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Low luminosity observations: Low luminosity observations:

a test for the Galactic models a test for the Galactic models

Degl’Innocenti S.1 , Cignoni M.1, Castellani V.2, Petroni S.1, Prada Moroni P.G.1

1Physics Department, University of Pisa2 Monte Porzio Astronomical Observatory, Rome

The first Galactic models for star counts

The present situation

Galactic models and white dwarf population

Future developments

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Galactic Models for star counts Observational data: magnitude and colour for the stars in Galactic fields

Colour magnitude diagram for stars in the field l=111o, b= - 46o (Kron 1980)

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disc

spheroid

Three components modelsGilmore & Reid (G&R 1983)Robin & Crèze (1986)

disc

thick disk

spheroid

Two components modelsBahcall & Soneira (B&S 1980,1984)

Structure of the Galactic Models

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Number of the stars at a given location of the Galaxy in a given range of apparent luminosity

=Spatial density law i (r,L)

from a model

X Absolute luminosity function i(L) observations

(where r = galactocentric distance, L = absolute luminosity, i=Galactic components)

By integrating over all the distances in the chosen direction and over all the luminosities

Luminosity star counts

Comparison between theory and observations

By adopting a colour -magnitude relation colour star counts

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Great uncertainty for Mv > 11 but it was not a problem because at thattime the observations did not reach low luminosities

Observations by McCuskey (1966), Luyten (1968), Wielen (1974)

The luminosity function adopted in the first Galactic Models

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Satisfactory fit of the observations (V<20-21) for the B&S and G&R models confirmation of the adopted spatial distribution

NGP 1 degree2

SA 57

Bahcall & Soneira (1984)

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spher(r)/spher(ro)(r/ro)-7/8 exp[-10.093 (r/ro)1/4](con r=galactocentric distance, ro=galactocentric distance of the Sun, spher(ro)=observed local density)

(r)/(ro) exp[-z/Hz] . exp[-(x - ro)/Hx]

(z= height over the galactic disc, x= galactocentric distance on the disc,

H = scale heights)

Spatial density laws

The spheroid

The disc/thick disc

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________________________1 Mendez et al. 1996, Reid et al. 1996, Mendez & Guzman 1998, Castellani et al. 2001, Kerber et al. 20012 Casertano et al. 1990 , Wyse & Gilmore 1995 ,Ojha et al. 1996.3 vedi ad es. : Reid & Majewski 1993, Yamagata & Yoshii 1992, Ojha et al. 1996

Present situation

Recent observational data at low luminosity new development of the Galactic codes Few tests at low luminosity based on a relative few number of stars1 star counts do not still allow to certainly discriminate between models with and without thick disk

The analysis of the velocity distribution of local stars confirms the presence of a thick disk2 However it is not still possible to discriminate among the various thick disk parameters suggested by the different authors3

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Observational data taken by the HST WFPC2 (King et al. 1998)

Example: simulation of the field of NGC6397 low latitude relevant number of stars

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The spatial parameters of the three components models by Gilmore & Reid and Haywood et al. 1997

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Satisfactory agreement between theory and observations up to V 26.5

________________________* Castellani, Degl’Innocenti, Petroni, Piotto 2001

It is not possible to distinguish among the results of three component models with different spatial parameters

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The Pisa Galactic code

SPHEROID: Age 12 Gyr, Z=0.0002

Three components THICK DISK: Age 9-11 Gyr, Z=0.0061

DISK: Age 50 Myr -9 Gyr, Z=0.02

Synthetic model which adopts: Homogeneous set of evolutionary tracks/isochrones for the different Galactic populations up to the white dwarf evolutionary phase

Updated initial mass function (IMF)3

_________________________________________1Gilmore, Wyse & Jones (1995)2Cassisi, Castellani, Degl’Innocenti, Weiss 1998, Castellani, Degl’Innocenti, Marconi 1999, Salaris et al. 2000, Cassisi et al. 20003 Kroupa 2001

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Magnitude and colour of the stars CM diagram at the various Galactic co-ordinates

Evaluation of the evolutionary phase of the stars

“handy” code Inclusion of the white dwarf population in an evolutionary consistent way

The shape of the luminosity functions obtained for the disc and the spheroid is in agreement with the observational one within the present uncertainties

In this way one can obtain:

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Fit of the globular cluster M68* (Z 0.0002) with the isochrones adopted in our code for the spheroid

*Cassisi, Castellani, Degl’Innocenti, Salaris, Weiss (1998)

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Fit of the Hyades* (Z0.024)

*Castellani, Degl’Innocenti, Prada Moroni (2001)

16Synthetic CMD for Z=0.001 Y=0.23 Age=15 Gyr (Brocato et al. 2000)

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The white dwarf population

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1 Salaris et al. (2000). Now updated white dwarf evolutionary tracks by Prada Moroni and Straniero are also available

2 Dominguez et al. 1999, Weideman 20003 Bergeron (2000)

Updated evolutionary tracks 1

Recent relations between the progenitor mass and the white dwarf mass2

Updated colour transformations3

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The local white dwarfs luminosity function

Good agreement with the local white dwarf LF without any normalization of the white dwarf population

Castellani, Cignoni, Degl’Innocenti, Petroni, Prada Moroni (2002)

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The WD population is barely sensitive to a change of theoretical WD models ...

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…or to a variation of the adopted relation between the WD mass and the progenitor mass

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Spheroid CMD for a field of 1 degree2 at the NGP

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l=0 b=500.5 degree2HST field

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Observations up to V28 mag. include the whole disc and white dwarf disc population

Apparent magnitude distribution

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White dwarfs only

The thick disk WD distribution is centered at V 30 mag. while the halo WD distribution at V 31 mag.

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The Fornax field

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V magnitude distribution

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Color distribution

V 28

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Observations down to V~27-28 could allow to distinguish the WDs in color

V 28

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The observational local luminosity function for the disc

For Mv>11 the shape of the disc LF is uncertain

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The halo LF is uncertain for Mv > 8

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This affects the evaluation of the IMF:

Observational LF+mass - luminosity relation

IMF results

Per M>0.5 Mo dN/dM M- (with 0.3

Per M<0.5 Mo the behaviour is not still well defined2

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* see e.g. Kroupa 2001, Massey 19952 see e.g.. Scalo 1998, Kroupa 1998, Kroupa 2001

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By adopting the Kroupa (2001) IMF and our evolutionary tracks weobtain theoretical halo and disc LFs in agreement with the observationalones within their uncertaintes

Note that the white dwarf population is not affected by the uncertainty on the low luminosity part of the LF (low mass IMF)

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The effects on the results of the LF uncertainty

V magnitude distribution in the field of NGC6397 for several assumptions about the disc/spheroid LFs

________________* Castellani, Degl’Innocenti, Petroni, Piotto 2000

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After the calibration of the spatial parameters thanks to the observations at high/intermediate luminosity

Comparison between theory and observations for several fields at low luminosity could constrain the shape of the disc/spheroid LF

Is it possible to constrain the low luminosity part of the LF ?

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Models with and without thick disc

At the high latitudes one expects a colour separation between the disc and the spheroid, while the thick disc should assume intermediate colours

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Colour star counts

As the luminosity decreases the differences in colour between models with and without thick disk increases

Star counts up to V 25 at latitudes 45o50o should discriminate between models with and without thick disk

___ without thick disc___ with thick disc

___ thick disc

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…and then…age-metallicity-relations, star formation history…

The work is just at the beginning!