Properize

properize

Authors:
(1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany;
(2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany;
(3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany;
(4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Numerical Example Conclusion and References IV. CONVERGENCE PROPERTIES We start with the following lemmas that are essential for the proofs presented in the paper. For the first term on the right-hand side of (21), we have which can then be used to obtain This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Authors: Authors: (1) Halil Yigit Oksuz, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany; (2) Fabio Molinari, Control Systems Group at Technische Universitat Berlin, Germany; (3) Henning Sprekeler, Exzellenzcluster Science of Intelligence, Technische Universit¨at Berlin, Marchstr. 23, 10587, Berlin, Germany and Modelling Cognitive Processes Group at Technische Universit¨at Berlin, Germany; (4) Jorg Raisch, Control Systems Group at Technische Universitat Berlin, Germany and Exzellenzcluster Science of Intelligence, Technische Universitat Berlin, Marchstr. 23, 10587, Berlin, Germany. Table of Links Abstract and Introduction Abstract and Introduction Problem Setup Problem Setup Federated fair over-the-air learning (FedAir) Algorithm Federated fair over-the-air learning (FedAir) Algorithm Convergence Properties Convergence Properties Numerical Example Numerical Example Conclusion and References Conclusion and References IV. CONVERGENCE PROPERTIES We start with the following lemmas that are essential for the proofs presented in the paper. For the first term on the right-hand side of (21), we have which can then be used to obtain This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Boosting Fairness and Robustness in Over-the-Air Federated Learning: Convergence Properties

Hello! My name is Artem and I am the author of the Android Insights YouTube channel Today we will enter the world of delegates and delegated properties in Kotlin. This topic might seem complex at first glance, but I'll do my best to explain it as clearly as possible. Let's get started! What Are Delegates? Before going into the details, let's clarify some fundamental concepts. A delegate is an object that another object, well, delegates certain tasks to. In Kotlin, delegation is a powerful tool that allows you to reuse code and implement complex behavior without the need for inheritance. Example of Delegation Let's consider a simple example: interface Base {
    fun print()
}

class BaseImpl(private val x: Int) : Base {
    override fun print() {
        println(x)
    }
}

class Derived(b: Base) : Base by b

fun main() {
    val b = BaseImpl(10)
    Derived(b).print() // Outputs: 10
} In this example: We define an interface Base with a method print().
The class BaseImpl implements this interface and holds a value x.
The class Derived delegates the implementation of Base to the object b. When we call print() on an instance of Derived, it actually executes the print() method of the BaseImpl object. This allows us to reuse code and add flexibility to the application's architecture without excessive inheritance. Delegated Properties Now, let's discuss delegated properties. A delegated property is a property that delegates its getter and setter to another object. The syntax for declaring a delegated property looks like this: class Example {
    var p: String by Delegate()
} Here, p is a delegated property. All accesses to p will be redirected to the Delegate() object. Built-in Delegates in Kotlin Kotlin provides several built-in delegates that simplify common tasks. lazy — Lazy Initialization The lazy delegate is used for lazy initialization of a property. The value is computed only upon the first access. val lazyValue: String by lazy {
    println("Computing the value...")
    "Hello"
}

fun main() {
    println(lazyValue) // Outputs: Computing the value... Hello
    println(lazyValue) // Outputs: Hello
} In this example, when we first access lazyValue, the code block inside lazy is executed, and the value is stored for subsequent uses. observable — Observable Property The observable delegate allows you to track changes to a property and react accordingly. import kotlin.properties.Delegates

var name: String by Delegates.observable("Initial value") { prop, old, new ->
    println("$old -> $new")
}

fun main() {
    name = "First"   // Outputs: Initial value -> First
    name = "Second"  // Outputs: First -> Second
} Here, every time name changes, the code block is executed, printing the old and new values. Creating Custom Delegates In addition to built-in delegates, we can create custom delegates to implement specific behavior. This can be done using the ReadOnlyProperty and ReadWriteProperty interfaces, or by directly implementing the getValue and setValue operators. Using ReadOnlyProperty Let's create a delegate that always returns the same value and logs each access. import kotlin.properties.ReadOnlyProperty
import kotlin.reflect.KProperty

class ConstantValue<T>(private val value: T) : ReadOnlyProperty<Any?, T> {
    override fun getValue(thisRef: Any?, property: KProperty<*>): T {
        println("Getting value of property '${property.name}'")
        return value
    }
}

class Example {
    val constant: String by ConstantValue("Hello, World!")
}

fun main() {
    val example = Example()
    println(example.constant)
    // Outputs:
    // Getting value of property 'constant'
    // Hello, World!
} Using ReadWriteProperty Now let's create a delegate that logs read and write operations of a property. import kotlin.properties.ReadWriteProperty
import kotlin.reflect.KProperty

class LoggingProperty<T>(private var value: T) : ReadWriteProperty<Any?, T> {
    override fun getValue(thisRef: Any?, property: KProperty<*>): T {
        println("Getting value of property '${property.name}': $value")
        return value
    }

    override fun setValue(thisRef: Any?, property: KProperty<*>, newValue: T) {
        println("Setting value of property '${property.name}' to $newValue")
        value = newValue
    }
}

class Example {
    var logged: String by LoggingProperty("Initial")
}

fun main() {
    val example = Example()
    println(example.logged)
    example.logged = "New Value"
    println(example.logged)
    // Outputs:
    // Getting value of property 'logged': Initial
    // Initial
    // Setting value of property 'logged' to New Value
    // Getting value of property 'logged': New Value
    // New Value
} Using ReadOnlyProperty and ReadWriteProperty allows us to explicitly indicate which operations the delegate supports, making the code more readable and understandable. Direct Implementation of getValue and setValue Alternatively, we can directly implement the getValue and setValue operators. import kotlin.reflect.KProperty

class StringDelegate {
    private var value: String = ""

    operator fun getValue(thisRef: Any?, property: KProperty<*>): String {
        println("Getting value of property '${property.name}'")
        return value
    }

    operator fun setValue(thisRef: Any?, property: KProperty<*>, newValue: String) {
        println("Setting value of property '${property.name}' to $newValue")
        value = newValue
    }
}

class Example {
    var str: String by StringDelegate()
}

fun main() {
    val example = Example()
    example.str = "Hello"
    println(example.str)
    // Outputs:
    // Setting value of property 'str' to Hello
    // Getting value of property 'str'
    // Hello
} This approach offers more flexibility, allowing us to implement only the necessary methods for our purposes. Practical Applications of Delegates Let's explore some practical scenarios where delegates can be particularly useful. Lazy Initialization of Resource-Intensive Objects The lazy delegate is perfect for deferred initialization of objects whose creation requires significant resources. class ResourceManager {
    val database by lazy {
        println("Connecting to the database...")
        Database.connect()
    }
}

fun main() {
    val manager = ResourceManager()
    println("ResourceManager created")
    // The database is not initialized yet
    manager.database.query("SELECT * FROM users")
    // The database is already initialized
    manager.database.query("SELECT * FROM products")
} In this example, the connection to the database occurs only upon the first access to database, conserving resources until they are actually needed. Implementing the Observer Pattern With the observable delegate, we can easily implement the Observer pattern by tracking property changes. import kotlin.properties.Delegates

class User {
    var name: String by Delegates.observable("") { prop, old, new ->
        println("User's name changed from '$old' to '$new'")
    }
}

fun main() {
    val user = User()
    user.name = "Alice"  // Outputs: User's name changed from '' to 'Alice'
    user.name = "Bob"    // Outputs: User's name changed from 'Alice' to 'Bob'
} This allows us to perform specific actions when properties change, such as updating the UI, validating data, or sending notifications. Conclusion Delegates are a powerful tool in the Kotlin developer's arsenal. They enable you to write cleaner, more modular, and flexible code, opening up new possibilities for implementing complex logic and design patterns. I hope this guide has helped you better understand delegates and delegated properties in Kotlin. Feel free to experiment and apply these concepts in your own projects! Thank you for your attention, and happy coding! Hello! My name is Artem and I am the author of the Android Insights YouTube channel Android Insights Today we will enter the world of delegates and delegated properties in Kotlin . This topic might seem complex at first glance, but I'll do my best to explain it as clearly as possible. Let's get started! Kotlin What Are Delegates? Before going into the details, let's clarify some fundamental concepts. A delegate is an object that another object, well, delegates certain tasks to. In Kotlin , delegation is a powerful tool that allows you to reuse code and implement complex behavior without the need for inheritance. Kotlin Example of Delegation Let's consider a simple example: Let's consider a simple example: interface Base {
    fun print()
}

class BaseImpl(private val x: Int) : Base {
    override fun print() {
        println(x)
    }
}

class Derived(b: Base) : Base by b

fun main() {
    val b = BaseImpl(10)
    Derived(b).print() // Outputs: 10
} interface Base {
    fun print()
}

class BaseImpl(private val x: Int) : Base {
    override fun print() {
        println(x)
    }
}

class Derived(b: Base) : Base by b

fun main() {
    val b = BaseImpl(10)
    Derived(b).print() // Outputs: 10
} In this example: We define an interface Base with a method print(). The class BaseImpl implements this interface and holds a value x. The class Derived delegates the implementation of Base to the object b. We define an interface Base with a method print() . Base print() The class BaseImpl implements this interface and holds a value x . BaseImpl x The class Derived delegates the implementation of Base to the object b . Derived Base b When we call print() on an instance of Derived , it actually executes the print() method of the BaseImpl object. This allows us to reuse code and add flexibility to the application's architecture without excessive inheritance. print() Derived print() BaseImpl Delegated Properties Now, let's discuss delegated properties. A delegated property is a property that delegates its getter and setter to another object. The syntax for declaring a delegated property looks like this: class Example {
    var p: String by Delegate()
} class Example {
    var p: String by Delegate()
} Here, p is a delegated property. All accesses to p will be redirected to the Delegate() object. p p Delegate() Built-in Delegates in Kotlin Kotlin provides several built-in delegates that simplify common tasks. lazy — Lazy Initialization lazy The lazy delegate is used for lazy initialization of a property. The value is computed only upon the first access. lazy val lazyValue: String by lazy {
    println("Computing the value...")
    "Hello"
}

fun main() {
    println(lazyValue) // Outputs: Computing the value... Hello
    println(lazyValue) // Outputs: Hello
} val lazyValue: String by lazy {
    println("Computing the value...")
    "Hello"
}

fun main() {
    println(lazyValue) // Outputs: Computing the value... Hello
    println(lazyValue) // Outputs: Hello
} In this example, when we first access lazyValue , the code block inside lazy is executed, and the value is stored for subsequent uses. lazyValue lazy observable — Observable Property observable The observable delegate allows you to track changes to a property and react accordingly. observable import kotlin.properties.Delegates

var name: String by Delegates.observable("Initial value") { prop, old, new ->
    println("$old -> $new")
}

fun main() {
    name = "First"   // Outputs: Initial value -> First
    name = "Second"  // Outputs: First -> Second
} import kotlin.properties.Delegates

var name: String by Delegates.observable("Initial value") { prop, old, new ->
    println("$old -> $new")
}

fun main() {
    name = "First"   // Outputs: Initial value -> First
    name = "Second"  // Outputs: First -> Second
} Here, every time name changes, the code block is executed, printing the old and new values. name Creating Custom Delegates In addition to built-in delegates, we can create custom delegates to implement specific behavior. This can be done using the ReadOnlyProperty and ReadWriteProperty interfaces, or by directly implementing the getValue and setValue operators. ReadOnlyProperty ReadWriteProperty getValue setValue Using ReadOnlyProperty ReadOnlyProperty Let's create a delegate that always returns the same value and logs each access. import kotlin.properties.ReadOnlyProperty
import kotlin.reflect.KProperty

class ConstantValue<T>(private val value: T) : ReadOnlyProperty<Any?, T> {
    override fun getValue(thisRef: Any?, property: KProperty<*>): T {
        println("Getting value of property '${property.name}'")
        return value
    }
}

class Example {
    val constant: String by ConstantValue("Hello, World!")
}

fun main() {
    val example = Example()
    println(example.constant)
    // Outputs:
    // Getting value of property 'constant'
    // Hello, World!
} import kotlin.properties.ReadOnlyProperty
import kotlin.reflect.KProperty

class ConstantValue<T>(private val value: T) : ReadOnlyProperty<Any?, T> {
    override fun getValue(thisRef: Any?, property: KProperty<*>): T {
        println("Getting value of property '${property.name}'")
        return value
    }
}

class Example {
    val constant: String by ConstantValue("Hello, World!")
}

fun main() {
    val example = Example()
    println(example.constant)
    // Outputs:
    // Getting value of property 'constant'
    // Hello, World!
} Using ReadWriteProperty ReadWriteProperty Now let's create a delegate that logs read and write operations of a property. import kotlin.properties.ReadWriteProperty
import kotlin.reflect.KProperty

class LoggingProperty<T>(private var value: T) : ReadWriteProperty<Any?, T> {
    override fun getValue(thisRef: Any?, property: KProperty<*>): T {
        println("Getting value of property '${property.name}': $value")
        return value
    }

    override fun setValue(thisRef: Any?, property: KProperty<*>, newValue: T) {
        println("Setting value of property '${property.name}' to $newValue")
        value = newValue
    }
}

class Example {
    var logged: String by LoggingProperty("Initial")
}

fun main() {
    val example = Example()
    println(example.logged)
    example.logged = "New Value"
    println(example.logged)
    // Outputs:
    // Getting value of property 'logged': Initial
    // Initial
    // Setting value of property 'logged' to New Value
    // Getting value of property 'logged': New Value
    // New Value
} import kotlin.properties.ReadWriteProperty
import kotlin.reflect.KProperty

class LoggingProperty<T>(private var value: T) : ReadWriteProperty<Any?, T> {
    override fun getValue(thisRef: Any?, property: KProperty<*>): T {
        println("Getting value of property '${property.name}': $value")
        return value
    }

    override fun setValue(thisRef: Any?, property: KProperty<*>, newValue: T) {
        println("Setting value of property '${property.name}' to $newValue")
        value = newValue
    }
}

class Example {
    var logged: String by LoggingProperty("Initial")
}

fun main() {
    val example = Example()
    println(example.logged)
    example.logged = "New Value"
    println(example.logged)
    // Outputs:
    // Getting value of property 'logged': Initial
    // Initial
    // Setting value of property 'logged' to New Value
    // Getting value of property 'logged': New Value
    // New Value
} Using ReadOnlyProperty and ReadWriteProperty allows us to explicitly indicate which operations the delegate supports, making the code more readable and understandable. ReadOnlyProperty ReadWriteProperty Direct Implementation of getValue and setValue getValue setValue Alternatively, we can directly implement the getValue and setValue operators. getValue setValue import kotlin.reflect.KProperty

class StringDelegate {
    private var value: String = ""

    operator fun getValue(thisRef: Any?, property: KProperty<*>): String {
        println("Getting value of property '${property.name}'")
        return value
    }

    operator fun setValue(thisRef: Any?, property: KProperty<*>, newValue: String) {
        println("Setting value of property '${property.name}' to $newValue")
        value = newValue
    }
}

class Example {
    var str: String by StringDelegate()
}

fun main() {
    val example = Example()
    example.str = "Hello"
    println(example.str)
    // Outputs:
    // Setting value of property 'str' to Hello
    // Getting value of property 'str'
    // Hello
} import kotlin.reflect.KProperty

class StringDelegate {
    private var value: String = ""

    operator fun getValue(thisRef: Any?, property: KProperty<*>): String {
        println("Getting value of property '${property.name}'")
        return value
    }

    operator fun setValue(thisRef: Any?, property: KProperty<*>, newValue: String) {
        println("Setting value of property '${property.name}' to $newValue")
        value = newValue
    }
}

class Example {
    var str: String by StringDelegate()
}

fun main() {
    val example = Example()
    example.str = "Hello"
    println(example.str)
    // Outputs:
    // Setting value of property 'str' to Hello
    // Getting value of property 'str'
    // Hello
} This approach offers more flexibility, allowing us to implement only the necessary methods for our purposes. Practical Applications of Delegates Let's explore some practical scenarios where delegates can be particularly useful. Lazy Initialization of Resource-Intensive Objects The lazy delegate is perfect for deferred initialization of objects whose creation requires significant resources. lazy class ResourceManager {
    val database by lazy {
        println("Connecting to the database...")
        Database.connect()
    }
}

fun main() {
    val manager = ResourceManager()
    println("ResourceManager created")
    // The database is not initialized yet
    manager.database.query("SELECT * FROM users")
    // The database is already initialized
    manager.database.query("SELECT * FROM products")
} class ResourceManager {
    val database by lazy {
        println("Connecting to the database...")
        Database.connect()
    }
}

fun main() {
    val manager = ResourceManager()
    println("ResourceManager created")
    // The database is not initialized yet
    manager.database.query("SELECT * FROM users")
    // The database is already initialized
    manager.database.query("SELECT * FROM products")
} In this example, the connection to the database occurs only upon the first access to database , conserving resources until they are actually needed. database Implementing the Observer Pattern With the observable delegate, we can easily implement the Observer pattern by tracking property changes. observable import kotlin.properties.Delegates

class User {
    var name: String by Delegates.observable("") { prop, old, new ->
        println("User's name changed from '$old' to '$new'")
    }
}

fun main() {
    val user = User()
    user.name = "Alice"  // Outputs: User's name changed from '' to 'Alice'
    user.name = "Bob"    // Outputs: User's name changed from 'Alice' to 'Bob'
} import kotlin.properties.Delegates

class User {
    var name: String by Delegates.observable("") { prop, old, new ->
        println("User's name changed from '$old' to '$new'")
    }
}

fun main() {
    val user = User()
    user.name = "Alice"  // Outputs: User's name changed from '' to 'Alice'
    user.name = "Bob"    // Outputs: User's name changed from 'Alice' to 'Bob'
} This allows us to perform specific actions when properties change, such as updating the UI, validating data, or sending notifications. Conclusion Delegates are a powerful tool in the Kotlin developer's arsenal. They enable you to write cleaner, more modular, and flexible code, opening up new possibilities for implementing complex logic and design patterns. I hope this guide has helped you better understand delegates and delegated properties in Kotlin. Feel free to experiment and apply these concepts in your own projects! Thank you for your attention, and happy coding! Thank you for your attention, and happy coding!

Delegates and Delegated Properties in Kotlin

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk);
(2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK;
(3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia;
(4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro
Observation
Orbital Ephemeris
Radial Velocity Analysis
Spectral Analysis
Analysis of the Light Curve
Physical Properties
Asteroseismic Analysis
Discussion
Conclusion, Data Availability, Acknowledgments, and References
Appendix A: Ephemeris Determination
Appendix B: Iteratively Prewhitened Frequencies
Appendix C: Detected Tidally Perturbed Pulsations 2 OBSERVATIONS 2.1 Photometry The Kepler space telescope (Koch et al. 2010) was launched in March 2009 with the primary aim of detecting Earth-like extrasolar planets around solar-like stars. However, the mission has also provided a huge amount of high-quality data on stars and stellar systems (Hong et al. 2022). The data were collected using two modes of observation (Gilliland et al. 2010), long cadence (29.5 min sampling rate) and short cadence (58.5 s sampling rate). To keep the ht). solar arrays pointed toward the Sun during its Earth-trailing heliocentric orbit, the spacecraft was rotated by 90◦ every three months (one quarter). Primary functions of the Kepler photometric analysis module of the Kepler science data processing pipeline are responsible for generating the Simple Aperture Photometric (SAP) flux time series of the observed objects, while secondary photometric analysis functions performed by the Pre-Search Data Conditioning (PDC) module support systematic error correction, giving rise to the PDCSAP fluxes (see Jenkins 2017, for further details on the SAP and PDCSAP measurements). KIC 9851944 was observed by Kepler in six quarters (0, 12, 13, 16). The light curves from the Kepler quarters and TESS sectors mentioned above were downloaded from the Mikulski Archive for Space Telescopes (MAST) and are used in Section 3 to determine the ephemeris of the system, as well as Section 6 to obtain the final model of the light curve. Both SAP and PDCSAP measurements are available; the SAP and PDCSAP fluxes were similar, which we verified by inspecting the SAP fluxes with the PDCSAP fluxes overplotted after dividing them by their median flux values to put them on the same scale. Thus, we used the SAP measurements to avoid possible biases due to the additional processing applied to the PDCSAP data. A second-order polynomial was fitted to fluxes that correspond to positions of quadrature, i.e., the maximum of the ellipsoidal brightening, to estimate systematic trends present in the light curves. Subtracting the difference between this polynomial and the median flux of the light curve yields a model for the local median level of out-of-eclipse flux. This model was then divided out to remove systematic trends. The residual value of a smoothed version of the light curve subtracted from the observed light curve was calculated and observed fluxes that deviated by more than 1% were rejected. Fluxes were converted to magnitudes and errors were propagated following Prša (2018). The short cadence Kepler light curve from Quarter 0 and the two-minute cadence TESS light curve from Sector 15, after performing these operations, are shown in the top and middle panels of Fig.1, respectively. ely. KIC 9851944 was also observed by the Wide Angle Search for Planets (WASP) telescope (Butters et al. 2010) between May 2007 and July 2010. WASP consisted of two robotic observatories, one in the Nothern Hemisphere at Observatorio del Roque de los Muchachos on La Palma and the other at the South African Astronomical Observatory (SAAO), each with eight 20 mm telescopes on a single mount. Observations of KIC 9851944 collected by WASP between May 2007 and July 2007 as well as between June 2008 and July 2008 are shown in the bottom panels of Fig.1 phase folded about the orbital period determined in Section 3. The data collected by WASP for KIC 9851944 were only used to constrain the times of primary minima when performing preliminary fits to the Kepler and TESS light curves in Section 3, to determine the orbital ephemeris. 2.2 Spectroscopy A set of 33 spectroscopic observations were obtained for the target using the Hamilton échelle spectrograph (Vogt 1987) on the Shane 3 m telescope at Lick Observatory during two observing runs, one in July 2012 and the other in June 2013. The data were obtained using CCD chip no. 4, giving a wavelength coverage of 340 – 900 nm over 89 échelle orders at a resolving power of R ≈ 60000. The data were reduced using the standard pipeline for the spectrograph (e.g. Fischer et al. 2014). Flat fields were obtained with a quartz lamp and divided from the spectra. The wavelength calibration was obtained from exposures of a thorium-argon emission lamp taken roughly every hour during the night. Details for the normalization of the one-dimensional extracted spectra are given in Sections 4 and 5 because each of those components of the analysis used different approaches. Table 1 gives the epochs of each of the 33 spectrosopic observations as well as the signal-to-noise ratio (S/N), estimated as the square root of the counts close to the peak of the best-exposed échelle order. Also given are the corresponding RVs of each component that are derived in Section 4. This paper is available on arxiv under CC 4.0 license. Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro Observation Orbital Ephemeris Radial Velocity Analysis Spectral Analysis Analysis of the Light Curve Physical Properties Asteroseismic Analysis Discussion Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Abstract and Intro Abstract and Intro Observation Observation Orbital Ephemeris Orbital Ephemeris Radial Velocity Analysis Radial Velocity Analysis Spectral Analysis Spectral Analysis Analysis of the Light Curve Analysis of the Light Curve Physical Properties Physical Properties Asteroseismic Analysis Asteroseismic Analysis Discussion Discussion Conclusion, Data Availability, Acknowledgments, and References Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Appendix C: Detected Tidally Perturbed Pulsations 2 OBSERVATIONS 2.1 Photometry The Kepler space telescope (Koch et al. 2010) was launched in March 2009 with the primary aim of detecting Earth-like extrasolar planets around solar-like stars. However, the mission has also provided a huge amount of high-quality data on stars and stellar systems (Hong et al. 2022). The data were collected using two modes of observation (Gilliland et al. 2010), long cadence (29.5 min sampling rate) and short cadence (58.5 s sampling rate). To keep the ht). solar arrays pointed toward the Sun during its Earth-trailing heliocentric orbit, the spacecraft was rotated by 90◦ every three months (one quarter). Primary functions of the Kepler photometric analysis module of the Kepler science data processing pipeline are responsible for generating the Simple Aperture Photometric (SAP) flux time series of the observed objects, while secondary photometric analysis functions performed by the Pre-Search Data Conditioning (PDC) module support systematic error correction, giving rise to the PDCSAP fluxes (see Jenkins 2017, for further details on the SAP and PDCSAP measurements). KIC 9851944 was observed by Kepler in six quarters (0, 12, 13, Kepler 16). The light curves from the Kepler quarters and TESS sectors mentioned above were downloaded from the Mikulski Archive for Space Telescopes (MAST) and are used in Section 3 to determine the ephemeris of the system, as well as Section 6 to obtain the final model of the light curve. Both SAP and PDCSAP measurements are available; the SAP and PDCSAP fluxes were similar, which we verified by inspecting the SAP fluxes with the PDCSAP fluxes overplotted after dividing them by their median flux values to put them on the same scale. Thus, we used the SAP measurements to avoid possible biases due to the additional processing applied to the PDCSAP data. A second-order polynomial was fitted to fluxes that correspond to positions of quadrature, i.e., the maximum of the ellipsoidal brightening, to estimate systematic trends present in the light curves. Subtracting the difference between this polynomial and the median flux of the light curve yields a model for the local median level of out-of-eclipse flux. This model was then divided out to remove systematic trends. The residual value of a smoothed version of the light curve subtracted from the observed light curve was calculated and observed fluxes that deviated by more than 1% were rejected. Fluxes were converted to magnitudes and errors were propagated following Prša (2018). The short cadence Kepler light curve from Quarter 0 and the two-minute cadence TESS light curve from Sector 15, after performing these operations, are shown in the top and middle panels of Fig.1, respectively. ely. KIC 9851944 was also observed by the Wide Angle Search for Planets (WASP) telescope (Butters et al. 2010) between May 2007 and July 2010. WASP consisted of two robotic observatories, one in the Nothern Hemisphere at Observatorio del Roque de los Muchachos on La Palma and the other at the South African Astronomical Observatory (SAAO), each with eight 20 mm telescopes on a single mount. Observations of KIC 9851944 collected by WASP between May 2007 and July 2007 as well as between June 2008 and July 2008 are shown in the bottom panels of Fig.1 phase folded about the orbital period determined in Section 3. The data collected by WASP for KIC 9851944 were only used to constrain the times of primary minima when performing preliminary fits to the Kepler and TESS light curves in Section 3, to determine the orbital ephemeris. 2.2 Spectroscopy A set of 33 spectroscopic observations were obtained for the target using the Hamilton échelle spectrograph (Vogt 1987) on the Shane 3 m telescope at Lick Observatory during two observing runs, one in July 2012 and the other in June 2013. The data were obtained using CCD chip no. 4, giving a wavelength coverage of 340 – 900 nm over 89 échelle orders at a resolving power of R ≈ 60000. The data were reduced using the standard pipeline for the spectrograph (e.g. Fischer et al. 2014). Flat fields were obtained with a quartz lamp and divided from the spectra. The wavelength calibration was obtained from exposures of a thorium-argon emission lamp taken roughly every hour during the night. Details for the normalization of the one-dimensional extracted spectra are given in Sections 4 and 5 because each of those components of the analysis used different approaches. Table 1 gives the epochs of each of the 33 spectrosopic observations as well as the signal-to-noise ratio (S/N), estimated as the square root of the counts close to the peak of the best-exposed échelle order. Also given are the corresponding RVs of each component that are derived in Section 4.

Physical Properties of the Eclipsing Binary KIC 9851944: Observation

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk);
(2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK;
(3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia;
(4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro
Observation
Orbital Ephemeris
Radial Velocity Analysis
Spectral Analysis
Analysis of the Light Curve
Physical Properties
Asteroseismic Analysis
Discussion
Conclusion, Data Availability, Acknowledgments, and References
Appendix A: Ephemeris Determination
Appendix B: Iteratively Prewhitened Frequencies
Appendix C: Detected Tidally Perturbed Pulsations 4 RADIAL VELOCITY ANALYSIS The spectral range between 4400–4800 Å is a suitable region to carry out the RV extraction procedure because there are many wellresolved spectral lines and the region does not contain any wide Balmer lines. Thirteen échelle orders within this range were corrected for cosmic ray spikes by first resampling onto a homogeneous wavelength grid before using a median filter to smooth them, then resampling the orders back to the original grid and subtracting them from the observed spectrum (Blanco-Cuaresma et al. 2014a). Pixels where the residual deviated by a threshold percentage, typically between 5 and 10%, were masked and their values were corrected for using linear interpolation. The appropriate value for the threshold was investigated for each order individually based on visual inspections of resulting flagged pixels. The blaze signature was removed using the method of Xu et al. (2019), where alpha shape fitting (see, Edelsbrunner et al. 1983) combined with local polynomial regression is used to estimate the continuum without dividing out important spectral features. Small errors in the continuum estimation are magnified where the blaze function approaches zero. Following Xu et al. (2019), a better estimation at the edges can be obtained by taking a weighted average in the overlapping regions and applying weights such that pixels further away from the edge within their own order are favoured. For this to be applied correctly, the orders were re-sampled onto grids with a common wavelength step so that the pixel averages were calculated for corresponding wavelength values between neighbouring orders. A useful result from the edge correction procedure is that neighbouring orders share a common edge and can be merged after truncating the orders in the centre of the overlapping regions. The following analysis was carried out after merging the 13 spectral orders with wavelengths between 4400-4800 Å using this process. The pulsating eclipsing binary KIC 9851944 Our own implementation of the TODCOR two-dimensional cross-correlation algorithm (Zucker & Mazeh 1994) was used to extract the RVs. Systematic errors arise when using the cross-correlation technique to extract RVs because neighbouring peaks and sidelobes in the doubled-peaked CCF disturb each other, and this is related to blending between the spectral lines of the two components (Andersen 1975; Latham et al. 1996). The result is that the estimated RVs may be shifted relative to the true value, where the size and direction of the shift depends on the phase (see Fig.4), i.e, the relative Doppler shifts between the components (Latham et al. 1996). This systematic error can be minimised by correcting the RVs for this effect (e.g., Latham et al. 1996; Torres et al. 1997; Torres et al. 2000; Torres & Ribas 2002; Southworth & Clausen 2007). A preliminary orbit was obtained by making an initial fit to the RVs extracted using TODCOR. A synthetic SB2 model was then produced with orbital parameters corresponding to the initial fit by Doppler shifting and adding the template spectra weighted by their relative light contributions as estimated by the resulting value for ℓB/ℓA from the initial TODCOR run. The TODCOR algorithm was then used to extract the known RVs from the synthetic SB2 model at orbital phases corresponding to the observations. The difference between the calculated RV and the known RV of the model gives an estimation for the magnitude and direction of the systematic error at that orbital phase. The correction was then added to the actual RVs measured from the observed spectra. This paper is available on arxiv under CC 4.0 license. Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro Observation Orbital Ephemeris Radial Velocity Analysis Spectral Analysis Analysis of the Light Curve Physical Properties Asteroseismic Analysis Discussion Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Abstract and Intro Abstract and Intro Observation Observation Orbital Ephemeris Orbital Ephemeris Radial Velocity Analysis Radial Velocity Analysis Spectral Analysis Spectral Analysis Analysis of the Light Curve Analysis of the Light Curve Physical Properties Physical Properties Asteroseismic Analysis Asteroseismic Analysis Discussion Discussion Conclusion, Data Availability, Acknowledgments, and References Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Appendix C: Detected Tidally Perturbed Pulsations 4 RADIAL VELOCITY ANALYSIS The spectral range between 4400–4800 Å is a suitable region to carry out the RV extraction procedure because there are many wellresolved spectral lines and the region does not contain any wide Balmer lines. Thirteen échelle orders within this range were corrected for cosmic ray spikes by first resampling onto a homogeneous wavelength grid before using a median filter to smooth them, then resampling the orders back to the original grid and subtracting them from the observed spectrum (Blanco-Cuaresma et al. 2014a). Pixels where the residual deviated by a threshold percentage, typically between 5 and 10%, were masked and their values were corrected for using linear interpolation. The appropriate value for the threshold was investigated for each order individually based on visual inspections of resulting flagged pixels. The blaze signature was removed using the method of Xu et al. (2019), where alpha shape fitting (see, Edelsbrunner et al. 1983) combined with local polynomial regression is used to estimate the continuum without dividing out important spectral features. Small errors in the continuum estimation are magnified where the blaze function approaches zero. Following Xu et al. (2019), a better estimation at the edges can be obtained by taking a weighted average in the overlapping regions and applying weights such that pixels further away from the edge within their own order are favoured. For this to be applied correctly, the orders were re-sampled onto grids with a common wavelength step so that the pixel averages were calculated for corresponding wavelength values between neighbouring orders. A useful result from the edge correction procedure is that neighbouring orders share a common edge and can be merged after truncating the orders in the centre of the overlapping regions. The following analysis was carried out after merging the 13 spectral orders with wavelengths between 4400-4800 Å using this process. The pulsating eclipsing binary KIC 9851944 The pulsating eclipsing binary KIC 9851944 The pulsating eclipsing binary KIC 9851944 Our own implementation of the TODCOR two-dimensional cross-correlation algorithm (Zucker & Mazeh 1994) was used to extract the RVs. Systematic errors arise when using the cross-correlation technique to extract RVs because neighbouring peaks and sidelobes in the doubled-peaked CCF disturb each other, and this is related to blending between the spectral lines of the two components (Andersen 1975; Latham et al. 1996). The result is that the estimated RVs may be shifted relative to the true value, where the size and direction of the shift depends on the phase (see Fig.4), i.e, the relative Doppler shifts between the components (Latham et al. 1996). This systematic error can be minimised by correcting the RVs for this effect (e.g., Latham et al. 1996; Torres et al. 1997; Torres et al. 2000; Torres & Ribas 2002; Southworth & Clausen 2007). A preliminary orbit was obtained by making an initial fit to the RVs extracted using TODCOR. A synthetic SB2 model was then produced with orbital parameters corresponding to the initial fit by Doppler shifting and adding the template spectra weighted by their relative light contributions as estimated by the resulting value for ℓB/ℓA from the initial TODCOR run. The TODCOR algorithm was then used to extract the known RVs from the synthetic SB2 model at orbital phases corresponding to the observations. The difference between the calculated RV and the known RV of the model gives an estimation for the magnitude and direction of the systematic error at that orbital phase. The correction was then added to the actual RVs measured from the observed spectra.

Physical Properties of the Eclipsing Binary KIC 9851944: Radial Velocity Analysis

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk);
(2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK;
(3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia;
(4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro
Observation
Orbital Ephemeris
Radial Velocity Analysis
Spectral Analysis
Analysis of the Light Curve
Physical Properties
Asteroseismic Analysis
Discussion
Conclusion, Data Availability, Acknowledgments, and References
Appendix A: Ephemeris Determination
Appendix B: Iteratively Prewhitened Frequencies
Appendix C: Detected Tidally Perturbed Pulsations 5 SPECTRAL ANALYSIS 5.1 Atmospheric parameters Since we planned to apply the method of SPD to extract the individual spectra of the components, normalisation of the observed spectra was of critical importance. We used a different approach than that in Section 4, where we extracted RVs. Here, we used the dedicated code described in Kolbas et al. (2015). First, the blaze function of échelle orders was fitted with a high-order polynomial function. Then, the normalised échelle orders were merged. When overlapping regions of successive échelle orders are sufficiently long, the very ends were cut off because of their low S/N. Échelle orders containing broad Balmer lines, in which it is not possible to define the blaze function with enough precision, were treated in a special way. For these échelle orders, the blaze function was interpolated from adjacent orders. This produces more reliable normalisation in spectral regions with broad Balmer lines than the usual pipeline procedures. For recent applications of this approach, please see Pavlovski et al. (2018, 2023); Lester et al. (2019, 2022); Wang et al. (2020, 2023). Overall, a slight difference in line depth between the two components is seen. The more massive component has deeper lines and slightly faster rotation. The Balmer lines are broadened by Stark broadening, and generally are not sensitive to the rotational broadening. Thus, we first optimised portions of the disentangled spectra free of the Balmer lines, primarily to discern the vsini values. We then performed optimal fitting of disentangled spectra centred on the Hβ and Hα lines, with fixed vsini. The light ratio from the optimal fitting of the wings of Hβ and Hγ lines, spectral segments containing only metal lines, and the Mg I triplet at around 5180 Å, are 1.315±0.018, 1.304±0.025 and 1.278±0.033 (Table 3). All three values for the light ratio are consistent within their 1σ uncertainties, with the light ratio determined from the wings of Hβ line being the most precise of the three. Guo et al. (2016) determined atmospheric parameters from tomographically reconstructed spectra of the components. Their spectra cover the wavelength range 3930–4610 Å at a medium spectral resolution of R = 6000. The analysis by Guo et al. (2016) was similar to ours, but with an important difference that they fitted complete separated spectra, whilst we concentrate on the wings of Balmer lines. Our results for the Balmer lines corroborate their findings to within 1σ. We also find good agreement for the vsini values, which are also within 1σ for both components. Guo et al. (2016) obtained a mean light ratio 1.34±0.03 from spectra centred at 4275 Å – this is slightly larger than but still consistent with our own results. 5.2 Direct fitting for the light ratio We were initially unable to constrain the light ratio of the system from the photometric analysis alone (see Section 3), so estimated it using several independent methods. The first method was the TODCOR light ratio reported in Table 2, the second was the optimal fitting of the disentangled spectra (ODS), and a third method is developed here. We repeated the process for all spectral orders showing sufficient well-resolved lines in regions unaffected by tellurics from Earth’s atmosphere. To save computing time, only the two observations closest to positions of quadrature were used. This approach resulted 036 30 spectral orders showing adequate fits with well defined minima in the sum of the square residuals. Fig.7 shows the result of this method applied to order 66, which demonstrates the effectiveness of optimizing the normalization of the observed spectra in the fitting routine for an order where line blending is significant. The resulting values for ℓB/ℓA after applying this method to the selected orders are shown in Fig.8, where each result is the average of the result from each of the two observations used. This paper is available on arxiv under CC 4.0 license. Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro Observation Orbital Ephemeris Radial Velocity Analysis Spectral Analysis Analysis of the Light Curve Physical Properties Asteroseismic Analysis Discussion Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Abstract and Intro Abstract and Intro Observation Observation Orbital Ephemeris Orbital Ephemeris Radial Velocity Analysis Radial Velocity Analysis Spectral Analysis Spectral Analysis Analysis of the Light Curve Analysis of the Light Curve Physical Properties Physical Properties Asteroseismic Analysis Asteroseismic Analysis Discussion Discussion Conclusion, Data Availability, Acknowledgments, and References Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Appendix C: Detected Tidally Perturbed Pulsations 5 SPECTRAL ANALYSIS 5.1 Atmospheric parameters Since we planned to apply the method of SPD to extract the individual spectra of the components, normalisation of the observed spectra was of critical importance. We used a different approach than that in Section 4, where we extracted RVs. Here, we used the dedicated code described in Kolbas et al. (2015). First, the blaze function of échelle orders was fitted with a high-order polynomial function. Then, the normalised échelle orders were merged. When overlapping regions of successive échelle orders are sufficiently long, the very ends were cut off because of their low S/N. Échelle orders containing broad Balmer lines, in which it is not possible to define the blaze function with enough precision, were treated in a special way. For these échelle orders, the blaze function was interpolated from adjacent orders. This produces more reliable normalisation in spectral regions with broad Balmer lines than the usual pipeline procedures. For recent applications of this approach, please see Pavlovski et al. (2018, 2023); Lester et al. (2019, 2022); Wang et al. (2020, 2023). Overall, a slight difference in line depth between the two components is seen. The more massive component has deeper lines and slightly faster rotation. The Balmer lines are broadened by Stark broadening, and generally are not sensitive to the rotational broadening. Thus, we first optimised portions of the disentangled spectra free of the Balmer lines, primarily to discern the v sin i values. We then performed optimal fitting of disentangled spectra centred on the Hβ and Hα lines, with fixed v sin i . v i v i The light ratio from the optimal fitting of the wings of Hβ and Hγ lines, spectral segments containing only metal lines, and the Mg I triplet at around 5180 Å, are 1.315±0.018, 1.304±0.025 and 1.278±0.033 (Table 3). All three values for the light ratio are consistent within their 1σ uncertainties, with the light ratio determined from the wings of Hβ line being the most precise of the three. Guo et al. (2016) determined atmospheric parameters from tomographically reconstructed spectra of the components. Their spectra cover the wavelength range 3930–4610 Å at a medium spectral resolution of R = 6000. The analysis by Guo et al. (2016) was similar to ours, but with an important difference that they fitted complete separated spectra, whilst we concentrate on the wings of Balmer lines. Our results for the Balmer lines corroborate their findings to within 1σ. We also find good agreement for the v sin i values, which are also within 1σ for both components. Guo et al. (2016) obtained a mean light ratio 1.34±0.03 from spectra centred at 4275 Å – this is slightly larger than but still consistent with our own results. v i 5.2 Direct fitting for the light ratio We were initially unable to constrain the light ratio of the system from the photometric analysis alone (see Section 3), so estimated it using several independent methods. The first method was the TODCOR light ratio reported in Table 2, the second was the optimal fitting of the disentangled spectra (ODS), and a third method is developed here. We repeated the process for all spectral orders showing sufficient well-resolved lines in regions unaffected by tellurics from Earth’s atmosphere. To save computing time, only the two observations closest to positions of quadrature were used. This approach resulted 036 30 spectral orders showing adequate fits with well defined minima in the sum of the square residuals. Fig.7 shows the result of this method applied to order 66, which demonstrates the effectiveness of optimizing the normalization of the observed spectra in the fitting routine for an order where line blending is significant. The resulting values for ℓB/ℓA after applying this method to the selected orders are shown in Fig.8, where each result is the average of the result from each of the two observations used.

Physical Properties of the Eclipsing Binary KIC 9851944: Spectral Analysis

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk);
(2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK;
(3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia;
(4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro
Observation
Orbital Ephemeris
Radial Velocity Analysis
Spectral Analysis
Analysis of the Light Curve
Physical Properties
Asteroseismic Analysis
Discussion
Conclusion, Data Availability, Acknowledgments, and References
Appendix A: Ephemeris Determination
Appendix B: Iteratively Prewhitened Frequencies
Appendix C: Detected Tidally Perturbed Pulsations 7 PHYSICAL PROPERTIES We determined the physical properties of KIC 9851944 from the spectroscopic and photometric results obtained above. For this we used the JKTABSDIM code (Southworth et al. 2005), modified to use the IAU system of nominal solar values (Prša et al. 2016) plus the NIST 2018 values for the Newtonian gravitational constant and the Stefan-Boltzmann constant. Errorbars were propagated via a perturbation analysis. The results are given in Table. 7. This paper is available on arxiv under CC 4.0 license. Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro Observation Orbital Ephemeris Radial Velocity Analysis Spectral Analysis Analysis of the Light Curve Physical Properties Asteroseismic Analysis Discussion Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Abstract and Intro Abstract and Intro Observation Observation Orbital Ephemeris Orbital Ephemeris Radial Velocity Analysis Radial Velocity Analysis Spectral Analysis Spectral Analysis Analysis of the Light Curve Analysis of the Light Curve Physical Properties Physical Properties Asteroseismic Analysis Asteroseismic Analysis Discussion Discussion Conclusion, Data Availability, Acknowledgments, and References Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Appendix C: Detected Tidally Perturbed Pulsations 7 PHYSICAL PROPERTIES We determined the physical properties of KIC 9851944 from the spectroscopic and photometric results obtained above. For this we used the JKTABSDIM code (Southworth et al. 2005), modified to use the IAU system of nominal solar values (Prša et al. 2016) plus the NIST 2018 values for the Newtonian gravitational constant and the Stefan-Boltzmann constant. Errorbars were propagated via a perturbation analysis. The results are given in Table. 7.

Physical Properties of the Eclipsing Binary KIC 9851944: Physical Properties

Physical Properties of the Eclipsing Binary KIC 9851944: Abstract and Intro

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk);
(2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK;
(3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia;
(4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro
Observation
Orbital Ephemeris
Radial Velocity Analysis
Spectral Analysis
Analysis of the Light Curve
Physical Properties
Asteroseismic Analysis
Discussion
Conclusion, Data Availability, Acknowledgments, and References
Appendix A: Ephemeris Determination
Appendix B: Iteratively Prewhitened Frequencies
Appendix C: Detected Tidally Perturbed Pulsations APPENDIX C: DETECTED TIDALLY PERTURBED PULSATIONS In this Appendix we illustrate all detected tidally perturbed pulsations of KIC 9851944. In each figure, the left panel shows a zoom-in of the associated frequency multiplet, as plotted in Fig. 11. In the top right panel, we see the orbital-phase folded light curve of the binary. In the middle and bottom right panels, we see the orbital-phase dependent modulations of the pulsation amplitudes and phases, respectively. These are calculated in 50 data bins, with the 1σ uncertainty range indicated by the dashed lines. This paper is available on arxiv under CC 4.0 license. Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro Observation Orbital Ephemeris Radial Velocity Analysis Spectral Analysis Analysis of the Light Curve Physical Properties Asteroseismic Analysis Discussion Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Abstract and Intro Abstract and Intro Observation Observation Orbital Ephemeris Orbital Ephemeris Radial Velocity Analysis Radial Velocity Analysis Spectral Analysis Spectral Analysis Analysis of the Light Curve Analysis of the Light Curve Physical Properties Physical Properties Asteroseismic Analysis Asteroseismic Analysis Discussion Discussion Conclusion, Data Availability, Acknowledgments, and References Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Appendix C: Detected Tidally Perturbed Pulsations APPENDIX C: DETECTED TIDALLY PERTURBED PULSATIONS In this Appendix we illustrate all detected tidally perturbed pulsations of KIC 9851944. In each figure, the left panel shows a zoom-in of the associated frequency multiplet, as plotted in Fig. 11. In the top right panel, we see the orbital-phase folded light curve of the binary. In the middle and bottom right panels, we see the orbital-phase dependent modulations of the pulsation amplitudes and phases, respectively. These are calculated in 50 data bins, with the 1σ uncertainty range indicated by the dashed lines.

Physical Properties of KIC 9851944: Appendix C: Detected Tidally Perturbed Pulsations

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk);
(2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK;
(3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia;
(4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro
Observation
Orbital Ephemeris
Radial Velocity Analysis
Spectral Analysis
Analysis of the Light Curve
Physical Properties
Asteroseismic Analysis
Discussion
Conclusion, Data Availability, Acknowledgments, and References
Appendix A: Ephemeris Determination
Appendix B: Iteratively Prewhitened Frequencies
Appendix C: Detected Tidally Perturbed Pulsations APPENDIX A: EPHEMERIS DETERMINATION This appendix presents the results from the preliminary JKTEBOP analaysis as well as times of primary minimum and fitted values calculated in section 3. This paper is available on arxiv under CC 4.0 license. Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro Observation Orbital Ephemeris Radial Velocity Analysis Spectral Analysis Analysis of the Light Curve Physical Properties Asteroseismic Analysis Discussion Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Abstract and Intro Abstract and Intro Observation Observation Orbital Ephemeris Orbital Ephemeris Radial Velocity Analysis Radial Velocity Analysis Spectral Analysis Spectral Analysis Analysis of the Light Curve Analysis of the Light Curve Physical Properties Physical Properties Asteroseismic Analysis Asteroseismic Analysis Discussion Discussion Conclusion, Data Availability, Acknowledgments, and References Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Appendix C: Detected Tidally Perturbed Pulsations APPENDIX A: EPHEMERIS DETERMINATION This appendix presents the results from the preliminary JKTEBOP analaysis as well as times of primary minimum and fitted values calculated in section 3.

Physical properties of the eclipsing binary KIC 9851944: Appendix A: Ephemeris Determination

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk);
(2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK;
(3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia;
(4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro
Observation
Orbital Ephemeris
Radial Velocity Analysis
Spectral Analysis
Analysis of the Light Curve
Physical Properties
Asteroseismic Analysis
Discussion
Conclusion, Data Availability, Acknowledgments, and References
Appendix A: Ephemeris Determination
Appendix B: Iteratively Prewhitened Frequencies
Appendix C: Detected Tidally Perturbed Pulsations 8 ASTEROSEISMIC ANALYSIS 8.1 Frequency analysis Following the binary modelling, we continue with the asteroseismic analysis of the target. Because the observed pulsations have much smaller amplitudes than the binary signal, the quality of the TESS and WASP data are insufficient for the asteroseismic analysis, and we limit ourselves to using the residual Kepler light curve. This is the merged light curve of all available Kepler short-cadence data after subtracting the best-fitting binary model, hereafter referred to as the pulsation light curve. To minimize the impact of outliers and instrumental effects on the asteroseismic analysis of small-amplitude pulsations, we apply additional processing to the data. Firstly, we remove those parts where coronal mass ejections (CMEs) or thermal and pointing changes of the spacecraft, such as at the start of a quarter or after a safe-mode event, have a visible impact on the quality of the light curve. Secondly, we apply preliminary iterative pre-whitening (as described by, e.g., Van Reeth et al. 2023) to build a tentative mathematical model of the 20 most dominant pulsations using a sum of sine waves 8.2 Tidal perturbation analysis 8.3 Orbital harmonic frequencies As pointed out by Guo et al. (2016), the detection of an orbital harmonic frequency comb is somewhat unexpected for synchronised binaries with circular orbits, though it has also been detected for other such systems (da Silva et al. 2014). Because the orbital eccentricity of the binary is zero, the equilibrium tides that are responsible for deforming the star and perturbing the pulsations are considerably larger than the dynamical tides that excite oscillations. Hence, this can indicate that this system has a slightly eccentric orbit or that one or both of the components is asynchronously rotating, within the uncertainty margins of our measurements. 8.4 Gravity-mode period-spacing pattern The error margins are smaller than the symbol sizes. This paper is available on arxiv under CC 4.0 license. Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail: z.jennings@keele.ac.uk); (2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK; (3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; (4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Table of Links Abstract and Intro Observation Orbital Ephemeris Radial Velocity Analysis Spectral Analysis Analysis of the Light Curve Physical Properties Asteroseismic Analysis Discussion Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Abstract and Intro Abstract and Intro Observation Observation Orbital Ephemeris Orbital Ephemeris Radial Velocity Analysis Radial Velocity Analysis Spectral Analysis Spectral Analysis Analysis of the Light Curve Analysis of the Light Curve Physical Properties Physical Properties Asteroseismic Analysis Asteroseismic Analysis Discussion Discussion Conclusion, Data Availability, Acknowledgments, and References Conclusion, Data Availability, Acknowledgments, and References Appendix A: Ephemeris Determination Appendix A: Ephemeris Determination Appendix B: Iteratively Prewhitened Frequencies Appendix B: Iteratively Prewhitened Frequencies Appendix C: Detected Tidally Perturbed Pulsations Appendix C: Detected Tidally Perturbed Pulsations 8 ASTEROSEISMIC ANALYSIS 8.1 Frequency analysis Following the binary modelling, we continue with the asteroseismic analysis of the target. Because the observed pulsations have much smaller amplitudes than the binary signal, the quality of the TESS and WASP data are insufficient for the asteroseismic analysis, and we limit ourselves to using the residual Kepler light curve. This is the merged light curve of all available Kepler short-cadence data after subtracting the best-fitting binary model, hereafter referred to as the pulsation light curve. To minimize the impact of outliers and instrumental effects on the asteroseismic analysis of small-amplitude pulsations, we apply additional processing to the data. Firstly, we remove those parts where coronal mass ejections (CMEs) or thermal and pointing changes of the spacecraft, such as at the start of a quarter or after a safe-mode event, have a visible impact on the quality of the light curve. Secondly, we apply preliminary iterative pre-whitening (as described by, e.g., Van Reeth et al. 2023) to build a tentative mathematical model of the 20 most dominant pulsations using a sum of sine waves 8.2 Tidal perturbation analysis 8.3 Orbital harmonic frequencies As pointed out by Guo et al. (2016), the detection of an orbital harmonic frequency comb is somewhat unexpected for synchronised binaries with circular orbits, though it has also been detected for other such systems (da Silva et al. 2014). Because the orbital eccentricity of the binary is zero, the equilibrium tides that are responsible for deforming the star and perturbing the pulsations are considerably larger than the dynamical tides that excite oscillations. Hence, this can indicate that this system has a slightly eccentric orbit or that one or both of the components is asynchronously rotating, within the uncertainty margins of our measurements. 8.4 Gravity-mode period-spacing pattern The error margins are smaller than the symbol sizes.

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