DETAINEE HEALTH CARE, a June 26, 2007 fact sheet from Immigration and Customs Enforcement says: "More than 260,000 detainees are held for some period of time each year. A daily average of 27,500 illegal aliens is in detention, with over 30,000 currently detained.
Since 2004, nearly one million persons have been detained by ICE....Approximately 15,000 of 29,000 total daily detainees are housed in facilities where DIHS staffs health services clinics and provides direct patient care. Approximately 14,000 detainees receive medical care at local and county jails and detention facilities located throughout the country.
DETENTION AND REMOVAL OPERATIONS: ALTERNATIVES TO DETENTION, a March 2007 fact sheet, says: "Every year the Department of Homeland Security arrests over 1.6 million aliens," and goes on to note shortage of bed space and the need to "...apply rigorous criteria to determine which apprehended aliens are detained."
Part of what complicates research on this is to differentiate arrests and detentions for misdemeanors or felonies, versus detention for simply not being in the U.S. legally. Also, we have to separate foreign born citizens and foreign nationals with visas who are incarcerated for crimes, versus illegal immigrants who are incarcerated. For example, a General Accounting Office 2005 report, Information on Criminal Aliens Incarcerated in Federal and State Prisons and Local Jails, talks only about aliens charged with crimes: "At the local level, in fiscal year 2002, SCAAP reimbursed about 750 local governments for incarcerating about 138,000 criminal aliens. In fiscal year 2003, SCAAP reimbursed about 700 local governments for about 147,000 criminal aliens, with 5 local jail systems4 accounting for about 30 percent of these criminal aliens."(page 3)
So this may take a lot of research to define just which undocumented immigrants the figures cited in any given report are referring to - and how accurate those figures are. For example, a cash-poor local jail may not have the resources to carefully double check the status of every inmate. It may save you some time to use a Google search as a means of getting to "official" sources indirectly. Most websites' search features do not do well with "stop" or "noise" words. The search "aliens since" gets one not very promising hit in the Dept of Homeland Security's site search. In Usa.gov, the search: "aliens since 9" gets 5 hits, which seem to concern arrests. Both "aliens incarcerated since" and "aliens detained since" get zero hits. But in Google, the search: "aliens incarcerated since" gets 2 sites. To be sure these are by no means "official" or "scholarly/peer reviewed" sites.
But the first one, Lighthouse Patriot Journal quotes Immigrationcounters.com, a 15 page website that lists many government sources, such as a Homeland Security Inspector General's report that gives quite a number of figures on arrests and incarcerations; and estimated percentage of illegal immigrants who are actually detained.
A careful study of this would no doubt take dozens of hours, including searching in commercial databases such as Academic Search, SocIndex, PAIS, Factiva, and others located at academic libraries. To actually critically evaluate what you found in such a search would take far longer, and could in fact become a very respectable Master's thesis or book.