We discuss the problem of data heterogeneity in the search and analysis of inhomogeneities in the light curves of gamma-ray bursts afterglow. We use well-sampled optical and X-ray light curves to find and identify deviations (inhomogeneities) from smooth power law decay of the light curve. We show, in particular that the duration of the inhomogeneities correlates with their peak time (relative to gamma-ray burst trigger) and the correlation is the same for all types of inhomogeneities. The study of inhomogeneities can give us the opportunity to understand the physics of the "central machine" of gamma-ray bursts, which is still far from understanding.
Several astrophysical objects are observed right across the full electromagnetic spectrum (from highly energetic gamma-rays to radio waves). Synchronous observations of them in different wavelengths represent “MultiFrequency Astronomy” (MFA). Also, observations of astrophysical events not only in electromagnetic waves, but in other channels, such as gravitational waves, introduce “Multi-Messenger Astronomy” (MMA).
The time-domain multi-frequency observations allow estimation of the physical parameters and discovery of the new features of the astrophysical object or event and make analysis more complex as a consequence.
MFA and MMA play a significant role in the
investigation of gamma-ray burst (GRB) phenomena.
E.g., analysis of the multi-color optical and
twofrequency radio observations showed that the GRB
ejecta are collimated in a jet [
GRBs have extragalactic origin [
The work continues the investigation [
In general, optical light curves of the gamma-ray
bursts in the afterglow phase are described fairly well by
smoothly broken-power law [
• Density-jump model [
• Two-component jet model [
• Energy-injection model [
But each model does not explain all features of the inhomogeneities, especially at late stages of the afterglow (dozens of days).
In the gamma-ray range (above 10 keV) many different experiments operate to investigate GRBs. Each instrument is unique and typically consists of detector and imaging segments.
Detectors in various experiments are made of different materials and consist of several large blocks or matrices of relatively small elements.
To the first category we can refer the scintillation and semiconductor detector blocks, working in the typical energy range of 10 keV – 10 MeV: 1. sodium iodide (NaI): Fermi/GBM [12] and GGC
Wind/Konus [13]; 2. bismuth germanate (BGO): INTEGRAL/SPI-ACS [13] and Fermi/GBM [11]; 3. cesium iodide (CsI):Vernov/RELEC [15]; 4. reverse-electrode n-type Ge
INTEGRAL/SPI [16] and RHESSI [17]. detectors:
More energetic gamma-rays (above 10 MeV) are registered by pair-conversion telescopes (e.g., Fermi/LAT [18]).
In the soft gamma-ray range (15 – 200 keV) largearea solid state CdZnTe detector arrays (e.g., Swift/BAT [19]) or multilayer cadmium telluride (CdTe) matrix detectors (e.g., INTEGRAL/ISGRI [20] and NuSTAR [21]) are common.
As for imaging segment, in the gamma-ray range the coded mask is commonly used (e.g., Swift/BAT, INTEGRAL/SPI, INTEGRAL/IBIS), which defines geometrically the telescope’s field of view. Images of the sky are reconstructed by decoding the detector shadowgram with the mask pattern. However, some gamma-telescopes do not maintain the coded mask and are omnidirectional (e.g. INTEGRAL/SPI-ACS, Fermi/GBM, GGC-Wind/Konus, CGRO/BATSE).
Electronics and software onboard the gammatelescopes run in different modes. Some of the experiments allow photon-by-photon mode (Swift/BAT, Fermi/GBM, INTEGRAL/SPI, INTEGRAL/IBISISGRI), while several instruments only provide binned light curve sin the single or several energy channels: e.g. the INTEGRAL/SPI-ACS is operating in the single energy channel 0.1 - 10 MeV with time resolution of 50 ms.
The energy range and spectral resolution also significantly differ for different types of detectors.
Thereby, the data obtained from different gamma-ray telescopes are heterogeneous and the joint analysis of these data is complicated. 2.2 X-rays
To date, the X-ray observations (above 0.1 keV) of GRBs are predominantly obtained by Swift/XRT, a focusing X-ray telescope operating in 0.2 - 10 keV energy range [22]. It was designed to measure the fluxes, spectra, and light curves of GRBs prompt emission and afterglow over a wide dynamic range.
Swift/XRT supports three (imaging, windowed an photon-counting) readout modes to extend the dynamic range and to reveal rapid variability expected from GRB afterglows and autonomously determines which readout mode to use.
INTEGRAL/JEM-X is operating in the photon-byphoton mode in the 3 – 35 keV energy range and uses coded aperture mask for imaging [23]. It has much lower sensitivity comparing with Swift/XRT, making the observations of the X-ray afterglows almost impossible.
But JEM-X is capable of registering the prompt phase of GRBs ‘by chance’ due to its large field of view (7.5 deg. in diameter), allowing the investigation of the GRB at the beginning of the prompt phase including searching for precursors (see, e.g. [24]). Swift/XRT starts the GRB observations with the delay of several dozens of seconds due to slewing of the spacecraft.
As the consequence Swift/XRT provides deep soft Xray afterglow observations, but INTEGRAL/JEM-X provides the prompt phase observations, so the data obtained by both experiment are not equivalent but complementary.
In optical range, GRBs are observed by both space- and ground-based telescopes.
Swift/UVOT is space telescope, operating in the 170 - 600 nm bandwidths [22].
On the ground, gamma-ray bursts are observed by a large number of telescopes (or collaborations of telescopes) with mirror diameters from 20 cm to 10 meters (corresponding upper limits of the registered flux are from 15th to 26th magnitudes).
Some of the collaborations providing follow-up GRB observations in optic are IKI FUN (IKI Follow-Up Network) and International Scientific Optical Network (ISON) [25].
In the GRB optical observations wide-band filters in the Johnson-Cousins UBVRI system and the Sloan Digital Sky Survey ugriz system are commonly used. The UBVRI system’s magnitude zero-points were set by defining Vega to have colours of zero. The sensitivity maximum of U-band is 366.3 nm, B-band - 436.1 nm, Vband - 544.8 nm, R-band - 640.7 nm, I-band - 798.0 nm. The Sloan Digital Sky Survey ugriz system is based on flux measurements that are calibrated in absolute units, namely spectral flux densities, with a zero-point of 3631 Jansky (Jy). The sensitivity maximum of u-band is 356.6 nm, g-band - 463.9 nm, r-band - 612.2 nm, i-band - 743.9 nm, z-band - 889.6 nm [26].
The R-band is the most used for GRBs observations due to significant galactic and extragalactic absorption at higher frequencies.
Optical raw data are formed by the detectors array such as charge-coupled device (CCD) and are represented as images. Because of the time variations of the CCD characteristics and of the telescope optics (e.g. dust accumulation) each individual run is reduced separately. However, in order to have a data set as homogeneous as possible, the data reduction strategy should be identical. In the optical range the brightness (energy flux) of the astrophysical objects is measured in stellar magnitudes.
We analyzed light curves of the GRB 030329, GRB 151027A, GRB 160131A, GRB 160227A and GRB 160625B in optical and X-ray range to find and identify deviations (inhomogeneities) from broken power law.
The optical data were obtained by Crimean Astrophysical Observatory (CrAO), Sayan Solar Observatory (Mondy), Tian Shan Astrophysical Observatory (TShAO), Maidanak High-Altitude Observatory, Abastumani Astrophysical Observatory (AbAO), Special Astrophysical Observatory (SAO), ISON-Kislovodsk, ISON-Khureltogoot, ISON-NM observatories and taken from GCN observation report circulars2. Observations were performed with an R-band of Johnson-Cousins system (approx. 90% of the total number of observations) and Clear filter. The optical photometrical data reduction is based on IRAF3 standard tasks (/noao/digiphot/apphot). Finally, we performed cross-calibration analysis of photometrical data obtained with Clear and R filters to minimize selection effects (convergence to R-band data).
Optical data of GRB 030329 and GRB 160625B were taken from [27, 28]. The X-ray afterglow data of GRB 030329 were obtained by Rossi-XTE and XMM-Newton [29] in 0.5–2 keV range, the X-ray light curves of other GRBs received by Swift/XRT4 in range of 0.3–10 keV.
The optical and X-ray light curves of the analyzed
The light curves of GRB 151027A, GRB 160131A and
GRB 160625B were approximated by a smoothly broken
power law (Beuermann function, see e.g. [
for this burst = 0
Beuermann functions: =
2 ∑ =1 0 [(
where α, β are the early and late power law indices, tbr is time of jet-break, ω is the smoothing parameter. The parameters α, β, tbr were fitted, t0 (time offset) and ω were fixed (t0 = 0, w = 1, 2, 3, 5, 7).
In case of GRB 160227A we use single power law model (see the formula 2), as we have only data for the first day after the burst trigger, probably before a jet-break time The GRB 030329 was modelled by a sum of two curves of GRB 030329 and GRB 160625B. (1) (2) (3) 2 https://gcn.gsfc.nasa.gov/gcn3 archive.html observatories. 3 IRAF is distributed by the National Optical astronomy
2 keV for GRB 030329 and 0.3–10 keV for other bursts. The host galaxy contribution was subtracted in the light
The optical light curves reveal a number of inhomogeneities, superposed over the power-law decay (see Table 1). The inhomogeneities were approximated by polynomials.
We separate the inhomogeneities into several classes.
Flares (positive residuals) were found for the first time in the X-ray light curve of GRB 970508 [30, 31], later they have been observed in all phases of the canonical X-ray light curve [32].
In several GRB light curves, flares in X-ray and optical are synchronous. In our sample we found two such X-ray/optical flashes in GRB 151027A.
bumps.
optical light curve has a complex structure with an additional component, which is not visible in X-rays. optical flares detected by UVOT/Swift found in [32] are also plotted. For the UVOT sample only start and stop times of flashes are available, i.e. total duration of the flares. We use half of duration for each flash to put it on the Figure 3. The correlation between FWHM and Tpeak found previously in [33] is evident. We fitted the FWHM - Tpeak scatterplot for the combined sample using the power-law logarithmic model: log ( 1 ⅆ ) = (1.05 ± 0.03) log ( ) Tpeak. Earlier, the positive correlation between the arrival time and duration of X-ray flares was noted in [29].
It is interesting that all types of inhomogeneities introduced previously (wiggle, flare, bump, etc.) follow the same correlation (see Figure 3), possibly indicating their similar physical nature.
The
Tpeak relation for inhomogeneities, constructed for ones from our sample and for flares detected by UVOT/Swift from [32]. Thick solid line represents power-law fit to the joint sample, dotted lines bound 2 sigma correlation region.
In this paper, we analyzed the inhomogeneities of several GRB afterglow optical light curves. There are totally 23 inhomogeneities identified in five well sampled light curves. The inhomogeneities were classified as flares, bumps, wiggles and nonclassified.
The sample of 119 UV/optical flares from [32], mostly observed at early times (Tpeak < 0.02 days) was jointly analyzed. We completed the sample by the late time inhomogeneities (21 at Tpeak > 0.08 days).
All types of inhomogeneities from our sample and UVOT flares follow the same correlation between FWHM and Tpeak, suggesting possible similar physical nature or strong selection effect. The power law index of the dependence is about 1 indicating a linear dependence of FWHM and Tpeak.
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