2 : Pulsar
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2 : Pulsar
In pulsar-perf, the default Pulsar client ioThread number is Runtime.getRuntime().availableProcessors() and users could not configure it in the command line. When running a pulsar-perf producer, it may cause messages to enqueue competition and lead to high latency.
Wave dispersion in a pulsar plasma is discussed emphasizing the relevance of different inertial frames, notably the plasma rest frame $\mathcalK$ and the pulsar frame $\mathcalK^\prime $ in which the plasma is streaming with speed $\unicode[STIX]x1D6FD_\texts$. The effect of a Lorentz transformation on both subluminal, $z1$, waves is discussed. It is argued that the preferred choice for a relativistically streaming distribution should be a Lorentz-transformed Jüttner distribution; such a distribution is compared with other choices including a relativistically streaming Gaussian distribution. A Lorentz transformation of the dielectric tensor is written down, and used to derive an explicit relation between the relativistic plasma dispersion functions in $\mathcalK$ and $\mathcalK^\prime $. It is shown that the dispersion equation can be written in an invariant form, implying a one-to-one correspondence between wave modes in any two inertial frames. Although there are only three modes in the plasma rest frame, it is possible for backward-propagating or negative-frequency solutions in $\mathcalK$ to transform into additional forward-propagating, positive-frequency solutions in $\mathcalK^\prime $ that may be regarded as additional modes.
NuSTAR resolves the Galactic pulsar wind nebula G11.2-0.3 into a shell of high-energy emission (3--35 keV) surrounding a bright source at the center associated with the pulsar. The shell emits due to synchrotron emission as charged particles are accelerated within the magnetized flow from the supernova explosion that created the pulsar. NuSTAR shows evidence of particle acceleration in this shell, implying that this Galactic remnant is less than a few thousand years old. NuSTAR also sees the shell radius decrease with increasing energy, which is due to the shorter synchrotron lifetime for higher energy X-rays. The bright white central source shows the location of the pulsar itself, which is sending out a strong wind of particles that are accelerated in the surrounding environment. For more information, see the paper recently published in the Astrophysical Journal ( ).
The potential existence of γ-ray emission in halo regions around energetic pulsars has long been known; their detectability has been predicted to depend on a low diffusion coefficient (Aharonian 1995). The formation of a halo is possible around any source class from which cosmic-ray electrons may escape before cooling. For GeV-emitting electrons, this has long been assumed to be the case for SNR, for example. For the >10 TeV electrons producing TeV γ-rays, radiative lifetimes are much shorter, yr, and it is less clear if escape before cooling is possible for SNR or for other galactic sources.
After long being discussed as a potential source of the locally measured cosmic-ray electrons (see e.g. Atoyan et al. 1995), pulsar wind nebulae are the only class of sources for which the escape of TeV-emitting electrons is now firmly established (Abeysekara et al. 2017a). There are also indications of missing (apparently escaped) high energy electrons in the case of the Vela system (Hinton et al. 2011); however, alternative explanations, such as rapid cooling due to an enhanced magnetic field, are possible (Bao & Chen 2019). Apparently escaped relativistic electrons are detected in X-rays around the GuitarNebula (e.g. Johnson & Wang 2010) and the Lighthouse Nebula (e.g. Pavan et al. 2014). The most obvious way to differentiate between escaped and confined radiating particles is to estimate the PWN boundary using multi-wavelength data. This process is often problematic due to the effects of instrumental sensitivity, non-uniform magnetic fields, and particle cooling. For example, it is very often the case that the zone in which imaging of a PWN is possible in the X-ray domain, with instruments such as Chandra or XMM-Newton, is much smaller than the physical size of the PWN as determined in other wavelengths. Within the X-ray domain, the physical PWN size is also often energy dependent, which is interpreted as a signature of the rapid cooling of the highest energy electrons producing the keV synchrotron emission. Indeed, the typical cooling time of electrons emitting photons with characteristic energy hνc is . In the radio domain, the cooling effect is unimportant, but surface brightness sensitivity is usually only sufficient for young and compact sources.
Here, we consider various estimates for the expected size of the nebulae around pulsars that have been associated to TeV emission, comparing these estimates to the measured sources sizes. We also assess the fraction of the power that is present in sources with and without halos and hence their contribution to the total γ-ray emission of all pulsars within star-forming systems.
To explore the relative sizes of the different components in a PWN-SNR system and their evolution, Table 1 compiles multi-wavelength measurements of the emission extent. The size of the SNR, RSNR, is given by the radius of a shell, which is often detected from radio information. The size of the central PWN, RPWN, is obtained from the extent of radio emission located immediately around the pulsar. The X-ray size, RX-ray, provided forcomparison is a measure of the central PWN size, which traces to the youngest energetic particles in the system. For the synchrotron emission seen in the radio to X-ray, the observed sizes relate to the magnetic field distribution as well as the particle distribution. In contrast the TeV size, RTeV, only depends on the particle distribution, at least in the usual case of close to uniform radiation density for inverse Compton scattering.
Compilation of TeV γ-ray sources with pulsar associations (i.e. PWN or associated Halos), together with estimated electron energy densities within the emission region (see notes below and text for details).
Clearly, more sophisticated treatments are possible, but all rely on models of the evolution of pulsars and their nebulae, which are not currently well constrained by the available data. Instead, we turned to existing measurements at TeV energies to empirically establish the current day electron population in (and/or around) these PWN.
We note that there is a strong correlation (coefficient 0.98) between the two different energy density estimates shown in Fig. 2. This indicates that the γ-ray properties of PWN are typically more closely related to the current spin-down power, rather than the early lifetime of their pulsars. Whilst for the majority of systems the estimator using γ-ray luminosity results in consistent or lower energy densities than the Case B estimates of Sect. 3.1, for a small number of PWN, the energy density is larger. This is likely due to significant energy injected during the early phase of pulsar evolution.
In our sample of TeV-bright systems with firm pulsar associations listed in Table 2, we note that the Crab and Geminga, both frequently used as canonical examples of the class, have the highest and lowest Ė, respectively. This suggests that both are extreme systems rather than typical of the population.
Whilst the fraction of halos in current TeV catalogues is low, these catalogues are clearly biased towards compact, that is, PWN-like, rather than halo-like, objects, given the reduction in sensitivity to lower surface brightness emission at a fixed flux for resolved objects. In addition, the highest power objects are young (Table 2) and would not be expected to form halos yet; only close-by (old, low-power) pulsars are likely to exhibit detectable halos. However, the older systems which do exhibit halos are much more numerous, and it is important to consider the entire pulsar population to assess what fraction of the integrated TeV γ-ray emission is likely to occur within, and outside of, PWN.
Cumulative fraction of the energy output of the known Galactic pulsar population with ages < 107 yr (Manchester et al. 2005) created using the instantaneous energy output into electrons Ee as well as the energy output integrated up to 104 and 105 yr electron lifetimes. For comparison purposes, we show the cumulative γ-ray luminosity at 1 TeV from a generic PWN model as a function of system age, both for a constant magnetic field and a magnetic field evolving in time. The cumulative fraction of pulsars indicates that the energy output into electrons andγ-ray luminosity is dominated by a small fraction of young, energetic pulsars.
H.E.S.S. observations of electrons at Earth with > 10 TeV energies place stronger constraints on the possibility of a low diffusion coefficient in our local environment than the boron-to-carbon ratio does. As demonstrated in Hooper & Linden (2018), cosmic rays must diffuse substantially faster through the bulk of the Galactic disc than around Geminga for local known pulsars to explain the detection of > 10 TeV electrons at Earth. Alternatively, the scenario of a low diffusion coefficient in our local ISM would remain viable if a nearby undetected pulsar contributes to the high-energy end of the all-electron spectrum measured at Earth (López-Coto et al. 2018). In the future, observations of halos around pulsars in different γ-ray energy ranges should help to constrain the spectrum and nature of the turbulence probed by the emitting electrons. Extended GeV emission has recently been measured with the Fermi satellite around Geminga (Di Mauro et al. 2019). 59ce067264
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