Nazarin Tsarin Taurari Biyu Masu Haɗuwa Guda Goma sha Ɗaya Masu Ƙarancin Ma'auni

2.1 Duban Hasken Taurari

An gudanar da duban hasken taurari na bandeji da yawa ga duk tsarin goma sha ɗaya ta amfani da na'urorin hangen nesa na ƙasa. Duban ya rufe cikakkun zagayowar kewayawa don tabbatar da ingantaccen binciken lanƙwan haske.

2.2 Binciken Wilson-Devinney

An yi amfani da shirin Wilson-Devinney don samar da mafita na auna haske, gami da ma'auni, abubuwan cikawa, da bambancin zafin jiki tsakanin sassan. Binciken ya yi amfani da ma'auni masu mahimmanci masu zuwa:

• Ma'auni ($q = m_2/m_1$)
• Ma'aunin cikawa ($f$)
• Karkatar kewayawa ($i$)
• Ma'aunin zafin jiki ($T_2/T_1$)

2.3 Binciken Bakan Hasken Taurari

An bincika bakan hasken LAMOST mai ƙaramin ƙuduri na abubuwa huɗu ta amfani da dabarun raguwa don gano aikin Layer na Hasken Taurari ta hanyar fitowar H𝛼.

3.1 Rarraba Tsarin

A cikin tsarin goma sha ɗaya, an gano biyu a matsayin W-subtype (CRTS J133031.1+161202 da CRTS J154254.0+324652), yayin da sauran tsarin tara sun kasance A-subtype. Ma'aunin cikawa ya kasance daga 18.9% (CRTS J155009.2+493639) zuwa 94.3% (CRTS J154254.0+324652).

3.2 Binciken Ma'auni

Duk tsarin goma sha ɗaya sun nuna ma'auni ƙasa da 0.1, wanda ke rarraba su azaman tsarin taurari biyu masu haɗuwa masu ƙarancin ma'auni (ELMR). Wannan halayen ya sa su zama ƴan takara masu yuwuwa don abubuwan haɗuwa na gaba.

3.3 Sauye-sauyen Lokaci

Binciken lokaci ya bayyana tsarin uku masu raguwar lokutan kewayawa, mai yiwuwa saboda asarar ƙarfin juzu'i, da tsarin shida masu ƙaruwar lokuta, suna nuna canja wurin taro daga sassa na biyu zuwa na farko.

3.4 Ayyukan Layer na Hasken Taurari

An gano fitowar H𝛼 a cikin tsarin huɗu ta hanyar raguwa, yana nuna muhimmin aikin Layer na Hasken Taurari da yuwuwar zagayowar aikin maganadisu.

4.1 Tsarin Lissafi

An ƙididdige ma'aunin rashin kwanciyar hankali ta amfani da dabarar da aka samo daga Rasio (1995):

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

inda $q$ shine ma'auni, $R_1$ shine radius na farko, kuma $a$ shine rabuwar kewayawa.

Ma'aunin ƙarfin juzu'i zuwa ƙarfin juzu'in kewayawa ana bayar da shi ta:

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

4.2 Sakamakon Gwaji

Zane-zanen taro-haske da taro-radius sun bayyana cewa sassan farko suna bin ci gaban jerin asali, yayin da sassan na biyu suke sama da Tsayayyen Lokacin Jerin Asali (TAMS), suna nuna ƙarfin haske. Wannan yana nuna matakan ci gaba da ci gaba da tasirin canja wurin taro.

Hoto na 1: Zanen Taro-Radius yana nuna sassan farko akan jerin asali da sassan na biyu sama da TAMS.

Hoto na 2: Mafita na lanƙwan haske don CRTS J154254.0+324652 yana nuna ma'aunin cikawa na 94.3%.

4.3 Aiwar Code

# 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 Matsayin Ci Gaba

Binciken ya nuna cewa sassan farko suna cikin ci gaban jerin asali, yayin da sassan na biyu ke nuna shaidar kasancewa sama da TAMS. Wannan ƙarfin haske yana nuna matakan ci gaba da ci gaba da tarihin canja wurin taro mai mahimmanci.

5.2 Binciken Kwanciyar Hankali

Lissafin ma'auni $J_s/J_o$ da ma'aunin rashin kwanciyar hankali yana nuna cewa CRTS J234634.7+222824 yana kan gab da haɗuwa. Wannan ya yi daidai da hasashen ka'idoji na Rasio (1995) da Eggleton & Kiseleva-Eggleton (2001) game da makomar tsarin taurari biyu masu haɗuwa mai zurfi tare da ma'auni mai ƙarfi.

5.3 Bincike na Asali

Wannan binciken na tsarin taurari biyu masu haɗuwa guda goma sha ɗaya masu ƙarancin ma'auni yana ba da mahimman bayanai game da ci gaban ƙarshe na tsarin taurari biyu masu kusanci. Gano tsarin da ma'auni ƙasa da 0.1 yana ƙalubalantar fahimtar al'ada na kwanciyar hankali na tsarin taurari biyu masu haɗuwa. Kamar yadda aka lura a cikin bayanan taurari biyu na Ƙungiyar Taurari ta Duniya, irin waɗannan tsare-tsaren masu tsanani ba su da yawa amma suna da mahimmanci don fahimtar hanyoyin haɗuwar taurari.

Gano CRTS J234634.7+222824 a matsayin kan gab da haɗuwa ya yi daidai da samfurin ka'idoji da ke hasashen cewa tsarin tare da $q < q_{inst}$ da manyan ma'aunin cikawa za su fuskanci rashin kwanciyar hankali. Wannan al'amari yana kama da ma'aunin rashin kwanciyar hankali da aka tattauna a cikin aikin farko na Rasio & Shapiro (1995) akan haɗuwar tsarin taurari biyu masu ƙarfi.

Kwatanta waɗannan sakamako tare da cikakken binciken Qian et al. (2017) akan ci gaban tsarin taurari biyu masu haɗuwa yana bayyana alamu masu daidaitawa a cikin sauye-sauyen lokaci da hanyoyin canja wurin taro. Gano fitowar H𝛼 a cikin tsarin huɗu yana ba da shaida kai tsaye na aikin Layer na Hasken Taurari, kama da binciken da aka samu a cikin aikin duban H-K na Mount Wilson Observatory wanda ke sa ido kan tsarin taurari biyu masu aiki.

Ƙarfin haske na sassan na biyu sama da TAMS yana nuna hanyoyin ci gaba masu rikitarwa, mai yiwuwa sun haɗa da saurin canja wurin taro. Wannan abin lura yana goyan bayan samfuran canja wurin taro da Eggleton & Kisseleva-Eggleton (2006) suka gabatar don ci gaban tsarin taurari biyu. Manyan ma'aunin cikawa (har zuwa 94.3%) suna nuna cewa waɗannan tsare-tsaren suna cikin matakan haɗuwa na ci gaba, mai yiwuwa kafin abubuwan haɗuwa waɗanda zasu iya haifar da taurarin FK Com ko masu shuɗi, kamar yadda aka rubuta a cikin binciken globular cluster na Kaluzny & Shara (1988).

Duban gaba tare da manyan kayan aiki kamar James Webb Space Telescope na iya ba da mafi girman bayanan bakan haske don ƙarin fahimtar yanayin yanayi da hanyoyin canja wurin taro a cikin waɗannan tsare-tsaren masu tsanani.