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To combine constraints from multiple experiments, simply add their Fisher matrices: F=ΕΙ+F5. | To combine constraints from multiple experiments, simply add their Fisher matrices: $F = F_1 + F_2$. |
Strictly speaking, anymarginalization should be performed after the addition. | Strictly speaking, anymarginalization should be performed after the addition. |
But if the nuisance parameters" are uncorrelated between the two data sets, then marginalization may be performed before the addition. | But if the “nuisance parameters” are uncorrelated between the two data sets, then marginalization may be performed before the addition. |
Given the badness of fit x?(x,y), your 2-D Fisher matrix can be calculated as follows: In other words,Fj;=21dx?0püpy | Given the badness of fit $\chi^2(x,y)$, your 2-D Fisher matrix can be calculated as follows: In other words, $F_{ij} = \displaystyle \frac{1}{2} \frac{\p \chi^2}{\p p_i \p p_j}$. |
'These derivatives are simple to calculate numerically: Suppose we are given a Fisher matrix in terms of variables p=(x,y,z) but we are interested in constraints on related variables p'= (a,b,c). | These derivatives are simple to calculate numerically: Suppose we are given a Fisher matrix in terms of variables $p = (x,y,z)$ but we are interested in constraints on related variables $p^\prime = (a,b,c)$ . |
We can obtain a new Fisher matrix as follows: | We can obtain a new Fisher matrix as follows: |
galaxies. | galaxies. |
Currently methods are being developed in order to relate galaxy luminosities to cark matter halocs in a statistical wav (e.@2?77).. | Currently methods are being developed in order to relate galaxy luminosities to dark matter haloes in a statistical way \cite[e.~g.~][]{Yang2004a, Vale2004a,
Cooray2005a, Conroy2006a}. |
Here we follow this idea and associate luminosities to the (sub-)haloes in the group. | Here we follow this idea and associate luminosities to the (sub-)haloes in the group. |
We assume simply that the most luminous galaxy is the central galaxy of the group host halo with circular velocity voici. | We assume simply that the most luminous galaxy is the central galaxy of the group host halo with circular velocity ${\rm v_{\rm circ,1}}$. |
Consequently. the halo with the second. highest circular velocity voies. will host the second brightest group galaxy. | Consequently, the halo with the second highest circular velocity ${\rm v_{\rm circ,2}}$ will host the second brightest group galaxy. |
llere the circular. velocity vere is always taken at. the maximum of the rotation curve. | Here the circular velocity ${\rm v_{circ}}$ is always taken at the maximum of the rotation curve. |
To model the magnitude-gap we adopt a similar approach as ? where we relate the the halo circular velocity to the luminosity of the central galaxy using an empirically measured mean I-band mass-to-light ratio (2).. | To model the magnitude-gap we adopt a similar approach as \citet[][]{Milosavljevic2006a} where we relate the the halo circular velocity to the luminosity of the central galaxy using an empirically measured mean R-band mass-to-light ratio \cite[][]{Cooray2005a}. |
Assuming a Sheth-Thormen (7) mass distribution function for the dark matter haloes and a functional form as in Equation 1. that expresses the halo mass in luminosity for the central ealaxies. ? [it the measured H-band luminosity function of 7.. | Assuming a Sheth-Thormen \cite[][]{Sheth1999a} mass distribution function for the dark matter haloes and a functional form as in Equation 1, that expresses the halo mass in luminosity for the central galaxies, \citet[][]{Cooray2005a} fit the measured R-band luminosity function of \citet[][]{Seljak2005a}. |
We convert our circular velocities to luminosities by the relation with Luη10L.. Mo22«103M. a 4.6=0.57. ο= 3.78. d= 0.23. where we substitute circular velocities for masses using the relation found by 7:: AL(hHAL.)-10"vus(kns1j “with a—43 and 3=3.4. | We convert our circular velocities to luminosities by the relation with $L_{0} = 5.7\times10^{9} L_{\odot}$, $M_{0} = 2\times10^{11}
{\rm M_{\odot}}$, $a = 4$, $b = 0.57$, $c = 3.78$ $d = 0.23$ , where we substitute circular velocities for masses using the relation found by \citet[][]{Bullock2001a}: $M/\left(h^{-1}\;{\rm M_{\odot}}\right) =
10^{\alpha}\cdot \left[{\rm v_{circ}}\right/\left({\rm km
\;s^{-1}}\right)]^{\beta}$ , with $\alpha = 4.3$ and $\beta = 3.4$. |
We then define fossil eroups as having masses in the range of 105Loyh1M. and a magnitucde-gap Ane mae in the It-band. | We then define fossil groups as having masses in the range of $(1\times 10^{13} -
5 \times 10^{13}) h^{-1}{\rm M}_{\odot}$ and a magnitude-gap $\mgap \ge 2$ mag in the R-band. |
Alass accretion onto haloes stops at the time when they become sub-halos of a more massive object like a group. | Mass accretion onto haloes stops at the time when they become sub-halos of a more massive object like a group. |
After infall they start to lose matter clue to tidal interactions. | After infall they start to lose matter due to tidal interactions. |
Since barvons tend to lic deeper in the potential well. they will be less prone to get tically stripped. | Since baryons tend to lie deeper in the potential well, they will be less prone to get tidally stripped. |
Fherefore. the total uminositv is more likely to be related to the mass at infall (scec.ο.ο). | Therefore, the total luminosity is more likely to be related to the mass at infall \cite[see
e.~g.~][]{Kravtsov2004a}. |
Following this idea we characterize the sub-ialoes of the groups by their masses and. circular velocities onto the group. | Following this idea we characterize the sub-haloes of the groups by their masses and circular velocities onto the group. |
Phe choice of. relating uminosities to the circular velocities of halos at infall time las been motivated by recent successes in matching the data » mocdeling the two- and three-point correlation functions (??7).. | The choice of relating luminosities to the circular velocities of halos at infall time has been motivated by recent successes in matching the data by modeling the two- and three-point correlation functions \cite[][]{Conroy2006a, Berrier2006a, Marin2007a}. |
In this section our main aim is to characterize the properties of the fossil groups of our group sample in order to guide the interpretation of future observational constraints. | In this section our main aim is to characterize the properties of the fossil groups of our group sample in order to guide the interpretation of future observational constraints. |
We begin by computing the abundance of fossil systems in our catalog. | We begin by computing the abundance of fossil systems in our catalog. |
Assuming a magnitude-gap of Anny.2 (see dashed line in Figure 1) 24 per cent of the groups of our catalog ave classified as fossil.X corresponding to a number density of 5.5«ο7. "Ph | Assuming a magnitude-gap of $\mgap \ge 2$ (see dashed line in Figure 1) 24 per cent of the groups of our catalog are classified as fossil, corresponding to a number density of $5.5 \times 10^{-5} h^{3}{\rm Mpc}^{-3}$. |
is rate is higher than previous estimates based on IN-body. simulations (?).. semi-analytic models (??).. ancl observational estimates (2277)... which all ect a fraction of around 10. per cent for groups in the mass range considered ποι | This rate is higher than previous estimates based on $N$ -body simulations \cite[][]{dOnghia2007a}, semi-analytic models \cite[][]{Sales2007a,
Dariush2007a}, and observational estimates \cite[][]{ Vikhlinin1999a,
Romer2000a, Jones2003a, vandenBosch2007a}, which all get a fraction of around 10 per cent for groups in the mass range considered here. |
ο— However. only 15 well stucied fossil groups are known at present with X-ray data. | Â However, only 15 well studied fossil groups are known at present with X-ray data. |
Therefore these abunclances present large uncertainties andA nueht be well underestimated. | Therefore these abundances present large uncertainties and might be well underestimated. |
We believe that the over-estimate comes from our adopted scheme for relating circular. velocities to luminosities of the central galaxies in eroups. where we followed 2? and. 2.. | We believe that the over-estimate comes from our adopted scheme for relating circular velocities to luminosities of the central galaxies in groups, where we followed \citet[][]{Milosavljevic2006a} and \citet[][]{Bullock2001a}. |
We are interested mainty in the formation process of systems with a large magnitude-gap. which clearly corresponds to systems with a large eap in circular velocities even if the related magnitudes are uncertain. | We are interested mainly in the formation process of systems with a large magnitude-gap, which clearly corresponds to systems with a large gap in circular velocities even if the related magnitudes are uncertain. |
We therefore stick to our adopted method. and study how our selected. fossil population dillers from the normal group population. | We therefore stick to our adopted method and study how our selected fossil population differs from the normal group population. |
Fossil groups are systems with many. properties tvpical for ealaxy clusters. | Fossil groups are systems with many properties typical for galaxy clusters. |
Hence. a further interesting test. concerns the question whether fossil groups are. isolated: svstenis that populate the low density regions or tend to reside in higher density regions of the Universe like galaxy. clusters. | Hence, a further interesting test concerns the question whether fossil groups are isolated systems that populate the low density regions or tend to reside in higher density regions of the Universe like galaxy clusters. |
A good test would be the cross-correlate the X-ray emitting fossil groups with galaxies in the nearby universe. c.g with SDSS data. | A good test would be the cross-correlate the X-ray emitting fossil groups with galaxies in the nearby universe, e.g with SDSS data. |
However the limited. number of fossil groups actually known makes an estimate of such correlations extremely dillicult. | However the limited number of fossil groups actually known makes an estimate of such correlations extremely difficult. |
Some observational indications. though still uncertain. would suggest that fossil groups could. be fairly isolated systems (e.g.2??).. | Some observational indications, though still uncertain, would suggest that fossil groups could be fairly isolated systems \cite[e.g.][]{Jones2000a, Jones2003a, Adami2007a}. |
We check in our simulated: sample of groups whether fossil systems populate preferentially low density. regions in the universe. | We check in our simulated sample of groups whether fossil systems populate preferentially low density regions in the universe. |
We estimate the environmental density on a scale of 4. | We estimate the environmental density on a scale of 4. |
. To this end. we determine. the environmental over-density AL=paffial. where pj is the dark matter density within 4 from the group center of mass. with the inner one virial radius is subtractect. and pus is the background. matter density. | To this end we determine the environmental over-density $\Delta_{4} = \rho_{4}/\rho_{\rm bg} - 1$, where $\rho_4$ is the dark matter density within 4 from the group center of mass, with the inner one virial radius is subtracted, and $\rho_{\rm bg}$ is the background matter density. |
Figure 2 shows the distribution of the over-clensity Ay for fossil and normal groups. | Figure \ref{density} shows the distribution of the over-density $\Delta_{4}$ for fossil and normal groups. |
Alost of the groups.in the range of mass considered here. independent of being fossil or not. populate | Most of the groups,in the range of mass considered here, independent of being fossil or not, populate |
effeclive radius 5ni are plotted in fig.2.. | effective radius $5 ~nm$ are plotted in \ref{fig2}. |
The exünction efficiency for nanociamonds of all shapes and the sizes is similar being negligible in the Ilt. visible aud increasing steeply in the UV. | The extinction efficiency for nanodiamonds of all shapes and the sizes is similar being negligible in the IR – visible and increasing steeply in the UV. |
The extinction from 7.1 to 7.6 yam+ (1400 to 1300 A)) becomes constant and even decreases slightly. | The extinction from 7.1 to 7.6 $\mu m^{-1}$ (1400 to 1300 ) becomes constant and even decreases slightly. |
This shape and size independent pause in extinction at 14100 is also seen in figure 1 of Binetteetal.(2005) lor spherical nanodiamonds. | This shape and size independent pause in extinction at 1400 is also seen in figure 1 of \citet{binette05} for spherical nanodiamonds. |
The exünction efficiency is more for non-spherical shapes and the pause al 1400 is more prominent for particles departing more from (he spherical. | The extinction efficiency is more for non-spherical shapes and the pause at 1400 is more prominent for particles departing more from the spherical. |
Mathis(1996) observed that extinction cross-section for spheroids are larger than those of spheres of same volume but. Voschonnikov(2004) points out that this is (rue for small particles and in the forward direction only. | \citet{mathis96} observed that extinction cross-section for spheroids are larger than those of spheres of same volume but \citet{voshchinnikov04} points out that this is true for small particles and in the forward direction only. |
This is also true for graphitie particles (Guptaetal.2005). | This is also true for graphitic particles \citep{rgupta05}. |
. The exünction efficiency. for ellipsoid of shape 432 for the four effective sizes is plotted in fie. 3((A). which shows increase in extinction with particle size. | The extinction efficiency for ellipsoid of shape 432 for the four effective sizes is plotted in \ref{fig3}( (A), which shows increase in extinction with particle size. |
The scattering and absorption efficiencies for shape 432 of effective radius 5 nm is shown in fig.3((D). | The scattering and absorption efficiencies for shape 432 of effective radius 5 nm is shown in \ref{fig3}( (B). |
The total extinction is almost all cue to absorption even in prolile. | The total extinction is almost all due to absorption even in profile. |
The scattering efficiency is much smaller in comparison. | The scattering efficiency is much smaller in comparison. |
The extinction increases almost linearly. with size for different wavelengths aud is shown in fig.4 for two extreme wavelengths 5 jan (IR) and 0.1. pam (far-UV). | The extinction increases almost linearly with size for different wavelengths and is shown in \ref{fig4} for two extreme wavelengths 5 $\mu $ m (IR) and 0.1 $\mu $ m (far-UV). |
This is πιο in general [or nanosized particles Draine&Malhotra(1993) ancl extinction [rom any in-between particle size can be extrapolated. | This is true in general for nanosized particles \citet{draine93} and extinction from any in-between particle size can be extrapolated. |
The polarization efficiency is defined as differenGal extinction cross-section in (wo orthogonal polarizations as Qy4={Qeer|e)—(Q,,Le} where e is unit vector perpendicular to the direction of propagation. | The polarization efficiency is defined as differential extinction cross-section in two orthogonal polarizations as $ Q_{pol}=\{Q_{ext}\parallel \textbf{e}\}- \{ Q_{ext}\perp \textbf{e} \} $ where $\textbf{e}$ is unit vector perpendicular to the direction of propagation. |
The polarization efficiency for shape 432 and size 5nim is shownin fig.5.. | The polarization efficiency for shape 432 and size $5 ~nm$ is shownin \ref{fig5}. |
Q, follows the same trend as total extinction and decreases with increasing erain orientation angle 9%. as defined in DDSCAT (Draine2004). | $Q_{pol}$ follows the same trend as total extinction and decreases with increasing grain orientation angle $\beta$, as defined in DDSCAT \citep{draine04}. |
. For 9=45". (Q,,||] and (Q,,,L] are equal ancl polarization efficiency is nearly negligible. | For $\beta = 45^0 $, $\{Q_{ext}\parallel \}$ and $\{Q_{ext}\perp \}$ are equal and polarization efficiency is nearly negligible. |
Small grains are hard to orient in a particular direction (Whittet 2003).. thus nanocdiamonds have negligible contribution in polarization. | Small grains are hard to orient in a particular direction \citep{whittet}, , thus nanodiamonds have negligible contribution in polarization. |
In case of bulk diamond (he energy band-gap £j is nearly 5.47 eV and For nanocdiamonds ana? gap size dependence gives 2,=Ey-0.38(a/nm)? (Li2004). | In case of bulk diamond the energy band-gap $E_0$ is nearly 5.47 eV and for nanodiamonds an $a^{-2}$ gap size dependence gives $E_g = E_0 + 0.38(a/nm)^{-2}$ \citep{li04}. |
. Variation in band-gap for nanocdiamoncds is observable only below 2ΠΠ size (Ratyοἱal.2003) and [ον smaller size cHiamoneloicds it is reported to be close to bulk diamond (Landtοἱal.2009). | Variation in band-gap for nanodiamonds is observable only below $2~nm$ size \citep{raty03} and for smaller size diamondoids it is reported to be close to bulk diamond \citep{landt09}. |
. The absorption of EM waves in nanodiamonds can be related to this band-gap as it starts [rom e 4.7 pant, | The absorption of EM waves in nanodiamonds can be related to this band-gap as it starts from $\sim$ 4.7 $\mu m^{-1}$ . |
The rise in extinction dueto nanodiamond in [αςδν) region is abrupt and with increasing steepness. | The rise in extinction dueto nanodiamond in far-UV region is abrupt and with increasing steepness. |
This huge extinction explains the Lu-UV quasar break (Dinetteοἱal.2005) | This large extinction explains the far-UV quasar break \citep{binette05} |
increasing number of low-mass X-rav. binaries. and systems exhibiting black-hole LLEXTDPOs are likely to have mass ratios q0.3 and therefore to have eccentric disces during at least some phases of their outbursts. | increasing number of low-mass X-ray binaries, and systems exhibiting black-hole HFQPOs are likely to have mass ratios $q\la0.3$ and therefore to have eccentric discs during at least some phases of their outbursts. |
ltecentlv. Kato(2007) argued that one-armed global oscillations. svmmetric with respect to the z=Q0 plane. can excite trapped oscillations. | Recently, \cite{kato2007} argued that one-armed global oscillations, symmetric with respect to the $z=0$ plane, can excite trapped oscillations. |
His conclusions are based on analvtical. Lagrangian calculations and are too crude to allow for more than simple estimates for the growth rates. | His conclusions are based on analytical, Lagrangian calculations and are too crude to allow for more than simple estimates for the growth rates. |
In this section we describe an excitation mechanism similar to the one reported. previously. but where an (m=lon0) eccentric mode has the role that. previously belonged to the (i=low1) warp wave. | In this section we describe an excitation mechanism similar to the one reported previously, but where an $(m=1,n=0)$ eccentric mode has the role that previously belonged to the $(m=1,n=1)$ warp wave. |
Using the same numerical method as before. we calculate the trapped r mode growth rales. | Using the same numerical method as before, we calculate the trapped r mode growth rates. |
As before. consider the set of equations (10)) (13)). | As before, consider the set of equations \ref{free1}) \ref{free2}) ). |
A global eccentric mode corresponds to à zero-frequency. wave with mΞ land n=0. ( | A global eccentric mode corresponds to a zero-frequency wave with $m=1$ and $n=0$. ( |
Lf the global eccentric mocde precesses freely. the frequency. is not exactly zero but is completely neeligible compared to the characteristic frequencies in the | If the global eccentric mode precesses freely, the frequency is not exactly zero but is completely negligible compared to the characteristic frequencies in the |
lis producing an intrinsically one-sided outflow. or that a counter-jet is present but cannot be seen. | is producing an intrinsically one-sided outflow, or that a counter-jet is present but cannot be seen. |
While multipole components to the neutron star magnetic field could indeed produce a one-sided jet (Chagelishvili.Bodo.&Trussoni 1996)). there is strong circumstantial evidence that the pulsar generates a collimated outflow to its north through which it is interacting with the RCW 89 region (Manchester&Dur-din 1983: Tamuraetal. 1996:; Brazier&Becker 1997:, G99). | While multipole components to the neutron star magnetic field could indeed produce a one-sided jet \cite{cbt96b}) ), there is strong circumstantial evidence that the pulsar generates a collimated outflow to its north through which it is interacting with the RCW 89 region \cite{md83}; \cite{tkyb96}; \cite{bb97}; G99). |
This conclusion is further bolstered by feature D in Figure 2.. which is significantly elongated along the main axis of the system and widens with increasing distance from the pulsar. | This conclusion is further bolstered by feature D in Figure \ref{fig_g320_acisi}, which is significantly elongated along the main axis of the system and widens with increasing distance from the pulsar. |
We propose that this feature represents a jet which produces no directly detectable emission. but for which we observe enhanced emission in a cylindrical sheath along the interface between the jet and its surroundings. | We propose that this feature represents a jet which produces no directly detectable emission, but for which we observe enhanced emission in a cylindrical sheath along the interface between the jet and its surroundings. |
Assuming that feature C and its unseen counterpart have similar intrinsic surface brightnesses and outflow velocities. relativistic Doppler boosting can account for the observed brightness contrast provided that 1;cos¢~0.28c. where ¢ is the inclination of the outflow to the line-of-sight. | Assuming that feature C and its unseen counterpart have similar intrinsic surface brightnesses and outflow velocities, relativistic Doppler boosting can account for the observed brightness contrast provided that $v_j \cos \zeta \sim 0.28c$, where $\zeta$ is the inclination of the outflow to the line-of-sight. |
Since cos¢<| for any inclination. we can infer a lower limit v;>0.28c. consistent with the estimate v;>0.2¢ determined above from the energetics of the system. | Since $\cos \zeta < 1$ for any inclination, we can infer a lower limit $v_j >
0.28c$, consistent with the estimate $v_j > 0.2c$ determined above from the energetics of the system. |
Brazier Becker (1997)) estimated ¢>70° on the basis of HHRI data. in which the PWN appears to have a "eross-shaped morphology suggestive of an edge-on torus. | Brazier Becker \nocite{bb97}) ) estimated $\zeta > 70^\circ$ on the basis of HRI data, in which the PWN appears to have a “cross”-shaped morphology suggestive of an edge-on torus. |
However. this inclination then results in an uncomfortably high velocity. v;>0.8c. | However, this inclination then results in an uncomfortably high velocity, $v_j >
0.8c$. |
In our oobservation, this eross-shaped morphology is not apparent: it presumably resulted from imaging of the inner and outer ares (features E and 5 respectively) at the lower spatial resolution and sensitivity of the HHRI. | In our observation, this cross-shaped morphology is not apparent; it presumably resulted from imaging of the inner and outer arcs (features E and 5 respectively) at the lower spatial resolution and sensitivity of the HRI. |
A more reasonable shock flow speed vj2c/3 citekeSda)) corresponds to à smaller inclination angle 307. | A more reasonable post-shock flow speed $v_j \approx c/3$ \\cite{kc84a}) ) corresponds to a smaller inclination angle $\zeta \sim 30^\circ$ . |
This low value of ¢ has additional support from radio polarization observations of PSRB1509—58.. which exclude the larger values of argued by Brazier Becker (1997)) at the ~3¢ level (Crawford.¢Manchester.&Kaspi 2001)). | This low value of $\zeta$ has additional support from radio polarization observations of PSR, which exclude the larger values of $\zeta$ argued by Brazier Becker \nocite{bb97}) ) at the $\sim3\sigma$ level \cite{cmk01}) ). |
Models 1n which the pulsar's high-energy emission originates in. outer gaps of the magnetosphere result in à viewing angle ¢45° (Romani&Yadigaroglu 1995)). while those in which the +-ray emission is produced in a polar cap generally require small values of (Kuiperetal. 1999)). | Models in which the pulsar's high-energy emission originates in outer gaps of the magnetosphere result in a viewing angle $\zeta \sim
45^\circ$ \cite{ry95}) ), while those in which the $\gamma$ -ray emission is produced in a polar cap generally require small values of $\zeta$ \cite{khk+99}) ). |
We are thus unable to distinguish between¢ these models from the available data. | We are thus unable to distinguish between these models from the available data. |
Feature E. the bright semi-circular are to the north of the pulsar. demarcates a clear transition between the collection of compact bright features within I’ of the pulsar and the diffuse nebula which extends to much larger scales. | Feature E, the bright semi-circular arc to the north of the pulsar, demarcates a clear transition between the collection of compact bright features within $1'$ of the pulsar and the diffuse nebula which extends to much larger scales. |
The arc-like morphology of this feature is suggestive of a bow-shock. as would result where the ram-pressure from a fast-moving pulsar balances the outflow from the relativistic pulsar wind. | The arc-like morphology of this feature is suggestive of a bow-shock, as would result where the ram-pressure from a fast-moving pulsar balances the outflow from the relativistic pulsar wind. |
For a bow-shock to result. the pulsar's motion must be supersonic with respect to the sound speed in the surrounding medium. | For a bow-shock to result, the pulsar's motion must be supersonic with respect to the sound speed in the surrounding medium. |
Since the PWN itself has a sound speed ον. this condition can only be met if the reverse shock from the surrounding SNR has collided with the PWN. bringing thermal material to the center of the system (Chevalier1998:: | Since the PWN itself has a sound speed $c/\sqrt{3}$, this condition can only be met if the reverse shock from the surrounding SNR has collided with the PWN, bringing thermal material to the center of the system \cite{che98}; \cite{vagt01}; \cite{bcf01}) ). |
vanderSwaluwetal. | However, it is unlikely that this stage in PWN evolution has yet occurred in this system, since the resulting PWN would be brighter and more compact than is observed, and would occupy only a small fraction of the SNR's interior volume. |
2001:: Blondin. | An alternative interpretation is suggested by the fact that the dominant features seen in X-ray emission from both the Crab and Vela PWNe are bright toroidal arcs surrounding the pulsar \cite{hss+95}; \cite{hgh01}) ). |
Chevalier. | In these cases, it is thought that these tori correspond to synchrotron-emitting particles from a pulsar wind focused into the equatorial plane of the system. |
&Frierson 2001)). However. it | Furthermore, in the case of the Crab, data show a ring of emission situated interior to the torus \cite{wht+00}) ), which may represent the point where the free-flowing pulsar wind first shocks. |
ts unlikely that this stage in PWN | In the case of PSR, features E and 5 both show an arc-like morphology which is bisected by the symmetry axis of the nebula, similar to what is seen in these other PWNe. |
evolution has | The orientation inferred from the outflow being along the spin axis implies that features E and 5 are closer to the observer than is the pulsar, and are produced by a wind whose line-of-sight velocity component is directed towards us. |
yet occurred in this | The upper limit on any departure from circularity in the projected appearance of feature E implies $\zeta \la 30^\circ$, in agreement with the estimate of the inclination angle determined in \\ref{sec_discuss_orient}. |
system. since the resulting PWN would be | Correcting for this inclination angle, we can infer a separation $r_5 = 0.4-0.5$ pc between the pulsar and feature 5, and $r_E = 0.75-0.85$ pc between the pulsar and feature E. In interpreting this emission, we first note that there are two characteristic time-scales associated with such features: $t_{flow}$, the time taken for particles to flow from the pulsar to this position, and $t_{synch}$, the synchrotron lifetime for these particles. |
brighter a | We parametrize the upstream relativistic wind by the ratio, $\sigma_1$, of the energy in electromagnetic fields to that carried in particles \cite{rg74}) ). |
nd more compa | This implies that $\sigma_1 = B_1^2/4\pi\rho_1 \gamma_1
c^2$, where $B_1$ is the toroidal magnetic field, $\rho_1$ is the lab frame total rest mass density, and $c\gamma_1 \gg c$ is the four-velocity of the wind, all just upstream of the termination shock in the pairs. |
ct than is o | We assume $\sigma_1 \ll 1$, and will show in \\ref{sec_wisps_struc} that this assumption is self-consistent. |
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