A new correlation has been discovered in optical observations of gamma ray bursts (GRBs) that may be the key to using GRBs as cosmological distance indicators, building on previous work last discussed here in Oct 2020. KIPAC alum Maria Dainotti, who is currently an assistant professor at the National Astronomical Observatory in Japan, mentored Samantha Livermore, a fourth-year physics major at Tufts University, for an optical wavelength study of an important characteristic of GRBs called the plateau emission. Dainotti worked with Livermore during Livermore’s Science Undergraduate Laboratory Internship (funded by the Department of Energy) at SLAC National Accelerator Laboratory and Stanford University in the summer of 2020.
Dainotti and Livermore worked with a large team of international collaborators located in the US, Europe, Mexico, and Australia to gather a large amount (267 individual observations) of optical GRB data and conduct a rigorous statistical analysis. This research, a continuation of previous work on the plateau emission of GRBs (Dainotti, et al., 2017 and earlier), features the largest sample of optical plateaus in the literature to date, and is published in an article entitled The Optical Luminosity-Time Correlation for More Than 100 Gamma-Ray Burst Afterglows (NASA/ADS link) (Jan 2020).
Finding plateaus beyond the X-ray wavelength
The "plateau emission" is a feature commonly found in X-ray observations of GRBs marked by, as the name suggests, a length of time (typically from a few minutes, 100 seconds all the way to ~105 seconds, or a few months) during which emissions remain relatively stable. This phase has been the subject of much study in the GRB community in recent years. The same length of time plateau is also observed in optical wavelengths (Figure 3). One of the possible explanations for the plateau emission is that it is due to the existence of a newly formed fast-spinning neutron star. This feature appears after the GRB's initial quick burst, called the prompt emission, and is followed by a steadily decaying afterglow as the GRB fades away.
The most interesting features of plateau emissions are their luminosity and the point in time when the plateau phase ends. These parameters are connected through the luminosity-time correlation in X-rays, which states that in X-ray observations of GRBs, there is an anticorrelation between the luminosity during the plateau phase and how long the plateau emission continues—in other words, the brighter the plateau, the shorter it lasts (Dainotti et al. 2008). This correlation has been tested previously against selection biases in collaboration with KIPAC professor Vahe Petrosian (previously discussed in a 2016 post). Thus, encouraged by the intrinsic nature of this correlation, in this most recent work Livermore, Dainotti, and collaborators find that this luminosity-time correlation also holds in optical observations, extending the correlation and its implications further across the electromagnetic spectrum.
The team studied 267 GRB optical light curves (mostly from the Neil Gehrels Swift Observatory) and found that 102 of them had well-defined plateaus seen by fitting the curves with a phenomenological model known as the Willingale model, shown in the left panel of Figure 1. Once the plateaus are identified, the luminosity-time parameters of each GRB are gathered for a large statistical analysis. When the luminosity-time data are plotted for the entire sample, it is clear that the luminosity-time correlation can also be found in optical plateaus, similar to the X-ray plateaus as had been shown previously.
This X-ray/optical correlation implies that the energy reservoir of the GRB is constant during the plateau emission (since it happens in two otherwise completely unrelated parts of the spectrum), which aids astrophysicists in unifying a large population of GRB events. It is an extremely interesting and challenging task to standardize groups of GRBs in order to take advantage of their incredible luminosity and use them as standard candles. The problem is that GRBs vary in duration, brightness, progenitor system, and morphological features. In order to use GRBs to measure distances in the Universe, we need to better understand their emission mechanisms and find features that unify their larger population—this is why the existence of the luminosity-time correlation in optical plateaus is so crucial. Looking at relationships between observable parameters of the plateau helps to define intrinsic patterns that could unify a diverse population of GRBs.
The possibility of magnetar sources
The model of the GRB arising from newly born, rapidly rotating neutron stars with extremely strong magnetic fields (called magnetars) predicts just such an observable plateau phase, with plateau durations and luminosities being determined by the magnetic fields and spin periods of the newly formed magnetar. The properties of the magnetar which relate the luminosity and the time in which the energy is injected into the plateau (which is related to the end time of the plateau) then determine the radius, magnetic field and spin period of a rapidly rotating newly born magnetar.
Previous work of Dainotti and other researchers (Rownlinson et al. 2014, Rea et al. 2015, Strata et al. 2018) determined that it is indeed possible in the magnetar scenario to easily derive a luminosity inversely proportional to the time duration of the plateau with the observed slope of -1. Thus, within the magnetar model it is possible to recover this correlation naturally, which suggests that magnetars are good candidates for the cause of the plateau emission. If magnetars are indeed the source of the observed light curves with their characteristic plateaus, it is possible that the source of the dispersion of the optical luminosity-time correlation (as seen in Figure 2) originates in the spread of initial spin periods and magnetic fields of the newly formed magnetar.
Not only was the familiar X-ray correlation reproduced in optical observations, but the correlation was found to be constant even in different sub-samples of GRBs. When the 102 GRBs were divided by classification and plateau inclination, the correlation did not vary significantly, showing that the optical luminosity-time correlation holds across a varied population of GRBs.
Besides the main correlation in question, the research uncovered another link between optical and X-ray observations of GRBs: the rest-frame end-time of the plateau emission. According to a standard t-test (a statistical measure of the similarity of two distributions), the plateau end-times in optical observations are not significantly different from the end-times in the corresponding X-ray data, as shown in Figure 3. The two histograms in optical and in X-ray show that the time at which the plateau emission ends is achromatic, or independent of the electromagnetic regime in which it is observed. This means that it may be related to the geometry of the emission of GRBs. It is compelling that the candidate feature, the plateau, to standardize GRBs is achromatic between the X-rays and optical, the two wavelengths in which the majority of plateaus are observed. This could eventually lead to us understanding much more about the fundamental mechanisms of these GRBs.
Determination of the intrinsic Luminosity Time Correlation in the X-ray Afterglows of GRBs Maria Giovanna Dainotti, Vahe' Petrosian, Jack Singal, Michal Ostrowski (arXiv version)
A fundamental plane for long gamma-ray bursts with X-ray plateaus Maria Giovanna Dainotti, Sergey Postnikov, Xavier Hernandex, Michel Ostrowski (arXiv version)
A Study of the Gamma-Ray Burst Fundamental Plane Dainotti, et al., 2017 (arXiv version)
Gamma-Ray Bursts: A 3d Step Toward Standard Candles NASA press release