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I present here a review of galaxy structure and morphology studies in the galaxy population through cosmic time from z = 8 until today. The approach taken in this review is largely observational with a limited amount of interpretation, although I do show where galaxy structure and morphology can test galaxy formation and even cosmological models in a new, largely unexplored way.

As of January 2014, the major conclusions concerning galaxy structure and its evolution, as discussed in this article, can be summarized as:

I. Galaxy structure and morphology is the longest studied observational feature of galaxies. In this review galaxy morphology is the apparent classification based on visual inspection, while structure is a way to quantify the light distributions in galaxies. In many ways morphology is still a descriptive science, and visual efforts continue to provide useful information in the form of large-scale projects to classify many galaxies, as in the Galaxy Zoo effort. The Hubble sequence has and likely will remain the major paradigm in which we consider galaxy morphology, although this system does not 'work' at high redshifts where most galaxies cannot be classified into a single Hubble type (Section 4.1).

II. Using the Hubble scheme the evolution of three broad classes of galaxies are now classified accurately out to z ~ 3 – namely ellipticals, spirals and peculiars. The relative abundance of these galaxies has been measured as a function of redshift out to these early times. What we find is that the peculiar galaxies dominate the galaxy population at z ~ 2.5 - 3, with a relative fraction of at least 70%. Galaxies which are elliptical and spiral like in appearance (but not necessarily in physical properties, see Section 4.1) become progressively more common at lower redshifts. The number densities of these two normal galaxies together equals that of the peculiars by z ~ 1.4 (Mortlock et al. 2013).

III. Since galaxy morphology by visual estimates is limited in its ability to derive the physics behind galaxy formation and by its nature is not quantitative, the use of parametric (Section 2.2) and non-parametric (Section 2.3) methods are essential for deriving in a quantitative way how galaxies are evolving. These quantitative indices also correlate to some degree with the present and past star formation history and properties of a galaxy. More work is needed to establish these relations with more certainty, but it appears that the Sérsic index and concentration correlate with the scale or mass of a galaxy, the clumpiness index with the star formation, and the asymmetry parameter with ongoing merging activity (Section 3).

IV. The merger history is now know from applying structural analyses to galaxy images in deep Hubble Space Telescope surveys such as the Hubble Deep Field (Section 4). The result of this is that the galaxy merger fraction increases with redshift at all stellar mass and luminosity selections. This increase can be fit well by a power-law (1 + z)m up to z ~ 3, although at higher redshifts the structurally derived merger fraction may plateau (Conselice & Arnold 2009). Using numerical/hydrodynamical simulations the time-scales for these mergers can be calculated, and thus merger fractions can be converted into merger rates (Section 4.3.2). The merger rate allows for the calculation of the number of mergers galaxies at various masses undergo, as well as the amount of stellar mass which is added to galaxies due to the merger process. The result of this is that it appears that up to half of the stellar mass in modern massive galaxies were formed in mergers between 1 < z < 3, although at z < 1 dry mergers are likely more responsible for the further formation of these galaxies.

V. The resolved structures of galaxies also allows us to measure the internal features of galaxies and how they are assembling. There is some controversy over the formation history bulges, disks and bars, although many of these are likely formed by secular processes produced internally by disk dynamical evolution. This is an area where significant progress could be made in the next few years. The most up to date results suggest that the bar fraction for spiral galaxies at z < 1 depends upon the stellar mass of the galaxy. The most massive galaxies have a similar bar fraction at z ~ 0.8 as they do today, yet lower mass and bluer disk galaxies have a significantly lower bar fraction than similarly low mass nearby disks. This mirrors the evolution of the Hubble sequence itself where more massive galaxies settle into normal ellipticals and disks before lower mass galaxies. Spiral structure is a difficult problem and while some examples exist at high redshift, even at z > 2, the general onset of when disks form spirals is almost totally unconstrained by observations.

VI. Resolved imaging also permits us to measure the spectral energy distributions and colors, of galaxy components and individual pixels of different galaxies. This is another area where more work needs to be performed, but it appears that bulges of spirals tend to be older than their disks at high redshift, but there are examples of many ellipticals which have blue cores and central star formation (Section 4.1.1). Pixel-pixel analyses show that galaxies have a mixed star formation history, and that the inner parts of galaxies are often older than their outer parts. Pixel studies also show that the clumps seen in distant star forming galaxies are composed of young stellar populations, and thus must have recently formed or regenerate themselves.

VII. Perhaps the most popular (at present) problem in galaxy structural evolution is the apparent compactness in size of galaxies at high redshifts. The observations show that massive galaxies at z > 1 have sizes which are a factor of 2-5 smaller than similar massive galaxies in today's universe. This result has been studied in many different ways, and the sizes of a stellar mass selected sample of galaxies increases gradually as a function of redshift with a power-law increase ~ (1 + z)β, where β varies from -0.8 to -1.5 depending upon whether the selected samples are disk-like or elliptical-like (Section 4.2). Results to date suggest that these galaxies are building up their outer parts over time to become larger systems, rather than adding mass to their centers. This process is unlikely driven by star formation, and theory suggests that this formation is produced by minor merger events (Section 4.2).

In summary, we have learned much about galaxy morphology and structure over the past 15 years. There are however many open questions still remaining on all aspects of using structure to determine evolution. More work needs to be done in tying galaxy structure to underlying physics, both through empirical work and in simulations. Furthermore, the time-scales for structural features such as mergers and large clump survival are critical to better understand. Broad morphological features will remain important over the next decades as telescopes such as JWST, Euclid, LSST, the Dark Energy Survey, amongst others, will all resolve many more galaxies than we can currently study, and at higher redshifts. This opens up entirely new possibilities, and the with careful thoughtful planning a new revolution in galaxy structure may be upon us soon.

A review such as this is written with help from many people. In particular I thank Alice Mortlock, Asa Bluck, Fernando Buitrago, Jamie Ownsworth, and Ken Duncan for illuminating conversations and collaboration on these topics over the past few years. I also thank Jennifer Lotz, Fernando Buitrago, Stijn Wuyts, Alice Mortlock for kindly providing figures. I personally thank the STFC and the Leverhulme Trust in the UK, as well as the NSF and NASA in the USA for financial support.

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