observations only. The dashed line corresponds to FT when clouds were removed by the division Ch1/Ch2. Of course, if the clouds were not removed, then FT gives a strong noise that can increase or decrease the real amplitudes (panel b). However, the clouds usually are removed from the light curves or if it is impossible, such data are not used for the further analysis.

9. ESTIMATION OF APPROXIMATE SPECTRAL TYPE OF COMPARISON STAR USING WET OBSERVATIONS Thus, it is important to know the spectral type of the comparison star if a division of Ch1/Ch2 is used for cloud corrections. This spectral type can be estimated using the WET observations and then Case III of the extinction correction may be used. This extinction correction procedure is described below. Atmospheric extinction correction for WET observations 237

μ Fig. 12. Amplitudes calculated from the light curve, when the neutral extinction eﬀect (clouds) was not removed (solid line) and when the eﬀect removed by division of Ch1/Ch2 (dashed line): (a) – for frequencies between 0 and 1800 μHz; (b) – for frequencies between 1200 and 1600 μHz.

Our synthetic observations of the variable star, spectral type of which is always known, is reduced using a dependence of extinction coefficient on air mass for blue stars. For the comparison star we may apply the same dependence calculated for many different spectral types of stars. After the extinction correction with the extinction coefficients of for different types of stars, for the comparison star we get a “happy smile”, a “sad smile” or just flat line of the reduced data during a night. The result depends on the chosen spectral type of the star. If the chosen spectral type is too hot, we will get a “happy smile”, if too cool – a “sad smile”. The case when we get a flat line indicates roughly the spectral type of the comparison star, and in this case we can divide Ch1 by Ch2 correctly. If the observations are carried out through clouds or are affected by other causes, e.g. if the dome covers part of the telescope, or the 238 E. Pakˇstien˙e, J.-E. Solheim sky extraction is not correct, then we can estimate the spectral type of the comparison star only after the division Ch1/Ch2. Figure 13 shows the results of spectral type estimation of the comparison star according to our synthetic observations. The flattest line appears when the extinction correction of a G0 V star is applied. In other cases the results are bent like “sad smile”. Thismethodcanbeusedalsoforreduction of real observations. Figure 14 shows the results of real observations with 6000 points from the XCov19 observing run on May 28, 2002 with the 2.1 m telescope of McDonald Observatory. The integration time was 5 s. In the middle of observations clouds have appeared. Applying of the described method for estimation of spectral type of the comparison star leads to F0 V. The best night for the estimation of spectral type of the comparison star by this method should be long and clear with stable extinction. Several nights can be used with averaging of the results. However, the best way is to choose the comparison star before a WET campaign and estimate its magnitude and spectral type by obtaining its photometry in the UBV or some other photometric system. The extra-atmospheric magnitude of the comparison star should be known, if we want to evaluate the extinction for every moment of observations.

10. CONCLUSIONS After investigation of the reduction methods with the QED program and by a new method for WET observations we conclude that the extinction correction in the QED program is not sufficient. The QED program uses too small extinction coefficients, does not consider the non-linear extinction dependence on air mass and on spectral type. Because of that, low frequency noise is found which can be decreased by division of Ch1/Ch2 light curves or by using polynomial fitting. Because of too small extinction coefficients which are determined by the QED program, we cannot estimate the real extra-atmospheric values of the magnitudes of the observed stars, but it does not influence the determined pulsation amplitudes for frequencies above 200 μHz. We propose to use Equation (6) for estimation of the extinction for every moment of observations, or the extinction can be calculated by Equation (6) only for some values of air masses between 1 and its largest value, and then a second order polynomial can be used for interpolation. By using this extinction correction method it is Atmospheric extinction correction for WET observations 239

Fig. 13. Determination of spectral type of the comparison star using the new extinction correction method for synthetic observations, when the light curve of the program star is divided by the light curve of the comparison star, assuming diﬀerent spectral types for the comparison star. 240 E. Pakˇstien˙e, J.-E. Solheim

Fig. 14. Determination of spectral type of the comparison star using the new extinction correction method for real observations (May 28, 2002, McDonald Observatory, XCov19), when the light curve of the program star is divided by the light curve of the comparison star, assuming different spectral types for the comparison star. Atmospheric extinction correction for WET observations 241 possible to estimate an approximate spectral type of the comparison star. This is necessary, if we apply the division of light curves from the two photometer channels. The best way is to choose the comparison star well before a WET observing campaign, to obtain its multicolor photometry in one of the photometric systems (the Vilnius seven-colorsystemorat least in UBV), and to estimate its magnitude and spectral type. Also we propose to use a filter that cuts out the ultraviolet from the WET passband shorter than 310 nm. That would decrease the variability of the extinction coefficient and would let us to better evaluate the extinction for every moment of observations. In any case, the wavelengths shorter than 300–310 nm are cut out by the ozone absorption, but such natural “filter” is not stable due to variable thickness of the ozone layer. Amplitudes of the variable star pulsations in FT power spectra practically do not depend on the accuracy of the extinction correction. Only low frequency amplitudes can be affected if the Bouguer line is used for the extinction correction. Amplitude values are in- fluenced mostly by other kinds of noises, like electronic noise, small variations of atmospheric transparency due to clouds, sky brightness fluctuations, etc., and the most important is the photon noise from the star itself, which can be reduced by increasing the number of the counted photons.

ACKNOWLEDGMENTS. One of the authors (E.P.) expresses her special thanks to K. Zdanaviˇcius and E. G. Meiˇstas for advises and help in preparation of this report and to everybody in the WET group, who presented their observations and helped us with the data reduction and analysis.

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