How Oort Cloud comets stay active even billions of kilometers from the Sun


  • Smaller comets appear CO₂-rich while large ones are CO-dominated.


  • Small comets lose all of their CO ice early in their lives, while they are orbiting near Neptune. From the model, a comet smaller than 4 km in diameter completely loses its CO.


  • Larger comets don’t lose all their CO, they become CO-poor only in their upper layers, CO ice survives deep below the surface around 500 m during the some million years near Neptune. 


  • For comets that have CO buried deep inside, when they move outward into the cold Oort Cloud their surface cools, and CO gas from the interior travels outward and refreezes near the surface. When they return toward the Sun, this refrozen CO layer becomes the main source of activity.


  • CO sublimation (turning directly from solid to gas) begins around 50 AU for a 10 km comet and even 150 AU for a 50 km comet. CO₂ activity starts closer to the Sun around 13 AU. Crystallization of amorphous water ice (which releases trapped gases) begins around 7 AU, causing strong outgassing bursts.


  • They calculated Solar heating (via boundary conditions at the surface), Internal heat transport, Sublimation and condensation, Crystallization of amorphous ice, radioactive energy release.


  • The second term on the left-hand side represents the transfer of heat by conduction and advection by flowing volatiles, if present, and the terms on the right-hand side include the rates of absorption/release of latent heat by sublimation/condensation in pores and radioactive energy release.


Engulfment of planet to Kepler 56


  • Kepler-56 is a red giant star, its outer layer spins faster and at a different orientation than its core.


  • Kepler-56’s fast spin cannot be explained just by the tidal pull of its two known planets. Two known planets orbiting Kepler-56 are too far away and too light to transfer enough angular momentum (AM) to make the star’s outer layer spin so fast.


  • Unusually fast rotation of the envelope and misaligned its core and envelope spin of star Kepler-56 might be due to the star once swallowing a close-orbiting hot Jupiter giant planet. It's called planetary engulfment.


  • Tidal torque depends on star radius and mass, orbital period, planet mass, Tidal quality factor Q.

  • Equation of Angular momentum gained by the star when it engulfs

  • Researchers used-

  • MESA code (Modules for Experiments in Stellar Astrophysics) to track how the star’s structure and rotation evolve,

  • Tidal interaction equations to estimate angular momentum transfer from known planets,

  • Engulfment simulation to calculate spin-up from swallowing a planet,

  • Obliquity damping to Study how the spin tilt changes with time.


Source: https://arxiv.org/html/2510.25680v1


Scattering coefficient (μs) method for blood clotting

Researchers compared their new scattering coefficient (μs) method with the traditional optical density (OD) method for clotting blood.

The Optical Density method measures the concentration of substances in the plasma by quantifying how much light it absorbs. 


They used Beer–Lambert law. 

μs is the scattering coefficient

P0 = transmitted power through buffer (no plasma scatterers)

P(t) transmitted optical power through the plasma

d  thickness of glass


When a graph of Scattering coefficient vs time is drawn, a temporal timing shift occurs compared to Optical Density measurements. It shows a function of plasma concentration.


As blood plasma changes from a liquid to a gel (clot), the scattering coefficient μₛ increases steadily  means the structure inside the plasma (fibrin fibers and networks) becomes more complex and scatters light more strongly.


Here μₛ method provides extra information such as specific times (t50%, t90%), time difference (Δt), and the clot formation rate (CFR), and structure of clot formation.


Source: https://iopscience.iop.org/article/10.1088/2057-1976/ae103c


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


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