Solution (source code)

= Solution

The relevant comparison is continuing <hierarchical galaxy formation> in the <Lambda-CDM model> against an idealized <monolithic galaxy formation> model in which both formation and assembly were essentially complete early. Each observation below concerns a population or a fossil record, rather than a currently merging pair. None individually proves that every <galaxy> formed through the same route.

\b[Fossil substructure in stellar halos.] Old <stars> in the <Milky Way>'s <stellar halo> include coherent groups in orbital-integral space, and external halos contain extended debris and shells. <Phase mixing> can erase spatial concentration while retaining correlations of orbital energy or <angular momentum>. Such <stellar streams>, when linked to a disrupted dwarf progenitor, record accretion of an already formed <stellar population>. A smooth single collapse followed by quiet passive evolution has no equally direct mechanism for creating several dynamically and chemically distinct accreted populations. This supports a composite assembly history, without requiring that every halo star was accreted or counting a current merging pair as evidence.

\b[Growth of the quiescent population.] The <galaxy red sequence> contains old <stellar populations>, yet its inferred stellar mass density grows between approximately redshift one and the present. Pure fading of an already fixed early population changes luminosities and colours, but cannot increase the mass in that population. Quenching adds newly passive systems, while subsequent assembly combines older <stellar populations> into larger galaxies. The observed evolution therefore requires demographic evolution after the putative completed collapse epoch. It is consistent with <hierarchical galaxy formation> plus quenching, although red-sequence growth alone does not distinguish assembly from all possible histories of in-situ <star formation>; stellar-mass estimates and survey selection must be treated consistently.

\b[Evolution of galaxy morphology.] Distant <galaxy> samples contain a larger prevalence of irregular and peculiar structures than a simple non-evolving extrapolation of the local population. Settled discs and smooth spheroids become common outcomes as time proceeds. Continued gas supply, dynamical interactions, and internal rearrangement in <hierarchical galaxy formation> naturally allow this <galaxy morphological evolution>. A model in which structure became fixed during one early collapse and then only stellar light faded has difficulty producing the population change. Rest-frame wavelength, resolution, and surface-brightness selection can affect the observed classifications, and clumpiness is not unique evidence for a <galaxy merger>: unstable gas-rich discs can also be irregular.

\b[Evolution of sizes at fixed stellar mass.] Massive high-redshift <galaxies>, including concentrated systems, are often more compact than comparable populations at low redshift. <Galaxy size evolution> implies structural growth beyond passive luminosity fading. In particular, deposition of accreted stars at large radii in <minor galaxy mergers> can enlarge the outer stellar body while preserving an old central <stellar population>; gas accretion can grow discs from the inside outward. A completed early collapse with a fixed stellar structure does not naturally supply those new outskirts. Changes in sample membership and expansion associated with stellar mass loss also contribute, so this is evidence requiring continued structural evolution rather than a unique quantitative measurement of a merger rate.

\b[Diffuse intracluster stars.] <Intracluster light> and extended outer envelopes show that some <stars> no longer belong to individual cluster <galaxies>. Their irregular distribution and substructure retain evidence of redistribution within an assembling cluster. <Tidal stripping> and disruption of member systems supply stars to the common environment, as expected when smaller bound systems are incorporated into a growing hierarchy. Passive evolution of independent galaxies formed in isolated early collapses cannot itself move their stars into the space between galaxies. Early stellar formation followed by later stripping remains possible, but admitting that later dynamical assembly already departs from the strict completed-collapse picture. This evidence concerns the cumulative stellar distribution, not merely the existence of an occasional present-day merging pair.