Local galaxies with specific star-formation rates (star-formation rate per unit mass; sSFR~0.2-10/Gyr) as high as distant galaxies (z~1-3), are very rich in HI. Those with low stellar masses, log M_star (M_sun)=8-9, for example, have M_HI/M_star~5-30. Using continuity arguments of Peng et al. (2014), whereby the specific merger rate is hypothesized to be proportional to the specific star-formation rate, and HI gas mass measurements for local galaxies with high sSFR, we estimate that moderate mass galaxies, log M_star (M_sun)=9-10.5, can acquire sufficient gas through minor mergers (stellar mass ratios ~4-100) to sustain their star formation rates at z~2. The relative fraction of the gas accreted through minor mergers declines with increasing stellar mass and for the most massive galaxies considered, log M_star (M_sun)=10.5-11, this accretion rate is insufficient to sustain their star formation. We checked our minor merger hypothesis at z=0 using the same methodology but now with relations for local normal galaxies and find that minor mergers cannot account for their specific growth rates, in agreement with observations of HI-rich satellites around nearby spirals. We discuss a number of attractive features, like a natural down-sizing effect, in using minor mergers with extended HI disks to support star formation at high redshift. The answer to the question posed by the title, Can galaxy growth be sustained through HI-rich minor mergers?, is maybe, but only for relatively low mass galaxies and at high redshift.
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