Koushik Sen

Nicolaus Copernicus University Torun

Astrophysics seminar of the PAU Astrophysics Committee, Krakow

April 5, 2023

Evolution of short-period massive binary stars in the Magellanic Clouds

Collaborators: Norbert Langer, Abel Schootemeijer, Tomer Shenar, Laurent Mahy, Goetz Grafener, Chen Wang, Hughes Sana, Athira Menon, Selma de Mink

The Magellanic Clouds

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Credit: J. C. Muñoz/ESO

Large Magellanic Cloud (LMC)

Small Magellanic Cloud (SMC)

Massive stars

• Mass greater than 8 M

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O type star

Early B type stars

• More massive stars are larger in radius
• More massive stars have shorter lifetimes

• Mass is fundamental in stellar evolution

Radiative envelope

Convective core

Multiplicity of massive stars

• Massive stars are mostly born in binaries (Sana+2012,2013)

• Almost all O stars will interact during their lifetime (Moe+2017)

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Fraction of interacting binaries

Sana+2012

Moe+2017

Mass M₁ (M )

What is the need?

• Progenitors of gravitational wave sources (Abbott+2016,2019).
• “Rapid binary evolution” predictions inaccurate (Laplace+2020,2021).
• Constrain “mass transfer efficiency” (Langer+2003, de Mink+2007).
• Source of ionising radiation and mechanical feedback (Maclow+2004).

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Kruckow+2018

Close binary evolution

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M₁ = 20 M M₂ = 12 M

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P_orb = 3 d

Images credit: Philip D. Hall - CC BY-SA 4.0

M₁ = 20 M M₂ = 12 M

M₁ = 20 M M₂ = 12 M

M₁ = 16 M M₂ = 16 M

M₁ = 8 M M₂ = 24 M

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Algol binaries and the Algol paradox

• Algol or 𝜷-Persei, is a star system that shows periodic variations in brightness

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• The Algol paradox: Less massive star is more evolved than its companion
• Resolution: Close binary evolution (Pustylnik+1998)

Credit: SpaceEngine

M₁ = 0.7 M , R₁ = 3.48 R

M₂ = 3.2 M , R₂ = 2.73 R P_orb = 2.87 days

Wind-fed black hole high-mass X-ray binaries

• Cygnus X-1: first ever black hole observed

• Maximally spinning, only one in our Galaxy

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collapse

Stripped star

M_BH = 21.2 M

M_O = 40.6 M

Credit: NASA

Kruckow+2018

Binary evolution modelling

• 1D stellar evolution code
• Individual binary components are evolved simultaneously
• Details of mass transfer is calculated at each timestep
• Essential for studying interacting binaries

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Detailed binary evolution with MESA (Paxton+2011,13,15,18,19)

PART I: MASSIVE ALGOL BINARIES

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Algol binaries: Context

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M_d = 8.7 M

M_a = 16.3 M

9.0

10.0

11.0

12.0

t [Myr]

Observations

Models

• Milky Way (~100 Algols): Surkova+2004, Budding+2004, Papageorgiou+2018, Malkov+2020
• SMC (~40 Algols): Harries+2003, Hilditch+2005
• LMC (7 Algols): Ostrov+2000,2002, Mahy+2020a,b

• Milky Way: Pols+1994, Nelson+2001, Mennekens+2017, Negu+2018
• SMC: de Mink+2007
• LMC:

No comprehensive binary population synthesis study of massive Algol binaries

Sen+2022A&A...659A..98S

long mass transfer phase

Algol binaries: Method

• 10,000 detailed binary evolution models (MESA, Marchant2016)
• M_d,i = 10 – 40 M_Sun, q_i (M_a,i/M_d,i) = 0.275 – 0.975, P_i >= 1.4 d
• Population synthesis of massive Algol binaries in the LMC
• Constant star formation and empirical binary distribution functions
• Compare with observed massive Algols in the LMC and Milky Way

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Mass transfer efficiency

Ꞷ_crit = (GM/R³)^0.5

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M, R, I, Ꞷ_i

ΔM?

ΔJ = (GMR)^0.5 ΔM

ΔM/M = 𝒇 (r_g², Ꞷ_i/Ꞷ_crit)

IꞶ

ΔM/M = 0.00-0.10 (Packet+1981)

I = r_g² MR²

In binaries, there are tidal forces!

Algol binaries: Results

• Models predict high mass transfer efficiency at P_orb < 5 days and vice versa

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Sen+2022A&A...659A..98S

• Evidence of efficient mass transfer in short orbital period massive Algols

Algol binaries: Takeaways from Part I

• Mass transfer is efficient at short orbital periods.
• Spin-dependent accretion can produce an orbital period dependent mass transfer efficiency.
• Around 90 O-type and early B-type Algol binaries in the LMC.

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PART II: WIND-FED BLACK HOLE HIGH-MASS X-RAY BINARIES (HMXBs)

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BH high-mass X-ray binaries: Context

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• Average lifetime of stripped+O star phase (0.4 Myrs) < BH+O star phase.
• BH-BH merger rates (Mennekens+2014; Belczynski+2016)

Stripped star

collapse

Kruckow+2018

BH high-mass X-ray binaries: Method

• Observed sample of 18 stripped+O star binaries (Vanbeveren+2020).
• Assume the stripped stars collapse to form BHs without recoil.
• Follow the O star evolution using stellar models (Ekstrom+2012).
• When will a BH+O binary be observable as an wind-fed High Mass X-Ray binary?

A. Formation of an accretion disk

B. X-Ray flux above detection threshold

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Formation of an accretion disk

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R_O

R_acc

Matter is accreted from the stellar wind (v_wind) of the O star

Accretion radius of the compact object (Davidson+1973)

Specific angular momentum (j) of the accreted matter (Shapiro+1976)

figure not to scale

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Formation of an accretion disk

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• This accreted matter can go in a Keplerian orbit of radius R_disk with �velocity v_disk = j/R_disk

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Equating centrifugal force to gravitational force, R_disk = j² / GM_BH

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Formation of an accretion disk

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• This accreted matter can go in a Keplerian orbit of radius R_disk with velocity v_disk = j/R_disk

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Equating centrifugal force to gravitational force, R_disk = j² / GM_BH

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• An accretion disk can form when: R_disk > R_ISCO where R_ISCO = 6GM_BHƔ/c²

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[ 𝛾_± = ⅙, 1, 3/2 ]

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X-Ray luminosity (L_X)

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-- mass accretion rate (Davidson & Ostriker 1973)

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-- X-ray luminosity (Frank+2002, El Mellah 2017)

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-- The L_x > 10³⁵ erg s^-1 to be observable (Wood+1984, Bradt+1991)

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BH high-mass X-ray binaries: Results

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Black hole spin

Sen+2021A&A...652A.138S

For Cygnus X-1

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M_{O star} = 40.6 M , M_BH = 21.2 M

Orbital period = 5.9 days

Non-rotating BH: R_disk / R_ISCO = 0.20

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Maximally rotating: R_disk / R_ISCO = 1.23

BH high-mass X-ray binaries: Takeaways

• BH+O star binaries are X-ray silent for most of their lifetime.
• Bias towards observing maximally rotating BHs.
• Recoil velocity not necessary to explain number discrepancy.

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Outlook

• A large spectroscopic survey of massive Algol binaries in the MCs and Milky Way will provide more constraints on binary evolution.
• Large population of X-ray quiet BH+O star binaries still to be discovered (Langer+2020, Shenar+2022, Mahy+2022).

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THANK YOU

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