Radial and elliptic flow at RHIC: Further predictions Page: 3 of 6
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ter sets as studied in that paper. For the 0 meson and
the Q hyperon we include two values, one for simulta-
neous freeze-out with all other hadrons, the other for
freeze-out directly after hadronization at T, = 164 MeV.
The latter option accounts for the expectation that the
heavy and weakly coupled Q is not likely to participate
after hadronization in any modifications of the previ-
ously established flow pattern [18]. Similar arguments
hold for the 0 meson. Even though at RHIC energies
a large fraction of the flow is already established be-
fore hadronization [8], the additional flow generated af-
terwards by hadronic rescattering is seen to affect the
Q quite strongly, for both v2 (Table 1) and the single-
particle slope (Figure 2).
For identified pions the dependence of v2 on EOS and
Tf is similar as for the sum of all charged hadrons (see
[9]): Lower freeze-out temperatures and harder EOS lead
to flatter single particle spectra and thereby to larger pt-
integrated elliptic flow. For identified hadrons we see
that, as their mass increases, there is stronger sensitivity
to the EoS than that to T (see also Figure 4 below).
12 -
Tr /
- - K+
10 P /
8---V' /4
2
00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
pt (GeV/c)
FIG. 3. pt-differential elliptic flow at midrapidity for vari-
ous hadrons from minimum bias Au+Au collisions at fs =
130 A GeV for EOS Q(120).
Figure 3 shows the differential momentum anisotropy
v2 (pt) for different hadron species for EOS Q and T ~
120 MeV. At a given value of pt, the elliptic flow is seen to
decrease with increasing particle mass. This is a conse-
quence of rest-mass-dependent radial flow effects on the
shape of the single-particle pt-spectrum, as will be ana-
lytically discussed in the following section.
The smaller differential anisotropy at fixed pt does not
contradict the results in Table 1 which generically give
larger pt-averaged elliptic flow for heavier particles. This
is a consequence of the fact that radial flow leads to a
flattening of the pt-spectra of heavier particles [19,20],
whose pt-averaged v2 thus receives more weight from the
high-pt region where v2 (Pt) is larger. Whether this largerspectral weight for high pt wins over the reduction of
v2 at fixed pt depends on the details of the expansion
dynamics.
The effect of the EOS and the freeze-out temperature
on the differential elliptic flow of pions and protons is
demonstrated in Figure 4. The EOS affects v2(pt) for
all hadrons in the same way: the stiffer EOS H leads to
larger v2 at low pt and to smaller v2 at high pt than the
softer EOS Q. The effect of the freeze-out temperature
on v2 (Pt) is more delicate: for pions the effect is small,
and for EOS Q an increase in the freeze-out tempera-
ture decreases both the pt-averaged and the differential
elliptic flow. The heavier protons behave oppositely: the
differential anisotropy increases with increasing freeze-
out temperature. The origin of this behaviour will be
studied in the following section. Clearly, the different
Tf-dependence of v2(pt) of different particles can be used
to constrain the freeze-out temperature independently of
the EOS.15
10
5
00.0 0.5 1.0 1.5
pt (GeV/c)0.5 1.0 1.5
pt (GeV/c)FIG. 4. The effect of the EOS and the freeze-out tem-
perature on the elliptic flow of midrapidity pions (left) and
protons (right) from minimum bias Au+Au collisions at
= 130 A GeV.
In view of the observed deviations from hydrodynamic
behaviour of charged particle elliptic flow at large impact
parameters [1] it will be interesting to study the central-
ity dependence of v2 separately for a variety of hadron
species. Corresponding hydrodynamic predictions are
shown in Figure 5 (again including the option that the Q
freezes out early at Tf = T,). Particle-specific deviations
from these predictions should provide valuable insights
into the thermalization and freeze-out mechanisms.
3. Analytical results.- In the remainder we try to un-
derstand the hydrodynamic behaviour of v2 (pt) and its
dependence on the hadron mass and freeze-out tempera-
ture, using a simple analytical model. Before going into
the technical details we give a simple intuitive argument
why, at small pt, the elliptic flow of heavier particles is
smaller than for lighter ones. It is well-known that radial
flow shifts the pt-distributions to larger values of pt, and3
--
- /
- /-
- /-
- -' -'- '-' 'r'1''1'1'1'1'iT Q(120) p
- - Q(140)
- - (10) <
- -/
/' ' ' ' ' ' ' ' ' ' ' '
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Huovinen, Pasi; Kolb, Peter F.; Heinz, Ulrich; Ruuskanen, P.V. & Voloshin, Sergei A. Radial and elliptic flow at RHIC: Further predictions, article, January 30, 2001; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc718958/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.