  Previous findings show that the existence of dense cores or bulges is the
prerequisite for quenching a galaxy, leading to a proposed two-step quenching
scenario: compaction and quenching. In this scenario, galaxies first grow their
cores to a stellar mass surface density threshold and subsequently quenching
occurs, suggesting that galaxies evolve from extended star-forming galaxies
(eSFGs), through compact star-forming galaxies (cSFGs), to quenched population.
In this work, we aim at examining the possible evolutionary link between eSFGs
and cSFGs by identifying the trends in star formation rate (SFR), gas-phase
metallicity and HI content, since one would naturally expect that galaxies
evolve along the track of cold gas consumption and metal enhancement. We select
a volume-limited sample of 15,933 galaxies with stellar mass above
$10^{9.5}M_{\odot}$ and redshift of 0.02 < z < 0.05 from the NASA-Sloan-Atlas
catalog within the ALFALFA footprint. The cSFGs on average exhibit similar or
slightly higher SFRs of $\sim$0.06 dex and significantly higher gas-phase
metallicity (up to 0.2 dex at low mass) with respect to the eSFGs, while the
cSFGs dominate the galaxy population of the most intense star formation
activities. More importantly, overall the median HI content and gas depletion
time of cSFGs are about half of eSFGs. Our result supports the compaction and
quenching scenario that galaxies evolve and grow their cores along the track of
cold gas consumption and metal enhancement. The environments of eSFGs and cSFGs
are indistinguishable, suggesting that the compaction process is independent of
any environmental effects at least for low-redshift universe.
