UR: GRBs – New Standard Candles for Cosmology

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Curtesy of Kamil Kalinowski

Kamil Krzysztof Kalinowski

Aarhus University, Denmark

Kamil Krzysztof Kalinowski graduated with a Bachelor’s degree in Astronomy from Jagiellonian University in Cracow, Poland (2019-2022). He is currently studying towards a Master’s degree in Astronomy at Aarhus University, Denmark. He worked remotely in a group supervised by Prof. Maria Dainotti of National Astronomical Observatory of Japan during the third year of his studies.

Gamma-Ray Bursts (GRBs) are transient bursts of photons that explode daily all over the sky and they are of a great variety. Their light curve consists of a relatively short part when a large fraction of the total energy is emitted — prompt emission, and much longer afterglow. Despite the name, their afterglow spectrum extends over all the wavelengths. Some of them are believed to originate from explosions accompanying massive stars that collapse in the final stage of their evolution (the long-duration GRBs). Others, having different characteristics, are associated with neutron star merging events or black hole-neutron star mergers (the short-duration GRBs). Even within those 2 classes, their light curves can differ significantly. For example, some of the GRBs from both classes exhibit a plateau, others don’t. The plateau is a flat part of the light curve that occurs right after the prompt emission phase in a fraction of 42% of GRBs. However, one commonality is an immense absolute brightness or luminosity. That is why we can spot them despite their tremendous distances up to 13.2 billions of light years away.

One of the fundamental tools astronomers use to measure distances are what we call standard candles. These are the objects for which we have figured out how to determine their absolute brightness by measuring their other parameters. A basic example would be the Cepheids periodically variable stars. They exhibit a simple relation between their period and absolute brightness, so they are widely used to map our cosmic neighbourhood.

However, with limited radiation power, Cepheids can be observed no further than in the near galaxies. It would be advantageous to know various types of standard candles for measuring distances of both close and distant objects. It is crucial to develop tools for measuring cosmological distances to study the pace of the expansion of the universe, especially in the context of the Hubble tension. That’s why it is worth considering taking a look at GRBs, which, as mentioned before, can be extremely distant. Thus, the challenge lies in extracting from their diversity a parameter (or parameters) that is somehow related to their absolute brightness. And this is what we did.

To begin with, we gathered archival photometric observations of long and short GRBs with known redshifts in 18 optical bands (B, H, I, IC , J, K, KS , R, RC , V, Z, b, g, i, r, u, v, and z) from numerous telescopes, including Subaru, RATIR ground-based telescopes and Swift space observatory. Brightness measures from different bands were then converted to the R band. Afterwards, we plotted the R-band magnitude against rest-frame time to form light curves. Next step: out of 500 light curves gathered, we separated 179 GRBs clearly possessing a plateau. It is worth noting here that our sample consists of all the GRBs observed during the last 24 years and is the largest sample in the literature. We proceeded with the analysis only with the 179-GRB subsample possessing a plateau. This is important, as 2 of the parameters we are going to make use of to make GRBs standard candles are related to the plateau. 

We fit 3 model functions to each light curve. Knowing the redshifts (or distances) of the GRBs, we also computed their luminosity during the end of the plateau and at the peak of the prompt emission, when possible (in some of the cases the observation started too late to capture the prompt phase). Operating on the fitted parameters, we discovered a correlation between the rest frame time at the end of the plateau, T*_opt, and the luminosity at this time, L_opt.

Furthermore, for a subsample of 58 light curves showing a peak in the prompt phase we found an extended correlation between T*_opt, L_opt, and the peak luminosity during the prompt emission L_peak,opt. This 3D relation forms a plane (Figure 1). The formula of the relation is , where a and b are the best fitting parameters and C_0 is normalisation. Those correlations are similar to correlations previously found by Prof. Dainotti in X-ray (Dainotti et al. 2016, 2017b, 2020a), but in our estimation, the optical relation serves better as a distance indicator. The a, b and C_0 coefficients agree between the optical and X-ray plane within 1\sigma, 4\sigma, and 4\sigma respectively. Those correlations can be used to determine the absolute brightness of GRBs based on the measurement of the time of the end of the plateau, just as the period-brightness relation can be used to determine the Cepheid absolute brightness based on its period. Thus, they transform a large fraction of GRBs into standard candles! But we did more than that! 

The plane discovered in the paper along with data points. Parameters: time at the end of the plateau, the luminosity at this time and the luminosity maximum. Each point’s shape represents the different GRB class it belongs to. For example, black circles represent the long-duration GRBs while red cuboids represent the short-duration GRBs. The full list of the different classes can be found in our paper. Credit: gif version of a panel of Figure 3 in our paper.

Continuing the analysis, we applied the Kolmogorov-Smirnov statistical test to check if the distributions of the time at the end of the plateau emission registered in X-ray and optical differ from each other. More specifically, we compared the samples of rest frame times at the end of the X-ray and optical plateaus for 89 GRBs. The result was clear: it is unlikely that their distributions are the same. This could mean that its emission is not related to the geometry of the progenitor. Instead, we argue that the physical phenomena behind that emission is rather a highly magnetized neutron star (magnetar) formed during a collapse of a dying star (long GRBs) or during the merging of two neutron stars (short GRBs). Since hyper-accreting black holes can be a result of a stellar collapse, magnetars compete with them as the power source of GRBs. Our statistical approach is an important contribution to the long-standing debate on this subject, as previous analyses were all one-to-one comparisons. Those results are published in ApJS (M. G. Dainotti et al 2022 ApJS 261 25) and a short video describing our discovery below.

Credit: Kamil Kalinowski, Delina Levine, Sam Young, Maria Dainotti

Edited by: Huei Sears

Featured Image Credit: Kamil Krzysztof Kalinowski

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