Measure color of natural satellite


  • Differential Color Refraction (DCR) effect is position error caused by the atmosphere, bending blue and red light differently.


  • Johnson–Cousins system (BVRI)  is color system used in astronomy which measures how bright an object looks through four color filters: B = blue, V = visible (green-yellow) R = red, I = infrared


  • Gaia system (G, BP, RP): is the modern color system used by the Gaia space telescope. Gaia measures brightness through: G = general (broad) brightness, BP = blue photometer, RP = red photometer


  • Scientists converted  traditional Johnson–Cousins filter data (like B and I) into Gaia’s BP–RP color through a “hidden transformation,” they achieved high precision (errors below 0.01 magnitudes). They corrected the DCR effect and improved the accuracy of the satellites’ position.


  • To Measure the color of a natural satellite (like Himalia or Triton) in the Gaia color system (BP − RP), they created a mathematical transformation


  • Fundamental Transformation Equation

This equation adjusts raw brightness measurement to make it comparable to a standard reference system. This equation tells us how to correct the raw brightness measured by a telescope for atmospheric and instrumental effects so it matches a standardized, true brightness scale like Gaia’s.

  • Hidden Transformation equation

  • m is the instrumental magnitude, X is the air mass for the observation, M denotes the standard system magnitude (e.g., V), and CI indicates the standard color index (e.g., V − R). 

  • K’ and k’’ are the first- and second-order extinction coefficients for filter f, Tf—the transformation coefficient, and ZPf—the nightly zero point


source

https://iopscience.iop.org/article/10.3847/1538-3881/adee0e

Tilt of sub saturn planet


  • Sub-Saturns planets orbiting stars that are hotter than about 6,100 K can have orbits that are highly tilted.


  • sub-Saturn is a planet whose size (radius) is between that of Neptune and Saturn.

  • Scientists used both transit data from TESS and radial-velocity / spectroscopic data (including the so-called Rossiter–McLaughlin effect) to measure how tilted the orbit is. 


  • Rossiter–McLaughlin effect: When a planet transits its star, it blocks part of the rotating stellar surface. Because one side of the star is moving toward us and the other side is moving away, the observed stellar spectrum is slightly distorted, causing an apparent shift in the star’s radial velocity.

  • Measured obliquities in hot-star sub-Saturn systems are not exactly 90°, but cluster around ~65°, which accords with a theoretical idea called secular resonance crossing.


  • Secular resonance crossing mechanism means that —

Over a long period of time, the gravitational pull from the star (and possibly other planets) slowly changes the direction of the planet’s orbit. It is slow, long-term gravitational process where the planet’s orbit gets strongly tilted (to near-polar) because its orbital motion and the star’s spin motion temporarily match.


  • 𝜓 final: final obliquity. By the above equation we can know that sub saturn planet obliquity depends on different parameters. 


Source: https://arxiv.org/html/2510.20740v1


Fe-doped YMnO3 properties


  • Scientists have used the Modified Becke–Johnson potential to calculate spin-polarized electronic and magnetic properties. It is an improved correction method in Density Function Theory that gives more accurate band gap and electronic structure.


  • ε (ω) = ε1 ω + iε2 ω

  • The frequency-dependent dielectric function of a material has a major impact on its applications. Here, the dispersion, or how the speed of light changes in a material, was described by using real part ε1 (ω) , and optical absorption was described by using the imaginary part ε2( ω)


  • the doped system Fe in YMnO3 has an overall smaller value of the Seebeck coefficient than the undoped one, as doping introduces additional charge carriers in a material, which reduces the Seebeck effect


  • They optimized the crystal structure using third order Birch–Murnaghan Equation of State.This tells how the crystal’s total energy changes when its volume is slightly stretched or compressed — used to find the most stable structure. It depends on bulk modulus, its derivative, Pressure and Volume ratio.


  • The magnetic susceptibility of YFexMn1-xO3 decreases with increasing temperature. This is because, as with the rise of temperature, the magnetic domains become increasingly disordered, which reduces the net magnetization. This pattern follows the Curie-Weiss law of magnetization.


  • Pure YMnO₃: mostly Mn 3d and O 2p orbitals dominate near the Fermi level. 

  • With Fe doping: Fe 3d orbitals appear and mix with Mn 3d states. This mixing shifts energy levels → smaller band gap and stronger magnetism. Increasing Fe adds asymmetry between spin-up and spin-down channels → ferromagnetic tendency.


Measuring Depth in ion beam radiotherapy:

In medical imaging or radiation physics, a phantom is an artificial object (a model) that mimics the physical or radiological properties of real biological tissue — like human organs, bone, or soft tissue.

A typical ion-beam radiograph gives only a 2D projection and you don’t know the depth of changes (i.e., how far into the beam the changed tissue is).

 The team developed a method to scan through different “depths” virtually in the image and choose the one where the change looks sharpest. They propose a “2.5D” method to retrieve some depth information.


Water-equivalent thickness WET was calculated. It  tells how much a material (like tissue) slows down an ion beam, measured as if it were a certain thickness of water. Denser or thicker tissue → higher WET. If the patient (or the phantom) changes like an air cavity appears, or tissue swells — the WET values change at those pixels.


Tenengrad focus‐measure method (image sharpness metric): This method measures  a focus/sharpness metric based on image gradients which was computed using Sobel operators.

M is gradient magnitude at each pixel. 

S is a sobel operator: simple image processing filter used to detect edges — places in an image where brightness (intensity) changes quickly. It calculates gradients — how steeply the pixel brightness changes in the x and y directions. 


Tenengrad score is computed by calculating the average gradient magnitude over the entire image.Tenengrad measures overall sharpness of the image. it shows which depth inside the phantom the reconstructed image is sharpest.


Source: https://iopscience.iop.org/article/10.1088/1361-6560/ae02de#pmbae02des5


Exocomet Transit and Kepler light curve


  • The Kepler light curve is basically a graph of a star’s brightness over time measured by the Kepler space telescope.

  • Below equation is the light curve of an exocomet transit, describing how the star’s brightness changes over time due to the comet passing in front of it.

  • K → depth factor of the transit (how strong the dimming is)

  • β → rate of exponential change (how fast the brightness decreases or recovers)

  • After t1 brightness slowly returns to normal as the comet tail passes.


  • They used the Adam optimization algorithm to minimize the cross-entropy error function for the classification of the light curves and the mean absolute error function for the position of the transit.

  • Cross-entropy is a way to measure how different two probability distributions are. Adam (Adaptive Moment Estimation) is an improved version of regular gradient descent that helps the model learn faster.


https://arxiv.org/html/2510.14687v1


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