2009 Fermi Symposium, Washington, D.C., Nov. 2-5 3
detailed variability analysis for one of two reasons:
(1) too few data points or (2) ﬂux measurement un-
certainties on the order of the amplitude of observed
variability. It is important to note that, due to dis-
crepancies between the sampling frequency in both
bands, the variability indices for the 850µm band may
be artiﬁcially depressed due to the fact that there are
not always corresponding measurements at higher fre-
quencies during ﬂaring epochs.
3.2. First-Order Continuous
Autoregression
We follow the method of Kelly et al. [9], who model
quasar optical light curves as a continuous time ﬁrst-
order autoregressive process (CAR(1)) in order to ex-
tract characteristic time scales and the amplitude of
ﬂux variations. Although ﬂaring behavior is not typi-
cally thought of as an autoregressive process, we ﬁnd
that the light curves are well-ﬁt by the models and
therefore adopt the method here to study blazar sub-
millimeter light curves.
The CAR(1) process is described by a stochastic
diﬀerential equation [9],
dS(t) = 1
τS(t) dt+ σ
√
dtϵ (t) + bdt, (3)
associated with a power spectrum of the form
PX(f) = 2σ2τ2
1 + (2πτf)2 . (4)
In equations 3 and 4, τ is called the “relaxation
time” of the process S(t) and is identiﬁed by the
break in PX(f). The power spectrum appears ﬂat
for timescales longer than this and falls oﬀ as 1/f2 for
timescales shorter than the characteristic timescale of
the process.
Taking the logarithm of the blazar light curve (in
Jy) to be S(t), we adopt τ (in days) as the character-
istic timescale of variability, after which the physical
process “forgets” about what has happened at time
lags of greater than τ. The two other relevant pa-
rameters, σ and µ = b/a, are the overall amplitude
of variability and the logarithm of mean value of the
light curve, respectively.
In the routine, we construct an autoregressive
model for the light curves for a minimum of 100,000
iterations and calculate the value of τ from the break
in the power spectrum in each instance. Due to the
limited number of observations in the 850 µm band,
we performed this autoregressive analysis only for the
1mm light curves, which typically have more than 10
points per light curve.
This method yielded some surprising results. In
Figure 3, we see that the BL Lacs and FSRQs exhibit
virtually no diﬀerence in characteristic timescale, with
Figure 3: Characteristic timescale (days) versus
submillimeter luminosity (erg s−1) in the 1mm band for
all objects. Physically, τ represents a “relaxation
timescale”, the timescale beyond which events are no
longer correlated.
both classes extending across a large range in τ. Be-
cause of the uncertainty for objects with shorter char-
acteristic timescales, it is hard to draw any deﬁnitive
conclusions about the diﬀerences between classes. It
is important to note that τ does not necessarily rep-
resent a ﬂaring timescale, which is a behavior that
typically operates on a scale of ∼10–100 days and not
on the longer timescales we see in τ.
4. CONNECTION WITH GAMMA-RAYS
In general, we ﬁnd that in the submillimeter, we
are observing these blazars at or near the peak of the
synchrotron component ( αS ∼ 0), but that Fermi-
detected sources have more negative energy spectral
indices overall than Fermi-nondetected sources. In
Figure 4, we see that while the majority of Fermi
blazars are observed on the rising part of the syn-
chrotron component (at lower energies than the peak),
all of the objects have very steeply fallingγ-ray energy
spectral indexes, putting the γ-ray peak at lower en-
ergies than the observed Fermi band. Knowing that
we are not observing the synchrotron and γ-ray com-
ponents at analagous points in the spectrum may al-
low us to better understand the magnetic ﬁeld in the
parsec-scale jet region and the population of external
photons that is being upscattered to γ-rays.
In Figure 5, the ratio between Lγ and νLν,1mm re-