High-resolution international LOFAR observations of 4C~43.15 -- Spectral ages and injection indices in a high-z radio galaxy

Abstract: Radio sources with steep spectra are preferentially associated with the most distant galaxies, the $\alpha-z$ relation, but the reason for this relation is an open question. The spatial distribution of spectra in high-z radio sources can be used to study this relation, and low-frequency observations are particularly important in understanding the particle acceleration and injection mechanisms. However, the small angular sizes of high-z sources together with the inherently low resolution of low-frequency radio telescopes until now has prevented high angular resolution low-frequency observations of distant objects. Here we present subarcsecond observations of a $z = 2.4$ radio galaxy at frequencies between $121$ MHz and $166$ MHz. We measure the spatial distribution of spectra, and discuss the implications for models of the $\alpha-z$ relation. We targeted 4C 43.15 with the High Band Antennas (HBAs) of the \textit{International LOFAR Telescope} (ILT) with a range of baselines up to $1300\ \mathrm{km}$. At the central frequency of $143$ MHz we achieve an angular resolution of $\sim 0.3''$. By complementing our data with archival \textit{Very Large Array} (VLA) data we study the spectral index distribution across 4C 43.15 between $55\ \mathrm{MHz}$ and $8.4\ \mathrm{GHz}$ at resolutions of $0.4''$ and $0.9''$. With a magnetic field strength of $B = 5.2$ nT and fitted injection indices of $\alpha^\mathrm{north}_\mathrm{inj} = -0.8$ and $\alpha^\mathrm{south}_\mathrm{inj} = -0.6$, fitting a Tribble spectral ageing model results in a spectral age of $\tau_\mathrm{spec} = 1.1 \pm 0.1$ Myr. We conclude that our data on 4C 43.15 indicates that inverse Compton losses could become comparable to or exceed synchrotron losses at higher redshifts and that inverse Compton losses could be a viable explanation for the $\alpha-z$ relation.

• The paper determines spectral ages (1.1 Myr) and injection indices (-0.8 and -0.6) using a Tribble spectral aging model.
• The study employs high-resolution ILT observations and VLA archival data to achieve subarcsecond spatial resolution of the radio lobes.
• The findings imply inverse Compton losses significantly influence the α–z relation in high-z radio galaxies, guiding future surveys.

High-resolution International LOFAR Observations of 4C 43.15: Insights into Spectral Ages and Injection Indices in a High-z Radio Galaxy

This paper presents a detailed analysis of the high-redshift radio galaxy 4C 43.15 using high-resolution observations from the International LOFAR Telescope (ILT) at frequencies between 121 MHz and 166 MHz. By achieving subarcsecond resolution through the array's long baselines, the authors address the spatial distribution of spectra within the radio galaxy and provide insights into the $\alpha-z$ relation, which describes the correlation between radio spectral index and redshift.

Observational Approach and Data Reduction

The study utilizes observations from the LOFAR High Band Antennas (HBAs) with baselines extending up to 1300 km, resulting in an angular resolution of approximately 0.3 arcseconds at a central frequency of 143 MHz. This resolution is crucial for resolving spatial details of the radio lobes. The authors complemented their LOFAR data with archival Very Large Array (VLA) observations, enabling a multi-frequency analysis from 55 MHz to 8.4 GHz.

Spectral Analysis and Key Findings

• Injection and Spectral Ages: By fitting a Tribble spectral aging model, the authors determine spectral ages for the plasma. The fitted injection indices are $\alpha^\mathrm{north}_\mathrm{inj} = -0.8$ and $\alpha^\mathrm{south}_\mathrm{inj} = -0.6$, with a spectral age of $\tau_\mathrm{spec} = 1.1 \pm 0.1$ Myr.
• Magnetic Field Strength: The magnetic field strength is estimated at 5.2 nT, suggesting that synchrotron cooling is the dominant mechanism, but very close to inverse Compton losses due to the cosmic microwave background (CMB) photons. This highlights the potential significance of inverse Compton losses in high-redshift radio galaxies.
• Implications for the $\alpha-z$ Relation: The observations and modeling suggest that inverse Compton losses could play a substantial role in explaining the $\alpha-z$ relation. The comparable losses imply that in environments with weaker magnetic fields, inverse Compton losses may dominate, providing a feasible explanation for the observed correlation.

Implications and Future Prospects

The findings support the hypothesis that increased inverse Compton losses at higher redshifts significantly affect spectral indices, contributing to the $\alpha-z$ relation. This highlights the necessity for further high-resolution, low-frequency studies of high-redshift radio galaxies to statistically evaluate the influence of inverse Compton losses and differentiate them from potential environmental effects or observational biases.

Future wide-area subarcsecond surveys with facilities like LOFAR will enable a more comprehensive statistical study of high-redshift radio sources. Such surveys will shed light on the systemic drivers of spectral shape changes with redshift, thus refining our understanding of how cosmic environments affect the evolution of radio-emitting regions in galaxies over cosmic time scales. This work sets a precedent for future explorations of radio spectral aging in the early universe, with implications for galaxy evolution and the interplay between AGN feedback and cosmic microwave background interactions.