Some even question whether the first bomb was "necessary"; here's a link to a thread from about a month ago that discusses a claim that it's the Soviet declaration of war that pushed the Japanese to surrender rather than the nuclear bombing.

EDIT: You also might want to clarify what you mean by "necessary". It is generally accepted that the Japanese didn't have much hope of winning the war by the time the bomb was dropped, and would eventually have to surrender. The big question is how soon they would surrender, and did the bombings hasten their capitulation.

I wrote a blog post on Why Nagasaki? a little while ago. Figuring out what the people who ordered that raid were thinking, only 3 days after the Hiroshima attack, is something historians have argued about for awhile — I present a few of the conclusions that have been put forward. There's no way to really know for sure whether the second bomb was "necessary" by any definition of "necessary," but there are different theories.

Actually, a day after Hiroshima was destroyed, Dr. Yoshio Nishina and other atomic physicists arrived at the city, and carefully examined the damage. They then went back to Tokyo and told the cabinets that Hiroshima was indeed destroyed by an atomic bomb. Admiral Soemu Toyoda, the Chief of the Naval General Staff, estimated that no more than one or two additional bombs could be readied so they decided to endure the remaining attacks, acknowledging "there would be more destruction but the war would go on."

Therefore, we decided since the Japanese chose to continue the war despite the first bomb, we had to stop the second to give the Japanese an impression we had stockpiles of atomic bombs in our arsenals. Shortly afterwards, the Japanese captured and tortured an American P-51 fighter pilot named Marcus McDilda in order to discover how many atomic bombs the Allies had and what the future targets were. McDilda, who knew nothing about the atomic bomb nor the Manhattan Project, "confessed" under torture that the U.S. had 100 atomic bombs and that Tokyo and Kyoto were the next targets. The Japanese said to the cabinet that "the Americans appeared to have 100 atomic bombs". That's why they wanted to surrender because they feared more of the bombs than so of anything, including the Soviets.

Emperor Hirohito said that:

Moreover, the enemy has begun to employ a new and most cruel bomb, the power of which to do damage is, indeed, incalculable, taking the toll of many innocent lives. Should We continue to fight, not only would it result in an ultimate collapse and obliteration of the Japanese nation, but also it would lead to the total extinction of human civilization.

Such being the case, how are We to save the millions of Our subjects, or to atone Ourselves before the hallowed spirits of Our Imperial Ancestors? This is the reason why We have ordered the acceptance of the provisions of the Joint Declaration of the Powers.

He didn't mention anything about the Soviets whatsoever.