Small and Complex II: Characterizing the Disk and Stellar Envelope of Edge-on $z \sim 0$ Massive Compact Galaxies

We present multi-component photometric decompositions of $r$-band Hyper Suprime-Cam images for a sample of 75 edge-on massive compact galaxies (MCGs) at $z < 0.1$, selected as $+2\sigma$ outliers in the stellar mass-velocity dispersion relation and $-2\sigma$ outliers in the velocity dispersion-size relation. MCGs are composed of compact bulges and disks embedded within stellar envelopes of unclear physical nature. Comparing MCGs to a mass- and redshift-matched control sample of non-compact edge-on S0 galaxies with a similar three-component structure, we find that the smaller sizes of MCGs are not driven by a single component. MCGs host more compact bulges and envelopes ($R_\mathrm{e,bulge} \sim 0.3$ versus $0.5$kpc; $R_\mathrm{e,env} \sim 4.4$ versus $5.7$kpc), as well as shorter and thicker disks ($h_R \sim 1.1$ versus $1.7$kpc; $h_R/z_0 \sim 3.9$ versus $5.3$). The sizes of the structural components are coupled, suggesting their formation processes are linked. Median bulge- and disk-to-total flux fractions are similar in both samples, with $B/T \sim 0.3$ and $D/T \sim 0.4$. Envelope ellipticities span $\epsilon_\mathrm{env} \sim 0$-$0.7$, with MCGs exhibiting rounder envelopes. Low- and high-ellipticity envelopes are broadly consistent with stellar halos and thick disks, respectively. However, the nature of intermediate ellipticity envelopes remains ambiguous from photometry alone. The coupling between component sizes, together with the survival of a substantial disk component, argues against dry minor mergers as the dominant envelope-building mechanism. A comparison with 8 relic galaxies reveals that MCGs and relics share similar bulge-disk-envelope structures and follow the same component size-mass relations, consistent with belonging to a common structural family.