Tracking X-ray Spectral Modulations of a
6-Hz Type-B Quasi-periodic Oscillation in
GX 339-4 using Hilbert-Huang Transform
Yi-Hao Su 1 , Christopher Reynolds 2 , Yi Chou
1 Institute
1
of Astronomy, National Central University, Taiwan
of Astronomy, University of Maryland, USA
[email protected]
2 Department
Shining from the heart of darkness: black hole accretion and jets
@Kathmandu, Nepal
October 18, 2016
Quasi-periodic Oscillations (QPOs) in GX 339-4
(Motta et al. 2011)
(Motta et al. 2011)
Phase-resolved Spectroscopy
6-Hz type-B QPO in GX 339-4
10 2
Leahy Power
Phase
Phase segments
10 1
Phase-resolved spectra
10 0 -1
10
10 0
Frequency (Hz)
10 1
First Step of Hilbert-Huang Transform (HHT)
Huang et al. (1998); non-stationary and non-linear signals
First step of HHT: Empirical mode decomposition (EMD)
Intrinsic mode functions (IMFs)
Data
9
3
c1 :c2
2
c3
(b)
0
−2
1
c4 :residual
(a)
6
(c)
0
−1
6.8 (d)
5.8
4.8
320
322
324
Time (s)
326
328
330
Second Step of Hilbert-Huang Transform (HHT)
Y3 (t) =
R∞
1000 (a)
0
−1000
1000 (b)
500
0
1.0
Frequency (Hz) Phase (2π)
Amplitude
c3
X3 (t) +
ν3 (t) =
X3 (t 0 )
dt 0 ← Hilbert transform
−∞ t−t 0
iY3 (t) = a3 (t)e iθ3 (t) ← Instantaneous amplitude
1 dθ3 (t)
← Instantaneous frequency
2π dt
1
P
π
(c)
0.5
0.0
12
(d)
6
0
320
322
324
Time (s)
326
328
330
& phase
HHT-based Timing Properties
1
0.8
1
0.5
Autocorrelation
Autocorrelation function of the
IMF c3
0
-0.5
0.6
Autocorrelation
0.4
-1
0.2
0
1
2
3
4
5
Lag (s)
0
-0.2
-0.4
-0.6
-0.8
-1
0
1
2
3
4
Lag (s)
5
6
7
(Su et al. 2015,
Intermittency of 4-Hz QPO in
XTE J1550-564)
HHT-based Timing Properties (conti.)
Confidence limit of the
instantaneous amplitude
1500
Amplitude
1000
500
0
−500
320
322
324
Time (s)
326
328
330
Distributions of the high
amplitude (top) and low
amplitude (bottom) durations
Spectral Modulations
1.2
Optical depth
Tcorona (keV)
τ
0.9
0.6
0.3
180
Corona temperature
140
100
60
fscatt
0.18
Scattered fraction
0.14
0.10
Tdisk (keV)
0.06
0.94
Disk temperature
0.90
0.86
0.82
0.0
0.5
1.0
Phase
1.5
2.0
Possible Interpretation
(Inspired by a recent simulation from Hogg & Reynolds)
Summary
Method
We utilized HHT to characterize the HHT-based timing
properties, extract the QPO instantaneous phases, and then
construct its phase-resolved spectra.
Results
HHT-based timing property: the QPO is composed of a
series of intermittent oscillations with ∼ 1 s coherence
time
Phase-resolved spectra: significant modulations of
Comptonization parameters with unignorable modulations
of thermal disk components
Future Works
Cts/s
4-15 keV
0.5
1.0
1.5
2.0
4-5 keV
Cts/s
3600
3400
3200
3000
2800
2600
0.0
1650
1600
1550
1500
1450
1400
1350
1300
0.0
1900
1800
1700
1600
1500
1400
1300
0.0
0.5
1.0
1.5
2.0
5-15 keV
Cts/s
Cts/s
Cts/s
Cts/s
Phase lag?
0.5
1.0
Phase
1.5
2.0
3120
3115
3110
3105
3100
3095
3090
3085
3080
3075
0.0
1470
1465
1460
1455
1450
1445
0.0
1660
1655
1650
1645
1640
1635
1630
1625
1620
0.0
4-15 keV
0.5
1.0
1.5
2.0
4-5 keV
0.5
1.0
1.5
2.0
5-15 keV
0.5
1.0
Phase
1.5
2.0
Sifting Process of Empirical Mode Decomposition
(Huang & Wu 2008)
Comparison between Analysis Methods
(Huang & Wu 2008)