Travel Times of a Descending Melting Probe on Europa

In this study, we calculated the travel times of a thermal probe that descends through Europa's ice shell. The ice column is simplified to a conductive layer. Using a cellular automaton model, the descent of the probe was simulated by tracking temperature changes, with cell interaction dictated by heat conduction and cell state transition rules determined by cell temperatures. Validation tests, including a soil column simulation, and comparison with experimental data, support the reliability of the model. Simulations were performed with 2 different cell sizes, 19 constant probe temperatures, and 5 ice thermal conductivities. A smaller cell size (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>Δ</mml:mtext><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn><mml:mo> </mml:mo></mml:mrow></mml:math>mm) produced shorter travel times (between 22 days for a probe temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>600</mml:mn><mml:mi>K</mml:mi></mml:mrow></mml:math> and ∼4 years for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>280</mml:mn><mml:mi>K</mml:mi></mml:mrow></mml:math>) than a larger cell size (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>Δ</mml:mtext><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo> </mml:mo></mml:mrow></mml:math>m), which produced travel times between 27 years (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow><mml:mo>=</mml:mo></mml:mrow></mml:math> 600K) and ∼10³ years (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow><mml:mo>=</mml:mo></mml:mrow></mml:math> 280K). The ice shell's thermal conductivity has a modest impact on descent times. The results are generally consistent with previous approaches that used more detailed probe engineering considerations. These results suggest that a probe relying solely on heat production may traverse Europa's conductive ice shell within a mission's timeframe.