MNRAS
489,
5365–5380 (2019)
doi:10.1093/mnras/stz2488
Advance Access publication 2019 September 07
The presence of interstellar scintillation in the 15 GHz interday variability
of 1158 OVRO-monitored blazars
J. Y. Koay,
1
‹
D. L. Jauncey,
2
,
3
T. Hovatta,
4
,
5
S. Kiehlmann
,
6
,
7
,
8
H. E. Bignall,
9
W. Max-Moerbeck,
10
T. J. Pearson
,
6
A. C. S. Readhead,
6
R. Reeves,
11
C. Reynolds
9
and H. Vedantham
12
,
13
1
Institute of Astronomy and Astrophysics, Academia Sinica, Section 4, Roosevelt Rd., Taipei 10617, Taiwan
2
CSIRO Astronomy and Space Science, Epping 1710, Australia
3
Research School of Astronomy and Astrophysics, Australian National University, Canberra 2611, Australia
4
Finnish Centre for Astronomy with ESO (FINCA), University of Turku, FI-20014 Turku, Finland
5
Aalto University Mets
̈
ahovi Radio Observatory, Mets
̈
ahovintie 114, FI-02540 Kylm
̈
al
̈
a, Finland
6
Owens Valley Radio Observatory, California Institute of Technology, Pasadena, CA 91125, USA
7
Institute of Astrophysics, Foundation for Research and Technology-Hellas, GR-71110 Heraklion, Greece
8
Department of Physics, University of Crete, GR-70013 Heraklion, Greece
9
CSIRO Astronomy and Space Science, Kensington 6151, Australia
10
Departamento de Astronom
́
ıa, Universidad de Chile, Camino El Observatorio 1515, Las Condes, Santiago, Chile
11
Departamento de Astronom
́
ıa, Universidad de Concepti
́
on, Concepci
́
on, Chile
12
Cahill Center for Astronomy and Astrophysics, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
13
Netherlands Institute for Radio Astronomy (ASTRON), Oude Hogeveensedijk 4, NL-7991 PD Dwingeloo, the Netherlands
Accepted 2019 September 3. Received 2019 September 1; in original form 2019 July 12
ABSTRACT
We have conducted the first systematic search for interday variability in a large sample
of extragalactic radio sources at 15 GHz. From the sample of 1158 radio-selected blazars
monitored over an
∼
10 yr span by the Owens Valley Radio Observatory 40-m telescope, we
identified 20 sources exhibiting significant flux density variations on 4-d time-scales. The
sky distribution of the variable sources is strongly dependent on the line-of-sight Galactic
H
α
intensities from the Wisconsin H
α
Mapper Survey, demonstrating the contribution of
interstellar scintillation (ISS) to their interday variability. 21 per cent of sources observed
through sightlines with H
α
intensities larger than 10 rayleighs exhibit significant ISS persistent
over the
∼
10 yr period. The fraction of scintillators is potentially larger when considering less
significant variables missed by our selection criteria, due to ISS intermittency. This study
demonstrates that ISS is still important at 15 GHz, particularly through strongly scattered
sightlines of the Galaxy. Of the 20 most significant variables, 11 are observed through the
Orion–Eridanus superbubble, photoionized by hot stars of the Orion OB1 association. The
high-energy neutrino source TXS 0506
+
056 is observed through this region, so ISS must
be considered in any interpretation of its short-term radio variability. J0616
−
1041 appears
to exhibit large
∼
20 per cent interday flux density variations, comparable in magnitude to
that of the very rare class of extreme, intrahour scintillators that includes PKS0405
−
385,
J1819
+
3845, and PKS1257
−
326; this needs to be confirmed by higher cadence follow-up
observations.
Key words:
scattering – ISM: general – galaxies: active – galaxies:jets – quasars: general –
radio continuum: galaxies.
E-mail:
jykoay@asiaa.sinica.edu.tw
1 INTRODUCTION
The radio variability of compact active galactic nuclei (AGNs)
provides a probe of extreme jet physics on scales comparable to or
even exceeding that probed using VLBI techniques. Based on light-
C
2019 The Author(s)
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5366
J. Y. Koay et al.
travel time arguments, variations observed on the shortest time-
scales are expected to originate from the most compact regions,
although this is complicated by the effects of relativistic beaming
in blazars.
A further complication arises from interstellar scintillation (ISS;
Heeschen & Rickett
1987
; Rickett
1990
; Jauncey et al.
2000
), which
has been shown to dominate blazar variability on time-scales of a
few days or less at cm wavelengths. The 5 GHz Micro-Arcsecond
Scintillation-Induced Variability (MASIV) Survey (Lovell et al.
2008
) found that
∼
60 per cent of 500 compact flat-spectrum AGNs
monitored exhibit 2–10 per cent flux density variations on 2-d time-
scales due to ISS. A follow-up survey (Koay et al.
2011a
) also
found ISS to dominate the intra and interday flux density variations
at 8 GHz, as seen in other scintillation studies (e.g. Rickett, Lazio &
Ghigo
2006
).
While ISS has been observed in individual sources at 15 GHz
(e.g. Savolainen & Kovalev
2008
), there are no similar large-scale
statistical studies of ISS at 15 GHz; variability at these frequencies
is typically assumed to be predominantly intrinsic to the sources
themselves.
The Owens Valley Radio Observatory (OVRO) blazar monitoring
program (Richards et al.
2011
) provides a rich data set for studying
AGN variability at 15 GHz. It is the largest and most sensitive
radio monitoring survey of blazars, and has been ongoing since
the year 2008. The full sample of this OVRO monitoring program
now comprises
∼
1830 sources, each observed at a cadence of about
twice a week, barring bad weather conditions and hardware issues.
The OVRO data have been used extensively to estimate the
variability brightness temperatures of blazars (e.g. Liodakis et al.
2018a
), study their radio–gamma-ray relationship (e.g. Max-
Moerbeck et al.
2014
; Richards et al.
2014
) and perform multi-
frequency cross-correlation studies of blazar flares (e.g. Hovatta
et al.
2015
; Liodakis et al.
2018b
; Pushkarev et al.
2019
). In these
studies, the 15 GHz flux density variations are always assumed
to be intrinsic to the blazar jets. Indeed the source variability
amplitudes from the OVRO light curves, as quantified by the
intrinsic modulation index (Richards et al.
2011
), broadly show no
significant Galactic dependence (Koay et al.
2018
), confirming that
intrinsic variations likely dominate. This is to be expected since this
method of variability characterization is biased towards the largest
inflections observed at the longest time-scales in the light curves,
most of which are expected to be intrinsic to the blazars.
The only major studies of interstellar scattering using data from
the OVRO monitoring program involved the sources J2025
+
3343
(Kara et al.
2012
; Pushkarev et al.
2013
) and J1415
+
1320 (Vedan-
tham et al.
2017a
). Symmetric U-shaped features observed in their
light curves were attributed to or modelled as extreme scattering
events (ESEs; Fiedler et al.
1987
), arising from lensing by high-
pressure intervening clouds of unknown origin in the interstellar
medium. ESEs were subsequently ruled out as an explanation for
J1415
+
1320 due to the achromatic behaviour of the U-shaped
features up to mm-wavelengths (Vedantham et al.
2017a
,
b
); the
variations are instead ascribed to gravitational lensing by interven-
ing structures.
Some questions remain – Is there significant variability in the
OVRO blazar light curves on the shortest observed interday time-
scales? If so, are these interday flux density variations intrinsic to
the AGN or due to ISS? How prevalent is ISS at 15 GHz? Answering
these questions is crucial for the interpretation of the OVRO light
curves on the shortest observed time-scales, e.g. in multiwavelength
studies of radio flares and jet physics like the ones referenced above.
It is also important for the design of future surveys to study the
radio variability of AGNs (and other compact sources) with next
generation radio telescopes such as the Square Kilometre Array
(Bignall et al.
2015
) and its precursors (Murphy et al.
2013
), where
being able to distinguish between both forms of variability is needed
to understand the underlying physics.
In this paper, we investigate the origin of the 15 GHz variability
of the OVRO-monitored blazars on the shortest observed time-
scale of
∼
4 d. We use the term interday variability to define
flux density variations occurring on a time-scale of days. This is
the first ever study of interday variability at 15 GHz for such a
large sample of sources. We describe the source sample briefly in
Section 2, then characterize the 4-d variability amplitudes using
the structure function in Section 3. In Section 4, we determine
if ISS is responsible for the interday variability of these OVRO
blazars by examining the Galactic dependence of their variability
amplitudes, and discuss the implications of our results on blazar
interday variability at 15 GHz. A summary of the paper is provided
in Section 5.
2 SOURCE SAMPLE
For this study, we use the original sample of 1158 sources monitored
by the OVRO 40-m telescope (Richards et al.
2011
), selected
from the Candidate Gamma-Ray Blazar Survey (CGRaBS; Healey
et al.
2008
). CGRaBS sources above a declination cut of
>
−
20
◦
were selected for monitoring by the OVRO telescope. The original
CGRaBS sample was selected such that the sources would have
spectral indices, radio flux densities, and X-ray flux densities similar
to those of Energetic Gamma Ray Experiment Telescope (EGRET)
detected sources, and would thus have a high chance of being
detected in gamma-rays by
Fer mi
. The CGRaBS sources were also
selected to be outside
±
10
◦
of the Galactic plane.
The OVRO telescope has been monitoring these sources at a
cadence of around twice per week since 2008 to the present, subject
to weather conditions and the instrument being operational. Addi-
tionally, about 20 per cent of the sources in the OVRO sample would
be randomly selected each week to be observed only once that week,
to fit into the schedule. Therefore, while the median time sampling
of each source is about 4 d, the time lag between consecutive flux
measurements in the OVRO light curves can be
∼
8 d or more. For
our analysis, we include flux density measurements up till 2018
April 10.
Richards et al. (
2011
) provide a detailed description of the obser-
vations and data reduction methodologies of the OVRO program.
3 CHARACTERIZATION OF VARIABILITY
AMPLITUDES
3.1 The structure function
We use the structure function amplitude to characterize the strength
of variability at different time-scales, given as:
D
(
τ
)
=
1
N
τ
∑
j,k
(
S
j
−
S
k
S
15
)
2
,
(1)
where
S
j
and
S
k
represent a pair of measured flux densities separated
by a time interval
τ
, binned to the nearest integer multiple of 4 d.
S
15
is the mean flux density calculated over the full light curve.
N
τ
is the number of pairs of flux densities in each time lag bin. We
selected bins in integer multiples of
τ
=
4 d since it is the typical
smallest time lag between successive data samples in the OVRO
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15 GHz interday variability of blazars
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0
500
1000
1500
2000
2500
3000
3500
Sidereal Days since MJD54471
0.2
0.4
0.6
0.8
S (Jy)
J0502+1338
10
0
10
1
10
2
10
3
(Sidereal Days)
10
-2
10
-1
D(
)
0 1020304050
(Sidereal Days)
0
0.005
0.01
Figure 1.
Top: Light curve for the source J0502
+
1338, where the horizontal
dashed line denotes the mean flux density of the source. The error bars are
given by equation (3) (Richards et al.
2011
). Bottom: Structure function,
D
(
τ
), calculated from the light curve using equation (1), shown in its
entirety in the left-hand panel, and for
τ
≤
50 d in the right-hand panel.
The horizontal dashed line denotes
D
m
15
(equation 2) derived from the
intrinsic modulation indices estimated by Richards et al. (
2014
).
program for the majority of the sources. We note that
N
τ
typically
decreases with increasing
τ
, with
N
4d
≈
2
N
8d
, and so on. Bins were
thus selected for plotting
D
(
τ
) and for our analysis only if
N
τ
≥
30.
An example of a source light curve and the corresponding structure
function is shown in Fig.
1
for the source J0502
+
1338. The error
bars for
D
(
τ
) shown in the bottom panels of Fig.
1
are estimated as
the standard error in the mean, defined as the ratio of the standard
deviation of the [(
S
j
−
S
k
)/
S
15
]
2
terms in that particular time lag
bin to
√
N
τ
−
1. This error estimate does not take into account the
statistical errors due to the finite span of the OVRO observations,
which would increase as
τ
increases relative to the total observing
timespan.
As a sanity check, we compare
D
(
τ
) against the intrinsic mod-
ulation index,
m
15
, as determined using the maximum likelihood
method by Richards et al. (
2014
). Since
m
15
is a measure of the
standard deviation, whereas
D
(
τ
) is a measure of the variance,
we convert
m
15
to an equivalent structure function amplitude
following:
D
m
15
=
2(
m
15
)
2
,
(2)
based on the assumption that the structure function amplitudes
have saturated. Fig.
2
shows that
D
(
τ
) approaches and becomes
comparable to
D
m
15
as
τ
increases to the order of 100–1000 d. This
confirms that
m
15
is more representative of the variability amplitude
on time-scales of a hundred days or longer. We note that the
D
(
τ
)
values shown here were derived from light curves in which outliers
have been flagged (described in Section 3.2 below). Also, the
m
15
values derived by Richards et al. (
2014
) were based only on the first
4yroftheOVROdata.
3.2 Data flagging and error estimation
Many of the OVRO light curves contain outliers that skew the
structure function amplitudes. To automatically flag off these out-
liers, we first divided each source light curve into three contiguous
segments of equal time period, then fit a sixth order polynomial
to each segment. This segmentation enables better fits to the light
curves, particularly those that exhibit rapid variations with many
inflections over the full 10 yr period. We then remove data points
for which the residuals are
≥
4 times that of the rms residuals over
10
-4
10
-2
10
0
10
-4
10
-2
10
0
D(
)
= 4d
10
-4
10
-2
10
0
10
-4
10
-2
10
0
= 12d
10
-4
10
-2
10
0
D
m15
10
-4
10
-2
10
0
D(
)
= 100d
10
-4
10
-2
10
0
D
m15
10
-4
10
-2
10
0
= 1000d
Figure 2.
Structure function amplitudes,
D
(
τ
), for
τ
=
4, 12, 100, 1000 d,
plotted against
D
m
15
derived using equation (2) from the intrinsic modulation
indices,
m
15
, published by Richards et al. (
2014
). The dashed line shows the
x
=
y
line.
0
500
1000
1500
2000
2500
3000
Sidereal Days since MJD54909
0
0.1
0.2
0.3
0.4
S (Jy)
0
500
1000
1500
2000
2500
3000
Sidereal Days since MJD54909
0
0.1
0.2
0.3
0.4
S (Jy)
J0251+7226
Figure 3.
Example of automated flagging of the light curves for the
source J0251
+
7226. Polynomial functions (dashed curves) are fit to three
contiguous segments, then data points for which the fit residuals are
≥
4 times
the rms residuals are flagged. The top panel shows the light curve prior to
flagging while the bottom panel shows the light curve after three outlier data
points have been flagged automatically.
the corresponding segment. An example of this automatic flagging
is shown in Fig.
3
, for the source J0251
+
7226.
Errors in flux density measurements due to instrumental and other
systematic effects contribute to the measured
D
(
τ
). One can be
very conservative and assume that the flux density variations on the
shortest measured time-scales, as characterized by
D
(4 d), provides
an upper limit on such errors in the flux density measurements.
However, using
D
(4 d) will overestimate the errors particularly in
sources that exhibit real variability (whether ISS or intrinsic) on
these short time-scales.
Since our goal is to examine if ISS is present in
D
(4 d), we use
instead the uncertainty of each single flux density measurement,
described in Richards et al. (
2011
) and given by
σ
err
=
√
σ
2
15
+
(
×
S
)
2
+
(
η
×
ψ
)
2
,
(3)
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5368
J. Y. Koay et al.
where
σ
15
is the scatter during each flux density measurement,
and accounts for thermal noise, atmospheric fluctuations, and other
stochastic errors.
accounts for all the flux-dependent errors,
including pointing and tracking errors.
ψ
is the switched power,
and the
η
term accounts for systematic effects between the dif-
ferent beam switching pairs in each observation, caused by rapid
atmospheric variations or pointing errors. The values of
and
η
were determined from data of sources that show little or very
slow variations, using the fitting methods described in Richards
et al. (
2011
). These were checked for different observing epochs,
and large changes were seen, for example, when the receiver was
upgraded in 2014 May. The value of
depends strongly on whether
the source was used as a pointing source (with values ranging
from 0.006–0.017) or if it was observed within 15
◦
of a pointing
source (classified as an ‘ordinary source’ with values between 0.014
and 0.036), with the former showing expectedly smaller pointing
induced errors. The value of
η
is also seen to differ between
pointing sources (values between 1.22 and 2.24) and ordinary
sources (values between 0.47 and 1.59), showing that the switched
power measurements also have a dependence on flux density, as the
pointing sources are typically brighter than the ordinary sources.
As described in Richards et al. (
2011
), in some cases it is evident
that the values of
η
and
result in too large uncertainties for some
objects, which clearly show common long-term trends with scatter
about the mean smaller than expected from the error model. In order
to account for this effect, a cubic spline fit was used to determine
a scaling factor that is then applied to scale the uncertainty due to
the flux density and switched power (see Richards et al.
2011
,for
details). This was not applied to the data taken after the receiver
upgrade in 2014 May so that some of the uncertainties in the data
may still be overestimated.
σ
err
in equation (3) also does not include the uncertainty intro-
duced by the flux density calibration, due to possible variability
of the flux calibrator sources. This is typically assumed to be
∼
5 per cent based on the observed long-term variability of the
flux calibrators, but is expected to be lower on interday time-scales.
We estimate the flux calibration errors on 4-d time-scales to be
∼
1 per cent of the source mean flux density; the justification for
this value is described in Appendix A.
For each source, we thus estimate the total contribution of
noise, calibration, and other systematic errors to the observed 4-
d modulation indices as the quadratic sum of the median value of
σ
err
and the
∼
1 per cent flux calibration errors, normalized by the
mean flux density (see equation in Appendix A)
m
σ
=
√
(median(
σ
err
))
2
+
(0
.
01
S
15
)
2
S
15
.
(4)
The rationale behind equation (4) is that the total error estimate
determines how much the flux densities can vary from one mea-
surement to the next, in the absence of real astrophysical variability;
m
σ
thus represents the estimated error contribution to the variability
amplitudes on the shortest observed time-scales. We use the median
instead of the mean
σ
err
value, since the presence of a few large
σ
err
in a light curve (as can be seen in Figs
1
and
3
) skews the mean
towards larger values, which in turn may overestimate the errors.
As a check, when we use the mean instead of the median
σ
err
value
to estimate
m
σ
, we find that the distribution of
m
D
(4 d)
/
m
σ
peaks
at values
<
1, where
m
D
(4d)
is the modulation index derived from
D
(4 d) using equation (2); this suggests that using the mean of
σ
err
overestimates
m
σ
for each source.
A diagnostic plot of
m
D
(4 d)
(in red) versus 15 GHz mean flux
density is shown in Fig.
4
. Overlayed are plots of
m
σ
(in blue) for
Figure 4.
Modulation indices derived from the 4-d structure function
amplitude,
m
D
(4 d)
, and the total contribution of instrumental, calibration,
and other systematic errors to the observed 4-d modulation indices of each
source,
m
σ
, plotted against the mean 15 GHz flux density. The red star
symbols denote sources for which
m
D
(4 d)
≥
2
m
σ
. The dashed line denotes
the best fit of equation (5) to
m
σ
. The black squares show
m
D
(4 d)
for
two blazars observed through the Galatic plane that were not included in our
sample but were also monitored by OVRO since 2008, i.e. 3EGJ 2016
+
3657
and 3EGJ 2027
+
3429 (see Section 4.3).
each source. The dashed line shows the following fit to
m
σ
:
m
σ,
fit
=
√
p
2
+
(
s/S
15
)
2
,
(5)
where
s
collates all the flux independent errors, i.e.
σ
15
and
η
×
ψ
in equation (3), while
p
collates all the flux dependent errors. We
obtained best-fitting values of
p
=
0.0194 and
s
=
0.009 Jy for
m
σ
.
From Fig.
4
,weseethat
m
D
(4 d)
is generally comparable to
m
σ
for the large majority of sources, displaying a similar flux density
dependence. This is to be expected if
m
D
(4 d)
is dominated by noise
and systematic uncertainties as characterized by equation (5) for the
majority of sources. This is also demonstrated in Fig.
5
where the
distribution of
m
D
(4 d)
/
m
σ
peaks at a value of
∼
1, for both the
S
15
≥
0.8 and
S
15
<
0.8 Jy sources. As shown in Fig.
A1
and discussed in
Appendix A, not including the estimated 1 per cent flux calibration
errors results in an underestimation of
m
σ
for the
S
15
≥
0.8 Jy. The
tail towards larger values of
m
D
(4d)
/
m
σ
(
>
1.5) suggests the presence
of real astrophysical variability in a fraction of the OVRO sources at
these 4-d time-scales; 21 of the 1158 sources (1.8 per cent) show 4-d
variability amplitudes
≥
2 times that of
m
σ
. We discuss the origin
of this variability in the next section.
4 RESULTS AND DISCUSSION
4.1 Galactic dependence of variability amplitudes
For our full sample of 1158 sources, we now examine if their
variability amplitudes on time-scales of days and weeks show a
Galactic dependence, which would provide strong evidence for the
presence of ISS. The top panel of Fig.
6
shows
D
(4 d) plotted against
the line-of-sight H
α
intensities (
I
α
) obtained from the Wisconsin
H-Alpha Mapper (WHAM) Survey (Haffner et al.
2003
). Since the
H
α
intensities are a measure of the integral of the squared electron
densities along the line of sight, they provide a proxy for the line-of-
sight interstellar scattering strength. Indeed, the intra and interday
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15 GHz interday variability of blazars
5369
Figure 5.
Histogram showing the distribution of the ratio of the 4-d
variability amplitudes to the flux normalized measurement uncertainties of
each source,
m
D
(4 d)
/
m
σ
. The histograms peak at a value of
∼
1 for both the
S
15
≥
0.8 and
S
15
<
0.8 Jy sources, when the 1 per cent flux calibration errors
are included. The errors in the
S
15
≥
0.8 Jy sources are likely underestimated
when excluding the flux calibration errors (Appendix A).
variability amplitudes of blazars at 2 GHz (Rickett et al.
2006
),
5 GHz (Lovell et al.
2008
), and 8 GHz (Koay et al.
2012
)show
significant correlations with line-of-sight Galactic H
α
intensities,
demonstrating that their flux density variations are dominated by
ISS.
For both the weak and strong source samples, there is a clear
excess of sources with larger amplitude variability for sightlines
where
I
α
≥
10 Rayleighs (R). Spearman correlation tests show a
statistically significant relationship between
D
(4 d) and the line-
of-sight H
α
intensities (
p
-value of 2.67
×
10
−
4
), as shown in
Ta b l e
1
. We have chosen a significance level of
α
=
0.05. This
H
α
dependence of the 15 GHz variability amplitudes demonstrates
the presence of ISS in the OVRO light curves, at least in sources
observed through heavily scattered lines of sight. In fact, this
correlation between
D
(
τ
)and
I
α
remains statistically significant up
to a time-scale of
τ
∼
80 d (Table
1
). However, on time-scales of
100 d and above, this correlation is no longer significant as intrinsic
variations likely begin to dominate.
The Spearman correlation tests may be biased by the extreme
I
α
≥
10 R sources. We therefore repeat the same tests using only
sources with line of sight
I
α
<
10 R. We find that the correlation
between
D
(
τ
)and
I
α
remains significant, up to a time-scale of
∼
20 d.
This suggests that at 15 GHz, while the variability of sources seen
through heavily scattered sightlines (
I
α
≥
10 R) may be dominated
by ISS up to time-scales of 80 d, ISS is significant up to only
∼
20 d
time-scales for more typical sightlines through the Galaxy where
I
α
<
10 R.
As further confirmation, we examine in Fig.
7
the distribution
of
D
(4 d) for sources with low (
I
α
<
1 R, top), moderate (1 R
≤
I
α
<
10 R, middle), and high (
I
α
≥
10 R, bottom) line-of-sight H
α
intensities. The Kolmogorov–Smirnov (K–S) test confirms that the
distribution of
D
(4 d) for sources with high
I
α
is significantly
different from that of the combined sample of sources with low
and moderate
I
α
,ata
p
-value of 6.45
×
10
−
6
. The mean value of
D
(4 d) for sources with
I
α
≥
10 R is 0.0143, a factor of
∼
2 higher
than the value of 0.0061 for that of sources with
I
α
<
10 R.
Although we see no obvious correspondence between
D
(4 d)
and the Galactic latitudes by eye (Fig.
6
, bottom), the Spearman
Figure 6.
Structure function amplitude at 4-d time-scales,
D
(4 d), versus
line-of-sight H
α
intensity (top) and Galactic latitude (bottom). The sources
are separated into two roughly equal samples of high flux density (
S
15
≥
0.3 Jy, red) and low flux density (
S
15
<
0.3 Jy, blue) sources. The star
symbols denote the most significant variables in our sample (discussed in
Section 4.2). The fact that the relationship between
D
(4 d) and
I
α
is evident
for both the weak and strong source samples confirms that this relationship
is not due the presence of noise in the
D
(4 d) of the weaker sources.
correlation test reveals a statistically significant anticorrelation
between
D
(
τ
)and
|
b
|
on time-scales of 4–20 d (Table
1
). The
correlation coefficients are weaker compared to that between
D
(4 d)
and
I
α
.TheH
α
intensities are therefore a better indicator of line-
of-sight scattering strength compared to the Galactic latitudes, due
to the complex structure of the ionized gas in the Galaxy. This is in
spite of the 1
◦
angular resolution of the WHAM Survey data.
4.2 ISS of the most significant interday variables
Since
D
(4 d) still comprises significant amounts of instrumental
and systematic errors in a large fraction of sources (i.e. the peak
of
m
D
(4 d)
/m
σ
is close to unity), we now examine only the most
significant variables at 4-d time-scales to determine the origin
of their variability. We consider sources satisfying the criteria
that
m
D
(4 d)
≥
2
m
σ
to be significantly variable, based on the tail
end of the
m
D
(4 d)
/m
σ
distribution in Fig.
5
. We initially find 21
MNRAS
489,
5365–5380 (2019)
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5370
J. Y. Koay et al.
Table 1.
Spearman rank correlation coeffficients,
r
s
, and corresponding
p
-values between pairs of parameters and for various source samples.
Parameter 1
Parameter 2
Source sample
No. of sources
r
s
p
-value
Significant?
(
α
=
0.05)
D
(4 d)
I
α
All
1158
0.107
2.67
×
10
−
4
Y
D
(8 d)
I
α
All
1158
0.111
1.47
×
10
−
4
Y
D
(12 d)
I
α
All
1158
0.121
3.54
×
10
−
5
Y
D
(16 d)
I
α
All
1158
0.118
5.97
×
10
−
5
Y
D
(20 d)
I
α
All
1158
0.112
1.35
×
10
−
4
Y
D
(40 d)
I
α
All
1158
0.073
1.26
×
10
−
2
Y
D
(60 d)
I
α
All
1158
0.068
2.03
×
10
−
2
Y
D
(80 d)
I
α
All
1158
0.063
3.17
×
10
−
2
Y
D
(100 d)
I
α
All
1158
−
0.055
5.95
×
10
−
2
N
D
(1000 d)
I
α
All
1158
−
0.047
1.12
×
10
−
1
N
D
(4 d)
I
α
I
α
<
10
1104
0.059
4.87
×
10
−
2
Y
D
(8 d)
I
α
I
α
<
10
1104
0.065
3.18
×
10
−
2
Y
D
(12 d)
I
α
I
α
<
10
1104
0.082
6.30
×
10
−
3
Y
D
(16 d)
I
α
I
α
<
10
1104
0.078
9.20
×
10
−
3
Y
D
(20 d)
I
α
I
α
<
10
1104
0.077
1.04
×
10
−
2
Y
D
(40 d)
I
α
I
α
<
10
1104
0.041
1.74
×
10
−
1
N
D
(60 d)
I
α
I
α
<
10
1104
0.036
2.39
×
10
−
1
N
D
(80 d)
I
α
I
α
<
10
1104
0.032
2.85
×
10
−
1
N
D
(100 d)
I
α
I
α
<
10
1104
−
0.029
3.44
×
10
−
1
N
D
(1000 d)
I
α
I
α
<
10
1104
−
0.018
5.42
×
10
−
1
N
D
(4 d)
|
b
|
◦
All
1158
−
0.072
1.40
×
10
−
2
Y
D
(8 d)
|
b
|
◦
All
1158
−
0.075
1.04
×
10
−
2
Y
D
(12 d)
|
b
|
◦
All
1158
−
0.090
2.30
×
10
−
3
Y
D
(16 d)
|
b
|
◦
All
1158
−
0.086
3.50
×
10
−
3
Y
D
(20 d)
|
b
|
◦
All
1158
−
0.084
4.40
×
10
−
3
Y
D
(40 d)
|
b
|
◦
All
1158
−
0.045
1.25
×
10
−
1
N
D
(60 d)
|
b
|
◦
All
1158
−
0.038
1.94
×
10
−
1
N
D
(80 d)
|
b
|
◦
All
1158
−
0.033
2.61
×
10
−
1
N
D
(100 d)
|
b
|
◦
All
1158
−
0.026
3.75
×
10
−
1
N
D
(1000 d)
|
b
|
◦
All
1158
−
0.217
4.75
×
10
−
1
N
Figure 7.
Histograms showing the distributions of
D
(4 d) for sources with
low (
I
α
<
1 R, top), moderate (1 R
≤
I
α
<
10 R, middle), and high (
I
α
≥
10 R, bottom) line-of-sight H
α
intensities. The dashed (red) and dash–
dotted (black) vertical lines show the median and mean values of
D
(4 d),
respectively. The
I
α
≥
10 R sample of sources contain a significantly higher
fraction of interday variables.
significant interday variables that meet these criteria. After careful
inspection (described in Appendix B), we found that the light curve
of J0259
−
0018, the weakest (
∼
0.1 Jy) and most variable (
m
D
(4 d)
∼
24 per cent) of these 21 sources, was severely affected by an error
in source coordinates in the OVRO and CGRaBS catalogues. We
therefore remove it from our sample of significant interday variables
and refer to the remaining 20 sources as ‘interday variables’ for the
rest of this paper. The full list of these interday variables is shown
in Table
2
, together with their variability amplitudes. Their light
curves are presented in Appendix C.
The flux density variations of these interday variables are clearly
dominated by ISS, as evidenced by the larger fraction of variables
detected among sources with larger
I
α
values. 11 (21 per cent) of
the 53 sources with line-of-sight
I
α
≥
10 R are classified as interday
variables, while only
∼
0
.
8 per cent (9/1104) of sources with
I
α
<
10 R are classified as such.
ISS arises due to the scattering of radio waves by density
inhomogeneities of the free electrons in the ionized interstellar
medium. This scattering process is often well-described as being
confined to a single thin scattering screen located between the
source and the observer; this screen changes the phases of an
incoming plane wave (Narayan
1992
). Compact AGN are known to
exhibit ISS in two different regimes (Rickett
1990
; Narayan
1992
),
weak ISS and strong refractive ISS (Blandford, Narayan & Romani
1986
; Rickett
1986
; Coles et al.
1987
). In the weak ISS regime,
phase changes in the wavefront due to diffractive scattering are
less than a radian, so that the scintillation pattern is dominated
by the Fresnel scale,
r
F
=
√
cD
L
/
(2
πν
), where
c
is the speed
of light,
D
L
is the distance from the observer to the scattering
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489,
5365–5380 (2019)
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