We demonstrate that the radiation emitted by ultrarelativistic electrons
in highly nonuniform, small-scale magnetic fields is different from synchrotron
radiation if the electron's transverse deflections in these fields are much
smaller than the beaming angle. A quantitative analytical theory
of this radiation, which we refer to as jitter radiation, is developed.
It is shown that the emergent spectrum is determined by statistical properties
of the magnetic field. As an example,
we then use the model of a magnetic field in internal shocks of Gamma-Ray
Bursts (GRBs) proposed by Medvedev \& Loeb (1999, \apj, 526, 697). The
spectral power distribution of radiation
produced by the power-law distributed electrons with a low-energy cutoff
is well described by a sharply broken power-law: $P(\omega)\propto\omega^1$
for $\omega\lesssim\omega_{jm}$ and $P(\omega)\propto\omega^{-(p-1)/2}$
for $\omega\gtrsim\omega_{jm}$, where $p$ is the electron power-law index and
$\omega_{jm}$ is the jitter break frequency which is independent of the
field strength but depends on the electron density in the ejecta,
$\omega_{jm}\propto\sqrt{n}$, as well as on the shock energetics and kinematics.
The total emitted power of jitter radiation is, however, equal to that of
synchrotron radiation.
Since large-scale fields may also be present in the ejecta, we construct
a two-component, jitter+synchrotron spectral model of the prompt $\gamma$-ray
emission. Quite surprisingly, this model seems to be readily capable of
explaining several properties of time-resolved spectra of some GRBs, such
as (i) the violation of the constraint on the low-energy spectral index called
the synchrotron ``line of death'', (ii) the sharp spectral break at the peak
frequency, inconsistent with the broad synchrotron bump, (iii) the evidence
for two spectral sub-components, and (iv) possible existence of emission
features called ``GRB lines''. We believe these facts strongly support both
the existence of small-scale magnetic fields and the proposed radiation
mechanism from GRB shocks. As an example, we use the composite model to
analyze GRB~910503 which has two spectral peaks. At last, we emphasize that
accurate GRB spectra may allow precise determination of fireball properties
as early as several minutes after the explosion.
Keywords: radiation mechanisms: non-thermal --- gamma rays: bursts --- magnetic fields
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