You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


---
abstract: 'Mass discrepancy is one of the problems that is pending a solution in (massive) binary star research field. The problem is often solved by introducing an additional near core mixing into evolutionary models, which brings theoretical masses of individual stellar components into an agreement with the dynamical ones. In the present study, we perform a detailed analysis of two massive binary systems, V380Cyg and $\sigma$ Sco, to provide an independent, asteroseismic measurement of the overshoot parameter, and to test state-of-the-art stellar evolution models.'
bibliography:
- 'MyBiblio.bib'
---

Introduction
============

One of the major problems that is currently pending a solution in binary star research field is the so-called mass discrepancy problem. It stands for the difference between the component masses inferred from binary dynamics (hereafter, dynamical masses) and those obtained from spectral characteristics of stars and evolutionary models (hereafter, theoretical masses). The mass discrepancy problem observed in massive O- and B-type stars has been known for more than 20 years already and has been discussed in detail by @Herrero1992. @Hilditch2004 pointed out that the discrepancy does not disappear when the effects of rotation are included into the models.

A remarkable mass discrepancy has been reported by @Guinan2000 for the primary components of the V380Cyg system. The authors showed that large amount of core overshoot ($\alpha_{ov}$ = 0.6 pressure scale height) can account for the difference between dynamical and theoretical mass of the primary component. This large amount of overshoot contradicts the typical value of $\alpha_{ov} <= 0.2$ Hp observed for single stars of similar mass (see e.g. Aerts 2013, Aerts et al. 2003, 2011; Briquet et al. 2011). Moreover, the second largest value after V380Cyg of $\alpha_{ov}\sim$0.45 has also been measured in a binary system, for the 8 M$_{\odot}$ primary component of the $\theta$ Ophiuchi system [@Briquet2007]. Recently, @Garcia2014 found that convective overshoot $\alpha_{ov}>$0.35 is required to reproduce observed absolute dimensions of both components of the V578Mon system. Thus, there seems to be a tendency of measuring larger core overshoot in binary stars than in single objects, within the same stellar mass range. The reason is that this parameter often effectively accounts for the above mentioned mass discrepancy, but we need to investigate the feasibility of using core overshoot alone to explain such a complex problem as discrepancy between dynamical and theoretical masses in binary stars.

In this paper, we present a study of two massive binary star systems, V380Cyg and $\sigma$ Sco, and aim at measuring core overshoot parameter for pulsating components using asteroseismic methods.

  -------------------------- --------------- ----------------- ----------------- ---------------- ----------------
                                                                                                  
                                                **Primary**      **Secondary**     **Primary**     **Secondary**
  Period,                    (day)                                                                
  Periastron passage time,   (HJD)                                                                
  Periastron long.,          (degree)                                                             
  eccentricity,                                                                                   
  RV semi-amplitude,         (kms$^{-1}$)     93.54$\pm$0.07    152.71$\pm$0.22   30.14$\pm$0.35   47.01$\pm$0.98
  Mass,                      (M$_{\odot}$)    11.43$\pm$0.19     7.00$\pm$0.14     14.7$\pm$4.5     9.5$\pm$2.9
  Radius,                    (R$_{\odot}$)    15.71$\pm$0.13    3.819$\pm$0.048    9.2$\pm$1.9      4.2$\pm$1.0
  $T_{\rm eff}$,             (K)               21700$\pm$300    22700$\pm$1200    25200$\pm$1500   25000$\pm$2400
  $\log$$g$,                 (dex)            3.104$\pm$0.006   4.120$\pm$0.011   3.68$\pm$0.15    4.16$\pm$0.15
  v$\sin$i,                  (kms$^{-1}$)        98$\pm$2          38$\pm$2        31.5$\pm$4.5     43.0$\pm$4.5
  -------------------------- --------------- ----------------- ----------------- ---------------- ----------------

  : Key orbital, physical, and atmospheric parameters of the V380Cyg and $\sigma$ Sco systems, as derived from our photometric and/or spectroscopic data.[]{data-label="tab1"}

V380Cyg\[V380Cyg\]
==================

V380Cyg is a bright ($V$ = 5.68) double-lined spectroscopic binary [SB2, @Hill1984] consisting of two B-type stars residing in an eccentric 12.4 day orbit. The primary component is an evolved star, whereas the secondary just started its life on the main-sequence. @Pavlovski2009 revisited the [*U, B, V*]{} light curves obtained by @Guinan2000 and collected about 150 high-resolution échelle spectra using several telescopes. The authors presented a revised orbital solution, and used spectral disentangling technique [@Simon1994] formulated in Fourier space [@Hadrava1995], as implemented in the [fdbinary]{} code [@Ilijic2004], to determine disentangled spectra of both binary components. Similar to the results of @Guinan2000, a remarkable mass discrepancy was found for the primary component of V380Cyg. Moreover, @Pavlovski2009 came to the same conclusion as @Hilditch2004 did, namely that the effects of rotation included into evolutionary models could not fully account for the observed discrepancy.

The discovery of seismic signal in the primary component of V380Cyg [@Tkachenko2012] opened up an opportunity of obtaining an independent measurement of the overshoot parameter for this binary system. We base our analysis on about 560 days long time-series of high-precision [*Kepler*]{} photometry, and about 400 high-resolution, high signal-to-noise ratio (S/N) spectra obtained with [hermes]{} spectrograph [@Raskin2011] attached to 1.2-meter Mercator telescope (La Palma, Canary Islands).

The effects of binarity in the [*Kepler*]{} light curve were modelled using the [jktwd]{} wrapper [@Southworth2011] of the 2004 version of the Wilson-Devinney code [@Wilson1971; @Wilson1979]. The time-series of spectra were analysed with the [fdbinary]{} code to determine spectroscopic orbital solution and disentangled spectra of both stellar components. We found that light curve yields poor constraints on the shape of the orbit, because of strong correlation between eccentricity $e$ and longitude of periastron $\omega$. Since the quantities $e\,\cos \omega$ and $e\,\sin \omega$ are respectively well constrained from photometry and spectroscopy, we constrained the orbital shape by iterating between the two analyses: the light curve was used to determine best fit $\omega$ for a given $e$, and the spectral disentangling to find the best $e$ for a given $\omega$. Analysis of the disentangled spectra delivered accurate atmospheric parameters and individual abundances for both binary components. Table \[tab1\] lists some key orbital, physical, and atmospheric properties of this binary system; for more details, reader is referred to @Tkachenko2014a.

![image](V380_Cyg_tracks.pdf) ![image](Sigma_Sco_tracks.pdf)

  ---------------- --------------- --------- --------- --------- --------- --------- ---------
                                                                                     
                                   Model 1   Model 2   Model 3   Model 1   Model 2   Model 3
  M,               (M$_{\odot}$)   11.43     12.00     12.90     7.00      7.42      7.42
  $Z$,             (dex)           0.014     0.012     0.012     0.014     0.012     0.012
  $\alpha_{ov}$,   (H$_{\rm p}$)   0.2       0.6       0.3       0.2       0.6       0.2
  $\upsilon$,      (kms$^{-1}$)    0         241       243       0         0         0
  Age,             (Myr)           –         21.5      18        –         21.5      18
  ---------------- --------------- --------- --------- --------- --------- --------- ---------

  : Evolutionary model parameters for both components of the V380Cyg system. $\alpha_{ov}$ and $\upsilon$ stand for the overshoot parameter and initial rotation rate, respectively.[]{data-label="tab2"}

Photometric residuals obtained after the subtraction of our best fit model were subjected for frequency analysis. The majority of the frequencies are variable both in appearance and amplitude, in agreement with the conclusions made by @Tkachenko2012 about stochastic nature of the signal. The variability consistent with the expected rotation period of the primary component has been detected on top of the binarity and stochastic oscillation signals in the star. We speculate that this signal comes from rotational modulation of spot-like chemical abundance or temperature structures on the surface of the primary component. To verify this hypothesis, spectral line profiles of the primary has been examined for spot signatures, after subtracting the contribution of the companion star from the composite spectra of V380Cyg. We found a remarkable variability in all observed silicon lines of more massive binary component, which could not be detected in spectral lines of other chemical elements and was found to be consistent with the rotational period of the star. [invers8]{} [@Piskunov1993] code was used to perform Doppler Imaging analysis based on several prominent lines of doubly ionized silicon found in the spectrum of the primary component. The obtained results suggest the presence of two high-contrast stellar surface abundance spots which are located either at the same latitude or longitude.

Finally, we compare our revised fundamental stellar parameters of both components of the V380Cyg system with the state-of-the-art evolutionary models computed with the [mesa]{} code [@Paxton2011; @Paxton2013]. Figure \[fig1\] (left) shows the location of both components of V380Cyg in the $T_{\rm
eff}$–-$\log$$g$ diagram along with the evolutionary tracks. The two models that fit the positions of both stars in the diagram, taking into account the error bars, are illustrated by long- and short-dashed lines (models 2 and 3 in Table \[tab2\], respectively). The dynamical mass models for both binary components are shown by solid lines (model 1 in Table \[tab2\]). The [mesa]{} model predictions clearly point to mass discrepancy for the primary component, in agreement with the findings by @Guinan2000 and @Pavlovski2009. **We conclude that present-day single-star evolutionary models are inadequate for this particular binary system, and lack a serious amount of near-core mixing.**

$\sigma$ Sco
============

Sigma Scorpii is a double-lined spectroscopic binary in a quadruple system. Two components are early B-type stars, residing in an eccentric, 33 day period orbit. Though the star was a subject of numerous photometric and spectroscopic studies in the middle of 20th century, its double-lined nature was discovered by @Mathias1991. So far, the studies by @Mathias1991, @Pigulski1992, and @North2007 have been the most extensive ones focusing on orbital and physical properties of the system.

Besides the $\sigma$ Sco system is a spectroscopic binary, its evolved primary component is known to be unstable to $\beta$ Cep-type stellar pulsations. Moreover, according to @Kubiak1980, the amplitude of the dominant, radial pulsation mode of the primary is comparable to the orbital semi-amplitude $K_1$ of this star. This fact was not taken into account in either of the previous studies focusing on orbital solution, but is taken into consideration in our study.

Our analysis is based on some 1000 high-resolution spectra collected with the CORALIE spectrograph attached to the 1.2-meter Euler Swiss Telescope (La Silla, Chile). Orbital parameters of the system were initially derived based on an iterative approach, and further on refined using the method of spectral disentangling. The spectral disentangling was applied to a couple of dozen carefully selected spectra and corresponding to a zero pulsation phase (unperturbed profile), since the method assumes no variability intrinsic to stellar components forming a binary system. For more details on the procedure, reader is referred to @Tkachenko2014b. The disentangled spectra were used to determine accurate atmospheric parameters and chemical composition of both stars. The final set of orbital parameters as well as the spectroscopically derived values of $T_{\rm eff}$ and $\log$$g$ are given in Table \[tab1\]. The masses and radii listed in this table were determined from our orbital parameters and interferometric value of the orbital inclination angle reported by @North2007.

  --------------------------- --------------- ------------------------ ---------------------------------
  Mass,                       (M$_{\odot}$)   13.5$^{+0.5}_{-1.4}$     8.7$^{+0.6}_{-1.2}$
  Radius,                     (R$_{\odot}$)   8.95$^{+0.43}_{-0.66}$   3.90$^{+0.58}_{-0.36}$
  Luminosity ($\log$($L$)),   (L$_{\odot}$)   4.38$^{+0.07}_{-0.15}$   3.73$^{+0.13}_{-0.15}$
  Age of the system,          (Myr)                                    
  Overshoot ($f_{ov}$),       (H$_{\rm p}$)   0.000$^{+0.015}$         
  $T_{\rm eff}$,              (K)             23945$^{+500}_{-990}$    **25000$^{+2\,400}_{-2\,400}$**
  $\log$$g$,                  (dex)           3.67$^{+0.01}_{-0.03}$   **4.16$^{+0.15}_{-0.15}$**
  --------------------------- --------------- ------------------------ ---------------------------------

  : Fundamental parameters of both components of the $\sigma$ Sco, after seismic modelling of the primary. Parameters determined spectroscopically are highlighted in boldface.[]{data-label="tab3"}

We further made use of the fact that the primary component of $\sigma$ Sco is a radial mode pulsator, and performed asteroseismic analysis of this star. Evolutionary models were computed with the [mesa]{} code, while p- and g-mode eigenfrequencies for mode degrees $l=0$ to 3 have been calculated in the adiabatic approximation with the [gyre]{} stellar oscillation code [@Townsend2013]. The addition of the seismic constraints to the modelling implied a drastic reduction in the uncertainties of the fundamental parameters, and provided an age estimate (see Table \[tab3\]). Figure \[fig1\] (right) shows the position of both components of the $\sigma$ Sco system in the $T_{\rm
eff}$–$\log$$g$ diagram, along with the evolutionary tracks. The error bars are those obtained from the evolutionary models and 3$\sigma$ spectroscopic uncertainties for the primary and secondary, respectively. **Though we make an a priori assumption in our seismic modelling that the models are appropriate for the primary component, similar to the case of V380Cyg, we still find mass discrepancy for the main-sequence secondary component of the $\sigma$ Sco system.**