THE VARIABLE STARS OF THE DRACO DWARF SPHEROIDAL GALAXY: REVISITED

Images of Draco were taken with the 1.0 m telescope of USNO in Flagstaff, AZ, during the 1995 and 1996 observing seasons. A Tektronix 2048 × 2048 CCD was used with a pixel size of 068, giving a field size of 232. Four fields were observed, each covering one quadrant of Draco, with 1' overlap between fields, thus covering approximately a square region of 45' size centered on Draco. The northeast field position was shifted to the east to avoid the bright star just north of Draco. Therefore, the northeast and northwest fields did not overlap, and three variable stars (V5, V10, and V117) were missed in this narrow gap. Figure 1 shows the field placement. This areal coverage is larger than any other study of the variable stars in Draco—it covers about four times more area and more than twice the number of variable stars than the study by Bonanos et al. (2004), and it provides a useful coverage of about two times more area than that of B&S. The Palomar 200 inch telescope used by B&S allowed discovery of some variable stars up to a distance of 24' from the center of Draco. However, the degraded image quality in the outer parts of their field prevented them from measuring magnitudes or deriving light curves and periods for most variables beyond an 8' radius from Draco. This coverage includes all known variable stars in Draco from the B&S study except for two stars they identified, which were found at large distances from the galaxy (one far east, V205, and the other far west, V333). Also missing from our study are the three stars that lie in the gap between the northeast and northwest fields near the bright star on the north side of Draco. The first part of Table 2 lists these stars.

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The images were taken with a Johnson V filter throughout the 1995 and 1996 observing seasons and with a Cousins I filter mostly during the 1996 season. The seeing was typically 2'', and the exposure times were 15–30 minutes depending on the seeing. Exposures were taken switching between quadrants, and alternating filters in 1996, so that each quadrant was observed 1–4 times on a given night with a given filter. An effort was made to minimize alias effects by observing each quadrant over 6–8 hr on several nights, by observing over three weeks during several months, and by observing over the full range of months possible each season. A total of 39–41 V images and 19–20 I images of each quadrant were taken and are included in the following analysis. DAOPHOT (Stetson 1987) was used to measure all images. A small radial correction for image distortion in the corners of each image was applied for the data taken at USNO.

For the goals of identifying variable stars and measuring accurate magnitudes and light curves, five sources contribute errors to these data. Some stars are crowded or near brighter stars and have erroneous measurements. The CCD has a few defects that produce spurious magnitudes for some stars that occasionally fall on a defect. The CCD is not physically flat, so the high center and low corners produce images of stars in the corners of the field that are not in perfect focus—together with astigmatism, the resulting magnitudes have some additional error. The desire for short exposure times has resulted in images that have typically 0.03 mag error for each observation for the RRL and other horizontal-branch (HB) stars in Draco. Finally, the inevitable cosmic rays occasionally affect a star image. Therefore, potential variable stars were examined by eye to decide on real versus spurious variables. Table 2 also lists those stars that B&S originally marked as variable candidates but which were found not to be variable in our survey. The instrumental magnitudes were shifted onto a common system, iteratively rejecting variable stars, using a method similar to that described by Honeycutt (1992).

Finally the USNO instrumental magnitudes were transformed to standard Johnson V and Cousins I magnitudes as follows. On three photometric nights when Draco images were taken in all quadrants, Landolt (1992) standards were also observed and used to determine transformation coefficients of the form

for V, with a similar form for I. On one additional photometric night, using a different Tektronix 1024 × 1024 CCD, images were taken centered on Draco, together with Landolt standards. Color coefficients were small, typically 0.01 and 0.03 in V and I, respectively. These coefficients are presented in Table 3 for both V and I bands and per photometric night. Three nights were used to determine mean V and I standard magnitudes for a subset of bright (16–18 mag) nonvariable stars in the Draco images. The transformation of instrumental magnitudes (after shifting onto the common system) to standard magnitudes for this subset of bright stars then was applied to all stars. A comparison of the resulting standard magnitudes for nonvariable stars with Stetson's Draco calibration region⁶ shows good agreement.

The resulting errors in photometry for a single observation are estimated to be 0.01 mag from calibration uncertainties, 0.02 mag from image distortion in the CCD corners, and photon noise that increases from 0.01 mag at V = 18 mag to 0.03 mag at V = 20 and to 0.05 mag at V = 21 mag. After combining frames, the errors in the mean magnitudes of nonvariable stars at the level of the HB (V = 20 mag) are estimated to be 0.03 mag in V, 0.03 mag in I, and 0.04 mag in V − I. The errors in the mean magnitudes of variable stars are generally larger.

The USNO data set was combined with data obtained at WIRO during the summer quarter observing season of 1993 and 1994. An RCA 337 × 527 pixel CCD camera was used, which had a 12 pixel⁻¹ plate scale. The field of view was much smaller compared with the USNO data set. The WIRO fields were 6.4 × 104 and overlapped with three quadrants of the USNO fields. One WIRO field is roughly 13% of one USNO field. Figure 1 shows where the WIRO fields are in relation to the USNO fields. The data were obtained with Johnson V and Cousins I filters. From WIRO, a maximum of 28 V- and 18 I-band images supplemented the USNO data. All available data from WIRO were used for light curve and period analysis of the variable stars. This brings a maximum of 69 V and 38 I images for stars found in USNO and WIRO fields.

The WIRO observations were placed on a standard system by using secondary standards from the USNO analysis. A total of 45 stars were used for the calibration, and the dominant source of uncertainty is from the original calibration done with the USNO data set for each bandpass (see Section 2.1). Equations (2) and (3) are the transformation equations for the WIRO data set. The coefficients α_V and α_I were field dependent and were determined from a weighted mean of differences. The coefficients β and γ were obtained from a linear least-squares fit between (V − v₀) and (V − I). The standard V magnitude was found through an iterative process, incorporating the standard I magnitude of that star. The values of the transformation coefficients for the WIRO data set are given in Table 4.

Photometry was performed on the WIRO data using Stetson's DAOPHOT II and ALLFRAME stand-alone packages (Stetson 1987; Stetson 1994).

We have kept the original numbering system of B&S for the first 203 variable stars plus number 204 assigned by Zinn & Searle (1976). All new variable star identifications, as well as the new long-period variable stars and the QSOs, are an extension of B&S's system, but organized by right ascension going east to west. Our new star identification, therefore, begins from V205 through V333.

Stars with high dispersion or high chi-square for their magnitude were considered to be potential variables and inspected further. For the USNO data set, we used a plot of chi-squared versus magnitude to identify potential variables. We did not use the Welch & Stetson variability index (Welch & Stetson 1993) because it is defined to make use of pairs of images taken at nearly the same time, and the USNO data generally included unpaired images in each quadrant each night. Image differencing might in retrospect be useful as an additional tool; however, it is more advantageous in fields more crowded than Draco.

For the WIRO data set, the variable stars were selected by using a simple variability index which compared the external to internal uncertainties of the observations. Our results were then compared with the B&S catalog and we identified the known variable stars. New variables were found and classified by their color, period, and location in the color–magnitude diagram (CMD). Due to the overlap of the WIRO fields with the USNO fields, the variable stars found were checked and confirmed between the two data sets.

A total of 270 RRL stars, 9 ACs, 12 semi-irregular or carbon stars, and 2 eclipsing binaries were discovered in this survey. We were able to recover all of the original B&S variable stars, and re-classified seven stars. We discuss the variable stars of Draco in more detail in Section 4.

As discussed in Section 2.1, our survey of Draco is nearly four times larger in area and includes twice the number of variable stars than that found in the Bonanos et al. (2004) survey. Because of a match-up error in preparing their tables, the periods, magnitudes, and the identifications of 48 stars do not match the right ascension/declination star names in Bonanos' Tables 1 and 2. We have used corrected versions of the tables, provided by A. Bonanos, to make the comparison here. We independently recovered 130 stars that had been found in both the original B&S and Bonanos et al. surveys. Those stars with the B04 designation in our Table 5 have been identified in Bonanos et al. They also identified 17 new RRL stars and one new eclipsing variable; we independently recover all 18 of these stars and make the same classifications, although we find one star (V289) to be an RRd that Bonanos et al. classified as RRab. For this star, we were able to find a period (P = 0.6607 days) close to the Bonanos et al. period, but it produced a noisy light curve with our data. Our solution produces a tighter light curve for our photometry. Bonanos et al. identified nine red variables with small amplitudes near the tip of the giant branch. We find that four of them vary, and find that the other five do not vary significantly in our data, so we omit them from our tables. Finally, the SX Phe star that Bonanos et al. found was too faint for our survey and was not included in our analysis. For most RRL stars, we find excellent agreement with the periods and RRab/RRc classifications with Bonanos et al. The typical difference between our periods and those of Bonanos et al. for the RRL stars is 0.00002 days. For a few stars, we find a different alias period. The greater number of nights covered by our observations usually make alias problems less important in our analysis, so we prefer our period solutions.

Figure 4 shows the phased V and I light curves. The V light curves have our best spline fit included to aid the eye. Fourier series fits to our light curves were not used because they often give biased results at rapidly changing phases (rising and maximum light) if few data points are available to constrain the fit. With typically 40 V observations, some stars in our data have few points at these phases. Table 5 lists the RRL positions (R.A. and decl. J2000.0), the period solutions (Column 4), the V amplitude (Column 5), the intensity-weighted mean magnitudes in V and I (Columns 6 and 7, respectively), and the type of RRL with additional notes (Column 8). We find in our survey 270 RRL stars, of which 214 are RRab, 30 RRc, and 26 RRd stars. Of these, 81 are new RRL compared to the B&S study. Including these new RRL stars, we find the average period of the RRab stars to be 〈P_ab〉 = 0.615 ± 0.003 days and for the RRc stars an average period 〈P_c〉 = 0.375 ± 0.006 days. In Figure 5, we show the period distribution of the RRL stars. The average period for the RRd stars is 〈P_d〉 = 0.407 ± 0.002 days. As originally noted by B&S, the mean period of the RRab stars is the Oosterhoff intermediate. The Oosterhoff properties of the Draco dwarf system are discussed in detail in Section 5.

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Foreground RRL have been found in our survey. Using the surface density for RRL in the SA57 field (Kinman et al. 1994), and assuming a halo space density of R^−3.5, we calculated the volume and RRL per magnitude along our line of sight. From the calculation, we expected 0.9 field RRL in the line of sight, but in actuality we find three field RRL (V327, V321, and V276). One of these stars (V327) was previously discovered by Wehlau et al. (1986). The distribution of stars per magnitude peaked around V = 17 mag, thus we should see field RRL around this magnitude. The three field RRL are flagged in the main RRL properties table, Table 5.

4.1.1. Double-Mode RR Lyrae Stars

Goranskij (1982) used the photometry of B&S to identify three RRL stars in Draco that were pulsating simultaneously in the first-overtone and fundamental radial modes. Also using the B&S observations, Nemec (1985a) identified seven more of these stars (RRd variables in Nemec's nomenclature, or RR01 stars in the nomenclature of Clement et al. 2001). Bonanos et al. (2004) redetermined periods for six of the RRd stars found by Nemec (1985a).

We carried out a search for double-mode behavior among the RRL stars that had light curves that did not seem to be adequately described by a single period. Using the CLEANest routine (Foster 1995) to prewhiten the V-band observations, we removed the primary frequency and its first four harmonics. A search was then undertaken for evidence of a significant secondary period. If a secondary period seemed possible, the CLEANest routine was used to simultaneously fit the primary and secondary periods and their first four harmonics. Although higher-order harmonics and cross-frequency terms have been detected in the light curves of double-mode RRL stars, the current set of observations is not sufficient to identify them. For suspected RRd stars, results from the CLEANest routine were verified using the Period04 program (Lenz & Breger 2005).

By this means we found all ten of the RRd stars identified by Goranskij (1982) and Nemec (1985a). In addition, we have identified 16 probable RRd variables, giving a total of 26. The first-overtone mode was the dominant mode in each case. First-overtone mode periods, fundamental mode periods, and period ratios for probable RRd stars are shown in Table 6. The listed uncertainties are the formal errors given by the CLEANest program. Results for stars with asterisks are more uncertain, usually because of the possibility of a period alias for the fundamental mode period. Deconvolved first-overtone and fundamental-mode period light curves for the RRd stars are shown in Figure 6.

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Table 6. Properties of the Draco RRd Stars

ID	P1	Error	P0	Error	P1/P0	Errora
11	0.41100	0.00002	0.55114	0.00010	0.7457	0.0002
72	0.40711	0.00002	0.54599	0.00006	0.7456	0.0001
83	0.40075	0.00002	0.53720	0.00006	0.7460	0.0001
112	0.42844	0.00002	0.57446	0.00005	0.7458	0.0001
131	0.40626	0.00002	0.54424	0.00006	0.7465	0.0001
138	0.40773	0.00003	0.54601	0.00012	0.7467	0.0002
143	0.40317	0.00004	0.54042	0.0003	0.7460	0.0006*
155	0.41393	0.00003	0.55476	0.00009	0.7461	0.0002*
156	0.40868	0.00002	0.54778	0.00006	0.7461	0.0001
165	0.35798	0.00002	0.48064	0.00004	0.7448	0.0001
169	0.40316	0.00003	0.54059	0.00008	0.7458	0.0002
190	0.39652	0.00001	0.53080	0.00006	0.7470	0.0001*
217	0.41166	0.00003	0.55149	0.00014	0.7465	0.0002*
221	0.40788	0.00003	0.54671	0.00008	0.7461	0.0002
228	0.41606	0.00003	0.55784	0.00010	0.7458	0.0002
232	0.41081	0.00001	0.55017	0.00007	0.7467	0.0001*
235	0.39954	0.00003	0.53560	0.00011	0.7460	0.0002
245	0.41105	0.00001	0.55029	0.00010	0.7470	0.0002*
247	0.41760	0.00002	0.55946	0.00006	0.7464	0.0001
248	0.41828	0.00002	0.56055	0.00005	0.7462	0.0001
250	0.40491	0.00002	0.54218	0.00014	0.7468	0.0003*
289	0.39743	0.00002	0.53258	0.00008	0.7462	0.0002
294	0.39998	0.00002	0.53622	0.00007	0.7459	0.0001*
301	0.41286	0.00002	0.55306	0.00007	0.7465	0.0002
306	0.39824	0.00002	0.53323	0.00009	0.7468	0.0002
318	0.40264	0.00004	0.53995	0.00007	0.7457	0.0002*

Note. ^aStars with an asterisk ^(*)denote some uncertainty with the period solutions due to aliasing.

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In plotting the Petersen diagram (Petersen 1973) of period ratio versus fundamental period, Nemec (1985a) discovered that V165 had a position in this diagram similar to those seen among RRd stars in Oosterhoff type I globular clusters, but that all of the other stars had properties similar to those of RRd stars in Oosterhoff type II clusters. Figure 7 shows the Petersen diagram for all 26 probable RRd stars. RRd stars whose locations in this diagram are somewhat uncertain (the asterisked stars in Table 6) are plotted as open points. For comparison, the locations of RRd stars in the Oosterhoff type I globular cluster IC 4499 (Walker & Nemec 1996) and the Oosterhoff type II globular clusters M15 and M68 (Nemec 1985b; Walker 1994) are also plotted. V165 still remains the only RRd star with properties similar to those of RRd stars in Oosterhoff type I clusters.

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Figure 8 plots the luminosity-weighted mean V magnitude against the primary period for all of the Draco RRL stars. V165, the sole Oosterhoff type I RRd star, is also the faintest RRd star. This is at least qualitatively consistent with other findings that RRL stars in Oosterhoff type I clusters are less luminous than those in Oosterhoff type II systems (e.g., Sandage 1958; Sandage et al. 1981).

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4.1.2. Blazhko Effect

The Fourier decomposition of the light curves was done only on the V data. Using Simon's MINFIT program (Simon 1979; Simon & Teays 1982), a cosine series up to 8th order was fit to the light curves:

Once the amplitude (A_i) and phase (ϕ_i) terms were obtained, the Fourier parameters, R_ji and ϕ_ji, were calculated up to the 4th order.

We applied the Jurcsik & Kovacs (1996) photometric metallicity relation using the Fourier decomposition parameter ϕ₃₁ and the period (their Equation (3)). The Jurcsik & Kovacs method works best when RRab light curves are fully sampled and where photometric uncertainties are relatively small. The light curves for individual RRab stars in our sample do not always meet these criteria. To test the quality of the RRab light curve for this method, a compatibility test called the D_M deviation parameter is calculated. This deviation parameter is determined from a comparison of the observed and predicted Fourier parameters. An updated version of this test is provided in Kovacs & Kanbur (1998). In order for a star to be a good candidate for the Jurcsik & Kovacs method, the D_M parameter criterion must be met. For our RRab sample, we chose D_M < 3.0 (as recommended by Jurcsik & Kovacs) and D_M < 5.0 (as recommended by Clement & Shelton 1999). Stars that have passed the criteria are listed in Table 7 with asterisks. Table 7 also lists the Fourier decomposition parameters and photometric metallicities of the Draco RRab stars. All photometric metallicities are on the metallicity scale of the Jurcsik & Kovacs method (Jurcsik 1995).

Table 7. Fourier Decomposition Parameters for RRab Stars

ID	A0	R21	R31	R41	ϕ21	ϕ31	ϕ41		[Fe/H]	σ[Fe/H]	DM Pass?a
2	20.9797	0.3221	0.0858	0.1693	3.5756	1.403	5.449	0.553	−2.43	0.75
3	21.0260	0.3453	0.2780	0.2168	3.9108	1.569	6.036	0.180	−2.51	0.25	*
4	21.1916	0.4781	0.1509	0.0581	3.8671	1.302	1.641	0.356	−2.76	0.48
6	20.9611	0.5028	0.2893	0.1936	3.8149	2.042	6.092	0.134	−2.11	0.18
7	21.2041	0.4867	0.3420	0.0415	3.7750	1.915	5.866	0.179	−1.86	0.24
8	21.1371	0.5084	0.3504	0.2033	3.8696	1.671	6.105	0.128	−1.92	0.17	*
9	21.0360	0.4902	0.2396	0.1688	3.7757	1.799	0.785	0.222	−2.39	0.30
12	21.2055	0.4099	0.2215	0.1029	3.8709	1.743	5.930	0.238	−1.86	0.32	*
13	21.1566	0.4181	0.2999	0.1742	3.8595	1.408	5.677	0.108	−2.10	0.15	*
14	21.0536	0.3410	0.3305	0.3288	3.8314	1.857	5.995	0.173	−1.93	0.23	*
15	21.2359	0.4504	0.2656	0.0374	3.5087	1.533	5.400	0.278	−2.16	0.38	*
16	21.1378	0.3367	0.1520	0.0652	4.0760	1.823	4.995	0.453	−2.02	0.61
17	21.1852	0.3700	0.2613	0.0471	3.5913	1.052	6.038	0.272	−2.96	0.37
19	21.1497	0.4018	0.2557	0.1974	4.1254	2.255	0.236	0.186	−1.45	0.25
20	21.1713	0.4051	0.3398	0.2134	3.8324	1.714	0.185	0.159	−2.15	0.22
21	21.3392	0.3626	0.2600	0.2263	3.7277	1.337	5.622	0.199	−2.34	0.27	*
22	21.1894	0.3796	0.3104	0.1628	4.1072	1.950	0.004	0.286	−1.59	0.39
23	21.1370	0.5135	0.2314	0.2189	3.7667	1.487	5.489	0.425	−2.45	0.57
24	21.1933	0.3830	0.2605	0.1930	4.0358	1.462	0.398	0.177	−2.57	0.24
25	21.2862	0.3835	0.3411	0.3119	4.0705	1.710	5.930	0.136	−1.82	0.18	*
27	20.9620	0.4201	0.3533	0.0944	3.9173	2.328	0.985	0.156	−2.09	0.21
28	21.1103	0.4367	0.3305	0.1880	3.9909	1.712	6.234	0.156	−2.18	0.21	*
29	21.0918	0.5195	0.6465	0.1672	3.4223	1.529	5.983	0.225	−2.12	0.30
30	21.2023	0.3684	0.2356	0.1205	3.6366	2.060	0.933	0.183	−1.71	0.25
32	21.0954	0.3225	0.3235	0.3422	3.9962	2.185	5.995	0.270	−1.09	0.36
33	21.1307	0.3173	0.3863	0.1106	3.7809	1.359	6.199	0.155	−2.59	0.21
34	21.2633	0.4045	0.2217	0.2377	4.2836	2.324	0.540	0.206	−0.86	0.28
36	21.0509	0.3891	0.3177	0.2871	3.9562	1.524	5.890	0.100	−2.44	0.14	*
37	21.2053	0.3731	0.2829	0.1995	3.6804	1.418	5.892	0.155	−2.19	0.21	*
40	21.1469	0.3599	0.2782	0.1971	3.8310	1.481	6.267	0.176	−2.45	0.24
42	21.0392	0.3932	0.3089	0.1697	3.6708	1.710	6.045	0.150	−2.56	0.20	*
43	21.1188	0.3645	0.3324	0.2243	3.8744	1.791	6.075	0.151	−1.94	0.20	*
45	21.1690	0.4129	0.3552	0.2593	3.8733	1.391	5.584	0.133	−2.38	0.18	*
47	21.1743	0.3426	0.2996	0.1977	3.6999	1.895	6.150	0.178	−1.96	0.24	*
49	21.1237	0.3706	0.2392	0.1690	3.6302	1.731	5.878	0.196	−2.12	0.26	*
51	21.1322	0.3698	0.2734	0.1621	3.9393	1.626	5.700	0.161	−2.19	0.22	*
52	21.1344	0.5317	0.3492	0.0578	4.3725	2.834	1.716	0.122	−0.46	0.17
53	21.0354	0.5495	0.3102	0.1556	4.0508	2.151	0.046	0.237	−1.65	0.32
54	21.1544	0.4462	0.2972	0.2325	3.7941	2.109	0.717	0.221	−1.69	0.30
55	21.0562	0.3807	0.2762	0.2315	3.9886	1.590	5.568	0.178	−2.21	0.24	*
56	21.1826	0.7219	0.7131	0.6050	4.0904	2.675	1.197	0.117	−0.64	0.16
57	21.0546	0.4037	0.2996	0.1998	3.7945	1.673	6.110	0.203	−2.12	0.28	*
58	21.1601	0.4425	0.3006	0.1511	3.8126	2.012	6.026	0.299	−1.63	0.40	*
59	21.1954	0.3742	0.3120	0.1503	3.8208	1.539	5.581	0.111	−2.22	0.15	*
60	21.0932	0.3856	0.3667	0.0409	4.5573	2.133	1.630	0.292	−1.49	0.39
62	21.1604	0.2769	0.2547	0.1082	3.6509	1.119	0.357	0.249	−2.89	0.34
63	21.1308	0.4094	0.3034	0.1444	3.8708	1.520	0.566	0.239	−2.37	0.32
64	21.1639	0.4044	0.2060	0.1087	3.5979	1.046	4.927	0.336	−2.97	0.46
65	21.1341	0.4056	0.3401	0.1892	3.7348	1.263	5.416	0.196	−2.61	0.27	*
66	21.1917	0.4033	0.2293	0.1271	3.8670	1.352	1.749	0.227	−2.81	0.31
69	21.1418	0.4391	0.3548	0.2247	3.8962	1.606	5.866	0.129	−2.15	0.18	*
70	21.0688	0.4295	0.3121	0.2121	3.6864	1.545	5.568	0.161	−2.41	0.22	*
74	21.1333	0.3436	0.3541	0.1874	3.8226	1.401	5.798	0.103	−2.43	0.14
76	21.0668	0.5111	0.4381	0.3828	3.8159	1.663	5.946	0.135	−2.01	0.18	*
80	21.1615	0.4577	0.3232	0.2484	4.0232	1.726	5.872	0.195	−2.03	0.26	*
81	20.9603	0.4094	0.3117	0.1080	3.6554	2.259	2.538	0.239	−2.01	0.32
82	21.1601	0.4776	0.2322	0.1698	3.8021	1.630	5.921	0.189	−2.11	0.26	*
84	21.0138	0.3621	0.2656	0.2341	3.9118	1.392	5.785	0.140	−2.44	0.19
85	21.1101	0.3688	0.3734	0.1821	3.8898	1.411	5.390	0.175	−2.53	0.24	*
86	21.1539	0.4207	0.2335	0.0733	3.7654	1.913	6.089	0.337	−1.91	0.45
87	21.2338	0.3278	0.4763	0.1339	4.5433	2.335	1.365	0.200	−1.24	0.27
88	21.1992	0.4304	0.3728	0.2675	3.6537	1.639	5.915	0.181	−2.15	0.25	*
89	21.1122	0.4373	0.2633	0.2134	3.9794	1.640	5.929	0.271	−2.18	0.37	*
92	21.2012	0.4593	0.2218	0.2490	4.0976	1.786	5.667	0.245	−1.73	0.33
93	21.1188	0.3776	0.3039	0.2448	4.0668	1.558	5.937	0.132	−2.17	0.18	*
94	21.1455	0.4514	0.2628	0.2586	3.7857	1.543	6.005	0.125	−2.05	0.17
95	21.0371	0.3973	0.2391	0.1905	3.8537	1.621	5.608	0.176	−2.26	0.24	*
98	21.0444	0.4845	0.3347	0.1981	3.8040	1.665	0.389	0.189	−2.26	0.26
100	20.9654	0.3373	0.1896	0.0863	4.1915	1.908	1.242	0.299	−2.57	0.40
101	21.1938	0.3419	0.4871	0.3298	3.9467	1.824	5.786	0.151	−1.99	0.20	*
102	21.0912	0.3846	0.1889	0.2116	3.5606	1.948	0.430	0.187	−1.60	0.25
103	21.1933	0.4730	0.3462	0.2441	3.8644	1.724	5.684	0.177	−2.05	0.24	*
104	21.1413	0.3145	0.3785	0.2147	3.9168	1.419	5.685	0.111	−2.40	0.16	*
105	21.2349	0.3906	0.3318	0.1716	3.8405	1.935	6.225	0.147	−1.79	0.20	*
107	21.1280	0.4623	0.3735	0.2258	3.5859	1.489	5.910	0.163	−2.24	0.22	*
114	20.8940	0.3156	0.1729	0.1486	3.9526	1.759	6.230	0.237	−2.23	0.32	*
115	21.0860	1.6991	1.7997	0.9826	2.0955	0.667	6.012	0.324	−3.47	0.44
116	21.1802	2.2240	2.8269	0.6754	0.1569	1.101	4.885	3.001	−3.35	4.04
119	21.1065	0.3107	0.2153	0.1698	4.1220	1.915	0.517	0.278	−2.11	0.38
122	21.1773	0.3763	0.3510	0.1807	3.8666	1.947	0.367	0.369	−1.92	0.50
124	21.1814	0.4343	0.2887	0.2845	3.7266	1.512	5.377	0.118	−2.07	0.16
125	21.0576	0.3962	0.2374	0.1322	3.9208	1.807	0.055	0.143	−2.36	0.19
126	21.1108	0.3502	0.3280	0.2460	3.6596	1.565	5.892	0.147	−2.20	0.20	*
127	21.1686	0.3964	0.2482	0.1976	3.9177	1.577	6.208	0.142	−2.59	0.20
128	21.1830	0.3977	0.3906	0.2593	3.6900	1.872	5.872	0.172	−2.00	0.23	*
129	21.2547	0.3290	0.1382	0.2019	4.1716	1.255	5.564	0.417	−2.62	0.56
132	21.0987	0.1121	0.3401	0.1890	3.5035	2.589	6.112	0.166	−0.98	0.23
133	21.0932	0.4467	0.2818	0.1231	3.8670	1.863	0.030	0.196	−1.88	0.26
135	21.0948	0.4023	0.3453	0.1891	3.8332	1.757	5.891	0.117	−2.15	0.16	*
136	21.1900	0.3180	0.2411	0.2928	3.9378	1.784	5.756	0.424	−1.68	0.57
137	21.2138	0.3758	0.2625	0.1822	3.9266	1.589	5.710	0.168	−2.22	0.23	*
140	21.0901	0.2879	0.1967	0.2204	2.3131	1.191	4.132	1.184	−2.92	1.59
142	21.0906	0.4665	0.3385	0.2569	3.7860	1.634	5.772	0.102	−2.36	0.14	*
144	21.3136	0.8180	0.2715	0.5360	2.4477	2.581	3.875	0.333	−0.74	0.45
149	21.2231	0.3700	0.1774	0.1194	3.9287	3.235	0.367	0.394	−0.31	0.54
150	21.0500	0.2377	0.1382	0.1382	4.3527	2.121	5.571	0.726	−1.89	0.98
151	21.1498	0.3626	0.3154	0.0990	3.9220	1.622	0.008	0.209	−2.28	0.28
152	21.1560	0.3985	0.3967	0.2306	3.6581	1.786	6.260	0.119	−2.08	0.16	*
154	21.0598	0.3671	0.3369	0.1177	3.8109	1.313	5.592	0.158	−2.78	0.22	*
159	21.0791	0.4384	0.2648	0.2246	4.0971	1.953	6.277	0.135	−1.99	0.18	*
161	21.2265	0.3989	0.3224	0.2057	3.7740	1.729	6.173	0.143	−2.13	0.19	*
162	21.1348	0.4299	0.2925	0.1395	3.9167	1.702	5.922	0.162	−2.17	0.22	*
163	21.2684	0.4072	0.3391	0.2046	4.0556	2.067	6.148	0.314	−1.31	0.42	*
164	21.1045	0.3637	0.3045	0.2021	3.6531	1.378	5.967	0.316	−2.64	0.43	*
167	21.1274	0.3788	0.2584	0.2988	3.9965	1.796	0.072	0.203	−2.30	0.28
171	21.1111	0.4379	0.2636	0.1877	3.8213	2.009	6.264	0.255	−1.61	0.34	*
172	20.9743	0.3988	0.3147	0.1148	3.7654	1.898	0.471	0.124	−2.13	0.17
174	20.9688	0.5443	0.2898	0.2588	4.2496	2.078	6.195	0.163	−1.95	0.22	*
175	21.1595	0.4584	0.2483	0.1598	3.8483	1.593	5.813	0.151	−1.99	0.20	*
176	20.7044	0.4697	0.2381	0.1348	3.7171	1.321	5.613	0.214	−2.60	0.29	*
177	21.0706	0.9609	0.5962	0.8721	5.1753	5.931	0.622	0.377	3.97	0.56
178	21.1075	0.3318	0.3033	0.2832	3.8723	1.613	0.042	0.133	−2.14	0.18
180	21.0667	0.4906	0.3366	0.1060	3.9508	2.642	1.553	0.367	−1.06	0.50
183	21.1632	0.4588	0.3604	0.2331	3.7826	1.490	5.939	0.153	−2.32	0.21	*
185	21.2703	0.4016	0.2601	0.1861	3.8097	1.540	5.831	0.242	−2.24	0.33	*
187	21.1778	0.6475	0.4987	0.3929	2.0980	2.169	3.850	0.154	−1.89	0.21
196	21.2136	0.4445	0.3840	0.1823	3.8577	1.506	5.976	0.137	−2.27	0.19	*
198	21.0808	0.3530	0.2225	0.0692	3.6715	1.804	1.183	0.255	−2.35	0.34
199	21.1064	0.4746	0.3464	0.1720	4.0304	2.074	0.341	0.148	−1.90	0.20
201	21.1134	0.3684	0.4381	0.2510	4.2339	1.746	0.049	0.216	−2.32	0.29
207	21.1579	0.3866	0.3150	0.2058	3.6818	1.372	5.550	0.217	−2.33	0.29	*
213	21.1666	0.4452	0.2605	0.1771	3.9542	2.009	5.510	0.276	−1.75	0.37
216	21.1330	0.4461	0.3912	0.2201	3.3530	1.542	6.217	0.105	−2.24	0.14
218	21.1418	0.4827	0.3112	0.2325	3.8122	1.236	4.587	0.253	−2.75	0.34
219	21.2374	0.4351	0.3167	0.1716	3.9298	1.522	5.540	0.164	−2.33	0.22	*
220	21.1473	0.4628	0.2067	0.1128	3.5244	1.388	5.629	0.286	−2.62	0.39	*
223	21.2273	0.3467	0.3532	0.1648	3.9499	1.824	0.257	0.109	−1.89	0.15
225	21.1668	0.3397	0.3088	0.1798	3.8777	1.429	5.352	0.268	−2.30	0.36	*
227	21.1436	0.4977	0.4236	0.2166	4.1281	1.515	0.083	0.167	−2.32	0.23
237	21.2335	0.4387	0.3462	0.1824	3.8619	1.578	5.537	0.127	−2.30	0.17	*
238	21.0892	0.3513	0.2782	0.1435	3.6480	1.495	5.621	0.130	−2.13	0.18	*
243	21.0025	0.2285	0.1968	0.1412	4.1500	2.210	1.336	0.314	−2.02	0.42
244	21.2050	0.2709	0.1472	0.1502	3.9090	1.318	5.572	0.206	−2.37	0.28	*
249	21.1367	0.3947	0.3224	0.2133	3.8850	1.689	5.687	0.086	−2.07	0.12	*
252	21.1382	0.4386	0.3597	0.2268	3.8585	1.453	5.479	0.133	−2.30	0.18	*
253	21.2784	0.2496	0.1984	0.5095	4.7083	4.776	4.581	0.357	2.34	0.51
258	21.0697	0.3559	0.3024	0.1948	3.7039	1.365	5.571	0.124	−2.45	0.17	*
260	21.1105	0.5214	0.3487	0.2697	3.9380	1.576	5.989	0.085	−1.98	0.12
261	21.1359	0.4000	0.2921	0.1263	3.7906	1.831	0.182	0.167	−1.62	0.22
262	21.1091	0.3866	0.3278	0.1781	3.5986	1.408	6.122	0.092	−2.56	0.13
265	21.0829	0.4074	0.2783	0.2220	3.7921	1.488	5.868	0.403	−2.26	0.54	*
269	21.0926	0.4347	0.3432	0.2381	3.7428	1.413	5.332	0.127	−2.14	0.17	*
270	20.9785	0.3460	0.3707	0.2696	3.7410	1.306	5.605	0.085	−2.41	0.12	*
273	20.9756	0.0759	0.0814	0.1433	5.2331	2.817	1.126	0.859	−1.55	1.16
278	21.1312	0.3491	0.3719	0.2490	3.7717	1.668	5.850	0.143	−2.20	0.19	*
279	21.0067	0.4360	0.2030	0.1760	3.6151	1.206	5.978	0.223	−2.79	0.31
281	20.8779	0.2710	0.6362	0.3831	1.8806	4.044	0.350	0.089	0.70	0.17
284	21.0144	0.1990	0.3959	0.2275	4.0643	1.113	5.740	0.228	−2.92	0.31
285	20.8499	0.3775	0.2681	0.1193	4.1360	1.897	0.200	0.281	−2.06	0.38
290	21.1048	0.4284	0.1804	0.1608	3.8519	1.824	1.108	0.491	−2.48	0.66
291	20.7762	0.7227	0.5494	0.4493	3.8448	1.340	4.926	0.102	−3.28	0.15
298	21.1788	0.3668	0.2674	0.2986	3.8061	0.882	4.773	0.257	−3.42	0.35
303	21.2060	0.3931	0.3419	0.1996	4.3250	2.005	0.412	0.102	−1.74	0.14
304	21.1033	0.4119	0.2785	0.1459	3.9121	1.802	5.678	0.234	−2.27	0.32	*
308	21.0490	0.3422	0.0718	0.2947	3.0191	0.890	4.789	0.953	−3.24	1.28
309	21.0466	0.3957	0.2182	0.2359	3.2974	1.333	5.126	0.208	−2.68	0.28
310	21.0316	0.4385	0.3614	0.3383	4.1751	2.114	0.496	0.170	−1.74	0.23
313	21.0945	0.3778	0.2171	0.1559	3.8761	1.283	4.963	0.184	−2.48	0.25	*
315	21.0593	0.4135	0.1561	0.1555	3.5577	1.364	0.402	0.316	−2.41	0.43
323	21.0327	0.3434	0.2483	0.2011	3.9195	1.239	5.380	0.153	−2.45	0.21	*
324	21.0505	0.4123	0.2956	0.1909	3.7772	1.367	5.935	0.132	−2.52	0.18
325	21.0045	0.2638	0.3611	0.1385	4.5856	2.350	0.748	0.269	−1.27	0.36
326	21.0456	0.4710	0.2458	0.2248	3.4030	1.104	5.710	0.160	−3.02	0.22
332	21.1832	0.2445	0.3541	0.4182	3.7120	0.430	5.168	0.443	−3.91	0.60

Note. ^aStars with an asterisk ^(*)have passed the D_M < 5.0 criterion.

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The [Fe/H] values derived from the Jurcsik & Kovacs (1996) method may in this case be more useful in deriving a mean [Fe/H] value for Draco than in the determination of metallicities for individual stars. It is quite likely that some of the outlying [Fe/H] values in Table 7, at both the high and low ends, do not really reflect the metallicities of the stars for which they are derived. The average [Fe/H] for Draco, as determined by the photometric metallicities of the RRab stars, is 〈[Fe/H]〉 = −2.19 ± 0.03 if we assume the stars are not undergoing the Blazhko effect (see Section 4.1.1) and have passed the D_M < 3.0 criterion. For the case where D_M < 5.0, and assuming no Blazhko effect, the average metallicity of Draco is 〈[Fe/H]〉 = −2.23 ± 0.03. Figure 9 shows the metallicity distribution of the RRab stars that have passed the D_M < 5.0 criterion with respect to period.

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Using Stromgren photometry, Faria et al. (2007) recently obtained a mean [Fe/H] of −1.74 for Draco and field red giant branch (RGB) stars, with most stars falling within the limits −2.0 < [Fe/H] < −1.5. This result is broadly consistent with the earlier results of Shetrone et al. (2001a) and Zinn (1978), although Shetrone et al. (2001a) did find one red giant star as metal poor as [Fe/H] = −2.97. Faria et al. (2007) calibrated their derived metallicities to the work of Hilker (2000), which analyzed the red giants of three globular clusters and spanned a metallicity range of −2.0 to 0.0 dex. Therefore, we must be cautious when comparing out metallicity results with those of other studies since there are dependences to various metallicity calibrations. However, there is a suggestion that the average metallicity of the Draco RRab stars is lower than that of the Draco red giant stars. The reality of this difference in metallicity is uncertain due to the nature of the different calibration methods. If this difference is real, then presumably the red HB stars in Draco would have to be more metal rich on average than the RRab stars.

Since RRL are excellent distance indicators, we calculate the distance to the Draco dwarf galaxy. We use the metal-poor ([Fe/H] < 1.5) relation from Cacciari & Clementini (2003) (their Equation (4)). As with the work of Bonanos et al. (2004), we use an E(B − V) = 0.027 from the Schlegel et al. (1998) reddening maps and the corrections for the extinction as suggested by the work of Cardelli et al. (1989), thus, A_V = 0.091. From our sample of RRL stars, the intensity-weighted mean V magnitude is 〈V〉 = 20.10 ±  0.04 mag (σ_RMS = 0.08). For this value, we omitted the magnitudes of the foreground RRL (V276, V321, and V327) and V176, since it is blended with a bright star. The uncertainties given for this mean magnitude account for the calibration errors, image distortion, and photon noise (see Section 2.1). The value of 〈V(RR)〉 = 20.10 ± 0.04 mag in this paper is brighter than those of Bonanos et al. (2004): 〈V(RR)〉 = 20.18 ± 0.02 mag, those of Aparicio et al. (2001): 〈V(HB)〉 = 20.2 ± 0.1 mag, and those of Bellazzini et al. (2002): 〈V(HB)〉 = 20.28 ± 0.10 mag, with a 2σ difference from the most precise value of Bonanos et al.

If we assume a metallicity for Draco from our Fourier decomposition analysis, [Fe/H] = −2.19 ± 0.03, and using the Cacciari & Clementini (2003) relation, our resultant absolute magnitude is 〈M_V〉 = 0.43 ± 0.13 mag. Therefore, using the present mean V magnitude of the RRL stars and accounting for the extinction, we derive a dereddened distance modulus to Draco of μ₀ = 19.58, or D = 82.4 ± 5.8 kpc. However, if we assume a different metallicity for Draco, our distance changes slightly. Shetrone et al. (2001a) obtained a mean metallicity of [Fe/H] = −2.00 ± 0.21 from high-resolution spectroscopy of Draco red giants, whereas Faria et al. (2007) found [Fe/H] = −1.74. If we assume the metallicity values of −2.00 and −1.74, and using the same Cacciari & Clementini relation and the present RRL mean V magnitude, the resultant distances are 81.2 and 79.8 kpc, respectively. Pritzl et al. (2002a) arrived at a distance to Draco independently of the AC stars (see Section 4.4). Their value is μ₀ = 19.49 or D = 79.1 kpc, but using a reddening value of E(B − V) = 0.03. Within our uncertainties, we agree with all these distance values from different Draco studies.

In our study of the Draco dwarf galaxy, we increase the number of known ACs to nine. B&S had identified what appeared to be five overly bright RRL stars in their original survey. Norris & Zinn (1975), followed by Zinn & Searle (1976), first classified these variables as AC stars (V134, V141, V157, V194, and V204). Nemec et al. (1988) re-identified the five stars in Draco as AC, based on a re-analysis of B&S's photographic survey. These five AC stars were confirmed in our study. We have been able to add four new ACs (V31, V230, V282, and V312) to the census. Table 8 lists all the photometrically-derived parameters.

Of the new ACs, one star, V31, has been re-classified. Originally, it was identified by B&S as an RRL variable star based on eye estimates only. However, it lies only 13'' from a bright BD star. The I and the V − I colors are particularly uncertain because of scattered light from the nearby bright red star. Our CCD data show that it is significantly brighter than other Draco RRL stars, so we believe it is a new AC. The bright star is saturated in our data and contributes significant scattered light around V31. Nevertheless, after doing careful background subtraction, the estimated errors in our photometry are 0.1 in V and 0.2 in I, leaving it 0.5 mag brighter than the HB. The other AC stars do not have companions visible in our data. Furthermore, most are either sufficiently bright or have large amplitudes that they cannot be an RRL star made brighter by an unresolved companion. However for V31, V230, and V282, we cannot exclude this possibility of RRL-plus-unresolved companion. In Figure 10, we present the light curves of all the ACs found in this survey with a spline fit added to aid the eye.

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Generally, these variable stars are brighter than the RRL population by 0.5 (for shorter period, P ∼ 0.3 days) to 2 mag (for longer period, P ∼ 2.0 days). These stars are also more massive than the RRL, typically 1.0-2.0 M_☉ (Pritzl et al. 2002a, and references therein), and must be relatively metal poor in order for the progenitor stars to reach the instability strip. ACs have been found in all the known dSph galaxies of the Local Group, however, they are not typically found in the Galactic globular clusters. The exceptions are V19 in NGC 5466 (Zinn & Dahn 1976) and two candidates in ω Cen (Wallerstein & Cox 1984). XZ Ceti is a well-known field AC. The origins of these stars still remains unsolved, but the leading theories suggest that they are either (1) intermediate-aged stars (t < 5 Gyr) or (2) primordial binary systems undergoing mass transfer. These mechanisms provide alternative origins for the blue straggler populations that have been speculated to be the progenitor stars of the AC.

Recently, Momany et al. (2007) investigated the frequency of blue straggler stars in the Local Group dSph population, compared with the frequency of such stars in Galactic globular clusters, open clusters, and the field. They find that, in general, the blue straggler frequency is higher in dSph galaxies than in globular clusters. If the blue straggler stars are progenitors of the ACs, then this higher frequency is consistent with a higher frequency of ACs among the dSph systems. It is noteworthy, too, that some mechanisms for creating blue stragglers by mass transfer may not operate in systems of low stellar density, such as the dSph. For example, it has been suggested that collisional binary systems might create blue straggler stars, but such collisions would be infrequent in dSph systems (Momany et al. 2007). Thus, to consider the blue straggler star frequency, one must only consider those stellar formation mechanisms that will be likely in a dSph environment if one wishes to correlate the frequency with the number of AC stars found.

ACs of dSph galaxies have also been used to create a period–luminosity (P–L) relation. Recent work by Dall'Ora et al. (2003), Pritzl et al. (2002a), and Nemec et al. (1994) have presented empirical AC P–L relations associated with the pulsational mode. Both empirical and theoretical P–L relations have shown that they are not parallel (Pritzl et al. 2002a; Bono et al. 1997). However, there is still some question as to whether the two apparent P–L relations are real, due to distinct fundamental and first-overtone mode relations, or whether the results might instead be interpreted as a single P–L relation with large scatter. That scatter might be a reflection of the range of AC masses as well as the finite width of the instability strip.

For the Draco AC sample, we applied the empirical P–L relations of Pritzl et al. (2002a) to see whether the location of the additional Draco stars would support the reality of two distinct P–L relations. We have calculated absolute magnitudes for the Draco AC stars assuming a distance modulus of (m − M)₀ = 19.49 and an E(B − V) = 0.03 (Pritzl et al. 2002a) in order to incorporate our results with their empirical P–L relations. Figure 11 shows the location of the Draco AC stars with respect to the AC stars found in other Local Group dwarf galaxies. We see that most of the Draco ACs (V31, V141, V157, V194, V230, V282, and V312) fall along the P–L relation for stars pulsating in the fundamental mode, but two, V134 and V204, fall closer to the first-overtone mode P–L relation. As discussed in Pritzl et al. (2002a), it is difficult to assign the pulsational mode in this manner, especially if phase coverage is not complete. We find this to be the case for the Draco ACs as well. Two possible first-overtone pulsators, V134 and V204, have light curves showing only modest asymmetry. Among RRL stars, that is a sign of RRc or first-overtone mode pulsation. However, the light curves for the supposed fundamental mode pulsator, V194, seem similar. Thus, we can only indicate that while there is evidence in Figure 11 for two distinct AC P–L relations, the actual situation is still uncertain. For example, a range of masses among the ACs might influence the positions of the Draco AC within the P–L diagram, and it perhaps cannot be entirely excluded that a single P–L relation with scatter could account for the observations.

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Four categories of variable stars other than RRLs and Cepheids appear in our data: two eclipsing binaries, 30 "bluish long-period variables," 12 red semi-regular or irregular variables, and carbon stars have been found and are listed in Tables 9 and 10. The following subsections discuss each of these types of stars.

4.5.1. Eclipsing Binary Stars

A field eclipsing binary star (V296) was found in the survey completed by Bonanos et al. (2004), which we have recovered in our work. We agree with their period solution for this star, with a period of 0.2435 days. Figure 12 shows the light curve of V296 phased to this period. Additionally, we have also found another possible eclipsing binary star with a small amplitude change. This star, V256, has few faint observations, and our period result is somewhat uncertain. In Table 9, we provide two plausible period solutions. However, to truly confirm the nature of this eclipsing binary, a careful follow-up will be needed to arrive at the correct period.

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4.5.2. Carbon Stars

4.5.3. Long-Period Variables and QSOs

The characteristics of the bluish long-period variables are slow variability, no apparent period, amplitudes typically of 0.25 mag, colors blueward of the Draco giant branch, and no clear concentration toward Draco. These characteristics suggest that most of them are background QSOs, and this hypothesis has been supported by available spectroscopy. The red semi-regular variables have colors and magnitudes placing them near the tip of the RGB in Draco, and they all have radial velocities and/or proper motions showing they are members of Draco. Figure 13 shows our time series photometric data of the red long-period variable stars. Spline fits were not included since we assume that the coverage of the full variation was not obtained through the time coverage of our data set. Also, due to the approximately 40 V observations, we cannot provide robust estimations in the amplitudes of these long-period variables. In Table 9, we list mean magnitudes rather than intensity-weighted mean magnitudes due to our spotty phase coverage and the low amplitudes of these objects.

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B&S remarked on the lack of red variables found in Draco. Bonanos et al. (2004) showed that there are variables among the stars near the tip of the giant branch, as also shown in Figure 2. Our 12 red variables are mostly of low amplitude, and the amplitudes must have been just below the threshold for detection by B&S. We now know that in metal-poor systems like Draco, high-amplitude red variables like Miras are absent, and low-amplitude semi-regular or irregular variables are more common (e.g., Harris 1987).

Distinguishing between background QSOs and red variables in Draco is not always obvious, however, because QSOs sometimes can be red, and some Draco variables might be bluish and without regular periods. For example, UU Her and RV Tauri stars are found in globular clusters and could be confused here with our limited data. Therefore, spectroscopy is useful to ensure accurate classification: 22 bluish long-period variables are confirmed as QSOs with spectra taken with the WIYN telescope and described in a separate paper (H. C. Harris & J. A. Munn 2008, in preparation), and/or spectra from the SDSS that put them in the SDSS DR3 QSO Catalog (Schneider et al. 2005). Eight additional variables with similar characteristics are listed in Table 10 as probable QSOs.

The prototype of the QSOs behind Draco, V203, was found by B&S and given in their Table VII, and the light curve spanning over six years was shown in their Figure 8. They did not understand its nature, but their light curve was the best study of variability of a QSO at that time. Of course, the redshift of QSOs and their characteristic variability were not discovered for two more years (Schmidt 1963; Matthews & Sandage 1963).