Mass Of Solid Material Research Articles

A Review to the Observational and Theoretical Studies of Planetary Systems around Red Dwarfs

Red dwarfs are one of the smallest and dimmest main-sequence stars. With the improvement of observation technology, a rich population of planets have been discovered around them, which exhibits distinct distribution characteristics from the planets around Solar-like stars. Earth-like planets have a higher occurrence rate around red dwarfs, and the planetary systems are tightly compact. The closer habitable zone makes it easier to search for habitable planets. The distribution of the radius valley between super-Earths and sub-Neptunes also differs from that around solar-like stars. Moreover, the discovery of giant planets around these low-mass stars can be hard to explain by current leading theories of planet formation. As the mass of solid material in the protoplanetary disk decreases with decreasing stellar masses, the formation of giant planets remains challenging. The observations from telescopes such as Transiting Exoplanet Survey Satellite (TESS), James Webb, and Atacama Large Millimeter/submillimeter Array (ALMA) have provided invaluable insights and opportunities for the study of planetary formation. In this paper, we review the observations of different populations of planets and summarize the up-to-date understanding of planetary formation around red dwarfs.

Fossil magnetic field of accretion disks of young stars

We elaborate the model of accretion disks of young stars with the fossil large-scale magnetic field in the frame of Shakura and Sunyaev approximation. Equations of the MHD model include Shakura and Sunyaev equations, induction equation and equations of ionization balance. Magnetic field is determined taking into account ohmic diffusion, magnetic ambipolar diffusion and buoyancy. Ionization fraction is calculated considering ionization by cosmic rays and X-rays, thermal ionization, radiative recombinations and recombinations on the dust grains.Analytical solution and numerical investigations show that the magnetic field is coupled to the gas in the case of radiative recombinations. Magnetic field is quasi-azimuthal close to accretion disk inner boundary and quasi-radial in the outer regions.Magnetic field is quasi-poloidal in the dusty “dead” zones with low ionization degree, where ohmic diffusion is efficient. Magnetic ambipolar diffusion reduces vertical magnetic field in 10 times comparing to the frozen-in field in this region. Magnetic field is quasi-azimuthal close to the outer boundary of accretion disks for standard ionization rates and dust grain size a d=0.1 μm. In the case of large dust grains (a d>0.1 μm) or enhanced ionization rates, the magnetic field is quasi-radial in the outer regions.It is shown that the inner boundary of dusty “dead” zone is placed at r=(0.1–0.6) AU for accretion disks of stars with M=(0.5–2) M ⊙. Outer boundary of “dead” zone is placed at r=(3–21) AU and it is determined by magnetic ambipolar diffusion. Mass of solid material in the “dead” zone is more than 3 M ⊕ for stars with M≥1 M ⊙.

Origin of the metallicity dependence of exoplanet host stars in the protoplanetary disc mass distribution

The probability of a star hosting a planet that is detectable in radial velocity surveys increases as Ppl(Z) ! (10 Z 2 , where Z is stellar metallicity. Models of planet formation by core accretion reproduce this trend, since the protoplanetary disc of a high-metallicity star has a high density of solids, and so forms planetary cores which accrete gas before the primordial gas disc dissipates. This paper considers the origin of the form of the metallicity dependence of Ppl(Z). We introduce a simple model in which detectable planets form when the mass of solid material in the protoplanetary disc, Ms, exceeds a critical value. In this model, the form of Ppl(Z) is a direct reflection of the distribution of protoplanetary disc masses, Mg, and the observed metallicity relation is reproduced if P(Mg > M ) ! (M ) # 2 . We argue that a protoplanetary disc’s dust mass measured in submillimetre observations is a relatively pristine indicator of the mass available for planet-building, and find that the disc mass distribution derived from suchobservationsisconsistentwiththeobservedPpl(Z)ifasolidmassMs >0.5MJ isrequired to form detectable planets. Any planet formation model which imposes a critical solid mass for detectable planets to form would reproduce the observed metallicity relation, and core accretionmodelsareempiricallyconsistentwithsuchathresholdcriterion.Whiletheoutcome of planet formation in individual systems is debatable, we identify seven protoplanetary discs which, by rigid application of this criterion, would be expected to form detectable planets and may provide insight into the physical conditions required to form such planets. A testable prediction of the model is that the metallicity dependence should flatten both for Z > 0.5 dex and as more distant and lower mass planets are discovered. Further, combining this model with one in which the evolution of a star’s debris disc is also influenced by the solid mass in its protoplanetary disc results in the prediction that debris discs detected around stars with planets should be more infrared luminous than those around stars without planets in tentative agreement with recent observations.

Analytical derivation of time required for dissolution of monodisperse drug particles

whereM is the mass of solid material at time t, k is the dissolution rate constant, A is the area available for mass transfer, D is the diffusion coefficient of the dissolving material, and h is the diffusion boundary layer thickness. Dosage forms rarely contain solid drug-containing particles that maintain constant surface area for mass transfer however, and the following considerations are required to model dissolution of monodisperse powders:

Determination of Selenium in Marine Biological Tissues by Transverse Heated Electrothermal Atomic Absorption Spectrometry with Longitudinal Zeeman Background Correction and Automated Ultrasonic Slurry Sampling

A fast, sensitive, and reliable method for determination of selenium in marine biological tissues by electrothermal atomic absorption spectrometry with slurry sampling was developed. Slurries were prepared from fresh and frozen seafood samples that were previously homogenized, dried, and ground; particle sizes <100 microm were taken for analysis. A 3% (v/v) HNO3 solution containing 0.01% (v/v) Triton X-100 was used as slurry diluent. Slurries were mixed on an automated ultrasonic slurry sampler at 20% amplitude for 30 s just before an aliquot was injected into the furnace. The method was successfully validated against the following certified reference materials: NRCC CRM DORM-2 (Dogfish muscle); NRCC CRM TORT-2 (Lobster hepatopancreas); NRCC CRM DOLT-2 (Dogfish liver); and BCR CRM 278 (Mussel tissue), and was subsequently applied to determination of Se in 10 marine biological samples. The influences of the drying procedure (oven-, microwave-, and freeze-drying), matrix modifier amount, mass of solid material in cup, and pipetting sequence are discussed. The limit of determination of Se was 0.16 microg/g and the repeatability, estimated as between-batch precision, was in the range of 4-8%. Se contents in the samples ranged from 0.6 to 2.8 microg/g. The proposed method should be useful for fast assessment of the daily dietary intake of Se.

Accumulation of the earth and its initial state

Abstract The dynamically founded model of the origin of planets is based on two main concepts: (1) the common formation of the Sun and planets from the same gas-dust cloud; and (2) the accumulation of planets from solid bodies and particles. In the solar nebula of a moderate mass there were no conditions for the formation of large gaseous protoplanets. At the end of collapse and the decay of turbulence, the dust component of the protoplanetary disc precipitated towards its central plane forming a dust layer which disintegrated into numerous condensation centres. After a short collisional evolution they transformed into solid bodies of different sizes. Larger bodies contained a major part of the total mass of solid material, and their gravitational perturbations increased the velocities of the bodies. The largest bodies grew faster than the others and became embryo-planets that swept out all solid material. The accumulation of terrestrial planets was grossly homogeneous and lasted 100 Ma. The surfaces of growing planets were subject to an intensive impact transformation and heating. While in the central region of the Earth the temperature was several times less than the melting temperature, the upper mantle was heated by impacts of the largest bodies (of asteroidal size) until the beginning of the melting of rocks. At the end of the accumulation the mean surface temperature was about 300 K. Mega-impacts created large-scale inhomogeneities in the upper mantle with pools of melted material where differentiation began. Within the first 1 Ga a core, a hydrosphere and an atmosphere comparable in mass with the present ones had formed providing conditions for the origin of prebiological compounds.