Low-mass contact binaries as probes of stellar merging events

. Gravitational interaction is important for nearly every aspect of Astrophysics. Theoretical models are tough tested in cases where strong, stellar winds, angular momentum loss, and mass transfer take place in the course of stellar evolution within a common envelope. Stellar interaction impacts the formation and evolution of diverse types of binary and multiple stellar systems. Therefore, evolution in a binary (and a multiple) stellar environment is still an open question in Astrophysics while contact binaries are challenging the well-established and solid theories that concern thermal equilibrium and orbital stability. There is a vast number of such systems observed in the Milky Way and the Magellanic Clouds. Systematic (independent or combined) observations, all-sky surveys, ground-based and space telescopes have oﬀered very detailed photometric and spectroscopic information about these systems. Special attention is given when extreme cases are observed, such as ultra-short orbital period contact binaries or extremely low mass ratio systems. These cases can give insights into the physical and orbital parameters of low-mass contact binaries and their temporal variations. For example, one can investigate the orbital period modulation, the spot activity, and the possibility of contact bi-naries to host planets, as well as predict a stellar merger, red nova events, and a possible connection with exotic stellar populations such as blue stragglers. The purpose of this work is to present the recent developments in observations of low-mass contact binaries, highlighting the most important ﬁndings, in combination with existing theories. The research of such systems, at an international level, is constantly challenging our current knowledge of stellar interactions and advances our understanding of stellar dynamics in common envelope and contact phases.


Introduction
Binarity in nature is something very common, expressed in a wide range of scales, from binary asteroids and dwarf planets to binary stars, clusters, and galaxies.Kepler's law and the two-body theory can be simply applied to understand the orbital behavior of the involved objects, assuming that there is no intrinsic variability or evolution that alters their physical properties.Consequently, the binary system behavior is dominated by the stellar interaction between the two components.This process is the dominant mechanism that leads the individual components and the system itself through the paths of binary evolution.Although most of the eclipsing binaries are observed to be members of triple, quadruple, or multiple systems in general, they are formed in a hierarchical configuration.Stellar evolution in a contact binary system is different than a single-star evolution in many aspects.Evolution alters the physical parameters of single (solar-type) stars in a timescale of 5-10 Gyr.On the contrary, the current theoretical models support that evolution within a binary environment can be even slower, exceeding the timescale of 10-15 Gyr (Gazeas & Stȩpień, 2008).Therefore, what we see today as a contact binary stellar system is just a snapshot of this long-lasting process.
Stellar evolution theories indicate that we should be able to observe stellar merging events (Webbink, 1976;Stȩpień, 2006) due to the gradual coalescence of contact binaries.However, this has not been the case until the detection of the merging event of V1309 Sco in 2008 (Tylenda et al., 2011).Even in this case, the contact binary nature of the progenitor was discovered only after the red nova event (Nova Sco 2008).Numerous observations of V1309 Sco are available in the OGLE-III and IV surveys (Udalski, 2003) before the red nova event and they helped to identify the nova progenitor as a low mass ratio contact binary in deep contact configuration with an orbital period of about 1.4 days.
A merging event is presumed to be driven by the instability of the two involved stellar components.A contact binary system can experience mass and angular momentum loss via mass outflow from the Lagrange point L 2 or via stellar wind and magnetic activity (e.g.flares).The system can be also unstable if the orbital angular momentum is less than three times the total spin angular momentum (Hut, 1980), also known as "Darwin instability".Systematic studies of such systems started to appear only very recently, suggesting that low mass ratio contact binary systems are promising merger candidates (Li et al., 2022;Wadhwa et al., 2023b,a;Liu et al., 2023).

Challenging theoretical models
From the observational aspect, there are efforts to increase the sample of wellstudied systems, derive their physical and orbital parameters with high accuracy, and eventually understand the nature of the contact binary configuration.Fortunately, there is a vast number of contact binary systems in the Milky Way and the Magellanic Clouds, and the majority of them (over 60%) are accompanied by tertiary members, as shown in past and recent studies (D'Angelo et al., 2006), (Loukaidou et al., 2022).Low-mass and low-temperature contact bina-ries are the most frequently observed types of eclipsing binary systems.Their components have smaller sizes in comparison with other main-sequence stars, and they belong to the old stellar population group (Rucinski, 2000).
In parallel to the observations, there are several attempts to understand the evolution processes within a binary environment.We have more than a century of knowledge of the existence of contact binary systems.In the early 50's and 60's, we had the first attempts to understand the physics within a common envelope environment.It was only after the 80's that the first statistical studies showed that low-mass contact binaries share common orbital and physical characteristics.It was also found that the members in such systems are surrounded by a common convective envelope that lies between the inner and outer critical Roche surfaces.
In most of cases, low-mass contact binaries are low-temperature Main Sequence (MS) stars of F, G, and K spectral type.They have solar-type characteristics and they belong to the old population group of our Galaxy, confirming that they are old stars that did not evolve towards the Red Giant Branch (RGB), remaining at the MS together with the rest of the young dwarf (single) stars.According to (Bilir et al., 2005) contact binaries have a kinematic age of 5-12 Gyr.Observations also show that there are several low-mass contact binaries with their total mass close to 1-1.4 M (Gazeas & Niarchos, 2006;Gazeas & Stȩpień, 2008).Magnetic activity (expressed by cool photospheric spots or even hot chromospheric flares) is something expected in cool stars with convection zone.Low-mass contact binaries are among the binary systems with the highest level of chromospheric activity.Therefore, they lose angular momentum and mass by the magnetized wind, as is observed in single, highly active stars.Cool spots can explain the observed asymmetries in light curves sufficiently.In addition, the heavily covered surface of the components by cool spots is the most likely explanation of the so-called 'W-phenomenon' (Stepien, 1980;Eaton et al., 1980;Zola et al., 2010).
Their contact configuration puts several constraints on their physical properties due to the Roche geometry.In addition, there is a link between the orbital and the physical properties, i.e. the mass, radius, temperature, and luminosity.This is how the first empirical relations started to appear in literature, correlating the physical parameters with quantities that are directly derived from observations, such as the orbital period or the mass ratio, as shown in Fig. 1.

Why contact binaries are so interesting?
A low-mass contact binary is formed when a short orbital period system undergoes stable mass transfer between its components.Angular momentum is lost due to stellar wind and magnetic braking phenomena, while both stars overflow their Roche lobes.This process eventually leads towards a contact configuration.The components of low-mass and low-temperature contact binaries follow Figure 1.The above 3D diagrams show that there is a direct correlation of the absolute physical parameters (M, R, L) with the directly observed parameters (orbital period P and mass ratio q) of low mass contact binary systems.The extracted empirical relations express the equations of the shaded flat surfaces (Gazeas, 2009).
certain empirical relationships, which closely correlate physical parameters with each other, due to the Roche geometry.As a result, contact binaries are excellent astrophysical tools for the determination of the fundamental physical parameters (mass, radius, luminosity) of low-temperature stellar components, that can be used to trace their evolutionary paths.They are of great interest to the study of stellar populations since they provide an excellent opportunity to investigate stellar merging scenarios.They can be very successfully used as distance indicators, a fact that was proposed and tested in several studies in the past (Rucinski, 1997;Rubenstein & Bailyn, 1996;Edmonds et al., 1996;Yan & Mateo, 1994).They provide an excellent opportunity to investigate evolution paths such as stellar merging, while their parameters can be measured or derived in a highly accurate way.This leads to the close monitoring of the orbital (and physical) parameter modulations, which can provide evidence of evolution toward merging.
Following careful methodology in data treatment, negligible modulation of parameters can be traced and therefore their temporal variation can be mon- of orbital period in two low mass contact binaries with ultra-short orbital period (Loukaidou et al., 2022).Both systems show an orbital period decrease (expressed as a negative parabolic trend), while the second one additionally shows the existence of a tertiary component orbiting the close binary.
itored.For example, Fig. 2 shows the O-C diagrams of two selected contact binaries with ultra-short orbital period (Loukaidou et al., 2022).Both systems exhibit a negative parabolic trend on their orbital period modulation, which is translated as an orbital shrinkage.On top of that, 1SWASP J173003.21+344509.4 shows an additional periodic modulation, as a consequence of a tertiary component orbiting the contact binary.The diagrams are so sensitive, that even tiny fluctuations of the orbital parameters can be detected.The overall trend, as derived from the diagrams, can quantify the orbital shrinkage, and therefore the merging timescale.Angular momentum and mass loss of the system via stellar wind may be the dominating mechanism, that explains the observed orbital period modulation.In addition, mass transfer between the components may alter the orbital period, and it can reverse the mass ratio between the two components (Stȩpień & Gazeas, 2008).

Physical and orbital properties of contact binaries
An alternative model of stellar evolution in a binary environment was proposed by Stȩpień & Gazeas (2012).The model is based on the idea that a detached binary system with an orbital period of ∼1.5-2 days loses angular momentum through stellar wind.Such a process can be dramatically accelerated through Kozai-Lindov cycles (Kozai, 1962), by the existence of a tertiary component that pumps angular momentum out of the close binary.The angular momentum loss shrinks the orbit and the two components come in contact, sharing a common photosphere, and therefore sharing thermal energy.However, such a process requires an exceptional amount of time, of about 10-12 Gyr.To have a good agreement of the model with the observed parameters in low mass contact binary systems as we observe them today, the angular momentum loss rate, as well as the mass loss rate, should be constrained within narrow limits (Fig. 3).).These values are compared with parameters derived after direct observations of contact binaries (Gazeas & Stȩpień, 2008).

Observations of low mass contact binaries
Information about the properties of contact binaries comes almost explicitly from photometric and spectroscopic observations.Dedicated observing campaigns collect high-resolution data, to provide analytical solutions to match theoretical models with the observations.Space telescopes provide ultra-high precision photometric data for a long uninterrupted period of time, which is essential for the orbital period determi-nation and its modulation.However, in most cases, space-borne spectroscopic data are still limited to low-resolution data, which are adequate for temperature determination, but not for radial velocity measurements.
On the other hand, ground-based sky surveys can also contribute to the long-term monitoring of the contact binaries with several photometric data and (again) limited spectroscopic observations.Large telescope facilities are needed for high-resolution spectra, which is not always easy, since long-term photometric observations are almost impossible, due to the limited observing time and availability in large aperture telescopes.

CoBiToM Project
The Contact Binaries Towards Merging (CoBiToM Project, Gazeas et al. (2021)) was initiated in 2012 under the idea of the long-term monitoring of low mass contact binaries and the modulations of their physical parameters.The ultimate goal is to investigate stellar coalescence and merging processes towards red nova events, as the final state of stellar evolution of low-mass contact binary systems.The program aspires to give insights into their physical and orbital parameters and their temporal variations, e.g. the orbital period modulation, spot activity, etc.The innovation of CoBiToM Project is based on a multi-method approach and a detailed investigation, that will shed light on the origin of stellar mergers and rapidly rotating stars for the first time.CoBiToM Project is closely connected with the WUMa program (Kreiner et al., 2003), which was initiated in 2002 and resulted in a list of 160 contact binary systems with high-resolution spectroscopy and mass ratio determination.
Fig. 4 shows the mass distribution over the orbital period of 118 well-studied contact binaries with combined photometric and spectroscopic techniques.The current investigation, in the frame of CoBiToM Project, focuses on the study of ultra-short orbital period systems (extreme left part of the plot), and investigates the systems with an extremely small secondary component, and therefore ultra-low mass ratio (systems with the smallest mass at the lower part of the plot).The preliminary results show that the ultra-short orbital period contact binaries are very stable systems, while over 60% of them are hosted within triple or multiple systems.In addition, half of them present orbital period modulation.systems with secondary components of very small mass.Note that the mass of the secondaries lies within the range of 0-1 M , while the mass of the primaries gradually increases proportionally to logP (Gazeas & Niarchos, 2006).

Observing challenges and future goals
The current and future trend of the research on low mass contact binaries is to further study the ultra-short orbital period systems and the prominent cut-off limit, detect systems with significant orbital period modulation via the O-C diagrams, investigate the ultra-low mass ratio systems, and search for possible unstable orbits among them.Furthermore, the study of contact binaries as common envelope systems investigates the possibility of discovering exoplanets hidden within the circumbinary material and the stellar ejecta from the stellar wind and the mass loss processes.Dedicated observing programs seek for red nova progenitors and future merger candidates and aspire to connect the merger results with fast rotating stars, such as the population of Blue Stragglers.

Summary
The evolution of low-mass contact binaries is mostly driven by mass transfer and angular momentum loss via the magnetized wind, which shrinks the orbit and makes both components overflow their outer Roche lobes.It is known that all low-mass contact binaries are old, with a typical age of 7-8 Gyr, although their contact phase lasts less than 1 Gyr, leading into coalescence (Stȩpień & Gazeas, 2012).There is an obvious need for dedicated sky surveys focusing on highresolution spectroscopy on such systems.Ground-based surveys and telescope networking, play an important role in time-domain Astrophysics and this is a key aspect for future research in this field.Long-term observing campaigns and active Pro-Am collaborations in data acquisition are essential for monitoring temporal modulations of physical and orbital parameters.

Figure 2 .
Figure2.The diagrams present the observed (O) minus the calculated (C) value of orbital period in two low mass contact binaries with ultra-short orbital period(Loukaidou et al., 2022).Both systems show an orbital period decrease (expressed as a negative parabolic trend), while the second one additionally shows the existence of a tertiary component orbiting the close binary.

Figure 3 .
Figure3.Left panel: The distribution of angular momentum of 112 contact binaries in cgs units (×10 51 ).Evolutionary tracks of models given byStȩpień & Gazeas (2012) are also shown.Parts of the tracks plotted with dotted lines correspond to pre-contact phases and those plotted with solid lines describe binary evolution while in contact configuration.Right panel: The components of low-mass contact binaries (open and filled circles) and of other contact binary systems ('plus' signs and triangles).These values are compared with parameters derived after direct observations of contact binaries(Gazeas & Stȩpień, 2008).

Figure 4 .
Figure4.The mass distribution for the two components of all 118 contact binaries in our sample.The mass of the primary components is plotted with full circles, while the mass of the secondary ones is plotted with open circles.Triangles represent the low-q systems with secondary components of very small mass.Note that the mass of the secondaries lies within the range of 0-1 M , while the mass of the primaries gradually increases proportionally to logP(Gazeas & Niarchos, 2006).