Gas Accretion onto
Magnetized Neutron Stars
Ken OHSUGA
Outflow
accretion disk
Neutron star

Takahashi+ 2018

Neutron Stars (Ns) & Black Holes (BHs)
NS-a few Msun / 10km
-produced by supernovae
Stellar mass BH-about 10 Msun / 30km
-produced by supernovae
Supermassive BH-106-9 Msun
-located at the galactic center
Soria et al. 2012
-formation mechanism is unknown

High-energy phenomena
NSs/BHs are thought to be engine Cyg X-1of powerful compact objects

SS433

Soria et al. 2012

Ultra-luminous X-ray sources (ULXs)
ULX;-Very large X-ray luminosity(>>1039erg/s)-NOT located at the galactic center

Soria et al. 2012

Central object of ULX ?
NS-a few Msun / 10km
-produced by supernovae

Big difficulty

Stellar mass BH-about 10 Msun / 30km
-produced by supernovae
Supermassive BH-106-9 Msun
-located at the galactic center
Soria et al. 2012
-formation mechanism is unknown←NOULXs are offcenter X-raysources.

Accretion Power
Potential energy is converted toradiation energy（and jet energy)

GMPotential energyṀ !
L timeper unitrMṀ ! Lr

Radiation energy
per unit time(Luminosity)

Radiation

BH/NSEddington Luminosity
Gravity = Radiation force

Radiation
force

gas

Eddington luminosity✓◆✓ BH/NS◆
4⇡cGM m4⇡cGMmM
M
3838
LEdd ⇠= 10⇠ 10erg/s
erg/s
Msun
TT Msun-Gas accretion stops if luminosity is larger than Eddington luminosity
because of GRAVITY < RADIATION FORCE.
-Thus, the Eddington luminosity is the upper limit of the luminosity.

Neither stellar mass BH (~10Msun) nor NS (~Msun)cannot explain large luminosity of ULXs (>>1039erg/s)

Pulsed ULXs

0.5011–0–c
TOA residual (ms)0–0.5–1c5ΔF3025FPMAFPMB

0TOA residual (s)1008–009

007006b0040.15

Period – 1372.5 (ms)ChandraBachetti et al.14

0.2

ObsID 002

Counts per s per moduleb

a

0.25

0.1
Period – 1372.5 (ms)Central objects of Pulsed
ULXs are probably NSs !

a 0.3(%)

However, X-ray pulse isdetected in some ULXs.

–0–50–12

Inconsistency-Pulsed emission can be explained by NS.
-But NS is rejected if the Eddington luminosity isupper limit of the luminosity.
Summary-By performing numerical simulations, we reveal that
the NS luminosity can exceed the Eddington limit.
-Accretion onto magnetized NS can explain basic
features of ULXs.

Basic equations
We solve a full set of general relativistic radiationmagnetohydrodynamic equations
mass cons.

MHD

Gauss’s law
Induction eq.
energy momentum
cons. for MHD
energy momentum
cons. for radiation
RadiationNon-magnetized NS
100km

Powerfuloutﬂow

Density

RadiationenergyDisk luminosity largely
exceeds the Eddington
luminosity.

NSEddington luminosity isNOT upper limit!

Accretion
disk
Takahashi et al. 2018see also Ohsuga 2007

Why is super-Eddington feasible?
Mass density
Radiation Outflow

Radiation energy mainly
goes in the verticaldirection.
→Radiation force deos
not prevent disk accretion.

Ohsuga et al. 2009

Accretion
disk

Ohsuga & Mineshige 2011see also Ohsuga et al. 2005

~50Rs

4

Magnetorotational instability
水平方向への磁力線の引き伸ばし・真横から見た断面図= 左右 80 ミリ
× 天地 70 ミリ

円盤Black hole
磁力線の引き伸ばしAABブラックホール

Magneticﬁeld lines

B

Gravity

・真上から見た図
Angularmomentum

図ックル

Magnetic ﬁeld lines

DiskA

BAA

BA

B

Angular momentum transportinduced by magnetorotational
instability (MRI)
leads to massABaccretion
A B
Hawley & Balbus 1991
See also Velikhov 1959

B

Angularmomentum

Centrifugal forceMagnetized NS
densityradiationenergy計算ボックスradiationenergydensity

NS~1010G

Takahashi, Ohsuga 201750km

Sim. of Accretion column
mass density

Radiation energy

Sim. Boxsimulation box

NSKawashima et al. 2016NS

Model for ULX PulsarSUMMARY•

We performed general relativistic radiation
magnetohydrodynamics simulations of gas
accretion and outﬂow around NSs.

•Our simulation revealed that the luminosity canexceed the Eddington luminosity (superEddington ﬂow is feasible).

•The central objects of pulsed ULXs would besuper-Eddington ﬂows onto the magnetized NSs.