Researcher: Lauren Wines, Madeline Shepley

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.

Figure 1: Star field with ensemble stars used for differential photometry marked. The variable star NSVS 6099331 is marked by the green target (T1). All ensemble stars are marked by the red apertures and designated the labels C2-C17. If a B band magnitude is known, it is given with each comparison. Image is a representative image taken with the BSUO 20-inch telescope. Further details for each comparison star are given below in Table 1. Further details regarding the telescope and detector used can be found on our BSU Observatory page.
Identification Position (J2000.0) Magnitudes
ID Catalog α δ V B Rc
C2 TYC 3208-2713-1 22:24:45.199 +41:20:39.24 11.94 ± 0.11 13.09 ± 0.22
C3 TYC 3208-2637-1 22:25:38.956 +41:20:50.52 11.89 ± 0.11 12.96 ± 0.21
C4 TYC 3208-1967-1 22:24:21.062 +41:27:35.69 11.41 ± 0.06 11.90 ± 0.07
C5 TYC 3208-2275-1 22:25:29.814 41:26:52.35 11.23 ± 0.05 11.58 ± 0.04
C6 TYC 3208-2481-1 22:25:17.226 +41:37:45.30 11.81 ± 0.10 12.24 ± 0.10
C7 TYC 3208-2439-1 22:25:19.702 +41:40:29.05 11.32 ± 0.06 12.67 ± 0.18
C9 TYC 3208-2518-1 22:26:15.089 +41:34:01.00 11.88 ± 0.11 12.58 ± 0.16
C10 TYC 3208-2774-1 22:25:47.025 +41:22:59.07 12.05 ± 0.12 13.53 ± 0.28
C11 TYC 3208-2737-1 22:24:30.131 +41:23:07.88 11.27 ± 0.06 11.63 ± 0.05
C12 TYC 3208-2528-1 22:25:02.101 +41:33:51.93 12.11 ± 0.11 12.90 ± 0.17
C13 22:24:38.625 +41:15:11.33
C14 22:25:02.965 +41:16:11.15
C15 22:25:34.298 +41:15:14.62
C16 22:26:14.085 +41:19:16.16

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 (Rc) 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 Rc 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.
Color Curve

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-Rc) 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

Times of minimum light were determined for the nights observed, and are given in the following table along with Observed minus calculated (O-C) times of minimum. All reported errors are 1σ error bars.

[HJD] [days]
Time of Minimum Error Eclipse (O-C) Error
2458696.750916 ± 0.000045 secondary 0.00012033 ± 0.000094
2458698.7737595 ± 0.000088 secondary

2458705.651004 ± 0.000135 secondary
± 0.000158
2458720.82271067 ± 0.000082 primary 0 ± 0.000082
2458723.65460067 ± 0.000082 primary -0.00009999 ± 0.0001164
2458724.66576367 ± 0.000078 secondary -0.000362 ± 0.00011381


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).

An observed minus calculated (O-C) time of minimum light analysis was performed and is shown in Figure 3. The analysis was performed using the reported times of minimum light given in Table 2. The O-C values are determined by the following linear ephemeris and are given in the above table.

Tmin [HJD] = 2458720.82271067 + 0.404570 · E (1)
±0.000082 ±0.000294

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

All modeling is performed using the PHysics Of Eclipsing BinariEs (PHOEBE) (v0.31a) software package.  PHOEBE is a graphical user interface (gui) to the WD code that is used to model binary stars.  Figure 4 shows the best fit WD model.  No spots were included in the best-fit model. Figure 5 shows a graphical representation of the stellar surface.


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
Below is a table of parameters and their values derived in the analysis of this system via the methods discussed above.

(1) (2) (3) (4)
Parameter Symbol [unit] Value Error
Period P [days] 0.404570 0.000293
Epoch T0 [HJD] 2458720.82271067 0.00008234
Inclination i [°]
Surface Temp. Teff,1 [K]
Teff,2 [K]
Surface Potential Ω1,2 [-]
Mass Ratio q [-]
Distance d [pc]
Filling Factor F [-]
Stellar Mass M1 [M]
M2 [M]
Stellar Radius R1 [R]
R2 [R]
Semi-major Axis a [R]

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.


Poster presentations and talks given by Lauren Wines at national, regional and local conferences for NSVS 6099331 are given below.

  1. A Photometric Analysis of the Eclipsing Binary Star NSVS 3792718, Ball State University Physics & Astronomy Annual Banquet Poster Presentation, Spring 2018.
  2. Eclipsing Variable Star NSVS 3792718, Ball State University Physics & Astronomy colloquium, December, 2018.
  3. NSVS 3792718, a Spotless W Ursae Majoris Star, Indiana Academy of Science 134th Annual Meeting, March 30, 2019.
  4. Multi-Band Photometric Study of the W Ursae Majoris Star NSVS 3792718, Ball State University Student Symposium, April 9, 2019.
  5. (Mentioned) NSVS 2854398 and Recent Developments, Physics & Astronomy colloquium. November 21, 2019.

Poster presentations and talks given by Madeline Shepley at national, regional and local conferences for NSVS 6099331 are given below.

  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.

Contact Information

All members of the Variable Star Research group are enthusiastic researchers with a passion for the work performed by the group. We are always happy to discuss any research projects and are always looking for like-minded and enthusiastic collaborators. For more information regarding any of the aforementioned research activities or the research activities of the Variable Star Research Group, please do not hesitate to contact Robert Berrington.