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The dynamics of this system is probably quite complex. but we can retain that there is a force pushing the body and/or its atmosphere away from its star. | The dynamics of this system is probably quite complex, but we can retain that there is a force pushing the body and/or its atmosphere away from its star. |
Maybe the atmosphere has been completely wiped out. and the day side of the body is ionised by the flux of X rays coming from the neutron star. | Maybe the atmosphere has been completely wiped out, and the day side of the body is ionised by the flux of X rays coming from the neutron star. |
Then. the current may flow along the dayside of the body's crust. directly pushing it away. | Then, the current may flow along the dayside of the body's crust, directly pushing it away. |
Actually. it remains that. when the field is azimuthal and the dissipation is maximal. the force is radial and proportional to 777 (Eq. (8)). | Actually, it remains that, when the field is azimuthal and the dissipation is maximal, the force is radial and proportional to $r^{-2}$ (Eq. \ref{eq_force_magnetique_max}) )). |
Therefore. it acts the same way as the gravitational force. and cannot have a secular influence on the orbit. | Therefore, it acts the same way as the gravitational force, and cannot have a secular influence on the orbit. |
When E; does not vary with the distance r of the body as Eo does. according to Eq. (7)). | When $E_i$ does not vary with the distance $r$ of the body as $E_0$ does, according to Eq. \ref{eq_force_magnetique}) ), |
a fraction of the force is not of a Keplerian nature. | a fraction of the force is not of a Keplerian nature. |
For an azimuthal field. this force is however still central and causes nothing more than a pertastron precession. | For an azimuthal field, this force is however still central and causes nothing more than a periastron precession. |
Since we are mainly interested in the evolution of the semi-major axis and of the eccentricity. we don't consider this case any further in this paper. | Since we are mainly interested in the evolution of the semi-major axis and of the eccentricity, we don't consider this case any further in this paper. |
But the unperturbed magnetic field also has à small radial component and the force is therefore not exactly central. | But the unperturbed magnetic field also has a small radial component and the force is therefore not exactly central. |
Our estimate that B~B"O,r/c shows that the small angle between the magnetic field and the azimuthal direction is: In the case of PSR 1257412. at 1 AU. 6=2x107°. | Our estimate that $B^\phi \sim B^r \Omega_* r/c$ shows that the small angle between the magnetic field and the azimuthal direction is: In the case of PSR 1257+12, at 1 AU, $\delta = 2\times 10^{-6}$ . |
In the general context of a vacuum dipole wave. or a pulsar wind. its sign does not vary. and its amplitude decreases gently with the distance. | In the general context of a vacuum dipole wave, or a pulsar wind, its sign does not vary, and its amplitude decreases gently with the distance. |
As the force density jxB is perpendicular to the magnetic field. the force is not strictly radial when the field is not strictly azimuthal. | As the force density $\ve{j} \times \ve{B}$ is perpendicular to the magnetic field, the force is not strictly radial when the field is not strictly azimuthal. |
In spite of the small value of this angle. this azimuthal force component acts constantly in the same direction. | In spite of the small value of this angle, this azimuthal force component acts constantly in the same direction. |
Therefore. this foree can work. | Therefore, this force can work. |
The tangential component of the force always has the same direction as the rotation of the neutron star. | The tangential component of the force always has the same direction as the rotation of the neutron star. |
Therefore. if the planets orbital angular momentum and the star's rotational spin are parallel (in the same direction). the jxB force contributes to its acceleration. and therefore it increases its semi-major axis and its eccentricity. | Therefore, if the planet's orbital angular momentum and the star's rotational spin are parallel (in the same direction), the $\ve{j} \times \ve{B}$ force contributes to its acceleration, and therefore it increases its semi-major axis and its eccentricity. |
The force modulus increases at smaller distance and the angle 6 also becomes larger. | The force modulus increases at smaller distance and the angle $\delta$ also becomes larger. |
These two effects cause the tangential force to become stronger at closer distances from the star. | These two effects cause the tangential force to become stronger at closer distances from the star. |
From Eqs. (8)) | From Eqs. \ref{eq_force_magnetique_max}) ) |
and (9)). a rough estimate ofthe tangential force Is Let v4(GM.r7? be the orbital velocity. | and \ref{eq_angle_champ_magnetique}) ), a rough estimate ofthe tangential force is Let $v_{orb} \sim (G M_*/r)^{1/2}$ be the orbital velocity. |
The power associated to the work of F; is | The power associated to the work of $F_t$ is |
WSRT images. | WSRT images. |
A compact source in the middle of RW is associated with a background galaxy. | A compact source in the middle of RW is associated with a background galaxy. |
The cluster also hosts a number of complex radio sources related to AGN activity, for a short discussion on these sources see Sect. 1.. | The cluster also hosts a number of complex radio sources related to AGN activity, for a short discussion on these sources see Sect. \ref{sec:agn}. |
A spectral index map was computed using both the WSRT and GMRT images, including only common UV ranges. | A spectral index map was computed using both the WSRT and GMRT images, including only common UV ranges. |
Both the WSRT and GMRT datasets have relatively good inner UV-coverage. | Both the WSRT and GMRT datasets have relatively good inner UV-coverage. |
The largest detectable angular scale is limited to about at 610 MHz, which is sufficient not to resolve out the extended radio relics. | The largest detectable angular scale is limited to about at 610 MHz, which is sufficient not to resolve out the extended radio relics. |
The inclusion of maps at four different frequencies enables us to map the spectral index over the low surface brightness radio relics. | The inclusion of maps at four different frequencies enables us to map the spectral index over the low surface brightness radio relics. |
Spectral index maps made with only two frequency images were too noisy to map the spectral index across the relics. | Spectral index maps made with only two frequency images were too noisy to map the spectral index across the relics. |
The spectral index map was created by fitting a single power-law through the flux measurements at 241, 610, 1382, and 1714 MHz. | The spectral index map was created by fitting a single power-law through the flux measurements at 241, 610, 1382, and 1714 MHz. |
In this way, we only fitted for the slope and normalization of the radio spectrum, ensuring the number of free variables in the fit remains as low as possible (at the cost of detecting spectral curvature). | In this way, we only fitted for the slope and normalization of the radio spectrum, ensuring the number of free variables in the fit remains as low as possible (at the cost of detecting spectral curvature). |
The technique of combining maps at more than two frequencies has another advantage that errors in the maps arising from RFI, calibration errors, deconvolution errors, slightly different UV coverage, etc., | The technique of combining maps at more than two frequencies has another advantage that errors in the maps arising from RFI, calibration errors, deconvolution errors, slightly different UV coverage, etc., |
are suppressed in the spectral index map as long as they do not correlate at the same location and spatial frequencies on the sky. | are suppressed in the spectral index map as long as they do not correlate at the same location and spatial frequencies on the sky. |
Pixels in the spectral index map were blanked if any of corresponding pixels in the individual maps fell below 1.50. | Pixels in the spectral index map were blanked if any of corresponding pixels in the individual maps fell below $1.5\sigma_{\rm{rms}}$. |
Special care was taken about the precise alignment of the maps, we slightly shifted the GMRT maps by about a quarter of the synthesized beam, removing a small spectral index gradient visible across all the point sources. | Special care was taken about the precise alignment of the maps, we slightly shifted the GMRT maps by about a quarter of the synthesized beam, removing a small spectral index gradient visible across all the point sources. |
The result is shown in Fig. 8.. | The result is shown in Fig. \ref{fig:spix}. |
For relic RW, the spectral index steepens to the north and eastwards to the cluster center, from —0.9 to —2.0. | For relic RW, the spectral index steepens to the north and eastwards to the cluster center, from $-0.9$ to $-2.0$. |
The spectral index for relic RE also varies roughly between —0.9 and --2.0. | The spectral index for relic RE also varies roughly between $-0.9$ and $-2.0$. |
The overall spectral index at the east side of relic RE is about —1.2 There is an overall trend of spectral steepening towards the west, see also Fig. 16.. | The overall spectral index at the east side of relic RE is about $-1.2$ There is an overall trend of spectral steepening towards the west, see also Fig. \ref{fig:relicprofile}. |
The spectral index is correlated with the surface brightness of the relic, the brightest parts have a flatter spectral index (see also Fig. 16)). | The spectral index is correlated with the surface brightness of the relic, the brightest parts have a flatter spectral index (see also Fig. \ref{fig:relicprofile}) ). |
The polarization map from the WSRT at 1382 MHz is shown in Fig. 9.. | The polarization map from the WSRT at 1382 MHz is shown in Fig. \ref{fig:polzwcl52}. |
No useful polarization information could be extracted from the WSRT 18 cm observations. | No useful polarization information could be extracted from the WSRT 18 cm observations. |
The polarization map reveals that most of the compact sources are polarized below the level. | The polarization map reveals that most of the compact sources are polarized below the level. |
Some polarized emission is detected from | Some polarized emission is detected from |
the three sets of combined IR. | SGZLINIZIU residuals are drawn from. dilferent. parent populations. | the three sets of combined RG $+$ SG/LINER residuals are drawn from different parent populations. |
A larger sample size is needed for log(A) «&—2. | A larger sample size is needed for $\lambda$ ) $< -2$. |
Thus. in summary. replacing total radio buminosities with core radio luminosities. and additionally applying a mass Correction. narrows the eap in radio loudness between the upper and lower sequences in the log(A?) log(A) plane by about an order of magnitudein therange 6κlog(A)<2. | Thus, in summary, replacing total radio luminosities with core radio luminosities, and additionally applying a mass correction, narrows the gap in radio loudness between the upper and lower sequences in the $R$ $\lambda$ ) plane by about an order of magnitude in the range $-6 < \log(\lambda) < -2$. |
RGs are on average more radio-loud. than the SCs and LINERs by ~1.6 dex. which is equivalent to a dillerence of about an order of magnitude in jet power (equation 7)). | RGs are on average more radio-loud than the SGs and LINERs by $\sim$ 1.6 dex, which is equivalent to a difference of about an order of magnitude in jet power (equation \ref{eqn_blandford}) ). |
We have clemonstrated that the significance ancl width of the radio loudness bimodality in the log(/?) log(A) plane is closely linked. to the measure of radio power adopted. and its dependence on DII mass. | We have demonstrated that the significance and width of the radio loudness bimodality in the $R$ $\lambda$ ) plane is closely linked to the measure of radio power adopted, and its dependence on BH mass. |
Table 3. summarises the advantages and disadvantages of using core or total racio luminosity as a measure of instantaneous jet power. | Table \ref{table: pros cons} summarises the advantages and disadvantages of using core or total radio luminosity as a measure of instantaneous jet power. |
The primary argument for not using core luminosities is that they are susceptible to relativistic beaming cllects (c.g.inthecontextof/2bimodalitybyLaor 2003).. depending on the orientation of the radio source with respect to the line of sight: we discuss this further in Section. ??.. | The primary argument for not using core luminosities is that they are susceptible to relativistic beaming effects \citep[e.g. in the context of $R$ bimodality by][]{laor03}, depending on the orientation of the radio source with respect to the line of sight; we discuss this further in Section \ref{section beaming}. |
On the other hand. for example. recent or renewed activity in the nucleus seen. sav. in the optical or N-rav. bands will not be related directly to the extended: radio emission from a jet that may have propagated hundreds of kpe over timescales of —10' vr. | On the other hand, for example, recent or renewed activity in the nucleus seen, say, in the optical or X-ray bands will not be related directly to the extended radio emission from a jet that may have propagated hundreds of kpc over timescales of $\sim$$10^{7}$ yr. |
In this situation. the total integrated Dux density is an average measure of the jet power over a much longer period of time. | In this situation, the total integrated flux density is an average measure of the jet power over a much longer period of time. |
Therefore. studies that compare total racio luminosities with nuclear optical or X-ray Iuminosities may be very misleading. especially if the sources are Iobe-dominated. | Therefore, studies that compare total radio luminosities with nuclear optical or X-ray luminosities may be very misleading, especially if the sources are lobe-dominated. |
By restricting the analysis to the nuclear region or all wavebands. we ensure that similar spatial scales. and importantly. similar timescales. are probed. | By restricting the analysis to the nuclear region for all wavebands, we ensure that similar spatial scales, and importantly, similar timescales, are probed. |
In Figure 3. we compare the core raclio powers oesented. in this paper with the total radio powers from SSLO07. | In Figure \ref{fig:plot3}, we compare the core radio powers presented in this paper with the total radio powers from SSL07. |
Core and total 5 €LIz radio power are observed to be correlated: similar correlations between core and total racio uminosity have been seen in other studies (e.g.Ciovanninietal.1988. 2001).. | Core and total 5 GHz radio power are observed to be correlated; similar correlations between core and total radio luminosity have been seen in other studies \citep[e.g.][]{giovannini88,giovannini01}. . |
Phe BLRGs and FR ERGs are typically dominated by an extended component: the median core-to-otal radio Luminosity ratios are 7 per cent (BLIRCSs) ane ~6 per cent (FRE Bs). | The BLRGs and FR I RGs are typically dominated by an extended component: the median core-to-total radio luminosity ratios are $\sim$ 7 per cent (BLRGs) and $\sim$ 6 per cent (FR I RGs). |
For the RLOs. as well as the SCGs and LINISHs. the majority of the radio power also originates rom an extended component. but not to the same exten as for the BLRGs and FR LRGs: the median core-to-tota ratios are ~25 per cent (RLOs) and ~20 per cent (SCs aux LINERs). | For the RLQs, as well as the SGs and LINERs, the majority of the radio power also originates from an extended component, but not to the same extent as for the BLRGs and FR I RGs: the median core-to-total ratios are $\sim$ 25 per cent (RLQs) and $\sim$ 20 per cent (SGs and LINERs). |
Phe PGQs may have the largest core fraction on average. but given that only core upper limits were obtainec for 40 per cent of this subsample. it is not possible to clraw a firm conclusion at this stage (median ratio 220 per cent). | The PGQs may have the largest core fraction on average, but given that only core upper limits were obtained for 40 per cent of this subsample, it is not possible to draw a firm conclusion at this stage (median ratio $\gtrsim 20$ per cent). |
Could relativistic beaming allect the logCA) log(A) plots shown in Figure 1?? | Could relativistic beaming affect the $R$ $\lambda$ ) plots shown in Figure \ref{fig:plot1}? |
The ratio of the core to extended radio luminosity. or [lux density. is commonly. used. as an orientation indicator (e.g.Orr&Browne1982). | The ratio of the core to extended radio luminosity, or flux density, is commonly used as an orientation indicator \citep[e.g.][]{orr82}. |
. We would expect a beamed core to lift this ratio at small viewing angles to the jet axis. | We would expect a beamed core to lift this ratio at small viewing angles to the jet axis. |
Lt is therefore possible that Figure 3. suggests a net orientation dillerence between the upper ancl lower sequences in Figure 1. with sources on the lower track being viewed. closer to pole-on on average. | It is therefore possible that Figure \ref {fig:plot3} suggests a net orientation difference between the upper and lower sequences in Figure \ref{fig:plot1}, with sources on the lower track being viewed closer to pole-on on average. |
Indeed. SSLOT chose those SCs and. LINES for which at least the La line is broad: in AGN orientation schemes (e.g.Antonucci.1993).. broad. lines are obscured by a torus of dense gas at large viewing angles to the jet. | Indeed, SSL07 chose those SGs and LINERs for which at least the $\alpha$ line is broad; in AGN orientation schemes \citep[e.g.][]{antonucci93}, broad lines are obscured by a torus of dense gas at large viewing angles to the jet. |
Hence. we might expect the lower track to be boosted upwards by a relatively larger amount. which would make any intrinsic bimodality less pronounced. | Hence, we might expect the lower track to be boosted upwards by a relatively larger amount, which would make any intrinsic bimodality less pronounced. |
Llowever. this interpretation is most likely far too simplistic. | However, this interpretation is most likely far too simplistic. |
Firstly. though the presence of relativistic jets has been suggested for raclio-quiet quasars (e.g.Falcke.2003:Barvainisetal. 2005).. 1ο situation appears to be less clear-cut for SCs. for which there is evidence for both sub-relativistic ancl relativistic expansion (e.g.Ulvestadetal.1999:Brunthaleret2000:Micldelberg 2004). | Firstly, though the presence of relativistic jets has been suggested for radio-quiet quasars \citep*[e.g.][]{falcke96,blundell03,barvainis05}, the situation appears to be less clear-cut for SGs, for which there is evidence for both sub-relativistic and relativistic expansion \citep[e.g.][]{ulvestad99,brunthaler00,middleberg04}. |
Moreover. recently Laletal.(2011). found. no evidence for relativistic beaming in SCs. | Moreover, recently \citet[][]{lal11} found no evidence for relativistic beaming in SGs. |
Furthermore. it has been proposed that SCs have thermallv-dominated. barvonic jets with sub-relativistic velocities. though the jet velocity might be mildly relativistic close to the 1211 (Bicknellοἱal.1998: 2002). | Furthermore, it has been proposed that SGs have thermally-dominated, baryonic jets with sub-relativistic velocities, though the jet velocity might be mildly relativistic close to the BH \citep[][]{bicknell98,bicknell02}. |
. Therefore. at Eelelington ratios <1 per cent. relativistic beaming may not be particularly significant forthe lower sequence. | Therefore, at Eddington ratios $<1$ per cent, relativistic beaming may not be particularly significant forthe lower sequence. |
We now attempt to quantify the possible beaming ellects for the RGs and RLQs. | We now attempt to quantify the possible beaming effects for the RGs and RLQs. |
In general.for a radio core with spectral index o. the observed. tux density S,n, is | In general,for a radio core with spectral index $\alpha$ , the observed flux density $S_{\nu, \rm \: obs}$ is |
the same velocity distribution as either the full sample or the blue control sample. | the same velocity distribution as either the full sample or the blue control sample. |
The right-hand panels of Figure 3 present equivalent comparisons for the radial distribution, adopting a cluster centre coincident with the giant elliptical galaxy NGC 4874. | The right-hand panels of Figure \ref{fig:histcomp} present equivalent comparisons for the radial distribution, adopting a cluster centre coincident with the giant elliptical galaxy NGC 4874. |
The GSE galaxies are markedly more concentrated towards the cluster core than are the blue control galaxies, with 12/13 pper cent) lying within MMpc, compared to 26/57 pper cent) of the control sample. | The GSE galaxies are markedly more concentrated towards the cluster core than are the blue control galaxies, with 12/13 per cent) lying within Mpc, compared to 26/57 per cent) of the control sample. |
A Kolmogorov-Smirnov (KS) test yields a 0.4 pper cent probability that the GSE galaxies were drawn from the same radial distribution as the control sample galaxies. | A Kolmogorov–Smirnov (KS) test yields a $0.4$ per cent probability that the GSE galaxies were drawn from the same radial distribution as the control sample galaxies. |
The GSEs are, in fact, consistent with being drawn from the much more concentrated distribution followed by all matched cluster members, which is dominated by passive galaxies. | The GSEs are, in fact, consistent with being drawn from the much more concentrated distribution followed by all matched cluster members, which is dominated by passive galaxies. |
Note also that the outermost GSE galaxy is GMP 5422 which is the least certain case of stripping identified here. | Note also that the outermost GSE galaxy is GMP 5422 which is the least certain case of stripping identified here. |
Removing it from the sample would the discrepancy between GSE and control-sample galaxies in terms of the radial distribution. | Removing it from the sample would the discrepancy between GSE and control-sample galaxies in terms of the radial distribution. |
Next we consider the fraction of all star-forming (NUV—i« 4) galaxies which are currently undergoing gaseous stripping. | Next we consider the fraction of all star-forming $NUV-i<4$ ) galaxies which are currently undergoing gaseous stripping. |
For the surveyed region as a whole, the GSE galaxies form a fraction Nasg/Nyue=13/700.19*008, | For the surveyed region as a whole, the GSE galaxies form a fraction $N_{\rm GSE}/N_{\rm blue}=13/70=0.19^{+0.06}_{-0.05}$. |
However, as shown above, the incidence of stripping is concentrated towards the cluster core. | However, as shown above, the incidence of stripping is concentrated towards the cluster core. |
Within a radius of MMpc from the cluster centre, the fraction becomes Nase,1Mpc/Nbiue,iMpe=12/380.32+0.07. | Within a radius of Mpc from the cluster centre, the fraction becomes $N_{\rm GSE, 1Mpc}/N_{\rm blue, 1Mpc}=12/38=0.32\pm0.07$. |
These fractions refer to the stripping features detectable in our data; future | These fractions refer to the stripping features detectable in our data; future |
The thermodvuamic stratificatious for the wubra. the pemmubra. and the quiet sun are xescribed bv the tripartite model. | The thermodynamic stratifications for the umbra, the penumbra, and the quiet sun are prescribed by the tripartite model. |
Within these stratificaions the pressure. po{z). the deusity. p(s). and the temperature. TG) depend only on cepth. | Within these stratifications the pressure, $p_{\rm b}(z)$, the density, $\rho_{\rm
b}(z)$, and the temperature, $T_{\rm b}(z)$ depend only on depth. |
Level := 0kli COITCSDOids to 7=2/3 level oftie quiet sun aud decreases downwards. | Level $z=0\,$ km corresponds to $\tau=2/3$ level of the quiet sun and decreases downwards. |
Fig. | Fig. |
2 shows tlie «epeudenuces of Ti. pj aud pi on : for the different stratificatious in the vicinity of the plotosphere. | \ref{figure3} shows the dependences of $T_{\rm b}$, $p_{\rm b}$ and $\rho_{\rm b}$ on $z$ for the different stratifications in the vicinity of the photosphere. |
The thermodvnamic variables inside the tube. at the center of cach cell. are obtaiuec with a use of logaritlinic splines defined on he background discretization. | The thermodynamic variables inside the tube, at the center of each cell, are obtained with a use of logarithmic splines defined on the background discretization. |
The tube Ixiug along the maenetopause is illuminated by the quiet suna on one side. | The tube lying along the magnetopause is illuminated by the quiet sun on one side. |
This effect is taken uto account iu the radiative heat exchange. | This effect is taken into account in the radiative heat exchange. |
The backerouncd magnetic field streneth. DGr.το. depends on the radial «istance. we. and on depth. :. | The background magnetic field strength, $B_{\rm b}(x,z)$, depends on the radial distance, $x$, and on depth, $z$. |
The radial distace o6 ds defined to be ZCLO at the eciter of the sunspot inocel. | The radial distance $x$ is defined to be zero at the center of the sunspot model. |
Bye.) for a certain posiion ds determiued usi1ο a bilinear interpolation. | $B_{\rm b}(x,z)$ for a certain position is determined using a bilinear interpolation. |
The maguctic pressure. Inὃπ. of the used backeround model is shown in Fie. | The magnetic pressure, $B^2_{\rm b}/8\pi$, of the used background model is shown in Fig. |
1 as a surface plot. | \ref{figure4} as a surface plot. |
One can clearly see the jump across the uagnetopause from finite field streng hin the peuunibra to a vanishing field in the quiet SUL. | One can clearly see the jump across the magnetopause from finite field strength in the penumbra to a vanishing field in the quiet sun. |
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