The C austic R ing M odelofthe M ilky W ay H alo

W epresenta proposalforthefullphasespacedistribution oftheM ilky W ay halo.Them odelis axially and reection sym m etricand itstim eevolution isself-sim ilar.Itdescribesthehalo asa set ofdiscretedark m atter owswith stated densitiesand velocity vectorseverywhere.W erstdiscuss thegeneralconditionsunderwhich thetim eevolution ofa cold collisionlessself-gravitating uid is self-sim ilar,and show thatsym m etry isnotnecessary forself-sim ilarity.W hen sphericalsym m etry isim posed,the m odelisthe sam e asdescribed by Fillm ore and Goldreich,and by Bertschinger, twenty-threeyearsago.Thespherically sym m etricm odeldependson onedim ensionlessparam eter � and two dim ensionfulparam eters.W eset � = 0.3,a valueconsistentwith theslopeofthepower spectrum ofdensity perturbationson galacticscales.Thedim ensionfulparam etersaredeterm ined bytheGalacticrotation velocity (220km /s)attheposition oftheSun and bytheageoftheGalaxy (13.7 Gyr). The propertiesofthe outercausticsare derived in the spherically sym m etric m odel. Thestructureoftheinnerhalo dependson theangularm om entum distribution ofthedark m atter particles. W e assum e that distribution to be axialand reection sym m etric,and dom inated by netoverallrotation. The innercausticsare ringswhose radiiare determ ined in term sofa single additionalparam eter jm ax. W e sum m arize the observationalevidence in support ofthe m odel. The evidence isconsistentwith jm ax = 0.18 in Concordance Cosm ology,equivalentto jm ax;old = 0.26 in Einstein -deSittercosm ology.W egiveform ulasto estim atethe ow densitiesand velocity vectorsanywherein theM ilky W ay halo.Thepropertiesoftherstforty owsatthelocation of theEarth arelisted.