The kinematic and Period–Luminosity–Colour distribution of O-rich Long-Period Variable stars of the solar neighbourhood is interpreted in terms of pulsation modes , masses and metallicities .
It is first shown that , because of input physics imperfections , the periods and mean colours derived from the existing linear and nonlinear nonadiabatic models must significantly depart from the actual behaviour of the stars .
As a consequence systematic corrections have to be applied , as a first approximation , to our linear model grid .
These free parameters , as well as the mixing length , are calibrated on the LPVs of the LMC and of some globular clusters , assuming a mean mass of 1 M _ { \odot } for the LMC Mira-like stars .
Then , the masses and metallicities corresponding to the four kinematic/photometric populations of local LPVs are evaluated .
The possibility of a varying mixing-length parameter is discussed and taken into account .
Stars of the old disk appear pulsating in the fundamental mode : one group , mainly composed of Miras , has mean mass < M > \simeq 0.9 M _ { \odot } and mean metallicity < Z > \simeq 0.02 , both strongly increasing with the period ; a second group , slightly older and mainly composed of SRb ’ s , has < M > \simeq 0.9 M _ { \odot } and < Z > \ga 0.03 .
Stars of the thin disk appear pulsating in the first and second overtones , with < M _ { 1 ov } > \approx 1.05 M _ { \odot } , < M _ { 2 ov } > > 0.75 M _ { \odot } and < Z > \geq 0.04 .
Stars of the extended disk/halo appear pulsating in the fundamental mode , with < M > \simeq 1.1 M _ { \odot } and < Z > \simeq 0.01 .
The mixing-length parameter probably decreases along the AGB by no more than 15 % per magnitude .
The large , positive period corrections ( more than 30 % for the fundamental and 8 % for the first overtone ) that have to be applied to the LNA models used in this study do not seem to be explained by imperfect sub-photospheric physics alone , especially when nonlinear effects are taken into account .
The origin of the extra period increase ( at least 15 % for the fundamental mode ) may be the stellar wind , which was neglected by all pulsation codes up to now .