In 2006, according to the magazine, the German carmakers agreed to limit the size of the tanks used to hold a chemical solution that helps neutralize diesel emissions. Volkswagen and its Audi division have previously admitted in court documents that the tanks they installed in their cars did not hold enough of the solution, known as AdBlue, to last between oil changes. The company did not want the tanks to take space from the cars’ sound systems, according to a criminal complaint against an Audi engineer filed earlier this month in the United States.

Rather than install bigger tanks, Volkswagen and Audi illegally programmed cars to ration the chemical solution — and produce excess emissions — except when engine software detected that an official test was underway.

Earlier in July, an Italian, Zaccheo Giovanni Pamio, who was head of thermodynamics in the engine development department at Volkswagen’s Audi division, was arrested by German authorities in Munich. His arrest was the first on German soil related to Volkswagen’s emissions fraud. Because he is not a German citizen, it is possible Mr. Pamio will be extradited to the United States.