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ACKNOWLEDGMENTS
We thank J. Cheng, X. Guo, and L. Jiao for helpful discussions.
Funding:This work is supported by the Natural Science
Foundation of China (91956000, 22031006, and 21861132003),
Tsinghua University Initiative Scientific Research Program,
and Haihe Laboratory of Sustainable Chemical Transformations.
We thank the Tsinghua Xuetang Talents Program for
computational support. L.Z. is supported by the National
Program of Top-notch Young Professionals.Author contributions:
S.L. conceived and directed the project. M.H. conducted the
experiments, with the help of T.P.; L.Z. performed the
computational studies. M.H. and S.L. wrote the manuscript, with
contributions from all authors.Competing interests:The authors
declare that they have no competing interests.Data andmaterials availability:All data are available in the main text or the
supplementary materials.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.abl4922
Materials and Methods
Supplementary Text
Figs. S1 to S33
Tables S1 to S7
References ( 28 – 52 )16 July 2021; resubmitted 4 November 2021
Accepted 25 January 2022
10.1126/science.abl4922BLACK HOLES
Black hole spinÐorbit misalignment in the x-ray
binary MAXI J1820+070
Juri Poutanen1,2,3*, Alexandra Veledina1,3,2, Andrei V. Berdyugin^1 , Svetlana V. Berdyugina^4 ,
Helen Jermak^5 , Peter G. Jonker6,7, Jari J. E. Kajava1,8, Ilia A. Kosenkov^1 , Vadim Kravtsov^1 ,
Vilppu Piirola^1 , Manisha Shrestha5,9, Manuel A. Perez Torres10,11, Sergey S. Tsygankov1,2
The observational signatures of black holes in x-ray binary systems depend on their masses, spins,
accretion rate, and the misalignment angle between the black hole spin and the orbital angular momentum.
We present optical polarimetric observations of the black hole x-ray binary MAXI J1820+070, from
which we constrain the position angle of the binary orbital. Combining this with previous determinations
of the relativistic jet orientation, which traces the black hole spin, and the inclination of the orbit, we
determine a lower limit of 40° on the spin-orbit misalignment angle. The misalignment must originate
from either the binary evolution or black hole formation stages. If other x-ray binaries have similarly large
misalignments, these would bias measurements of black hole masses and spins from x-ray observations.
B
lack holes can be characterized with just
two parameters: mass and spin. When
a black hole resides in a binary system,
accreting material from a companion
donor star through the accretion disk,
there are additional parameters that deter-
mine its observational signatures: the mass
accretionrateandthemisalignmentangle
between the black hole spin and the orbital
axis. Standard methods to measure black hole
spin from x-ray observations—iron line spec-
troscopy ( 1 ) or modeling of the accretion disk
spectrum ( 2 )—assume that the misalignment
angle is small. Conversely, the standard inter-
pretation of low-frequency quasi-periodic os-
cillations in x-ray and optical observations of
black hole x-ray binaries as precession of the
accretion disk ( 3 – 5 ) requires the assumption
that the misalignment angle is non-negligible.
Substantial misalignment is theoretically pre-
dicted for x-ray binaries that received high ve-
locities during formation ( 6 ). The misalignment
angle must be inherited from the formation
process, because it can only decrease when
the black hole is accreting ( 7 ). Gravitational
wave observations of merging black holes
have detected signatures of orbital preces-
sion ( 8 ), indicating nonzero misalignment in
these systems ( 9 ), though they might not be
representative of the wider population.
Measuring the misalignment angle in x-ray
binaries requires determining the three-
dimensional orientation of the black hole spin
and orbital axis. Accreting black holes often
show relativistic jets, which are launched along
an axis determined by the black hole spin di-
rection ( 10 ). The jet inclination angle can be
directly obtained in some cases from radio
observations ( 11 ), whereas the jet position
angle can be measured using either radio or
x-ray imaging. Combining these two angles
allows the black hole spin orientation to be
determined. Orbital parameters such as period
and orbital inclination can be determinedusing spectroscopic measurements of radial
velocities of the donor star taken during qui-
escence, the stage at which accretion to the
black hole is reduced and optical emission is
not dominated by the accretion disk, through
orbital modulation of the optical photometry
and using constraints from the presence or
absence of x-ray and optical disk eclipses ( 12 ).
Theblackholex-raybinaryMAXIJ1820+070
was discovered as a transient x-ray source on
11 March 2018 ( 13 ). X-ray quasi-periodic os-
cillations detected shortly after this discovery
were observed for >100 days ( 14 ). Ejections of
material traveling at relativistic velocities have
been observed from this source in both radio
and x-rays, indicating that the jet inclination
(measured from the line of sight) isijet¼
63°T3° and the position angle (measured on
the plane of the sky from north to east) is
qjet¼ 25 :° 1 T 1 :°4( 15 – 17 ). Both angles were
determined to be stable over the observed874 25 FEBRUARY 2022•VOL 375 ISSUE 6583 science.orgSCIENCE
(^1) Department of Physics and Astronomy, FI-20014 University
of Turku, Finland.^2 Space Research Institute (IKI) of
the Russian Academy of Sciences, 117997 Moscow, Russia.
(^3) Nordic Institute for Theoretical Physics (Nordita), KTH
Royal Institute of Technology and Stockholm University,
SE-10691 Stockholm, Sweden.^4 Leibniz-Institut für
Sonnenphysik, 79104 Freiburg, Germany.^5 Astrophysics
Research Institute, Liverpool John Moores University, L3 5RF
Liverpool, UK.^6 Department of Astrophysics, Institute for
Mathematics, Astrophysics and Particle Physics (IMAPP),
Radboud University, NL-6500 GL Nijmegen, Netherlands.
(^7) Space Research Organisation of the Netherlands (SRON),
Netherlands Institute for Space Research, NL-2333, CA
Leiden, Netherlands.^8 Centro de Astrobiología, Villanueva de
la Cañada, S-28692 Madrid, Spain.^9 Department of Physics
and Astronomy, University of Denver, Denver, CO 80208,
USA.^10 Instituto de Astrofísica de Canarias, E-38205
La Laguna, Tenerife, Spain.^11 Departamento de Astrofísica,
Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain.
*Corresponding author. Email: [email protected]
0
1
2
3
4
5
6
PD (%)
A
0.0 0.2 0.4 0.6 0.8 1.0
Phase
-40
-30
-20
-10
0
10
PA (deg)
B
Fig. 1. Observed optical polarization properties of
MAXI J1820+070.(A) Intrinsic PD and (B)PAof
MAXI J1820+070 during quiescence are shown as a
function of orbital phase (using a published ephemeris)
( 23 ). The intrinsic values were obtained from the
observed ones by subtracting the foreground interstellar
polarization, which is measured from nearby field stars.
Blue circles, green triangles, and red squares correspond
to the B, V, and R bands, respectively, with error bars
showing the 68% confidence levels. Polarization is
strongest in the B band and weakest in the R band,
although the angle does not change substantially.
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