| Summary: | We explore the chemodynamical properties of a sample of very metal-poor (VMP) stars selected from the Hamburg/ESO survey, matched with Gaia EDR3, in the phase space identified by the three integrals of motion ( L _z , E , I _3 ). Disk and halo orbits are separated by using the criteria defined in Carollo & Chiba. We found 26 stars with [Fe/H] ≤ −2.5 possessing disk kinematics, of which 13 are extremely metal-poor. At these metallicities, the number of stars with disk kinematics is three times its retrograde counterpart. In the same range of metallicity we also identified 37 halo stars most tightly bound to the gravitational potential of the progenitor halo. The origins of these stars are investigated by comparing the observational results with simulated galaxies from the Aquarius Project and the IllustrisTNG simulations. We found two mechanisms of formation of VMP stars with disk kinematics: accretion from early satellites (which is dominant), and in situ formation. These stars are very old, with ages >12.5 Gyr ( z > 5), and they are α -enriched. Accretion and in situ formation are also found for the retrograde counterparts, with accretion also being the dominant mode. Contributing accreted satellites have stellar masses in the range 10 ^6 –10 ^9 M _☉ and are very gas-rich. The most bound halo stars are the oldest detected, with a median age of ∼13.3 Gyr ( z ∼ 11), and are α -enriched. Our finding clearly shows that very old, VMP stars store important information on the first stages of assembly of our Galaxy and its halo.
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