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162 - O.C. de Jager 2009
In this paper we explore the evolution of a PWN while the pulsar is spinning down. An MHD approach is used to simulate the evolution of a composite remnant. Particular attention is given to the adiabatic loss rate and evolution of the nebular field s trength with time. By normalising a two component particle injection spectrum (which can reproduce the radio and X-ray components) at the pulsar wind termination shock to the time dependent spindown power, and keeping track with losses since pulsar/PWN/SNR birth, we show that the average field strength decreases with time as $t^{-1.3}$, so that the synchrotron flux decreases, whereas the IC gamma-ray flux increases, until most of the spindown power has been dumped into the PWN. Eventually adiabatic and IC losses will also terminate the TeV visibility and then eventually the GeV visibility.
Morphologically it appears as if the Vela X PWN consists of two emission regions: whereas X-ray (1 keV) and very high energy (VHE) H.E.S.S. gamma-ray observations appear to define a cocoon type shape south of the pulsar, radio observations reveal an extended area of size 2 deg by 3 deg (including the cocoon area), also south of the Vela pulsar. Since no wide field of view (FoV) observations of the synchrotron emission between radio and X-rays are available, we do not know how the lepton (e+/-) spectra of these two components connect and how the morphology changes with energy. Currently we find that two distinct lepton spectra describe the respective radio and X-ray/VHE gamma-ray spectra, with a field strength of 5 muG self-consistently describing a radiation spectral break (or energy maximum) in the multi-TeV domain as observed by H.E.S.S. (if interpreted as IC radiation), while predicting the total hard X-ray flux above 20 keV (measured by the wide FoV INTEGRAL instrument) within a factor of two. If this same field strength is also representative of the radio structure (including filaments), the implied IC component corresponding to the highest radio frequencies should reveal a relatively bright high energy gamma-ray structure and Fermi LAT should be able to resolve it. A higher field strength in the filaments would however imply fewer leptons in Vela X and hence a fainter Fermi LAT signal.
In this paper we show that the high energy $gamma$-ray flux in the GeV domain from mature pulsar wind nebulae (PWN) scales as the change in rotational kinetic energy $I(Omega_0^2-Omega^2)/2$ since birth, rather than the present day spindown power $IO megadot{Omega}$. This finding holds as long as the lifetime of inverse Compton emitting electrons exceeds the age of the system. For a typical $gamma^{-2}$ electron spectrum, the predicted flux depends mostly on the pulsar birth period, conversion efficiency of spindown power to relativistic electrons and distance to the PWN, so that first order estimates of the birth period can be assessed from {it GLAST/LAT} observations of PWN. For this purpose we derive an analytical expression. The associated (``uncooled) photon spectral index in the GeV domain is expected to cluster around $sim 1.5$, which is bounded at low energies by an intrinsic spectral break, and at higher energies by a second spectral break where the photon index steepens to $sim 2$ due to radiation losses. Mature PWN are expected to have expanded to sizes larger than currently known PWN, resulting in relatively low magnetic energy densities and hence survival of GeV inverse Compton emitting electrons. Whereas such a PWN may be radio and X-ray quiet in synchrotron radiation, it may still be detectable as a {it GLAST/LAT} source as a result of the relic electrons in the PWN.
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