Main properties of HP 1 stars. Panel (a: color–magnitude diagram in the Gaia bands for cluster stars with a membership probability greater than 90% (black dots) and <90% (gray dots), taken from Vasiliev & Baumgardt (2021). The 11 stars analyzed in this work are marked with cyan symbols in all the panels. The APOGEE-2 footprint stars toward HP 1 are marked with gray dots in panels b, c, d, and e. Panel b: sky position of stars centered on HP 1; the large overlaid dashed red circle refers to the cluster tidal radius (r_t). Panel c: PM distribution for stars toward the field of HP 1, with the inner zoomed window highlighting the distribution of our sample within a 0.5 mas yr⁻¹ radius around the nominal PM of the cluster. Panel d: [Fe/H] versus the projected angular cluster distance, with the blue line showing the assumed initial mean cluster metallicity and the cyan shadow region indicating ±0.3 dex from the initial metallicity. Panel e: Radial velocity versus [Fe/H] of our member stars compared to APOGEE-2 field stars. The red box delimited by ±0.30 dex and ±20 km s⁻¹, centered on [Fe/H] = −1.06 and RV = +39.76 km s⁻¹, encloses our potential cluster members (see Sect. 2). The metallicity values shown in panels d and e were taken from the ASPCAP pipeline.