New constraints on the exhumation history of the western Tauern Window (European Alps) from thermochronology, thermokinematic modeling, and topographic analysis

The Brenner normal fault bounds the Tauern Window to the west and accommodated a significant portion of the orogen-parallel extension in the Eastern Alps. Here, we use zircon (U–Th)/He, apatite fission track, and apatite (U–Th)/He dating, thermokinematic modeling, and a topographic analysis to constrain the exhumation history of the western Tauern Window in the footwall of the Brenner fault. ZHe ages from an E–W profile (parallel to the slip direction of the fault) decrease westwards from ~ 11 to ~ 8 Ma and suggest a fault-slip rate of 3.9 ± 0.9 km/Myr, whereas AFT and AHe ages show no spatial trends. ZHe and AFT ages from an elevation profile indicate apparent exhumation rates of 1.1 ± 0.7 and 1.0 ± 1.3 km/Myr, respectively, whereas the AHe ages are again spatially invariant. Most of the thermochronological ages are well predicted by a thermokinematic model with a normal fault that slips at a rate of 4.2 km/Myr between ~ 19 and ~ 9 Ma and produces 35 ± 10 km of extension. The modeling reveals that the spatially invariant AHe ages are caused by heat advection due to faulting and posttectonic thermal relaxation. The enigmatic increase of K–Ar phengite and biotite ages towards the Brenner fault is caused by heat conduction from the hot footwall to the cooler hanging wall. Topographic profiles across an N–S valley in the fault footwall indicate 1000 ± 300 m of erosion after faulting ceased, which agrees with the results of our thermokinematic model. Valley incision explains why the Brenner fault is located on the western valley shoulder and not at the valley bottom. We conclude that the ability of thermokinematic models to quantify heat transfer by rock advection and conduction is crucial for interpreting cooling ages from extensional fault systems.


Introduction
Low-temperature thermochronological data record the cooling history of rocks on their way to the Earth's surface and are routinely used to quantify rates of rock exhumation and slip rates of normal faults (e.g., Fitzgerald et al. 1993;Foster and John 1999;Brady 2002;Brichau et al. 2010;Buscher et al. 2013). When determining rates of faulting and exhumation from thermochronological data, it is important to consider temporal changes of the temperature field in the crust, because faulting and erosion cause advection of hot rocks towards the Earth's surface, which increases the geothermal gradient (Stüwe et al. 1994;Ketcham 1996Ketcham , 2005Batt and Braun 1997;Mancktelow and Grasemann 1997;Braun 2016). For normal faults, the syntectonic conduction of heat from the exhuming footwall into the cooler hanging wall should lead to enhanced cooling of the footwall block near the fault; an effect that may be fortified by the circulation of fluids (Ehlers and Chapmann 1999;Wawrzyniec et al. 1999;Tagami 2005;Ault and Selverstone 2008;Luijendijk 2019). As a result, cooling ages in the footwall are expected to increase towards the fault, although this effect has rarely been investigated with thermochronological data Ehlers et al. 2001;Seward et al. 2009). When faulting and heat advection stop, heat conduction during thermal relaxation decreases the geothermal gradient in the entire footwall block and may cause rapid posttectonic cooling (Braun 2016;Wolff et al. 2020). Owing to the processes of syntectonic heat advection and posttectonic thermal relaxation, it is essential to apply thermokinematic modeling to derive fault-slip histories from thermochronological data (e.g., Ketcham 1996;Campani et al. 2010;Styron et al. 2013;McCallister et al. 2014;Wolff et al. 2019).
The position of active faults in mountain belts is often marked by valleys, as brittle fault rocks such as fault gouge and cataclasite have relatively higher erodibility than less deformed rocks adjacent to the fault (e.g., Koons et al. 2012). This is particularly important for normal faults, where the process of footwall uplift causes a relative downward movement of the hanging wall, which causes the flow of water or ice to be focused at or near the fault trace. Hence, faults may control the pathways along which sedimentary material is transported from the mountains towards sedimentary basins in the foreland.
In this study, we present new structural, topographic, and thermochronological data from the Brenner normal fault in the European Alps. These data complement a recent study that applied thermokinematic modeling to a thermochronological data set from a vertical transect (including a 1000-m-long drill core) and showed that posttectonic thermal relaxation affected the rock cooling history in the fault footwall (Wolff et al. 2020). Our new data and thermokinematic modeling provide improved constraints on the evolution of the Brenner normal fault, the cooling history of its footwall (the western Tauern Window), and the amount of erosion and valley incision after faulting stopped.

Geological setting
The European Alps formed during two orogenic cycles that took place in the Cretaceous and Cenozoic (e.g., Trümpy 1960;Frisch 1978;Froitzheim et al. 1994;Schmid et al. 1996). The first phase of mountain building was related to the closure of the Meliata ocean between the Late Jurassic and the Early Cretaceous, whereas the second phase was caused by the southeastward subduction of the Penninic ocean and the subsequent collision between the European and Adriatic plates (e.g., Stampfli 2000;Froitzheim et al. 1994;Schmid et al. 2004;Handy et al. 2010). The Penninic ocean consisted of a southern and a northern branch (i.e., the Piedmont-Ligurian ocean adjacent to the Adriatic plate and the Valais ocean near the European plate), which were separated by the Brianconnais microcontinent (Trümpy 1960;Frisch 1978;Froitzheim and Manatschal 1996;Stampfli 2000). After the closure of the Penninic oceans, the European passive margin entered the subduction zone in the Early Eocene, which caused nappe stacking and crustal thickening (e.g., Termier 1903;Schmid et al. 1996;Bousquet et al. 2008;Handy et al. 2010). The presence of Tertiary intrusions and mafic dykes along the Periadriatic Line ( Fig. 1) has been interpreted to indicate the breakoff of the European slab in the Early Oligocene, because the intrusive rocks have a geochemical affinity to the mantle and formed mainly between 34 and 24 Ma, with few intrusive rocks being as old as 42-38 Ma (Bögel 1975;Exner 1976;Laubscher 1983a;von Blanckenburg and Davies 1995;Kissling et al. 2006). During the following plate convergence, the southeastward subduction of the European passive margin continued west of the Tauern Window, whereas east of the window, geophysical data seem to indicate a northeastward subduction of the Adriatic plate beneath Europe (e.g., Lippitsch et al. 2003;Kissling et al. 2006;Kästle et al. 2020 and references therein). In the area of the Tauern Window ( Fig. 1), recent geophysical data suggest that the subducted European slab is detached from the orogenic crust and dips steeply to the NNE (Handy et al. 2021;Paffrath et al. 2021). A recent switch in subduction polarity with a northward subduction of the Adriatic plate may have occurred here in the Miocene (Kästle et al. 2020;Eizenhöfer et al. 2021).

The Brenner normal fault system
The 40-km-long Brenner fault system extends from Innsbruck to Sterzing (Fig. 2). Its northern part between Innsbruck and Matrei is developed as a brittle normal fault without mylonites and referred to as Silltal fault (Schmidegg 1964;Fügenschuh et al. 1997). Farther south, the Brenner fault sensu stricto between Matrei and Sterzing comprises west-dipping mylonites with a thickness of ~ 1.5 km and a brittle normal fault at the top of the mylonites (Behrmann 1988;Selverstone 1988;Fügenschuh et al. 1997;Rosenberg and Garcia 2011;Rosenberg et al. 2018). In the hanging wall of the Brenner fault occur Austroalpine basement and cover nappes (Fig. 2), which include the Variscan basement of the Ötztal complex and its Mesozoic cover (Brenner Mesozoic), as well as the Paleozoic basement rocks of the Steinach nappe and its Mesozoic cover (Schmidegg 1964;Froitzheim 1994;Fügenschuh et al. 2000). Thermochronological data of samples from the western Tauern Window indicate that cooling during the Miocene is related to normal faulting and footwall exhumation along the Brenner fault (Grundmann and Morteani 1985;von Blanckenburg et al. 1989;Fügenschuh et al. 1997;Most 2003;Bertrand et al. 2017). A thermokinematic modeling study that used new zircon and apatite (U-Th)/He (ZHe, AHe, respectively) as well as apatite fission-track (AFT) ages from a near-vertical transect (including a 1000-m-long drill    core) showed that the Brenner fault was active from 19 ± 2 to 8.8 ± 0.4 Ma at a slip rate of 4.2 ± 0.9 km/Myr (Wolff et al. 2020). Farther west in the hanging wall, AFT and ZFT ages from the Ötztal-Stubai Complex and the Brenner Mesozoic indicate an older phase of cooling between ~ 90 and ~ 60 Ma (Fügenschuh et al. 2000). Samples from the Steinach nappe, collected only 0.5-3.0 km west of the Brenner fault, yielded ZHe ages between 71 ± 10 and 63 ± 7 Ma, indicating that their post-Eoalpine cooling was not affected by the Miocene activity of the Brenner normal fault (Lünsdorf et al. 2012).

Structural data and topographic analysis
In the central part of the Brenner fault, the mylonites in the footwall consist of strongly deformed calc-micaschists (Bündner schists) of the Matrei Zone and mylonitic calcphyllites of the Glockner nappe (Fig. 3A). The mylonites contain quartz, K-feldspar, calcite, chlorite with accessory muscovite, biotite, epidote, and rutile. Quartz grains show bulging and subgrain rotation recrystallization typical for low-grade metamorphic conditions. Together with the occurrence of chlorite, these microstructures indicate deformation during retrograde greenschist-facies metamorphic conditions. The well-developed mylonitic foliation dips gently to the west (10°-36°), and the stretching lineation plunges gently to the WSW to WNW (255°-290°) (Fig. 3). Asymmetric extensional shear bands indicate a consistent top-to-the-W shear sense, as reported in earlier studies, which also showed that quartz-c-axis fabrics formed during top-to-the-W shearing (Behrmann 1988;Selverstone 1988). Adjacent to the Brenner fault, both Austroalpine hanging wall rocks and footwall mylonites are affected by intense brittle deformation. Dolomites of the Mesozoic cover of the Ötztal complex and quartzphyllites of the Steinach nappe are intensely brecciated. Likewise, the mylonites near the top of the Brenner shear zone are overprinted by brittle faulting. These normal faults dip W to SW at angles between 20° and 50°, and contain layers of fault gouge with a thickness of up to 0.4 m. It is noteworthy that these brittle faults are either parallel or only slightly steeper than the mylonitic foliation ( Fig. 4A, B). This spatial relation is typical for low-angle normal fault systems that progressively exhume mid-crustal rocks in their footwalls.
It is important to note that the trace of the Brenner fault is not situated at the bottom of the N-S valley of the Sill and Eisack rivers, but on the western shoulder of this valley (Figs. 3 and 4C). Five profiles, P1-P5, across the valley between the villages Gries am Brenner and Sterzing show the presence of low-relief surfaces dipping gently (10°-25°) to the west (Fig. 3D). The Brenner fault runs along the western margin of these low-relief surfaces. Near profile P4, a minor normal fault is located east of the main Brenner fault.
The absolute elevation of the low-relief surfaces is highest on profile P3 (2020 m a.s.l.) and decreases towards the north and south to ~ 1700 m (P1) and ~ 1750 m (P5), respectively. The position of the Brenner fault several hundred meters above the main valley suggests that faulting must have ceased before the incision of the valley, and is consistent with the lack of crustal seismicity in the western Tauern Window, which indicates that the Brenner fault is not active (Reiter et al. 2018). The results of thermokinematic modeling by Wolff et al. (2020) indicate that normal faulting stopped 8.8 ± 0.4 Ma ago. The envisioned paleotopography at the end of faulting is shown in Fig. 3C, which explains how we determine minimum and maximum amounts of valley incision after faulting. A minimum amount can be estimated from the vertical distance between the valley bottom and the highest points on the low-relief surfaces (Fig. 3C). This distance ranges from 340 m on profile 1 to 630 m on profile 3 (Fig. 3D). A maximum amount of incision can be obtained by extrapolating the Brenner fault towards the east assuming a fault dip of 35° (dashed lines in Fig. 3D). This approach leads to maximum incision values between 750 and 1200 m.

Sampling and analytical methods
We employed ZHe, AHe, and AFT thermochronology to further constrain the cooling history of the Brenner normal fault (Table 1). Along a ~ 16 km long WSW-ESE profile, which extends from the Brenner fault (near Brennerbad) along a prominent mountain ridge to Olperer mountain (Fig. 5), we collected four orthogneiss samples (17A15, 17A14, 17A22, and 17A19) that complement the five samples dated by Wolff et al. (2020). The elevation of the nine samples along this profile increases eastward from 1342 to 3236 m (Table 1). On the northern and southern flanks of Olperer mountain, we took four orthogneiss samples (16A19, 17A20, 17A21, and 17A25; Table 1). Together with the easternmost sample of the WSW-ENE profile (17A19), these samples cover a vertical distance of ~ 1.5 km. Close to the Brenner fault, we collected another six samples at two sites, A and B, located west of Brenner lake and west of Brennerbad, respectively ( Fig. 3B). At site A, two samples that are ~ 2 m apart were collected in the footwall close to the fault, whereas a third sample was taken 100 m farther west in the hanging wall. At site B, where a second normal fault occurs ~ 400 m east of the Brenner fault ( Fig. 3A), we took three samples between the two faults over a distance of 40 m.
For (U-Th)/He thermochronology, we selected euhedral zircon and apatite crystals without inclusions by handpicking after heavy-liquid separation. The single crystals were wrapped in 1 × 1 mm-sized platinum capsules and degassed in high vacuum by heating with an infrared diode 1 3 laser at the GÖochron Laboratories, University of Göttingen. The extracted gas was purified using an SAES Ti-Zr getter at 450 °C and spiked with 3 He. The chemically inert noble gases and a minor amount of other trace gases were then expanded into a Hiden triple-filter quadrupole mass spectrometer equipped with an ion counting detector. Crystals were checked for complete degassing of helium by sequential reheating and helium measurement. Following degassing, crystals were retrieved from the gas extraction line, unpacked, and spiked with calibrated 230 Th and 233 U solutions and dissolved in pressurized teflon bombs at 220 °C using distilled 48% HF + 65% HNO 3 for 5 days, or in 4% HNO 3 for 1 day, for zircons and apatites, respectively. Spiked solutions were analyzed by the isotope dilution method using an iCAP Q ICP-MS equipped with an APEX micro-flow nebulizer. Crystal shape parameters were determined by multiple microphotographs and used to determine correction factors for alpha-ejection (Farley et al. 1996) with the constants of Hourigan et al. (2005).
Apatite fission track dating by the external detector method (Gleadow 1981) was carried out at the Institute of Geological Sciences, Polish Academy of Sciences in Krakow (Poland). The selected apatite crystals were embedded in epoxy resin and polished using Al 2 O 3 suspensions. Then, they were etched in 5N HNO 3 at a temperature of 21 °C for 20 s to reveal spontaneous fission tracks (Zaun and Wagner 1985;Donelick et al. 1999). Neutron irradiation of samples, age standards (Fish Canyon Tuff, Durango and Mount Dromedary apatites), and CN5 glass dosimeter was performed at the TRIGA reactor (Oregon State University, USA). After irradiation, the induced fission tracks in the mica detectors were revealed by etching in 40% HF for 45 min. Track counting and length measurements were made with a NIKON Eclipse E-600 microscope computer-controlled stage system (Dumitru 1993) with 1250 × magnification. Calculations and plots were done with the software TRACKKEY (Dunkl 2002). The fission-track ages were determined by the zeta method (Hurford and Green 1983) using age standards listed in Hurford (1998). The error was calculated following the procedure of Green (1981). The fission-track annealing kinetics was assessed by measuring the etch pit diameters (Dpar) (Burtner et al. 1994).

Results of thermochronology and thermokinematic modeling
In this section, we describe our thermochronological data set and the thermokinematic model ( Fig. 6A) that we use to predict the cooling ages obtained from the three different thermochronometers (ZHe, AFT, and AHe). The single-crystal ZHe and AHe ages and the unweighted average ages for all samples (including those of Wolff et al. 2020) are reported in Tables 2 and 3. The radiation damage densities of the apatite and zircon crystals range from 1.6 × 10 13 to 3.4 × 10 15 alpha decay events/gram and from 6.5 × 10 15 to 2.6 × 10 17 alpha decay events/gram, respectively. These ranges are well below the thresholds for a damage-induced decrease of closure temperatures (Flowers et al. 2009;Gautheron et al. 2009;Guenthner et al. 2013). The AFT data are given in Table 4. All AFT samples passed the Chi-square test and are therefore considered to form one age population. In the following, we describe the cooling ages obtained from the WSW-ENE profile and the age-elevation profile at Olperer mountain, followed by the age results at the sites A and B near the Brenner fault.

Profile in fault footwall and age-elevation profile near Olperer mountain
The ZHe, AFT, and AHe ages of the nine samples collected along the mountain ridge in the footwall of the Brenner fault are shown in Fig. 7. The ZHe ages range from 7.9 ± 0.3 to 11.1 ± 1.1 Ma and show a trend of increasing ages towards the east, although there is considerable scatter in the data (Fig. 7B). This is the reason why a regression line in the age-versus-distance plot with an inverse slope of 6.9 km/ Myr is not well defined (R 2 = 0.4). A least-square regression (York 1966) through the ZHe ages yields a different inverse slope of 3.9 ± 0.9 km/Myr. The AFT and AHe ages along the profile range from 7.3 ± 2.2 to 10.8 ± 2.0 Ma and from 8.5 ± 0.3 to 9.8 ± 5.4 Ma, respectively. In contrast to the ZHe ages, neither the AFT ages (with their relatively large errors) nor the AHe ages show a significant correlation between cooling ages and distance to the Brenner fault (Fig. 7C, D).
Owing to the relatively large errors of two He ages (ZHe age of sample 17A17 and AHe age of 17A19), it is not surprising that local age inversions occur along the profile.
The results from the elevation profile at Olperer mountain (see Fig. 5) are shown in Fig. 8. By adding published AFT ages (Grundmann and Morteani 1985;Most 2003; see rectangle in Fig. 5), we increased the vertical distance covered by the profile from 1.5 to 1.8 km. The ZHe ages range between 8.6 ± 1.3 and 10.7 ± 0.7 Ma and least-square fitting yields a regression line with a slope of 1.1 ± 0.7 km/Myr. For our AFT ages, we obtain a similar slope of 1.0 km/Myr, but with a large uncertainty of ± 1.3 km/Myr. If the AFT ages of Most (2003) and Grundmann and Morteani (1985) are included, the slope is only 0.5 ± 0.1 km/Myr. The nominal AHe ages do not vary with elevation (three of the four AHe ages are 9.5 Ma old), and therefore, it is not possible to derive a meaningful slope value.
Although thermochronological ages from normal fault footwalls are often used to estimate rates of faulting and exhumation (e.g., Brady 2002;Brichau et al. 2010;Buscher et al. 2013), geologically meaningful rates can only be obtained if the slopes of regression lines are well defined, and if the isotherms remained spatially and temporally invariant during the episode of faulting and exhumation recorded by the data. Thermokinematic modeling can be used to test whether these assumptions are met and can help to interpret age data in a meaningful way.

Thermokinematic modeling
To predict ZHe, AFT, and AHe cooling ages for the samples described in Sect. 6.1, we used the thermokinematic model of Wolff et al. (2020), which is based on the finite-element code PECUBE (Braun et al. 2012). To calculate ages with PECUBE, we used the same diffusion and annealing models as employed by Wolff et al. (2020). These are the diffusion model of Farley (2000) for AHe, the annealing model of Ketcham (2005) for AFT, and the diffusion model of Reiners et al. (2004) for ZHe. The latter was adjusted using a D 0 /a 2 value of 37,800 1/s and an activation energy of 168 kJ/ mol to account for the rather low radiation damage of the zircon samples (cf. Guenthner et al. 2013). This model was able to predict the ZHe, AFT, and AHe cooling ages from a vertical profile close to the Brenner fault, which included a 1000-m-long drill core, within their uncertainties (see Fig. 5 for location of the profile and the drill core). The only difference of the current model to the one of Wolff et al. (2020) is the model size, which was increased to 55 × 20 km to B The temperature evolution in the fault footwall is shown at model times of 10, 9, and 8 Ma. Heat advection due to normal faulting has shifted the isotherms in the fault footwall towards the surface, which causes rapid syntectonic cooling. When faulting stops at 8.8 Ma, the upper crust cools rapidly during thermal relaxation as can be seen by the downward shift of the isotherms between 9 and 8 Ma Amount of helium is given in nano-cubic-cm at standard temperature and pressure c Radiation density is calculated according to Nasdala et al. (2004) and using the (U-Th)/He age of the aliquot d Amount of radioactive elements is given in nano-grams e Ejection correction (Ft): correction factor for alpha-ejection (according to Farley et al. 1996) f Uncertainty of the single-grain age is given with 2 sigma error. The error includes both, the analytical uncertainty and the estimated uncertainty of the ejection correction Amount of helium is given in nano-cubic-cm at standard temperature and pressure c Radiation density is calculated according to Nasdala et al. (2004) and using the (U-Th)/He age of the aliquot d Amount of radioactive elements is given in nano-grams e Ejection correction (Ft): correction factor for alpha-ejection (according to Farley et al. 1996) f Uncertainty of the single-grain age is given with 2 sigma error. The error includes both, the analytical uncertainty and the estimated uncertainty of the ejection correction enable the tracking of all samples during normal faulting and footwall exhumation (Fig. 6). The model parameters used in PECUBE are given in Table 5. The timing of faulting (from 19.0 until 8.8 Ma) and the fault-slip rate (4.2 km/Myr) were taken from the best-fit model of Wolff et al. (2020). The cooling ages predicted by our thermokinematic model are shown as red dots in Figs. 7 and 8. It can be seen that our model roughly predicts the ZHe ages on the long profile (Fig. 7B), although the measured ZHe ages for the two westernmost samples are ~ 1.5 Ma lower than the modelled ones. The three closely spaced samples at a distance of ~ 6 km from the Brenner fault yielded two ZHe ages that are younger than predicted by the model (~ 8.3 and ~ 9.4 Ma), whereas the third age is older (~ 11.1 Ma). Despite this variability, the mean of the three ZHe ages (i.e., 9.6 ± 0.8 Ma) is in good agreement with the modelled ages of ~ 9.9 Ma. The nearly invariant ZHe ages calculated by our model result from the fact that the 200 °C isotherm in the model is nearly horizontal at a distance of greater than ~ 5 km away from the surface trace of the fault (Fig. 6B) and that the rate of rock exhumation during faulting in the footwall is everywhere the same. In nature, the amount and rate of exhumation commonly decrease away from normal faults over a distance of 20-30 km, because of syntectonic footwall tilting. To take this effect into account, we introduced a kink in the fault plane, which changes its dip from 35° to 20° at a distance of 5 km from of the surface trace of the fault. As the footwall in the model must move parallel to the fault plane, this kink causes footwall tilting and changes the modelled exhumation paths of the samples (cf. Braun et al. 2012;Campani et al. 2010;Styron et al. 2013). As a result, the ZHe ages predicted by this second model become older with increasing distance from the fault (green dots in Fig. 7). Both models predict the measured ages from all three thermochronometers reasonably well (for reasons outlined in the discussion, we prefer the model without footwall tilting). At the elevation profile near Olperer mountain, the predicted ZHe, AFT, and AHe of the two models are also in good agreement with the measured cooling ages, except for three previously published AFT ages (Fig. 8).

Sites A and B near Brenner fault
The westernmost sample at site A (19A12) yields ZHe and AHe ages of 36 ± 15 and 32 ± 13 Ma, respectively, whereas the ZHe ages of the mylonite samples are 6.7 ± 1.6 Ma and 7.8 ± 0.7 Ma (Fig. 9, Table 2). Hence, the Brenner normal fault causes an abrupt jump from young ages in the footwall to much older ages in the hanging wall. The age data also demonstrate that the Brenner fault is indeed located on the western shoulder of the valley (Fig. 9).
At site B, the three ZHe ages range from 7.2 ± 0.2 to 8.1 ± 0.8 Ma and are similar to the ZHe age of 8.0 ± 0.7 Ma for the westernmost sample 17A9 on the long profile (Fig. 9). Hence, the main Brenner fault must be located west of the samples and the minor normal fault east of the samples has no significant effect on their cooling history. The AHe ages for the three samples range from 8.8 ± 1.4 to 10.8 ± 0.4 Ma, with all nominal ages being higher than the respective ZHe ages (possible reasons are discussed in Sect. 7.2).

Interpretation of thermochronological ages in fault footwall
The ZHe ages predicted by our thermokinematic models (with and without footwall tilting) are broadly in agreement with those measured along the profile in the footwall of the Brenner normal fault (Fig. 7B). As the misfit ϕ between our ZHe ages and the ages predicted by the two models is smaller for the model without footwall tilting (misfit ϕ of 1.9 versus ϕ of 2.6; calculated after Braun et al. 2012), we prefer this model over the one with footwall tilting. A regression line through the ZHe ages yields an inverse slope of A  Red and green dots indicate the ages predicted by the thermokinematic models described in Sect. 6.2. The horizontal grey line in C and D indicates the end of normal faulting on the Brenner fault at 8.8 ± 0.4 Ma (Wolff et al. 2020) 1 3 6.9 km/Myr (dashed line in Fig. 7B). Without caution, this value could be interpreted as the fault-slip rate during crustal extension; however, the following reasons argue against such a simple interpretation. First, there is considerable scatter in the age data and the uncertainties of the individual ZHe ages are quite variable. Second, a least-square fit, which takes these different uncertainties into account, gives an inverse slope of only 3.9 ± 0.9 km/Myr. This lower value agrees with the fault-slip rate of 4.2 ± 0.9 km/Myr obtained from a PECUBE model that accurately predicts the ZHe, AFT, and AHe ages from a ~ 2-km-long elevation profile near the Brenner fault (Wolff et al. 2020). According to this model, the Brenner fault was active for ~ 10 Ma (i.e., from 19 ± 2 to 8.8 ± 0.4 Ma) and caused 35 ± 10 km of crustal extension. If we would use the inverse slope value of 6.9 km/Myr and a faulting period of 10 Ma, this would imply a much higher amount of extension of ~ 70 km. Although such a high value was initially proposed for the Brenner fault (Fügenschuh et al. 1997), it was later revised to a value of ~ 44 km (Fügenschuh et al. 2012), which is compatible with our data and preferred model. Therefore, we argue that our new ZHe data and our enlarged PECUBE model confirm the results of Wolff et al. (2020). Finally, we note that both the AFT and the AHe ages show no correlation with distance to the Brenner fault (Fig. 7C, D) and can therefore not be used to derive a fault-slip rate. At least for the AHe ages, we interpret this lack of correlation to result from the rapid cooling of the  Grundmann & Morteani (1985) Most (2003 slope: Fig. 8 ZHe, AFT, and AHe ages with uncertainties for samples of the elevation profile near Olperer mountain. Red and green dots indicate the ages predicted by the thermokinematic models described in Sect. 6.2. Regression lines obtained by least-square fit through the data are shown for the ZHe and the AFT ages   (Fig. 6B). For the AFT ages, a trend in the ages with distance to the fault may be obscured by the relatively large errors of the ages.
The ZHe, AFT, and AHe ages of the elevation profile are also rather well reproduced by our two thermokinematic models (Fig. 8). Again, the misfit ϕ between the measured and predicted thermochronological ages is smaller for the model without footwall tilting (ϕ of 1.2 versus ϕ of 1.4). The inverse slopes obtained by least-square regressions through the ZHe and AFT age data are 1.1 ± 0.7 and 1.0 ± 1.3 km/ Myr, respectively (Fig. 8). These values could be interpreted as exhumation rates during normal faulting, provided that the isotherms in the upper crust were spatially and temporally invariant during the period of cooling recorded by the data. As the vertical slip rate of the Brenner fault derived from our thermokinematic model is 2.4 ± 0.4 km/Myr, the nominal slope values underestimate the modelled exhumation rate. Whatever may be the reasons for this discrepancy, the relatively large uncertainties of the slope values imply that they are still roughly consistent with our model.
The nominal AHe ages on the elevation profile are nearly invariant (Fig. 8) and the same is true for the upper part of the age-elevation profile near the Brenner fault studied by Wolff et al. (2020); for location, see Fig. 5. Here, the nearly identical AHe ages were interpreted to be caused by rapid tectonic exhumation followed by thermal relaxation after the end of normal faulting (Wolff et al. 2020). The similarity between both elevation profiles and the observation that the AHe ages along the WSW-ENE profile are also invariant (see Fig. 7D), indicates that the processes of heat advection during normal faulting and the subsequent thermal relaxation after faulting are reflected in our entire age data set (i.e., up to a distance of at least 16 km from the Brenner fault).

Interpretation of thermochronological data at sites A and B
At site A, there is a significant age difference between our two ZHe ages in the footwall (~ 7 and ~ 8 Ma) and the ZHe age of 36 ± 15 Ma in the hanging wall of the Brenner fault (Fig. 9). The ZHe ages for three samples at distances of 0.5-3 km west of the Brenner fault (Fig. 5) range from 63 ± 7 to 71 ± 10 Ma and show no spatial trend (Lünsdorf et al. 2012). We interpret the overall age pattern to be caused by a local heating of the fault hanging wall during its emplacement against the hot footwall. This heating has affected only our sample with the ZHe age of ~ 36 Ma (~ 100 m away from the fault), but not the three samples of Lünsdorf et al. (2012).
At site B, the nominal AHe ages of the three mylonitic samples in the fault footwall are slightly older than their ZHe ages, with the oldest AHe age being 10.8 ± 0.4 Ma (Fig. 9). Processes that may cause such elevated AHe ages include the incorporation of excess He from hydrothermal fluids (e.g., Zeitler et al. 2017), in particular in or near fault zones (e.g., Wölfler et al. 2010;Louis et al. 2019;Milesi et al. 2019), and the mobilization of U from apatite by acidic fluids (e.g., Milesi et al. 2019). In this context, it is important to note that the U concentration of apatite in the Bündner schists of the Matrei zone is rather low. The apatites analyzed at site B have U concentrations of 0.4-2.9 ppm, significantly lower than those of apatite in the coarse-grained orthogneiss samples discussed above, which range from 4 to 107 ppm (Table 3). Owing to the low U content of apatite and the small grain size of the Bündner schists, the rocks near the Brenner fault are likely susceptible to fluid flow, hydrothermal alteration, and a change of their (U-Th)/He systematics either during or after faulting. Therefore, the elevated AHe ages at site B should not be interpreted as geologically meaningful cooling ages.

Effect of enhanced footwall cooling near the Brenner fault
During normal faulting and heat advection, isotherms in the fault footwall are shifted towards the surface and the conduction of heat into the hanging wall leads to a warping of the isotherms (Grasemann and Mancktelow 1993;Ketcham 1996;Seward et al. 2009). When faulting stops, the upper crust in the fault footwall cools rapidly during thermal relaxation (Braun 2016). To illustrate these processes, we use the thermokinematic model without footwall tilting described in Sect. 6.2 and the faulting history of the Brenner fault (Wolff et al. 2020). The thermal structure in this model is shown at four different time steps (Fig. 10A). Due to the warping of the isotherms, the cooling ages predicted for different thermochronometers in the fault footwall increase towards the fault over a distance of up to 30 km (Fig. 10B). It is important to note that the increase in cooling ages is larger for systems with higher closure temperature and smaller for low-temperature thermochronometers. Hence, for low-temperature systems such as AHe and AFT, the effect may not be detectable. However, for geochronological systems with higher closure temperature, this effect is recognizable and needs to be considered as illustrated by K-Ar phengite and biotite ages from two sites located ~ 6 and ~ 13 km east of the Brenner fault (i.e., Landshuter Hütte and Pfitscher-Joch; for location see Fig. 5). The mean K-Ar ages for phengite (15.6 ± 2.0 and 14.5 ± 1.1 Ma) and biotite (13.8 ± 0.8 and 12.9 ± 0.2 Ma) at these two sites (von Blanckenburg et al. 1989) are in good agreement with our model predictions (Fig. 10B). The position of the two sites during and after faulting is shown in Fig. 10A. The K-Ar ages for phengite and biotite predicted by our model correspond to closure temperatures of 450 and 400 °C, respectively, and fall in the range of closure temperatures previously inferred for these systems (e.g., Villa 1998;Chew and Spikings 2015).
Phengite Rb-Sr ages in the westernmost Tauern Window are more variable (i.e., 20.3 ± 0.3 to 15.6 ± 0.4 Ma), but they do not increase towards the Brenner fault (von Blanckenburg et al. 1989). This observation can be explained by our finding that the Brenner fault became active 19 ± 2 Ma ago. At this time, the warping of the isotherms as a result of normal faulting was just about to start. Therefore, a significant cooling of the footwall of the Brenner fault has not yet occurred when the samples cooled through the closure temperature of Rb-Sr in phengite.

Folding and erosion as a mechanism for the exhumation of the Tauern Window
On N-S profiles through the Tauern Window, cooling ages from different thermochronological systems (AFT, ZFT, K-Ar mica, U-Pb apatite) form a U-shaped pattern, with ages increasing towards the north and south. Based on predictions by two-dimensional thermomechanical models for compressional orogens (Batt and Braun 1997), this spatial distribution of cooling ages has been interpreted to reflect N-S shortening, folding, and coeval erosion (Rosenberg and Garcia 2011;Schneider et al. 2015;Bertrand et al. 2017;Rosenberg et al. 2018). Although this interpretation is able to explain the available age data in the central part of the Tauern Window, the effect of the Brenner normal fault on the cooling and exhumation history of the westernmost 20-30 km of the window is not adequately accounted for in this interpretation for the following reasons. First, the age difference between ZFT and AFT ages along an ~ E-W profile through the Tauern Window decreases markedly in its western part (Bertrand et al. 2017, their Fig. 10), which suggests an increase in the rates of cooling and exhumation towards the west. We interpret this pattern to reflect the combined effect of heat advection and thermal relaxation during and after normal faulting on the Brenner fault. A similar pattern of ZFT and AFT ages is seen in the eastern Tauern Window and seems to be caused by the Katschberg normal fault (cf. Genser and Neubauer 1988;Scharf et al. 2013), although this interpretation remains to be evaluated by thermokinematic modeling. Second, the westward increase in K-Ar phengite and biotite ages towards the Brenner fault (Fig. 10) is caused by cooling of the footwall during normal faulting (see Sect. 7.3) and cannot be explained by folding around E-W trending axes and erosion. Third, the E-W gradient in ZHe cooling ages (Fig. 7b) reflects the progressive exhumation of the western Tauern Window by normal faulting, whereas the largely invariant AHe and AFT ages on the vertical transect at Olperer mountain (Fig. 8) are best explained by heat advection during normal faulting and exhumation followed by posttectonic thermal relaxation  Fig. 10 A Results of thermokinematic model illustrating how heat advection during normal faulting (from 19 to 8.8 Ma) shifts the isotherms in the fault footwall towards the surface. As a result of warping of the isotherms, cooling ages in the fault footwall increase towards the fault. When faulting stops, the upper crust cools rapidly during thermal relaxation (compare the two model stages at 8.8 and 5 Ma). The model used to generate this figure is identical to that described in Sect. 6.2, except that the model surface is horizontal. B Predicted cooling ages in the fault footwall increase towards the normal fault. Note that the effect is minor for low-temperature thermochronometers (AHe, AFT, and ZHe) but becomes more pronounced for thermochronometers with higher closure temperature. The phengite and biotite K-Ar ages of samples from Landshuter Hütte and Pfitscher-Joch Haus (see Fig. 5 for location) are from von Blanckenburg et al. (1989). The position of these samples is shown in (A) by yellow stars at 15, 8.8, and 5 Ma ( Fig. 6) (cf. Wolff et al. 2020). Finally, we note that erosion can only have affected the rocks of the western Tauern Window once they were tectonically exhumed from beneath the hanging wall by slip on the Brenner fault. As long as the rocks were buried below the fault hanging wall (i.e., Steinach nappe and Ötztal nappe with its sedimentary cover; Figs. 2 and 5), erosion can only have affected units in the hanging wall. However, these units experienced only a limited amount of erosion during the past ~ 20 Ma as shown by AFT, ZHe, and ZFT ages that are much older than those in the western Tauern Window (Fügenschuh et al. 1997(Fügenschuh et al. , 2012Lünsdorf et al. 2012;Wolff et al. 2020).

Amount and rate of valley incision after cessation of normal faulting
After normal faulting on the Brenner fault had ceased, an N-S trending valley has been incised into the fault footwall. The location of this valley was presumably controlled by differences in rock strength between the resistant hanging wall units (Steinach nappe and Brenner Mesozoic) and weaker rocks in the fault footwall (Matrei zone, Glockner, and Modereck nappes) (Fig. 3). The maximum estimates for the amount of valley incision (750-1200 m on profiles P1-P5) are based on a fault dip of 35° (broadly consistent with our field observations; Fig. 4). With respect to the fault dip, we note that Rosenberg and Garcia (2011) estimated quite variable fault dips of 19°-57° between Sterzing and Gries am Brenner (for location of these towns, see Figs. 2 and 3). Based on our topographic profiles, we suggest that a value of 1000 m is a reasonable average for the amount of incision and assign an uncertainty of ± 300 m to this value. If we combine this estimate (1000 ± 300 m) with the time constraint for the end of normal faulting (8.8 ± 0.4 Ma; Wolff et al. 2020), we obtain a time-averaged incision rate of about 110 m/Myr in the Brenner pass area. This incision rate is in agreement with the exhumation rate of 0.1 km/Myr after the end of normal faulting derived from the PECUBE model (Wolff et al. 2020). Given that the valley is situated in the internal part of the Alpine mountain chain, this long-term incision rate is surprisingly low. One may argue that erosion and valley incision have accelerated in the Quaternary as a result of frequent climate oscillations and enhanced glacial or fluvial erosion (e.g., Valla et al. 2011;Leith et al. 2018). However, even if we assume that rates of erosion and valley incision increased by a factor of four after 2.5 Ma, we obtain a Quaternary incision rate of only ~ 250 m/Myr, while the pre-Quaternary rate would be ~ 60 m/Myr. In this scenario, the Quaternary incision rate is still much lower than rates of erosion and valley deepening inferred in other parts of the Alps. In the central Alps, for example, incision rates of 1.0-1.5 km/Myr have been derived from burial dating of cave sediments (Haeuselmann et al. 2007), 4 He/ 3 He thermochronometry (Valla et al. 2011), and topographic signatures indicative of fluvial incision (Leith et al. 2018). In the high part of the western Alps, exhumation rates of > 1 km/Myr over the last 3 Ma were estimated from low-temperature thermochronological data (Glotzbach et al. 2008).
We suggest that the main reasons for the limited amount of valley incision (either by fluvial or glacial processes) in the area of the Brenner pass are the position of the Alpine drainage divide, which runs through the study area (Fig. 3). As the location of the drainage divide coincides with the maximum displacement on the Brenner fault (cf. Rosenberg et al. 2011), the N-S trending valley with its low-channel gradient appears to be related to the Brenner normal fault. As glacial erosion rates scale with ice discharge and basal sliding speed, which increase with valley gradient (e.g., Hallet 1979;Anderson et al. 2006), the amount of glacial (and fluvial) erosion during the Quaternary was limited by the low valley gradient near the Brenner drainage divide. This is consistent with a recent ice-flow modeling study, which indicates that the ice-flow divide during the last glaciation of the Alps was located near the current drainage divide and that the ice-surface velocity in the Brenner pass region was below ~ 20 m/yr (Seguinot et al. 2018). Our interpretation of a limited amount of erosion (~ 1000 m) after the end of normal faulting is consistent with the absence of well-developed U-shaped valleys in the Brenner region.

Conclusions
Our thermochronological data and thermokinematic modeling show that the Brenner normal fault exerted an important control on the cooling and exhumation history of the rocks exposed in the westernmost ~ 25 km of the Tauern Window. Normal faulting caused the advection of hot rocks towards the surface and the conduction of heat into the cooler hanging wall. After faulting ended at ~ 9 Ma, posttectonic thermal relaxation induced rapid cooling of the upper crust, which explains the invariant AHe ages on horizontal and vertical profiles. Farther to the east, the effect of the Brenner normal fault seems to vanish and the exhumation of the metamorphic rocks in the Tauern Window may have largely been controlled by prolonged N-S shortening, folding, and erosion (e.g., Rosenberg et al. 2018). The topography of the Brenner area-where the Brenner normal fault runs along the western shoulder of a N-S valley, which was incised into the fault footwall after faulting ceased-indicates that fluvioglacial erosion and valley incision near the drainage divide of the Alps were limited to about 1 km in the past ~ 9 Ma.