1) LETTING THE KOHEN GADOL STAY WITH HIS WIFE
QUESTION: The Gemara asks why the Kohen Gadol must separate from his wife during his Perishah before Yom Kippur. She should be permitted to remain in isolation together with him.
How can the Gemara suggest that the Kohen Gadol remain together with his wife when he isolates himself in the Lishkas Parhedrin? The Lishkah is located in the Azarah (11a), and a Ba'al Keri is prohibited not only from entering the Azarah but also from entering any part of Har ha'Bayis altogether (Pesachim 67b). How, then, could the Kohen Gadol be permitted to remain there with his wife?
(a) RASHI (DH mi'Beiso) proves that the Lishkas Parhedrin does not have the Kedushah of the Azarah. If it did, the Kohen Gadol would be required to stand there for all seven days without sitting down at all, because one is forbidden to sit in the Azarah. Therefore, a Ba'al Keri is also permitted to be there.
TOSFOS (DH mi'Beiso) rejects this answer. He argues that even if the Lishkah does not have the Kedushah of the Azarah because it opens into Har ha'Bayis and not into the Azarah (and as a result it is considered part of Har ha'Bayis and not part of the Azarah, and thus sitting there is permitted), it still has the Kedushah of Har ha'Bayis, and a Ba'al Keri is not permitted to enter Har ha'Bayis.
Perhaps Rashi means that the Lishkah does not have Kedushah at all because it is built on the roof of another structure. The Gemara in Pesachim (86a) teaches that the roofs of the structures on Har ha'Bayis do not have Kedushah at all.
(b) TOSFOS and the TOSFOS YESHANIM explain that the Gemara's question is why the Kohen Gadol must isolate himself in the Azarah in the first place; let him go to a place which has no Kedushas Azarah, such as the underground chambers (Mechilos) beneath Har ha'Bayis (which have no Kedushah, as the Gemara says in Pesachim 86a).
(c) TOSFOS YESHANIM adds that the Kohen Gadol does not have to be in seclusion for the entirety of the seven days. He is permitted to go out for short periods of time to take care of his needs, just as Aharon ha'Kohen went out of the Machaneh Leviyah during his Perishah at the time of the Milu'im (his Perishah was in the Mishkan, and the Mishkan was dismantled every night and had no Kedushah when it was dismantled). The Gemara's question is that even though the Kohen Gadol is isolated in the Azarah, he should be allowed to go out to meet his wife in the underground chambers during the short periods that he goes out of seclusion.
2) SEPARATING THE KOHEN GADOL FROM A "SAFEK NIDAH"
QUESTION: The Gemara says that the Kohen Gadol must separate from his wife during the seven days of Perishah, because if he is allowed to be with her she might discover that she is a Nidah a short time after they have relations. Consequently, she had the status of a Safek Nidah at the time they were together.
Why does the Gemara not say simply that she might discover immediately afterwards that she is a Nidah, and thus she had the status of a Vadai Nidah at the time they were together?
(a) TOSFOS in Nidah (15a) and the TOSFOS YESHANIM here explain that there is no concern that she will discover that she is a Nidah immediately after relations, because such a case is very unusual. The only concern is that she will discover that she is a Nidah a short time afterwards, in which case she had the status of a Safek Nidah at the time they were together.
(b) The TOSFOS RID says that the Gemara's intention is to emphasize how important it is that the Kohen remain Tahor on Yom Kippur. In order to ensure his Taharah, the Rabanan instituted an enactment that will prevent the Kohen Gadol from inadvertently living even with a Safek Nidah, and not only with a Vadai Nidah.
3) THE PRIVATE KORBAN OF THE KOHEN GADOL OVERRIDES "TUM'AH"
QUESTION: The Gemara points out that the Kohen Gadol is isolated only from his wife to prevent him from becoming Tamei with Tum'as Bo'el Nidah (or Safek Nidah). He is not isolated from all other people to prevent him from becoming Tamei with Tum'as Mes. The Gemara proves from here that "Tum'ah Hutrah b'Tzibur": even if the Kohen Gadol becomes Tamei, he may perform the Avodah, even l'Chatchilah, for a Korban Tzibur while he is Tamei with Tum'as Mes.
However, besides the Korbanos that the Kohen Gadol offers on Yom Kippur on behalf of the Tzibur, he also brings a Korban Yachid for himself (the Par and Ayil of the Kohen Gadol). The principle of "Tum'ah Hutrah b'Tzibur" applies only to a Korban of the Tzibur, but not to an individual's private Korban. The Gemara (7a) teaches that the "Ayil of Aharon" of Yom Kippur is a Korban Yachid. (Although that Korban is similar to a Korban Tzibur in that it has a set time ("Zeman Kavu'a"), it is not considered a Korban Tzibur because it is not owned by the Tzibur.) Why does the Gemara here assume that the Kohen Gadol may offer all of the Korbanos of Yom Kippur while he is Tamei with Tum'as Mes?
(a) The RITVA explains that the Par of Aharon, although privately owned, is considered a Korban Tzibur (so that Tum'ah is Hutrah for it). It is considered a Korban Tzibur because the atonement of the Tzibur depends on it, since its blood must be sprinkled in the Kodesh ha'Kodashim together with the blood of the Sa'ir (the Korban which provides atonement for the Tzibur). The Acharonim (see SI'ACH YITZCHAK) explain that this is also the intention of Rashi (DH Hutrah) when he says that "the Korban [of the Jewish people] depends on it" (on the Par of Aharon).
However, this explains only why the Kohen Gadol's Par is considered a Korban Tzibur. Why, though, is his Ayil considered a Korban Tzibur, such that Tum'ah is Hutrah for it?
The Ritva explains that the principle of "Tum'ah Hutrah b'Tzibur" means that every effort must be made to avoid offering a Korban in a state of Tum'ah. The Gemara here is not discussing the actual offering of the Korban in a state of Tum'ah. Rather, the Gemara is discussing whether the Rabanan were so stringent as to require that the Kohen Gadol separate from all people for seven days to avoid becoming Tamei with Tum'as Mes. He is not actually Tamei with Tum'as Mes now. With regard to the extent of effort that must be exerted in order to ensure that the Ayil is not offered in a state of Tum'ah, the Rabanan said that Tum'ah is Hutrah and did not require that such extreme measures be taken to prevent the Kohen Gadol from becoming Tamei with Tum'as Mes.
(b) Alternatively, the Ritva in the name of TOSFOS says that the fact that the Ayil of Aharon cannot be offered in a state of Tum'ah (since it is not a Korban Tzibur) is not a reason to require that the Kohen Gadol separate from all people for seven days. Since it is only a single Korban, and it is only a Korban Yachid, the Rabanan did not find it necessary to separate the Kohen Gadol from all people merely to ensure that he brings his Ayil in a state of Taharah. (If he becomes Tamei, he will not bring his Ayil.)
(c) The TOSFOS YESHANIM (DH v'Tisbera) and the SHA'AGAS ARYEH (#38) answer that mid'Oraisa anything that has a set time (Zeman Kavu'a) is Hutrah b'Tzibur, even if it is a Korban Yachid. When the Gemara later says that the Ayil of Aharon is not offered in a state of Tum'ah because it is a Korban Yachid, it means that the Rabanan decreed that it not be offered. The Rabanan decreed that Tum'ah be avoided because the Ayil is a private Korban. Since mid'Oraisa it may be offered in a state of Tum'ah because it has a set time, the Rabanan did not require that the Kohen Gadol separate for seven days from all people to avoid becoming Tamei with Tum'as Mes. (See also TOSFOS to 8a, DH Iy Savar.)