Philip F Sexton

Richard D Norris

Paul A Wilson

Heiko Pälike

Thomas Westerhold

Ursula Röhl

Clara T Bolton

Samantha Gibbs

Eocene global warming events driven by ventilation of oceanic dissolved organic carbon

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

reservoirs rather than carbon exhumation from, and subsequent burial back into, the sedimentary reservoir. Specifically, we interpret our records to indicate repeated, large-scale releases of dissolved organic carbon (at least 1600 gigatonnes) from the ocean by ventilation. The rapid recovery of the carbon cycle following each Eocene hyperthermal strongly suggests that carbon was re-sequestered by the ocean, rather than the much slower process of silicate rock weathering proposed for the PETM [START_REF] Zachos | Rapid acidification of the ocean during the Paleocene-Eocene thermal maximum[END_REF][START_REF] Zachos | An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics[END_REF] . Our findings suggest that these pronounced climatic warming events were driven not by repeated releases of carbon from buried sedimentary sources [START_REF] Zachos | An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF][START_REF] Dickens | Rethinking the global carbon cycle with a large, dynamic and microbially mediated gas hydrate capacitor[END_REF][START_REF] Panchuk | Sedimentary response to Paleocene-Eocene Thermal Maximum carbon release: A model-data comparison[END_REF] , but, rather, by patterns of surficial carbon redistribution familiar from younger intervals of Earth history.

Earth's climate attained its warmest state of the past 80 million years (Myr) during the early Palaeogene Period (~45 to 65 million years ago [Ma]) (Fig. 1a). Centered within this interval at 55 Ma, the Palaeocene-Eocene Thermal Maximum (PETM) marks a rapid 2.5 to >3.0 ‰ excursion in the carbon isotope composition ( 13 C) of marine carbonates [START_REF] Zachos | Rapid acidification of the ocean during the Paleocene-Eocene thermal maximum[END_REF][START_REF] Zachos | An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics[END_REF] and terrestrial organic matter concurrent with widespread dissolution of carbonate sediments [START_REF] Zachos | Rapid acidification of the ocean during the Paleocene-Eocene thermal maximum[END_REF][START_REF] Zachos | An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics[END_REF] and deep ocean warming by 6 to 7 °C3 . The source of carbon triggering this large perturbation to the exchangeable carbon reservoirs at Earth's surface (ocean, atmosphere and biosphere) is widely acknowledged to have come from an 'external' sedimentary reservoir(s) [START_REF] Zachos | Rapid acidification of the ocean during the Paleocene-Eocene thermal maximum[END_REF][START_REF] Zachos | An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF][START_REF] Dickens | Dissociation of oceanic methane hydrate as a cause of the carbon isotope excursion at the end of the Paleocene[END_REF][START_REF] Dickens | Methane oxidation during the late Palaeocene thermal maximum[END_REF][START_REF] Dickens | Rethinking the global carbon cycle with a large, dynamic and microbially mediated gas hydrate capacitor[END_REF][START_REF] Panchuk | Sedimentary response to Paleocene-Eocene Thermal Maximum carbon release: A model-data comparison[END_REF] . A long-standing hypothesis attributes this event to the release of massive amounts of methane from sedimentary gas hydrate deposits [START_REF] Zachos | Rapid acidification of the ocean during the Paleocene-Eocene thermal maximum[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF][START_REF] Dickens | Dissociation of oceanic methane hydrate as a cause of the carbon isotope excursion at the end of the Paleocene[END_REF][START_REF] Dickens | Methane oxidation during the late Palaeocene thermal maximum[END_REF][START_REF] Dickens | Rethinking the global carbon cycle with a large, dynamic and microbially mediated gas hydrate capacitor[END_REF] , with attendant oxidation to CO 2 causing climatic warming through a greenhouse feedback [START_REF] Zachos | An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics[END_REF] . Because of the relative rapidity of its onset, and the estimated quantity of sedimentary-sourced carbon involved, the PETM has attracted interest as a natural analogue to the ongoing anthropogenic perturbation to Earth's surficial carbon cycle.

In recent years, a number of transient warming events comparable in character to the PETM, but less extreme in magnitude and duration, have been discovered throughout the early Palaeogene (at approx. 65.2, 58.2, 53.7, 53.2, 52.5 & 41.8 Ma [START_REF] Thomas | Deep sea environments on a warm earth[END_REF][START_REF] Cramer | Orbital climate forcing of delta C-13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Petrizzo | An early late Paleocene event on Shatsky Rise, northwest Pacific Ocean (ODP Leg 198): evidence from planktonic foraminiferal assemblages[END_REF][START_REF] Sexton | Testing the Cenozoic multisite composite δ18O and δ13C curves: New monospecific Eocene records from a single locality, Demerara Rise (Ocean Drilling Program Leg 207)[END_REF][START_REF] Westerhold | On the duration of magnetochrons C24r and C25n and the timing of early Eocene global warming events: Implications from the Ocean Drilling Program Leg 208 Walvis Ridge depth transect[END_REF][START_REF] Edgar | No extreme bipolar glaciation during the main Eocene calcite compensation shift[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF][START_REF] Quillévéré | Transient ocean warming and shifts in carbon reservoirs during the early Danian[END_REF][START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] ). These 'hyperthermals' [START_REF] Thomas | Deep sea environments on a warm earth[END_REF] have not been found during the later part of the Eocene (after ~40 Ma) as global climate cooled (Fig. 1a). The number of these hyperthermals, and the relative temporal spacing between some of them, is suggestive of the operation of common mechanisms [START_REF] Cramer | Orbital climate forcing of delta C-13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF] . Although various mechanisms have been proposed for the origin of these comparatively modest events [START_REF] Cramer | Orbital climate forcing of delta C-13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)[END_REF][START_REF] Petrizzo | An early late Paleocene event on Shatsky Rise, northwest Pacific Ocean (ODP Leg 198): evidence from planktonic foraminiferal assemblages[END_REF][START_REF] Quillévéré | Transient ocean warming and shifts in carbon reservoirs during the early Danian[END_REF] , it is widely considered that they too were triggered by large-scale releases of carbon from sedimentary reservoirs [START_REF] Zachos | An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF][START_REF] Dickens | Rethinking the global carbon cycle with a large, dynamic and microbially mediated gas hydrate capacitor[END_REF][START_REF] Panchuk | Sedimentary response to Paleocene-Eocene Thermal Maximum carbon release: A model-data comparison[END_REF] , probably methane hydrates [START_REF] Zachos | An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF][START_REF] Dickens | Rethinking the global carbon cycle with a large, dynamic and microbially mediated gas hydrate capacitor[END_REF] . Yet, the typical magnitude of the  13 C anomalies across known hyperthermals (up to ~1.0 ‰) is, in fact, not unusual for  13 C records from the better chronicled Neogene Period and, more importantly, these anomalies are not so large that they necessitate a source of carbon that is as extremely isotopically depleted as methane hydrate ( 13 C = -60 ‰). °C at about 3000 m 8 water depth (Fig. 1b). This warm deep ocean state is punctuated by 13 excursions to lower  18 O values indicative of short-term warming by ~2 to 4 °C (Fig. 1b; Fig. 2a; events numbered in Fig. 1c). These transient warming events develop very rapidly (<5 to 10 thousand years [kyr]) and decay to 'background' temperatures more slowly (over ~30 kyr).

Our accompanying benthic foraminifer  [START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] C record shows that each warming event is marked by an excursion to lower  13 C values by 0.7 to 1.0 ‰ (Fig. 1c). Where planktic records are available for the most prominent negative excursions in the benthic  [START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] C record, these also reveal negative  13 C excursions of 0.6 to 0.9 ‰ (Fig. 2), suggesting that these events represent whole-ocean decreases in  13 C of total dissolved inorganic carbon (CO 2 ).

All of the benthic  13 C excursions are associated with brown clay-rich layers at Demerara Rise (arrows in Fig. 1), a hallmark of other reported early Palaeogene hyperthermals [START_REF] Zachos | Rapid acidification of the ocean during the Paleocene-Eocene thermal maximum[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Petrizzo | An early late Paleocene event on Shatsky Rise, northwest Pacific Ocean (ODP Leg 198): evidence from planktonic foraminiferal assemblages[END_REF][START_REF] Edgar | No extreme bipolar glaciation during the main Eocene calcite compensation shift[END_REF][START_REF] Quillévéré | Transient ocean warming and shifts in carbon reservoirs during the early Danian[END_REF][START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] , that suggests increased calcium carbonate (CaCO 3 ) dissolution.

Yet not all clay layers are associated with a numbered  13 C excursion (Fig. 1c). However, those that are not are still associated with a  13 C excursion, but one of smaller magnitude. This is consistent with the largest hyperthermals (those numbered in Fig. 1c) simply being prominent end-members in a spectrum of carbon cycle perturbations that scale up from orbitally paced 'background' cycles. Records of estimated CaCO 3 concentrations from Demerara Rise (palaeo-water depth ~3 km [START_REF] Sexton | Testing the Cenozoic multisite composite δ18O and δ13C curves: New monospecific Eocene records from a single locality, Demerara Rise (Ocean Drilling Program Leg 207)[END_REF] ) and sites in the southern Atlantic and central Pacific (palaeo-water depths ~3 and 2 km, respectively [Supplementary Discussion]) reveal synchronous, globally widespread decreases in CaCO 3 accumulation (Supplementary Fig. 2e to g). Calculations of carbonate dissolution associated with the clay layers in the Atlantic and Pacific (Supplementary Discussion), indicate that CaCO 3 dissolution events (Fig. 3b to d) are coeval with the large negative benthic  13 C excursions at Demerara Rise (Fig. 3a). This correspondence strongly suggests that global increases in deep ocean acidity were associated with intervals of isotopically 'light' carbon pervading the world's oceans.

Our age model indicates that the Demerara Rise hyperthermals have overall durations of ~40 kyr (Fig. 1b andc; Fig. 2), consistent with pacing by the 41 kyr obliquity cycle in Earth's axial tilt. The timing of individual hyperthermals is not perfectly cyclic, but does appear to occur within orbital frequency bands of 400 and 100 kyr (Fig. 1b andc). For example, spectral analysis of the benthic foraminifer  13 C record shows spectral power at the 127 kyr 'short' eccentricity frequency (Supplementary Fig. 3). Furthermore, even though our 2.4 Myr-long  13 C record can only contain a maximum of six 'long' 405 kyr eccentricity cycles, power and highly significant coherency with the astronomical prediction is also found at this longer frequency (Supplementary Fig. 3).

Moreover, shorter period fluctuations in the estimated % CaCO 3 record from Demerara Rise are modulated in amplitude at this ~405 kyr frequency (Supplementary Fig. 2e). This strong 405 kyr response in carbon cycling compared to the relative amplitude of this cycle in the insolation forcing [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF] has been attributed [START_REF] Cramer | Orbital climate forcing of delta C-13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)[END_REF][START_REF] Palike | The heartbeat of the Oligocene climate system[END_REF] to the long residence time (~140 kyr [START_REF] Dickens | Dissociation of oceanic methane hydrate as a cause of the carbon isotope excursion at the end of the Paleocene[END_REF][START_REF] Dickens | Methane oxidation during the late Palaeocene thermal maximum[END_REF] ) of CO 2 in the oceans. Our new data demonstrate that the long 405 kyr eccentricity cycle, a major component of secular carbon cycling in the ocean [START_REF] Cramer | Orbital climate forcing of delta C-13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)[END_REF][START_REF] Palike | The heartbeat of the Oligocene climate system[END_REF] , was also intimately involved in pacing Eocene hyperthermals. These perturbations to oceanic carbon cycling could have been fuelled by carbon input from a number of different potential sources. Besides methane hydrates, erosion of sedimentary organic carbon (C org ) could supply carbon with a  13 C composition (-25‰) that is less depleted than that of methane (-60‰). A third potential source is redistribution of carbon within the exchangeable reservoirs at Earth's surface (ocean, atmosphere and biosphere). Redistribution of isotopically light carbon among the internal, readily exchangeable reservoirs should produce  13 C excursions with fundamentally different size, shape, duration and recovery trends than carbon input from an external, sedimentary reservoir.

Mass balance considerations (assuming masses of Eocene carbon reservoirs similar to modern) dictate that the ~1 ‰  13 C excursions we observe are compatible with injection of a mass of carbon from methane hydrates (-60‰) of about 650 gigatonnes (Gt). But this volume of carbon is far too small to have driven our corresponding deep ocean warmings of 3 to 4 °C (Fig. 1b; Fig. 2a), particularly given that deep ocean warming of 6 to 7 °C at the PETM 3 was triggered by release of >>2000 1 to 6800 [START_REF] Panchuk | Sedimentary response to Paleocene-Eocene Thermal Maximum carbon release: A model-data comparison[END_REF] Gt of carbon. The large and widespread increases in CaCO 3 dissolution associated with our hyperthermals also appear to demand a much larger input of carbon than the 650 Gt permitted by a methane hydrate source.

The  13 C composition of sedimentary C org (-25 ‰) permits a much larger carbon release (~1600 Gt) to be accommodated within the observed 1 ‰  13 C excursions of hyperthermals, but problems also exist with this carbon source. The ~140 kyr residence time () of carbon in Earth's exchangeable reservoirs [START_REF] Dickens | Dissociation of oceanic methane hydrate as a cause of the carbon isotope excursion at the end of the Paleocene[END_REF][START_REF] Dickens | Methane oxidation during the late Palaeocene thermal maximum[END_REF] suggests that the liberation of a substantial quantity of isotopically light carbon from an external, deeply buried source should have a persistent imprint on oceanic and atmospheric  13 C for a very long time (approaching  20 until it is ultimately sequestered back into the long-term sedimentary carbon reservoir by weathering reactions [START_REF] Archer | Fate of fossil fuel CO2 in geologic time[END_REF] . This behaviour is demonstrated at the PETM which shows a  13 C excursion ~170 kyr in duration 2 with a very long recovery 'tail' [START_REF] Zachos | Rapid acidification of the ocean during the Paleocene-Eocene thermal maximum[END_REF][START_REF] Zachos | An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics[END_REF][START_REF] Cramer | Orbital climate forcing of delta C-13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF] that produces a very asymmetrical excursion and reflects the long timescales required for weathering to draw down this external CO 2 and return it to the sedimentary reservoir as CaCO 3 . However, our  13 C excursions are too short (only ~40 kyr total duration), return to pre-excursion values too fast (within 30 kyr, Fig. 1c, Fig. 2a), and to a post-excursion baseline that is isotopically no different from pre-excursion, to be compatible with largescale injection of light carbon from a deeply buried source. The recoveries seen for other hyperthermals [START_REF] Cramer | Orbital climate forcing of delta C-13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Sexton | Testing the Cenozoic multisite composite δ18O and δ13C curves: New monospecific Eocene records from a single locality, Demerara Rise (Ocean Drilling Program Leg 207)[END_REF][START_REF] Edgar | No extreme bipolar glaciation during the main Eocene calcite compensation shift[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF][START_REF] Quillévéré | Transient ocean warming and shifts in carbon reservoirs during the early Danian[END_REF][START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] are also too rapid to represent sequestration of substantial amounts of sedimentary-sourced carbon.

The incompatibility of hyperthermals with external, sedimentary carbon sources indicates that the carbon that fuelled them was likely redistributed from within the readily exchangeable reservoirs at Earth's surface. The oceans are by far the largest of these exchangeable reservoirsthe present-day oceans contain 13 times as much carbon as the combined biosphere and atmosphereall told about 40,000 Gt of carbon. Today, about 700-1800 Gt of this carbon (between 1 and 2 times the mass of the atmospheric reservoir) is stored as dissolved C org ( 13 C = -25‰), but this reservoir size would likely grow, perhaps many fold, under more oxygen-depleted deep ocean conditions. Redistribution of a mass of carbon equivalent to this entire modern reservoir (~1600 Gt C) would be required to produce the ~1.0 ‰  13 C excursions seen for our events and previously reported ones [START_REF] Cramer | Orbital climate forcing of delta C-13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Sexton | Testing the Cenozoic multisite composite δ18O and δ13C curves: New monospecific Eocene records from a single locality, Demerara Rise (Ocean Drilling Program Leg 207)[END_REF][START_REF] Edgar | No extreme bipolar glaciation during the main Eocene calcite compensation shift[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF][START_REF] Quillévéré | Transient ocean warming and shifts in carbon reservoirs during the early Danian[END_REF][START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] . Within the oceans, the two principal reservoirs for storing large volumes of carbon are marginal basins or the abyssal ocean. Because of its sheer size, the deep abyssal reservoir of carbon has long been implicated in the regular, ~100 parts per million by volume (ppmv) fluctuations of atmospheric CO 2 and ~5 °C surface temperature changes seen across the late Pleistocene glacial cycles. It has recently become clear that the abyssal Southern Ocean has played a pivotal role in Pleistocene carbon cycling though its gradual amassing of respired CO 2 during glacials [START_REF] Hodell | Pleistocene vertical carbon isotope and carbonate gradients in the South Atlantic sector of the Southern Ocean[END_REF][START_REF] Toggweiler | Midlatitude westerlies, atmospheric CO2, and climate change during the ice ages[END_REF][START_REF] Skinner | Ventilation of the Deep Southern Ocean and Deglacial CO2 Rise[END_REF] and subsequent release via increased ventilation [START_REF] Hodell | Pleistocene vertical carbon isotope and carbonate gradients in the South Atlantic sector of the Southern Ocean[END_REF][START_REF] Toggweiler | Midlatitude westerlies, atmospheric CO2, and climate change during the ice ages[END_REF][START_REF] Skinner | Ventilation of the Deep Southern Ocean and Deglacial CO2 Rise[END_REF] during deglaciation.

Several observations suggest that the source of CO 2 fuelling Eocene hyperthermals was the abyssal ocean. First, our dissolution records provide clues to the place of storage of CO 2 in the exchangeable carbon reservoirs. Numerical modelling indicates that CaCO 3 dissolution should be most intense close to the source of carbon release [START_REF] Dickens | Methane oxidation during the late Palaeocene thermal maximum[END_REF] . In our estimates of CaCO 3 dissolution, dissolution intensity appears to be consistently highest in the southern Atlantic (Fig. 3e) compared to the other sites. This raises the possibility that the abyssal reservoir of carbon was located in the Southern Ocean. Second, all our hyperthermals are approximately 40 kyr in duration (Fig. 1b andc, Fig. 2). The similarity of this period to the 41 kyr obliquity cycle suggests that the forcing for individual hyperthermal events had its origin at high latitudes. This is consistent with an obliquity pacing of high latitude surface ocean stratification controlling CO 2 ventilation, as proposed for the last deglaciation [START_REF] Sigman | Antarctic stratification, atmospheric water vapor, and Heinrich events: A hypothesis for late Pleistocene deglaciations. in Past and Future Changes of the Oceanic Meridional Overturning Circulation: Mechanisms and Impacts[END_REF] .

If the source of CO 2 driving Eocene hyperthermals was the deep ocean, a number of observations suggest that our Eocene sites may be somewhat analogous to intermediate-depth sites during Pleistocene glacials that were located above a deeper CO 2 storage reservoir [START_REF] Hodell | Pleistocene vertical carbon isotope and carbonate gradients in the South Atlantic sector of the Southern Ocean[END_REF][START_REF] Marchitto | Marine radiocarbon evidence for the mechanism of deglacial atmospheric CO2 rise[END_REF] . First, although very few lower Eocene deep-sea sedimentary sections have paleo-water depths greater than about 3 km, their lithologies are almost universally dominated by CaCO 3 , suggesting that any early Eocene corrosive abyssal reservoir of respired CO 2 must have been restricted to depths >3 km. Second, the absence prior to our hyperthermals of either gradually decreasing benthic  13 C or increasing dissolution intensity (Fig. 1c, Fig. 2) indicates that our mid-depth (2 to 3 km) sites did not 'sense' the gradual (~10 4 to 10 5 year) build-up of a CO 2 reservoir until its final release.

Early Eocene hyperthermals were superimposed on an already warm climate (Fig. 1a,b) with high background partial pressures of atmospheric CO 2 (pCO 2 ) (available proxies suggest 2 to 12 times pre-industrial levels, ~500 to 3500 ppmv [START_REF] Royer | CO2-forced climate thresholds during the Phanerozoic[END_REF] ). Assuming that Eocene climate sensitivity (to a CO 2 doubling) lay within expected ranges (1.5 to 4.5 °C), this range of high background pCO 2 implies that, in comparison to ocean degassing during Pleistocene deglacials, much larger Eocene releases of carbon would have been required to rapidly raise deep ocean temperatures by the observed 3.5 °C (e.g. 830-2500 Gt for a background pCO 2 of 500 ppmv, 1660-5000 Gt for 1000 ppmv and 3330-10,000 Gt for 2000 ppmv). Our estimate of carbon releases ~1600 Gt appears most compatible with the lower end of background pCO 2 concentrations (~500 ppmv).

In the modern oceans, dissolved C org concentrations decrease during the water mass aging process, owing to progressive bacterial respiration primarily of young, labile components [START_REF] Hansell | Deep-ocean gradients in the concentration of dissolved organic carbon[END_REF] . This relationship with water mass age might argue against a larger-thanmodern Eocene reservoir of dissolved C org driven solely by longer residence times of deep water in the Eocene ocean. However, under anoxic conditions, dissolved C org may build-up. For example, concentrations of dissolved C org in the anoxic depths (>2000 m) of the modern Black Sea are ~2.5 times those of the global deep ocean [START_REF] Ducklow | Dissolved organic carbon and nitrogen in the Western Black Sea[END_REF] . An early Eocene decoupling of marine burial rates of C org versus pyrite indicates that the deep ocean during this interval may have regularly experienced pronounced anoxia [START_REF] Kurtz | Early Cenozoic decoupling of the global carbon and sulfur cycles[END_REF] . We suggest that this persistent anoxia in the early Eocene abyss [START_REF] Kurtz | Early Cenozoic decoupling of the global carbon and sulfur cycles[END_REF] , at least partly driven by the lower solubility of oxygen at warmer temperatures (Fig. 1a,b), would have promoted the build-up of a reservoir of dissolved C org large enough to have fuelled hyperthermal carbon releases ~1600 Gt. Anoxia in the Eocene abyss is consistent with modelling projections for the next few millenia indicating a large reduction in abyssal ventilation (by up to 75%) [START_REF] Schmittner | Future changes in climate, ocean circulation, ecosystems, and biogeochemical cycling simulated for a business-as-usual CO2 emission scenario until year 4000 AD[END_REF] in response to climatic warming induced by an 'anthropogenic' atmospheric pCO 2 (1700 ppmv) similar to that of the early Eocene. Furthermore, we suggest that the relatively long ~100 or 400 kyr intervals between CO 2 release events (Fig. 1) would also have contributed to the build-up of a large Eocene abyssal reservoir of dissolved C org (see Supplementary Discussion).

Further support for the existence of a larger-than-modern Eocene deep (>3 km) ocean reservoir of dissolved C org is found in surface-to-deep profiles of seawater temperature and  13 C reconstructed from multiple species of planktic and benthic foraminifera (Supplementary Fig. 4). In comparison to Recent core-top data, Eocene data suggest a steeper vertical gradient of  13 C of DIC versus temperature along with a greater total surface-to-seafloor  [START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] C difference (Supplementary Fig. 4), together consistent with a deeper mean C org remineralisation depth. The much greater species diversity of calcareous nannofossils relative to diatoms throughout the early Palaeogene 31 may have accelerated the abyssal transfer of C org from the surface owing to the greater ballasting efficiency of CaCO 3 relative to opal [START_REF] Klaas | Association of sinking organic matter with various types of mineral ballast in the deep sea: Implications for the rain ratio[END_REF] . Interestingly, a major switch to greater species diversity of diatoms relative to calcareous nannofossils (at ~40 Ma) [START_REF] Falkowski | The evolution of modern eukaryotic phytoplankton[END_REF] coincides with the last documented early Cenozoic 'hyperthermal' event [START_REF] Edgar | No extreme bipolar glaciation during the main Eocene calcite compensation shift[END_REF] .

Although the PETM must have been fuelled by carbon injection from an external, sedimentary source(s), we suggest that astronomically paced changes in ocean ventilation of dissolved C org may explain the numerous less extreme hyperthermals that are being discovered [START_REF] Thomas | Deep sea environments on a warm earth[END_REF][START_REF] Cramer | Orbital climate forcing of delta C-13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Petrizzo | An early late Paleocene event on Shatsky Rise, northwest Pacific Ocean (ODP Leg 198): evidence from planktonic foraminiferal assemblages[END_REF][START_REF] Sexton | Testing the Cenozoic multisite composite δ18O and δ13C curves: New monospecific Eocene records from a single locality, Demerara Rise (Ocean Drilling Program Leg 207)[END_REF][START_REF] Westerhold | On the duration of magnetochrons C24r and C25n and the timing of early Eocene global warming events: Implications from the Ocean Drilling Program Leg 208 Walvis Ridge depth transect[END_REF][START_REF] Edgar | No extreme bipolar glaciation during the main Eocene calcite compensation shift[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF][START_REF] Quillévéré | Transient ocean warming and shifts in carbon reservoirs during the early Danian[END_REF][START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] throughout the early Palaeogene. CO 2 ventilation is a viable mechanism with which to sustain the repeated, frequent carbon releases that define hyperthermals over a geologically extended interval (Fig. 1b andc) [START_REF] Thomas | Deep sea environments on a warm earth[END_REF][START_REF] Cramer | Orbital climate forcing of delta C-13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)[END_REF][START_REF] Lourens | Astronomical pacing of late Palaeocene to early Eocene global warming events[END_REF][START_REF] Petrizzo | An early late Paleocene event on Shatsky Rise, northwest Pacific Ocean (ODP Leg 198): evidence from planktonic foraminiferal assemblages[END_REF][START_REF] Sexton | Testing the Cenozoic multisite composite δ18O and δ13C curves: New monospecific Eocene records from a single locality, Demerara Rise (Ocean Drilling Program Leg 207)[END_REF][START_REF] Westerhold | On the duration of magnetochrons C24r and C25n and the timing of early Eocene global warming events: Implications from the Ocean Drilling Program Leg 208 Walvis Ridge depth transect[END_REF][START_REF] Edgar | No extreme bipolar glaciation during the main Eocene calcite compensation shift[END_REF][START_REF] Nicolo | Multiple early Eocene hyperthermals: Their sedimentary expression on the New Zealand continental margin and in the deep sea[END_REF][START_REF] Quillévéré | Transient ocean warming and shifts in carbon reservoirs during the early Danian[END_REF][START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] since the recharge times of the abyssal ocean (via remineralisation of C org ) are rapid compared to the slow, multi-million year filling of sedimentary methane hydrate reservoirs [START_REF] Buffett | Global inventory of methane clathrate: sensitivity to changes in the deep ocean[END_REF] . The extraordinarily warm mean state of the Palaeogene oceans (Fig. 1a,b) also raises the question as to whether largescale methane hydrate reservoirs would even have existed at this time [START_REF] Buffett | Global inventory of methane clathrate: sensitivity to changes in the deep ocean[END_REF] . Despite the extreme nature of these repeated Palaeogene climatic warming events, our findings indicate that they were driven by changes in storage of carbon within the oceans.

METHODS SUMMARY

 [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF] O and  13 C data were generated using mono-specific analyses of the benthic foraminifers Cibicidoides subspiratus and C. eoceanus at the National Oceanography Centre, Southampton. High resolution Eocene records of CaCO 3 concentrations were calculated, by regression, using sediment physical property data and measurements of sediment CaCO 3 content. We developed an astronomically calibrated age model for Site 1258 (Demerara Rise). Detailed chronologies for Sites 1267 and 1210 were generated by tuning clear, correlatable events in their respective % CaCO 3 records to the astronomically calibrated % CaCO 3 record from Site 1258.

Full Methods are available at the end of this manuscript. Figure 2. Detail of isotope data across two 'hyperthermal' events (asterisks in Fig. 1). X-axis labels are at 40 kyr spacing, highlighting the similarity of the duration (i.e. 'trough to trough') of these events to the obliquity frequency. We define the 'onset' phase of events as 'trough to peak', with their 'recovery' being 'peak to trough'. Early Eocene through middle Eocene sediments at ODP Site 1258 (Demerara Rise) host well preserved benthic foraminifera [START_REF] Sexton | Testing the Cenozoic multisite composite δ18O and δ13C curves: New monospecific Eocene records from a single locality, Demerara Rise (Ocean Drilling Program Leg 207)[END_REF] . Cibicidoides subspiratus was used as the primary species for stable isotope analysis. However, in certain intervals, notably in the younger part of our record (after 48.5 Ma), a decline in abundance of C. subspiratus dictated that we also use Cibicidoides eoceanus. Although modern core top samples show significant inter-species stable isotope offsets between certain species of Cibicidoides 34 , our calculated inter-species offsets for the two Eocene species of Cibicidoides (from paired mono-specific analyses, n = 168) are statistically indistinguishable from zero for both  18 O and  13 C ( 18 O = -0.031 [1 = 0.128];  13 C = 0.009 [1 = 0.133]). This provides justification for our strategy of using these two species in combination. Benthic foraminiferal taxonomy follows that of refs [START_REF] Tjalsma | Paleocene-Eocene bathyal and abyssal benthic foraminifera from the Atlantic Ocean[END_REF][START_REF] Van Morkhoven | Cenozoic cosmopolitan deep water benthic foraminifera[END_REF] .

Figure captions

All  18 O data are corrected to equilibrium calcite using the Oridorsalis spp. -Cibicidoides spp. correction factor of +0.28‰ derived from an assessment of isotopic offsets for Eocene benthic foraminifera [START_REF] Katz | Early Cenozoic benthic foraminiferal isotopes: Species reliability and interspecies correction factors[END_REF] . Use of this correction factor is based on evidence (summarised in ref. [START_REF] Sexton | Testing the Cenozoic multisite composite δ18O and δ13C curves: New monospecific Eocene records from a single locality, Demerara Rise (Ocean Drilling Program Leg 207)[END_REF] ) that Eocene Oridorsalis umbonatus secreted its calcite in  [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF] O equilibrium with seawater. Paleotemperatures were calculated using eq. 1 of ref. [START_REF] Bemis | Reevaluation of the oxygen isotopic composition of planktonic foraminifera: Experimental results and revised paleotemperature equations[END_REF] .

This equation provides excellent agreement with a global core top Cibicidoides spp.  18 O calibration for a temperature range from 0 to 7 °C38 . In keeping with the view that there were no significant continental ice sheets during the early to early middle Eocene [START_REF] Zachos | Trends, rhythms, and aberrations in global climate 65 Ma to present[END_REF][START_REF] Browning | Global implications of lower to middle Eocene sequence boundaries on the New Jersey coastal plain: The icehouse cometh[END_REF] , our  18 O records can be interpreted in terms of change in bottom water temperature at Demerara Rise.

Age models. Site 1258 recovered an unusually continuous, relatively expanded (sedimentation rates up to 2.5 cm/kyr) sedimentary section across the lower to middle Eocene boundary with unprecedented magneto-, bio-and cyclo-stratigraphic control for this interval [START_REF] Erbacher | Proc. ODP, Init. Repts[END_REF][START_REF] Suganuma | Campanian through Eocene magnetostratigraphy of Sites 1257-1261[END_REF][START_REF] Westerhold | High resolution cyclostratigraphy of the early Eocene new insights into the origin of the Cenozoic cooling trend[END_REF] . We developed an astronomically calibrated age model for Site 1258 by tuning clear and pronounced obliquity (~40 kyr) cycles in the magnetostratigraphically calibrated magnetic susceptibility (MS) time series (Supplementary Fig. 1a) to computed obliquity cycles from the most recent astronomical solution [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF] . Our tuning strategy is validated by the presence in our tuned MS time series of substantial power (and coherency with our tuning target) at frequencies of 23, 21 and 19 kyr (precession), 54 kyr (obliquity) and 96 kyr (eccentricity) (Supplementary Fig. 1b), even though these frequencies were not used in the tuning process. An absolute calibration to the astronomical solution is, at present, unattainable for the early to middle Eocene because of limitations in the precision of computed orbital variations pre-40 Ma [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF] and because of significant uncertainties in radiometric age calibrations [START_REF] Berggren | A revised Cenozoic geochronology and chronostratigraphy[END_REF][START_REF] Machlus | Eocene calibration of geomagnetic polarity time scale reevaluated: Evidence from the Green River Formation of Wyoming[END_REF] 2 and3). This tuning strategy was held as relaxed as possible, using a minimum of tie points.

Eocene records of CaCO 3 concentrations. We use sediment colour and magnetic susceptibility data in conjunction with measurements of sediment CaCO 3 content 41 to calculate, by regression, sediment CaCO 3 content at high resolution at Demerara Rise (Fig. 1d; Supplementary Fig. 2e). We use comparable data [START_REF] Zachos | Proc. ODP, Init. Repts[END_REF][START_REF] Bralower | Proc. ODP, Init. Repts[END_REF] data for our zero dissolution point, rather than the much lower resolution measured % CaCO 3 data [START_REF] Erbacher | Proc. ODP, Init. Repts[END_REF][START_REF] Zachos | Proc. ODP, Init. Repts[END_REF][START_REF] Bralower | Proc. ODP, Init. Repts[END_REF] , is validated by the fact that estimated % CaCO 3 is a good predictor of measured % CaCO 3 (Supplementary Fig. 2a to c). We assume that these zero dissolution points represent intervals when the local lysocline lay deeper than the seafloor at each particular drill site. Second, we assume that the rain ratio of CaCO 3 to C org to the seafloor remained constant through the study interval at each site. While we acknowledge that this is unlikely, the sampling interval for our estimated % CaCO 3 time series (~2.5 kyr at Demerara; ~5.0 kyr at Shatsky and Walvis) should average out seasonal to inter-annual variability in rain ratios.

Locating an Eocene abyssal reservoir of carbon

Progressive build-up of carbon in the abyssal ocean and its episodic, rapid release to shallower water depths should, via CaCO 3 compensation [START_REF] Broecker | The role of CaCO3 compensation in the glacial to interglacial atmospheric CO2 change[END_REF] , impart a distinctive pattern to the abyssal sedimentary recordlong intervals of CaCO 3 -free to CaCO 3 -poor sedimentation followed by a pulse of CaCO 3 upon degassing. The release of a large abyssal reservoir of respired CO 2 during the last deglaciation led to the well-known deglacial 'CaCO 3 preservation spike' [START_REF] Berger | Deep-sea carbonate and the deglaciation preservation spike in pteropods and foraminifera[END_REF][START_REF] Marchitto | Deep Pacific CaCO3 compensation and glacial-interglacial atmospheric CO2[END_REF]

A 2 .

 2 4 million year-long benthic foraminifer stable isotope record (Supplementary Discussion) from Demerara Rise in the tropical western Atlantic (Ocean Drilling Program Site 1258) shows that events exhibiting the characteristics of previously identified hyperthermals are abundant in the Palaeogene deep-sea palaeoceanographic record. Spanning the early Eocene to middle Eocene transition (47.6 to 50.0 Ma), these records indicate that average temperatures in the early Eocene equatorial Atlantic were 12 to 14

Figure 1 .

 1 Figure 1. High-resolution records across the early to middle Eocene transition

Figure 3 .

 3 Figure 3. Eocene records of benthic foraminifer  13 C and CaCO 3 dissolution. a, Benthic  13 C from Fig. 1c (Demerara Rise, ODP Site 1258, western tropical

  . Consequently, we develop a 'floating' astronomically tuned timescale, using the C21r/C22n magnetochron boundary (age = 49.037 Ma 44 ) identified at Site 1258[START_REF] Suganuma | Campanian through Eocene magnetostratigraphy of Sites 1257-1261[END_REF] as our anchor point.

	Age models for the estimated % CaCO 3 records for ODP 1267 (Walvis Ridge)
	and ODP 1210 (Shatsky Rise) are derived by correlating the stratigraphic position of a
	biostratigraphic datum (Last Appearance Datum [LAD] of the nannofossil D. lodoensis)
	at both of these sites to its position at Site 1258 (Supplementary Table 1). Further age
	model refinement was achieved by tuning clear, correlatable events in % CaCO 3 records
	from Sites 1267 and 1210 to the astronomically calibrated % CaCO 3 record from Site
	1258 (Supplementary Tables

  taken place at the seafloor during these dissolution events. But no a priori reason exists why  13 C (and especially  18 O) should be offset to much lower values by

	recrystallisation at the seafloor. Second, visual inspection of benthic foraminifera under
	reflected light reveals no obvious signs of deteriorated taphonomy within the isotope
	'excursion' intervals.
	Eocene proxy records of CaCO 3 dissolution
	Our records of estimated % CaCO 3 display similar secular trends at all three
	locations (Supplementary Fig. 2e to g), although amplitudes of variance differ,
	presumably largely governed by the initial fractional component of CaCO 3 in the
	sediment and by paleo-water depth (Demerara ~3000 m 8 , Walvis ~3000 m 46 , Shatsky
	~2000 m 47 ). Because of the non-linear relationship between CaCO 3 dissolution and
	sediment CaCO 3 content 48 , we use our estimated % CaCO 3 time series (Supplementary
	to perform the same Fig. 3e to g) to calculate the extent of CaCO 3 dissolution at each site (Fig. 3b to d). We
	regressions for two other deep sea drill sites (ODP 1267, Walvis Ridge, southern Atlantic do this by attempting to identify the primary, unaltered fractional component of CaCO 3 in
	and ODP 1210, Shatsky Rise, central Pacific) (Supplementary Fig. 2f and g). At all three the sediment (our 'zero-dissolution point'). We then calculate changes in % dissolution of
	sites, estimated CaCO 3 concentrations prove to be a good predictor of measured CaCO 3 the sedimentary CaCO 3 component away from this zero-dissolution point using our
	concentrations (Supplementary Fig. 2a to c). For methods for calculating CaCO 3 estimated % CaCO 3 time series. Calculating CaCO 3 dissolution in this manner involves
	dissolution from our Eocene CaCO 3 records, see Supplementary Information. two assumptions. First, we assume that the zero dissolution point is represented by the
	maximum % CaCO 3 value in each of our 2.4 Myr-long estimated % CaCO 3 time series
	34. (shown by blue arrows in Supplementary Fig. 2e to g). Our use of estimated % CaCO 3 Curry, W.B., Slowey, N.C. & Lohmann, G.P. Oxygen and carbon isotopic
	fractionation of aragonitic and calcitic benthic foraminifera on Little Bahama
	Bank, Bahamas (abstract). EOS, Transactions of the American Geophysical Union
	74, 368 (1993).

likely

  . In searching for Eocene abyssal CaCO 3 pulses we are hamstrung by the lack of very deep sites drilled during modern 'palaeoceanographic' expeditions. Nevertheless, a few rare abyssal sites provide preliminary indications that abyssal CaCO 3 preservation spikes may have occurred during Eocene hyperthermals. Early Eocene sediments recovered from sites on the Iberian margin (DSDP Site 398 and ODP Site 1068) and off Bermuda (DSDP Site 386)(paleodepths = ~4500 m) comprise upward-darkening sequences of claystone overlying nannofossil claystone or nannofossil chalk[START_REF] Tucholke | Initial Reports of the Deep Sea Drilling Project[END_REF][START_REF] Sibuet | Initial Reports of the Deep Sea Drilling Project[END_REF][START_REF] Whitmarsh | Proc. ODP, Init. Repts[END_REF] . The calcareous layers have frequently

	171.33 179.48	tie to tie to	43.02 54.98	43.68 54.98	48.456 49.908
	171.56 179.67	tie to tie to	43.19 55.22	43.82 55.22	48.478 49.923
	171.81 172.89 180.45 173.61 180.82	tie to tie to tie to tie to tie to	43.54 44.12 57.19 44.44 58.06	44.10 44.53 57.19 44.78 58.06	48.519 50.013 48.596 48.661 50.050
	173.91	tie to	44.77	45.06	48.722
	174.21	tie to	45.17	45.39	48.777
	174.36	tie to	45.40	45.59	48.809
	174.63	tie to	46.08	46.15	48.897
	174.96	tie to	46.72	46.72	48.979
	175.26	tie to	47.29	47.29	49.058
	175.35	tie to	47.47	47.47	49.076
	175.50	tie to	47.72	47.72	49.110
	175.68	tie to	48.17	48.17	49.177
	175.98	tie to	48.35	48.35	49.206
	176.07	tie to	48.47	48.47	49.221
	176.43	tie to	48.73	48.73	49.246
	176.74	tie to	49.05	49.07	49.283
	177.00	tie to	49.35	49.35	49.327
	177.27	tie to	49.67	49.67	49.389
	177.57	tie to	50.40	50.40	49.465
	177.88	tie to	50.92	50.92	49.526
	177.99	tie to	51.05	51.05	49.544
	178.29	tie to	51.24	51.24	49.575
	178.49	tie to	51.35	51.34	49.599
	178.71	tie to	51.47	51.46	49.617
	178.95	tie to	51.93	51.93	49.701
	179.40	tie to	52.69	52.69	49.747
	179.67	tie to	53.48	53.48	49.801
	180.00	tie to	54.03	54.03	49.841
	180.54	tie to	55.08	55.08	49.914
	180.66	tie to	55.31	55.31	49.929
	180.87	tie to	55.53	55.53	49.943
	181.20	tie to	55.78	55.78	49.954
	181.44	tie to	56.16	56.16	49.970
	181.62	tie to	56.59	56.59	49.988
	181.83	tie to	57.17	57.17	50.013
	182.19	tie to	58.06	58.06	50.050

been interpreted as turbidites, primarily because some have graded beds[START_REF] Mccave | Diagnosis of Turbidites at Sites 386 and 387 by Particle-Counter Size Analysis of the Silt (2-40 µm) Fraction[END_REF] . Indeed, erosive contacts of calcareous layers with underlying clay, occasionally with pebbles overlying the calcareous layer, are indicative of turbidites. Yet many of the CaCO 3 -rich layers at these sites have graded basal contacts with the underlying clay, raising the possibility that they represent pulses of in-situ, abyssal CaCO 3 sedimentation following a rapid reduction in the acidity of the abyss. But these abyssal sites typically have poor age control, partly because they generally lack the calcareous microfossils useful for biostratigraphic dating and partly because of incomplete sediment recovery associated with early drilling technology and the out-dated strategy of spot-coring. Despite these previous impediments, future detailed chronostratigraphic research should enable secure correlations between these abyssal sites and those (utilized here) at mid-depths in order to better understand the dynamics of Eocene oceanic carbon cycling.

Acknowledgements We thank M. Bolshaw for laboratory assistance and the Shipboard Party and crew of Ocean Drilling Program (ODP) Leg 207 for a successful drilling expedition. Discussions with H. Brinkhuis, G. Dickens, M. Huber, S. Kirtland, E. Rohling and J. Zachos were particularly helpful. This research used samples and data provided by the ODP. ODP (now IODP) is sponsored by the US National Science Foundation (NSF) and participating countries under the management of Joint Oceanographic Institutions (JOI), Inc. Financial support for this research was provided by a European Commission Marie Curie Outgoing International Fellowship (to P.F.S.), a Leverhulme Trust Fellowship (to P.F.S.), a Natural Environment Research Council UK ODP grant (to P.A.W. & P.F.S.), the DFG-Leibniz Center for Surface Process & Climate Studies at the University of Potsdam, and the Deutsche Forschungsgemeinschaft (DFG) (U.R. & T.W.).

Supplementary

 1 to 4Supplementary Tables 1 to 3 Supplementary Notes 1 to 2

Supplementary Discussion

Controls on stable isotope records from Demerara Rise

We interpret the rapid and large excursions to lower values in our benthic foraminifer  [START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] C record from Demerara Rise to be representative of 'global' trends in  [START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] C of Total Dissolved Inorganic Carbon (CO 2 ), as opposed to this site being at the boundary between two fluctuating water masses with contrasting  13 C signatures. All of our negative excursions in  13 C are coeval with globally widespread calcium carbonate (CaCO 3 ) dissolution events in the western tropical Atlantic, the southern Atlantic and the Pacific (Fig. 3), suggesting that the  13 C and dissolution anomalies represent injection (or, more accurately, redistribution) of isotopically light carbon into upper abyssal depths and shallower, and not regional water mass fluctuations.

The prominent and concurrent benthic foraminifer  18 O and  13 C excursions in our Demerara Rise data correlate with CaCO 3 dissolution horizons. Yet these isotope excursions are unlikely to be an artefact of foraminiferal diagenetic alteration for two reasons. First, if CaCO 3 dissolution (and recrystallisation of benthic foraminifera) was to occur within the sediment column under the influence of sedimentary pore waters (having a lower  13 C value than seawater, because of organic carbon [C org ] remineralisation), this would be expected to impart anomalously low  13 C values, but not lower  18 O, into recrystallised foraminiferal tests. Furthermore, our evidence for concurrent dissolution events in several different ocean basins (Fig. 3b to d) suggests that, if any post-mortem diagenetic alteration of Demerara Rise benthic foraminifera had occurred, it would have Supplementary Figure 1. Spectra of the magnetic susceptibility (MS) records used in the astronomical tuning process. a, Spectrum of MS data from Demerara Rise (ODP Site 1258) versus the paleomagnetic age model 42 for this site. Substantial power exists at the obliquity frequencies (41 and 54 kyr), in addition to precession (19, 21 and 23 kyr) and eccentricity (~100 kyr) frequencies. b, Cross-spectrum of our astronomically tuned MS time series versus ETP, created using the multi-taper method [START_REF] Ghil | Advanced spectral methods for climatic time series[END_REF] (and also using software from ref. [START_REF] Paillard | Macintosh program performs time-series analysis[END_REF] ). ETP represents a calculated mix of the main orbital parameters -eccentricity, obliquity (tilt) and climatic precession [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF] . MS data were used to create an astronomical age model by tuning clear, pronounced obliquity cycles in the data to calculated obliquity in the latest [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF] 1) from e, Demerara Rise (ODP Site 1258, tropical Atlantic), f, Shatsky Rise (ODP Site 1210, Pacific) and g, Walvis Ridge (ODP Site 1267, southern Atlantic). Age models for estimated % CaCO 3 records in f and g are derived by tuning clear, correlatable events in both records to the astronomically calibrated % CaCO 3 record in e (Demerara Rise, Site 1258). This tuning strategy was held as relaxed as possible, using a minimum of tie points. 'LAD' -Last Appearance Datum. Blue arrows mark our assumed 'zero-dissolution points' for each site, used in calculating '% CaCO 3 dissolution' (see Fig. 2 and Supplementary Discussion). Supplementary Figure 3. Cross-spectrum of the benthic foraminifer  13 C record from Fig. 1c versus ETP, created using the multi-taper method [START_REF] Ghil | Advanced spectral methods for climatic time series[END_REF] (and using software from ref. [START_REF] Paillard | Macintosh program performs time-series analysis[END_REF] ). ETP represents a calculated mix of the main orbital parameters -eccentricity, obliquity (tilt) and climatic precession [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF] . The 95 and 90% confidence intervals are shown for the  13 C spectrum. The  13 C spectrum displays power and is highly coherent (well above the 95% confidence level) with ETP at the 405 kyr frequency, despite our 2.4 Myrlong  13 C record only containing a maximum of six of these 'long' 405 kyr eccentricity cycles.

Supplementary Figure 4. Multi-species stable isotope arrays of the  13 C and  18 O of multiple species of planktic and benthic foraminifera from the early Middle Eocene (45 Ma), the late middle Eocene (39 Ma) and from Recent core-top sediments. Horizontal grey lines indicate the highest  13 C of inferred mixed layer dwellers (dashed lines) and the lowest  13 C of benthics (solid lines). Benthic equilibrium  13 C and  18 O values for Recent samples calculated from modern seawater  13 C 58 and temperature [START_REF]WOCE Data Products Committee, World Ocean Circulation Experiment Global Data, version 3.0[END_REF] datasets owing to absence of data from foraminiferal calcite. Note that, in comparison to Recent data, Eocene data show i) a steeper vertical gradient of  13 C of DIC versus temperature and ii) a greater total surface-to-seafloor  [START_REF] Stap | High-resolution deep-sea carbon and oxygen isotope records of Eocene Thermal Maximum 2 and H2[END_REF] C difference (grey vertical arrows). This larger Eocene surface-to-seafloor  13 C difference and steeper gradient of  13 C with depth is observed in typical 'frosty' (sensu ref. [START_REF] Sexton | Microstructural and geochemical perspectives on planktic foraminiferal preservation: "Glassy'' versus "Frosty[END_REF] ) foraminifera (black plot frames) as well as 'glassy' ones (red plot frames), demonstrating that this larger Eocene vertical  13 C differential is not a diagenetic artefact. Furthermore, most Recent core-top planktic foraminifera are far from glassy, also typically having a somewhat frosty appearance. Planktic foraminifera with a lower  13 C value than co-occurring benthics likely indicate species with a strong 'vital effect' offset or a habitat in a pronounced oxygen minimum in the thermocline or intermediate waters. a, DSDP Site 94, Caribbean [START_REF] Sexton | Microstructural and geochemical perspectives on planktic foraminiferal preservation: "Glassy'' versus "Frosty[END_REF] . b, DSDP Site 523, S. Atlantic [START_REF] Sexton | Microstructural and geochemical perspectives on planktic foraminiferal preservation: "Glassy'' versus "Frosty[END_REF] . c, ODP Site 865, Eq. Pacific [START_REF] Sexton | Microstructural and geochemical perspectives on planktic foraminiferal preservation: "Glassy'' versus "Frosty[END_REF] . d, Tanzania Drilling Project (TDP) Site 2, Tanzania [START_REF] Sexton | Microstructural and geochemical perspectives on planktic foraminiferal preservation: "Glassy'' versus "Frosty[END_REF] . e, ODP Site 1052B, NW. Atlantic [START_REF] Sexton | Palaeoecology of late middle Eocene planktic foraminifera and evolutionary implications[END_REF] . f, ODP Site 1052F, NW. Atlantic [START_REF] Sexton | Microstructural and geochemical perspectives on planktic foraminiferal preservation: "Glassy'' versus "Frosty[END_REF][START_REF] Sexton | Palaeoecology of late middle Eocene planktic foraminifera and evolutionary implications[END_REF] . g, ODP Site 865, Eq. Pacific [START_REF] Sexton | Microstructural and geochemical perspectives on planktic foraminiferal preservation: "Glassy'' versus "Frosty[END_REF] . h, Istra More 5 well, Adriatic Sea [START_REF] Sexton | Microstructural and geochemical perspectives on planktic foraminiferal preservation: "Glassy'' versus "Frosty[END_REF][START_REF] Sexton | Palaeoecology of late middle Eocene planktic foraminifera and evolutionary implications[END_REF] . i, core OC28, NW. Atlantic [START_REF] Erez | Comparison of isotopic composition of planktonic foraminifera in plankton tows, sediment traps, and sediments[END_REF] . j, DSDP Site 361, SW. Indian [START_REF] Shackleton | Oxygen and carbon isotope studies in Recent foraminifera from the southwest Indian Ocean[END_REF] . k, DSDP Site 366, SW. Indian [START_REF] Shackleton | Oxygen and carbon isotope studies in Recent foraminifera from the southwest Indian Ocean[END_REF]

Supplementary

Supplementary Note 1

Data compilation in Figure 1a from refs [START_REF] Zachos | An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics[END_REF][START_REF] Sexton | Testing the Cenozoic multisite composite δ18O and δ13C curves: New monospecific Eocene records from a single locality, Demerara Rise (Ocean Drilling Program Leg 207)[END_REF][START_REF] Edgar | No extreme bipolar glaciation during the main Eocene calcite compensation shift[END_REF][START_REF] Dutton | Insights from the Paleogene tropical Pacific: Foraminiferal stable isotope and elemental results from Site 1209, Shatsky Rise[END_REF][START_REF] Norris | Mid-Eocene deep water, the Late Palaeocene Thermal Maximum and continental slope mass wasting during the Cretaceous-Palaeogene impact[END_REF] .

Supplementary Note 2