{'fraction_non_alphanumeric': 0.02774931020890816, 'fraction_numerical': 0.012219156484036263, 'mean_word_length': 4.54700480979449, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Orbital Period Changes in IO Cep, IM Cep and TX Ari: Path to Masses of Distant Components

Three Algol-type binary systems (IO Cep, IM Cep and TX Ari) showing cyclic orbital period changes are studied. The combination of time of minimum data from the ground-based observations together with high precision photometric data from the TESS satellite enabled us to estimate the basic light curve elements of binary systems and mass functions for distant components around the systems. The relation of mass ratio to the system geometry in semi-detached binary stars allowed us to determine the mass ratio of the binary components without using spectra. By using the color and distance information from the GAIA EDR3 and light contributions of the components from the light curve analysis, the astrophysical parameters of the binary components as well as the minimum masses of the distant components are obtained with an uncertainty of ~10-20 per cent indicating that the method can be a good guide for those studying with faint systems where spectra with sufficient resolution and S/N ratio are difficult to acquire.


Introduction
A perturbation on the mid-eclipse timing of eclipsing binaries due to an external body is known as Light Travel Time (LTT) effect. LTT effect is a powerful tool to investigate distant components in eclipsing systems where an eclipsing pair moves about the center of mass of a wider triple system, (a lesser chance a quadruple system) which causes a periodic variations in the mid-eclipse times of the eclipsing binary. Eclipses behave as an accurate clock in detecting distance variations of the eclipsing pair from the center of mass of the triple (or quadruple) system. Who possibly inspired by Ole Roomer's calculation (1676) on the speed of light using LTT effect on Io and Jupiter, [1] is first to discuss LTT effect as a possible mechanism to explain period changes of Algol. Formulation of the problem is given by [2] and [3].
The LTT effect on O − C diagrams was revised by [4], [5] and [6]. Recently, the LTT effect was used for triple star investigations among the KEPLER binaries [7]. There are many applications of LTT effect formulations, for example on HW Vir systems ( [8]; [9]), on the eclipsing binaries of DA + dM ( [10]: [11]; [12]), on Cataclysmic systems [13] and RS CVn systems [14]; [15] on Algol-type binaries. Study of [16] and [17], in which Hipparcos astrometry and LTT effect are analyzed together, is a good example of how it can be effectively used to access the mass of the third body. LTT effect could be useful even on detecting circum-binary planets [18] and black holes [19,20]. We may count [21] and [22] for the recent applications of LTT effect.
In this study, we are performing the period analysis of three semi-detached Algol-type systems for the first time ( §3). Period analysis indicates that there should be at least one additional component in two systems and one system needs further evidence. We analyzed available photometric data from the TESS satellite [23] to estimate the minimum mass of the distant objects ( §4). Using the GAIA distance for each system, we arrived at the absolute parameters of the binaries and then the minimum mass of the additional component. At the end of the study ( §5), we discuss the minimum mass of the additional components.

Observations and Data Reduction
The observations of IO Cep, IM Cep and TX Ari have been performed within the framework of a program where we systematically obtain the times of minima of the eclipsing binary stars using the remotely controlled AUT25 telescope of the Akdeniz University Space Sciences and Technologies Department. AUT25 telescope optical tube assembly (OTA) is a Ritchey-Chretien type with a primary mirror of 10-inch and the mounting system is EQ-8 model german-equatorial type. The telescope is equipped with a QSI-632ws CCD and Johnson UBVRI filters. The autoguiding is performed with a Orion StarShoot camera attached to a 80mm refractor which is also attached to the OTA. The autoguiding unit allows the observer to take CCD frames up to exposure time of 1200s which enables it to observe stars down to 18 magnitude in Johnson V-band.
The program stars have been observed between December 2017-December 2019 in different filters. The selection of the filter has been done on the basis of the brightness of the object during the eclipse in order to keep the S/N ratio as high as possible. The mid-eclipse time was measured using the Kwee-van Woerden method [24] and parabolic fitting to the centeral part of the minimum.
The final time of minimum and its uncertainty have been determined by taking the weighted mean of the measurements. The measured times of minima, their uncertainties, types of minimum and the filters used for IO Cep, IM Cep and TX Ari have been given in Table 1.  [25].
Since the linear ephmeris for IM Cep does not exist in [25], it is adopted from As can be seen from the Figs where a 12 is semi-major axis length, i 12 is inclination, e 12 is eccentricity, w 12 is longitude of periastron of the orbit, ν 12 is true anomaly and c is speed of light.
Together with the linear and parabolic terms, the O − C data have been analyzed with Eq. 2 which calculates the expected value of the time of minimum.
The difference of observed times of minima from Eq. 2 constructs the O − C residuals.
where ∆T 0 , ∆P and ∆t are the correction terms for reference time, orbital period and light travel time, respectively, E is epoch number and Q is the quadratic term which is used for estimating the mass loss and/or transfer in the system. In the case of conservative mass transfer, the Q parameter is related to the amount of mass transfer rate between components as in Eq.3.
where m 1,2 are masses of the components and ∆m 1 is the amount of the transferred mass from secondary to primary component.
As can be seen from the Eq.3, besides the Q-parameter, the total mass of the system must be known in order to determine the amount of mass transfer.
The mass function for the physically bound third body is given as in Eq.4, which tells us that the total mass of the binary system must be known priori in order to calculate the minimum mass of the physically bound distant component.
The methodology used to determine the total mass of the binary star is explained in detail in §4.
The third body orbital parameters obtained as a result of the application of the Eq.2 are given in Table 2

Astrophysical Parameters
The best way to find the absolute parameters of an eclipsing binary star is to analyze the photometric data and spectral data together. However, in most cases, especially in Algol-type semi-detached systems, it is not possible to see the spectral lines of both components in the combined spectrum due to the relatively less light contribution of the secondary component. In such cases, it may be a good option to use the mass-ratio (q) search method for the system's mass ratio.  Ari are taken from the NSVS catalog [27].
Before starting the solution of light curves, the temperature of one of the components must be known. For this, either spectral or photometric color information is required. While atmospheric parameters can be accessed directly using spectral data, it is necessary to purify the colors from interstellar reddening (IS) in order to switch from photometric data to intrinsic colors and from there to temperature. Since all the systems we have considered are later than A0 spectral type, we cannot use the Q-method of [28] as with early-type stars.
However, if we know the amount of interstellar reddening for the color indices we have considered, we can find the color excesses from here and switch to the true colors of the systems and from there to the temperature.   Table 3, we give the photometric colors of the systems and the corresponding temperatures which are adopted from [31].
By obtaining the temperatures, mass ratio (q) distribution with respect to χ 2 of model fits is established by analyzing the light curve of each system. The light curve solutions were performed using the well-known Wilson-Devinney analysis code [32] under graphical interface of phoebe [33]. The code WD uses Roche equipotentials of the stars for the geometry of the system and the fitting is done with differential corrections algorithm. Before running differential corrections, the corresponding light curve with the input parameters such as inclination, equipotentials, secondary component temperature, light contribu-tion of the primary component and spot parameters are calculated and plotted on observations. The radius of each star is a function of two parameters: its equipotential and the mass ratio of the system [34]. Therefore, adopting the best fitting mass ratio as the mass ratio of the system is a good method. The q − χ 2 graphs are given in Fig.6. As can be seen from Fig.6, a reliable massratio for each system could be determined. Light curve models made with the obtained mass ratio and the corresponding Roche geometry of the systems are given in Figs Both spots are at 90 • latitude and their temperature is four percent cooler than the surface temperature of the secondary component. Now, we have 3 systems with light curve parameters. However, all of these parameters are relative parameters and separation between components to be able to derive the absolute parameters such as mass and radius. One drawback might be that we don't have spectroscopic orbital elements. However, we can now make very accurate distance determinations with the parallax data from the GAIA mission. The following methodology could be used to compromise the absolute parameters of components using distance information. The total absolute magnitude M V of the system is obtained by using the distance and IS absorption (A v = 3.1E(B − V )) using the distance modulus. After obtaining the absolute magnitude of the components with the light contribution of each component (see Table 4), the bolometric brightness of the components is obtained by using the bolometric corrections (BC) given by [31]. From the bolometric magnitudes, the absolute radius of each component is derived. Since we know the relative radii from the light curve analysis, the separation between components is found from the relationship a = R absolute /r relative . By finding the separation between the components and using the mass-ratio, the mass of each component and thus the total mass of each system can be derived. The absolute parameters of the components are derived and given in Table 4. Now, the minimum mass of the distant components in each system can be derived by using Eq.4. Moreover, masses for the case of coplanar orbit (same inclination of the wide and close binary orbits) can be derived. Mass estimates of the distant components are given Table 5 for each system.

Discussion and Conclusion
The distance information provided by the Gaia satellite has enabled us to reach the physical properties of the components of three selected Algol-type binary stars. The current parameter accuracy is still not at the desired level of < 1 percent, although, it offers a good opportunity to obtain a lower limit for the mass of physically bonded components around the systems under study.
Looking at the derived physical parameters of the components of the IO Cep system, it is seen that the temperature of the primary component is close to the solar value while its mass and radius point to an earlier type system (F5-7).
In parallel to this, the radius of the secondary component is larger than the radius of a star with 0.30 M mass. These differences could not be explained by a single star evolution as there is mass transfer between the components in Algols, which separates the evolution of components from the evolution of single stars. It is clear that both components in IO Cep evolved and increased their radius. The primary star is more massive for its temperature (5770 K) while the secondary is less massive for its temperature (4380 K). The cyclic period change in the O-C diagram of the system is due to a distant companion as the theoretical model provides an eccentricity of e = 0.32 which rules out orbital period modulation due to magnetic activity (see [36]). Using the total mass of The evolution of semidetached binaries on the basis of their angular momen-tum change are very well described by [38]. Three cases of mass transfer occurs in semidetached Algols: Case A, B and C. In case A, the transfer occurs during core hydrogen burning phase, in Case B, during shell hydrogen burning phase and in Case C, the mass transfer occurs when the star has exhausted helium in its core. In Fig.9,