The stylebook of the New York Times seems to advise against using diacritical marks, even when they're part of someone's name. But it would be hard to write an article about Arvo Pärt without that ä. However, as part of the article, the conductor Neemi Järvi and the composer Erkki-Sven Tüür rate only an a and us.
Unlike the Germans, who refer to those two dots as an umlaut and see them as modifying the (literally) underlying letter, the Estonians (at least the ones I've talked to about this) see ä as a different letter from a, and therefore don't seem to have a name for those two dots. "(pronounced PAIRT)" - well, not too bad, NYT, but you have to roll that r just a bit, and the P is aspirated less than we Americans do.
It's a pretty good article, although marred by the usual US overbroad characterizations of the countries that once were part of the Soviet Union and the reporter's failure to recognize the wealth of musical composition that Estonia offers.
Plus the Times has done some wonderfully self-referential thing that makes it awfully hard to copy from its articles. Maybe those responsible thought that an article about a composer from such a strange country with such a strange name needed a lot more information from the Times. Or maybe they are defacing all their articles this way in an effort to incorporate the wonders of the Web.