**4. Discussion**

## *4.1. Thermal History*

Transforming the concentrations of tetravalent cations (Figure 7) into apparent temperatures and plotting against 207Pb-corrected dates yielded a temperature–time path for the Alta–Little Cottonwood system (Figure 8). Ti-in-zircon thermometry produced temperatures of ~650–850 ± 40 ◦C (using αTiO2 = 0.5 ± 0.1 and αSiO2 = 0.8 ± 0.1) with a mode of ~718 ◦C for both intrusions (MSWD = 1.8). This mode was consistent with the zircon saturation temperature (~725 ± 25 ◦C), the likely solidus (675–725 ◦C [94,95]) for these rocks, and the petrographically determined crystallization sequence. Titanium-in-zircon apparent temperatures from the Alta–Little Cottonwood system are hotter than results from other felsic and intermediate rocks [62]. Other studies [62,96,97] have reported Ti-in-zircon apparent temperatures lower than that predicted by Ti-in-quartz, Zr saturation, and δ18O quartz-magnetite pair thermometers, as well as temperatures of zircon paragenesis from phase relationships. The inconsistency reported in other studies and general sources of uncertainty could reflect: (1) misestimation (likely overestimation) of the TiO2 and SiO2 activities during zircon crystallization, (2) the pressure dependence of the thermometer, (3) the subsolidus open system behavior of zircon, and/or (4) prolonged Zr saturation in the magma and real low-temperature crystallization of zircons. Multiple indicators of the TiO2 activity (see the Materials and Methods Section), including the absence of rutile from all samples, sugges<sup>t</sup> that the TiO2 activity of 0.5 ± 0.1 was reasonable, reflects the phase assemblage, and encompasses the mode (<sup>α</sup>TiO2 ~ 0.4) and 50% of the αTiO2 of experimental granitic melts [97]. TiO2 activity may be lower (i.e., further from rutile saturation) during earlier crystallization of zircon and plagioclase in the magma [96], and it is unlikely that it is much higher than 0.6–0.7 at temperatures closer to the solidus. As previously noted in the Materials and Methods Section, lowering or raising the TiO2 activity to a minimum of 0.3 or maximum of 0.9 changed the temperature by ±50 ◦C. This range of TiO2 activity is possible over the entire span of zircon crystallization in magmas, but a TiO2 activity near 1.0 is unlikely. Thus, a propagating uncertainty of ±0.1 (~±40 ◦C) encompassed nearly the entire range of temperature variation caused by any inaccuracy resulting from the αTiO2. Schiller and Finger [97] sugges<sup>t</sup> that the Ferry and Watson [83] Ti-in-zircon thermometer should not be applied to TiO2 undersaturated rocks, such as the I-type Alta and Little Cottonwood stocks, since it underestimates temperatures for these magmas despite the αTiO2 term in Ferry and Watson's [83] calibration. Schiller and Finger [97] further sugges<sup>t</sup> a temperature-dependent correction for the αTiO2 based on rhyolite-MELTS [86] or a general +70 ◦C upward correction of Ti-in-zircon temperatures (Figure 8) to account for the temperature underestimate. An ad hoc +70 ◦C correction raised the average Ti-in-zircon temperatures from the Alta and Little Cottonwood stocks above the range of TZr temperatures (≥25 ◦C) and the mean of the Zr-in-titanite population interpreted as magmatic (see below). Although a stronger pressure dependence of 100 ◦C/GPa [87] has been suggested, the pressure variations possible in this shallow system would only serve to raise apparent temperatures an additional ~5–10 ◦C above the TZr and mean Zr-in-titanite apparent temperatures (see the Data Repository File). Several observations further corroborated the Ti-in-zircon temperatures and sugges<sup>t</sup> that zircons were not altered or were otherwise open systems following initial crystallization, including the low common-Pb content of most zircons, the near concordant and concordant nature of most of the U-Pb analyses, the dates that were consistent with the inclusion of zircon in titanite, the consistent intragrain isotopic dates and crystal growth zoning, and the oscillatory zoning as opposed to patchy or sector zoning. Persistent zirconium saturation is possible based on the bulk rock chemistry, agreemen<sup>t</sup> between the Ti-in-zircon and the Zr saturation thermometers, and the inherited zircons in both the Alta and Little Cottonwood stocks. Conversely, the resorbed cores and mantles in some zircons sugges<sup>t</sup> that Zr saturation did not persist the entire time during the crystallization of the stocks. We conclude that accounting for a lower, non-unity αTiO2 in the original calibration [83] and propagating the uncertainty on the activity terms

sufficiently reconciles the thermometry with likely zircon crystallization temperatures [96,97] and that the Ti-in-zircon apparent temperatures are likely accurate within the reported uncertainty.

**Figure 8.** Plots of 207Pb-corrected dates versus Ti-in-zircon (**left**) and Zr-in-titanite (**right**) apparent temperatures calculated separately for each sample (see the Data Repository File for thermometry inputs) and colored by lithologic unit (Alta = dark grey, Little Cottonwood = white, Alta endoskarn = purple). The crosses (+) are the data transformed +70 ◦C, as suggested by Schiller and Finger [97], to account for a low αTiO2. The typical uncertainty bars are shown for each method but have been omitted from individual analyses for clarity. The Ti-in-zircon apparent temperatures calculated by Ferry and Watson [83] defined a unimodal population below the predicted zircon saturation temperature of ~725 ◦C (TZr; grey bar), while the Zr-in-titanite apparent temperatures defined a bimodal population that largely did not overlap the Ti thermometry data.

The Zr-in-titanite apparent temperatures formed two groups: (1) grains from both the Alta and Little Cottonwood stocks that recorded apparent temperatures ranging from ~650–800 ◦C with a mode at ~725 ◦C and were interpreted to have grown from a silicate melt, and (2) grains that recorded ~575 ± 50 ◦C conditions and were interpreted to have (re)crystallized in the presence of hydrothermal fluids in the solid state. These populations of Zr temperatures were consistent with the multiple textural populations of titanite observed in the Little Cottonwood and Alta stocks. The Zr-in-titanite thermometer is susceptible to similar sources of uncertainty as for the Ti-in-zircon thermometer discussed above, with a much stronger dependence on pressure. For the reasons previously outlined in the Materials and Methods and Discussion Sections, we interpreted the Zr-in-titanite temperatures as being accurate within the reported uncertainty. Samples included in the second group were LCS-02, 88-I-9, and 12-12-A2. The ranges of titanite dates from the two groups overlapped but the colder population was skewed slightly younger than the hotter population. This relationship was interpreted to record simultaneous titanite crystallization from silicate melt and fluid-mediated (re)crystallization of titanite in different parts of the system, with titanite (re)crystallization continuing after crystallization of the magmatic titanite had ceased.

#### *4.2. Hydrothermal Permeability Structure through Time*

The permeability structure surrounding intrusions fundamentally controls the process of fluid-infiltration-driven contact metamorphism [3,33,98]. The lack of pervasive hydrothermal titanite (re)crystallization in either the majority of the border phase or any of the central phase Alta stock samples suggests there was scarce infiltration of the hydrothermal fluids flowing through the abundant fractures and veins into unfractured volumes of the Alta stock [99] into the bulk of the non-fractured AS. Samples 88-I-9 and 12-12-A2 (Figure 4) were located at or proximal to the Alta stock wall-rock contact (0–40 m) and a recorded ≥11 Myr of titanite (re)crystallization, which is much longer than calcsilicate skarn sample 11-1 from the inner aureole (~8 Myr; ~37–29 Ma). These data sugges<sup>t</sup> that the locus of hydrothermal infiltration migrated through time (Figure 9), and further suggests that infiltration in the Alta metamorphic aureole (for example, sample 11-1) and the calcsilicate and endoskarns adjacent to the Alta stock (sample 12-12-A2) reflected different and/or multiple stages of fluid infiltration during emplacement of Alta–Little Cottonwood magmas. A diachronous and perhaps stochastic process of infiltration may reflect a feedback between prograde mineral reactions and skarn mineralization, which both exploit pore space, and the permeability structure of the host rocks [33,100].

**Figure 9.** (**A**) Interpretation of the process behind the simultaneous (re)crystallization of titanite in both magmatic and hydrothermal processes suggested by the bimodal Zr-in-titanite thermometry. (**B**) A summary schematic illustrating the sequence of geologic events in the Alta stock–Little Cottonwood stock (AS–LCS) system that illustrates how incremental magmatism and pulsed hydrothermal activity could produce multiple populations (oldest = i, younges<sup>t</sup> = iii) of (re)crystallized titanite and zircon. The unit colors in (B) (dark grey = Alta, light grey = Ferguson stock, white = Little Cottonwood stock, and purple = Alta aureole) match Figures 1, 2, 4, 5, 7 and 8. The lithologic contacts and spatial extents of different units are diagrammatic and are meant to represent processes such as incremental magma emplacement, magma transport in a conduit, episodic hydrothermal infiltration, and protracted volcanic activity at the paleosurface.

#### *4.3. Magma Accumulation vs. Eruptive Discharge*

The total eruptive volumes of volcanic rocks related to the Alta and Little Cottonwood stocks are likely ≥10<sup>3</sup> km<sup>3</sup> based on a minimum thickness of ~500 m [24] and a minimum outcrop area of ~1600 km<sup>2</sup> [101]. The areal exposure of the genetically related intrusive rocks is ~225 km2, but the thicknesses of the intrusions are unknown. If the intrusions are assumed to be ~5–10 km thick [102], then the volume of the intrusive rocks (~1–2 × 10<sup>3</sup> km3) is the same order of magnitude as the volume of erupted material. If this is the case, then the ~11 Myr intrusive duration implies a pluton growth rate that is 2–5× slower than the eruptive discharge from the system, which lasted only ~4.5 Myr (~36.5 to 32 Ma [23,24]). These rates are based on assumptions of the physical dimensions just presented and these estimates have large uncertainties and are therefore speculative. However, these very preliminary discharge estimates are consistent with other better-characterized systems [103,104] that sugges<sup>t</sup> that magma discharge is a first-order control on the eruptibility of magma batches.
