Study of Eleven Extremely Low Mass Ratio Contact Binary Systems

2.1 Photometric Observations

Multi-band photometric observations were conducted for all eleven systems using ground-based telescopes. The observations covered complete orbital cycles to ensure accurate light curve analysis.

2.2 Wilson-Devinney Analysis

The Wilson-Devinney program was employed to derive photometric solutions, including mass ratios, fill-out factors, and temperature differences between components. The analysis utilized the following key parameters:

• Mass ratio ($q = m_2/m_1$)
• Fill-out factor ($f$)
• Orbital inclination ($i$)
• Temperature ratio ($T_2/T_1$)

2.3 Spectral Analysis

LAMOST low-resolution spectra for four objects were analyzed using spectral subtraction techniques to detect chromospheric activity through H𝛼 emission lines.

3.1 System Classification

Among the eleven systems, two were identified as W-subtype (CRTS J133031.1+161202 and CRTS J154254.0+324652), while the remaining nine systems were A-subtype. The fill-out factors ranged from 18.9% (CRTS J155009.2+493639) to 94.3% (CRTS J154254.0+324652).

3.2 Mass Ratio Analysis

All eleven systems exhibited mass ratios less than 0.1, classifying them as extremely low mass ratio (ELMR) contact binaries. This characteristic makes them potential candidates for future merger events.

3.3 Period Variations

Period analysis revealed three systems with decreasing orbital periods, likely due to angular momentum loss, and six systems with increasing periods, suggesting mass transfer from secondary to primary components.

3.4 Chromospheric Activity

H𝛼 emission lines were detected in four systems through spectral subtraction, indicating significant chromospheric activity and potential magnetic activity cycles.

4.1 Mathematical Framework

The instability parameter was calculated using the formula derived from Rasio (1995):

$q_{inst} = \frac{J_s}{J_o} = \frac{(1+q)^{1/2}}{3^{3/2}} \left(\frac{R_1}{a}\right)^2$

where $q$ is the mass ratio, $R_1$ is the primary radius, and $a$ is the orbital separation.

The spin angular momentum to orbital angular momentum ratio is given by:

$\frac{J_s}{J_o} = \frac{(1+q)}{q} \left(\frac{R_1^2 + R_2^2}{a^2}\right)$

4.2 Experimental Results

The mass-luminosity and mass-radius diagrams revealed that primary components follow main sequence evolution, while secondary components lie above the Terminal Age Main Sequence (TAMS), indicating overluminosity. This suggests advanced evolutionary stages and potential mass transfer effects.

Figure 1: Mass-Radius diagram showing primary components on main sequence and secondary components above TAMS.

Figure 2: Light curve solutions for CRTS J154254.0+324652 showing 94.3% fill-out factor.

4.3 Code Implementation

# Wilson-Devinney light curve analysis pseudocode
import numpy as np

def wilson_devinney_analysis(light_curve, initial_params):
    """
    Perform Wilson-Devinney analysis for contact binaries
    
    Parameters:
    light_curve: array of flux measurements
    initial_params: dictionary of initial parameters
    
    Returns:
    optimized_params: dictionary of fitted parameters
    """
    
    # Initialize parameters
    q = initial_params['mass_ratio']  # mass ratio
    i = initial_params['inclination']  # orbital inclination
    f = initial_params['fill_out']     # fill-out factor
    
    # Iterative fitting process
    for iteration in range(max_iterations):
        # Calculate model light curve
        model_flux = calculate_model_flux(q, i, f)
        
        # Compute chi-squared
        chi2 = np.sum((light_curve - model_flux)**2 / errors**2)
        
        # Update parameters using gradient descent
        params = update_parameters(params, chi2_gradient)
    
    return optimized_params

# Example usage for CRTS J154254.0+324652
initial_params = {
    'mass_ratio': 0.08,
    'inclination': 78.5,
    'fill_out': 0.85
}
result = wilson_devinney_analysis(light_curve_data, initial_params)

5.1 Evolutionary Status

The analysis indicates that primary components are in main sequence evolution, while secondary components show evidence of being above TAMS. This overluminosity suggests advanced evolutionary stages and significant mass transfer history.

5.2 Stability Analysis

Calculation of $J_s/J_o$ ratios and instability parameters suggests that CRTS J234634.7+222824 is on the verge of merger. This aligns with theoretical predictions by Rasio (1995) and Eggleton & Kiseleva-Eggleton (2001) regarding the fate of deep contact binaries with extreme mass ratios.

5.3 Original Analysis

This study of eleven extremely low mass ratio contact binaries provides significant insights into the late-stage evolution of close binary systems. The detection of systems with mass ratios below 0.1 challenges conventional understanding of contact binary stability. As noted in the International Astronomical Union's binary star database, such extreme systems are rare but crucial for understanding stellar merger processes.

The identification of CRTS J234634.7+222824 as being on the verge of merger aligns with theoretical models predicting that systems with $q < q_{inst}$ and high fill-out factors will undergo dynamical instability. This phenomenon is analogous to the instability criteria discussed in the seminal work by Rasio & Shapiro (1995) on the coalescence of compact binaries.

Comparing these results with the comprehensive study by Qian et al. (2017) on contact binary evolution reveals consistent patterns in period changes and mass transfer directions. The detection of H𝛼 emission in four systems provides direct evidence of chromospheric activity, similar to findings in the Mount Wilson Observatory H-K project monitoring active binaries.

The overluminosity of secondary components above TAMS suggests complex evolutionary pathways, possibly involving rapid mass transfer episodes. This observation supports the mass-transfer models proposed by Eggleton & Kisseleva-Eggleton (2006) for binary system evolution. The high fill-out factors (up to 94.3%) indicate these systems are in advanced contact phases, potentially preceding merger events that could produce FK Com-type stars or blue stragglers, as documented in globular cluster studies by Kaluzny & Shara (1988).

Future observations with advanced facilities like the James Webb Space Telescope could provide higher resolution spectral data to better understand the atmospheric dynamics and mass transfer processes in these extreme systems.