371 research outputs found
Emden-Chandrasekhar axisymmetric, solid-body rotating polytropes II - Power series solutions to EC associated equations of degree 0 and 2
No full textAccording to the general results of a previous work (Caimmi, 1980), solutions to EC equation, which expresses a necessary and sufficient condition for equilibrium of Emden-Chandrasekhar axisymmetric solid-body rotating polytropes, are taken into account. The author extends the methods used by Seidov and Kuzakhmedov (1977), and Mohan and Al-Bayaty (1980), to construct power series related to the solid-body rotating configurations. Comparison between results of this paper and the accurate results by Linnell (1977, 1981) obtained using a different approach lead to a fair agreement
Bivariate least squares linear regression: towards a unified analytic formalism. II. Extreme structural models
No full textConcerning bivariate least squares linear regression, the
classical results obtained for extreme structural
models in earlier attempts (Isobe et al., 1990;
Feigelson and Babu, 1992) 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 a variant of the usual additive model.
The classes of linear models considered are
regression lines in the limit of
uncorrelated errors in X and in Y.
The following models are
considered in detail: (Y) errors
in X negligible (ideally null) with
respect to errors in Y; (X) errors
in Y negligible (ideally null) with
respect to errors in X; (C) oblique
regression; (O) orthogonal regression;
(R) reduced major-axis regression;
(B) bisector regression.
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 (York, 1966; Caimmi, 2011).
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
The G-dwarf problem in the Galaxy
No full textThis paper has two parts: one about observational constraints, and the other about chemical evolution models. In the first part, the empirical differential metallicity distribution (EDMD) is deduced from three different samples involving (i) local thick disk stars derived from Gliese and scaled in situ samples within the range, -1.20⩽[Fe/H]⩽-0.20 [Wyse, R.F.G., Gilmore, G., 1995. AJ 110, 2771]; (ii) 46 likely metal-weak thick disk stars within the range, -2.20⩽[Fe/H]⩽-1.00 [Chiba, M., Beers, T.C., 2000. AJ 119, 2843]; (iii) 287 chemically selected G dwarfs within 25 pc from the Sun, with the corrections performed in order to take into account the stellar scale height [Rocha-Pinto, H.J., Maciel, W.J., 1996. MNRAS 279, 447]; in addition to previous results [Caimmi, R., 2001b. AN 322, 241; Caimmi, R., 2007. NewA 12, 289] related to (iv) 372 solar neighbourhood halo subdwarfs [Ryan, S.G., Norris, J.E., 1991. AJ 101, 1865]; and (v) 268 K-giant bulge stars [Sadler, E.M., Rich, R.M., Terndrup, D.M., 1996. AJ 112, 171]. The metal-poor and metal-rich EDMD related to the thick disk shows similarities with their halo and bulge counterparts, respectively. Then the thick disk is conceived as made of two distinct regions: the halo-like and the bulge-like thick disk, and the related EDMD is deduced. Under the assumption that each distribution is typical for the corresponding subsystem, the EDMD of the thick disk, the thick + thin disk, and the Galaxy, is determined by weighting the mass. In the second part, models of chemical evolution for the halo-like thick disk, the bulge-like thick disk, and the thin disk, are computed assuming the instantaneous recycling approximation. The EDMD data are fitted, to an acceptable extent, by simple models of chemical evolution implying both homogeneous and inhomogeneous star formation, provided that star formation is inhibited during thick disk formation, with respect to the thin disk. The initial mass function (IMF) is assumed to be a universal power law, which implies the same value of the true yield in different subsystems. The theoretical differential metallicity distribution (TDMD) is first determined for the halo-like thick disk, the bulge-like thick disk, and the thin disk separately, and then for the Galaxy by weighting the mass. An indicative comparison is performed between the EDMD deduced for the disk both in presence and in absence of [O/Fe] plateau, and its counterpart computed for (vi) N=523 nearby stars within the range, -1.5<[Fe/H]<0.5, for which the oxygen abundance has been determined both in presence and in absence of the local thermodynamical equilibrium (LTE) approximation [Ramirez, I., Allende Prieto, C., Lambert, D.L., 2007. A&A 465, 271]. Both distributions are found to exhibit a similar trend, although systematic differences exist. In addition, the related empirical age-metallicity relation (EAMR) cannot be fitted by the theoretical age-metallicity relation (TAMR) predicted by the model, and the reasons for this discrepancy are explained
Emden-chandrasekhar axisymmetric, rigidly rotating polytropes III - Determination of equilibrium configurations by an improvement of Chandrasekhar's method
No full textThe author determines equilibrium configurations of Emden-Chandrasekhar axisymmetric, solid-body rotating polytropes, defined as EC polytropes, for polytropic indices ranging from 0 (homogeneous bodies) to 5 (Roche-type bodies). To this aim, he improves Chandrasekhar's method to determine equilibrium configurations in two respects: namely, (1) no distinction exists between undistorted and distorted terms in the expression of the potential, and (2) the comparison between the expressions of gravitational potential and its first derivatives inside and outside the body has to be made on the boundary of a sphere of radius ξ0 ≥ ΞE, which does not necessarily coincide with the undistorted Emden's sphere of radius ΞE. The author also allows different values of ξ0 for different physical parameters, and chooses a special set which fits more refined results (involving more complicated and more expensive computer codes) by James (1964)
Bivariate least squares linear regression: Towards a unified analytic formalism. I. Functional models
No full textConcerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts (York, 1966, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted 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 general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter (Isobe et al., 1990; Feigelson and Babu, 1992). 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 the exception of Y 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 selected samples and assigned methods, different regression models yield consistent results within the errors (∓σ) 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 the presence of large dispersion data. An extension of the formalism to structural models is left to a forthcoming paper
Test of Clausius' Virial Dynamical Theory of Fundamental Plane By Homogeneous + γ-Free Two Component Galaxy Model
No full textIntroduction: the theory of the Fundamental Plane (FP) proposed by Secco (2000, 2001,2005) is based on the existence of a maximum in the Clausius' Virial potential energy (CV) of a stellar component when it is
completely embedded inside a dark matter (DM) halo. At the first order approximation the theory was developed by modeling the two-components with two power-law density profiles and two homogeneous cores. In order to test the extension of the theory to an higher order we explore the effect on an homogeneous stellar component due to a DM halo with a density profile characterized by a inner slope γfree and an outer slope -3, according to high resolution rotation curves of Sps (Garrido et al. 2004). The aim is to investigate the role of the dark to bright mass ratio m and of the halo concentration C[D] in order to produce the maximum of CV. Particular attention is devoted to the slope of the density halo profile at the maximum location, to its height in comparison with the CV value when the two component coincide, V[n.] For all the models we choose γ=0. Method: we follow the general method
proposed by Caimmi (1993) for two striated ellipsoidals with Zhao-density profiles. Virial equilibrium is described by tensor virial equations extended to two subcomponents (Caimmi & Secco,1992). The interaction terms are numerically performed for different values of m and C [D] and sequences of CV as function of the ratio baryonic to halo virial semi-axis are taken into account. Results: the special configuration at the CV maximum with all the properties discovered with the theory of first order appears if m is greater than a given threshold.The corresponding slope (in absolute value) on the halo DM profile decreases either as m increases at fixed C[D] or as C[D] decreases at fixed m. The same conspiracy between m and C[D] appears in order to obtain the highest values of V[n]. Discussion: the test is relevant in order to confirm the main results of the first order approach and then to move the description of the main features of galaxy FP toward more realistic models
Simple MCBR models of chemical evolution: An application to the thin and the thick disk
No full textSimple multistage closed-(box+reservoir) (MCBR) models of chemical evolution,
formulated in an earlier attempt, 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 (EDOD), which can be linearly fitted, a family of theoretical
differential oxygen abundance distribution (TDOD) curves is built up with the
following prescriptions: (i) the initial and the ending points of the linear
fit are common to all curves; (ii) the flow parameter k ranges from an
extremum point to ± ∞, where negative and positive k correspond to inflow and
outflow, respectively; (iii) the cut parameter ζO ranges from an extremum
point (which cannot be negative) to the limit (ζO) ∞ related to |k|→ + ∞. For
curves with increasing ζO, the gas mass fraction locked up into long-lived
stars and remnants is found to attain a maximum and then decrease towards
zero as |k|→ + ∞ while the remaining parameters show a monotonic trend. The
theoretical integral oxygen abundance distribution (TIOD) is also expressed.
An application is made to the EDOD 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, namely: assembling (A), formation
(F), contraction (C), equilibrium (E). The EDOD related to any stage is
fitted by all curves where 0 ≤ ζO ≤ (ζO) ∞ for inflowing gas and (ζO) ∞ ≤ ζO
≤ 1.2 for outflowing gas, with a single exception related to the thin disk (A
stage), where the range of fitting curves is restricted to 0.35 ≤ ζO ≤ (ζO)
∞. The F stage may safely be described by a steady inflow regime (k= -1),
implying a flat TDOD, 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 EDOD, 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
Emden-Chandrasekhar axisymmetric, rigid-body rotating polytropes IV - Exact configurations for n = 5
No full textIn connection with the basic theory reported in a previous paper for EC1 (rigidly rotating) polytropes, exact configurations are defined as configurations for which the equilibrium equation has solutions which are infinitely close to some analytical function and the related gravitational potential coincides, in fact, with the gravitational potential due to mass distribution, at any point not outside the system. The author restricts to the special case n = 5 and divides the related polytropes into two components, a massive body where each mass element has a finite (polytropic) distance from the centre, and a massless atmosphere where each mass element has an infinite (polytropic) distance from the centre. In the special case n = 0 it is shown that a particular configuration, the spheroidal one, is an exact configuration and evidence is given that spheroidal configurations are the most stable among all the allowed (axisymmetric) configurations. It is also pointed out that EC1 polytropes with n = 0 and incompressible Maclaurin spheroids belong to different sequences, even if they exhibit some common features
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