What is meant by “when he slept he used to breathe deeply” and “hearing him breathing deeply audibly”?
Question

I read some hadiths about the way in which the Messenger of Allah (blessings and peace of Allah be upon him) slept. Some of the reports mention that his wives and companions would know that the Prophet was sleeping from his deep breathing or audible breathing. When I told one of the brothers about that, he said: This is not possible, because breathing deeply or aundibly is contrary to what we know of the perfect characteristics of the Prophet (blessings and peace of Allah be upon him), and if this were true, he would be aware of it, because he did not really sleep, and he would have dealt with it. How can we respond to this specious argument?
Praise be to Allah.When the Prophet (blessings and peace of Allah be upon him) slept, he would breathe deeply, and sometimes he would breathe audibly. His heart never slept although his eyes slept, and his wudu’ would not be rendered invalid by sleep. All of that is proven in the sahih hadiths.
Al-Bukhari (698) and Muslim (763) narrated that Ibn ‘Abbas (may Allah be pleased with him) said: I slept in the house of Maymunah, and the Messenger of Allah (blessings and peace of Allah be upon him) was with her that night. He did wudu’, then he stood and prayed, and I stood on his left. He took hold of me and made me stand on his right. On that night he prayed thirteen rak‘ahs, then the Messenger of Allah (blessings and peace of Allah be upon him) slept until he started to breathe deeply, for when he slept he used to breathe deeply. Then the mu’adhdhin came to him and he went out and prayed, and he did not do wudu’.
An-Nawawi (may Allah have mercy on him) said in Sharh Muslim: Regarding the words “then he lay down and slept until he started to breathe deeply, then he got up and prayed, and did not do wudu’”: this was one of his unique characteristics, that if he slept lying down, his wudu’ was not rendered invalid, because although his eyes slept, his heart did not sleep, so if his wudu’ had been rendered invalid, he would have been aware of it, unlike other people. End quote.
Abu’l-Hasan al-Mubarakfuri said in Mir‘at al-Mafatih (4/174): “then he lay down and slept until he started to breathe deeply” means: breathing audibly, to the extent that the sound of his breathing from the mouth could be heard from him, as it is usually heard from one who is sleeping. End quote.
Al-Bukhari (7231) and Muslim (2410) narrated that ‘A’ishah said:  The Messenger of Allah (blessings and peace of Allah be upon him) could not sleep one night and said: “Would that a righteous man from among my companions would guard me tonight.” We heard the rattling of a weapon and the Messenger of Allah (blessings and peace of Allah be upon him) said: “Who is this?” Sa‘d ibn Abi Waqqaas said: O Messenger of Allah, I have come to guard you. ‘Aa’ishah said: Then the Messenger of Allah (blessings and peace of Allah be upon him) slept until I could hear him breathing audibly.
Al-Fayyumi said in al-Misbah al-Munir (2/449): The audible breathing of a sleeper refers to his inhalation reaching his throat, so that those around him can hear it. End quote.
Al-Khattabi (may Allah have mercy on him) said in Sharh al-Bukhari (1/479): Audible breathing is a sound made by one who is breathing in and out, like the sound of one who is being strangled. …  The meaning of this hadith has been discussed above. End quote.
This audible breathing is not the same as snoring, which comes from the nose. Al-Mulla ‘Ali al-Qari has refuted those who say that deep breathing and audible breathing come from the nose.
He (may Allah have mercy on him) said in al-Mirqat (3/904): “then he lay down and slept until he started to breathe deeply” means: breathing audibly, to the extent that the sound of his breathing from the mouth could be heard from him, as it is usually heard from one who is sleeping. Ibn Hajar [al-Haytami] said: He breathed deeply from his nose, hence it as referred to in another report as audible breathing, which is a sound from the nose which is an elongated sound. And it was said that they both mean the same thing; it is a sound heard from breathing in and out or when breathing with a movement of the head. End quote.
However, we have not found anything in the dictionaries to indicate that it is a sound from the nose. In an-Nihayah it says: Deep breathing is the sound that is heard when a sleeping person breathes, which is breathing in and out when the airways are not smooth. And he said: It is a sound made by one who is sleeping. In al-Qamus it says that deep breathing refers to a sound made by one who is sleeping. And Allah knows best. End quote.
Al-Bukhari (3569) narrated from Abu Salamah ibn ‘Abd ar-Rahman that he asked ‘A’ishah: How did the Messenger of Allah (blessings and peace of Allah be upon him) pray during Ramadan? She said: In Ramadan and at other times, he did not pray more than eleven rak‘ahs. He would pray four rak‘ahs, and do not ask how long and beautiful they were. Then he would pray four (more) rak‘ahs, and do not ask how long and beautiful they were. Then he would pray three. I said: O Messenger of Allah, do you sleep before you pray Witr? He said: “My eyes sleep but my heart does not sleep.”
Conclusion
Deep breathing and audible breathing do not mean that the heart cannot be awake, and they are not contrary to the perfect state and appearance of the Messenger of Allah (blessings and peace of Allah be upon him). They do not come under the heading of snoring, which comes from the nose.
And Allah knows best.