MNRAS
000
, 1–14 (2017)
Preprint 5 September 2019
Compiled using MNRAS L
A
T
E
X style file v3.0
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
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, 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 XXX. Received YYY; in original form ZZZ
ABSTRACT
We have conducted the first systematic search for interday variability in a large sam-
ple of extragalactic radio sources at 15 GHz. From the sample of 1158 radio-selected
blazars monitored over a
∼
10 year span by the Owens Valley Radio Observatory 40-m
telescope, we identified 20 sources exhibiting significant flux density variations on 4-day
timescales. 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, demon-
strating the contribution of interstellar scintillation (ISS) to their interday variability.
21% of sources observed through sight-lines with H
α
intensities larger than 10 rayleighs
exhibit significant ISS persistent over the
∼
10 year 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 sight-lines of the Galaxy. Of the
20 most significant variables, 11 are observed through the Orion-Eridanus superbub-
ble, 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% 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 observa-
tions.
Key words:
scattering, galaxies: active, galaxies:jets, quasars: general, radio contin-
uum: galaxies, ISM: general
?
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
c
©
2017 The Authors
arXiv:1909.01566v1 [astro-ph.GA] 4 Sep 2019
2
J. Y. Koay et al.
techniques. Based on light-travel time arguments, variations
observed on the shortest timescales 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 scintilla-
tion (ISS, Heeschen & Rickett 1987; Rickett 1990; Jauncey
et al. 2000), which has been shown to dominate blazar vari-
ability on timescales of a few days or less at cm wavelengths.
The 5 GHz Micro-Arcsecond Scintillation-Induced Variabil-
ity (MASIV) Survey (Lovell et al. 2008) found that
∼
60%
of 500 compact flat-spectrum AGNs monitored exhibit 2 to
10% flux density variations on 2-day timescales 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 et
al. 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; vari-
ability at these frequencies is typically assumed to be pre-
dominantly intrinsic to the sources themselves.
The Owens Valley Radio Observatory (OVRO) blazar
monitoring program (Richards et al. 2011) provides a rich
dataset 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 esti-
mate the variability brightness temperatures of blazars (e.g.,
Liodakis et al. 2018a), study their radio-gamma ray rela-
tionship (e.g., Max-Moerbeck et al. 2014; Richards et al.
2014) and perform multi-frequency cross-correlation stud-
ies 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 lightcurves, as quantified by the intrinsic
modulation index (Richards et al. 2011), broadly show no
significant Galactic dependence (Koay et al. 2018), confirm-
ing 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
timescales in the lightcurves, most of which are expected to
be intrinsic to the blazars.
The only major studies of interstellar scattering us-
ing data from the OVRO monitoring program involved the
sources J2025+3343 (Kara et al. 2012; Pushkarev et al. 2013)
and J1415+1320 (Vedantham et al. 2017a). Symmetric U-
shaped features observed in their lightcurves were attributed
to or modelled as extreme scattering events (ESEs, Fiedler
et al. 1987), arising from lensing by high-pressure interven-
ing clouds of unknown origin in the interstellar medium.
ESEs were subsequently ruled out as an explanation for
J1415+1320 due to the achromatic behavior of the U-shaped
features up to mm-wavelengths (Vedantham et al. 2017a,b);
the variations are instead ascribed to gravitational lensing
by intervening structures.
Some questions remain – Is there significant variability
in the OVRO blazar lightcurves on the shortest observed
interday timescales? 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 lightcurves on the shortest
observed timescales, 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 timescale of
∼
4 days. We use the term interday
variability to define flux density variations occurring on a
timescale 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 char-
acterize the 4-day variability amplitudes using the structure
function in Section 3. In Section 4, we determine if ISS is re-
sponsible 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 pa-
per 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 Sur-
vey (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 be-
ing detected in gamma-rays by
Fermi
. 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. Additionally, about 20% 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 days, the time lag between consecutive flux mea-
surements in the OVRO lightcurves can be
∼
8 days 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 observations and data reduction methodologies of the
OVRO program.
MNRAS
000
, 1–14 (2017)
15 GHz interday variability of blazars
3
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
10
20
30
40
50
(Sidereal Days)
0
0.005
0.01
Figure 1.
Top: Lightcurve 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 lightcurve
using Equation 1, shown in its entirety in the left panel, and for
τ
≤
50d in the right panel. The horizontal dashed line denotes
D
m
15
(Equation 2) derived from the intrinsic modulation indices
estimated by Richards et al. (2014).
3 CHARACTERIZATION OF VARIABILITY
AMPLITUDES
3.1 The structure function
We use the structure function amplitude to characterize the
strength of variability at different timescales, 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 days.
S
15
is the mean flux density calculated
over the full lightcurve.
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 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 anal-
ysis only if
N
τ
≥
30. An example of a source lightcurve and
the corresponding structure function is shown in Figure 1
for the source J0502+1338. The error bars for
D
(
τ
) shown
in the bottom panels of Figure 1 are estimated as the stan-
dard 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 intrin-
sic modulation index,
m
15
, as determined using the maxi-
mum 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 ampli-
tudes have saturated. Figure 2 shows that
D
(
τ
) approaches
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 days, plotted against
D
m
15
derived using Equa-
tion 2 from the intrinsic modulation indices,
m
15
, published by
Richards et al. (2014). The dashed line shows the
x
=
y
line.
and becomes comparable to
D
m
15
as
τ
increases to of order
100 to 1000 days. This confirms that
m
15
is more representa-
tive of the variability amplitude on timescales of a hundred
days or longer. We note that the
D
(
τ
) values shown here
were derived from lightcurves in which outliers have been
flagged (described in Section 3.2 below). Also, the
m
15
val-
ues derived by Richards et al. (2014) were based only on the
first 4 years of the OVRO data.
3.2 Data flagging and error estimation
Many of the OVRO lightcurves contain outliers that skew
the structure function amplitudes. To automatically flag off
these outliers, we first divided each source lightcurve into 3
contiguous segments of equal time period, then fit a 6th or-
der polynomial to each segment. This segmentation enables
better fits to the lightcurves, particularly those that exhibit
rapid variations with many inflections over the full 10 year
period. We then remove datapoints for which the residuals
are
≥
4 times that of the rms residuals over the correspond-
ing segment. An example of this automatic flagging is shown
in Figure 3, for the source J0251+7226.
Errors in flux density measurements due to instrumen-
tal 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 timescales, as
characterized by
D
(4d), provides an upper limit on such er-
rors in the flux density measurements. However, using
D
(4d)
will overestimate the errors particularly in sources that ex-
hibit real variability (whether ISS or intrinsic) on these short
timescales.
Since our goal is to examine if ISS is present in
D
(4d),
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)
MNRAS
000
, 1–14 (2017)
4
J. Y. Koay et al.
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 lightcurves for
the source J0251+7226. Polynomial functions (dashed curves) are
fit to 3 contiguous segments, then data points for which the fit
residuals are
≥
4 times the rms residuals are flagged. The top
panel shows the lightcurve prior to flagging while the bottom
panel shows the lightcurve after 3 outlier datapoints have been
flagged automatically.
where
σ
15
is the scatter during each flux density measure-
ment, and accounts for thermal noise, atmospheric fluctua-
tions 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 system-
atic effects between the different 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, us-
ing 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 up-
graded in May 2014. The value of
depends strongly on
whether the source was used as a pointing source (with val-
ues 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
−
0
.
036), with the former show-
ing expectedly smaller pointing induced errors. The value
of
η
is also seen to differ between pointing sources (values
between 1
.
22
−
2
.
24) and ordinary sources (values between
0
.
47
−
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 May 2014 so that some of the
uncertainties in the data may still be overestimated.
σ
err
in Equation 3 also does not include the uncertainty
introduced by the flux density calibration, due to possible
variability of the flux calibrator sources. This is typically
assumed to be
∼
5% based on the observed long-term vari-
ability of the flux calibrators, but is expected to be lower
on interday timescales. We estimate the flux calibration er-
rors on 4-day timescales to be
∼
1% 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 ob-
served 4-day modulation indices as the quadratic sum of the
median value of
σ
err
and the
∼
1% flux calibration errors,
normalized by the mean flux density (see Equation A1 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 esti-
mate determines how much the flux densities can vary from
one measurement to the next, in the absence of real astro-
physical variability;
m
σ
thus represents the estimated er-
ror contribution to the variability amplitudes on the short-
est observed timescales. We use the median instead of the
mean
σ
err
value, since the presence of a few large
σ
err
in
a lightcurve (as can be seen in Figures 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 distri-
bution of
m
D
(4d)
/m
σ
peaks at values
<
1, where
m
D
(4d)
is
the modulation index derived from
D
(4d) using Equation 2;
this suggests that using the mean of
σ
err
overestimates
m
σ
for each source.
A diagnostic plot of
m
D
(4d)
(in red) vs. 15 GHz mean
flux density is shown in Figure 4. Overlayed are plots of
m
σ
(in blue) for 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 fit values of
p
= 0
.
0194 and
s
=
0
.
009 Jy for
m
σ
.
From Figure 4, we see that
m
D
(4d)
is generally compara-
ble to
m
σ
for the large majority of sources, displaying a simi-
lar flux density dependence. This is to be expected if
m
D
(4d)
is dominated by noise and systematic uncertainties as char-
acterised by Equation 5 for the majority of sources. This
is also demonstrated in Figure 5 where the distribution of
m
D
(4d)
/m
σ
peaks at a value of
∼
1, for both the
S
15
≥
0
.
8 Jy
and
S
15
<
0
.
8 Jy sources. As shown in Figure A1 and dis-
cussed in Appendix A, not including the estimated 1% 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 day timescales;
21 of the 1158 sources (1.8%) show 4-day variability ampli-
tudes
≥
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 timescales of days and weeks show
a Galactic dependence, which would provide strong evidence
MNRAS
000
, 1–14 (2017)
15 GHz interday variability of blazars
5
-2
-1
0
1
2
log(S
15
/Jy)
-2.5
-2
-1.5
-1
-0.5
0
log(m)
m
D(4d)
m
m
,fit
Figure 4.
Modulation indices derived from the 4-day structure
function amplitude,
m
D
(4d)
, and the total contribution of instru-
mental, calibration and other systematic errors to the observed
4-day 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
(4d)
≥
2
m
σ
. The dashed line denotes the best fit
of Equation 5 to
m
σ
. The black squares show
m
D
(4d)
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).
Figure 5.
Histogram showing the distribution of the ratio of the
4-day variability amplitudes to the flux normalized measurement
uncertainties of each source,
m
D
(4d)
/m
σ
. The histograms peak
at a value of
∼
1 for both the
S
15
≥
0
.
8 Jy and
S
15
<
0
.
8 Jy
sources, when the 1% 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).
for the presence of ISS. The top panel of Figure 6 shows
D
(4d) 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-
10
0
10
2
I
(R)
10
-4
10
-3
10
-2
10
-1
10
0
D(4d)
S
15
< 0.3 Jy
S
15
0.3 Jy
0
20
40
60
80
|b| (
°
)
10
-4
10
-3
10
-2
10
-1
10
0
D(4d)
S
15
< 0.3 Jy
S
15
0.3 Jy
Figure 6.
Structure function amplitude at 4 day timescales,
D
(4d), vs line-of-sight H
α
intensity (top) and Galactic latitude
(bottom). The sources are separated into two roughly equal sam-
ples 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
(4d) and
I
α
is evident for
both the weak and strong source samples confirms that this re-
lationship is not due the presence of noise in the
D
(4d) of the
weaker sources.
sight interstellar scattering strength. Indeed, the intra and
interday 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 den-
sity 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 sight-lines where
I
α
≥
10 rayleighs (R). Spearman cor-
relation tests show a statistically significant relationship be-
tween
D
(4d) and the line-of-sight H
α
intensities (
p
-value of
2
.
67
×
10
−
4
), as shown in Table 1. We have chosen a signifi-
cance level of
α
= 0
.
05. This H
α
dependence of the 15 GHz
variability amplitudes demonstrates the presence of ISS in
MNRAS
000
, 1–14 (2017)
6
J. Y. Koay et al.
Figure 7.
Histograms showing the distributions of
D
(4d) 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
intensi-
ties. The dashed (red) and dash-dotted (black) vertical lines show
the median and mean values of
D
(4d) respectively. The
I
α
≥
10 R
sample of sources contain a significantly higher fraction of inter-
day variables.
the OVRO lightcurves, at least in sources observed through
heavily scattered lines of sight. In fact, this correlation be-
tween
D
(
τ
) and
I
α
remains statistically significant up to a
timescale of
τ
∼
80d (Table 1). However, on timescales of
100 days 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 sig-
nificant, up to a timescale of
∼
20 days. This suggests that at
15 GHz, while the variability of sources seen through heav-
ily scattered sight-lines (
I
α
≥
10 R) may be dominated by
ISS up to timescales of 80 days, ISS is significant up to only
∼
20 day timescales for more typical sightlines through the
Galaxy where
I
α
<
10 R.
As further confirmation, we examine in Figure 7 the dis-
tribution of
D
(4d) for sources with low (
I
α
<
1 R, top), mod-
erate (1 R
≤
I
α
<
10 R, middle), and high (
I
α
≥
10 R, bot-
tom) line-of-sight H
α
intensities. The Kolmogorov-Smirnov
(K-S) test confirms that the distribution of
D
(4d) for sources
with high
I
α
is significantly different from that of the com-
bined sample of sources with low and moderate
I
α
, at a
p
−
value of 6
.
45
×
10
−
6
. The mean value of
D
(4d) 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
(4d) and the Galactic latitudes by eye (Figure 6, bottom),
the Spearman correlation test reveals a statistically signifi-
cant anti-correlation between
D
(
τ
) and
|
b
|
on timescales of 4
to 20 days (Table 1). The correlation coefficients are weaker
compared to that between
D
(4d) and
I
α
. The H
α
intensi-
ties are therefore a better indicator of line-of-sight scatter-
ing 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
(4d) still comprises significant amounts of instru-
mental and systematic errors in a large fraction of sources
(i.e., the peak of
m
D
(4d)
/m
σ
is close to unity), we now exam-
ine only the most significant variables at 4-day timescales to
determine the origin of their variability. We consider sources
satisfying the criteria that
m
D
(4d)
≥
2
m
σ
to be significantly
variable, based on the tail end of the
m
D
(4d)
/m
σ
distribution
in Figure 5. We initially find 21 significant interday variables
that meet this criteria. After careful inspection (described in
Appendix B), we found that the lightcurve of J0259
−
0018,
the weakest (
∼
0
.
1 Jy) and most variable (
m
D
(4d)
∼
24%)
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 in-
terday 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 lightcurves 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%) of the 53 sources with line-of-sight
I
α
≥
10 R are classified as interday variables, while only
∼
0
.
8%
(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 interstel-
lar 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). Com-
pact AGN are known to exhibit ISS in two different regimes
(Narayan 1992; Rickett 1990), weak ISS and strong refrac-
tive ISS (Blandford et al. 1986; Rickett 1986; Coles et al.
1987). In the weak ISS regime, phase changes in the wave-
front 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 screen,
and
ν
is the observing frequency. In other words, weak ISS
is observed at frequencies and sight-lines where the diffrac-
tive length-scale,
r
diff
, is much larger than
r
F
. On the other
hand, the focussing and defocussing of coherent patches of
waves due to the large-scale density fluctuations on the
scattering screen lead to strong refractive ISS, observed
when
r
diff
r
F
. ISS amplitudes are typically strongest at
the transition frequency,
ν
0
, between weak and strong ISS
(Narayan 1992). The modulation index of flux density varia-
tions scale as (
ν
0
/ν
)
17
/
12
for weak ISS (observed at
ν
ν
0
)
and scale as (
ν/ν
0
)
17
/
30
for strong refractive ISS (Walker
1998) observed at
ν
ν
0
. These assume a Kolmogorov
power spectrum of turbulence, as typically observed for the
MNRAS
000
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