Researcher: Kyle Koeller

Observations suggest that NSVS 896797 is an eclipsing variable star of W Ursae Majoris type. This star is located at α=13:27:50.5 δ=+75:39:45.4 (J2000.0) and has the following alternate stellar designations: TYC 4558-1877-1, NSVS 896797, Gaia DR1 1712924526347844224, Gaia DR2 1712924526347844224, 2MASS J13275048+7539453, and [GGM2006] 922168. Star Field with stars used in ensemble differential photometry are shown in Figure 1.
Figure 1: Star field with ensemble stars used for differential photometry marked. The eclipsing variable star NSVS 896797 is marked by the label T1. All ensemble stars are marked by the apertures and designated by the labels C2-C10. If a B band magnitude is known, it is given with each comparison in Table 1. Field-scale is given on the bottom left corner of the image.
(J2000.0) Magnitudes
Comparison Catalog α δ B V Rc
C2 TYC 4558-825-1 13:27:40.48 +75:40:40.50 12.32 ± 0.17 11.61 ± 0.11 —
C3 TYC 4558-2171-1 13:26:17.48 +75:40:05.66 12.80 ± 0.24 11.74 ± 0.12 —
C4 — 13:27:10.17 +75:40:35.83 — — —
C5 — 13:27:22.63 +75:40:41.13 — — —
C6 — 13:28:07.94 +75:40:44.06 — — —
C7 — 13:26:36.13 +75:42:22.25 — — —
C8 — 13:28:04.09 +75:43:29.66 — — —
C9 — 13:28:34.38 +75:42:38.81 — — —
C10 TYC 4558-255-1 13:27:26.00 +75:44:00.77 11.69 ± 0.07 11.14 ± 0.07 —

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 bandpasses. 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. We checked the magnitudes for all comparison stars by comparing with APASS magnitudes and results are comparable to the quoted Tycho magnitudes.

 
NSVS 896797 Color Light CurveFigure 2: Folded color light curve for NSVS 896797. 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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3: V band differential photometry for each comparison star versus orbital phase. An offset of 0.5 magnitudes was applied to each comparison star for clarity. Each comparison star is denoted by the name of the comparison on the right side of the panel. Error bars are not shown for clarity.

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4: χ2 versus mass ratio of NSVS 896797. A q search over a wide range was conducted with an offset of 0.046 added or subtracted from the initial q value found from PHOEBE for a total of 46 values.

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
2457143.76136 ±0.00014 primary 0.000 ±0.00014
2457143.91777 ±0.00024 secondary -0.00008 ±0.00028
2457161.75649 ±0.00017 secondary -0.00088 ±0.00022
2457161.91298 ±0.00014 primary -0.00088 ±0.00019

Table 2: Heliocentric Julian dates [HJD] for times of minimum (first column) are reported along with 1σ error 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.
Figure 5: 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.

Figure 6: 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).

Figure 7: Stellar models showing best-fit stellar models for the light curves shown in Figure 4. Orbital phases (Φ) for each panel are included with each panel. The model includes three stellar spots with one spot on each stellar component and are apparent at orbital phases 0.25 and 0.5.

Derived System Parameters
Below is a Table 3, which lists parameters and their values derived in the analysis of this system via the methods discussed above. Note that the ns subscript represents values/errors without spots (“no spots”), and the subscript s denotes values/errors with spots. See the table caption for more details and/or clarification.

No Spots Spots
(1) (2) (3) (4) (5) (6)
Parameter Symbol [unit] Value Error Value Error
Period P [days] 0.31297 0.00032 “ “
Epoch T0 [HJD] 2457143.76136 0.00014 “ “
Inclination i [deg] 81.023930 0.14 80.653676 0.14
Surface Temp. Teff,1 [K] 5307 314 5307 314
Teff,2 [K] 4871 314 4872 314
Surface Potential Ω1,2 [-] 5.203792 0.073 4.734902 0.073
Mass Ratio q [-] 1.79647 0.05 1.710595 0.05
Stellar Mass‡ M1 [M☉] 0.94075 0.102115 0.94075 0.102115
M2 [M☉] 1.6092 0.188784 1.6092 0.188784
Semi-major Axis‡ a [R☉] 2.6503 0.1247 2.6503 0.1347
Luminosity [L1/(L1+L2]B 1.534463 0.018 0.104819 0.018
[L1/(L1+L2]V 3.259696 0.041 0.223763 0.041
[L1/(L1+L2]RC 3.542751 0.048 0.243875 0.048
Limb Darkening xbol,1,2 0.60837 – 0.60837 –
ybol,1,2 0.16253 – 0.16253 –
xB,1,2 0.753772 – 0.753772 –
yB,1,2 -0.148888 – -0.148888 –
xV,1,2 0.738404 – 0.738404 –
yV,1,2 0.094340 – 0.094340 –
xRC,1,2 0.676580 – 0.676580 –
yRC,1,2 0.214988 – 0.214988 –
Spot Colatitude φ1[°] – – 90 –
φ2[°] – – 90 –
φ3[°] – – 90 –
Spot Longitude λ1[°] – – 150 –
λ2[°] – – 335 –
λ3[°] – – 180 –
Spot Radius ρ1[°] – – 6 –
ρ2[°] – – 17 –
ρ3[°] – – 12 –
Temp Factor τ1[-] – – 1.03 –
τ2[-] – – 0.90 –
τ3[-] – – 1.05 –

Table 3: System parameters of NSVS 896797.  Column (1) gives the name of the parameter, (2) gives the parameter symbol and [units], (3) and (4) give the parameter value and error, respectively, without spots (ns), while (5) and (6) give the parameter value and error with spots (s). Some values aren’t dependent on spots and remain constant regardless, so the second instance is marked with a quotation mark (“). Any blanks in the table denote data which is, as of the last edit, unknown and/or unavailable.
‡These values were calculated using 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.

 

Parameter Filter 1 Error Filter 2 Error Filter 3 Error
a1 −0.03948 ±0.00022 -0.03879 ±0.00017 −0.035 ±0.00346
a2 −0.22536 ±0.00048 −0.21807 ±0.0002 −0.21331 ±0.00347
a4 −0.05628 ±0.00021 -0.05685 ±0.00019 −0.05544 ±0.00331
a2(0.125-a2) −0.07895 ±0.00028 −0.07481 ±0.00011 −0.07216 ±0.00192
2b1 -0.01982 ±0.0008 -0.01617 ±0.00039 -0.01013 ±0.00658
∆IFT -0.02374 ±0.0022 -0.01901 ±0.00141 -0.01357 ±0.01515
∆Iave -0.02223 ±0.0007 -0.0179 ±0.00056 -0.0104 ±0.00827
OER 0.96967 ±0.00155 0.9739 ±0.00084 0.98458 ±0.01312
LCA 0.01235 ±0.00223 0.01048 ±0.00131 0.0091 ±0.00901

Table 4: Calculated O’Connell effect quanitites. The given filters are Johnson B (Filter 1), Johnson V (Filter 2), and Cousins
RC (Filter 3) with parameters an being specific Fourier fits. Paramters 2b1, IFT , and Iave are quantifying parameters in
terms of the difference in maxima of the light curve peaks (Figure 2). OER is the ratio of area under the light curve between
φ = 0.0 and φ = 0.5. The LCA measures deviance from symmetry of the two halves of the light curve as seen in Figure 2.

Presentations

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.