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Today's Halacha:
If a person, for whatever reason, is not fasting on a public fast day, such as Ta’anit Ester, may he be called for an Aliya to the Torah during the congregational Torah reading? On fast days we conduct the special Torah reading of "Vayehal" both at Shaharit and at Minha. May a person receive an Aliya during those readings if he is not observing the fast?
The general rule is that one may not receive an Aliya to the Torah on a fast day if he is not fasting, even if he is legitimately exempt from the fast due to health reasons and the like. Even if the only Kohen in the synagogue is not fasting, he should not receive the first Aliya. Instead, he should be asked to leave and somebody else should be called in his place. And even if this Kohen was invited to come for an Aliya, he must decline, since he is not observing the fast, and somebody else should be called for the Aliya. Although normally a person who is called for an Aliya must oblige, in this instance, the Kohen should decline and explain that he is not observing the fast.
This applies to a Levi, as well. If the only Levi in the synagogue is not observing the fast, he should leave and somebody else should be called for the second Aliya in his place.
This applies even if somebody has not eaten yet in the morning, but plans on eating at some point during the day. Since he intends to eat during the fast, he is not considered as observing the fast even before he eats, and should thus not be given an Aliya.
The exception to this rule is a situation where a fast is observed on Monday or Thursday. (For example, this year, 5771, the day of Ta’anit Ester falls on Shabbat, and the fast is therefore observed on the previous Thursday, 11 Adar.) On Monday and Thursday, we read the Torah during Shaharit irrespective of the fast day. Therefore, since the Torah would be read that day even if it were not a fast day, a person who is not fasting may receive an Aliya. Of course, this applies only during Shaharit. The Torah is not read at Minha on an ordinary Monday or Thursday, and therefore a person who does not observe the fast may not receive an Aliya during Minha on a fast day, even if it falls on Monday or Thursday. This ruling appears in Yalkut Yosef – Purim (p. 75), and is cited from Hazon Ovadia – Hilchot Ta’anit (p. 112).
Summary: A person who, for whatever reason, is not fasting on a public fast day may not receive an Aliya to the Torah, even if he is not fasting due to a valid Halachic exemption, and even if he is the only Kohen or Levi present in the synagogue. The exception to this rule is a fast day that is observed on Monday or Thursday, in which case one who is not fasting may receive an Aliya during the reading at Shaharit (but not at the reading during Minha).
