Why is it essential to cook the yolks for an egg based sauce over a gentle heat and to whisk them continuously?

Cooking the yolks for an egg-based sauce over gentle heat is essential to prevent them from curdling or becoming scrambled. Gentle heat allows for a gradual thickening, ensuring a smooth, creamy texture. Continuous whisking helps to evenly distribute the heat and incorporates air, which contributes to the sauce's lightness and prevents the yolks from setting too quickly. This technique is crucial for achieving a stable emulsion in sauces like hollandaise or mayonnaise.