Probing Core Collapsewith Binaries
Vicky Kalogera	

Northwestern U.

Key Questions!

Can We Constrain the SN mechanism ?
What is the Origin of SN kicks ?
Do Black Holes Receive Kicks ?

Key Questions!

Can We Constrain the SN mechanism ?
What is the Origin of SN kicks ?
Do Black Holes Receive Kicks ?
Progenitor Mass at SN ?
SN Kick Magnitude ?

Double Neutron Stars

Double Neutron Stars

Progenitor Mass at SN

Since
arecorrelated,
wepresent
ourresu
Since thethe V
Vkickand M
M2i
constraints areare correlated,correlated, we
we present
present ourourresul
resu
kick and2i constraints
Since
theVandM
constraints
kick
2iinplotsof
22 dimensional
dimensional
joint-Min thethe form
form ofof confidence
confidence level
level plots
plots ofof 2
dimensional joint
joint VV
Vkick
-M
kick
kick-Mintheform
ofconfidence
level
PDF,
1.
The
derivedconfidence
levelsofPDF, which
which areare shown
shown inin Figure
Figure 1.
1. TheThe derived
derived confidence
confidence levels
levels ofofVV
Vkk
PDF,
which
areshowninFigure
andand M
M2i
are listed
listed inin Table
Table 3.
3.
2i areandM
arelistedinTable
3.
Wong et al 2010
2i

SN Kick Magnitudedimensional joint
joint VVkick-M2iprobability distribution
distributionfunction
functionof
ofthe
the8
observedGalactic
GalacticDNS.
DNS.Red,Red,yellow,yellow,andandblue
blu
Figurethe88observed
observed
Galactic
DNS.
Red,yellow,and
blu
Figure 1:
1: 22 dimensional
dimensionaljoint
2i probability
kick-M2ikick
represent confidence
confidence level
level ofof 60%,60%, 90%,90%, andand 95%.
95%.
represent
represent
confidence
SystemSystemSystem60 %% confidence
confidence
6095
95%%%confidence
confidence95
confidenceTauris & van den Heuvel 2004

NS-NS	

Formation	

ChannelTauris & van den Heuvel 2004

NS-NS	

Formation	

ChannelHe star
1st NS(just before SN)
Step 2(2nd SN)
Step 1(present time)

2nd NS

Step 1:
Step 2:
Step 3:

Step 3

L

Step 1

Step 2

Step 3kick

NS1
He Star

Observational Constraints:
NS Masses, current A and e, PSR age
Spin-Orbit Tilt Angle ( for B193, B1534, J0737 only )Sky Location, Distance, Proper Motion

(Wong et al. 2010)

red = 60%
yellow = 90%
blue = 95%

VMVM

(Wong et al. 2010)

red = 60%
yellow = 90%
blue = 95%

VM

VM

NS2 formed in an Fe core collapse supernova

(Wong et al. 2010)

red = 60%
yellow = 90%
blue = 95%

VM

(Wong et al. 2010)

red = 60%
yellow = 90%
blue = 95%

VM

NS2 (pulsar B) formed in anelectron capture supernova

red = 60%
yellow = 90%
blue = 95%

ECS?

red = 60%
yellow = 90%
blue = 95%

ECS?

Fe-core?

red = 60%
yellow = 90%
blue = 95%

ECS?

Fe-core?
Fe-core?

red = 60%
yellow = 90%
blue = 95%

ECS?

Fe-core?
Fe-core?

ECS?

red = 60%
yellow = 90%
blue = 95%

red = 60%
yellow = 90%
blue = 95%

ECS?

Fe-core?
Fe-core?

ECS?

???

red = 60%
yellow = 90%
blue = 95%

ECS?
e=0.25e=0.2
Fe-core?
Fe-core?

ECS?

???
e=0.09e=0.83e=0.14

MSHeCore
Collapse

MSMS

Black
Hole

High mass X-ray Binary(Wind-fed)MS

Low mass X-ray Binary(Roche lobe overflow)!10MSHeCore
Collapse

MSMS

BlackHoleHigh mass X-ray Binary(Wind-fed)MS

Low mass X-ray Binary(Roche lobe overflow)

Step 1:
Step 2:
Step 3:
Step 4:!10

MSHeCore
CollapseMSMS

Black
HoleHigh mass X-ray Binary(Wind-fed)MS

Low mass X-ray Binary(Roche lobe overflow)

Observational Constraints:
BH companion L, Teff, and Mass
BH Mass, Orbital Period
Proper Motion, Radial Velocity
Sky Location, Distance!11

M33 X-7
IC 10 X-1

(from Orosz/Bailyn)

BH XRB Results(Willems et al. 2005)(Fragos et al. 2009)12

GRO J1655-40

XTE J1118+480

18161014812610846050100150200250

Understanding Compact Object formation. IV.

(Wong et al. 2013)

IC10 X-1
F IG . 9.— Two dimensional joint Vk –MBH pro confidence levels: 68.3%(red), 95.4% (yellow), and 99.7% (blue).

100150200250300
11ciency (Webbink 1984) can explain physically the post-CE
binary properties of the IC 10 X-1 progenitor. Finally, we
perform a Monte Carlo simulation on the orbital dynamics involved in the core collapse event. Each data point contains
seven free parameters drawn from uniform and isotropic dis(Wonget al. 2012)tributions, which describe the properties of the pre-SNbinary
and the natal kick imparted to the BH. Besides the constraints
related to the core collapse event, we also use what we learned
about the CE event involved in the formation of IC 10 X-1
as additional constraints to reject data points. If a data point
satisfies all the constraints mentioned in §6, such as the survival of the binary through the core collapse event and thecommon envelope efficiency αCE being ≤ 1, we classify it asa successful data point. Our constraints (at 95.4% of confiCygdence) related to the BH formation andthe CE event occurredin the past of IC 10 X-1 are derived from all successful data
X-1(He rich) progenitor
points. We find that the BH immediate
has a mass of 45.6+14.4−14.0 M⊙ and constrain the magnitude of thenatal kick imparted to the BH to be ≤ 128 km/s.
We also find that the existence of IC 10 X-1 gives verystrong constraints on the physics of CE evolution. It is theBH XRB Results
Observed Current
BH mass(M⊙)

Post-SNBH mass(M⊙)

Immediate
Progenitor mass(M⊙)

Natal Kick(km/s)

GRO J1655-40

6.3 ± 0.5

5.5 − 6.3

5.5 − 11.0

30 − 160(Greene et al. 2001)(early-type, P>1d)5.4 ± 0.3

3.5 − 5.4

3.5 − 9.0

≤ 210

SystemXTE J1118+480(late-type, P<1d)(Beer & Podsiadlowski 2002)

8.0 ± 2.0
(McClintock et al. 2001, Wagneret al. 2001, Gelino et al. 2006)

13.5 − 20.0

M33 X-7(Willems et al. 2005)(Willems et al. 2005)(Willems et al. 2005)

6.0 − 10.0

6.5 − 20.0

80 − 310(Fragos et al. 2009)(Fragos et al. 2009)(Fragos et al. 2009)13.5 − 14.5

15.0 − 16.1

10 − 850(wind-fed, H-rich)(Orosz et al. 2007,
Valsecchi et al.2010)(Valsecchi et al.2010)(Valsecchi et al.2010)(Valsecchi et al.2010)

Cygnus X-1

14.81 ± 0.98

13.8 − 15.8

15.0 − 20.0

≤ 77

(wind-fed, H-rich)(Orosz et al. 2011)(Wong et al. 2012)(Wong et al. 2012)(Wong et al. 2012)

IC 10 X-1

25 — 39

25 — 3932 − 60≤ 130(wind-fed, He-rich)(Wong et al. 2013)(Wong et al. 2013)(Wong et al. 2013)(Wong et al. 2013)

Some BHs must have received	

a kick at formation

Probing the Kick Mechanism?
What do BH Kick Magnitudes Correlate with? 	

BH mass? 	

He-star mass?	

mass loss at core collapse? (absolute/fractional?)	

!

What is the underlying shape of the global correlation?	

!

Can we probe the kick mechanism?

Probing the Kick Mechanism?
What do BH Kick Magnitudes Correlate with? 	

BH mass? 	

He-star mass?	

mass loss at core collapse? (absolute/fractional?)yr(Farr et al. 2013)
ani
bestf(MHe): 	miler!
pMaxwellian kick	distribution with:	

!

<Vk> ~ 1/MHe

Probing the Kick Mechanism?
What do BH Kick Magnitudes Correlate with? 	

BH mass? 	

He-star mass?	

mass loss at core collapse? (absolute/fractional?)yr(Farr et al. 2013)
ani
best
f(MHe): 	

miler!
pMaxwellian kick	

distribution with:	!

<Vk> ~ 1/MHe

The Double Pulsar

The Double Pulsar
The Astrophysical Journal, 742:81 (5pp), 2011 December 1Farr et al. 2011(a)

Farr e(b)(c)

Figure 1. Effect of SN kick on binary orbit. The pre-SN orbit containing pulsar A and pulsar B’s progenitor is shown in (a). The effect of an on-center SN kickslightly changes the inclination of the orbit is illustrated in (b). Note the post-SN alignment of the two pulsars’ spin axes. Part (c) illustrates the present-day orbit
a 130 deg misalignment between pulsar B’s spin axis and the orbital axis.
(A color version of this figure is available in the online journal.)

If kick imparts only 	

linearmomentum:	

orbital plane causesa change inthe eccentricity and semimajor
is the spin colatitude), but not the azimuthal orientation. T
axis of the orbit; the component perpendicular to the pre-SN
the colatitude of S relative to the normal to the current orAa andBtheshould
be closely
orbital plane canPSRs
also causechange ininclination ofplane is equal aligned
to the colatitude of the current spin—130
SN

the orbital plane. In the PSR J0737−3039 system, pulsar A’s
small spin-tilt angle (less than 14 deg at 95% confidence using
a two-pole emission model; Burgay et al. 2003; Lyne et al.
2004; Ferdman et al. 2008) is indicative of a relatively small
out-of-plane kick from the SN that formed pulsar B (Wonget al. 2010). Pulsar A’s spin-orbit misalignment occurs only
because the orbital plane is tilted by the SN kick, while pulsar
A’s spin remains fixed in the inertial frame aligned with thepre-SN orbital angular momentum axis (Figure 1). Such a spin

Based on the spin of pulsar A, the current orbital plane cbe tilted at most 14 deg relative to the pre-SN orbital pl
Therefore, the colatitude of SSN relative to the pre-SN orplane—and therefore relative to S0 —is at least 116 deg.
is also the minimum angle between S0 and !S. The ang
momentum produced by the SN must be significantly misalig
with the progenitor spin. To date, most SN simulations hfocused on non-rotating progenitors (for example, see Blo& Mezzacappa 2007; Rantsiou et al. 2011; Wongwathan

The Double Pulsar
The Astrophysical Journal, 742:81 (5pp), 2011 December 1Farr et al. 2011(a)Farr e(b)(c)

Figure 1. Effect of SN kick on binary orbit. The pre-SN orbit containing pulsar A and pulsar B’s progenitor is shown in (a). The effect of an on-center SN kickslightly changes the inclination of the orbit is illustrated in (b). Note the post-SN alignment of the two pulsars’ spin axes. Part (c) illustrates the present-day orbit
a 130 deg misalignment between pulsar B’s spin axis and the orbital axis.
(A color version of this figure is available in the online journal.)

Spin-Orbit Tilts Measured:	!

orbital plane causes a change in the eccentricity and semimajor
is the spin colatitude), but not the azimuthal orientation. Taxis of the orbit; the component perpendicularto the(Ferdmanet pre-SNal. 2008) the colatitude of SSN relative to the normal to the current ororbital plane can also cause a change in the inclination ofplane is equal to the colatitude of the current spin—130
the orbital plane. In the PSR J0737−3039 system, (Lyutikov
pulsar A’s & Thompson
Based on thespin Bretonof pulsar etA, al.
the2008)
current orbital plane c2005;
small spin-tilt angle (less than 14 deg at 95% confidence using
be tilted at most 14 deg relative to the pre-SN orbital pla two-pole emission model; Burgay et al. 2003; Lyne et al.
Therefore, the colatitude of SSN relative to the pre-SN or2004; Ferdman et al. 2008) is indicative of a relatively small
plane—and therefore relative to S0 —is at least 116 deg.
out-of-plane kick from the SN that formed pulsar B (Wongis also the minimum angle between S0 and !S. The anget al. 2010). Pulsar A’s spin-orbit misalignment occurs only
momentum produced by the SN must be significantly misalig
because the orbital plane is tilted by the SN kick, while pulsar
with the progenitor spin. To date, most SN simulations hA’s spin remains fixed in the inertial frame aligned with thefocused on non-rotating progenitors (for example, see Blo
pre-SN orbital angular momentum axis (Figure 1). Such a spin& Mezzacappa 2007; Rantsiou et al. 2011; Wongwathan

PSR A: < 14 deg
PSR B: 130 +- 1.3 deg	The Double Pulsar
The Astrophysical Journal, 742:81 (5pp), 2011 December 1

Farr et al. 2011
(a)

(b)

Farr e(c)Figure 1. Effect of SN kick on binary orbit. The pre-SN orbit containing pulsar A and pulsar B’s progenitor is shown in (a). The effect of an on-center SN kickslightly changes the inclination of the orbit is illustrated in (b). Note the post-SN alignment of the two pulsars’ spin axes. Part (c) illustrates the present-day orbit
a 130 deg misalignment between pulsar B’s spin axis and the orbital axis.
(A color version of this figure is available in the online journal.)

Spin-spin misalignment: 	

!

orbital plane causes a change in the eccentricity and semimajor
axis of the orbit; the component perpendicular to the pre-SN
orbital plane can also cause a change in the inclination ofthe orbital plane. In the PSR J0737−3039 system, pulsar A’s
small spin-tilt angle (less than 14 deg at 95% confidence using
a two-pole emission model; Burgay et al. 2003; Lyne et al.
2004; Ferdman et al. 2008) is indicative of a relatively small
out-of-plane kick from the SN that formed pulsar B (Wonget al. 2010). Pulsar A’s spin-orbit misalignment occurs only
because the orbital plane is tilted by the SN kick, while pulsar
A’s spin remains fixed in the inertial frame aligned with thepre-SN orbital angular momentum axis (Figure 1). Such a spinis the spin colatitude), but not the azimuthal orientation. T
the colatitude of SSN relative to the normal to the current orplane is equal to the colatitude of the current spin—130
Based on the spin of pulsar A, the current orbital plane cbe tilted at most 14 deg relative to the pre-SN orbital pl
Therefore, the colatitude of SSN relative to the pre-SN orplane—and therefore relative to S0 —is at least 116 deg.
is also the minimum angle between S0 and !S. The ang
momentum produced by the SN must be significantly misalig
with the progenitor spin. To date, most SN simulations hfocused on non-rotating progenitors (for example, see Blo& Mezzacappa 2007; Rantsiou et al. 2011; Wongwathan

requires AM production during SN collapse	

if spin & kick linked physically, 	

an off-center `bulk’ kick is required too (~2-5km)

All Thanks to:Will Farr

Tassos Fragos

Francesca
Valsecchi

Kyle Kremer
Tsing-Wai
Wong

Bart Willems

1690

WONG, WILLEMS, & KALOGERA

Vol. 721

Table 1
Parameters of the Eight Known DNS in Our Galaxy
SystemαaδbDcµα dµδ eτc f

M1 g

M2 hAcur iecur jθt k

PSR B1534+12r1
PSR B1913+16r2
PSR J0737−3039r3
PSR J1518+4904r4
PSR J1756−2251r5

15 37 09.96
19 15 28.00
07 37 51.25
15 18 16.80
17 56 46.63

1.02
8.3(1.4)
1.15
0.625
2.5

250
110
210
20000
443

1.3332(10)1.4408(3)1.337(5)0.72+0.51−0.58
1.312(17)

0.274
0.617
0.08780.249
0.181

25(155) ± 3.818(162) ± 6<15l...
...

...

...

1830

40.7

0.828

...

PSR J1829+2456r7
PSR J1906+0746r818 29 34.60
19 06 48.67

...
...

...
...

12400
0.112

1.62+0.22−0.55

1.3452(10)1.3873(3)1.250(5)2.00+0.58−0.51
1.258+0.018−0.017

3.28
2.80
1.26
24.7
2.70

18 11 55.03

1.34(1)−3.27(35)−3.82(62)−0.67(4)−0.7(2)−25.05(2)−1.04(42)2.13(23)−8.53(4)...

PSR J1811−1736r6

11 55 55.55
16 06 27.40−30 39 40.71
49 04 34.25−22 51 59.40

1.36+0.50−0.17
1.248(18)

6.36
1.75

0.139
0.0853...
...

−17 36 37.70

24 56 19.00
07 46 28.60

6.0
1.2
5.4

1.14+0.28−0.48
1.365(18)

1.11+0.53−0.15

Notes.
a Right ascension (J2000.0) (hours, minutes, and seconds).
b Declination (J2000.0) (degrees, arcminutes, and arcseconds).
c Distance (kpc).
d Proper motion in R.A. (mas yr−1 ).
e Proper motion in decl. (mas yr−1 ).
f Characteristic age (Myr).
g Mass of 1st born NS (M ).
⊙h Mass of 2nd born NS (M ).
⊙i Current semimajor axis (R ).
⊙j Current orbital eccentricity.
k Misalignment angle between pulsar spin axis and post-supernova orbital angular momentum axis (degree). The number in parenthesis correspond to another possible
angle.
l Different data analysis model gives a different upper limit on this angle. See Section 3.3 for details.
r1 Wolszczan 1991; Arzoumanian et al. 1999; Stairs et al. 2002; Konacki et al. 2003; Stairs et al. 2004.
r2 Hulse & Taylor 1975; Taylor et al. 1976, 1979; Taylor & Weisberg 1982, 1989; Damour & Taylor 1991; Arzoumanian et al. 1999; Wex et al. 2000.
r3 Burgay et al. 2003; Lyne et al. 2004; Lorimer et al. 2007; Ferdman 2008; Ferdman et al. 2008; Breton 2008; Deller et al. 2009.
r4 Thorsett & Chakrabarty 1999; Janssen et al. 2008.
r5 Faulkner et al. 2005; Ferdman 2008.

Step 2: Orbital Dynamics at Core Collapse
Step 2• random magnitude and direction of natal kick	• map post-SN binary parameters to pre-SN parameters

using conservation of E
• constraints: 	a) survival of the binary	b) mass ratio between NS1 and immediate progenitor of NS2	c) spin—orbit misalignment angle (forLorbitLorbit
NS2kick

2nd SNNS1He StarNS1