Researcher: Alec Neal

Observations suggest that NSVS 3792718 is an eclipsing variable star of W Ursae Majoris type. This star is located at α=00:50:46.7 δ=+41:50:15.4 and has the following alternate stellar designations:  2MASS J00504670+4150154, CRTS J005046.7+415015, [GGM2006] 3792717.  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 3792718 is marked by the green target (T1). All ensemble stars are marked by the red apertures and designated the labels C2-C12. If a B band magnitude is known, it is given with each comparison. Field scale is given along the top and on the left side of the image. 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 2806-966-1 00:50:57.21 +41:50:29.60 11.43 ± 0.09 12.25 ± 0.15
C3 TYC 2806-586-1 00:50:43.70 +41:53:04.42 11.78 ± 0.13 12.60 ± 0.20
C4 TYC 2805-916-1 00:49:49.51 +41:49:09.72 10.91 ± 0.06 12.29 ± 0.18
C5 TYC 2806-852-1 00:50:12.86 +42:00:00.96 12.37 ± 0.17 12.27 ± 0.12
C6 TYC 2806-26-1 00:50:20.29 +41:37:49.01 11.48 ± 0.08 12.08 ± 0.11
C7 TYC 2806-260-1 00:51:27.73 +41:39:56.88 11.36 ± 0.08 12.35 ± 0.17
C8 TYC 2806-742-1 00:51:40.03 +41:42:43.93 12.04 ± 0.15 12.51 ± 0.18
C9 TYC 2806-150-1 00:51:08.59 +41:44:27.88 12.58 ± 0.19 12.96 ± 0.23
C10 TYC 2806-691-1 00:51:27.59 +41:37:57.65 11.58 ± 0.10 12.31 ± 0.15
C11 TYC 2805-38-1 00:49:47.69 +41:44:59.38 12.09 ± 0.14 12.60 ± 0.18
C12 TYC 2805-1503-1 00:49:27.27 +41:37:06.74 12.02 ± 0.14 12.77 ± 0.19

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.

Figure 2: Folded color light curve for NSVS 3792718. All photometry is differential multi-aperture photometry performed by the AstroImageJ (AIJ) software package. Top panel shows folded V-band curve. Bottom panel shows folded (B-V) color curve. 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=0.181), the color index of the system was determined to be (B-V)0 = 0.463 ± 0.067, corresponding to a primary star surface temperature of 6439 ± 288 K, and a spectral type of about F6 V. 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
2457288.80898 ± 0.00024 primary 0 ± 0.00024
2457287.71474 ± 0.00022 secondary 0.00124 ± 0.00034
2457313.78437 ± 0.00024 primary -0.00139 ± 0.00032

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] = 2457288.808977 + 0.438189 · E (1) ±0.000236 ±0.000706

\begin{align*}&space;T_{\textup{min}}[\textup{HJD}]&space;&=2457288.808977+0.438189\times&space;E\\&space;&&space;\;\;\;\;\pm&space;0.000236&space;\;\;\;\;\;\;\;\;\pm&space;0.000236&space;\end{align}&space;\indent\indent\indent\indent\indent\indent\indent\indent(1)

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 visualizations showing best-fit stellar models for the light curves shown in Figure 4. The phases show the system through the first half of the orbit.  Because of the symmetry, these phases represent mirror images of the other half (-Φ). Spots were not used for the final best-fit model. The diagram was plotted by applying the star’s best-fit mass ratio, inclination, and surface potential, given in Table 3 below, to the standard Roche model for close binaries.

Below is a cool animation of NSVS 3792718 created by Alec Neal 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] 0.438168 0.000147
Epoch T0 [HJD] 2457288.809054 0.000330
Inclination i [°] 80.61 0.07
Surface Temp. Teff,1 [K] 6498 77
Teff,2 [K] 6340 77
Surface Potential Ω1,2 [-] 2.35 0.02
Mass Ratio q [-] 0.269 0.011
Distance d [pc] 820 86
Filling Factor F [-] 0.28 0.056
Stellar Mass M1 [M] 1.31 0.09
M2 [M] 1.09 0.08
Stellar Radius R1 [R] 1.36 0.10
R2 [R] 1.27 0.10
Semi-major Axis a [R] 3.25 0.08

Table 3: System parameters of NSVS 3792718.  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

Poster presentations and talks given by Alexander J. Neal (Alec Neal) at national, regional and local conferences for NSVS 3792718 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.

### Publications

1. Rough draft, updated November 18, 2020.

#### 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.