Probing cosmic isotropy with Gamma-ray bursts: A dipole and quadrupole analysis of BATSE and Fermi GBM data

TL;DR

The paper tests the cosmological principle by analyzing the angular distribution of gamma-ray bursts from BATSE and Fermi GBM. It uses a dipole and quadrupole analysis via spherical-harmonic decomposition on HEALPix sky maps, comparing observed amplitudes to 500 isotropic Monte Carlo realizations to assess significance. A key finding is that BATSE’s apparent quadrupole excess is eliminated after applying the sky exposure function, while Fermi GBM shows a moderate quadrupole excess that remains inconclusive due to the lack of a full-sky exposure model; both datasets show no significant dipole anisotropy. Overall, the GRB sky is consistent with statistical isotropy at large angular scales, underscoring the importance of accurate exposure modeling in cosmological isotropy tests and demonstrating the robustness of the method across independent GRB catalogs.

Abstract

The cosmological principle, asserting large-scale homogeneity and isotropy, underpins the standard model of cosmology. Testing its validity using independent astronomical probes remains crucial for understanding the global structure of the Universe. We investigate the angular distribution of Gamma-Ray Bursts (GRBs) using two of the most comprehensive all-sky datasets available, the BATSE (CGRO) and Fermi GBM catalogs, to test the isotropy of the GRB sky at large angular scales. We perform spherical harmonic decomposition of the GRB sky maps and estimate the dipole and quadrupole amplitudes. Statistical significance is evaluated by comparing the observed multipole amplitudes against distributions derived from 500 Monte Carlo realizations of isotropic skies. Our results show that the observed dipole amplitudes for both BATSE and Fermi GBM datasets lie within the $1σ$ region of their respective null distributions. However, the quadrupole amplitude in the raw, uncorrected BATSE and Fermi GBM skies appears elevated at $3.7σ$ and $3.0σ$, respectively. After incorporating the BATSE sky exposure function, this apparent quadrupole anisotropy vanishes, indicating that instrumental non-uniformities fully account for the signal in that case. Owing to the absence of a publicly available full-sky exposure model for Fermi GBM, the Fermi analysis is restricted to the raw sky distribution. Our method's reliability is validated through controlled simulations, which show it can detect the injected dipoles in BATSE-sized isotropic skies. These findings reinforce the statistical isotropy of the GRB sky and underscore the importance of accurate exposure corrections in cosmological anisotropy analyses.

Figures (25)

• Figure 1: This shows the angular distribution of 2702 GRBs from the BATSE catalog (top panel) and a uniform random distribution of 2702 simulated points (middle panel), shown in Mollweide projection and Galactic coordinates. Bottom panel shows HEALPix map of fluctuation of GRBs from the BATSE catalog using $\mathrm{N_{side}=8}$.
• Figure 2: This shows the angular distribution of 4032 GRBs from the Fermi GBM catalog (top panel) and a uniform random distribution of 4032 simulated points (middle panel), shown in Mollweide projection and Galactic coordinates. Bottom panel shows HEALPix map of fluctuation of GRBs from the Fermi GBM catalog using $\mathrm{N_{side}=8}$.
• Figure 3: Comparison of dipole amplitudes from four simulated dipole skies ($a = 0.09, 0.10, 0.12, 0.14$) with the estimated PDF obtained from $500$ Monte Carlo simulations of isotropic skies (2702 GRBs each). All injected dipole amplitudes lie beyond the 1$\sigma$ region of the null distribution. The HEALPix resolution parameter $\mathrm{N_{side}}=8$ has been used for this analysis.
• Figure 4: Same as \ref{['fig:5']}, but for simulated isotropic and dipole skies each containing $20{,}000$ points. Four dipole skies with amplitudes $a = 0.022, 0.032, 0.042,$ and $0.052$ were generated, maintaining the same dipole direction used in \ref{['fig:5']}.
• Figure 5: This shows the comparison of the observed dipole amplitude for the BATSE dataset with the PDF obtained from Monte Carlo simulations of 500 isotropic skies containing 2702 points each. The red step histogram shows the binned PDF, while the dashed black line represents the KDE-smoothed curve. The shaded region marks the $\pm1\sigma$ interval around the mean. The vertical dashed blue line represents the mean of the distribution and the downward black arrow indicates the observed BATSE dipole amplitude, which lies within the $1\sigma$ range, suggesting no significant deviation from isotropy. The analysis was performed using a HEALPix resolution parameter of $\mathrm{N_{side}} = 8$.