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❊♥③♦✲❊ ✴ ❈❡❧❧♦

❆❞❛♣t✐✈❡ ▼❡s❤ ❘❡✜♥❡♠❡♥t ❆str♦♣❤②s✐❝s ✉s✐♥❣ ❈❤❛r♠✰✰ ❏❛♠❡s ❇♦r❞♥❡r✱ ▼✐❝❤❛❡❧ ▲✳ ◆♦r♠❛♥

❯♥✐✈❡rs✐t② ♦❢ ❈❛❧✐❢♦r♥✐❛✱ ❙❛♥ ❉✐❡❣♦ ❙❛♥ ❉✐❡❣♦ ❙✉♣❡r❝♦♠♣✉t❡r ❈❡♥t❡r

✶✼t❤ ❆♥♥✉❛❧ ❲♦r❦s❤♦♣ ♦♥ ❈❤❛r♠✰✰ ❛♥❞ ■ts ❆♣♣❧✐❝❛t✐♦♥s ✷✵✶✾✲✵✺✲✵✶✴✵✷

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❙❝✐❡♥t✐✜❝ q✉❡st✐♦♥s ✐♥ ❛str♦♣❤②s✐❝s ❛♥❞ ❝♦s♠♦❧♦❣②

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u m e s , g a l a x y c l u s t e r s [ 7 5 M p c ] ❬ ❏♦❤♥ ❲✐s❡ ❪ ❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❚❤❡ ❊◆❩❖ ▼P■✲♣❛r❛❧❧❡❧ ❛str♦♣❤②s✐❝s ❛♣♣❧✐❝❛t✐♦♥

❆♣♣❧✐❝❛❜❧❡ t♦ ❛ ✇✐❞❡ r❛♥❣❡ ♦❢ ❛str♦♣❤②s✐❝❛❧ ❛♥❞ ❝♦s♠♦❧♦❣✐❝❛❧ ♣r♦❜❧❡♠s ❙❝✐❡♥t✐✜❝ ◗✉❡st✐♦♥s✿ t♦♣✐❝s ♦❢ ✐♥t❡r❡st

❼ ❙t❛r ❢♦r♠❛t✐♦♥ ❼ ▼♦❧❡❝✉❧❛r ❝❧♦✉❞ t✉r❜✉❧❡♥❝❡ ❼ ■♥t❡rst❡❧❧❛r ♠❡❞✐✉♠ ❼ ●❛❧❛①② ❢♦r♠❛t✐♦♥ ❼ ■♥t❡r❣❛❧❛❝t✐❝ ♠❡❞✐✉♠ ❼ ●❛❧❛①② ❝❧✉st❡rs ❼ ❈♦s♠✐❝ r❡✐♦♥✐③❛t✐♦♥ . . .

P❤②s✐❝s ❊q✉❛t✐♦♥s✿ ♠❛t❤❡♠❛t✐❝❛❧ ♠♦❞❡❧s

❼ ❍②❞r♦❞②♥❛♠✐❝s ✭❊✉❧❡r ❡q✉❛t✐♦♥s✮ ❼ ●r❛✈✐t② ✭∇✷Φ = ✹πGρ✮ ❼ ❈❤❡♠✐str②✴❝♦♦❧✐♥❣ ❼ ▼❛❣♥❡t✐s♠ ❼ ❘❛❞✐❛t✐♦♥ tr❛♥s♣♦rt . . .

◆✉♠❡r✐❝❛❧ ▼❡t❤♦❞s✿ ❛♣♣r♦①✐♠❛t❡ ❛♥❞ s♦❧✈❡

❼ PP▼✱ ❼ ❩❊❯❙✱ ❼ ▼❯❙❈▲ ❼ ❋❋❚ ❼ ♠✉❧t✐❣r✐❞ ❼ ●❛❞❣❡t ❝♦♦❧✐♥❣ ❼ ❈❧♦✉❞② ❝♦♦❧✐♥❣ ❼

• r❛❝❦❧❡ ❼ ❉❡❞♥❡r ▼❍❉ ❼ ▼❍❉✲❈❚ ❼ ■♠♣❧✐❝✐t ❋▲❉ ❼ ▼♦r❛② . . .

❉❛t❛ ❙tr✉❝t✉r❡s✿ ❝♦♠♣✉t❡r r❡♣r❡s❡♥t❛t✐♦♥

❼ ❆❞❛♣t✐✈❡ ▼❡s❤ ❘❡✜♥❡♠❡♥t ✭❙❆▼❘✮ ❼ ❊✉❧❡r✐❛♥ ✜❡❧❞s ❼ ▲❛❣r❛♥❣✐❛♥ ♣❛rt✐❝❧❡s . . .

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❚❤❡ ❊◆❩❖ ▼P■✲♣❛r❛❧❧❡❧ ❛str♦♣❤②s✐❝s ❛♣♣❧✐❝❛t✐♦♥

❙✉♣♣♦rts ♠❛♥② r❡❧❛t❡❞ ♣❤②s✐❝s ❝❛♣❛❜✐❧✐t✐❡s ❙❝✐❡♥t✐✜❝ ◗✉❡st✐♦♥s✿ t♦♣✐❝s ♦❢ ✐♥t❡r❡st

❼ ❙t❛r ❢♦r♠❛t✐♦♥ ❼ ▼♦❧❡❝✉❧❛r ❝❧♦✉❞ t✉r❜✉❧❡♥❝❡ ❼ ■♥t❡rst❡❧❧❛r ♠❡❞✐✉♠ ❼ ●❛❧❛①② ❢♦r♠❛t✐♦♥ ❼ ■♥t❡r❣❛❧❛❝t✐❝ ♠❡❞✐✉♠ ❼ ●❛❧❛①② ❝❧✉st❡rs ❼ ❈♦s♠✐❝ r❡✐♦♥✐③❛t✐♦♥ . . .

P❤②s✐❝s ❊q✉❛t✐♦♥s✿ ♠❛t❤❡♠❛t✐❝❛❧ ♠♦❞❡❧s

❼ ❍②❞r♦❞②♥❛♠✐❝s ✭❊✉❧❡r ❡q✉❛t✐♦♥s✮ ❼ ●r❛✈✐t② ✭∇✷Φ = ✹πGρ✮ ❼ ❈❤❡♠✐str②✴❝♦♦❧✐♥❣ ❼ ▼❛❣♥❡t✐s♠ ❼ ❘❛❞✐❛t✐♦♥ tr❛♥s♣♦rt . . .

◆✉♠❡r✐❝❛❧ ▼❡t❤♦❞s✿ ❛♣♣r♦①✐♠❛t❡ ❛♥❞ s♦❧✈❡

❼ PP▼✱ ❼ ❩❊❯❙✱ ❼ ▼❯❙❈▲ ❼ ❋❋❚ ❼ ♠✉❧t✐❣r✐❞ ❼ ●❛❞❣❡t ❝♦♦❧✐♥❣ ❼ ❈❧♦✉❞② ❝♦♦❧✐♥❣ ❼

• r❛❝❦❧❡ ❼ ❉❡❞♥❡r ▼❍❉ ❼ ▼❍❉✲❈❚ ❼ ■♠♣❧✐❝✐t ❋▲❉ ❼ ▼♦r❛② . . .

❉❛t❛ ❙tr✉❝t✉r❡s✿ ❝♦♠♣✉t❡r r❡♣r❡s❡♥t❛t✐♦♥

❼ ❆❞❛♣t✐✈❡ ▼❡s❤ ❘❡✜♥❡♠❡♥t ✭❙❆▼❘✮ ❼ ❊✉❧❡r✐❛♥ ✜❡❧❞s ❼ ▲❛❣r❛♥❣✐❛♥ ♣❛rt✐❝❧❡s . . .

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❚❤❡ ❊◆❩❖ ▼P■✲♣❛r❛❧❧❡❧ ❛str♦♣❤②s✐❝s ❛♣♣❧✐❝❛t✐♦♥

■♠♣❧❡♠❡♥ts ❛ ✈❛r✐❡t② ♦❢ s♦♣❤✐st✐❝❛t❡❞ ♥✉♠❡r✐❝❛❧ ♠❡t❤♦❞s ❙❝✐❡♥t✐✜❝ ◗✉❡st✐♦♥s✿ t♦♣✐❝s ♦❢ ✐♥t❡r❡st

❼ ❙t❛r ❢♦r♠❛t✐♦♥ ❼ ▼♦❧❡❝✉❧❛r ❝❧♦✉❞ t✉r❜✉❧❡♥❝❡ ❼ ■♥t❡rst❡❧❧❛r ♠❡❞✐✉♠ ❼ ●❛❧❛①② ❢♦r♠❛t✐♦♥ ❼ ■♥t❡r❣❛❧❛❝t✐❝ ♠❡❞✐✉♠ ❼ ●❛❧❛①② ❝❧✉st❡rs ❼ ❈♦s♠✐❝ r❡✐♦♥✐③❛t✐♦♥ . . .

P❤②s✐❝s ❊q✉❛t✐♦♥s✿ ♠❛t❤❡♠❛t✐❝❛❧ ♠♦❞❡❧s

❼ ❍②❞r♦❞②♥❛♠✐❝s ✭❊✉❧❡r ❡q✉❛t✐♦♥s✮ ❼ ●r❛✈✐t② ✭∇✷Φ = ✹πGρ✮ ❼ ❈❤❡♠✐str②✴❝♦♦❧✐♥❣ ❼ ▼❛❣♥❡t✐s♠ ❼ ❘❛❞✐❛t✐♦♥ tr❛♥s♣♦rt . . .

◆✉♠❡r✐❝❛❧ ▼❡t❤♦❞s✿ ❛♣♣r♦①✐♠❛t❡ ❛♥❞ s♦❧✈❡

❼ PP▼✱ ❼ ❩❊❯❙✱ ❼ ▼❯❙❈▲ ❼ ❋❋❚ ❼ ♠✉❧t✐❣r✐❞ ❼ ●❛❞❣❡t ❝♦♦❧✐♥❣ ❼ ❈❧♦✉❞② ❝♦♦❧✐♥❣ ❼

• r❛❝❦❧❡ ❼ ❉❡❞♥❡r ▼❍❉ ❼ ▼❍❉✲❈❚ ❼ ■♠♣❧✐❝✐t ❋▲❉ ❼ ▼♦r❛② . . .

❉❛t❛ ❙tr✉❝t✉r❡s✿ ❝♦♠♣✉t❡r r❡♣r❡s❡♥t❛t✐♦♥

❼ ❆❞❛♣t✐✈❡ ▼❡s❤ ❘❡✜♥❡♠❡♥t ✭❙❆▼❘✮ ❼ ❊✉❧❡r✐❛♥ ✜❡❧❞s ❼ ▲❛❣r❛♥❣✐❛♥ ♣❛rt✐❝❧❡s . . .

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❚❤❡ ❊◆❩❖ ▼P■✲♣❛r❛❧❧❡❧ ❛str♦♣❤②s✐❝s ❛♣♣❧✐❝❛t✐♦♥

❊♥❛❜❧❡❞ ❜② ❛❞❛♣t✐✈❡ ♠❡s❤ r❡✜♥❡♠❡♥t ✇✐t❤ ♣❛rt✐❝❧❡s ❛♥❞ ✜❡❧❞s ❙❝✐❡♥t✐✜❝ ◗✉❡st✐♦♥s✿ t♦♣✐❝s ♦❢ ✐♥t❡r❡st

❼ ❙t❛r ❢♦r♠❛t✐♦♥ ❼ ▼♦❧❡❝✉❧❛r ❝❧♦✉❞ t✉r❜✉❧❡♥❝❡ ❼ ■♥t❡rst❡❧❧❛r ♠❡❞✐✉♠ ❼ ●❛❧❛①② ❢♦r♠❛t✐♦♥ ❼ ■♥t❡r❣❛❧❛❝t✐❝ ♠❡❞✐✉♠ ❼ ●❛❧❛①② ❝❧✉st❡rs ❼ ❈♦s♠✐❝ r❡✐♦♥✐③❛t✐♦♥ . . .

P❤②s✐❝s ❊q✉❛t✐♦♥s✿ ♠❛t❤❡♠❛t✐❝❛❧ ♠♦❞❡❧s

❼ ❍②❞r♦❞②♥❛♠✐❝s ✭❊✉❧❡r ❡q✉❛t✐♦♥s✮ ❼ ●r❛✈✐t② ✭∇✷Φ = ✹πGρ✮ ❼ ❈❤❡♠✐str②✴❝♦♦❧✐♥❣ ❼ ▼❛❣♥❡t✐s♠ ❼ ❘❛❞✐❛t✐♦♥ tr❛♥s♣♦rt . . .

◆✉♠❡r✐❝❛❧ ▼❡t❤♦❞s✿ ❛♣♣r♦①✐♠❛t❡ ❛♥❞ s♦❧✈❡

❼ PP▼✱ ❼ ❩❊❯❙✱ ❼ ▼❯❙❈▲ ❼ ❋❋❚ ❼ ♠✉❧t✐❣r✐❞ ❼ ●❛❞❣❡t ❝♦♦❧✐♥❣ ❼ ❈❧♦✉❞② ❝♦♦❧✐♥❣ ❼

• r❛❝❦❧❡ ❼ ❉❡❞♥❡r ▼❍❉ ❼ ▼❍❉✲❈❚ ❼ ■♠♣❧✐❝✐t ❋▲❉ ❼ ▼♦r❛② . . .

❉❛t❛ ❙tr✉❝t✉r❡s✿ ❝♦♠♣✉t❡r r❡♣r❡s❡♥t❛t✐♦♥

❼ ❆❞❛♣t✐✈❡ ▼❡s❤ ❘❡✜♥❡♠❡♥t ✭❙❆▼❘✮ ❼ ❊✉❧❡r✐❛♥ ✜❡❧❞s ❼ ▲❛❣r❛♥❣✐❛♥ ♣❛rt✐❝❧❡s . . .

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❚❤❡ ❊◆❩❖ ▼P■✲♣❛r❛❧❧❡❧ ❛str♦♣❤②s✐❝s ❛♣♣❧✐❝❛t✐♦♥

❆❧t❤♦✉❣❤ ♣♦✇❡r❢✉❧✱ ❊◆❩❖✬s ♣❛r❛❧❧❡❧ s❝❛❧✐♥❣ ✐s ❧✐♠✐t❡❞ ❍P❈ ❛❞✈❛♥❝❡s ❛✛❡❝t s♦❢t✇❛r❡ r❡q✉✐r❡♠❡♥ts

❊◆❩❖ ✇❛s ❞❡✈❡❧♦♣❡❞ st❛rt✐♥❣ ✐♥ ✶✾✾✹

• r❡❣ ❇r②❛♥✱ ▼✐❝❤❛❡❧ ◆♦r♠❛♥

✏♠❛ss✐✈❡ ♣❛r❛❧❧❡❧✐s♠✑ ♠❡❛♥t P ≈ ✶✵✸ P ≈ ✶✵✼ t♦❞❛②

❆✛❡❝ts ❞✐✛❡r❡♥t ♣❛rts ♦❢ ❊◆❩❖ ❞✐✛❡r❡♥t❧②

♣❤②s✐❝s r❡q✉✐r❡♠❡♥ts ✉♥❝❤❛♥❣❡❞ ♥✉♠❡r✐❝❛❧ ♠❡t❤♦❞s ♠♦st❧② ✈✐❛❜❧❡ ❞❛t❛ str✉❝t✉r❡s ❧✐♠✐t ❊◆❩❖✬s s❝❛❧❛❜✐❧✐t②

▼♦t✐✈❛t❡❞ ❆▼❘ ❞❛t❛ str✉❝t✉r❡ r❡❞❡s✐❣♥

❊♥③♦✲P✿ ✏P❡t❛s❝❛❧❡✑ ❜r❛♥❝❤ ♦❢ ❊◆❩❖ ❦❡❡♣ ❊◆❩❖✬s ♣❤②s✐❝s ❛♥❞ ♠❛♥② ♠❡t❤♦❞s ❈❡❧❧♦ s❝❛❧❛❜❧❡ ❆▼❘ ❢r❛♠❡✇♦r❦

❬ ❙❛♠ ❙❦✐❧❧♠❛♥✱ ▼❛tt ❚✉r❦ ❪ ❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❚❤❡ ❊◆❩❖ ▼P■✲♣❛r❛❧❧❡❧ ❛str♦♣❤②s✐❝s ❛♣♣❧✐❝❛t✐♦♥

❆❧t❤♦✉❣❤ ♣♦✇❡r❢✉❧✱ ❊◆❩❖✬s ♣❛r❛❧❧❡❧ s❝❛❧✐♥❣ ✐s ❧✐♠✐t❡❞ ❍P❈ ❛❞✈❛♥❝❡s ❛✛❡❝t s♦❢t✇❛r❡ r❡q✉✐r❡♠❡♥ts

❊◆❩❖ ✇❛s ❞❡✈❡❧♦♣❡❞ st❛rt✐♥❣ ✐♥ ✶✾✾✹

• r❡❣ ❇r②❛♥✱ ▼✐❝❤❛❡❧ ◆♦r♠❛♥

✏♠❛ss✐✈❡ ♣❛r❛❧❧❡❧✐s♠✑ ♠❡❛♥t P ≈ ✶✵✸ P ≈ ✶✵✼ t♦❞❛②

❆✛❡❝ts ❞✐✛❡r❡♥t ♣❛rts ♦❢ ❊◆❩❖ ❞✐✛❡r❡♥t❧②

♣❤②s✐❝s r❡q✉✐r❡♠❡♥ts ✉♥❝❤❛♥❣❡❞ ♥✉♠❡r✐❝❛❧ ♠❡t❤♦❞s ♠♦st❧② ✈✐❛❜❧❡ ❞❛t❛ str✉❝t✉r❡s ❧✐♠✐t ❊◆❩❖✬s s❝❛❧❛❜✐❧✐t②

▼♦t✐✈❛t❡❞ ❆▼❘ ❞❛t❛ str✉❝t✉r❡ r❡❞❡s✐❣♥

❊♥③♦✲P✿ ✏P❡t❛s❝❛❧❡✑ ❜r❛♥❝❤ ♦❢ ❊◆❩❖ ❦❡❡♣ ❊◆❩❖✬s ♣❤②s✐❝s ❛♥❞ ♠❛♥② ♠❡t❤♦❞s ❈❡❧❧♦ s❝❛❧❛❜❧❡ ❆▼❘ ❢r❛♠❡✇♦r❦

❬ ❙❛♠ ❙❦✐❧❧♠❛♥✱ ▼❛tt ❚✉r❦ ❪ ❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❚❤❡ ❊◆❩❖ ▼P■✲♣❛r❛❧❧❡❧ ❛str♦♣❤②s✐❝s ❛♣♣❧✐❝❛t✐♦♥

❆❧t❤♦✉❣❤ ♣♦✇❡r❢✉❧✱ ❊◆❩❖✬s ♣❛r❛❧❧❡❧ s❝❛❧✐♥❣ ✐s ❧✐♠✐t❡❞ ❍P❈ ❛❞✈❛♥❝❡s ❛✛❡❝t s♦❢t✇❛r❡ r❡q✉✐r❡♠❡♥ts

❊◆❩❖ ✇❛s ❞❡✈❡❧♦♣❡❞ st❛rt✐♥❣ ✐♥ ✶✾✾✹

• r❡❣ ❇r②❛♥✱ ▼✐❝❤❛❡❧ ◆♦r♠❛♥

✏♠❛ss✐✈❡ ♣❛r❛❧❧❡❧✐s♠✑ ♠❡❛♥t P ≈ ✶✵✸ P ≈ ✶✵✼ t♦❞❛②

❆✛❡❝ts ❞✐✛❡r❡♥t ♣❛rts ♦❢ ❊◆❩❖ ❞✐✛❡r❡♥t❧②

♣❤②s✐❝s r❡q✉✐r❡♠❡♥ts ✉♥❝❤❛♥❣❡❞ ♥✉♠❡r✐❝❛❧ ♠❡t❤♦❞s ♠♦st❧② ✈✐❛❜❧❡ ❞❛t❛ str✉❝t✉r❡s ❧✐♠✐t ❊◆❩❖✬s s❝❛❧❛❜✐❧✐t②

▼♦t✐✈❛t❡❞ ❆▼❘ ❞❛t❛ str✉❝t✉r❡ r❡❞❡s✐❣♥

❊♥③♦✲P✿ ✏P❡t❛s❝❛❧❡✑ ❜r❛♥❝❤ ♦❢ ❊◆❩❖ ❦❡❡♣ ❊◆❩❖✬s ♣❤②s✐❝s ❛♥❞ ♠❛♥② ♠❡t❤♦❞s ❈❡❧❧♦ s❝❛❧❛❜❧❡ ❆▼❘ ❢r❛♠❡✇♦r❦

❬ ❙❛♠ ❙❦✐❧❧♠❛♥✱ ▼❛tt ❚✉r❦ ❪ ❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❈❡❧❧♦ s❝❛❧❛❜❧❡ ❛❞❛♣t✐✈❡ ♠❡s❤ r❡✜♥❡♠❡♥t

❑❡② ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ ❊◆❩❖ ❛♥❞ ❊♥③♦✲P

❊♥③♦✲P✴❈❡❧❧♦ ❛rr❛② ♦❢ ♦❝tr❡❡s ❆▼❘ ❈❤❛r♠✰✰ ♣❛r❛❧❧❡❧✐③❛t✐♦♥ r❡✉s❛❜❧❡ ❆▼❘ ❢r❛♠❡✇♦r❦ ❊◆❩❖ str✉❝t✉r❡❞ ❆▼❘ ▼P■✰❖♣❡♥▼P ♣❛r❛❧❧❡❧✐③❛t✐♦♥ ♥♦♥✲r❡✉s❛❜❧❡ ❆▼❘ ❞❛t❛ str✉❝t✉r❡

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❈❡❧❧♦ s❝❛❧❛❜❧❡ ❛❞❛♣t✐✈❡ ♠❡s❤ r❡✜♥❡♠❡♥t

❑❡② ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ ❊◆❩❖ ❛♥❞ ❊♥③♦✲P

❊♥③♦✲P✴❈❡❧❧♦ ❛rr❛② ♦❢ ♦❝tr❡❡s ❆▼❘ ❈❤❛r♠✰✰ ♣❛r❛❧❧❡❧✐③❛t✐♦♥ r❡✉s❛❜❧❡ ❆▼❘ ❢r❛♠❡✇♦r❦ ❊◆❩❖ str✉❝t✉r❡❞ ❆▼❘ ▼P■✰❖♣❡♥▼P ♣❛r❛❧❧❡❧✐③❛t✐♦♥ ♥♦♥✲r❡✉s❛❜❧❡ ❆▼❘ ❞❛t❛ str✉❝t✉r❡

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❈❡❧❧♦ s❝❛❧❛❜❧❡ ❛❞❛♣t✐✈❡ ♠❡s❤ r❡✜♥❡♠❡♥t

❑❡② ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ ❊◆❩❖ ❛♥❞ ❊♥③♦✲P

❊♥③♦✲P✴❈❡❧❧♦ ❛rr❛② ♦❢ ♦❝tr❡❡s ❆▼❘ ❈❤❛r♠✰✰ ♣❛r❛❧❧❡❧✐③❛t✐♦♥ r❡✉s❛❜❧❡ ❆▼❘ ❢r❛♠❡✇♦r❦ ❊◆❩❖ str✉❝t✉r❡❞ ❆▼❘ ▼P■✰❖♣❡♥▼P ♣❛r❛❧❧❡❧✐③❛t✐♦♥ ♥♦♥✲r❡✉s❛❜❧❡ ❆▼❘ ❞❛t❛ str✉❝t✉r❡

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❊♥③♦✲P✴❈❡❧❧♦✴❈❤❛r♠✰✰ ❝❧❛ss ♦r❣❛♥✐③❛t✐♦♥

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❈❡❧❧♦ ❞✐str✐❜✉t❡❞ ❛❞❛♣t✐✈❡ ♠❡s❤ r❡✜♥❡♠❡♥t

❍♦✇ ✜❡❧❞ ❞❛t❛ ❛r❡ ❝♦♠♠✉♥✐❝❛t❡❞ ❜❡t✇❡❡♥ ❜❧♦❝❦s

❉❛t❛✲❞r✐✈❡♥ ❡①❡❝✉t✐♦♥

s❡♥❞ ❋✐❡❧❞ ❢❛❝❡ ❞❛t❛ ✇❤❡♥ ❛✈❛✐❧❛❜❧❡ ✐♥❞❡①❡❞ ✉s✐♥❣ ❜✐t✲❝♦❞✐♥❣ ✐♥ ❤✐❡r❛r❝❤② ❝♦✉♥t ❢❛❝❡ ❞❛t❛ ♠❡ss❛❣❡s r❡❝❡✐✈❡❞ ❧❛st r❡❝❡✐✈❡ tr✐❣❣❡rs ❝♦♠♣✉t❛t✐♦♥

❉②♥❛♠✐❝ t❛s❦ s❝❤❡❞✉❧✐♥❣

♠✉❧t✐♣❧❡ ❇❧♦❝❦s ♣❡r ♣r♦❝❡ss ♦✈❡r❧❛♣♣❡❞ ❝♦♠♠✉♥✐❝❛t✐♦♥✴❝♦♠♣✉t❛t✐♦♥

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❈❡❧❧♦ ❞✐str✐❜✉t❡❞ ❛❞❛♣t✐✈❡ ♠❡s❤ r❡✜♥❡♠❡♥t

❍♦✇ ♣❛rt✐❝❧❡ ❞❛t❛ ❛r❡ ❝♦♠♠✉♥✐❝❛t❡❞ ❜❡t✇❡❡♥ ❇❧♦❝❦s

❈♦♠♠✉♥✐❝❛t✐♦♥ ✐s r❡q✉✐r❡❞ ✇❤❡♥ ♣❛rt✐❝❧❡s ♠♦✈❡ ♦✉ts✐❞❡ ❛ ❇❧♦❝❦ ❚❤✐s ✐s ❞♦♥❡ ✉s✐♥❣ ❛ ✹①✹①✹ ❛rr❛②

❛rr❛② ❝♦♥t❛✐♥s ♣♦✐♥t❡rs t♦ P❛rt✐❝❧❡❉❛t❛ ✭P❉✮ ♦❜❥❡❝ts ♦♥❡ P❉ ♦❜❥❡❝t ♣❡r ♥❡✐❣❤❜♦r ❇❧♦❝❦

▼✐❣r❛t✐♥❣ ♣❛rt✐❝❧❡s ❛r❡

s❝❛tt❡r✭✮✲❡❞ t♦ P❉ ❛rr❛② ♦❜❥❡❝ts s❡♥t t♦ ❛ss♦❝✐❛t❡❞ ♥❡✐❣❤❜♦rs ❣❛t❤❡r✭✮✲❡❞ ❜② ♥❡✐❣❤❜♦rs

❖♥❡ s✇❡❡♣ t❤r♦✉❣❤ ♣❛rt✐❝❧❡s ❖♥❡ ❝♦♠♠✉♥✐❝❛t✐♦♥ st❡♣ ♣❡r ♥❡✐❣❤❜♦r

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❊♥③♦✲P✴❈❡❧❧♦ ◆❙❋ ❇❧✉❡ ❲❛t❡rs s❝❛❧✐♥❣

✏❆❧♣❤❛❜❡t ❙♦✉♣✑ t❡st✿ ❤②❞r♦ ❛♥❞ ♣❛rt✐❝❧❡s

❇❛s✐❝ ❊♥③♦✲P ❤②❞r♦❞②♥❛♠✐❝s ❛♥❞ ♣❛rt✐❝❧❡s s❝❛❧❛❜✐❧✐t② ✈❛r✐❛t✐♦♥ ♦❢ ✏❛rr❛② ♦❢ ❙❡❞♦✈ ❇❧❛st✑ t❡st ❧❡tt❡rs ✐♥st❡❛❞ ♦❢ s♣❤❡r❡s

✐♥❤✐❜✐ts ❧♦❝❦st❡♣ ❝♦❛rs❡♥✴r❡✜♥❡

♦♥❡ ❜❧❛st ♣❡r ❇❲ ❢♣✲❝♦r❡ t❡st❡❞ ✇✐t❤✴✇✐t❤♦✉t tr❛❝❡r ♣❛rt✐❝❧❡s ✸✷✸ ♦r ✷✹✸ ❝❡❧❧s ♣❡r ❜❧♦❝❦ ❞❡❝❡♥t s✐③❡❞ ❆▼❘ ♣r♦❜❧❡♠ ❢♦r ✷✵✶✻

✷✻✷K ❢♣✲❝♦r❡s ✺✵M ❇❧♦❝❦s ✶.✼T ❝❡❧❧s❀ ✵.✼T ✭❝❡❧❧s ✰ ♣❛rt✐❝❧❡s✮

❊◆❩❖ ✇♦✉❧❞ ♥❡❡❞ ✼✷GB ♣❡r ♣r♦❝❡ss✦

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❊♥③♦✲P✴❈❡❧❧♦ ◆❙❋ ❇❧✉❡ ❲❛t❡rs s❝❛❧✐♥❣

✏❆❧♣❤❛❜❡t ❙♦✉♣✑ t❡st✿ ❤②❞r♦ ❛♥❞ ♣❛rt✐❝❧❡s

100 101 102 103 104 105 106 Processes (FP cores) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Efficiency

parallel efficiency memory efficiency

Enzo-P Weak Scaling on Blue Waters: Efficiency

Alphabet Soup Test (with tracer particles): 161110 100 101 102 103 104 105 106 Processes (FP cores) 10-4 10-3 10-2 10-1 100 101 102 Time (s)

compute adapt time adapt sync refresh time refresh sync stopping total

Enzo-P Weak Scaling on Blue Waters: Time

Alphabet Soup Test (with tracer particles): 161110

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❊♥③♦✲P✴❈❡❧❧♦ ◆❙❋ ❇❧✉❡ ❲❛t❡rs s❝❛❧✐♥❣

✏❯♥✐❣r✐❞ ❈♦s♠♦❧♦❣②✑ t❡st✿ ❤②❞r♦✱ ♣❛rt✐❝❧❡s✱ ❣r❛✈✐t②

❙❝❛❧✐♥❣ ♦❢ ❜❛s✐❝ ❝♦s♠♦❧♦❣② s✐♠✉❧❛t✐♦♥s

❬ ❘❡♥②✉❡ ❈❡♥ ❪

PP▼ ❤②❞r♦❞②♥❛♠✐❝s ✏❞❛r❦ ♠❛tt❡r✑ ♣❛rt✐❝❧❡s ❈■❈ ♣❛rt✐❝❧❡✲♠❡s❤ ❣r❛✈✐t② ♠✉❧t✐❣r✐❞ s♦❧✈❡r✖✏✉♥✐❣r✐❞✑ ♦♥❧② t❡st❡❞ ✉♣ t♦ ✶✸✶K ❢♣✲❝♦r❡s

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❊♥③♦✲P✴❈❡❧❧♦ ◆❙❋ ❇❧✉❡ ❲❛t❡rs s❝❛❧✐♥❣

✏❯♥✐❣r✐❞ ❈♦s♠♦❧♦❣②✑ t❡st✿ ❤②❞r♦✱ ♣❛rt✐❝❧❡s✱ ❣r❛✈✐t②

23 25 27 29 211 213 215 217 Processing units (FP cores) 2

4

2

2

20 22 24 26 28 Time per cycle (s)

Enzo-P Cosmology Weak Scaling on Blue Waters

N64 N128 N256 N512 N1024 N2048 23 25 27 29 211 213 215 217 Processing units (FP cores) 2

4

2

2

20 22 24 26 28 Time per cycle (s)

Enzo-P Cosmology Strong Scaling on Blue Waters

N64 N128 N256 N512 N1024 N2048

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

P✉rs✉✐t ♦❢ s❝❛❧❛❜❧❡ ❣r❛✈✐t②

▲✐♥❡❛r s♦❧✈❡rs ❢♦r ∇✷Φ = ✹πGρ

❘❡❝❡♥t ✇♦r❦ ❤❛s ❢♦❝✉s❡❞ ♦♥ s❝❛❧❛❜❧❡ ❧✐♥❡❛r s♦❧✈❡rs ❊♥③♦❙♦❧✈❡r❈❣✿ ❈♦♥❥✉❣❛t❡ ●r❛❞✐❡♥t ✭❈●✮ ❑r②❧♦✈ s♦❧✈❡r

❊❛s② t♦ ✐♠♣❧❡♠❡♥t ✭✈❡❝t♦r ✉♣❞❛t❡s✱ ♠❛t✈❡❝s✱ ❞♦t ♣r♦❞✉❝ts✮ ▼❛② ♥♦t ❝♦♥✈❡r❣❡ ❢♦r ♥♦♥s②♠♠❡tr✐❝ ♣r♦❜❧❡♠s ✭❆▼❘✮ P♦♦r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ✐❢ ♥♦t ♣r❡❝♦♥❞✐t✐♦♥❡❞

❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜✿ ❇✐❈●✲❙❚❆❇ ❑r②❧♦✈ s♦❧✈❡r

❊❛s② t♦ ✐♠♣❧❡♠❡♥t ❆♣♣❧✐❝❛❜❧❡ t♦ ♥♦♥✲s②♠♠❡tr✐❝ ♣r♦❜❧❡♠s P♦♦r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ✐❢ ♥♦t ♣r❡❝♦♥❞✐t✐♦♥❡❞

❊♥③♦❙♦❧✈❡r▼❣✵✿ ▼✉❧t✐❣r✐❞ ❱✲❝②❝❧❡

❚r✐❝❦✐❡r t♦ ✐♠♣❧❡♠❡♥t ✭✐♥t❡r✲❧❡✈❡❧ tr❛♥s❢❡rs✮

• ♦♦❞ s❝❛❧❛❜✐❧✐t②

▲✐♠✐t❡❞ t♦ ♥♦♥✲❛❞❛♣t✐✈❡ ♠❡s❤❡s ✭❡✳❣✳ r♦♦t✲❧❡✈❡❧✮

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

P✉rs✉✐t ♦❢ s❝❛❧❛❜❧❡ ❣r❛✈✐t②

▲✐♥❡❛r s♦❧✈❡rs ❢♦r ∇✷Φ = ✹πGρ

❘❡❝❡♥t ✇♦r❦ ❤❛s ❢♦❝✉s❡❞ ♦♥ s❝❛❧❛❜❧❡ ❧✐♥❡❛r s♦❧✈❡rs ❊♥③♦❙♦❧✈❡r❈❣✿ ❈♦♥❥✉❣❛t❡ ●r❛❞✐❡♥t ✭❈●✮ ❑r②❧♦✈ s♦❧✈❡r

❊❛s② t♦ ✐♠♣❧❡♠❡♥t ✭✈❡❝t♦r ✉♣❞❛t❡s✱ ♠❛t✈❡❝s✱ ❞♦t ♣r♦❞✉❝ts✮ ▼❛② ♥♦t ❝♦♥✈❡r❣❡ ❢♦r ♥♦♥s②♠♠❡tr✐❝ ♣r♦❜❧❡♠s ✭❆▼❘✮ P♦♦r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ✐❢ ♥♦t ♣r❡❝♦♥❞✐t✐♦♥❡❞

❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜✿ ❇✐❈●✲❙❚❆❇ ❑r②❧♦✈ s♦❧✈❡r

❊❛s② t♦ ✐♠♣❧❡♠❡♥t ❆♣♣❧✐❝❛❜❧❡ t♦ ♥♦♥✲s②♠♠❡tr✐❝ ♣r♦❜❧❡♠s P♦♦r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ✐❢ ♥♦t ♣r❡❝♦♥❞✐t✐♦♥❡❞

❊♥③♦❙♦❧✈❡r▼❣✵✿ ▼✉❧t✐❣r✐❞ ❱✲❝②❝❧❡

❚r✐❝❦✐❡r t♦ ✐♠♣❧❡♠❡♥t ✭✐♥t❡r✲❧❡✈❡❧ tr❛♥s❢❡rs✮

• ♦♦❞ s❝❛❧❛❜✐❧✐t②

▲✐♠✐t❡❞ t♦ ♥♦♥✲❛❞❛♣t✐✈❡ ♠❡s❤❡s ✭❡✳❣✳ r♦♦t✲❧❡✈❡❧✮

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

P✉rs✉✐t ♦❢ s❝❛❧❛❜❧❡ ❣r❛✈✐t②

▲✐♥❡❛r s♦❧✈❡rs ❢♦r ∇✷Φ = ✹πGρ

❘❡❝❡♥t ✇♦r❦ ❤❛s ❢♦❝✉s❡❞ ♦♥ s❝❛❧❛❜❧❡ ❧✐♥❡❛r s♦❧✈❡rs ❊♥③♦❙♦❧✈❡r❈❣✿ ❈♦♥❥✉❣❛t❡ ●r❛❞✐❡♥t ✭❈●✮ ❑r②❧♦✈ s♦❧✈❡r

❊❛s② t♦ ✐♠♣❧❡♠❡♥t ✭✈❡❝t♦r ✉♣❞❛t❡s✱ ♠❛t✈❡❝s✱ ❞♦t ♣r♦❞✉❝ts✮ ▼❛② ♥♦t ❝♦♥✈❡r❣❡ ❢♦r ♥♦♥s②♠♠❡tr✐❝ ♣r♦❜❧❡♠s ✭❆▼❘✮ P♦♦r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ✐❢ ♥♦t ♣r❡❝♦♥❞✐t✐♦♥❡❞

❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜✿ ❇✐❈●✲❙❚❆❇ ❑r②❧♦✈ s♦❧✈❡r

❊❛s② t♦ ✐♠♣❧❡♠❡♥t ❆♣♣❧✐❝❛❜❧❡ t♦ ♥♦♥✲s②♠♠❡tr✐❝ ♣r♦❜❧❡♠s P♦♦r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ✐❢ ♥♦t ♣r❡❝♦♥❞✐t✐♦♥❡❞

❊♥③♦❙♦❧✈❡r▼❣✵✿ ▼✉❧t✐❣r✐❞ ❱✲❝②❝❧❡

❚r✐❝❦✐❡r t♦ ✐♠♣❧❡♠❡♥t ✭✐♥t❡r✲❧❡✈❡❧ tr❛♥s❢❡rs✮

• ♦♦❞ s❝❛❧❛❜✐❧✐t②

▲✐♠✐t❡❞ t♦ ♥♦♥✲❛❞❛♣t✐✈❡ ♠❡s❤❡s ✭❡✳❣✳ r♦♦t✲❧❡✈❡❧✮

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

P✉rs✉✐t ♦❢ s❝❛❧❛❜❧❡ ❣r❛✈✐t②

▲✐♥❡❛r s♦❧✈❡rs ❢♦r ∇✷Φ = ✹πGρ

❘❡❝❡♥t ✇♦r❦ ❤❛s ❢♦❝✉s❡❞ ♦♥ s❝❛❧❛❜❧❡ ❧✐♥❡❛r s♦❧✈❡rs ❊♥③♦❙♦❧✈❡r❈❣✿ ❈♦♥❥✉❣❛t❡ ●r❛❞✐❡♥t ✭❈●✮ ❑r②❧♦✈ s♦❧✈❡r

❊❛s② t♦ ✐♠♣❧❡♠❡♥t ✭✈❡❝t♦r ✉♣❞❛t❡s✱ ♠❛t✈❡❝s✱ ❞♦t ♣r♦❞✉❝ts✮ ▼❛② ♥♦t ❝♦♥✈❡r❣❡ ❢♦r ♥♦♥s②♠♠❡tr✐❝ ♣r♦❜❧❡♠s ✭❆▼❘✮ P♦♦r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ✐❢ ♥♦t ♣r❡❝♦♥❞✐t✐♦♥❡❞

❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜✿ ❇✐❈●✲❙❚❆❇ ❑r②❧♦✈ s♦❧✈❡r

❊❛s② t♦ ✐♠♣❧❡♠❡♥t ❆♣♣❧✐❝❛❜❧❡ t♦ ♥♦♥✲s②♠♠❡tr✐❝ ♣r♦❜❧❡♠s P♦♦r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ✐❢ ♥♦t ♣r❡❝♦♥❞✐t✐♦♥❡❞

❊♥③♦❙♦❧✈❡r▼❣✵✿ ▼✉❧t✐❣r✐❞ ❱✲❝②❝❧❡

❚r✐❝❦✐❡r t♦ ✐♠♣❧❡♠❡♥t ✭✐♥t❡r✲❧❡✈❡❧ tr❛♥s❢❡rs✮

• ♦♦❞ s❝❛❧❛❜✐❧✐t②

▲✐♠✐t❡❞ t♦ ♥♦♥✲❛❞❛♣t✐✈❡ ♠❡s❤❡s ✭❡✳❣✳ r♦♦t✲❧❡✈❡❧✮

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❊♥③♦✲P✴❈❡❧❧♦ P✉rs✉✐t ♦❢ s❝❛❧❛❜❧❡ ❧✐♥❡❛r s♦❧✈❡rs

▲✐♥❡❛r s♦❧✈❡rs ❢♦r ∇✷Φ = ✹πGρ

❈❛♥ ✇❡ ❜✉✐❧❞ ❛ s❝❛❧❛❜❧❡ ❆▼❘ s♦❧✈❡r ✉s✐♥❣ t❤❡s❡ s♦❧✈❡rs❄ ✏❍●✑ ❍✐❡r❛r❝❤✐❝❛❧ ●r✐❞ s♦❧✈❡r ✭❉✳ ❘❡②♥♦❧❞s✮

❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜ s♦❧✈❡r ❊♥③♦❙♦❧✈❡r▼❣✵ ♣r❡❝♦♥❞✐t✐♦♥❡r ❆♣♣❧✐❝❛❜❧❡ t♦ ❆▼❘ ♣r♦❜❧❡♠s ❇❡tt❡r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ▲✐♠✐t❡❞ ♣❛r❛❧❧❡❧ s❝❛❧❛❜✐❧✐t② ✭✐♥♥❡r✲♣r♦❞✉❝ts✮

✏❉❉✑ ❉♦♠❛✐♥ ❉❡❝♦♠♣♦s✐t✐♦♥ s♦❧✈❡r ✭▼✳▲✳ ◆♦r♠❛♥✮

❊♥③♦❙♦❧✈❡r▼❣✵ ❢♦r ✏❧♦♥❣✲r❛♥❣❡✑ ✐♥t❡r❛❝t✐♦♥s ❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜ ♦♥ ✐s♦❧❛t❡❞ ♦❝tr❡❡s ❢♦r ✏s❤♦rt✲r❛♥❣❡✑ ❋✐♥❛❧ s♠♦♦t❤✐♥❣ t♦ ❝❧❡❛♥ ✉♣ s✉❜❞♦♠❛✐♥ ❜♦✉♥❞❛r✐❡s Pr♦♠✐s✐♥❣ ✐♥✐t✐❛❧ r❡s✉❧ts ✭♠❡♠♦r② ❧❡❛❦✦✮

✏❆❋❆❈✑ ❆s②♥❝❤r♦♥♦✉s ❢❛st ❛❞❛♣t✐✈❡ ❝♦♠♣♦s✐t❡

■❢ ❉❉ ✐s ✐♥s✉✣❝✐❡♥t✱ ✇✐❧❧ tr② ♠✉❧t✐❣r✐❞ ❛❞❛♣t❡❞ t♦ ❆▼❘

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❊♥③♦✲P✴❈❡❧❧♦ P✉rs✉✐t ♦❢ s❝❛❧❛❜❧❡ ❧✐♥❡❛r s♦❧✈❡rs

▲✐♥❡❛r s♦❧✈❡rs ❢♦r ∇✷Φ = ✹πGρ

❈❛♥ ✇❡ ❜✉✐❧❞ ❛ s❝❛❧❛❜❧❡ ❆▼❘ s♦❧✈❡r ✉s✐♥❣ t❤❡s❡ s♦❧✈❡rs❄ ✏❍●✑ ❍✐❡r❛r❝❤✐❝❛❧ ●r✐❞ s♦❧✈❡r ✭❉✳ ❘❡②♥♦❧❞s✮

❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜ s♦❧✈❡r ❊♥③♦❙♦❧✈❡r▼❣✵ ♣r❡❝♦♥❞✐t✐♦♥❡r ❆♣♣❧✐❝❛❜❧❡ t♦ ❆▼❘ ♣r♦❜❧❡♠s ❇❡tt❡r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ▲✐♠✐t❡❞ ♣❛r❛❧❧❡❧ s❝❛❧❛❜✐❧✐t② ✭✐♥♥❡r✲♣r♦❞✉❝ts✮

✏❉❉✑ ❉♦♠❛✐♥ ❉❡❝♦♠♣♦s✐t✐♦♥ s♦❧✈❡r ✭▼✳▲✳ ◆♦r♠❛♥✮

❊♥③♦❙♦❧✈❡r▼❣✵ ❢♦r ✏❧♦♥❣✲r❛♥❣❡✑ ✐♥t❡r❛❝t✐♦♥s ❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜ ♦♥ ✐s♦❧❛t❡❞ ♦❝tr❡❡s ❢♦r ✏s❤♦rt✲r❛♥❣❡✑ ❋✐♥❛❧ s♠♦♦t❤✐♥❣ t♦ ❝❧❡❛♥ ✉♣ s✉❜❞♦♠❛✐♥ ❜♦✉♥❞❛r✐❡s Pr♦♠✐s✐♥❣ ✐♥✐t✐❛❧ r❡s✉❧ts ✭♠❡♠♦r② ❧❡❛❦✦✮

✏❆❋❆❈✑ ❆s②♥❝❤r♦♥♦✉s ❢❛st ❛❞❛♣t✐✈❡ ❝♦♠♣♦s✐t❡

■❢ ❉❉ ✐s ✐♥s✉✣❝✐❡♥t✱ ✇✐❧❧ tr② ♠✉❧t✐❣r✐❞ ❛❞❛♣t❡❞ t♦ ❆▼❘

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❊♥③♦✲P✴❈❡❧❧♦ P✉rs✉✐t ♦❢ s❝❛❧❛❜❧❡ ❧✐♥❡❛r s♦❧✈❡rs

▲✐♥❡❛r s♦❧✈❡rs ❢♦r ∇✷Φ = ✹πGρ

❈❛♥ ✇❡ ❜✉✐❧❞ ❛ s❝❛❧❛❜❧❡ ❆▼❘ s♦❧✈❡r ✉s✐♥❣ t❤❡s❡ s♦❧✈❡rs❄ ✏❍●✑ ❍✐❡r❛r❝❤✐❝❛❧ ●r✐❞ s♦❧✈❡r ✭❉✳ ❘❡②♥♦❧❞s✮

❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜ s♦❧✈❡r ❊♥③♦❙♦❧✈❡r▼❣✵ ♣r❡❝♦♥❞✐t✐♦♥❡r ❆♣♣❧✐❝❛❜❧❡ t♦ ❆▼❘ ♣r♦❜❧❡♠s ❇❡tt❡r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ▲✐♠✐t❡❞ ♣❛r❛❧❧❡❧ s❝❛❧❛❜✐❧✐t② ✭✐♥♥❡r✲♣r♦❞✉❝ts✮

✏❉❉✑ ❉♦♠❛✐♥ ❉❡❝♦♠♣♦s✐t✐♦♥ s♦❧✈❡r ✭▼✳▲✳ ◆♦r♠❛♥✮

❊♥③♦❙♦❧✈❡r▼❣✵ ❢♦r ✏❧♦♥❣✲r❛♥❣❡✑ ✐♥t❡r❛❝t✐♦♥s ❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜ ♦♥ ✐s♦❧❛t❡❞ ♦❝tr❡❡s ❢♦r ✏s❤♦rt✲r❛♥❣❡✑ ❋✐♥❛❧ s♠♦♦t❤✐♥❣ t♦ ❝❧❡❛♥ ✉♣ s✉❜❞♦♠❛✐♥ ❜♦✉♥❞❛r✐❡s Pr♦♠✐s✐♥❣ ✐♥✐t✐❛❧ r❡s✉❧ts ✭♠❡♠♦r② ❧❡❛❦✦✮

✏❆❋❆❈✑ ❆s②♥❝❤r♦♥♦✉s ❢❛st ❛❞❛♣t✐✈❡ ❝♦♠♣♦s✐t❡

■❢ ❉❉ ✐s ✐♥s✉✣❝✐❡♥t✱ ✇✐❧❧ tr② ♠✉❧t✐❣r✐❞ ❛❞❛♣t❡❞ t♦ ❆▼❘

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❊♥③♦✲P✴❈❡❧❧♦ P✉rs✉✐t ♦❢ s❝❛❧❛❜❧❡ ❧✐♥❡❛r s♦❧✈❡rs

▲✐♥❡❛r s♦❧✈❡rs ❢♦r ∇✷Φ = ✹πGρ

❈❛♥ ✇❡ ❜✉✐❧❞ ❛ s❝❛❧❛❜❧❡ ❆▼❘ s♦❧✈❡r ✉s✐♥❣ t❤❡s❡ s♦❧✈❡rs❄ ✏❍●✑ ❍✐❡r❛r❝❤✐❝❛❧ ●r✐❞ s♦❧✈❡r ✭❉✳ ❘❡②♥♦❧❞s✮

❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜ s♦❧✈❡r ❊♥③♦❙♦❧✈❡r▼❣✵ ♣r❡❝♦♥❞✐t✐♦♥❡r ❆♣♣❧✐❝❛❜❧❡ t♦ ❆▼❘ ♣r♦❜❧❡♠s ❇❡tt❡r ❛❧❣♦r✐t❤♠✐❝ s❝❛❧❛❜✐❧✐t② ▲✐♠✐t❡❞ ♣❛r❛❧❧❡❧ s❝❛❧❛❜✐❧✐t② ✭✐♥♥❡r✲♣r♦❞✉❝ts✮

✏❉❉✑ ❉♦♠❛✐♥ ❉❡❝♦♠♣♦s✐t✐♦♥ s♦❧✈❡r ✭▼✳▲✳ ◆♦r♠❛♥✮

❊♥③♦❙♦❧✈❡r▼❣✵ ❢♦r ✏❧♦♥❣✲r❛♥❣❡✑ ✐♥t❡r❛❝t✐♦♥s ❊♥③♦❙♦❧✈❡r❇✐❈❣❙t❛❜ ♦♥ ✐s♦❧❛t❡❞ ♦❝tr❡❡s ❢♦r ✏s❤♦rt✲r❛♥❣❡✑ ❋✐♥❛❧ s♠♦♦t❤✐♥❣ t♦ ❝❧❡❛♥ ✉♣ s✉❜❞♦♠❛✐♥ ❜♦✉♥❞❛r✐❡s Pr♦♠✐s✐♥❣ ✐♥✐t✐❛❧ r❡s✉❧ts ✭♠❡♠♦r② ❧❡❛❦✦✮

✏❆❋❆❈✑ ❆s②♥❝❤r♦♥♦✉s ❢❛st ❛❞❛♣t✐✈❡ ❝♦♠♣♦s✐t❡

■❢ ❉❉ ✐s ✐♥s✉✣❝✐❡♥t✱ ✇✐❧❧ tr② ♠✉❧t✐❣r✐❞ ❛❞❛♣t❡❞ t♦ ❆▼❘

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

◆❡①t st❡♣s ❋✐♥✐s❤ ✉♣ ✭✜♥❛❧❧②✦✮ s❝❛❧❛❜❧❡ ❆▼❘ ❣r❛✈✐t② Pr❡♣❛r❡ ❢♦r ✐♥✐t✐❛❧ ♣✉❜❧✐❝ r❡❧❡❛s❡

❊♥③♦✲❊ ❞❡✈❡❧♦♣❡r ♠❡❡t✐♥❣ ♥❡①t ✇❡❡❦ ❋❧✉①✲❝♦rr❡❝t✐♦♥ ❙❝❛❧❛❜❧❡ ■✴❖ ✭❊①♣❧♦r❛t✐♦♥s ■♥ ❊①❛s❝❛❧❡ ■✴❖ ❧✐❜r❛r②❄✮

◆❡✇ ♣❤②s✐❝s ❝❛♣❛❜✐❧✐t✐❡s

▼❍❉ s♦❧✈❡rs ❙t❛r♠❛❦❡r ♠❡t❤♦❞s ❈♦s♠✐❝ r❛② tr❛♥s♣♦rt ❆❝t✐✈❡ ♣❛rt✐❝❧❡s

❋✉rt❤❡r ♣❡r❢♦r♠❛♥❝❡ ✐♠♣r♦✈❡♠❡♥ts

❇❧♦❝❦✲❛❞❛♣t✐✈❡ t✐♠❡✲st❡♣♣✐♥❣ ❆❝❝❡❧❡r❛t♦r s✉♣♣♦rt ❉②♥❛♠✐❝ ❧♦❛❞ ❜❛❧❛♥❝✐♥❣ ✭❙❋❈❄✮

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❆❝❦♥♦✇❧❡❞❣❡♠❡♥ts

❋✉♥❞✐♥❣ ❢♦r ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❊♥③♦✲P✴❈❡❧❧♦ ❤❛s ❜❡❡♥ ♣r♦✈✐❞❡❞ ❜② t❤❡ ◆❛t✐♦♥❛❧ ❙❝✐❡♥❝❡ ❋♦✉♥❞❛t✐♦♥ ❣r❛♥ts ❖❆❈✲✶✽✸✺✹✵✷✱ ❙■✷✲❙❙❊✲✶✹✹✵✼✵✾✱ P❍❨✲✶✶✵✹✽✶✾✱ ❛♥❞ ❆❙❚✲✵✽✵✽✶✽✹✳ ❚❤✐s r❡s❡❛r❝❤ ✐s ♣❛rt ♦❢ t❤❡ ❇❧✉❡ ❲❛t❡rs s✉st❛✐♥❡❞✲♣❡t❛s❝❛❧❡ ❝♦♠♣✉t✐♥❣ ♣r♦❥❡❝t✱ ✇❤✐❝❤ ✐s s✉♣♣♦rt❡❞ ❜② t❤❡ ◆❛t✐♦♥❛❧ ❙❝✐❡♥❝❡ ❋♦✉♥❞❛t✐♦♥ ✭❛✇❛r❞s ❖❈■✲✵✼✷✺✵✼✵ ❛♥❞ ❆❈■✲✶✷✸✽✾✾✸✮ ❛♥❞ t❤❡ st❛t❡ ♦❢ ■❧❧✐♥♦✐s✳ ❇❧✉❡ ❲❛t❡rs ✐s ❛ ❥♦✐♥t ❡✛♦rt ♦❢ t❤❡ ❯♥✐✈❡rs✐t② ♦❢ ■❧❧✐♥♦✐s ❛t ❯r❜❛♥❛✲❈❤❛♠♣❛✐❣♥ ❛♥❞ t❤❡ ◆❛t✐♦♥❛❧ ❈❡♥t❡r ❢♦r ❙✉♣❡r❝♦♠♣✉t✐♥❣ ❆♣♣❧✐❝❛t✐♦♥s✳ ❤tt♣✿✴✴❝❡❧❧♦✲♣r♦❥❡❝t✳♦r❣✴

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❍♦✇ t❤❡ ❇❧♦❝❦ ❝❤❛r❡ ❛rr❛② ✐s ✐♥❞❡①❡❞

Octree Forest Block x y z 31 indices encoding level

❯s❡r✲❞❡✜♥❡❞ ❝❤❛r❡ ❛rr❛② ✐♥❞✐❝❡s s✉♣♣♦rt❡❞ ❈❡❧❧♦ ✐♥❞✐❝❡s ❢♦r ❇❧♦❝❦ ❛rr❛②s✿

✸ × ✶✵ ❜✐ts ❢♦r ❛rr❛② ✐♥❞✐❝❡s ✸ × ✷✵ ❜✐ts ❢♦r t❤❡ ♦❝tr❡❡ ❡♥❝♦❞✐♥❣ ✻ ❜✐ts ❢♦r t❤❡ ❜❧♦❝❦ ❧❡✈❡❧

❯♣ t♦ ✶✵✷✹✸ ❛rr❛② ♦❢ ♦❝tr❡❡s ❯♣ t♦ ✷✵ ♦❝tr❡❡ ❧❡✈❡❧s

−✸✶ ❧❡✈❡❧ ✸✶

❇❧♦❝❦ ✐❞✬s ✉s❡ ✐♥❞❡①✿ ❡✳❣✳ ❇✶✵✵✿✶✶❴✶✿✵✶

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾

❍♦✇ P❛rt✐❝❧❡ ♦❜❥❡❝ts st♦r❡ ♣❛rt✐❝❧❡ ❞❛t❛

Types "trace" "dark" y z vx vy vz mass x x y z id

Batches

♠✉❧t✐♣❧❡ ♣❛rt✐❝❧❡ t②♣❡s ♣❛rt✐❝❧❡s ❛❧❧♦❝❛t❡❞ ✐♥ ❜❛t❝❤❡s

✜①❡❞ s✐③❡ ❛rr❛②s ❢❡✇❡r ♥❡✇✴❞❡❧❡t❡ ♦♣❡r❛t✐♦♥s ❡✣❝✐❡♥t ✐♥s❡rt✴❞❡❧❡t❡ ♦♣❡r❛t✐♦♥s ♣♦t❡♥t✐❛❧❧② ✉s❡❢✉❧ ❢♦r ●P❯✬s

❜❛t❝❤❡s st♦r❡ ♣❛rt✐❝❧❡ ❛ttr✐❜✉t❡s

✭♣♦s✐t✐♦♥✱ ✈❡❧♦❝✐t②✱ ♠❛ss✱ ❡t❝✳✮ ✽✱✶✻✱✸✷✱✻✹✲❜✐t ✐♥t❡❣❡rs ✸✷✱✻✹✱✶✷✽✲❜✐t ✢♦❛ts

♣❛rt✐❝❧❡ ♣♦s✐t✐♦♥s ♠❛② ❜❡ ✢♦❛t✐♥❣✲♣♦✐♥t ♦r ✐♥t❡❣❡rs

✢♦❛t✐♥❣✲♣♦✐♥t ❢♦r st♦r✐♥❣ ❣❧♦❜❛❧ ♣♦s✐t✐♦♥s ✐♥t❡❣❡rs ❢♦r ❇❧♦❝❦✲❧♦❝❛❧ ❝♦♦r❞✐♥❛t❡s

s♦❧✈❡s r❡❞✉❝❡❞ ♣r❡❝✐s✐♦♥ ✐ss✉❡ ❢♦r ❞❡❡♣ ❤✐❡r❛r❝❤✐❡s ❧❡ss ♠❡♠♦r② r❡q✉✐r❡❞ ❢♦r ❣✐✈❡♥ ❛❝❝✉r❛❝②

❏✳❇♦r❞♥❡r✱ ▼✳▲✳◆♦r♠❛♥ ❊♥③♦✲❊ ✴ ❈❡❧❧♦ ❈❤❛r♠✰✰ ✷✵✶✾