We describe the spectra and essential spectra of Toeplitz operators with piecewise continuous symbols on the Hardy space
H
p
(
Γ
,
ω
)
H^p(\Gamma ,\omega )
in case
1
>
p
>
∞
1>p>\infty
,
Γ
\Gamma
is a Carleson Jordan curve and
ω
\omega
is a Muckenhoupt weight in
A
p
(
Γ
)
A_p(\Gamma )
. Classical results tell us that the essential spectrum of the operator is obtained from the essential range of the symbol by filling in line segments or circular arcs between the endpoints of the jumps if both the curve
Γ
\Gamma
and the weight are sufficiently nice. Only recently it was discovered by Spitkovsky that these line segments or circular arcs metamorphose into horns if the curve
Γ
\Gamma
is nice and
ω
\omega
is an arbitrary Muckenhoupt weight, while the authors observed that certain special so-called logarithmic leaves emerge in the case of arbitrary Carleson curves with nice weights. In this paper we show that for general Carleson curves and general Muckenhoupt weights the sets in question are logarithmic leaves with a halo, and we present final results concerning the shape of the halo.