Space Science Reviews

, Volume 177, Issue 1–4, pp 31–74 | Cite as

Arc Statistics

  • M. MeneghettiEmail author
  • M. Bartelmann
  • H. Dahle
  • M. Limousin


The existence of an arc statistics problem was at the center of a strong debate in the last fifteen years. With the aim to clarify if the optical depth for giant gravitational arcs by galaxy clusters in the so called concordance model is compatible with observations, several studies were carried out which helped to significantly improve our knowledge of strong lensing clusters, unveiling their extremely complex internal structure. In particular, the abundance and the frequency of strong lensing events like gravitational arcs turned out to be a potentially very powerful tool to trace the structure formation. However, given the limited size of observational and theoretical data-sets, the power of arc statistics as a cosmological tool has been only minimally exploited so far. On the other hand, the last years were characterized by significant advancements in the field, and several cluster surveys that are ongoing or planned for the near future seem to have the potential to make arc statistics a competitive cosmological probe. Additionally, recent observations of anomalously large Einstein radii and concentrations in galaxy clusters have reinvigorated the debate on the arc statistics problem. In this paper, we review the work done so far on arc statistics, focussing on what is the lesson we learned and what is likely to improve in the next years.


Cosmology Galaxy clusters Gravitational lensing 



We are grateful to the International Space Science Institute of Bern for supporting us in the work for the preparation of this manuscript. M.M. acknowledges support from PRIN INAF 2009 and ASI (agreement Euclid phase B2/C).


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • M. Meneghetti
    • 1
    • 2
    Email author
  • M. Bartelmann
    • 3
  • H. Dahle
    • 4
  • M. Limousin
    • 5
  1. 1.INAF—Osservatorio Astronomico di BolognaBolognaItaly
  2. 2.INFN—Sezione di BolognaBolognaItaly
  3. 3.ZAH, ITAU. HeidelbergHeidelbergGermany
  4. 4.Institute of Theoretical AstrophysicsUniversity of OsloOsloNorway
  5. 5.LAM (Laboratoire d’Astrophysique de Marseille), UMR 7326Aix Marseille Université, CNRSMarseilleFrance

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