Observations suggest that NSVS 6099331 is an eclipsing variable star of W Ursae Majoris type. This star is located at α=22:25:16.03 δ=+41:27:51.99 and has the following alternate stellar designations: NSVS 6099330, GSC 03208-01986, [GGM2006] 6099330, Gaia DR2 1957495533442807808, Gaia DR1 195495529143310464, 2MASS J22251603+4127520, TYC 3208-1986-1.  Star field with the target star and comparison stars used in ensemble differential photometry are shown in Figure 1.

Table 1: List of comparison stars used in differential ensemble photometry analysis. First column gives the comparison designation. Columns 2 & 3 give the Right Ascension (α) and Declination (δ) of the comparison in J2000.0. Columns 3-6 report measured Johnson B (B), Johnson V (V) and Cousins R (R_c) band magnitudes. Magnitudes are used to calibrate the magnitudes of the target star. Calibrated magnitudes are used to determine magnitudes in the Johnson-Cousins system.

We have observed this star with the Ball State University Observatory (BSUO) 20-inch (0.5m) telescope in the B, V, and R_c band passes.  All stellar photometry is performed by the AstroImageJ (AIJ) software package.  All photometry is performed with similar ensemble stars.  If a calibrated magnitude for a comparison star is known, then it is used by AIJ to calibrate the magnitude for the target star.  Folded light curves for Johnson V and (B-V) color are shown in Figure 2.

Figure 2: Folded color light curve for NSVS 6099331. All photometry is differential multi-aperture photometry performed by the AstroImageJ (AIJ) software package. Top panel shows folded B-band (blue),  V-band (green), and R-band (red) curves. Bottom panel shows folded (B-V) and (V-R_c) color curves (both in black). All magnitudes are calibrated by the known magnitudes of the ensemble stars. Error bars are not shown for clarity.
By analyzing the B-V at quadrature (Φ = ± 0.25) and accounting for interstellar reddening (Av=0.416), the color index of the system was determined to be (B-V)₀ = 0.473881± 0.01112, corresponding to a primary star surface temperature of 7014 K, and a spectral type of about F2 . This temperature was calculated using the polynomial coefficients given in Flower 1996.

Observed Minus Calculated (O-C) Time of Minimum Analysis

Table 2: Heliocentric Julian dates [HJD] for times of minimum (first column) are reported along with 1σ errors bars (second column). All times of minimum light are first determined for each filter (B, V, and R) light curve, and are determined by the method described by Kwee & van Woorden (1976). Similar times of minimum for differing filter light curves are averaged together and reported in column Times of Minimum. Eclipses are designated by primary for the primary eclipse and secondary for the secondary eclipse in the Eclipse column (third/middle column). Values of (O-C) (fourth column) are given in units of days along with 1σ errors (fifth column).

Figure 3: Observed time of minimum minus calculated time of minimum (O-C) plot with best-fit linear linear line (solid line) versus epoch number (E). Error bars are 1σ error bars assuming the period of the system is known with out errors. All O-C values are given in units of days and are determined by the linear ephemeris given in equation (1). Best-fit linear line is determined by an unweighted linear least squares analysis. Slope of best-fit line represents a negligible correction to the ephemeris given in equation (1).

Best fitting Wilson-Devinney (WD) Models

Figure 4: Best-fit WD model fit with no spots (red solid curve) to the folded light curve for differential Johnson B (left panel), V (center/middle panel), and Cousins R (right panel) band magnitudes.  In each panel the top panel shows the folded light curve for B, V, or R bands, and the bottom panel shows the deviation of the observed values from the best-fit WD model.

Figure 5: Stellar models showing best-fit stellar models for the light curves shown in Figure 4. Orbital phases (Φ) are Φ = 0 (top left panel, primary eclipse), Φ = 0.1 (Top right panel), Φ = 0.25 (bottom right panel, quadrature) and Φ = 0.5 (bottom left panel, secondary eclipse). The final best-fit model did not require spots.

Below is a cool animation of NSVS 6099331 created by Lauren Wines that helps to visualize the orbit of the system as viewed from the Earth.  The animation was created by the EZGif Animated Gif Maker.  Orbital phase is given at the bottom of the frame.

Best-fit Model Parameters

Table 3: System parameters of NSVS 6099331.  Column (1) gives the name of the parameter, (2) gives the parameter symbol and [unit], (3) and (4) give the parameter value and error, respectively. Any blanks in the table denote data which is, as of the most recent entry, unknown and/or unavailable.
^‡These values were calculated using the the equations in Harmanec (1988). These equations assume our star(s) are main sequence, which is suspect. We only include the values as crude estimates, as spectral and radial velocity data will be required to obtain more certain values.

Presentations

1. A Reanalysis of PHOEBE Models for W Ursae Majoris Variable NSVS 609931, American Astronomical Society 241st Winter Meeting, January 11, 2023.
2. A Reanalysis of PHOEBE Models for W Ursae Majoris Variable NSVS 609931, Indiana University-Bloomington Astronomy Colloquium, January 31, 2023.
3. A Reanalysis of PHOEBE Models for W Ursae Majoris Variable NSVS 609931, Indiana Academy of Sciences 138th Annual Meeting, March 18, 2023.
4. (Mentioned) Windows to the Universe: Making Connections Between Planetarium and Variable Star Activities, Olivet Nazarene University Special Guest Presentation, March 30, 2023.

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