Model calculation

We used a coupled atmosphere–ocean global climate model developed at the Meteorological Research Institute, MRI-CGCM332. Detailed descriptions and evaluations of the model calculations are provided in the Supplementary Information of Kaiho et al.1. Following this method, we performed two 10-year experiments with the BC ejection due to the Chicxulub asteroid impact (using the 20-Tg and 200-Tg BC cases), based on pre-industrial climate conditions. We also used model calculation results for the 500-Tg, 1500-Tg, and 2600-Tg BC cases and a 30-year control experiment with no BC ejection1. In these cases, BC was ejected into one column of the model grid box at 21°N, 90°W (Yucatan Peninsula) in the current geographical setting using the vertical distribution obtained by Saito et al.33. We also performed an additional 10-year experiment for the high-latitude 200-Tg BC ejection case, where BC was ejected at the late-Eocene Popigai crater (71°N, 111°E); all other conditions were the same as those for the Chicxulub cases. In these calculations, we assumed spherical particles for atmospheric aerosols and their optical properties in the solar and terrestrial spectral range were calculated on the basis of microphysical data such as the size distribution and spectra refractive index using the software package Optical Properties of Aerosols and Clouds (OPAC)34. We evaluated the climate response due to BC ejection by subtracting the monthly climatology (30-year mean) of the control experiment from the monthly mean results of the other experiments.

The particle size distributions could affect the atmospheric lifetime of BC and its radiative effects. Evaluations of the climate effects caused by the size distributions of BC particles for the Chicxulub case are provided in the Supplementary Information of Kaiho et al.1. They conducted a 10-year sensitivity experiment for the 1500-Tg BC injection with a larger BC size distribution (i.e., mode radius of 43.7 nm and geometric standard deviation of 1.64 for the lognormal number size distribution), which was observed by recent aircraft measurements, and values were larger than the OPAC values (i.e., the mode radius of 11.8 nm and the geometric standard deviation of 2.00). Compared with the 1500-Tg BC case, this experiment for a larger BC size distribution led to less BC loading in the atmosphere, resulting in a smaller cooling effect amplitude (up to 1.5 °C difference in the monthly global mean surface air temperature; Supplemental Fig. 1). The maximum temperature difference due to the size distributions will be less than 1.5 °C for <500 Tg BC cases, because the amplitudes of the cooling effect of <500-Tg BC cases were smaller than those of the 1500-Tg BC case (Fig. 1). These results indicate that the temperature difference (<1.5 °C) caused by the different size distributions will be less than the maximum temperature anomalies caused by the different amounts of BC (i.e., 3 °C, 6 °C, and 10 °C for the 200, 500, and 1500-Tg BC cases, respectively). The climate model calculation assumed spherical particles for all aerosol species, although soot particles generally consist of aggregated carbon spherules. Numerical studies have shown that the aerosol optical properties (e.g., absorption) at visible wavelengths were enhanced by aggregation by no more than about 30%35. They have also shown that the relative difference in direct radiative forcing of soot particles between uncoated spheres and these aggregates was about 3% (global annual mean at the top of the atmosphere) in the present-day atmosphere36. These results suggest that climate changes caused by BC injection would be more greatly influenced by the amount of BC than the particle size and shape for the Chicxulub-scale asteroid impact.

Hydrocarbon (organic carbon) content

The average weight of hydrocarbons in sedimentary rocks is 0.5%, based on the average organic carbon content (%) of shales, carbonates, and sandstones and their relative proportions37, with lower content in pelagic oceans (Table 1)38. The organic carbon content (%) in continental, coastal, and upwelling areas at the end of the Cretaceous was estimated at an average of 0.5 wt% and that in the pelagic oceans was estimated at an average of 0.1 wt%, based on the organic carbon content (%) of surface marine sediments38 and pre-Cenozoic sedimentary rocks39,40,41,42.

Thickness of sedimentary rocks

The total thickness of sedimentary rocks in the present-day crust43 was revised by removing thick Cenozoic sedimentary rocks. Exceptionally thick Cenozoic sediments, such as those found in India due to the Himalayas, were removed and the white and olive areas were added in paleoceans located between the North and South American continents and between Asia and Africa–India at the end of the Cretaceous (Fig. 4). We also used the thickness ratio between the pre-Cenozoic and Cenozoic, or the thickness of the Cenozoic, in selected hydrocarbon-rich areas (orange and magenta areas, Fig. 4; Supplemental Table 2), to obtain the distribution of the total thickness of sedimentary rocks at the end of the Cretaceous. We divided the globe into four types of areas based on the thickness of sedimentary rocks: low-hydrocarbon areas (<0.5 km thick, mostly 0.1–0.2 km; approximately pelagic), medium-hydrocarbon areas (0.5–2 km thick; approximately hemipelagic), high-hydrocarbon areas (2–5 km thick), and very high-hydrocarbon areas (5–20 km thick); we then divided these types into oceanic and continental (composed of continental and shelf rocks) crusts, resulting in 12 bins. The areas (%) of the 12 regions were calculated using ArcGIS10.3 (ESRI, Redlands, CA, USA; Supplemental Table 3). All values are approximate; estimated values are sufficient to obtain approximate areas and the probabilities of mass extinctions.

Amount of stratospheric soot

Impact velocities were constant in this calculation, because we assumed that the asteroid impact would be the same at random locations on the Earth’s surface. Temperature in the bulk impact-induced vapor is similar between 30° and 90° impact angles, but pressure depends strongly on the impact angles (higher angles correspond to higher pressure) in 10-km asteroid impact cases44. In the impact angle range, pressure rapidly decreases from > ~30 GPa to <~20 GPa at 5–10 km distance from the impact center on rocks44. An experimental study shows that soot-like materials were formed at 20–30 GPa and effect of pressure for soot formation is small at <20 GPa45,46,47. Therefore, all the impact-angle cases cause a change from soot-formation states to no soot-formation states at the 5–10 km distance. The volume of sedimentary rocks ejected into the stratosphere is similar in 15–90° impact angle cases (the maximum volume [30° impact angle for calcite] is 1.7 times of minimum volume [15° impact angle for calcite])44. There were no significant latitudinal differences in rates among organic carbon-rich areas (Supplemental Table 3). The volume of granite (crust) and mantle melt was higher at higher-impact angles, but granite and mantle rock are not a source of soot33,44. Overall, impact angles >30° did not likely to change significantly the probability of mass extinction.

An asteroid approximately 9 km in diameter ejects target rocks, including sedimentary rocks, crust, and mantle (in the case of oceanic crust impact), within a transient crater, i.e., the hole made during the initial impact, which has an estimated diameter of 80–110 km (the final crater size is 170 km)48. Temperatures inside this transient crater would have reached near the ignition point of hydrocarbon compounds (~600 K) within a diameter of about 70 km13,44. Therefore, all sedimentary rocks (usually < 5 km in thickness) and part of the continental crust would have been ejected in >15° oblique impacts on continents, and all sedimentary rocks (usually <0.5 km in thickness), oceanic crust (~5 km in thickness), and part of the mantle would have been ejected in >15° oblique impacts on oceans44. There are few hydrocarbons in the crust and mantle; therefore, we used only sedimentary rocks to estimate the amount of hydrocarbon. The product of the burned weight and averaged hydrocarbon content provides the amount of hydrocarbon ejected by the impact of a 9-km asteroid on the Earth (Table 1). The amount of stratospheric soot generally depends on the soot emission factor, the fraction of soot injection to the stratosphere (0.23 in the 90° impact angle case)1, and the surviving soot fraction remaining in the stratosphere due to the short-term rapid removal after the impact (e.g., sedimentation due to coagulation with large particles ejected by the impact). The efficiency of soot formation from hydrocarbon may be also dependent on the chemical composition and the redox conditions in the bulk impact-induced vapor. These factors are included in the soot emission factor (ranging 3–10%)13,49 and we used the average value (6.5%) in this study. The overall surviving fraction in ejected soot that could be spread globally in the stratosphere is assumed to be 4.2%, to fit the 1500-Tg BC K–Pg case (350 Tg BC in the global stratosphere), which may explain the extinction of dinosaurs and ammonites and the survival of crocodiles1. The surviving fraction of the 350-Tg BC case was applied to all BC cases and the amounts of surviving stratospheric soot after the impact were estimated for every case (Table 1). The effect of stratospheric soot on the global mean surface air temperature anomaly was estimated using the K curve shown in Fig. 5. The temperature reductions might be underestimated for <350-Tg BC cases and overestimated for >350-Tg BC cases, because the surviving fraction of BC would decrease among the cases with more BC, probably due to the greater likelihood of particle-size growth by coagulation.

Amount of stratospheric sulfate

The main source of sulfate aerosols is evaporites [anhydrite (CaSO 4 ) and gypsum (CaSO 4 2H 2 O)] in sedimentary rocks deposited in a closed shallow sea on continental crust (the rate of sulfur/rocks is calculated as 13,000 ppm S in high-concentration areas, Table 2). The amount of sulfur from other sedimentary rocks is minor compared to that from evaporite-rich sedimentary rocks, so sulfur content was calculated as the average sulfur content in sedimentary rocks: 1500 ppm S (Table 2). The main source of sulfate aerosols in an oceanic crust impact is the mantle beneath the oceanic crust, because the volume of mantle materials ejected following an approximately 9-km asteroid impact is very large compared to oceanic crust and sedimentary rocks, calculated as having a 30-km diameter of melting44, 15-km thickness44, and 150–250 ppm sulfur content50,51 (Table 2). Recent impact experiments have shown that an impact produces a high sulfur trioxide (SO 3 )/sulfur dioxide (SO 2 ) ratio, approximately 30 for asteroids and Jupiter family comets (3% SO 2 ), whose velocity is approximately 20 km/s12. According to the results of those studies, SO 3 cannot form global stratospheric sulfate aerosols because of the rapid formation of sulfuric acid aerosols, resulting in efficient scavenging of sulfuric acid aerosols (1 μm in size) due to coagulation with larger falling silicate dust particles (100 μm in size)12. These phenomena would occur near the impact location within a few days. Remaining SO 2 in the stratosphere, corresponding to 3% of ejected sulfur, would gradually be converted into sulfate aerosols and would be spread globally (Table 2). We used two cases to estimate the amount of stratospheric sulfate (SO 4 ) that survived after an impact. Following Ohno et al.12, the amount of surviving SO 4 in case 1 was estimated to be the product of the weights of melted sulfur, the sulfur emission factor (0.4: (2000-1200)/2000 [ppm])52, the sulfur surviving fraction in the stratosphere due to short-term rapid removal after impact (0.03)12, the fraction of injection to the stratosphere (0.23), and the mass ratio of SO 4 /S (3), as summarized in Table 2. Case 2 assumed that all sulfur was ejected as sulfate and that the surviving rate of sulfate was the same as that of soot. The amount of sulfate surviving in the stratosphere in case 2 was estimated to be the product of the weights of melted sulfur, the sulfur emission factor (0.4), the surviving rate (0.042), and the mass ratio of SO 4 /S (3).

Reason of survival of soot

In case 1 we assumed the removal of all SO 4 produced from SO 3 from the atmosphere after the impact and the survival of a portion of soot. SO 3 and SO 2 are released from rocks evaporated or melted by an impact that covers a 30-km-diameter area. Most silicate particles are sourced from silicate vapor from within the same impact area11. In contrast, soot is mainly formed in 70-km-diameter area. The difference of source areas could cause that the sulfate particles were efficiently scavenged from the atmosphere by large falling silicate particles in their path; however, soot particles were less scavenged resulting in their survival.

Temperature anomaly caused by sulfate aerosols