Key Points: atmosphere of exoplanets and its magnetic field

 

Ohmic heating: The variations of the time varying magnetic field can induce currents in the upper atmosphere of some exoplanets, which dissipate and locally heat it up; it is called ohmic heating.


Equation for Induction and heating within a planet (which is described from ohm’s law, Ampere law, Faraday’s law) is:

where

 

Ap(x) is the steady magnetic field, the conductivity tensor σα depends on the magnetic field, and time.


Parallel conductivity is for the direction parallel to the magnetic field line.  

Pedersen conductivity is for the direction vertical to the magnetic field and parallel to the electric field. It is denoted as σp.

Hall conductivity is for the direction vertical to both the magnetic and electric fields. It is denoted as σH. In the ionosphere this conductivity is due to the drift motion of the electron (ExB drift).

Heating Rate,

Skin depth δ is defined as the depth where the current density is 1/e (about 37%) of the value at the surface; It depends on the oscillation frequency Ω  of the time-varying field and on the Pedersen conductivity in the atmosphere σp.

For constant σP, we see the maximum heating rate decreases with increasing orbital period.


Here In study, Trappist 1b and πMenc exoplanets are observed.

The differences in the electron number density lead to significant differences in the parallel, Hall and Pedersen conductivities of the upper atmospheres of the Earth, Trappist-1 b and π Men c.

Electron density of planets: Earth <Trappist 1b< πMenc.


The Pedersen conductivity is determined by the ions and electrons mixture in the atmosphere and planetary Magnetic Field.

The Pedersen conductivity of Trappist-1 b is dominated by the contribution from H2O+ and O+2 , whereas in π men c it is dominated by H+ , C+ and O+.


Due to the different XUV flux the planets receive and the π Men c atmosphere presents more electrons than Trappist-1 b, π Men c  have much stronger upper atmosphere conductivities than Trappist-1 b. therefore more efficient Ohmic heating.


Ohmic heating is expected to be important for the atmosphere only on a range of intermediate magnetic Bp values. For Trappist-1 b it matters if Bp ∈ [0.08, 0.2]G, and in the case of π Men c if BP ∈ [0.03, 0.1]G.


Source: https://arxiv.org/abs/2412.14072#:~:text=Indeed%2C%20close%2Din%20exoplanets%20are,it%20up%20through%20Ohmic%20heating.


Overview: Study of magnetization temperature in ferromagnetic crystals


EuO and EuS Materials are used in study. As per Weiss mean field approximation (MFA), below certain critical temperature(Tc) ferromagnetic materials have spontaneous magnetization — i.e., a sizable macroscopic magnetic moment even in the absence of an external magnetic field. The effective field acting on a magnet in a ferromagnetic medium is H+gM(T), term gM(T) is called self-consistent molecular field.

Magnetization M is given by,

 

Langevin function describes the average alignment of magnetic moments with an applied magnetic field at a given temperature.

x=uB/kT

For very large T, x becomes small and Langevin function becomes

For H = 0 and T slightly below TC , The equation  becomes

Brillouin function is a quantum mechanical function that describes the magnetization of a system of spins in response to an applied magnetic field at a given temperature.

The study shows that M(T) exhibits anomalous scaling near Tc, with a scaling index β≈1/3, consistent with experimental data for EuO and EuS.

This result differs from the classical MFA prediction of β=1/2


The Weiss-Heisenberg MFA value of the Curie Temperature Tc wh ≈ 86.6K in EuO was observed.(about 20 % larger than its experimental value Tc exp≈ 69.8 K). spin-wave included  MFA equations match with experimental data across all temperature ranges. 


Source: https://arxiv.org/abs/2412.10124







Summary of article about Transit Simulator for Objects Orbiting Stars


The quadratic limb darkening law was used in study. It is a model that describes the variation in the intensity of a star's photosphere as a function of the viewing angle.

I(μ) is the intensity of the star at u = cos (theta), i.e., the cosine of the angular separation of a point with respect to the center of the star.


As per transit principle the relative change in the observed flux is proportional to the relative area of the blocking object with respect to the area of the star.

They converted the intensity to a cumulative distribution function. 

The orbital phase angle is a phase value corresponding to the location of the planet in its orbit at a certain time. Ω is the orbital velocity and P refers to the orbital period,

the overlapped area was calculated using the Monte Carlo technique.

The asymmetric parameter q is calculated as,

 r0 is the distance between the planet and the star, hf is the second fluid Love number. The second fluid Love number is a parameter that describes the rigidity of a body under the effect of gravity.


Scientists developed a numerical transit simulator which is designed to generate light curves for objects of any arbitrary shape transiting stars.


Source: https://iopscience.iop.org/article/10.3847/1538-3881/ad7d8d

Summary of article: Ultrasonic Atomization for Liquid Metals

 

Ultrasonic atomization is a process that uses ultrasound waves to create tiny droplets from a liquid.

As per study Particle diameter d is

ρ and σ are respectively the density and surface tension of the atomized fluid and

f is a vibration frequency. Particle diameter also depends on Weber, Ohensorge and intensity number.


A liquid film is placed on a smooth surface that vibrates perpendicularly to the surface. The liquid absorbs some of the vibrational energy and creates waves called capillary waves. When the amplitude reaches a critical level, the waves collapse and eject tiny drops of liquid. 


The amplitude of vibrations at 10 um is too small to induce atomization of liquids with parameters similar to water. After a time of 0.0119 [s], the liquid layer does not atomize, it only agglomerates into larger droplets with a thickness of approx(87 μm).


The amplitude necessary for the process of initiating atomization is about 60–70% higher than theoretically predicted. As the frequency increases to 22 kHz, the amplitude necessary to start the atomization process decreases to about 2 μm and then increases linearly to about 3 μm. 


Droplet diameter (in micrometer):  Water(36.3), Al(49.6), Zn(34.8), Steel(52.1) observed in study.

The droplets do not always atomize in the direction perpendicular to the vibrating surface and to the surface of the liquid; their trajectory is changed by the forces of coherence.


Source: https://www.mdpi.com/1996-1944/17/24/6109#:~:text=It%20attempts%20to%20close%20a,surface)%20and%20obtained%20atomization%20results%20(



Summary of Article: melanin as a material for solar light absorbers

 

The infrared transmission spectra, Optical Density spectra, atomic force microscopy is used in study.

As per Lambert-Beer law

d is the melanin film thickness, ln(Ub/Us)  is measured from Optical Density.


The absorption coefficient decreases to ~ 10^4 cm−1 in the visible and near infrared region. So it is reasonable to consider these films as efficient light absorbers of near-ultraviolet radiation.


Melanin conductivity is due to extensive π-conjugation, at which electrons are delocalized across the entire oligomer stack(Oligomer stacks are a result of intermolecular π-π stacking, which is a process that involves the overlap of π-orbitals in the rings of a molecule)


An exponential growth in conductivity with increasing hydration level was observed for melanin film in experiment. 


Fourier Transform Infrared transmission spectrum of eumelanin film has found the presence of OH groups and CHn bonds with both sp3 and sp2 hybridizations. The ratio between the sp2 and sp3 hybridized CHn bonds may play a role in defining the film optical and electrical properties. Higher concentrations of sp2 hybridized bonds may lead to an increase in conductivity.

Source: https://arxiv.org/pdf/2412.07609#:~:text=The%20films%20demonstrate%20indirect%20allowed,in%20photovoltaic%20solar%20energy%20converters.


Overview of article: Study of magnetic field change in Sun


Parker Solar Probe(PSP) has discovered the prevalence of switchbacks (SBs)-switchbacks are sudden reversals in the magnetic field in the solar wind. The researchers used the Adaptively Refined Magnetohydrodynamics Solver (ARMS) method.


Solar wind velocity has a similar behavior characterised by a logarithmic dependence, approximately resembling ln(r)^½.


Mass density, magnetic field decrease as radius increases. Alfvén Velocity (velocity of propagation of Alfvén waves in the direction of the magnetic field) for low plasma beta increases with radius and then decreases. Low plasma beta means that magnetic pressure is dominant over thermal pressure in a plasma.




Magnetic Energy Initially increases, Later decreases with time. The imposed clockwise flow

induces a counter-clockwise twist to the closed magnetic field lines, boosts the total field strength and reduces the pressure. This behaviour explains the magnetic energy’s upward trend and the internal energy’s decline.  Gravitational Energy gradually increases. 

 


Photospheric flow, tangential velocity vb, depends on the gradient of the radial magnetic field, Br, and is given by


Source: https://www.aanda.org/articles/aa/full_html/2024/12/aa52019-24/aa52019-24.html


Key Points of Study of Deformation of the ice front by particle


As the freezing front approaches the droplet, the temperature on one side of the droplet is different than on the other side. That causes a difference in surface tension which occurs as a force, thermal Marangoni force.


As per observation in solidification front of ceramic Zirconia and polystyrene (PS) particle, If the particle is more thermally conductive, heat flows through it, and the ice front bends away and if the particle is less thermally conductive, heat avoids the particle, and the ice front bends toward it. The heat flux chooses the path of least thermal resistance.


As per observation in liquid, at low freezing velocity, the ice front bends toward the droplet.


Marangoni number  indicates the influence of surface tension gradients on fluid flow as a result of the applied thermal gradient.


Application: This study helps in understanding behavior of biology cells, freezing in the casting process, material science.


Source: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.214002


Summary of article: V2O3 metallic property at external V, I

 

Topological defects: These are imperfections in the structure of a material that arise when its internal arrangement (lattice or order parameter) cannot be perfectly aligned.

Resistive switching is a sudden transition between insulating and metallic states triggered by an electric field.

When V2O3 temperature is changed from high to low, the structure changes from rhombohedral shape to less symmetric shape (monoclinic phase) as the material becomes metallic to an insulator.

Researchers used  PhotoEmission Electron Microscopy (PEEM) combined with X-rays. The V2O3​ film is placed between two gold electrodes that apply the electric field. By measuring the current and voltage, they observe that initially, the material resists the current, but once the voltage reaches a certain threshold, the resistance suddenly drops—indicating the formation of conducting pathways.

Source: https://www.nature.com/articles/s41467-024-53726-z

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