# Stringent Upper Bounds on Atmospheric Mass Loss from Three Neptune-Sized Planets in the TOI-4010 System

## TL;DR

This study uses helium transit observations to set stringent upper limits on atmospheric mass loss rates for three Neptune-sized planets in the TOI-4010 system, challenging existing hydrodynamic escape models.

## Contribution

It provides the first upper bounds on atmospheric escape for multiple planets in a single system, highlighting discrepancies with standard hydrodynamic models.

## Key findings

- Upper bounds on helium absorption are below 1.3%.
- Mass loss rate limits are around 10^10.5 g/s.
- Results challenge predictions from one-dimensional hydrodynamic models.

## Abstract

Photoevaporative models predict that the lower edge of the Neptune desert is sculpted by atmospheric mass loss. However, the stellar high energy fluxes that power hydrodynamic escape and set predicted mass loss rates can be uncertain by multiple orders of magnitude. These uncertainties can be bypassed by studying mass loss for planets within the same system, as they have effectively undergone scaled versions of the same irradiation history. The TOI-4010 system is an ideal test case for mass loss models, as it contains three Neptune-sized planets with planet b located in the `Neptune desert', planet c in the `Neptune ridge', and planet d in the `Neptune savanna'. Using Keck/NIRSPEC, we measured the metastable helium transit depths of all three planets in order to search for evidence of atmospheric escape. We place upper bounds on the excess helium absorption of 1.23\%, 0.81\%, and 0.87\% at 95\% confidence for TOI-4010~b, c and d respectively. We fit our transmission spectra with Parker wind models and find that this corresponds to 95th-percentile upper limits of $10^{10.17}$g~s$^{-1}$, $10^{10.53}$g~s$^{-1}$, and $10^{10.50}$g~s$^{-1}$ on the mass loss rates of TOI-4010~b, c, and d respectively. Our non-detections are inconsistent with expectations from one-dimensional hydrodynamic models for solar composition atmospheres. We consider potential reductions in signal from a decreased host star XUV luminosity, planetary magnetic fields, enhanced atmospheric metallicities, and fractionation, and explore the implications of our measurements for the past evaporation histories of all three planets.