1. 1 Low luminosity observations: a test for the Galactic models Degl’Innocenti S. 1, Cignoni M. 1, Castellani V. 2, Petroni S. 1, Prada Moroni P.G. 1 1 Physics Department, University of Pisa 2 Monte Porzio Astronomical Observatory, Rome  The first Galactic models for star counts  The present situation  Galactic models and white dwarf population  Future developments

2. 2 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=111 o, b= - 46 o (Kron 1980)

3. 3 disc spheroid Three components models Gilmore & Reid (G&R 1983) Robin & Crèze (1986) disc thick disk spheroid Two components models Bahcall & Soneira (B&S 1980,1984) Structure of the Galactic Models

4. 4 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 

5. 5 Great uncertainty for M v > 11 but it was not a problem because at that time the observations did not reach low luminosities Observations by McCuskey (1966), Luyten (1968), Wielen (1974) The luminosity function adopted in the first Galactic Models

6. 6 Satisfactory fit of the observations (V<20-21) for the B&S and G&R models  confirmation of the adopted spatial distribution NGP 1 degree 2 SA 57 Bahcall & Soneira (1984)

7. 7  spher (r)/  spher (r o )  (r/r o ) -7/8 exp[-10.093 (r/r o ) 1/4 ] (con r=galactocentric distance, r o =galactocentric distance of the Sun,  spher (r o )=observed local density)  (r)/  (r o )  exp[-z/H z ]. exp[-(x - r o )/H x ] (z= height over the galactic disc, x= galactocentric distance on the disc, H = scale heights) Spatial density laws The spheroid The disc/thick disc

8. 8 ________________________ 1 Mendez et al. 1996, Reid et al. 1996, Mendez & Guzman 1998, Castellani et al. 2001, Kerber et al. 2001 2 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 stars 1   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 disk 2   However it is not still possible to discriminate among the various thick disk parameters suggested by the different authors 3

9. 9 Observational data taken by the HST WFPC2 (King et al. 1998) Example: simulation of the field of NGC6397 low latitude   relevant number of stars

10. 10 The spatial parameters of the three components models by Gilmore & Reid and Haywood et al. 1997

11. 11  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

12. 12 The Pisa Galactic code SPHEROID: Age 12 Gyr, Z=0.0002  Three components THICK DISK: Age 9-11 Gyr, Z=0.006 1 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  _________________________________________ 1 Gilmore, Wyse & Jones (1995) 2 Cassisi, Castellani, Degl’Innocenti, Weiss 1998, Castellani, Degl’Innocenti, Marconi 1999, Salaris et al. 2000, Cassisi et al. 2000 3 Kroupa 2001

13. 13  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:

14. 14 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)

15. 15 Fit of the Hyades * (Z  0.024) * Castellani, Degl’Innocenti, Prada Moroni (2001)

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

17. 17 The white dwarf population ________________________________________ 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 2000 3 Bergeron (2000)  Updated evolutionary tracks 1  Recent relations between the progenitor mass and the white dwarf mass 2  Updated colour transformations 3

18. 18

19. 19 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)

20. 20 The WD population is barely sensitive to a change of theoretical WD models...

21. 21 …or to a variation of the adopted relation between the WD mass and the progenitor mass

22. 22 Spheroid CMD for a field of 1 degree 2 at the NGP

23. 23 l=0 b=50 0.5 degree 2 HST field

24. 24  Observations up to V  28 mag. include the whole disc and white dwarf disc population Apparent magnitude distribution

25. 25 White dwarfs only  The thick disk WD distribution is centered at V  30 mag. while the halo WD distribution at V  31 mag.

26. 26 The Fornax field

27. 27 V magnitude distribution

28. 28 Color distribution V  28

29. 29 Observations down to V~27-28 could allow to distinguish the WDs in color V  28

30. 30 The observational local luminosity function for the disc For Mv>11 the shape of the disc LF is uncertain

31. 31 The halo LF is uncertain for M v > 8

32. 32 This affects the evaluation of the IMF: Observational LF + mass - luminosity relation IMF results  Per M>0.5 M o dN/dM  M -  (with  0.3    Per M<0.5 M o the behaviour is not still well defined 2 ______________________________________________________________ * see e.g. Kroupa 2001, Massey 1995 2 see e.g.. Scalo 1998, Kroupa 1998, Kroupa 2001

33. 33  By adopting the Kroupa (2001) IMF and our evolutionary tracks we obtain theoretical halo and disc LFs in agreement with the observational ones 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)

34. 34 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

35. 35 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 ?

36. 36 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

37. 37 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 45 o  50 o should discriminate between models with and without thick disk ___ without thick disc ___ with thick disc ___ thick disc

38. 38 …and then…age-metallicity-relations, star formation history… The work is just at the beginning!