Researcher: Tyler Redfern
Observations suggest that NSVS 4161544 is an eclipsing variable star of W Ursae Majoris type. This star is located at α=03:26:38.8 δ=+42:43:24.8 (J2000.0) and has the following alternate stellar designations: BD+42 765,  GSC 02869-00639, PPM 46177, Wolf 164, AG+42 381, 2MASS J03263887+4243246, SAO 38833, Gaia DR1 238082612883284096, NSVS 4161544, and TYC 2869-639-1.  Star Field with stars used in ensemble differential photometry are shown in Figure 1.
Star Field Figure 1: Star field with ensemble stars used for differential photometry marked. The eclipsing variable star NSVS 4161544 is marked by the green target (T1). All ensemble stars are marked by the red apertures and designated the labels C2-C8. If a B band magnitude is known, it is given with each comparison. Field scale is given on the left side and top 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.
(J2000.0) Magnitudes
Comparison Catalog α δ B V Rc
C2 TYC 2869-963-1 03:26:31.88 +42:47:39.80 11.85 ± 0.10 11.40 ± 0.10
C3 TYC 2869-893-1 03:27:01.75 +42:38:38.86 11.81 ± 0.08 11.57 ± 0.11
C4 TYC 2869-668-1 03:26:10.37 +42:41:54.98 11.19 ± 0.06 10.41 ± 0.04
C5 03:27:21.539 +42:51:00.70
C6 03:27:03.471 +42:48:43.06
C7 03:26:26.678 +42:47:12.10
C8 TYC 2869-869-1 03:26:45.34 +42:51:42.91 11.62 ± 0.09 10.73 ± 0.06

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 (0.6-m) 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 are shown for B, V, and Rc in Figure 2.
Color Light Curve Figure 2: Folded color light curve for NSVS 4161544. All photometry is differential ensemble 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.

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
2457697.59542 ±0.00017 secondary 0.00042 ±0.00024
2457697.77085 ±0.00017 primary 0.0 ±0.00017
2457702.69444 ±0.00020 primary -0.000103 ±0.000262
2457703.57484 ±0.00023 secondary 0.001071 ±0.000286
2457703.74970 ±0.00023 primary 0.000086 ±0.000286
2457704.63021 ±0.00021 secondary 0.001371 ±0.000270
2457704.80457 ±0.00020 primary -0.000114 ±0.000262

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] = 2457697.77085 + 0.351692 · E (1)
±0.00017 ±0.002083

NSVS 4161544 O-C PlotFigure 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 with a single star spot. Figure 5 shows a graphical representation of the stellar surface with stellar spots resulting in best-fit model presented in Figure 4.
Best-Fit Models
Figure 4: Best-fit WD model fit with spots (red solid curve) to the folded light curve for differential B, V, and Rc (from left to right) band magnitudes (top panel). The bottom panel shows the residuals from the best-fit WD model (red solid curve).  Error bars are not shown for clarity.  Resulting stellar models with spots are presented in immediately below in Figure 5.
Spots model
Figure 5: Stellar models showing best-fit stellar models for the light curves shown in Figure 3. Orbital phases (Φ) for each panel are included in the upper right corner of each panel. The model includes two stellar spots with one spot on each stellar component and are apparent at orbital phases 0.25 and 0.5. Best fitting parameters are presented in Table 3.
The following table gives the best-fitting parameters for the WD models presented above. All reported errors are 1σ error bars. Both models with out stellar spots and with stellar spots are presented.


Presentations given are listed below along with date given and venue.

  1. Place presentations here.

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.