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rt t r rs rt t r rs

slide-1
SLIDE 1

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡

❚❛❧ ❆❧❡①❛♥❞❡r

❲❡✐③♠❛♥♥ ■♥st✐t✉t❡ ♦❢ s❝✐❡♥❝❡

  • ∆

ra BH

c

R

slide-2
SLIDE 2

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ■♥tr♦❞✉❝t✐♦♥

❖✈❡r✈✐❡✇

◮ ❙t❡❧❧❛r ♠❛ss ❇❍ s❡❡❞s ❛❝❝r❡t❡ q✉❛s✐✲s♣❤❡r✐❝❛❧❧② ❛♥❞ ❣r♦✇

s✉♣r❛✲❡①♣♦♥❡♥t✐❛❧❧② ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ✐♥ st❡❧❧❛r ❝❧✉st❡rs ❢❡❞ ❜② ❞❡♥s❡ ❝♦❧❞✲✢♦✇s✱ ❛♥❞ r❡❛❝❤ ♠❛ss❡s ♦❢ ✶✵✹ ▼⊙ ❜② ③ ∼ ✶✺✳

◮ ❙❧♦✇ ❞✐s❦ ❛❝❝r❡t✐♦♥ ❝❛♥ t❤❡♥ ❣r♦✇ t❤❡♠ t♦ t❤❡ ♦❜s❡r✈❡❞

▼• ✶✵✾ ▼⊙ ◗❙❖ ❛t ③ ∼ ✼✳

◮ ❚❤❡ ❊❞❞✐♥❣t♦♥ ❧✐♠✐t ♦♥ t❤❡ ♠❛ss ❛❝❝r❡t✐♦♥ r❛t❡ ❞♦❡s ♥♦t ❛♣♣❧②✳ ◮ ❚❤❡ ❛♥❣✉❧❛r ♠♦♠❡♥t✉♠ ❜♦tt❧❡♥❡❝❦ ✐s ❝✐r❝✉♠✈❡♥t❡❞ ❜② t❤❡ ❞②♥❛♠✐❝s

♦❢ t❤❡ ❧✐❣❤t ❇❍ s❡❡❞ ✐♥ t❤❡ ❜✐rt❤ ❝❧✉st❡r✳

◮ ◆❡✇ ❡❧❡♠❡♥t✿ ❚❤❡ ❛❝❝r❡t♦r ❛s ❛ st♦❝❤❛st✐❝ ❞②♥❛♠✐❝❛❧ ♦❜❥❡❝t✳ ✭❆❧❡①❛♥❞❡r ✫ ◆❛t❛r❛❥❛♥✱ ✷✵✶✹✱ ❙❝✐❡♥❝❡✱ ✸✹✺✱ ✶✸✸✵✮

slide-3
SLIDE 3

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ■♥tr♦❞✉❝t✐♦♥

❈♦♥✈❡♥t✐♦♥❛❧ st❛t❡♠❡♥t ♦❢ t❤❡ ♣r♦❜❧❡♠

◮ ❖♥❧② ❦♥♦✇♥ ❢♦r♠❛t✐♦♥ ♣❛t❤✿ ❙◆ → O(✶✵ ▼⊙) ❇❍✳ ◮ ❊❛r❧② ♠❛ss✐✈❡ ◗❙❖✿ ▼•,❢ ✶✵✾ ▼⊙ ❛t ③❢ ∼ ✼ ↔ t❢ ∼ ✵.✽ ●②r

(e.g. Mortlock et al 2011)✳

◮ ■❢ ❊❞❞✐♥❣t♦♥✲❧✐♠✐t❡❞ ❛❝❝r❡t✐♦♥✿ ˙

▼❊ ∼ ▲❊/❝✷ηr❛❞✳

◮ ❡✲❢♦❧❞✐♥❣ t✐♠❡ t❊ = ✹.✺ × ✶✵✼ ②r ❢♦r ηr❛❞ = ✵.✶✳

◮ ❊①❛♠♣❧❡✿ ❢♦r ③✐ ∼ ✶✻ ↔ t✐ ∼ ✵.✷✺ ●②r✿

▼•,✐ = ▼•,❢ / ❡①♣[(t❢ − t✐)/t❊] ∼ ✺✵✵✵ ▼⊙✳

◮ ◆❛t✉r❡ ♠❛♥❛❣❡s t♦ ❝r❡❛t❡ ♠❛ss✐✈❡ ❇❍ s❡❡❞s✱ ♦r ❡①❝❡❡❞ ˙

▼❊✳

slide-4
SLIDE 4

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ■♥tr♦❞✉❝t✐♦♥

❈♦rr❡❝t r❡st❛t❡♠❡♥t ♦❢ t❤❡ ♣r♦❜❧❡♠

◮ ❚❤❡ ❊❞❞✐♥❣t♦♥ ❧✐♠✐t ✐s ♥♦t ❛ ♣r♦❜❧❡♠✳

◮ ▲ ▲❊ ❜✉t ˙

▼ ≮ ˙ ▼❊ ✱ ❡✈❡♥ ❢♦r s♣❤❡r✐❝❛❧ ❛❝❝r❡t✐♦♥✦

◮ ❆r❜✐tr❛r② ❤✐❣❤ ˙

▼ ❞✉❡ t♦ ❛♥ ❡✛❡❝t✐✈❡ ❤♦r✐③♦♥ ❜② ♣❤♦t♦♥ tr❛♣♣✐♥❣✳

◮ ❆♥❣✉❧❛r ♠♦♠❡♥t✉♠ ✐s t❤❡ ♣r♦❜❧❡♠✦

◮ ❋❛st ❢r❡❡✲❢❛❧❧ ❛❝❝r❡t✐♦♥ ♦♥❧② ✐❢ ❝✐r❝✉❧❛r✐③❛t✐♦♥

r❛❞✐✉s r❝ = ❏✷/●▼• < r• ✭❡✈❡♥t ❤♦r✐③♦♥✮✱

◮ ❖t❤❡r✇✐s❡✱ ❞✐s❦ ❢♦r♠s ♦✉ts✐❞❡ r❝ > r•

❛♥❞ s❧♦✇ ✈✐s❝♦s✐t②✲❧✐♠✐t❡❞ ❛❝❝r❡t✐♦♥✳

(Begelman 1978)

vr vr vr r γ c/τ vr c/τ

slide-5
SLIDE 5

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❙✉♣r❛✲❡①♣♦♥❡♥t✐❛❧ ❛❝❝r❡t✐♦♥

P❤♦t♦♥ tr❛♣♣✐♥❣

rγ = ˙ ▼κ ✹π❝ , ηr❛❞ =

  • ▼•

❝✷ ♠❛①(r•, rγ)

  • ∝ ✶

˙ ▼ ✐❢ rγ >r•

  • ⇒ ▲=ηr❛❞( ˙

▼) ˙ ▼❝✷ ≤ ✹π●❝ κ =▲❊

r• dM/dt (dM/dt)E dM•/dt LE L

slide-6
SLIDE 6

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❙✉♣r❛✲❡①♣♦♥❡♥t✐❛❧ ❛❝❝r❡t✐♦♥

P❤♦t♦♥ tr❛♣♣✐♥❣

rγ = ˙ ▼κ ✹π❝ , ηr❛❞ =

  • ▼•

❝✷ ♠❛①(r•, rγ)

  • ∝ ✶

˙ ▼ ✐❢ rγ >r•

  • ⇒ ▲=ηr❛❞( ˙

▼) ˙ ▼❝✷ ≤ ✹π●❝ κ =▲❊

rγ = r• LE L dM/dt (dM/dt)E dM•/dt

slide-7
SLIDE 7

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❙✉♣r❛✲❡①♣♦♥❡♥t✐❛❧ ❛❝❝r❡t✐♦♥

P❤♦t♦♥ tr❛♣♣✐♥❣

rγ = ˙ ▼κ ✹π❝ , ηr❛❞ =

  • ▼•

❝✷ ♠❛①(r•, rγ)

  • ∝ ✶

˙ ▼ ✐❢ rγ >r•

  • ⇒ ▲=ηr❛❞( ˙

▼) ˙ ▼❝✷ ≤ ✹π●❝ κ =▲❊

rγ L LE dM/dt (dM/dt)E dM•/dt

slide-8
SLIDE 8

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❙✉♣r❛✲❡①♣♦♥❡♥t✐❛❧ ❛❝❝r❡t✐♦♥

❩❡r♦✲❛♥❣✉❧❛r ♠♦♠❡♥t✉♠ ❛❝❝r❡t✐♦♥

◮ ❇♦♥❞✐✲❍♦②❧❡✲▲②tt❧❡t♦♥ ✭s♣❤❡r✐❝❛❧ ✴ ✇✐♥❞✮ ❛❝❝r❡t✐♦♥ ✿

˙ ▼ ∼ πr✷

❛ ✈∞ρ∞∝ ▼✷

  • ,

r❛ = ✷●▼• ✈✷

∞

, ✈✷

∞ = ❝✷ ∞ + ✈✷

  • ◮ ❉✐✈❡r❣❡♥❝❡ ✐♥ ❛ ✜♥✐t❡ t✐♠❡ ✭s✉♣r❛✲❡①♣♦♥❡♥t✐❛❧✮✿

▼•(t) = ▼•,✐ ✶ − t/t∞ , t∞ ≃ ✸ √ ✷π ❝✸

∞

  • ✷▼✐ρ∞

(⋆)

⋆ ■♥❝❧✉❞✐♥❣ O(✶) ✐♥❝r❡❛s❡ ✐♥ ❇♦♥❞✐✬s t∞ ❞✉❡ t♦ r❛❞✐❛t✐♦♥ ❜❛❝❦✲♣r❡ss✉r❡ ✭❇❡❣❡❧♠❛♥ ✶✾✼✽✮✳

slide-9
SLIDE 9

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❘❛♣✐❞ ❇❍ ❣r♦✇t❤ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡

■♥✐t✐❛❧ ❝♦♥❞✐t✐♦♥s✿ ❉❡♥s❡ ❝♦❧❞✲✢♦✇s ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡

Dekel et al 2009 Wise, Turk & Abel 2008

❇❊▲❘✲❧✐❦❡ ❞❡♥s✐t✐❡s ♦♥ s✉❜✲♣❝ s❝❛❧❡ ✇✐t❤♦✉t ❛ ❝❡♥tr❛❧ ▼❇❍✦

slide-10
SLIDE 10

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❘❛♣✐❞ ❇❍ ❣r♦✇t❤ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡

❉❡♠♦♥str❛t✐♦♥ ♦❢ ❝♦♥❝❡♣t

❈♦♠♣❛❝t ❝❧✉st❡r ✐♥ ❝♦❧❞ ✢♦✇ ♥♦❞❡

  • ∆

ra BH

c

R

③

  • ✶✺

▼• = ✶✵ ▼⊙ ▼⋆ = ✶ ▼⊙ ❘❝ = ✵.✷✺ ♣❝ ▼❝ = ▼❣ +▼s = ✹ × ✶✵✹ ▼⊙ ▼❣ = ✷ × ✶✵✹ ▼⊙ ▼s = ◆⋆×▼⋆ = ✷ × ✶✵✹ ▼⊙ t∞ = ✸.✺ × ✶✵✼ ②r (< t❊!)

Alexander & Natarajan 2014

slide-11
SLIDE 11

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❘❛♣✐❞ ❇❍ ❣r♦✇t❤ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡

❚❤❡ ❝❤❛❧❧❡♥❣❡s ♦❢ ❛ ❧♦✇ ♠❛ss ❇❍ s❡❡❞

✶✳ ▼♦r❡ ❣r♦✇t❤ ♥❡❡❞❡❞ t♦ r❡❛❝❤ ✶✵✾ ▼⊙✳ ✷✳ ❯♥❛✈♦✐❞❛❜❧❡ ❛❝❝❡❧❡r❛t✐♦♥ ♦❢ ❧♦✇ ♠❛ss ❇❍ ✐♥ t❤❡ ❝❧✉st❡r ✐♥❞✉❝❡s ❛♥❣✉❧❛r ♠♦♠❡♥t✉♠ ✐♥ t❤❡ ✢♦✇ ✐♥ ✐ts ♥♦♥✲✐♥❡rt✐❛❧ r❡st✲❢r❛♠❡✿

◮ ❆❝❝❡❧❡r❛t✐♦♥✲✐♥❞✉❝❡❞ ✈❡❧♦❝✐t② ❣r❛❞✐❡♥t

❥❛ ∼ Ω❝r ✷

❛ > ✵ ◮ ❉❡♥s✐t②✲✐♥❞✉❝❡❞ ❣r❛❞✐❡♥t

❥❛ ∼ ❞ ❧♦❣ ρ

❞ ❧♦❣ r Ω❝r ✷ ❛ < ✵ ◮ ■♥ ❤②❞r♦st❛t✐❝ ❡q✉✐❧✐❜r✐✉♠ ❛♥❞ ❞②♥❛♠✐❝❛❧

❡q✉✐♣❛rt✐t✐♦♥✱ ♥❡❛r✲✉♥✐✈❡rs❛❧ ❥❛(▼•/▼⋆)✳

  • ∆

ra BH

c

R

  • r

y r a x

slide-12
SLIDE 12

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❘❛♣✐❞ ❇❍ ❣r♦✇t❤ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡

❖✈❡r❝♦♠✐♥❣ t❤❡ ❛♥❣✉❧❛r ♠♦♠❡♥t✉♠ ❜❛rr✐❡r ✭✶✮

◮ ❘❛♣✐❞ r❛♥❞♦♠✐③❛t✐♦♥ ♦❢ t❤❡ ♠♦t✐♦♥ ♦❢ t❤❡ ❇❍✳

◮ ❘❡s♦♥❛♥t r❡❧❛①❛t✐♦♥ ♦❢ ♦r❜✐t❛❧ ♦r✐❡♥t❛t✐♦♥✳

◮ ❉❡❝❡❧❡r❛t✐♦♥ ❜② ❛❝❝r❡t✐♦♥ ❞r❛❣✳

◮ ❲❤❡♥ t❛❝❝ < tr❧① ✭▼• ∼ ✷✺ ▼⊙✮✱

❇❍ ❞❡❝♦✉♣❧❡s ❢r♦♠ t❤❡ ❝❧✉st❡r ✳

slide-13
SLIDE 13

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❘❛♣✐❞ ❇❍ ❣r♦✇t❤ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡

❖✈❡r❝♦♠✐♥❣ t❤❡ ❛♥❣✉❧❛r ♠♦♠❡♥t✉♠ ❜❛rr✐❡r ✭✷✮

◮ ■♥✐t✐❛❧ ❝❛♥❝❡❧❧❛t✐♦♥ ♦❢ t❤❡ ✐♥❞✉❝❡❞ ❛♥❣✉❧❛r ♠♦♠❡♥t✉♠✳

◮ ❉❡♥s✐t② ❣r❛❞✐❡♥ts ❝❛♥❝❡❧ ✈❡❧♦❝✐t② ❣r❛❞✐❡♥ts ✭▼• ∼ ✷✵ ▼⊙✮✳

◮ ▲♦✇ ❡✣❝✐❡♥❝② ♦❢ ❛♥❣✉❧❛r ♠♦♠❡♥t✉♠ ❛❝❝r❡t✐♦♥✳

◮ ❙❡❧❢✲r❡❣✉❧❛t✐♥❣ ❝❛♣t✉r❡ ❢r♦♠ ✐♥❤♦♠♦❣❡♥❡♦✉s ✇✐♥❞✿ η❥ ∼ ✶/✸✳

Fleischer & Alexander, 2015, in prep.

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SLIDE 14

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❘❛♣✐❞ ❇❍ ❣r♦✇t❤ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡

❆♥❣✉❧❛r ♠♦♠❡♥t✉♠ ❡✈♦❧✉t✐♦♥

0.01 0.1 1 10 100 10 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 |ja| / jISO Mbh (Mo) t/t∞

tr,0 > M/(dM/dt) Meq = 25.1 Mo Analytic ja (ηj=1/3) no RR no damping Monte Carlo ja (ηj=1/3) no RR no damping RR-suppressed ja

❚♦ ❞♦✿ ❈❛❧✐❜r❛t❡ ❛♥❞ ❝♦♠❜✐♥❡ ❛❧❧ ❥❛✲r❡❞✉❝✐♥❣ ❡✛❡❝ts✳

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SLIDE 15

❘❛♣✐❞ ❜❧❛❝❦ ❤♦❧❡ ❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❡❛r❧② ✉♥✐✈❡rs❡ ❙✉♠♠❛r②

❈♦♥❝❧✉s✐♦♥s

◮ ❙t❡❧❧❛r ❇❍s ✐♥ ✈❡r② ❞❡♥s❡ ❝♦❧❞ ✢♦✇s ❛t r❡❞s❤✐❢ts ③ > ✶✺ ❝❛♥ ❜❡

❧❛✉♥❝❤❡❞ ❜② st❡❧❧❛r ❞②♥❛♠✐❝❛❧ ♣r♦❝❡ss❡s ✐♥t♦ ❛ ♣❤❛s❡ ♦❢ s✉♣r❛✲ ❡①♣♦♥❡♥t✐❛❧ ❛❝❝r❡t✐♦♥✳

◮ ❚❤❡ ❣r♦✇t❤ ✐s s✉♣♣❧② ❧✐♠✐t❡❞✿ st❡❧❧❛r ❇❍s ❣r♦✇ r❛♣✐❞❧② ✐♥ ❛

❢❡✇ × ✶✵✼ ②❡❛rs ✐♥t♦ ✶✵✹ ▼⊙ ✐♥t❡r♠❡❞✐❛t❡ ♠❛ss ❇❍s✳

◮ ❙✉❜s❡q✉❡♥t s❧♦✇❡r ❣r♦✇t❤ ❜② ❞✐s❦ ❛❝❝r❡t✐♦♥ s✉✣❝❡s t♦ ♣r♦❞✉❝❡ t❤❡

s✉♣❡r♠❛ss✐✈❡ ❇❍s t❤❛t ♣♦✇❡r t❤❡ ❜r✐❣❤t❡st ❡❛r❧② q✉❛s❛rs✳

◮ ❖♥❧② O(✵.✵✶) ♦❢ ❉▼ ❤❛❧♦s ✇❤❡r❡ t❤❡ ✜rst st❛rs ❢♦r♠ ♥❡❡❞ ✉♥❞❡r❣♦

t❤✐s ♣r♦❝❡ss t♦ ❛❝❝♦✉♥t ❢♦r t❤❡ ③ > ✻ q✉❛s❛rs✳

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SLIDE 16

❆♣♣❡♥❞✐①✿ ❚❤❡ ♣❤❛s❡✲s♣❛❝❡ ❢♦r s✉♣r❛✲❡①♣♦♥❡♥t✐❛❧ ❛❝❝r❡t✐♦♥

103 104 105 106 10-2 10-1 100 101 103 104 105 106 N* Mc [Mo] Rc [pc] N* 10-2 10-1 100 101 103 104 105 106 Rc [pc] Mc [Mo] 103 104 105 106 103 104 105 106 N* Mc [Mo] 103 104 105 106 10-2 10-1 100 101 N* Rc [pc]

❈♦♥❞✐t✐♦♥s ❢♦r ❡✣❝✐❡♥t s✉♣r❛✲❡①♣♦♥❡♥t✐❛❧ ❛❝❝r❡t✐♦♥✿ ✶✳ P❤②s✐❝❛❧ s❝❛❧❡s ❝♦♥s✐st❡♥t ✇✐t❤ s✐♠✉❧❛t✐♦♥s✳ ✷✳ ❙❊ ❞✐✈❡r❣❡♥❝❡ ❢❛st❡r t❤❛♥ ❝❧✉st❡r ✴ ❝♦❧❞✲✢♦✇ ❧✐❢❡t✐♠❡s✳ ✸✳ ❥❛(▼•) → ✵ ♥❡❛r ▼• ∼ ▼❞❡❝✳ ✹✳ ❊✣❝✐❡♥t ❥❛ ❝❛♥❝❡❧❧❛t✐♦♥ ❜② r❡s♦♥❛♥t r❡❧❛①❛t✐♦♥ ♦r❜✐t❛❧ ✢✐♣s

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SLIDE 17

❆♣♣❡♥❞✐①✿ ❚❤❡ ♣❤❛s❡✲s♣❛❝❡ ❢♦r s✉♣r❛✲❡①♣♦♥❡♥t✐❛❧ ❛❝❝r❡t✐♦♥

0.02 0.04 0.06 0.08 0.1 0.12

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Normalized histogram log10 ρ [g/cm3]’ Gas W08 Stars W08 0.01 0.02 0.03 0.04 0.05 0.06 0.07

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Normalized histogram log10 s W08

  • ❛s✱ st❛rs ❞❡♥s✐t②

❙t❡❧❧❛r ♠❛ss ❢r❛❝t✐♦♥ ❖♥❧② O(✵.✵✶) ♦❢ ❉▼ ❤❛❧♦s ✇❤❡r❡ t❤❡ ✜rst st❛rs ❢♦r♠ ✭∼✸.✺σ ❞❡♥s✐t② ♣❡❛❦s ❛t ③❃✶✺✮ ♥❡❡❞ ✉♥❞❡r❣♦ t❤✐s ♣r♦❝❡ss t♦ ❛❝❝♦✉♥t ❢♦r t❤❡ ③ > ✻ q✉❛s❛rs ✭∼ ✹σ−✺σ ❞❡♥s✐t② ♣❡❛❦s✮✳

Alexander, Natarajan & Rossi, 2015, in prep.