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\IBVShead{5705}{30 May 2006}

\IBVStitle{UZ UM\lowercase{a}: an RR\lowercase{ab} Star with Double-Periodic Modulation}

\IBVSauth{S\'odor,~\'A.$^1$; Vida,~K.$^2$; Jurcsik,~J.$^1$; V\'aradi,~M.$^1$; Szeidl,~B.$^1$;  Hurta,~Zs.$^2$; D\'ek\'any,~I.$^2$; Posztob\'anyi,~K.$^2$; Vityi,~N.$^2$; Szing,~A.$^3$; Kuti,~A.$^2$; Lakatos,~J.$^2$; Nagy,~I.$^2$; Dobos,~V.$^2$}

\IBVSinst{Konkoly Observatory of the Hungarian Academy of Sciences, P.O. Box 67, 
          H-1525 Budapest, Hungary; e-mail: sodor, jurcsik, varadi@konkoly.hu}
\IBVSinst{E\"otv\"os Lor\'and University, Department of Astronomy, P.O. Box 32,
          H-1518 Budapest, Hungary}
\IBVSinst{University of Szeged, Dept. of Exp. Physics and Astron. Obs., 
          H-6720 Szeged, D\'om t\'er 9, Hungary}

\SIMBADobj{UZ UMa}
\GCVSobj{UZ UMa}

\IBVStyp{  RRab  }
\IBVSkey{Variable stars, RR Lyrae stars, Blazhko effect}
\IBVSabs{Our CCD V observations show that the fundamental mode RR Lyrae star}
\IBVSabs{UZ UMa displays double periodic Blazhko modulation of its light curve.}
\IBVSabs{The Blazhko periods are 26.7 and approx. 143 days. UZ UMa is estimated to be}
\IBVSabs{a relatively metal poor RRab star with [Fe/H]=-1.2.}

\begintext

\vspace*{-0.8cm}

UZ~UMa was discovered to be variable by Baker (1938). He classified it as an irregular or 
semiregular type variable based on the photographic observations of Kapteyn. The correct 
classification (RRab) and period (P=0.4668795 d) were given by Meinunger (1968).

UZ~UMa was observed in the course of our survey of short period ($P_{\mathrm puls} < 
0.48\,\mathrm d$), fundamental mode, northern RR~Lyrae stars, that aims to determine the
real incidence rate of Blazhko variables in this sample and to study the modulation
properties in detail. 
The observations were made with the 60\,cm automatic telescope of Konkoly Observatory, 
Sv\'abhegy, Budapest, equipped with a Wright 750$\times$1100 CCD camera through a Cousins V filter.
1584 brightness measurements were obtained on 30 nights between 27 January and 23 May in 2006 
(JD 2453763--878). Data reduction was performed using standard IRAF\footnote{{\sc IRAF} is 
distributed by the National Optical Astronomy Observatories, which are operated by the 
Association of Universities for Research in Astronomy, Inc., under cooperative agreement with 
the National Science Foundation.} packages. As no appropriate comparison star was found in the 
field of view, magnitude
differences of UZ~UMa from the average magnitude of 5 neighboring stars (GSC~21322-01261, 
GSC~21322-014531, GSC~21322-01252, GSC~21322-014679 and GSC~21322-01255) were calculated
in order to reduce the noise of the comparisons' magnitudes.
Instrumental magnitude differences of UZ~UMa are given in Table~1, available 
only electronically.\footnote{Available on the IBVS website as {\tt 5705-t1.txt}.}

\IBVSedata{5705-t1.txt}
\IBVSdataKey{5705-t1.txt}{UZ UMa}{}

The following elements for light maxima were derived:
$$t_{\mathrm max} {\mathrm[HJD]} = 2453763.3368 + 0.4668413\,{\mathrm d} \cdot E$$
The original light curve and the light curve prewhitened with the pulsation frequency and 
its harmonics phased with the pulsation period are shown in Fig.~1--2. The plots clearly show 
the sign of the Blazhko modulation. The residual light curve indicates that the modulation 
is the largest on the rising branch and around maximum brightness,
significant changes in the shape of the bump preceding minimum light also occur. The 
light curve is the most stable at minimum  and on the mid part of the descending branch.

The Fourier spectrum of the light curve prewhitened with the 18 harmonics of the pulsation 
shows a complex structure of peaks around the pulsation frequencies. We assume that the 
Blazhko modulation can be described with the same, symmetric pattern
of modulation frequency components of the residual spectrum around the frequency
components of the pulsation. In this case the true modulation frequency can be
identified more clearly in a \emph{cumulative spectrum} defined as the sum of the two 
sides of the spectrum's segments in the vicinities of the pulsation peaks up to a given 
order according to the following formula:
$$A'(f)=\sum_{i=1}^n \left[ A(i\cdot f_{\mathrm p}+f) + A(i\cdot f_{\mathrm p}-f)\right ],
\ \ \ f < f_{\mathrm r}.$$
\noindent
$A(f)$ is the original spectrum, $f_{\mathrm p}$ is the pulsation frequency, $i$ is 
the harmonic order, $f_{\mathrm r}$ is the length of the examined frequency range 
and $A'(f)$ is the yielded cumulative spectrum, which has better S/N properties than
the original spectrum.
\IBVSfig{5.9cm}{5705-f1.ps}{The $V$ light curve of UZ~UMa phased with the pulsation period.}
\IBVSfigKey{5705-f1.ps}{UZ UMa}{phased light curve}
\IBVSfig{5.9cm}{5705-f2.ps}{The prewhitened $V$ light curve of UZ~UMa phased with the
pulsation period.}
\IBVSfigKey{5705-f2.ps}{UZ UMa}{phased light curve}
The cumulative spectrum of the prewhitened light curve  shows two modulation peaks
of different shapes, one at  0.065 c/d and another, wider component at around 0.03 c/d 
(see Fig. 3). The wideness of this latter frequency component indicates that there might be some 
differences in its position in the different harmonic orders and at the different sides 
of the pulsation components. However, to examine this possibility in more detail a more 
extended dataset is needed.

\vspace*{-10cm}

\IBVSfig{4cm}{5705-f3.ps}{The cumulative residual spectrum of UZ~UMa summed for the first 8
pulsational harmonics.}
\IBVSfigKey{5705-f3.ps}{UZ UMa}{periodogram}

\IBVSfig{16cm}{5705-f4.ps}{The light curves in different phases of the 26.7-day and 143-day
modulations
after removing the modulation corresponding to the other modulation period. 
In the electronic edition animated
figures of the modulations are available.}
\IBVSfigKey{5705-f4.ps}{UZ UMa}{light curve}

\newpage

\IBVSefigure{5705-f5.ps}
\IBVSecomment{Animated figure (GIF) of the 26.7 day modulation. 
The 143 day modulation has been removed.}

\IBVSfigKey{5705-f5.ps}{UZ UMa}{light curve}
\IBVSefigure{5705-f6.ps}
\IBVSecomment{Animated figure (GIF) of the 143 day modulation. 
The 26.7 day modulation has been removed.}
\IBVSfigKey{5705-f6.ps}{UZ UMa}{light curve}

In accordance with the two frequency peaks appearing in the cumulative residual
spectrum, the light curve of UZ UMa cannot be fitted with the required accuracy assuming
a single modulation period.  Instead, even with two different modulation periods the residual
scatter remains larger than observational inaccuracies would explain.
Though the modulations of many Blazhko stars are known not to be strictly regular,
the light curve of only XZ Cyg (LaCluyz\'e et al., 2004) has been previously described
by two pairs of equidistant modulation components. 

Data analysis was performed using the utilities of the  program package MUFRAN (Koll\'ath, 
1990). First we determined the modulation 
frequency values, $f_{\mathrm mod\,1}$ and $f_{\mathrm mod\,2}$  simultaneously through 
an iterative process, as the frequencies that 
yield the best fit to the residual light curve prewhitened by the
pulsation frequency components up to the 18\,th harmonics.
The modulation components up to the 8\,th harmonic order and also $f_{\mathrm mod\,1}$ and 
$f_{\mathrm mod\,2}$ were considered.
The following modulation frequencies were thus determined: 
$f_{\mathrm mod\,1} = 0.0374\,{\mathrm c/d}$ and 
$f_{\mathrm mod\,2} = 0.0070\,{\mathrm c/d}$ ($P_{\mathrm mod\,1} = 26.7\,{\mathrm d}$ 
and $P_{\mathrm mod\,2} = 143\,{\mathrm d}$).
If the modulation frequencies are not determined simultaneously but in consecutive steps, 
then very similar results arise. The first modulation 
frequency is then at 0.0372\,c/d,
and the other modulation frequency 
gives the best fit with 0.0065\,c/d  value. 
The observations span over only 115 days, thus the period 
of the secondary modulation is somewhat uncertain. Its value is most probably somewhere 
between 125\,d and 170\,d.

The 0.017 mag r.m.s. scatter of the residual indicates  even more complex behaviour of the modulation,
but no further real frequency component can be resolved.

In Kov\'acs (2005) it was noted that in case of good data sampling 
the mean light curve of Blazhko stars can be used to define the physical properties 
from the Fourier parameters of the light curve. We came to the same conclusion 
using the data of the small amplitude modulation RRab stars: RR Gem and SS Cnc 
(Jurcsik et al., 2005; Jurcsik et al., 2006).
Based on the Fourier parameters of the mean light curve of UZ UMa [Fe/H$]=-1.17$ 
can be determined using the formulae of Jurcsik \& Kov\'acs (1996). 
Our previous multicolour measurements with the same instrumentation indicate that if 
instrumental $v$ magnitudes are used instead of standard $V$ magnitudes, then the calculated 
[Fe/H] overestimates the metal content only by $0.02 - 0.04$.

Acknowledgements: The financial support of OTKA grants T-043504, T-046207 and T-048961 is
acknowledged.

\references

Baker, E. A. 1938, {\it MNRAS}, {\bf 98}, 65 

Jurcsik, J., \& Kov\'acs, G. 1996, {\it A\&A}, {\bf 312}, 111 

Jurcsik, J., S\'odor, \'A., V\'aradi, M., Szeidl, B., Washuettl, A. et al., 2005, {\it A\&A}, {\bf 430}, 1049 

Jurcsik, J., Szeidl, B., S\'odor, \'A., D\'ek\'any, I., Hurta, Zs. 
et al. 2006 {\it AJ}, in press (astro-ph/0603496)

Koll\'ath, Z. 1990, Occ. Techn. Notes Konkoly Obs., No. 1, \\ {\tt http://www.konkoly.hu/staff/kollath/mufran.html}

Kov{\'a}cs, G., 2005, {\it A\&A}, {\bf 438}, 227 

LaCluyz{\'e} A., Smith, H., Gill, E-M., Hedden, A., Kinemuchi, K. et al. 2004, {\it AJ}, {\bf 127}, 1653 

Meinunger, L. 1968, {\it MVS 4}, {\bf 7}, 179

\endreferences


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