In the line of our good practice in previous years, Nicolaus Copernicus Astronomical Center will organize the summer student program this year in a hybrid form. That means that we will allow the students to come to CAMK building to work on the projects. The accommodation will be available in dormitories in Warsaw if there are vacancies. The exact form of the collaboration is up to the project supervisor and is indicated in the project description, but in the case of the on-site form the project supervisor is expected to be available on-site for the student. On-line form of the program is also possible.

We invite 2nd, 3rd, or 4th year undergraduate physics or astronomy students (in exceptional circumstances we would accept younger students). The duration of an individual programme should be 4-6 weeks. Suggested topics are listed below. If you are interested in participating in the internship in the on-line only form, please contact the selected scientist directly to arrange for the details. For on-site form, please first contact the supervisor and fix the exact time and duration of the project and then send your application (the supervisor's name, date of the project, scientific CV). Applications should be submitted in PDF form to praktyki@camk.edu.pl. There is no deadline for applications and they will be considered once submitted. The successful candidates will be informed by email.

Please, be aware that the on-site form is limited to EU citizens only.

1. Fatemeh Kayanikhoo, fatima@camk.edu.pl

Title: **The last stable orbit of a neutron star - quark star binary.**

Supervisors: F. Kayanikhoo, M.Čemeljić

Project for CAMK Summer Program July/Sep 2023, Hybrid and/or on-site form.

**Project description:**

Quark stars (QS) are hypothetical stellar remnants that are more compact than neutron stars (NS). They may be formed after the accretion of mass onto a neutron star, or a proto-neutron star, depending on the astrophysical situation. The associated gravitational implosion may be accompanied by a luminous ejection of the envelope that is called a Quark-Nova. The existence of quark stars is related to the fundamental question of the stability of baryonic matter.

One possible way of detecting quark stars would be by observing their coalescence with a binary companion. The gravitational waves detected by the LIGO-VIRGO detectors carry information about the interior material of the compact and about the deformation of components in the last orbit of the binary system. The last stable orbit separates the binary phase from the coalescence, and as such its radius and orbital frequency are important to know. The student will rigorously compute the parameters of the last stable orbit and the interior structure of the QS and NS in general relativity, using the numerical code LORENE.

Work-plan:

The problem and approach will first be explained in a few lessons. The student will learn the LORENE library (https://lorene.obspm.fr) and the equation of the state (EOS) of QS. We will proceed with the LORENE code for binary neutron stars with a simple adiabatic EOS and an understanding of the parameters of the binary system. Next, we will work on the improvement of the run and make a model of binary SQS-NS with realistic EOS. The objective of this study is to determine the last stable orbit of binary QS-NS, while also examining the influence of the EoS on such configuration.

Requirement:

Working knowledge of C++ or/and Python is required.

2. Tomasz Krajewski, tkrajewski@camk.edu.pl

Title: **Analytical vs numerical solutions in magnetohydrodynamics**

Supervisors: Tomasz Krajewski (tkrajewski@camk.edu.pl), Angelos Karakonstantakis (karakonang@camk.edu.pl)

Form: on-site or on-line.

Time: July-September, flexible.

**Project description:**

We are seeking a motivated summer student with some experience in programming and mathematical skills. The summer internship will allow a hands-on experience with numerical methods for solving problems in magnetohydrodynamics.

Magnetohydrodynamics is broadly used to describe many astrophysical objects, for example accretion disk around black holes or neutron stars. Even though, some analytic solutions of equations of magnetohydrodynamics exist, they are very rare and correspond to highly symmetric settings, usually equivalent to low dimensional problems. Modeling realistic systems requires usage of numerical methods to obtain some approximations of exact solutions.

The aim of this project is to compare numerically obtained results with analytical ones for problems in which the latter are known. As an example we can mention: Sod shock tube problem, propagation of smooth Alfvén waves, Taylor–von Neumann-Sedov blast waves and so called (1-2-0-3) problem.

Magnetohydrodynamic simulations is one of the most powerful tool for understanding the origin and evolution of a wide variety of phenomena including large-scale cosmic structure and galaxies, binary systems up to smaller structures such as the plasma of expanding supernova ejecta or star/planet atmospheres. The study of such a wide variety of phenomena requires different implementations of numerical methods, as well as, resources to reveal the underlying physics in these highly nonlinear systems as accurately as possible. Depending on the complexity of the physical system, simulations may include shocks, relativistic effects, turbulence, amplification and dissipation of magnetic fields and so on.

Understanding the imperfection of various numerical scheme will be helpful in deciding which one should be used for studied astrophysical phenomena and help to develop the new more precise or robust one. In addition, calculating numerical solutions of standard one-dimensional problems are an important test for correctness of implementation of numerical code which was extensively used in the past. Finally, knowledge of analytical solution gives rare occasion to evaluate effectiveness of so called a posteriori error estimator used to estimate the quality of numerical solutions and are necessary ingredient of algorithms based on advance method of adaptive mesh refinement.

Requirements:

Working knowledge of C++ or/and Python is required.

3. Ruchi Mishra, rmishra@camk.edu.pl

Title : **1D simulations of levitating atmosphere around naked singularities using KORAL**

Supervisors : Ruchi Mishra, Tomasz Krajewski and Angelos Karakonstantakis rmishra@camk.edu.pl , tkrajewski@camk.edu.pl, karakonang@camk.edu.pl

**Project Description:**

We are seeking for a motivated summer student looking for hands-on experience with magneto-hydrodynamic simulations in the context of a real research problem in astrophysics. We propose contribution in the exciting project that focuses on the levitating atmospheres around naked singularities in General Relativity (GR). In GR gaseous atmospheres can be in hydrostatic balance in the absence of a supporting stellar surface. Additionally, any spherically symmetric naked singularity exhibits a fundamental characteristic known as the zero-gravity radius, where a test particle would remain at rest. Inside of it gravity is repulsive and outside of it gravity is attractive. An atmosphere can be formed at the zero gravity sphere which is supported only by gravity alone. In this project, the student will have the opportunity to simulate the static atmospheres around spherically symmetric naked singularities. The primary goal is to understand the behavior of these atmospheres and investigate their radial modes of oscillations by perturbing them. The simulations will be performed in one spacial dimension using the General Relativistic Mangeto-HydroDynamics (GRMHD) code KORAL, and the results will be analyzed using Python. During the course of the project, the student will receive a thorough explanation of the basic theoretical background, followed by installing and testing KORAL on their laptop. In the next step the student will focus on learning how to set up levitating atmospheres around naked singularities and how to analyze the results using plotting techniques in Python.

REQUIREMENTS:

Basic understanding of C and Python.

Additional information:

Throughout the project, at least one supervisor will be available on-site to assist the student, answer any questions and provide guidance whenever required.

4. Megan Lewis: mlewis@camk.edu.pl

Bartek Zgirski and I (Megan Lewis) would like to plan to supervise a student **in the context of the Araucaria project** (Grzegorz Pietrzynski) with the following description of the work:

**Project Description: **

The statistical method of distance determinations using near infrared photometry of carbon stars (JAGB method) is very promising. Just single-epoch photometry is needed for precision determinations of distances, with statistical uncertainties compared to those associated with determinations based on Cepheids. Being as bright in the J−band as classical Cepheids with periods of around 20 days, JAGB stars provide an excellent tool to determine distances to Supernova host galaxies in the Hubble flow. Carbon stars allow checking calibrations of other methods from the cosmic distance ladder and tracing geometrical structures of nearby galaxies. The calibration of the JAGB method gives very satisfying results that are in agreement with distances obtained using multi-band period luminosity relations for classical Cepheids. Further research can only improve the method. The cross check of the calibration through the determination of distances to individual Galactic carbon Miras based on their period-luminosity relations will provide valuable insight into precision and accuracy of the two methods. The candidate will use the OGLE catalog of long-period variable stars to estimate the distances and luminosities of carbon-rich Mira variable stars in the Milky Way. With the advent of the new generation of telescopes such as the Extremely Large Telescope and the James Webb Space Telescope, the method may reach distances of even 50−60 Mpc, which would allow determining distances to Supernova host galaxies, and calibrate the Hubble parameter independently. Therefore, carbon stars may help to settle one of the fundamental controversies of modern astronomy - the Hubble tension.

5. Miljenko Cemeljic: miki@camk.edu.pl

Title: **Aurora on Venus and Mars encircling a pulsar **

Supervisors: M. Čemeljić (SU, CAMK), Ruchi Mishra (CAMK), J. Varela (UC3 Madrid)

**Description:**

Star-planet magnetospheric interaction provides a channel for observational evidence about exoplanets through radio emission from aurora-like features. In numerical simulations with the magnetohydrodynamic code PLUTO, we will investigate magnetospheric interaction of Mars- and Venus-like planets encircling compact objects like pulsars and white dwarfs.

Workplan:

After learning to use the PLUTO code with our star-planet setup and visualize the results using Paraview and Python scripts, student will work to obtain a suite of simulations for the chosen type of object. Results of this work will be used in publications on star-planet magnetospheric interaction in our international collaboration.

Location: Warsaw

Time: July-September, flexible.

6. Miljenko Čemeljić: miki@camk.edu.pl

Title: **Listening of the Galaxy with a wire**

Supervisors: M. Čemeljić (SU, CAMK), F. Kayanikhoo (CAMK)

**Description:**

With the era of Software Defined Radio, amateur radio-astronomy obtained a new impulse. It is possible to build a small radio telescope at low cost (less than 100 eur) and use it to observe the neutral hydrogen line in our Galaxy and also radio emissions from the Sun and Jupiter. There are even amateur observations of pulsars with such devices. Such projects, involving the astronomy and radio technics are a welcome feature for STEM teaching at various levels. We will guide a student in building such a telescope from scratch, testing and using it for the observation of the Galaxy rotation curve.

Workplan:

After basic theoretical and technical explanations, student will embark, with out instructions, on building her own radio telescope. We will provide the needed electronic components and a laptop with installed software. We will guide the student towards understanding of the GNUradio/Pothos Flow software, to build a simple spectrometer. After testing, student will perform measurements to obtain the few points of velocity curve for our Galaxy, and will learn to interpret it.

Location: Warsaw

Time: July-September, flexible.

7. Felipe Espinoza-Arancibia, fespinoza@camk.edu.pl

Title:** Instability Strip of Classical Cepheids in the Large Magellanic Cloud**

Supervisors: Felipe Espinoza-Arancibia (CAMK PAN), Bogumił Pilecki (CAMK PAN)**Description:**

Cepheids are one of the most important classes of variable stars, crucial for different areas of astrophysics. Because of the relationship between their period and luminosity, they are important distance indicators in the local Universe. They are also key objects for testing the predictions of stellar evolution and pulsation theories. Workplan: The student will learn about the evolution of intermediate-mass stars and the modeling of classical Cepheids. The student will work with stellar evolutionary tracks computed using the state-of-the-art code Modules for Experiments in Stellar Astrophysics (MESA) and with MESA functionality Radial Stellar Pulsations (RSP). The objective of the project is to study the evolutionary tracks to obtain the crossing times of the instability strip and calculate a theoretical period-luminosity-color relation. The results of this project will be compared with available empirical results and will be used in a publication (with the possibility of the student becoming a co-author). The program may be extended according to the skills and will of the student. Programming skills will be important for the necessary analyses and visualization and will be an asset.

Form: on-site, hybrid.

Time: July - August (4 weeks), TBD

8. Rajeev Singh Rathour, rajeevsr@camk.edu.pl

Title: **Modeling Classical Cepheids in Open Clusters with MESA**

Supervisors: Rajeev Singh Rathour, Oliwia Ziółkowska and Radosław Smolec

**Description:**

Classical Cepheids are a class of pulsating stars (∼3-13 solar mass) which are a cornerstone to test both stellar evolution and pulsation theory. Their importance increases manifold due to their well-known Period-Luminosity relation that makes them the backbone to the extragalactic distance ladder, to eventually measure the Hubble constant. Understanding Cepheids in different environments is necessary to test the dependence of their physical parameters on metallicity. Open clusters provide a valuable resource for such requirements. We will build upon the recent literature-reported results on 33 open clusters Cepheids. Since, Cepheids and their host open cluster have similar metallicity, age, and distance, we will utilize this information to narrow down the physical parameters of these stars using evolutionary modeling. Such predictions under a variety of metallicity environments will help uncover their key properties such as Cepheid’s period–age relation.

Workplan:

The student will be given a few lectures to introduce the basics of stellar evolution and then will learn to use state-of-the-art MESA code and generate evolutionary tracks for Cepheids at cluster metallicities. We will carefully select a sample of Cepheids with their host open clusters, suited for modeling, with adequate range cluster metallicity. Then the student will launch a grid of evolutionary models for the selected Cepheid sample. We will utilize the publically available MIST and PARSEC isochrones to fit the evolutionary tracks. Depending upon the progress, we will proceed with pulsation modeling of the Cepheids under investigation. In a broader context, the student will receive good knowledge of working with stellar evolution code and computational cluster experience.

Form: off-line (recommended) or hybrid

Project duration: August-September, flexible