arXiv subjects

R. Caimmi

Publications and source records attributed to R. Caimmi.

At least 19 recordsLinked to original sources

arXiv2019

On the desert between neutron star and black hole remnants

The occurrence of a desert between neutron star (NS) and black hole (BH) remnants is reviewed. The dependence of stellar remnants on the zero age main sequence (ZAMS) progenitor mass for solar metallicity is taken from a recent investigation and further effort is devoted to NS and BH remnants. In particular, a density parameter is defined and related to NS mass and radius. Spinning BHs in Kerr metrics are considered as infinitely thin, homogeneous, rigidly rotating disks in Newtonian mechanics. Physical parameters for nonrotating (TOV) and equatorial breakup (EQB) configurations are taken or inferred from a recent investigation with regard to 4 NS and 3 quark star (QS) physically motivated equation of state (EOS) kinds. A comparison is performed with counterparts related to nonrotating and maximally rotating BHs. The results are also considered in the light of empirical relations present in literature. With regard to $J$-$M$ relation, EQB configurations are placed on a sequence of similar slope in comparison to maximally rotating BHs, but shifted downwards due to lower angular momentum by a factor of about 3.6. Under the assumption heavy baryons are NS constituents and instantaneously undergo quark-level reactions, the energy released (or adsorbed) is calculated using results from a recent investigation. Even if NSs exclusively host heavy baryons of the kind considered, the total amount cannot exceed about 10\% of the binding energy, which inhibits supernova explosions as in supramassive white dwarf (WD) remnants or implosions into BH. Alternative channels for submassive ($2<=M/m_\odot<=4$) BH formation are shortly discussed.

astro-ph.SR↗

arXiv2018

Updating a simple model of lunar recession

A classical model of lunar recession is reviewed and updated, where input parameters are taken or inferred from earlier astronomical computation of insolation quantities on Earth back to 0.25 Gyr. Free parameters are (i) the transition age, where mean lunar recession is suddenly lowered, and (ii) the merging age, where Earth-Moon distance (EMD), drops to zero. Predicted mean EMD and length of day (LOD) slightly overstimate their counterparts from the above mentioned astronomical computation. Predicted LOD, where the effect of atmospheric tides and nontidal processes is considered and supposed to be time independent, slightly understimates a linear interpolation from paleontological data related to Phanerozoic, inferred in earlier investigations. If short-period ($Δt\approx10^{-3}$ Gyr) EMD fluctuations ($Δa\approx\mp0.5R_\oplus$), resulting from the above mentioned astronomical computation back to 0.25 Gyr, occur along the whole evolution of Earth-Moon system (EMS), then the predicted mean EMD is consistent with values inferred from three well studied paleontological data sets: Elatina-Reynella (ER), Big Cottonwood (BC), Weeli Wolli (WW), for a suitable choice of input parameters. The same holds for LOD where, in addition, computed values are consistent with a linear interpolation from paleontological data related to Proterozoic, inferred in earlier investigations. The effect of atmospheric tides and nontidal processes is also discussed. In conclusion, the current model can be considered as a useful zeroth-order approximation to the evaluation of lunar recession and LOD. More accurate paleontological data, expecially in connection with error evaluation, would be desirable in view of improved results and further constraints involving both Astronomy and Paleontology.

astro-ph.EP↗

arXiv2017

Bivariate least squares linear regression: towards a unified analytic formalism. II. Extreme structural models

Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the limit of uncorrelated errors in X and in Y. For homoscedastic data, the results are taken from earlier attempts and rewritten using a more compact notation. For heteroscedastic data, the results are inferred from a procedure related to functional models. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For low-dispersion samples and assigned methods, different regression models yield results which are in agreement within the errors for both heteroscedastic and homoscedastic data, while the contrary holds for large-dispersion samples. In any case, samples related to different methods produce discrepant results, due to the presence of (still undetected) systematic errors, which implies no definitive statement can be made at present. Asymptotic expressions approximate regression line slope and intercept variance estimators, for normal residuals, to a better extent with respect to earlier attempts. Related fractional discrepancies are not exceeding a few percent for low-dispersion data, which grows up to about 10% for large-dispersion data. An extension of the formalism to generic structural models is left to a forthcoming paper.

astro-ph.IM↗

arXiv2017

Evolving statistical systems: application to academic courses

Statistical systems are conceived from the standpoint of statistical mechanics, as made of a (generally large) number of identical units and exhibiting a (generally large) number of different configurations (microstates), among which only equivalence classes (macrostates) are accessible to observations. Further attention is devoted to evolving statistical systems, and a simple case including only a possible event, E, and related opposite event, $\neg$E, is examined in detail. In particular, the expected evolution is determined and compared to the random evolution inferred from a sequence of random numbers, for different sample populations. The special case of radioactive decay is considered and results are expressed in terms of the fractional time, $t/Δt$, where the time step, $Δt$, is related to the decay probability, $p=p(Δt)$. An application is made to data collections from selected academic courses, focusing on the extent to which expected evolutions and model random evolutions fit to empirical random evolutions inferred from data collections. Results could be biased by the assumed number of students who abandoned their course, defined as suitable impostors (SI). Extreme cases related to a lower and an upper limit of the SI number are considered for a time step, $Δt=(1/12)$y, where fitting expected evolutions relate to $0.003\le p\le0.200$. In conclusion, evolving statistical systems made of academic courses are similar to poorly populated samples of radioactive nuclides exhibiting equal probabilities, $p$, and time steps, $Δt$, where inferred mean lifetimes, $τ$, and half-life times, $t_{1/2}$, range within $0.37<τ/{\rm y}<27.73$ and $0.25<t_{1/2}/{\rm y}<19.22$, respectively, and upper limits are related to incomplete data collections.

physics.gen-ph↗

arXiv2017

Musical intervals under 12-note equal temperament: a geometrical interpretation

Musical intervals in multiple of semitones under 12-note equal temperament, or more specifically pitch-class subsets of assigned cardinality ($n$-chords) are conceived as positive integer points within an Euclidean $n$-space. The number of distinct $n$-chords is inferred from combinatorics with the extension to $n=0$, involving an Euclidean 0-space. The number of repeating $n$-chords, or points which are turned into themselves during a circular permutation, $T_n$, of their coordinates, is inferred from algebraic considerations. Finally, the total number of $n$-chords and the number of $T_n$ set classes are determined. Palindrome and pseudo palindrome $n$-chords are defined and included among repeating $n$-chords, with regard to an equivalence relation, $T_n/T_nI$, where reflection is added to circular permutation. To this respect, the number of $T_n$ set classes is inferred concerning palindrome and pseudo palindrome $n$-chords and the remaining $n$-chords. The above results are reproduced within the framework of a geometrical interpretation, where positive integer points related to $n$-chords of cardinality, $n$, belong to a regular inclined $n$-hedron, $Ψ_{12}^n$, the vertexes lying on the coordinate axes of a Cartesian orthogonal reference frame at a distance, $x_i=12$, $1\le i\le n$, from the origin. Considering $Ψ_{12}^n$ as special cases of lattice polytopes, the number of related nonnegative integer points is also determined for completeness. A comparison is performed with the results inferred from group theory.

math.CO↗

arXiv2016

Pontential energies and potential-energy tensors for subsystems: general properties

With regard to generic two-component systems, the theory of first variations of global quantities is reviewed and explicit expressions are inferred for subsystem potential energies and potential-energy tensors. Performing a conceptual experiment, a physical interpretation of subsystem potential energies and potential-energy tensors is discussed. Subsystem tidal radii are defined by requiring an unbound component in absence of the other one. To this respect, a few guidance examples are presented as: (i) an embedding and an embedded homogeneous sphere; (ii) an embedding and an embedded truncated, singular isothermal sphere where related centres are sufficiently distant; (iii) a homogeneous sphere and a Roche system i.e. a mass point surrounded by a vanishing atmosphere. The results are discussed and compared with the findings of earlier investigations.

astro-ph.GA↗

arXiv2016

The intrinsic beauty of polytropic spheres in reduced variables

The concept of reduced variables is revisited with regard to van der Waals' theory and an application is made to polytropic spheres, where the reduced radial coordinate is ${\rm red}(r)=r/R=ξ/Ξ$, $R$ radius, and the reduced density is ${\rm red}(ρ)=ρ/λ=θ^n$, $λ$ central density. Reduced density profiles are plotted for several polytropic indexes within the range, $0\le n\le5$, disclosing two noticeable features. First, any point of coordinates, $({\rm red}(r),{\rm red}(ρ))$, $0\le{\rm red}(r)\le1$, $0\le{\rm red}(ρ)\le1$, belongs to a reduced density profile of the kind considered. Second, sufficiently steep i.e. large $n$ reduced density profiles exhibit an oblique inflection point, where the threshold is found to be located at $n=n_{\rm th}=0.888715$. Reduced pressure profiles, ${\rm red}(P)=P/\varpi=θ^{n+1}$, $\varpi$ central pressure, Lane-Emden fucntions, $θ=(ρ/λ)^{1/n}$, and polytropic curves, ${\rm red}(P)={\rm red}(P)({\rm red}(ρ))$, are also plotted. The method can be extended to nonspherical polytropes with regard to a selected direction, ${\rm red}(r)(μ)=r(μ)/R(μ)=ξ(μ)/Ξ(μ)$. The results can be extended to polytropic spheres made of collisionless particles, for polytropic index within a more restricted range, $1/2\le n\le5$.

astro-ph.GA↗

arXiv2016

Multi-component, rigidly rotating polytropes: improved and extended theory

With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with intersecting boundaries. The formulation is restricted to two subsystems for simplicity but, in principle, can be extended to $N$ subsystems. Equilibrium configurations are independent of the nature of the fluid i.e. collisional or collisionless, provided the polytropic index lies within the range, $1/2\le n\le5$, as in one-component systems. The solution of the equilibrium equations is expanded in power series, which can be continued up to the boundary and outside via starting points placed at increasingly larger distance from the centre of mass. A detailed analysis is devoted to special cases where the solution of the equilibrium equations can be expressed analytically. Finally a guidance example is shown, involving homogeneous subsystems with intersecting boundaries, where a substantially flattened component extends outside a slightly flattened one.

astro-ph.GA↗

arXiv2016

Gravitation, holographic principle, and extra dimensions

Within the context of Newton's theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable vortex-like surface, under the action of a tidal gravitational field along the symmetry axis. An interpretation is made in the light of a holographic principle, in the sense that motions in ordinary space are connected with motions on a selected surface and vice versa. Then ordinary space is conceived as a 3-hypersurface bounding a $n$-hypervolume where gravitation takes origin, within a $n$-hyperspace. The extension of the holographic principle to extra dimensions implies the existence of a minimum distance where test particles may still be considered as distinct from the central body. Below that threshold, it is inferred test particles lose theirs individuality and "glue" to the central body via unification of the four known interactions and, in addition, (i) particles can no longer be conceived as point-like but e.g., strings or membranes, and (ii) quantum effects are dominant and matter turns back to a pre-big bang state. A more detailed formulation including noncircular motions within the context of general relativity, together with further knowledge on neutron stars, quark stars and black holes, would provide further insight on the formulation of quantum gravity.

physics.class-ph↗

arXiv2015

Gravitational acceleration and tidal effects in spherical-symmetric density profiles

Pure power-law density profiles, $ρ(r)\propto r^{b-3}$, are classified in connection with the following reference cases: (i) isodensity, $b=3$, $ρ=$ const; (ii) isogravity, $b=2$, $g=$ const; (iii) isothermal, $b=1$, $v=[GM(r)/r]^{1/2}=$ const; (iv) isomass, $b=0$, $M=$ const. A restricted number of different families of density profiles including, in addition, cored power-law, generalized power-law, polytropes, are studied in detail with regard to both one-component and two-component systems. Considerable effort is devoted to the existence of an extremum point (maximum absolute value) in the gravitational acceleration within the matter distribution. Predicted velocity curves are compared to the data inferred from observations. Tidal effects on an inner subsystem are investigated and an application is made to globular clusters within the Galaxy. To this aim, the tidal radius is defined by balancing the opposite gravitational forces from the Galaxy and the selected cluster on a special point of the cluster boundary, lying between related centres of mass. The position of 17 globular clusters with respect to the stability region, where the tidal radius exceeds the observed radius, is shown for assigned dark-to-visible mass ratios and density profiles, among those considered, which are currently used for the description of galaxies and/or dark matter haloes.

astro-ph.GA↗

arXiv2015

O and Fe abundance correlations and distributions inferred for the thick and thin disk

A linear [Fe/H]-[O/H] relation is found for different stellar populations in the Galaxy (halo, thick disk, thin disk) from a data sample obtained in a recent investigation (Ram{\'ı}rez et al. 2013). These correlations support previous results inferred from poorer samples: stars display a "main sequence" expressed as [Fe/H] = $a$[O/H$]+b\mpΔb$ where a unit slope, $a=1$, implies a constant [O/Fe] abundance ratio. Oxygen and iron empirical abundance distributions are then determined for different subsamples, which are well explained by the theoretical predictions of multistage closed-(box+reservoir) (MCBR) chemical evolution models by taking into account the found correlations. The interpretation of these distributions in the framework of MCBR models gives us clues about inflow/outflow rates in these different Galactic regions and their corresponding evolution. Outflow rate for the thick and the thin disks are lower than the halo outflow rate. Moreover if the thin disk built up from the thick disk, both systems result of comparable masses. Besides that, the iron-to-oxygen yield ratio and the primary to not primary contribution ratio for the iron production are obtained from the data, resulting consistent with SNII progenitor nucleosynthesis and with the iron production from SNIa supernova events.

astro-ph.GA↗

arXiv2015

A double power-law fit to the computed stellar $\log(\tau/{\rm y})$-$\log(m/m_\odot)$ relation

The computed $\log(\tau/{\rm y})$-$\log(m/m_\odot)$ relation for the stellar initial mass range, 0.6-120.0, and the stellar initial metallicity range, 0.0004-0.0500, tabulated in an earlier attempt (Portinari et al. 1998) is fitted to a good extent by a four-parameter curve, expressed by a double power-law, for assigned stellar initial metallicity, which can be reduced to a three-parameter curve, expressed by a single power-law, for the whole set of stellar initial metallicities. The relative errors do not exceed about 2% and 4%, respectively. The extent to which the interpolation curve, expressed by a single power-law, can be extrapolated towards both high-mass and low-mass stars, is also investigated. High-mass star lifetimes are understimated by a factor less than 2 up to $m/m_\odot= 1000$ and by a fiducial factor less than 4 up to infinite. Low-mass star lifetimes are overstimated by a factor of about 3 down to $m/m_\odot=0.25$ and by an unacceptably large factor down to $m/m_\odot=0.08$. As a simple application, the star mass fraction of a single star generation with stellar initial mass function defined by a power-law, is plotted vs. the logarithmic stellar lifetime. The star mass fraction declines in time at a decreasing rate for mild stellar initial mass function and at an increasing rate for steep stellar initial mass function, where a linear trend is exhibited for a value of the exponent close to the Salpeter's value, equal to -2.35.

astro-ph.SR↗

arXiv2014

Emden-Chandrasekhar, axisymmetric, rigidly rotating polytropes. VI. Self-consistency and continuity

Axisymmetric, rigidly rotating polytropes are considered in the framework of both the original Chandrasekhar (C33) approximation and a different version (extended C33 approximation). Special effort is devoted to two specific points, namely (i) a contradiction between the binomial series evaluation and the vanishing density on the boundary, which affects the self-consistency of the above mentioned approximations, and (ii) the continuity of selected parameters as a function of the polytropic index. Concerning (i), it is shown the Emdem-Chandrasekhar (EC) associated functions are defined at any internal point even if related EC associated equations hold only for a particular subvolume, in the framework of both the C33 and the extended C33 approximation. Concerning (ii), the continuity may safely be established, on the boundary of the domain, for part of the parameters, while additional data are needed for the remaining part. Simple fitting curves, valid to a good extent for a wide range of polytropic index, involve exponential functions and, in a single case, two straight lines joined by a parabolic segment. The expression of physical parameters in terms of the polytropic index can be used in building up sequences of configurations with changing density profile for assigned mass and angular momentum.

astro-ph.GA↗

arXiv2013

Fractional yields inferred from halo and thick disk stars

Linear [Q/H]-[O/H] relations, Q = Na, Mg, Si, Ca, Ti, Cr, Fe, Ni, are inferred from a sample (N=67) of recently studied FGK-type dwarf stars in the solar neighbourhood including different populations. Regression line slope and intercept estimators and related variance estimators are determined. With regard to the straight line, [Q/H] = aQ [O/H] + bQ, sample stars display along a "main sequence", [Q,O] = [aQ,bQ, Delta bQ], leaving aside the two OL stars which, in most cases (e.g., Na), lie outside. A unit slope, aQ = 1, implies Q is a primary element synthesised via SNII progenitors in presence of universal stellar initial mass function (defined as simple primary element). To this respect, Mg, Si, Ti, show aQ = 1 within 2 sigma(aQ); Cr, Fe, Ni, within 3 sigma(aQ); Na, Ca, exceeding 3 sigma(aQ). The empirical, differential element abundance distributions are inferred from different subsamples, where related regression lines represent their theoretical counterparts within the framework of simple MCBR (multistage closed box + reservoir) chemical evolution models. Hence the fractional yields are determined and (as an example) a comparison is shown with their theoretical counterparts inferred from SNII progenitor nucleosynthesis under the assumption of a power-law stellar initial mass function. The generalized fractional yields are determined regardless from the chemical evolution model. The ratio of outflow to star formation rate is compared for different populations, in the framework of simple MCBR models. The opposite situation of element abundance variation entirely due to cosmic scatter is also considered under reasonable assumptions. The related differential element abundance distribution fits to the data as well as its counterpart inferred in the opposite limit of instantaneous mixing in presence of chemical evolution.

astro-ph.GA↗

arXiv2013

Globular cluster star classification: application to M13

Starting from recent determination of Fe, O, Na abundance on a restricted sample (N=67) of halo and thick disk stars, a natural and well motivated selection criterion is defined for the classification of globular cluster stars. An application is performed to M13 using a sample (N=112) for which Fe, O, Na abundance has been recently inferred from observations. A comparison is made between current and earlier M13 star classification. Both O and Na empirical differential abundance distributions are determined for each class and the whole sample (with the addition of Fe in the last case) and compared with their theoretical counterparts due to cosmic scatter obeying a Gaussian distribution whose parameters are inferred from related subsamples. The procedure is repeated with regard to four additional classes according if oxygen and sodium abundance is above (stage CE) or below (stage AF) a selected threshold. Both O and Na empirical differential abundance distributions, related to the whole sample, exhibit a linear fit for AF and CE stage. Within the errors, the oxygen slope for CE stage is equal and opposite in sign with respect of the sodium slope for AF stage, while the contrary holds in dealing with the oxygen slope for AF stage with respect to the sodium slope for CE stage. In the light of simple models of chemical evolution applied to M13, the O-Na anticorrelation and the primordial to current M13 mass ratio are discussed. The proposed classification of globular cluster stars may be extended in a twofold manner, namely to (i) elements other than Na and Fe and (ii) globular clusters other than M13.

astro-ph.GA↗

arXiv2012

Simple MCBR models of chemical evolution: an application to the thin and the thick disk

Simple MCBR models of chemical evolution are extended to the limit of dominant gas inflow or outflow with respect to gas locked up into long-lived stars and remnants. For an assigned empirical differential oxygen abundance distribution, which can be linearly fitted, a family of theoretical curves is built up with assigned prescriptions. For curves with increasing cut parameter, the gas mass fraction locked up into long-lived stars and remnants is found to attain a maximum and then decrease towards zero as the flow tends to infinity, while the remaining parameters show a monotonic trend. The theoretical integral oxygen abundance distribution is also expressed. An application is performed to the empirical distribution deduced from two different samples of disk stars, for both the thin and the thick disk. The constraints on formation and evolution are discussed in the light of the model. The evolution is tentatively subdivided into four stages, A, F, C, E. The empirical distribution related to any stage is fitted by all curves for a wide range of the cut parameter. The F stage may safely be described by a steady inflow regime, implying a flat theoretical distribution, in agreement with the results of hydrodynamical simulations. Finally, (1) the change of fractional mass due to the extension of the linear fit to the empirical distribution, towards both the (undetected) low-metallicity and high-metallicity tail, is evaluated and (2) the idea of a thick disk-thin disk collapse is discussed, in the light of the model.

astro-ph.GA↗

arXiv2012

Tidal interactions and principle of corresponding states: from micro to macro cosmos. A century after van der Waals' Nobel Prize

The current attempt is aimed to honor the first centennial of Johannes Diderik van der Waals (VDW) awarding Nobel Prize in Physics. The VDW theory of ordinary fluids is reviewed in the first part of the paper, where special effort is devoted to the equation of state and the law of corresponding states. In addition, a few mathematical features involving properties of cubic equations are discussed, for appreciating the intrinsic beauty of the VDW theory. A theory of astrophysical fluids is shortly reviewed in the second part of the paper, grounding on the tensor virial theorem for two-component systems, and an equation of state is formulated with a convenient choice of reduced variables. Additional effort is devoted to particular choices of density profiles, namely a simple guidance case and two cases of astrophysical interest. The related macroisothermal curves are found to be qualitatively similar to VDW isothermal curves below the critical threshold and, for sufficiently steep density profiles, a critical macroisothermal curve exists, with a single horizontal inflexion point. Under the working hypothesis of a phase transition (assumed to be gas-stars) for astrophysical fluids, similar to the vapour-liquid phase transition in ordinary fluids, the location of gas clouds, stellar systems, galaxies, cluster of galaxies, on the plane scanned by reduced variables, is tentatively assigned. A brief discussion shows how van der Waals' two great discoveries, namely a gas equation of state where tidal interactions between molecules are taken into account, and the law of corresponding states, related to microcosmos, find a counterpart with regard to macrocosmos. In conclusion, after more than a century since the awarding of the Nobel Prize in Physics, van der Waals' ideas are still valid and helpful to day for a full understanding of the universe.

physics.class-ph↗

arXiv2011

Bivariate least squares linear regression: towards a unified analytic formalism

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. Linear models of regression lines are considered in the general case of correlated errors in X and in Y for heteroscedastic data. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases. In the limit of homoscedastic data, the results determined for functional models are compared with their counterparts related to extreme structural models. While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with a single exception. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors for both heteroscedastic and homoscedastic data. Conversely, samples related to different methods produce discrepant results, due to the presence of (still undetected) systematic errors, which implies no definitive statement can be made at present. A comparison is also made between different expressions of regression line slope and intercept variance estimators, where fractional discrepancies are found to be not exceeding a few percent, which grows up to about 20% in presence of large dispersion data.

astro-ph.IM↗