# Planetary line-to-accretion luminosity scaling relations: Extrapolating to higher-order hydrogen lines

## TL;DR

This paper extends existing hydrogen-line luminosity scaling relations for planetary-mass objects to higher energy levels, improving the accuracy of accretion luminosity estimates from observed spectral lines.

## Contribution

It introduces a method to extrapolate scaling relations to higher-n hydrogen lines, enhancing the applicability of these relations to new observational data.

## Key findings

- Extended the scaling relations to higher-n hydrogen lines.
- Validated the extrapolation method under accretion shock assumptions.
- Provided improved tools for analyzing planetary accretion luminosities.

## Abstract

Aoyama et al. (2021, ApJL) provided scaling relations between hydrogen-line luminosities and the accretion luminosity for planetary-mass objects. These fits should be an improvement over blind extrapolations of stellar relations. The fits go up only to the n = 8 electron energy level, but higher-n Balmer lines have been observed in the near-UV at Delorme 1 (AB)b with UVES (Ringqvist et al. 2023). We extend the scaling relations to higher-n levels for the Balmer and other series by fitting the fit coefficients (a, b) themselves and extrapolating them. Within the assumption of an accretion shock as the source of line emission, these fits should be robust for accreting planetary-mass objects.