Step 1: Recall what triggers this hypothalamic response.
The blood that reaches the brain through the carotid artery is checked for its osmolality before it even reaches the general circulation. A group of cells in the hypothalamus called osmoreceptors sense this.
Step 2: Locate the osmoreceptors.
These osmoreceptor cells sit next to, and functionally overlap with, the supraoptic nucleus. The supraoptic nucleus is the same nucleus that makes ADH (vasopressin) and sends it down the pituitary stalk to the posterior pituitary for release.
Step 3: Connect the carotid injection to the nucleus.
In the classic experiments that mapped this pathway (Verney's dog experiments), saline of a different tonicity from plasma was injected straight into the carotid artery, so it reached the hypothalamus first, before dilution by the rest of the blood. This let researchers show that a change in the osmolality of carotid blood switches the firing rate of cells in and around the supraoptic nucleus, which then adjusts ADH release.
Step 4: Rule out the other nuclei.
The medial nucleus of the hypothalamus is tied to feeding behaviour and satiety, not blood osmolality.
The preoptic nucleus is mainly the body's temperature control centre.
The paraventricular nucleus also makes ADH and oxytocin, but the osmoreceptor field that responds first to a change in blood tonicity through the carotid artery is centred on the supraoptic nucleus.
Final Answer:
The hypothalamus is switched on through the supraoptic nucleus.
\[ \boxed{\text{Supraoptic nucleus of the hypothalamus}} \]