The new complete multi-color light curves of IW UMa in Johnson − Cousin B V R c I c filters (Ažusienis and Straižys, 1969; Bessell, 1983) were observed on 30 January and 24–26 March, 2023 and on 7 February, 2024, with a PI VersArray 1300B LN CCD (size: 1340 × 1300 pixel) photometric system attached to the 80 c m telescope (Tsinghua-NAOC Telescope) at the Xinglong Station of the National Astronomical Observatories of China (NAOC). New complete Johnson − Cousin B V R c I c (Ažusienis and Straižys, 1969; Bessell, 1983) multi-color light curves of V367 Gem were observed on 11–13 January, 2024. The observations were also made with the 80 c m telescope (Tsinghua-NAOC Telescope) at NAOC. The PHOT package of IRAF was used to process all images. The comparison and check stars were chosen to determine the differential magnitudes. For IW UMa, the non-variable star TYC 2997-1178-1 was selected as the comparison, and TYC 2997-1377-1 and TYC 2997-1501-1 were the check stars. GSC 01342-01119 and UCAC4 555-033241 were selected as comparison stars for V367 Gem, and TYC 1342-417-1 was the check star. Table 1 shows information for the comparison and check stars and for both targets. The comparison stars have a similar brightness to the targets. The observed CCD images of both targets are shown in Figures 1 and 2; the variable star is marked “V”, the comparison star is marked “C”, and the check star is marked “Ch”. The two check stars for IW UMa are marked “Ch1” and “Ch2” in Figure 1, and the two comparison stars for V367 Gem are marked “C1” and “C2” in Figure 2. The light curves of IW UMa and V367 Gem are shown in Figures 3 and 4, respectively. The data observed on different nights are marked with different colors, and the B, V, R c and I c band data are represented by a square, circle, triangle, and inverted triangle, respectively. The magnitude difference of the comparison and check stars in all filters are shown at the bottom of the figures. In Figure 3, the mean standard deviations of the magnitude difference in each filter are approximately 0.00678 in the B band, 0.00637 in the V band, 0.00589 in the R c band, and 0.00527 in the I c band. In Figure 4, the mean standard deviations of the magnitude difference of each filter are 0.01075 in the B band, approximately 0.01175 in the V band, 0.00695 in the R c band, and 0.00818 in the I c band.

The Transiting Exoplanet Survey Satellite (TESS) is an all-sky transit survey whose principal goal is to detect Earth-sized planets orbiting bright stars that are amenable to follow-up observations to determine planet masses and atmospheric compositions (Ricker et al., 2014). These targets are read out as postage stamps and made available to the community as target pixel files (TPFs) and corrected light curves. These files comprise several time series, including a simple aperture photometry, a corrected light curve, position vectors, and quality flags. The aperture photometry flux series is termed “SAP_FLUX”, while the flux series that has the common instrumental systematics removed using cotrending basis vectors (CBV) files is termed “PDCSAP_FLUX”. SAP_Flux was used to obtain the light curves of IW UMa and V367 Gem in this study.

IW UMa (TESS target identifier: TIC 105439439) and V367 Gem (TESS target identifier: TIC 56897408) have been observed by TESS for many days in different sectors. The data were retrieved using the Python package l i g h t k u r v e (Lightkurve Collaboration et al., 2018) from the MAST data archive (http://https://mast.stsci.edu/), which provides three different types of data products. Two kinds of light curves from the authors TESS-SPOC and QLP, and the other is the TESScut cutouts of the calibrated full frame images from the author TESScut. Using the TESScut tool, we downloaded 20 × 20 pixel files centered on IW UMa and V367 Gem. Then, the Python procedure dat.to_lightcurve was used to obtain a simple aperture photometry light curve. The flux data are normalized. We thus obtained the light curves of IW UMa from sector 48 with a cadence of 600 s and that of V367 Gem from sectors 71 and 72 with a cadence of 200s. The observation time of the light curves of IW UMa from sector 48 lasted from 29 January to 11 February and from 14 to 25 February 2023. The observation time of light curves of V367 Gem from sectors 71 and 72 lasted 19–28 October, 1–10 and 15–24 November, and 28 November to 7 December 2023. The time-series light curves of each sector and phase-binned light curve of IW UMa and V367 Gem obtained from the TESS database are presented in Figures 5 and 6. The phase-binned light curves of both targets were based on the part of the data in corresponding sectors.

The spectra of IW UMa and V367 Gem were observed using the Beijing Faint Object Spectrograph and Camera (BFOSC), which was mounted on the 2.16 m telescope of the Xinglong station of the National Astronomical Observatories of China (NAOC), Chinese Academy of Sciences (CAS). The observations were made on 14 January 2023, using a low-dispersion spectrometer BFOSC and grism G6. The slit width and line dispersion of grism G6 are 1.8 arcsec and 88 Å mm − 1 , respectively. The observations cover the wavelength range 330–545 nm (Fan et al., 2016). The spectra resolution per pixel is 1.98 Å. IRAF was used to process the observation images and extract the spectra. Normalized flux was obtained, and the atmospheric absorption lines were also corrected. Low-resolution spectra can only show the spectral lines of the primary star, and the lines of the secondary star may be too faint to be detected. The observed spectra of both targets are shown in Figure 7 with black lines.

University of Lyon Spectroscopic Analysis Software (ULySS) (Koleva et al., 2009) was employed to obtain atmospheric parameters by fitting full spectra with model spectra generated by an interpolator with the ELODIE library (Prugniel and Soubiran, 2001).

The red lines in Figure 8 represent the fitting spectra. The atmospheric stellar parameters were derived—for IW UMa: T eff = 7378   ±   70 K, log g = 4.18   ±   0.04 cm/s², [Fe/H] = −0.29   ±   0.04 dex; for V367 Gem: T eff = 8290   ±   52 K, log g = 4.28   ±   0.04 cm/s², [Fe/H] = 0.04   ±   0.05 dex. For the two targets, the spectra were analyzed as single-star spectra, ignoring the secondary (faint) component in the spectra analysis program, the spectra of the primary component, which is casually diluted by the secondary component, will mimic a low metallicity. The atmospheric parameters obtained by ULySS can be used to describe the atmospheric characteristics of the primary star.

The physical properties of the primary can be estimated from the atmosphere parameters by matching with stellar isochrones for normal single stars, assuming that the mass-accreting component is in thermal equilibrium (Zhang et al., 2019), using the PARSEC (Padova and Trieste Stellar Evolution Code) isochrone database (Bressan et al., 2012; Chen et al., 2014; 2015; Tang et al., 2014) along with the lognormal form initial mass function by Chabrier (2001). The primary stars’ physical properties can then be determined, including mass and radius—for IW UMa: M 1 = 1.3 8 − 0.01 + 0.05 M ⊙ , R 1 = 1.5 8 − 0.04 + 0.10 R ⊙ , l o g L 1 = 0.81 9 − 0.054 + 0.057 L ⊙ ; for V367 Gem: M 1 = 1.7 5 − 0.05 + 0.02 M ⊙ , R 1 = 1.5 8 − 0.09 + 0.08 R ⊙ , l o g L 1 = 1.02 5 − 0.061 + 0.049 L ⊙ .

The blue-violet spectrum (3800–4600 Å) of IW UMa, V367 Gem, and part of the spectrum of two MK standard spectra with a type of A3 V (Bet Leo) and F0 III are shown in Figure 8. It is clear that the Ca II K lines of IW UMa and V367 Gem are quite weaker in strength than that of the A3 and F0 MK standards, which exhibit typical characteristics similar to Am stars. The low resolution of the spectral data means that many metallic properties are not adequately captured. Indeed, the Am classification of the primary components of Algol undergoing mass accretion and experiencing high atmospheric turbulence dynamics contradicts the theories of Am star formation. The accurate determination of chemical composition should be based on multi-element chemical composition analysis conducted through high-resolution spectroscopy.

A total of 95 eclipse times of IW UMa spanning approximately 28 years were used to structure the O − C diagram, including two eclipse times observed by us and 62 eclipse times obtained from the TESS data. All eclipse times used for the period analysis are listed in the Supplementary Table A1 Appendix. For the reference items marked “*”, the original publications unavailable online. The corresponding O − C were obtained with the following ephemeris: M i n . I = H J D   2460030.1425 2 +   0.7747182 1 d   ×   E (1) In Equation 2, “Min I” are the observed primary eclipse times and 2460030.1425 (2) is the primary eclipse time of the multi-color light curves.

The O − C diagram of IW UMa is shown in Figure 9. In particular, the open square was used to mark the light minimum obtained from the TESS database. The same weight of 1 was taken for all CCD data, including the TESS data in the O − C analysis. Using the least squares method, Equation 2 can be used to describe the O − C diagram: M i n . I = H J D 2460030.1433 41 + 0.7747187 1 × E + 1.78 ±   8.03 × 1 0 − 11 × E 2 (2)

The error associated with the coefficient of the quadratic term is quite large. The black line in Figure 9 represents the fitting curve. We noticed that this parabolic fit is statistically insignificant. The fitting residuals are shown in the middle panel of Figure 9, which may indicate a cyclic variation. The final residuals are shown at the bottom of Figure 9. The period of IW UMa is likely increasing over the long term superposed with cyclic variation. Considering the large fitting error, this conclusion requires further confirmation.

For V367 Gem, 117 eclipse times crossing approximately 25 years were used to calculate the O − C diagram, including two new observed and 103 eclipse timings estimated from the TESS data by this study (Supplementary Table B1 Appendix). Equation 3 is used to obtained the corresponding O − C and E. M i n I = H J D 2460322.2221 3 + 0.69922 9 d × E (3)

The O − C diagram with error bars of V367 Gem based on all the eclipsing times is shown in the top − left panel of Figure 10; the light minimum obtained from the TESS database is marked with green color. In the O − C analysis program, the same weight of 1 was adopted for all the CCD data. Using the least square method, the O − C of V367 Gem can be described by Equation 4. M i n I = H J D 2460322.2232 1 + 0.699227234 78 × E − 0.71 41 × 1 0 − 10 × E 2 (4)

The quadratic term in the above polymerization indicates that the period is undergoing a long-term decrease at a rate of d P / d t = − 7.40 ( ±   0.43 ) × 1 0 − 8 d ⋅ y r − 1 . The black line in Figure 10 represents the corresponding fitting curve. The fitting residuals are shown in the left-bottom panel of Figure 10. We found that the O − C diagram constructed by the light eclipse timings obtained from TESS data may exhibit an incomplete cycle of a sinusoidal variation with a short period. The cyclic variation can be fitted by Equation 5: τ = A 1 − e 2 sin ν + ω 1 + e ⁡ cos ν + e ⁡ sin ω = A 1 − e 2 sin E * ⁡ cos ⁡ ω + cos E * ⁡ sin ⁡ ω (5) in which: A = a 12 ′ ⁡ sin i ′ / c ( d a y ) is the projected semi-major axis and c is the velocity of light; e , ν , and ω are the eccentricity, true anomaly, and longitude of the periastron passage, respectively; E * is the eccentric anomaly.

The O − C diagram based only on the mid-times of eclipses obtained from TESS are shown in the top-right panel in Figure 10, and the residuals are shown in the right-bottom panel. The incomplete cyclic variation fits the O − C diagram only based on TESS data well, indicating a cyclic variation with a short period of P 3 = 0.26 (37) years and an amplitude of A = 0.002 (24) days. The O − C diagram analysis demonstrates that the orbital period of V367 Gem is undergoing a continuous decrease and a probable cyclic variation simultaneously. The cyclic variation shown in the O-C of TESS mid-times requires further confirmation.

The first multi-color light curves of IW UMa were observed. The TESS observation data from sector 48 (covering HJD 2459625 to HJD 2459636) were utilized to generate the light curve for analysis. The light curves are shown at the bottom of Figure 5. In the figures below, the observed multi-color light curve is labeled “LC_ B V R c I c ”, while the light curve obtained from the TESS database is labeled “LC_TESS”. Different linear ephemerides were used to calculate the phased light curves. For the multi-color light curves, the ephemeris given by Equation 1 was employed. For the TESS-based light curve, the linear ephemeris Equation 6 was used: M i n I = H J D 2459625.7383 17 + 0.7747182 1 d × E (6) in which the epoch 2460030.14246 (12) is the new observed eclipse time and 2459625.73832 (168) is the eclipse time based on the TESS database.

The effective temperature of the primary star obtained as T 1 = 7378 K from our spectral analysis. The effective temperature of the primary star was fixed at 7378 K in the WD modeling. The gravity-darkening coefficients and bolometric albedos are taken as g 1 = 1, g 2 = 0.32, A 1 = 1, and A 2 = 0.5 (Ruciński, 1969). The third light L 3 was set as an adjustable parameter, but no converged result was obtained. The process of q search was confirmed. For all assumed values of q, the sums of weighted square deviations ( ∑ ( O − C ) i 2 ) based on two sets of light curves are displayed in Figure 11. The minimal values achieved at q = 0.15 and q = 0.20 were based on the observed multi-color light curves and the TESS-based light curves, respectively. Then, q was made as an adjustable parameter, and q = 0.15 and q = 0.20 were taken as the initial value in the WD modeling for the two sets of light curves, respectively. The theoretical light curves for the multi-color light curves and TESS-based light curve are shown in Figures 12, 13 in red lines, respectively. The theoretical light curves fitted the light curves very well. All converged photometric solutions are listed in Table 2. The geometric structure is shown in Figure 14.

The first multi-color light curves of V367 Gem were observed. Different linear ephemeris was used to calculate the phased light curves for the observed multi-color light curves and TESS observation. For multi-color light curves, the ephemeris given by Equation 3 was used. For the TESS-based light curves, the linear ephemeris Equation 7 was used: M i n I = H J D 2460264.18578 8 + 0.699229 1 d × E (7) in which the epoch 2460322.22210 (25) is the new observed eclipse times and 2460264.18578 (8) is the eclipse times based on the TESS data.

In the WD modeling, the effective temperature of the primary star was fixed at 8280 K, which was obtained from our spectral analysis. The convergent solutions were confirmed with Mode 5. The third light L 3 was set as an adjustable parameter, and a converged solution was obtained. The mass ratio search was also confirmed for V367 Gem based on the two sets of light curves. The sums of the weighted square deviations ( ∑ ( O − C ) i 2 ) for all assumed values of q are displayed in Figure 15 based on the two sets of light curves. In order to make the minimal q value more obvious, only the trend of change from q = 0.3 to q = 1 was plotted. The minimal value achieved q = 0.49 and q = 0.46 for observed multi-color light curves and TESS light curves, respectively. We thus make “q” an adjustable parameter and set q = 0.49 and q = 0.46 as the initial value in the WD modeling for the two sets of light curves, respectively. The theoretical light curves with and without a third light for multi-color light curves are shown in Figure 16 in red and green lines, respectively. The residual of the theoretical light curves with a third light is shown at the bottom of Figure 16, where the theoretical light curves with a third light fit the light curves better. For LC_TESS, the converged solution with a third light was obtained. The theoretical light curves with a third light for the TESS light curve are shown in Figure 17 in red lines. All of the converged photometric solutions with a third light are listed in Table 2. The geometric structure of V367 Gem is plotted in Figure 18.