2.  Collision of heavy nuclei at relativistic energies leads to formation of Quark- Gluon Plasma (QGP).  Strong confirmation arises from the recent observation @ Relativistic Heavy Ion Collider (RHIC) of strong anisotropic flow.  Bulk evolution is described by relativistic fluid dynamics. The application of fluid-dynamics implies that the medium is in local thermal equilibrium!  Large anisotropies in the particle emission are a collective phenomenon.  If the nucleus – nucleus collisions were a simple super position of independent nucleon - nucleon collisions, then resultant particle distribution would be isotropic in momentum spectra.

3. Co ordinate space anisotropy is converted into momentum space anisotropy via the action of azimuthally asymmetric pressure gradient. Non-central collision of spherical nuclei or central collision of deformed nuclei or central collision of deformed nuclei Non-central collision of spherical nuclei or central collision of deformed nuclei or central collision of deformed nuclei Overlapping zone is of almond shape Elliptic flow Reaction plane plane x z y  Elliptic flow is a measure of collectivity and early thermalisation of the new form of matter.  It is sensitive to the early phase and does not depend on the freeze–out dynamics of the system.  Fluid-dynamics can not make any statements how the medium reached the equilibrium stage. P.F. Kolb and U. Heinz, in Quark Gluon Plasma, nucl-th/0305084 Elliptic Flow: self quenching The driving force of elliptic flow dominates at “early” times. Elliptic flow acts against its own cause, it shuts itself off after some time as pressure gradient vanishes. ` y x Coordinate space pypy pxpx Momentum space Elliptic Flow

4. Photons come out from every stage of the expanding system hadronic phase qgp phase mixed phase pre-equilibrium phase freeze-out surface z t Mean free path of photons is larger than system size. Once produced, photons leave the system without any re-scattering. Carry undistorted information from the production point to the detector. Prompt photons: control the initial state of the collision, modification of structure functions etc. Jet-matter interaction: test matter density. Thermal photons: temperature and equation of state of the hot matter. 1/p t n ptpt ~5 GeV ~3 GeV e -p t /T d 3 N/dyd 2 p T Jet-matter

5. The thermal photon emissions from the QGP and the hadronic phases are obtained by integrating the rates of emission over the space time history of the fireball. E dN  /d 3 p= ∫ [{…} exp (p .u  /T )] d 4 x E dN  /d 3 p= ∫ [{…} exp (p .u  /T )] d 4 x p  =( p T coshY, p x, p y, p T sinhY ) → 4-momentum of the photons, p  =( p T coshY, p x, p y, p T sinhY ) → 4-momentum of the photons, u  =  T (cosh , v x (x,y), v y (x,y), sinh  ) → 4 velocity of the flow field. Taking the azimuthal angle for transverse momentum as  (in the reaction plane ) we can write : p .u  =  T [ p T cosh(Y-  )–p x v x –p y v y ] p .u  =  T [ p T cosh(Y-  )–p x v x –p y v y ] Elliptic flow is quantified as the 2 nd Fourier co-efficient of particle distribution in transverse momentum plane: distribution in transverse momentum plane:

6.      are the dominant photon producing channels upto p T ~ 0.5 GeV. Above that p T range    becomes significant. Relative contributions of different channels in the hadronic phase U. Heinz, R. Chatterjee, E. Frodermann, C. Gale, D. K. Srivastava, Nucl. Phs. A 783, 379. (2007)

7. Thermal photon elliptic flow @ RHIC Elliptic flow of thermal photons as function of transverse momentum p T shows interesting nature……………..  v 2 (QM) is small at high p T and rises for smaller values p T. It peaks around 1.5-2.0 GeV & then drops as p T  0. around 1.5-2.0 GeV & then drops as p T  0.  v 2 (HM) rises monotonically with p T. R. Chatterjee, E. Frodermann U. Heinz, D. K. Srivastava. PRL 96, 202302 (2006)

8. Thermal photon elliptic flow @ RHIC Sum v 2 tracks v 2 (QM) at high p T, reflects anisotropies of the partonic phase at early times. phase at early times. Interesting structure at p T  0.4 – 0.5 GeV, should sustain in the experimental data. experimental data. v 2 (  ) & v 2  ) are plotted to compare with v 2 (HM). R. Chatterjee, E. Frodermann U. Heinz, D. K. Srivastava. PRL 96, 202302 (2006)

9. Time evolution of spectra and flow from Quark Matter & Hadronic Matter For p T > 3 GeV, most of the photons are emitted within 1.0 fm time period, however the flow is not very strong at that time. Below 2 GeV p T range, 20 to 60 % QGP photons are emitted within 1 fm and only 5% of the total v 2 (QM) is generated by that time at low p T. After 2.5 fm photon flow in QGP phase becomes significant.  Contribution of hadronic photons to the sum photon spectrum becomes significant only after a time period of 3.5 - 4.0fm.  Temporal contours of v 2 are of a nature similar to those for the temporal contours of the spectra.

10. Time evolution of spectra and elliptic flow at b=7 fm For p T > 2.0 GeV most of the photons are from QGP phase and within a time period of 4 fm. For very low p T, radiation from HM is significant. At early times and high p T, sum v 2 reflects anisotropies of the partons from QGP phase.

11. Time evolution of p T integrated elliptic flow at b = 7 fm v 2 (  ) as function of  from different phases are shown separately. v 2 (  ) as function of  from different phases are shown separately. v 2 (QM) saturates within a time period of 4-5 fm. v 2 (QM) saturates within a time period of 4-5 fm. v 2 (HM) continuously grows upto time of freeze out. v 2 (HM) continuously grows upto time of freeze out. R. Chatterjee, D. K. Srivastava, U. Heinz (in preparation) Plot shown by Kentaro Miki @QM2008 Photon v 2 from hydrodynamics and PHENIX data and PHENIX data Direct photon v 2, Turbide et al. Phys.Rev.C77:024909,2008

12. R. Chatterjee & D. K. Srivastava, arXiv:0809.0548

13. Summary & conclusions  Elliptic flow of electromagnetic radiation has a great potential to explore the properties and early time dynamics of Quark Gluon Plasma.  Photon flow at large p T reflects the anisotropies of the initial partonic phase.  Temporal contours of elliptic flow and spectra show the gradual build up of flow and the relative contribution of quark matter and hadronic matter in the total flow with changing time.  Initial thermalization time can be estimated from thermal photon elliptic flow. My collaborators Dinesh K. Srivastava Variable Energy Cyclotron Centre, Kolkata Ulrich W. Heinz The Ohio State University, Columbus Evan S. Frodermann The Ohio State University, Columbus My collaborators Dinesh K. Srivastava Variable Energy Cyclotron Centre, Kolkata Ulrich W. Heinz The Ohio State University, Columbus Evan S. Frodermann The Ohio State University, Columbus Thank you

15. All v 2 (p T )=0 at b=0 v 2 (p T ) increases with rise in impact parameter b. With rise in b, relative contributions of QM & HM in the total v 2 changes. HM contribution increases compared to QM at larger b values. p T integrated v 2 (b) rises with rise in b. v 2 ’s from QM, HM and QM+HM are shown separately. For b  2R A,( R A is the nuclear radius) v 2 (b) drops as system size itself becomes very small. R. Chatterjee, E. Frodermann, U. Heinz, D. K.Srivastava. PRL 96, 202302 (2006) R. Chatterjee, D. K. Srivastava. U. Heinz (in preparation)

16. Initial spatial eccentricity (  ) scaled v 2 of thermal photons: Initial spatial eccentricity Ideal hydrodynamics is scale invariant and does no depend on the system size. v 2 /  from different phases along with pions remain invariant with change of impact parameter. R. Chatterjee, D. K. Srivastava. U. Heinz (in preparation)

17. Invariant mass dependent thermal dilepton spectra: Contributions from QM, HM are shown separately along with total spectrum. spectrum. Sum spectrum shows well defined peak structures at  masses, which are mainly the contributions from hadronic phase. which are mainly the contributions from hadronic phase. QGP radiation becomes significant above the  mass. Larger peaks of  mesons (post freeze-out) show the long life time of theses two vector mesons. time of theses two vector mesons. b = 0 fm QM HM QM+HM Post freeze-out  R. Chatterjee, D. K. Srivastav, U. Heinz, C. Gale PRC 75, 054909 (2007)

18. v 2 of thermal dileptons at b= 7 fm v 2 (QM) shows similar nature of thermal photon v 2, small at large M and then increases with lower M values. increases with lower M values. At the resonance masses sum v 2 touches the v 2 (HM). For M>M , v 2 (HM) much higher than v 2 (QM), however sum v 2 approaches v 2 (QM) as dileptons from HM are negligible compared to those from QM at v 2 (QM) as dileptons from HM are negligible compared to those from QM at that mass range. that mass range. R. Chatterjee, D. K. Srivastav, U. Heinz, C. Gale. PRC 75, 054909 (2007)

19. Differential elliptic flow of thermal dileptons at M=m  and M=m  For both spectra and v 2, hadronic phase dominance is clearly visible. R. Chatterjee, D. K. Srivastav, U. Heinz, C. GalePRC 75, 054909 (2007)

20. Thermal dileptons and hadrons at M=m  and M=m  p T spectra of  and  mesons are flatter compared to that of thermal dileptons at M=m  and M=m  respectively. Dileptons come out from the entire expansion history, whereas hadrons are emitted only from the freeze-out surface. Elliptic flow shows opposite nature of spectra. R. Chatterjee, D. K. Srivastav, U. Heinz, C. Gale. PRC 75, 054909 (2007)

21. Spectra and v 2 of thermal dileptons at M = 2 GeV  At invariant mass M=2 GeV, QGP spectra is almost 3 order of magnitude larger than hadronic spectra and almost identical to the magnitude larger than hadronic spectra and almost identical to the sum spectra. sum spectra.  v 2 (HM) is almost 20 times larger than v 2 (QM), still sum v 2 is similar to v 2 (QM). to v 2 (QM).  v 2 measurement at high invariant masses will give pure QGP signature, where subtraction of hadronic contribution is not required. signature, where subtraction of hadronic contribution is not required. R. Chatterjee, D. K. Srivastav, U. Heinz, C. Gale. PRC 75, 054909 (2007)