Page 260 - Special Topic Session (STS) - Volume 1

STS426 Guillaume B.

1 1
= ∑ cos ∅ and = ∑ sin ∅ . (4)

=1 =1
The other terms are defined as follows:
1
〈 〉 = [sin ] 2 , (5)

1
1
〈 〉 = [cos ] , (6)
2

1
1 1
2
2 = (1 + [sin cos ] ) − 〈 〉 , (7)
2
2 1
1
1
2
2
= 2 (1 − [sin cos ] ) − 〈 〉 , (8)
2

1
1
2
= 2 [ ] − 〈 〉〈 〉 , (9)
2

1

2
2
The terms 〈 〉 and 〈 〉 are the expectation values, and are the

variances, and is the covariance of and . The modified Z
2

2
2
statistic, Ƶ , is a sum of ℛ components,

2
2
Ƶ = ∑ ℛ , (10)

and is also ideal for harmonic decomposition of the pulse profile (see details
in Belanger, 2016).

3. Results
As a demonstration, we consider a hypothetical observation in X-rays of a
bright (500 s−1) accreting system whose variable emission comes mostly from
two components: the accretion disk, and the hot and turbulent gas in the inner
flow. In both, the emission processes are connected on all timescales, and thus
each gives rise to a red noise component. The accretion disk is much larger in
extent and has a sharp inner radius. It dominates at lower frequencies with a
power-law index α = −1, and has a high-frequency cutoff beyond which it does
not contribute to the power spectrum. The turbulent inner flow is much
smaller in extent because it is bounded by the inner edge of the disk. Its
emission is more variable and dominates the high-frequency part of the
spectrum with a power-law index α = −3.
We are interested in monitoring the range of frequencies between 0.1 and
10 Hz for a weak, short-lived,transient QPO that we expect to appear at or near
the break in the power spectrum at 1 Hz, which marks the boundary between
the disk and the turbulent inner flow. For this, we make a periodogram every
10 s with the events accumulated during this time interval, and monitor the
power. Because we are interested in a short-lived transient, we cannot rely on
it persisting in more than one “measurement”, and therefore must establish a
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