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Fig. 6

Fig. 6 Refer to the following caption and surrounding text.

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Age-iron abundance [Fe/H] relation for 243 617 stars generated by interpolating distributions obtained by Carrillo et al. (2023) (left panel) and for the estimate based on Fig. 4 from Fernández-Alvar et al. (2025) (right panel; assuming the same dispersion as our baseline age-metallicity relation). The age-metallicity relation plays an important role in our population synthesis as the occurrence of substellar companions depends strongly on stellar metallicity. The strict upper limit (assuming all companions survive stellar evolution) for the occurrence rate of companions to white dwarfs increases by a factor of -2 (from 4.4 ± 2.4 to 8.2 ± 4.4%), and old WDs are much more likely to host a companion when we assumed the age-metallicity relation from Fernández-Alvar et al. (2025).

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