HE & VHE emissions
from rapidly rotating
black holes

Side view of BH
magnetosphereE||(r,q)

Kouichi HIROTANIASIAA, Taiwan,ICRR, U. of Tokyo

ICRR
Dec 16, 2016

§1 Introduction
So far, 77 X-ray binary BHs and BHCs have found in
MW & LMC.
BlackCAT (Corral-Santana + ’16, AA 587, A61)
WATCHDOG (Tetarenko + ’16, ApJS 222, 15)

In these BH X-ray binaries, material transfers from acompanion star onto the BH primary.
HMXBs 6 are fed by wind, 1 by Roche-lobe overflow
Companion: O-B stars (M>10Mʘ)LMXBs 45 are fed by Roche-lobe overflow.
Companion: K-M (M<Mʘ) or B-F (M~Mʘ)(Companion nature ofother 26 ’16
BHXBs are unknown.)
WATCHDOG

§1 Introduction
So far, 77 X-ray binary BHs and BHCs have found in
MW & LMC.
BlackCAT (Corral-Santana + ’16, AA 587, A61)
WATCHDOG (Tetarenko + ’16, ApJS 222, 15)

In these BH X-ray binaries, material transfers from acompanion star onto the BH primary.
HMXBs 6 are fed by wind, 1 by Roche-lobe overflow
Companion: O-B stars (M>10Mʘ)LMXBs 45 are fed by Roche-lobe overflow.
Companion: K-M (M<Mʘ) or B-F (M~Mʘ)(Companion nature of other 26 BHXBs are unknown.)§1 Introduction
The mass accretion rate 𝑀 near the compact object
determines their emission properties.
6 BH-HMXBs and 4 BH-LMXBs have 𝑀 >10-8 Mʘyr -1,
showing persistent X-ray emission with LX~LEdd.
Tanaka & Shibazaki 1996, ARA&A 34, 607

47 BH-LMXBs have much lower long-term accretionrate, 𝑀 <10-9 Mʘyr -1, showing transient X-ray emission:Sporadic outbursts after long-time quiescence.
Tanaka & Lewin 1995, in X-ray binaries, p. 126

Outburst recurrence period ranges 100-2 yrs.
WATCHDOT, BlackCAT§1 Introduction
For transient BH binaries, HE & VHE emissions areexpected in the shock-in-jet model.
Marscher & Gear 1985, ApJ 298, 114

HE/VHE flux increases w/ increasing 𝑀.
However, HE/VHE emissions are also predicted to beemitted in the BH-gap model from transient BHBs.
KH & Pu 2016, ApJ 818, 50; KH + 2016, ApJ in press

HE/VHE flux increases w/ decreasing 𝑀.
Today, we will focus on the BH-gap model and discuss its
theoretical predictions.

§1 Introduction
A quick review of the BH gap model:
Beskin et al. (1992, Sov. Astron., 36, 642) first proposed theBH gap model, extending the pulsar gap model(Cheng + 1986, ApJ 300, 500).

K.H. & Okamoto (1998, ApJ 497, 563) then showed thatsufficient plasmas can be supplied via g-g pair production
around super-massive BHs.
However, predicted g-ray fluxes were undetectable,
because they assumed high accretion rates (as in QSOs),
which leads to a very thin gap width (w«rg) along B lines,where rg=GMc-2.

§1 Introduction
A quick review of the BH gap model:
Thus, Neronov & Aharonian (2007, ApJ 671, 85) andLevinson & Rieger (2011, ApJ 730, 123) revisited the BH gap
model, adopting much thicker gap width (w~rg) andexamined M87* and Sgr A*.
Then Broderick & Tchekhovskoy (2015, ApJ 809, 97) showedthat two-stream instability does not grow in BH gaps.
Subsequently, KH & Pu (2016, ApJ 818, 50) showed thatSMBHs can emit detectable gap emission in VHE if
located within a few tens of Mpc.

§1 Introduction
Due to frame dragging, the GR Goldreich-Julian charge
density, rGJ, vanishes near the W=w surface (and hencein the direct vicinity of the horizon).
WF=0.3wH

KH & Pu (2016, ApJ 818, 50)

§1 Introduction
Around this null surface (rGJ =0), a stationary vacuum
gap (i.e., e± accelerator) arises.
Fig. Side view of a BH
gap. Copious HE/VHE
emissions are emitted
from the green shaded
region.

KH & Pu (2016, ApJ 818, 50)

§2 Method
Since the null surface appears near the horizon, thesame method as the pulsar outer-gap model can beapplied to the BH-gap model.
e’s are accelerated by E||Relativistic e+/e- emit g-rays via
synchro-curvature, and IC processes
g-rays collide with soft photons/B tomaterialize as pairs in the accelerator

§2 Method: Basic equations
Poisson eq.

From  E  4r , we obtain

Beskin + (1992)

 E||  4 ( r  r GJ ),where

: redshift factor

1
 WF  w
rGJ      ,   0 @ horizon
4  2 c  1 @ infinity
Bp  e  2,  : distance from rotation axis.

If r≠rGJ in any region, E||≠0 arises around it.

rGJ=0 near w=W F. Thus, pulsar-like ‘null charge surface’appears near the horizon. A vacuum gap can arise there.

§2 Method: Basic equations
KH+ (‘06, ApJ in press)

E|| is solved from the Poisson eq.
Near the horizon (   r 2  2 Mr  a 22

r a   2   r*222M 2 ), it becomes2(r  rg )(r 2  a 2 ) 2r*  sin q     (n  n  nGJ ) 22  sin q q   q   r  a 
2where E||  (B ) / B and   r  a cos q .
22

2

The tortoise coordinate r* is related to the polar r by
dr* r 2  a 2
dr

§2 Method: Basic equations
KH+ (‘06, ApJ in press)

Tortoise coordinate
vs. Boyer-Lindquistr coordinate
Horizon corresponds to r*=-∞.

The tortoise coordinate r* is related to the polar r by
dr* r 2  a 2dr§2 Method: Basic eqs.
Poisson eq.: r  a   2  2(r  rg )(r  a ) 
22r

r* *22222
  sin q     (n  n  nGJ ) 22  sin q q   q   r  a 2

Instead of solving the e± Boltzmann eqs., we assume that
the Lorentz factors are saturated by curvature- or IC-dragforces and put g  min(g curv , g ICS ) . Solve n+ & n- from thepair production, which is solved from the g-ray specificintensity, In at each point.

dIn
Radiative transfer eq.: n In  jndl§3 Results: the case of stellar-mass BHs
Consider a stellar-mass BH, M=10Mʘ, assuming B=Beq.

E||(r*,q)

KH+ (‘06, ApJ in press)§3 Results: stellar-mass BHs
M=10Mʘ, B=Beq.
Slice E||(r*,q ) at six q ’s.
0o15o

30o

37.5o 45o

52.5o

E||(r*,q)

KH+ (‘06, ApJ in press)§3 Results: stellar-mass BHs
M=10Mʘ, B=Beq Acceleration electric field along B
E||(r*,q ) at six q ’s.

E||(r*,q ) littledepends on qin polar region,q <38o.

KH+ (‘06, ApJ in press)§3 Results: stellar-mass BHs
M=10Mʘ, B=Beq

g-ray spectra

SED little changes
in q <38o.
To estimate themaximum flux,
we adopt q =0o.

KH+ (‘06, ApJ in press)§3 Results: stellar-mass BHs
M=10Mʘ, B=Beq; Lepton densities per B flux @ q =0o

Electron density,2 cen  N
WF B

Positron density,2 cen  N
WF B

KH+ (‘06, ApJ in press)§3 Results: stellar-mass BHs
M=10Mʘ, B=Beq; E||(r-r0,q ) @ q =0om=10-3.5m=10-4m=7.49×10-5

E||(r*,q0) @ m=5.62×10-5

KH+ (‘06, ApJ in press)§3 Results: stellar-mass BHs
M=10Mʘ, B=Beq; outer & inner boundaries @ q =0o
Gap width increases with decreasing accretion rate.

WidthKH+ (‘06, ApJ in press)§3 Results: stellar-mass BHs
M=10Mʘ, B=Beq; SED vs. current density, j (q =0).
j~0.7 optimizes HE & VHE fluxes.
0.50.6Conserved current density,0.7 j  n  n   2 ce ( N  N )
0.8



WF B



j=0.9

j=0.4

KH+ (‘06, ApJ in press)§3 Results: stellar-mass BHs
M=10Mʘ, B=Beq; SEDs @ five discrete m (q =0o)m=10-3
W F= 0.5wH

10-3.510-4
10-4.25
10-4.125
KH+ (‘06, ApJ in press)§3 Results: stellar-mass BHs
M=10Mʘ, B=Beq; SEDs @ five discrete m (q =0o)

HE flux is detectable
if -3
m=10d<severalkpc
W F= 0.5wH and5.7 105  M / M Edd  10410-3.5
10-410-4.25
10-4.125
KH+ (‘06, ApJ in press)§3 Results: stellar-mass BHs
M=10Mʘ, B=Beq; Emission components (q =0o)

W F= 0.5wHPrimary
curvature
SecondaryIC+sync.
Tertiary
IC+sync.

PrimaryIC

KH+ (‘06, ApJ in press)§4 Detectability of BH transients
We can approximately estimate Lgap by the BlandfordZnajek flux, FBZ=LBZ/4d 2 at Earth.
Four greatest FBZ BHTs (descending order):mass distance obs. 𝑀 Comments*Mʘ kpc
𝑀Edd
1A 0620-006.60 1.06 2.08×10-3 L, T, V616 Mon
4U 1956+350 14.81 1.86
H, P, Cyg X-1
XTE J1118+480 7.30 1.72 4.96×10-4 L, T, KV UMa
GS 2023+338
7.15 2.39 .017-.224 L, T, V404 Cyg
Name* Low-mass/High-mass companion, Transient/Persistent

We exclude Cyg X-1, because M

104 M Edd .

§4 Detectability of BH transients
Although the observed 𝑀 exceeds 10 -4 for all the 3 BHTs,
there may be a certain fraction of time in which

5.7 105  M / M Edd  104 is satisfied.
mass distance obs. 𝑀 Comments*Mʘ kpc
𝑀Edd
1A 0620-00
6.60 1.06 2.08×10-3 L, T, V616 Mon
4U 1956+350 14.81 1.86
H, P, Cyg X-1
XTE J1118+480 7.30 1.72 4.96×10-4 L, T, KV UMa
GS 2023+338
7.15 2.39 .017-.224 L, T, V404 Cyg
Name* Low-mass/High-mass companion, Transient/Persistent

We thus examine these three BH LMXBs w/ greatest FBZ.

§4 Detectability of BH transients
J0620-0020: LAT 7-yr averaged flux appears below thetheoretical prediction.
Obs. acc.
rate (19171975):𝑚~0.002.

m=10-310-3.510-4

10-4.25

Duty cycle ofgap activation
6×10-5< 𝑚 <10-4
is very small(«1).
10-4.125

Lin + (’16),
in prep.

§4 Detectability of BH transients
J1118+4802: LAT 7-yr averaged flux also appears below
prediction.
Obs. acc.
rate (19982015):
𝑚~ 5×10-4.

m=10-310-3.510-4

10-4.25

Duty cycle ofgap activation
6×10-5< 𝑚 <10-4
is very small(«1).
10-4.125

Lin + (’16),
in prep.

§4 Detectability of BH transients
V404 Cyg: LAT 7-yr averaged flux appear slightly below
prediction.
Obs. acc.
rate (19952005):
𝑚 > 0.02.

m=10-310-3.510-4

10-4.25

Duty cycle ofgap activation
6×10-5< 𝑚 <10-4is at least
moderately
small (<1).
-4.125
10Lin + (’16),
in prep.

Summary on BH gap modelBH gap emits copious HE/VHE g-rays, if mass accretion
resides rate is 104  M / M Edd  5.7 105 near the horizon.
For stellar-mass BHs, e±’s are accelerated in the gap andsaturate @ g~107 by curvature-radiation drag forces.
For stellar-mass BHs, curvature photons appear at ~GeV
and are detectable w/ Fermi/LAT, and IC photons appear at3-30 TeV and are detectable w/ CTA, both during quiescent.
We can discriminate gap vs. jet emissions by anticorrelation vs. correlations at IR/opt & HE/VHE. Thus, we
propose to observe BHTs, J0620-0020, GRO J1655-40,
V404 Cyg, J1118+4802, at IR/opt & VHE simultaneously.
The same method can be applied to arbitrary BH masses,e.g., IMBHs and SMBHs.