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with a degree of structure that can be attributed to the distinct disk and spheroid components. | with a degree of structure that can be attributed to the distinct disk and spheroid components. |
This similarity is not so surprising really. since consideration of the galaxy luminosity function shows that most of the stellar light comes from galaxies with Juminosities around the break in the Schechter function. and at these lummosities a galaxy is typically a spiral system like that modeled in Fig. 1.. | This similarity is not so surprising really, since consideration of the galaxy luminosity function shows that most of the stellar light comes from galaxies with luminosities around the break in the Schechter function, and at these luminosities a galaxy is typically a spiral system like that modeled in Fig. \ref{fig:mwphase}. |
More interestingly. though. we can now begin to look systematically at the properties of different sub-classes of galaxies and individual components. | More interestingly, though, we can now begin to look systematically at the properties of different sub-classes of galaxies and individual components. |
As a simple illustration. | As a simple illustration, |
than Mwp=1.1Me most probably have ONe cores. and for these white dwarfs we adopt the cooling sequences of Althaus et al. ( | than $M_{\rm WD}=1.1\, M_{\sun}$ most probably have ONe cores, and for these white dwarfs we adopt the cooling sequences of Althaus et al. ( |
2007). | 2007). |
AM these cooling sequences incorporate the most accurate physical inputs for the stellar interior (including neutrinos. erystallization. phase separation and Debye cooling) and. for the case of DA white dwarfs. reproduce the blue turn at low luminosities (Hansen 1998). | All these cooling sequences incorporate the most accurate physical inputs for the stellar interior (including neutrinos, crystallization, phase separation and Debye cooling) and, for the case of DA white dwarfs, reproduce the blue turn at low luminosities (Hansen 1998). |
To assign a spectral type to each of the white dwarfs in the simulated sample we proceeded as follows. | To assign a spectral type to each of the white dwarfs in the simulated sample we proceeded as follows. |
In a first set of simulations we adopted the canonical fraction of of white dwarfs of the spectral type DA and of the non-DA class. independently of the effective temperature of the white dwarf. | In a first set of simulations we adopted the canonical fraction of of white dwarfs of the spectral type DA and of the non-DA class, independently of the effective temperature of the white dwarf. |
We regard this as our fiducial model. and we refer to it as model A. However. several observations indicate that this ratio is a function of the effective temperature. | We regard this as our fiducial model, and we refer to it as model A. However, several observations indicate that this ratio is a function of the effective temperature. |
For instance. the well-known DB-gap. where no white dwarfs of the DB spectral class can be found. occurs at effective temperatures between 45.0000 K and 300000 K. Additionally. Bergeron. Leggett Ruiz (2001) found that most white dwarfs with effective temperatures ranging from 60000 K to 50000 K are DAs. | For instance, the well-known DB-gap, where no white dwarfs of the DB spectral class can be found, occurs at effective temperatures between 000 K and 000 K. Additionally, Bergeron, Leggett Ruiz (2001) found that most white dwarfs with effective temperatures ranging from 000 K to 000 K are DAs. |
Finally. Bergeron Leggett (2002) argued that all white dwarfs cooler than 40000 K have mixed H/He atmospheres. | Finally, Bergeron Leggett (2002) argued that all white dwarfs cooler than 000 K have mixed H/He atmospheres. |
Many of these early findings have been corroborated by the wealth of data obtained from recent large surveys. like the Sloan Digital Sky-Survey (Harris et al. | Many of these early findings have been corroborated by the wealth of data obtained from recent large surveys, like the Sloan Digital Sky-Survey (Harris et al. |
2006: Kilic et al. | 2006; Kilic et al. |
2006). | 2006). |
Accordingly. we have have produced a second set of simulations. and we refer to them as model B. following these observational results. | Accordingly, we have have produced a second set of simulations, and we refer to them as model B, following these observational results. |
Basically. in model B we adopt the same fraction of DA white dwarfs )) for temperatures above 60000 K. All white dwarfs in. the range of effective temperatures between 60000 K and 0000 K were considered to be DA white dwarfs. | Basically, in model B we adopt the same fraction of DA white dwarfs ) for temperatures above 000 K. All white dwarfs in the range of effective temperatures between 000 K and 000 K were considered to be DA white dwarfs. |
Finally. for effective temperatures below this value we adopt a fraction of (Bergeron Legget 2002; Gates et al. | Finally, for effective temperatures below this value we adopt a fraction of (Bergeron Legget 2002; Gates et al. |
2004). | 2004). |
We would like to note that we model the transitions between the different spectral classes in à purely heuristic way because currently there are no cooling sequences which correctly reproduce these transitions. as this is a long-standing problem. which is indicative of a failure of the theoretical cooling models. | We would like to note that we model the transitions between the different spectral classes in a purely heuristic way because currently there are no cooling sequences which correctly reproduce these transitions, as this is a long-standing problem, which is indicative of a failure of the theoretical cooling models. |
However. our model correctly reproduces the observations. and thus we consider it to be a fair approach. | However, our model correctly reproduces the observations, and thus we consider it to be a fair approach. |
Finally. to check the sensitivity of our results to the adopted cooling tracks we have also computed a third set of simulations. based on model B. in which we use the cooling sequences of Bergeron et al. ( | Finally, to check the sensitivity of our results to the adopted cooling tracks we have also computed a third set of simulations, based on model B, in which we use the cooling sequences of Bergeron et al. ( |
1995). | 1995). |
We refer to this model as model C. We have adopted a spherically symmetric halo. | We refer to this model as model C. We have adopted a spherically symmetric halo. |
In particular the model used here is the typical isothermal sphere of a radius of 5 kpe. also called the "S-model". which has been extensively used by the MACHO collaboration (Alcock et al. | In particular the model used here is the typical isothermal sphere of a radius of $5$ kpc, also called the “S-model”, which has been extensively used by the MACHO collaboration (Alcock et al. |
2000: Griest 1991), | 2000; Griest 1991). |
Despite the fact that other models as for instance the exponential power-law models or the Navarro. French White (1997) density profiles have been proposed. our studies (Gareraa—Berro et al. | Despite the fact that other models as for instance the exponential power-law models or the Navarro, French White (1997) density profiles have been proposed, our studies a–Berro et al. |
2004) have shown that no relevant differences are found when these models are used. | 2004) have shown that no relevant differences are found when these models are used. |
Furthermore. we do not consider non-standard models of the Galactic halo. such as models with flattened density profiles. oblate halo models and others because a thorough study of these models is beyond the scope of this paper. | Furthermore, we do not consider non-standard models of the Galactic halo, such as models with flattened density profiles, oblate halo models and others because a thorough study of these models is beyond the scope of this paper. |
The kinematical properties of the halo population have been modeled according to Gaussian. laws (Binney Tremaine 1987) with radial and tangential velocity dispersions accordingly related by the Jeans equation and fulfilling the flat rotation curve of our Galaxy. | The kinematical properties of the halo population have been modeled according to Gaussian laws (Binney Tremaine 1987) with radial and tangential velocity dispersions accordingly related by the Jeans equation and fulfilling the flat rotation curve of our Galaxy. |
We have adopted standard values for the circular velocity Vo=220 km/s as well as for the peculiar velocity of the Sun (Uo.Vo.We)=(10.0.15.0.8.0) km/s (Dehnen Binney 1998). | We have adopted standard values for the circular velocity $V_{\rm
c}=220$ km/s as well as for the peculiar velocity of the Sun $(U_{\sun}, V_{\sun},W_{\sun})=(10.0, 15.0, 8.0)$ km/s (Dehnen Binney 1998). |
Besides. we have rejected stars with velocities higher than 750 km/s. because they would have velocities exceeding 1.5 times the escape velocity. | Besides, we have rejected stars with velocities higher than 750 km/s, because they would have velocities exceeding 1.5 times the escape velocity. |
Finally. since white dwarfs usually do not have determinations of the radial component of the velocity. the radial velocity i5 eliminated wher a comparison with the observational data is needed. | Finally, since white dwarfs usually do not have determinations of the radial component of the velocity, the radial velocity is eliminated when a comparison with the observational data is needed. |
Finally. to compare the simulated results with the observational ones. a normalization criterion should be used. | Finally, to compare the simulated results with the observational ones, a normalization criterion should be used. |
We have proceeded as in our previous papers (Camacho et al. | We have proceeded as in our previous papers (Camacho et al. |
2007: Garctaa-Berro et al. | 2007; a–Berro et al. |
2004: Torres et al. | 2004; Torres et al. |
2008). | 2008). |
That is. we have normalized our simulations to the local density of halo white dwarfs obtained from the halo white dwarf luminosity function of Torres et al. ( | That is, we have normalized our simulations to the local density of halo white dwarfs obtained from the halo white dwarf luminosity function of Torres et al. ( |
1998). but taken into account the new halo white dwarf candidates found in the SDSS Stripe 82 (Vidrth et al. | 1998), but taken into account the new halo white dwarf candidates found in the SDSS Stripe 82 (Vidrih et al. |
2007). | 2007). |
Nevertheless. we emphasize that when normalizing to the local density of halo white dwarfs obtained using the white dwarf luminosity function we only consider those stars with velocities higher than 250 km/s. given that only those stars would be genumely considered as halo members and would be used to build the observational halo luminosity function (Liebert et al. | Nevertheless, we emphasize that when normalizing to the local density of halo white dwarfs obtained using the white dwarf luminosity function we only consider those stars with velocities higher than $250$ km/s, given that only those stars would be genuinely considered as halo members and would be used to build the observational halo luminosity function (Liebert et al. |
1989: Torres et al. | 1989; Torres et al. |
1998). | 1998). |
This is totally equivalent to the adopted cut in reduced proper motion employed by Flynn et al. ( | This is totally equivalent to the adopted cut in reduced proper motion employed by Flynn et al. ( |
2001). | 2001). |
Additionally. only the number density of DA white dwarfs was considered to normalize the simulations. since all but one of the white dwarfs used to obtain the luminosity function of Torres et al. ( | Additionally, only the number density of DA white dwarfs was considered to normalize the simulations, since all but one of the white dwarfs used to obtain the luminosity function of Torres et al. ( |
1998) were of the DA spectral type. | 1998) were of the DA spectral type. |
Obviously. imposing this normalization we implicitly assume that the MACHO results and the direct surveys are complementary and seem to be probing the same populations. whatever the nature of those populations (Hansen Liebert 2003). | Obviously, imposing this normalization we implicitly assume that the MACHO results and the direct surveys are complementary and seem to be probing the same populations, whatever the nature of those populations (Hansen Liebert 2003). |
The structure and kinematics of the Galactic disk remain a source of controversy and discussion. | The structure and kinematics of the Galactic disk remain a source of controversy and discussion. |
In particular the nature of the thick disk is an active field of research. | In particular the nature of the thick disk is an active field of research. |
Consequently we have used two different models in our simulations. | Consequently we have used two different models in our simulations. |
The first of these is a canonical thick disk model. which we consider | The first of these is a canonical thick disk model, which we consider |
Figure 5 is an example of a GaussFit model file. | Figure \ref{fig:model} is an example of a GaussFit model file. |
It describes a binary with a fixed positiona offset between the components aa lone-period binary). | It describes a binary with a fixed positional offset between the components a long-period binary). |
The model paralcters are thus the astrometric parameters of the primary relative to the reference point (x1=Aax,. yt= Aé,. par=Aw. xdot=Aji... ydot=Ajrys). the position of the secondary relative to the reference poiut (x2= Ans. yl= Ady): and the intensities of the compoucuts. AL=4. AQ=.». | The model parameters are thus the astrometric parameters of the primary relative to the reference point ${\tt x1}=\Delta\alpha*_1$ , ${\tt y1}=\Delta\delta_1$ , ${\tt par}=\Delta\pi$, ${\tt xdot}=\Delta\mu_{\alpha*}$, ${\tt ydot}=\Delta\mu_\delta$ ), the position of the secondary relative to the reference point ${\tt x2}=\Delta\alpha*_2$ , ${\tt y1}=\Delta\delta_2$ ); and the intensities of the components, ${\tt A1}=A_1$, ${\tt A2}=A_2$. |
The components are assumed to have the same parallax and proper motion. | The components are assumed to have the same parallax and proper motion. |
The expressions within the export() functions are casily recognized as the equations of condition. Eq. (11)). | The expressions within the $\tt export()$ functions are easily recognized as the equations of condition, Eq. \ref{eq:phaseelem}) ), |
written in terms of the model paramcters. | written in terms of the model parameters. |
The five export() statements are divided among two import(} oops (which means that the data file is forced to be read twice in cach iteration): the reason is that GaussFit in its standard distribution version cannot handle more than four simultaneous equatious of coudition. | The five $\tt export()$ statements are divided among two $\tt import()$ loops (which means that the data file is forced to be read twice in each iteration): the reason is that GaussFit in its standard distribution version cannot handle more than four simultaneous equations of condition. |
The model iu Fig. | The model in Fig. |
ὃ was applied to the TD of IIIP 97237. using as starting approximation (3600. 3600. 0. 0. 0. Ομ. £000. 1300. 0.02) for the variables in the paralcter list SSect. L3)). | \ref{fig:model} was applied to the TD of HIP 97237, using as starting approximation (3600, 3600, 0, 0, 0, 0.04, 4000, 4300, 0.02) for the variables in the parameter list Sect. \ref{sec:images}) ). |
The ‘fair’ netric with iu asvinptotic relative efficiency. of 0.95 was used for robust estimation of the parameters (Jefferys et citeef)). | The `fair' metric with an asymptotic relative efficiency of 0.95 was used for robust estimation of the parameters (Jefferys et \\cite{gf}) ). |
Part of the output file. coutainiug the results of the final (10th) iteration. is shown in Fig. 9.. | Part of the output file, containing the results of the final (10th) iteration, is shown in Fig. \ref{fig:output}. |
It should be noted that the estimated standard errors (ignia values) given iu the output file have already been scaled by (Cp. using. the chi-square⋅ 9 (47) and degrees of freedom (7) given at the cud of the file. | It should be noted that the estimated standard errors (sigma values) given in the output file have already been scaled by $(\chi^2/\nu)^{1/2}$, using the chi-square $\chi^2$ ) and degrees of freedom $\nu$ ) given at the end of the file. |
Adding the results of the model fitting to the reference point data (Sect. [.3)) | Adding the results of the model fitting to the reference point data (Sect. \ref{sec:images}) ) |
aud usine the magnitude conversion formula Jp—2.5logCA/N) we obtain the following estimated paraimcters of the binary UIP 97257 (ICRS. epoch J1991.25): These data are in reasonable agrecnmieut with the values derived by Sódderhjeha (1999)) iu an orbital solution combining the TD with erouud-based speckle observations. | and using the magnitude conversion formula $Hp=-2.5\log(A/K)$ we obtain the following estimated parameters of the binary HIP 97237 (ICRS, epoch J1991.25): These data are in reasonable agreement with the values derived by Södderhjelm \cite{ss99}) ) in an orbital solution combining the TD with ground-based speckle observations. |
Fortran programs interfacing the TD with aperture svuthesis software and with CaussFit are available via the Luud Observatory Tateruct address ww.astro.u.se/leunart/TD/. The program td2uv.f extracts the TD for a eiven TIP ideuti&er aud converts them iuto a UV-FITS file that cal be used bby Difinap. | Fortran programs interfacing the TD with aperture synthesis software and with GaussFit are available via the Lund Observatory Internet address $\sim$ lennart/TD/. The program td2uv.f extracts the TD for a given HIP identifier and converts them into a UV-FITS file that can be used by Difmap. |
The program td2eff similarly extracts TD data and eeuerates a data file suitable as input for CaussEit. | The program td2gf.f similarly extracts TD data and generates a data file suitable as input for GaussFit. |
Sample data files. additional information on the TD (Guechiding descriptions of the known errors). and links for retrieving aperture svuthesis software and CGaussFit are also eiven at this site. | Sample data files, additional information on the TD (including descriptions of the known errors), and links for retrieving aperture synthesis software and GaussFit are also given at this site. |
The Iippareos Transit Data. published as part of the Tipparcos aud Tycho Catalogues (ESA 1997)). provide data from an intermediate step in the data reduction process of the NDAC data analysis cousortimm. | The Hipparcos Transit Data, published as part of the Hipparcos and Tycho Catalogues (ESA \cite{hip}) ), provide data from an intermediate step in the data reduction process of the NDAC data analysis consortium. |
Transit Data are ggiven for all kuown or suspected double or iultiple star svstenis iun the Iüpparcos Cataloge. or about a third of the objects in the catalogue. | Transit Data are given for all known or suspected double or multiple star systems in the Hipparcos Catalogue, or about a third of the objects in the catalogue. |
There were several reasons to include hese data in the published catalogue. | There were several reasons to include these data in the published catalogue. |
A main reason was the realization that every stellar system could not be examined for every possible type of solution within the time available for completing the catalogue. | A main reason was the realization that every stellar system could not be examined for every possible type of solution within the time available for completing the catalogue. |
Ideally. such examination should also take iuto account eround-based obscrvations. | Ideally, such examination should also take into account ground-based observations. |
The Transit Data allow the user to re-exanunue such solutions. should the need arise. | The Transit Data allow the user to re-examine such solutions, should the need arise. |
Basically the Transit Data coutaiu the Fourier cocfficieuts which describe the modulation of the detector signal caused by the object's motion across the modulating exid. | Basically the Transit Data contain the Fourier coefficients which describe the modulation of the detector signal caused by the object's motion across the modulating grid. |
As such they retain all the photometric and astrometric information on the object gathered during its transit across the eric. | As such they retain all the photometric and astrometric information on the object gathered during its transit across the grid. |
The Transit Data have been carefully calibrated and referred to the TWipparcos photometric and astrometric svstems. so that any data derived from them should be directly comparable with other results in the published catalogue. | The Transit Data have been carefully calibrated and referred to the Hipparcos photometric and astrometric systems, so that any data derived from them should be directly comparable with other results in the published catalogue. |
By eiving lis review of how the Transit Data were recorded. what they plysically represcut aud examples of their practical uses. we lope to encourage readers to utilize the data in their own exploitatious of the Tipparcos results. | By giving this review of how the Transit Data were recorded, what they physically represent and examples of their practical uses, we hope to encourage readers to utilize the data in their own exploitations of the Hipparcos results. |
To aid this process. we have made prograis available which provide interfaces with publicly available software packages. iu particular Difinap and GaussFit. | To aid this process, we have made programs available which provide interfaces with publicly available software packages, in particular Difmap and GaussFit. |
Mauv other applications could be thought of the combination of Transit Data with eround-based speckle observations of double stars to improve orbits. parallaxes and mass ratios bySÓdderhjeha (1999)) is anexample. | Many other applications could be thought of – the combination of Transit Data with ground-based speckle observations of double stars to improve orbits, parallaxes and mass ratios bySödderhjelm \cite{ss99}) ) is anexample. |
What las been covered aud demonstrated here mught just be a stepping stone to new and creative exploitations of the Transit Data. | What has been covered and demonstrated here might just be a stepping stone to new and creative exploitations of the Transit Data. |
issues: 1) how the presence of the nonuniform velocity Ποἰ affects the propagation of the waves (through the stellar plasma: 2) what kind of energy. exchange processes between the different. collective modes and between the modes and the ambient flow may happen: ancl 3) what other astrophysical consequences these processes could have. | issues: 1) how the presence of the nonuniform velocity field affects the propagation of the waves through the stellar plasma; 2) what kind of energy exchange processes between the different collective modes and between the modes and the ambient flow may happen; and 3) what other astrophysical consequences these processes could have. |
Originally. we develop the three-dimensional (3D) model. allowing the ambient flow to have velocity shearing in both transversal (prior to the gravitv field) directions. | Originally, we develop the three-dimensional (3D) model, allowing the ambient flow to have velocity shearing in both transversal (prior to the gravity field) directions. |
Further on. the study is focused. by a number of simplifving assumptions. enabling the solution of the equations. | Further on, the study is focused by a number of simplifying assumptions, enabling the solution of the equations. |
First of all. we consider only. two spatial dimensions (2D) bearing in mind that il is quite straightforward (0 extend (the analysis to the fully three-dimensional case. | First of all, we consider only two spatial dimensions (2D) bearing in mind that it is quite straightforward to extend the analysis to the fully three-dimensional case. |
Second. we assunie a constant steady-state (or stationarv) shear flow. an assumption that allows us to use the (Goldreich&Lvnden-Dell.1965). | Second, we assume a constant steady-state (or stationary) shear flow, an assumption that allows us to use the \citep{gl65}. |
. And third. we use theapprozimalion.. and hence we study the dynamics of relatively perturbations of the low-Irequeney modes. tthe Gravito-Alfvénn waves (GAW) and the Entropy Mode (EM) perturbations. | And third, we use the, and hence we study the dynamics of relatively perturbations of the low-frequency modes, the Gravito-Alfvénn waves (GAW) and the Entropy Mode (EM) perturbations. |
Our study leads to the conelusion that lor shear in the flow. there exists a finite interval of time in which the evolution of the modes is highly non-adiabatic. | Our study leads to the conclusion that for shear in the flow, there exists a finite interval of time in which the evolution of the modes is highly non-adiabatic. |
Outside this interval. the evolution is adiabatic and can be accurately described by a WIND approximation. | Outside this interval, the evolution is adiabatic and can be accurately described by a WKB approximation. |
Therefore. we have an asvinplolic problem. equite common for various quantunm-mechianmical applications. where one needs (to obtain connecüon l[ormulae in (Landau&Lilshitz1977). | Therefore, we have an asymptotic problem, quite common for various quantum-mechanical applications, where one needs to obtain connection formulae in \citep{ll77}. |
.. The relevant analvsis is done in (his paper and it is found that the non-adiabatic behavior of the considered modes manilests itself in the form of two phenomena. (the of the GAW and the of the GAW hy the EM perturbations. | The relevant analysis is done in this paper and it is found that the non-adiabatic behavior of the considered modes manifests itself in the form of two phenomena, the of the GAW and the of the GAW by the EM perturbations. |
We show that for flows will moderate and high shearing rates both these processes are very effective converters of the equilibrium flow energy into the energy of the Waves, | We show that for flows with moderate and high shearing rates both these processes are very effective converters of the equilibrium flow energy into the energy of the waves. |
In the context of above-discussed astrophysical problems our results imply that efficient eeneration of the GAW by the EM perturbations takes place for shearing rates of about an order of magnitude smaller (hen necessary [or development of shear instability. | In the context of above-discussed astrophysical problems our results imply that efficient generation of the GAW by the EM perturbations takes place for shearing rates of about an order of magnitude smaller then necessary for development of shear instability. |
The remainder of the paper is organized in the following wav: (he general mathematical and heuristie formalism is presented in the Sec. | The remainder of the paper is organized in the following way: the general mathematical and heuristic formalism is presented in the Sec. |
2. | 2. |
The over-reflection of GAW is studied in the Sec. | The over-reflection of GAW is studied in the Sec. |
3: and the second non-adiabatie process. (the generation of the GAW by the EM perturbations. is studied in the Sec. | 3; and the second non-adiabatic process, the generation of the GAW by the EM perturbations, is studied in the Sec. |
4. | 4. |
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