Peremennye Zvezdy (Variable Stars) 33, No. 8, 2013 Received 21 November; accepted 10 December.
N.L. Kroussanova, A.V. Mironov, A.I. Zakharov
Sternberg Astronomical Institute, Lomonosov Moscow
State University, 13, University Ave., Moscow 119991, Russia

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This comparison was performed using a special algorithm, so that coefficients of the nonlinear polynomial relating the difference to , , and color indices were calculated. The comparison proved that the difference of the observed and that calculated using the polynomial, , namely did not exceed for 8766 stars. The frequency distribution of the differences is shown in Fig. 1. The rms deviation is .
Obviously, the spectral energy distributions of these stars give a possibility to calculate magnitudes in one catalog (Hipparcos) from magnitudes in the other catalog rather accurately. This property allows us to consider the stars of this sample as candidate photometric standards in the northern sky. Since common stars in the two catalogs were observed at different times, using completely different methods, and from different positions (in space and on the Earth), the close agreement between calculated and observed values indicates that these stars are not variable or, at least, have low variability amplitudes. However, to be valuable standards, the stars should be carefully examined for variability.
Observations obtained during the Hipparcos mission and contained in the "Hipparcos Epoch Photometry Annex" and "Tycho Epoch Photometry Annex" lists provide such an opportunity. A technique was developed in the SAI (Mironov et al. 2003) permitting to discover brightness variations of stars on the basis of simultaneous multichannel observations. According to this technique, an parameter is calculated; this parameter evaluates the degree of correlation of individual magnitude measurements in several channels.
Suppose that, for a star with the number in the pair of channels with numbers and , we have simultaneous observations. Then we can calculate the linear correlation coefficient, assuming a normal distribution of the variables and , according to the formula:
Since there exist channels, one can construct a vector with components being generally correlated. From components of the vector, one can calculate an integrated statistics for every star:
Note that does not mean that the star cannot be considered variable. It only means that the Hipparcos material is not good enough to discover its variability. This is primarily due to the fact that the standard error of measurements in the and channels is large (about ).
Fig. 2. Histograms of the three parameters, illustrating the shifts of distribution modes because of correlation between channels. 
Most stars of our sample are not variables; nevertheless, their distribution modes are not zero, as it should be for independent random variables. For the pair of and , the mode was found to be 0.11865; for the pair of and , 0.1672; and for the pair of and , 0.8047. Thus, all the channels are correlated. The same conclusion was earlier made from other considerations (Zakharov et al. 2000; Krutyakov et al. 2000). The correlation for the channel pairs and , and is poor, but for the pair of and it is strong enough. The presence of a correlation shifts the parameter from zero, even when there is no true variability. Before calculating the generalized statistics according to formula (6), it is necessary to take into account the influence of the crosscorrelation and to subtract corresponding values of the distribution modes, found for nonvariable stars, from the obtained , getting and . The corrected data points are denoted , , , and generalized as .
An analysis of the statistics for the stars identified as variables allows us to estimate the effectiveness of the technique for discovering lowamplitude stars on the base of Hipparcos and Tycho data.
First, consider the stars with GCVS names. There are 181 of them in our sample of 8636 stars.
The fields H4950 in the Hipparcos catalog contain respectively the 5th and 95th percentiles of the epoch photometry, i.e. (0.05) and (0.95). Thus, they provide an estimate of the magnitudes at maximum and minimum brightness detected during the time of observations.
We compared the differences to the parameter. The results for the 181 GCVS stars are shown in Figs. 3, 5, and 7.
Fig. 3. The relation between and the difference for the GCVS stars in our sample. The three stars with the highest values are marked. 
Fig. 4. The light curves of the variable V2093 Cyg in the , and bands. Hereafter, the figures showing light curves have and magnitudes labeled along the left ordinate axis, and magnitudes, along the right one. 
Figure 3 shows that most points are grouped in an area where does not exceed 10 and the difference is not larger than . The highest values of were found for the stars TX UMa, V505 Per, and V2093 Cyg. TX UMa is an eclipsing system of the EA/SD type. It has an amplitude of in band and the period . It is clear that the star was observed by Hipparcos in different phases and is easily detected by the technique. The eclipsing variable V505 Per belongs to the EA/DM type, its amplitude being . Hipparcos observed four eclipses, permitting the technique to detect the variability reliably. V2093 Cyg has the type LB and an amplitude of . As an example, the light curve of V2093 Cyg is shown in Fig. 4. Synchronous brightness changes in the three channels are clearly seen. is about 50; this value is very reliable and indicates that the star is variable.
The area of is shown in more detail in Fig. 5.
The variables in the range are marked in the figure. The figure convinces us that the technique makes it possible to discover such variables as OW Hya, AF Ari, IO UMa, and MP Del without difficulties. These stars are eclipsing variables with amplitudes not exceeding . More interesting are the discoveries of EN UMa (DSCTC, amplitude ) and V1133 Tau (LPB, amplitude ). They confirm that the method is able to detect variability with amplitudes below the standard error in most channels. The light curve of EN UMa is shown in Fig. 6.
Fig. 6. Brightness of EN UMa in the , , and channels versus the ordinal number of observation. The vertical dashed lines mark the main correlated features of brightness variations that provided the high value. 
Figure 7 shows, in most detail, the area of the smallest values.
It follows from Fig. 7 that if , then, according to the theory, we should expect the star to be variable. 54 stars are situated in the range. The area of mainly contains variables with amplitudes of . They are not detected, primarily because of large errors in the and channels.
Figure 8 shows the light curve of Eri. The star's variability type is BY. Despite the small number of observations (only 9 reliable simultaneous measurements in , , and ), there is a strong correlation.
Thus, on the base of simultaneous measurements in individual , , and bands of the Hipparcos experiment, from 174 GCVS stars having below , the technique found 43 variables (25%) at and 59 variables (34%) at .
Consider now the stars of our sample contained in the NSV list. There are 504 such stars. They all lie in the range. Their positions in the diagram are shown in Fig. 9. The following distribution of was found for these 504 stars:
Number of stars  
164  
112  
106  
62  
28  
20  
13  
Total  504 
Among the stars under consideration, for 123 objects (24.4%); for 61 stars (12%); for 33 stars; and for 13 stars. Many of these stars should actually be variable. For example, the relation of , , on the serial number of observation for NSV 24420 = HIP 89981 is shown in Fig. 10, and a similar relation for NSV 24923 = HIP 97757, in Fig. 11.
Fig. 10. Simultaneously measured , , magnitudes for NSV 24420 = HIP 89981 versus the ordinal number of the observation. . The vertical dashed lines mark the most prominent correlated parts of the light curves. This star is variable with a high probability. 
Fig. 11. Simultaneously measured , , magnitudes for NSV 24923 = HIP 97757 versus the ordinal number of the observation. . The vertical dashed lines mark the most prominent correlated parts of the light curves. For clarity, the curves were shifted along the ordinate, by downwards for the band and by upwards for . This star is variable with a high probability. 
Both diagrams show repeated simultaneous deviations of brightness from the mean values.
Among the 504 NSV stars, 467 are listed in the AAVSO VSX database; 47 NSV stars do not enter the AAVSO list. The latter stars have the following NSV numbers:
02990,  05426,  09915,  13336,  15165,  15478,  15594,  15755,  15816,  16228, 
16351,  16353,  16390,  16738,  16744,  17418,  17882,  18090,  19580,  19751, 
19940,  20099,  20109,  20215,  20429,  20619,  20902,  20927,  23672,  23850, 
24040,  24405,  24406,  24626,  24669,  24848,  24872,  24881,  24891,  24943, 
25003,  25772,  25781,  25891,  25922,  25999,  26115. 
The numbers in boldface are stars with .
Let us now consider briefly the stars from the AAVSO list. Among the 8636 stars in our sample, 792 stars enter the AAVSO Variable Star Index (VSX). 632 of them have GCVS names or NSV numbers (173 and 459 stars, respectively). 160 AAVSO stars are present neither in the GCVS nor in the NSV catalog, while 140 of them, according to the AAVSO data, are periodic variables with known periods.
Of the 181 stars listed in the GCVS, 8 stars are not contained in the VSX. We present these stars, with their MZ0 values, in Table 1.
star  MV Dra  V0668 Lyr  V0831 Her  EZ UMa 
0.695  0.512  0.894  1.304  
star  FX UMa  V0917 Ori  V0449 Aur  DP Cet 
4.704  0.244  5.673  10.596  
The table shows that the technique confirms the variability only for FX UMa, V0449 Aur, and DP Cet, but it should be remembered that using Hipparcos data for stars with amplitudes that low permits to detect only about 20% of all variables by means of the technique.
First, we quote the description of the variability characteristics (flags in the field H52), as it is given in the documentation of the Hipparcos catalog.
"C" : "constant" stars or, more strictly, stars not detected as variable. These include stars used as photometric standards. The category also included cases noted as variable in the Hipparcos Input Catalogue. Caution must be exercised in assuming that entries flagged "C" are nonvariable: they may be variable at levels below the Hipparcos detectability threshold, or they may have shown variability in the past (e.g. Be stars, or longperiod eclipsing binaries);
"D": a "duplicityinduced variability" flag was assigned according to the difference between the "dc" and "ac" magnitudes and according to the angular separation and magnitude difference of a double or multiple system. If "D" is set the entry is not necessary a physical variable, and not necessary seen as variable in ("dc scale");
"M": "possibly microvariable", with amplitude below 0.03 mag (stars classified with high confidence as microvariable are flagged "U");
"P": "periodic variable". This flag may supersede entries for which flag "D" is also appropriate;
"R": "revised colour index". When the flag "R" is set the index was corrected during the variability analysis, The effect of an erroneous index is a spurious linear trend in the magnitude of the epoch photometry, with no physical origin. When identified during the data analysis, this could be taken into account in classifying the type of variability, i.e. whether spurious or not;
"U": "unsolved variable". Entries are classified as "unsolved" if they do not fall into the other variability categories  this class also includes irregular or semiirregular variables, and possible variables with amplitudes more than 0.03 mag;
"": a "blank" indicates that the entry could not be classified as variable or constant with any degree of certainty (e.g. due to presence of one of more outliers in the epoch photometry).
181 GCVS stars of our sample have the following types of variability by Hipparcos:
"" (blank)  39 
"M" (possibly microvariable)  13 
"P" (periodic variable)  49 
"U" (unsolved variable)  58 
"C" (constant)  22 
22 stars are of type "C". They are V1728 Aql, AY Ari, KZ Cam, AV Cap, HT Cet, EP Cnc, KX Cnc, KU Com, LW Com, LS Com, LU Del, V0377 Gem, V0831 Her, V0401 Hya, HR Lib, V2711 Oph, V1260 Ori, V0400 Peg, BU Psc, PV UMa, FI UMa and EV Vir. All these stars have , therefore, the technique, strictly speaking, does not permit to establish variability of these stars based on the results of Hipparcos and Tycho photometry.
Among the 49 stars of "P" type, 33 stars have , and 29 of them have . Thus, the technique confirms variability for most "P"type stars.
Among the 58 stars of "U" type, 34 stars have , and their variability is not in doubt. V2093 Cyg has the largest parameter, .
Among the 13 stars of "M" type, three stars have large probabilities to be variable. These are Eri (see Fig 8), Vir, Aqr. For these stars, . All the others have .
39 stars of the "blank" type have values ranging from to . Only two stars have , and 3 stars have . It appears that most stars of the "blank" type are not variable.
We have decided that, in spite of the particular parameter, all stars contained in the GCVS, NSV catalog, in the AAVSO VSX database, or having the "U", "P", "D", and "M" Hipparcos variability types, as well as stars for which we are not able to calculate the parameter, should be excluded from the candidate standard stars. A total of 7249 stars was left at this stage.
Our further examination showed that there were numerous cases of stars with only one value: , or , or , considerably in excess of 3, while the other parameters were within 2, or maybe even negative. Most often, we encounter , while and do not suggest simultaneous brightness variations. An example of deviations that are not due to the star's variability but to other causes is shown in Fig. 12. Such cases require additional future analysis.
Fig. 12. An example of the relation of on . The group of data points stretching along the ordinate at does not reflect variability of the stars but instrumental features of the sky mapper channels. 
As a result, we have decided to exclude all stars that have as well as those for which at least one of the parameters, , , or exceeds 3, from the list of the 7249 candidate standards. Thus, the list of candidates was reduced to 6484 stars. This list is given in Table 2. The columns of the Table contain HIP numbers; HD numbers; RA(J2000), DE(J2000); spectral types from the Hipparcos catalog; magnitudes, , , and color indices from the Tien Shan catalog; and the parameters.
We recommend to use these stars as standards in various astrophotomeric measurements.
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