Flux Variability

Based on the properties of their gamma-ray light curves, i.e. the time series of the source luxes, variable sources can be grouped into three broad families: noisy and aperiodic, periodic, and one- time transients such as novae and GRBs, for which no continuous emission is found.

Gamma-ray light curves from AGN and the Crab nebula often show lares and long-term variability. Two examples are presented in the irst two panels of Fig.3.9. The power-spectral density (PSD,Klis,

1989_{) of their light curves is well approximated by a power-law function of the frequency ν, PSD(ν) ∝}

ν−β over a wide range of frequencies (see, e.g.Abdo et al.,2010a). This relation, characteristic of so-called red-noise processes, implies that luctuations on longer timescales account for a greater fraction of the power of the light curve than the ones at higher frequencies. Values of β measured for gamma-ray light curves of blazars are around ∼ 1.2 on average (Ackermann et al.,2011). Values of β as high as ∼ 1.7 were detected from some very bright source (Abdo et al.,2010a). For the Crab nebula β is found to be ∼ 0.9 (Buehler et al.,2012). Although AGN are variable at all the observed wavelengths, strong gamma-ray variability of the Crab nebula was unexpected and has not been observed by VHE gamma-ray observatories.

Chapter 3 The high-energy gamma-ray sky

Other features of blazar light curves can be extracted by looking at the distribution of the lux points. These distributions appears skewed to larger lux values (the lares) and often can be well reproduced by log-normal distributions (Ackermann et al.,2015b). The log-normal behavior seems to hint at multiplicative processes at the basis of the emission: it is the natural outcome of a process whose output is the product of a large number of independently varying elements. Log-normality is also linked to a linear relation between the mean lux in a given period and the root mean square (rms) amplitude of lux variations in the time interval (see, e.g.,Uttley et al.,2005;Biteau and Giebels,2012). That is, variability is enhanced when the source is brighter. This rms-lux proportionality implies that variability at the low frequencies (which determines the mean lux of each time range) is coupled to variability at the high frequencies (responsible for the variance inside the time range). This relation has been observed at all the accessible timescales, most notably in X-rays (Vaughan et al.,2003), but also in HE gamma rays (see, e.g.,Larsson et al.,2016), and in VHE gamma rays, for example in the case of the bright blazars PKS 2155-304 (Abramowski et al.,2010) and Mkn 421 (Tluczykont et al.,2010). There is some indication that variability properties difer for the two blazar families, BL Lacs and FSRQs. As of today, a larger fraction of FSRQs are found to be variable than BL Lacs (Ackermann et al.,

2015b). Looking at the lux distributions and shape of the light curves, BL Lacs seem to have fewer large lares and smoother light curves than FSRQs (Paggi et al.,2011).

In pulsars and binary systems, a varying degree of periodicity is induced by rotation in the for- mer, or orbital motion in the latter. Pulsars are the archetype of a periodic source. Their collimated radiation beams sweep the Earth at regular intervals giving rise to distinct pulses with periods rang- ing from milliseconds to seconds. This periodicity is not perfect and the period between the pulses constantly increases as the system loses rotational energy. Besides this predictable behavior, several types of timing irregularities have been detected in pulsars (Lyne et al.,2010) such as, for example, glitches and timing noise. Glitches are changes in the rotational state of the neutron star where the rotation frequency abruptly increases, often followed by a decay to its normal value (Espinoza et al.,

2011). Timing noise manifests itself as a non-gaussian distribution of the timing residuals (the difer- ences between the expected and measured time of the pulse) which shows quasi-periodic patterns for some objects (Hobbs et al.,2010). Additionally, abrupt changes in the gamma-ray lux of two pulsars have recently been observed. The gamma-ray emission of PSR J2021+4026 dropped abruptly in Octo- ber 2011 after a slight and gradual increase in the preceding three years (Allafort et al.,2013). For the millisecond pulsar binary PSR J1023+0038, an increase of the gamma-ray lux was observed around June 2013, probably as a consequence of the development of an accretion disk (Takata et al.,2014).

As seen in Section 3.1.1, the emission of gamma-ray binaries originates from the interaction be- tween the stellar and the compact object’s winds. It is modulated by the orbital motion of these sys- tems. The orbital periods of the known gamma-ray binaries range from_{≲ 4 days for LS 5039 to ∼} 3.5 years for PSR B1259−63. The maximum of the HE emission is found at diferent orbital phases for

3.2 Variability in gamma-rays

each of these objects. Highly variable gamma-ray emission and bright lares have also been observed for PSR B1259−63, roughly a month after its 2010 periastron passage (Tam et al.,2011). In the bottom panel of Fig. 3.9 we report, as an example, the HE gamma-ray light curve of LSI+61 303.

Modulation with the orbital period is also found in high-energy gamma rays in the microquasar Cygnus X−3 (Abdo et al.,2009d). This source also shows very bright gamma-ray lares correlated with radio and X-ray emission (Corbel et al.,2012_{). The steady-state emission of Cygnus X−1 is not}

detected in gamma-rays, and the source is only visible during laring states (Del Monte et al.,2010;

Bodaghee et al.,2013). In X-ray, microquasars show red-noise variability similar to the one described in the above paragraph (see e.g.Axelsson et al.,2009). This is not surprising considering the similarity between those two source types.

Like in many other attempts to classify natural phenomena, there are some objects that defy any simplistic scheme such as the one proposed above. For example, some novae can repeat on timescales of tens to one hundred years: these are the so-called recurrent novae (Anupama,2013). Another example is the blazar PG 1553+113: for this source, quasi-periodic variability of the gamma-ray lux has been observed (Ackermann et al.,2015a). Although the signiicance of the gamma-ray periodicity is marginal, it is strengthened by correlations with optical and radio observations.