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bser | In this case, the bulk velocity in the post-shock flow at a distance $r$ from the pulsar is \cite{kc84a}) ): where $r_s$ is the distance from the pulsar to the termination shock. |
ved. and | We then find that: For pairs emitting at energy $\varepsilon$ keV in a magnetic field $B$ $\mu$ G, the synchrotron lifetime is For the Crab Nebula, we adopt $r_s \approx 0.15$ pc and $B \sim 100$ $\mu$ G, and consider the Crab's X-ray torus at $r \approx 0.4$ pc. |
wo | At an energy $\varepsilon=5$ keV, we find $t_{flow} \sim 30$ yr and $t_{synch} \sim 20$ yr, so that these time scales are comparable. |
uld oc | In the case of PSR, we assume that the location of the termination shock corresponds approximately to that of feature 5 (the inner arc), and so adopt $r_s \approx r_5$. |
cu | For a magnetic field $B \sim B_n = 8$ $\mu$ G, we then find that in feature E, $t_{flow} \sim 25$ yr $\ll
t_{synch} \sim 800$ yr. |
py only a smal | Since the post-shock magnetic field in the inner nebula is generally weaker than the mean value for the PWN \cite{kc84a}) ), this value of $t_{synch}$ is likely to be a lower limit, further widening the discrepancy between the two time-scales. |
l fraction of the SNR's | Thus while the bright torus seen in the Crab simply corresponds to the region in which most of the X-ray emitting particles radiate their energy, synchrotron cooling is not significant at this distance from PSR even at X-ray energies, and the brightness enhancement in feature E cannot be due to rapid dumping of pairs' energy into X-ray photons. |
in | The long synchrotron lifetimes require that most of the X-ray emission comes from a much larger volume, as is indeed observed. |
terior | It is therefore not valid to argue that feature E is the analog of the X-ray torus seen in the Crab; the much lower nebular magnetic field in the case of PSR demands a different interpretation. |
volu | This conclusion is supported by the fact that feature E has a distinctly harder photon index than the overall nebula and also shows a clear radio counterpart (see Fig. \ref{fig_g320_pol}) ), |
me. | neither of which would be expected if this feature were primarily due to radiative losses. |
ofa | wavepacket separated in 2 by 2Ay. | of a $+$ wavepacket separated in $z$ by $\ga\Lambda^-_\lambda$. |
Thus they inupriut their parallel scales ou the | ve waves. aud IHeuceforth we denote the common parallel scales by Ay. Thisdisc | Thus they imprint their parallel scales on the $+$ ve waves, and Henceforth we denote the common parallel scales by $\Lambda_\lambda\,$. |
overy that the parallel scales are similar iu au inbalanuced cascadeis a nont | This that the parallel scales are similar in an imbalanced cascadeis a result. |
rivial result. Equatious (1)) aud (5)) vield that the cascade of νο waves ds critically valance. | Equations \ref{eq:Lambdaminus}) ) and \ref{eq:equal}) ) yield that the cascade of $-$ ve waves is critically balanced. |
Tt remains to calculate the | ve waves’ cascade time. | It remains to calculate the $+$ ve waves' cascade time. |
All of the following material up to equation (9)). as well as he material in the Appendix. is devoted to the result: 7~Afi. | All of the following material up to equation \ref{eq:fluxplus2}) ), as well as the material in the Appendix, is devoted to the result: $\tau_\lambda^+\sim\lambda/w_\lambda^-$. |
This result is remarkable. | This result is remarkable. |
It shows hat the straining rate imposed bv the ve waves on | ve ones. iyfA. is Iniposed coliereutly over a time Aft,. | It shows that the straining rate imposed by the $-$ ve waves on $+$ ve ones, $w_\lambda^-/\lambda$, is imposed coherently over a time $\lambda/w_\lambda^-$. |
Yet he waveperiod of νο waves is mich shorter than this. by he factor since yy 1. one nüght be tempted to conclude, erroneously. that | ve waves undergo a weal cascade. 1.6.. that νο waves impose on them small. short uncorrelated strains of amplitude ὧνover time intervals ~Αλτι resulting in τν~(yy)Αν)Αλ ων). | Yet the waveperiod of $-$ ve waves is much shorter than this, by the factor Since $\chi_\lambda^-\ll 1$ , one might be tempted to conclude, erroneously, that $+$ ve waves undergo a weak cascade, i.e., that $-$ ve waves impose on them small, short uncorrelated strains of amplitude $\chi_\lambda^-$over time intervals $\sim
\Lambda_\lambda/\va$ resulting in $\tau_\lambda^+\sim
(\chi_\lambda^-)^{-2}(\Lambda_\lambda/\va)\sim
(\chi_\lambda^-)^{-1}(\lambda/w_\lambda^-)$ . |
Tusteack. the correct couclusion is that a (NAcolierent strain is inposed over tine interval | Instead, the correct conclusion is that a coherent strain is imposed over time interval $\lambda/w_\lambda^-$ . |
Tow cau the cobhereuce time Aaexceed X4/V47? | How can the coherence time exceed $\Lambda_\lambda/\va$? |
The kevpoint is that the straining of the| ve waves is duc to the νν field as seen from the | ve waves’ rest frame (which has 4jurea!myeiDOVt.4= of) | The keypoint is that the straining of the$+$ ve waves is due to the ${\bf
w}^-$ field as seen from the $+$ ve waves' rest frame (which has $x'=x, \;y'=y, \;z' = z - \va t, \;t'=t$ ). |
In this frame. the MIID equations (1)) transform to To appreciate that the correlation time of w— iu the primed frame can exceed Ayτε, consider the limiting case in which w— ds πο stall that backreaction outo the | ve waves can be neglected. | In this frame, the MHD equations \ref{eq:mhd}) ) transform to To appreciate that the correlation time of ${\bf w}^-$ in the primed frame can exceed $\Lambda_\lambda/\va$, consider the limiting case in which ${\bf w}^-$ is so small that backreaction onto the $+$ ve waves can be neglected. |
Then w! is iudepeudent of £. aud is a function oulv of r/. so ν satisfies a linear (integrodifferential) equation. whose coefficients are iudependoeut of #. | Then ${\bf w}^+$ is independent of $t'$, and is a function only of ${\bf r}'$, so ${\bf w}^-$ satisfies a linear (integro--differential) equation, whose coefficients are independent of $t'$. |
Tf ve waves are injected ou a leugthliscale nich larecr than the scale of iterest. with a long coherence time T. then as they cascade down to snaller scales their colercuce time remains fixed. 7...=T. where !corr. yas defined as the correlation time ofthe ve waves in the frame of the | ve waves. | If $-$ ve waves are injected on a lengthscale much larger than the scale of interest, with a long coherence time $T$, then as they cascade down to smaller scales their coherence time remains fixed, $\tau_{\rm corr,\lambda}^-=T$, where $\tau_{\rm corr,\lambda}^-$ is defined as the correlation time ofthe $-$ ve waves in the frame of the $+$ ve waves. |
In the lamiting case that wis held fixed at the injection scale (Fo— x). then on smaller scales wo ds independeut of £ (£z, x). even though it is nuderegoineg an active cascade to small scales. | In the limiting case that ${\bf w^-}$ is held fixed at the injection scale $T=\infty$ ), then on smaller scales ${\bf w}^-$ is independent of $t'$ $\tau_{\rm corr,\lambda}^-=\infty$ ), even though it is undergoing an active cascade to small scales. |
To estimate 7... When w is not imfuutesimally sux. it is necessary to account for backreaction: ve waves alter | ve waves. which react back on the νο ones | To estimate $\tau_{\rm corr,\lambda}^-$ when ${\bf
w}^-$ is not infinitesimally small, it is necessary to account for backreaction: $-$ ve waves alter $+$ ve waves, which react back on the $-$ ve ones. |
Ax ve waves cross a plane atfixed z/. the | ve waves at that plane are changing on their cascade time scale 7 . Hence. over times separated by ry. the ve waves crossing z are cascaded by eutirelv different. |ve waves. | As $-$ ve waves cross a plane atfixed $z'$, the $+$ ve waves at that plane are changing on their cascade time scale $\tau_\lambda^+$ Hence, over times separated by $\tau_\lambda^+$, the $-$ ve waves crossing $z^\prime$ are cascaded by entirely different $+$ ve waves. |
This inplies that T,corr.À~r8A Because the | voe waves are strained at rate wyfA. dt follows that AΑν. | This implies that $\tau_{\rm
corr,\lambda}^-\sim \tau_\lambda^+$ Because the $+$ ve waves are strained at rate $w_\lambda^-/\lambda$, it follows that $\tau_\lambda^+\sim\lambda/w_\lambda^-$. |
Thus Tuvoking Kohnosorov's lypothesis of the scale (ic. A} independence of the cucrey fluxes eiven by equations (3)) and (9)). we obtain the inertialrange scalings. The [ve wave cascade shares some characteristics with both weak aud strong balanced) MIID. cascades. | Thus Invoking Kolmogorov's hypothesis of the scale (i.e. $\lambda$ ) independence of the energy fluxes given by equations \ref{eq:fluxminus}) ) and \ref{eq:fluxplus2}) ), we obtain the inertial–range scalings, The $+$ ve wave cascade shares some characteristics with both weak and strong balanced MHD cascades. |
Iu the weak cascades. the cascade time is longer than the waveperiod. aud a wave experiences multiple. raudonilv-phased perturbations during its cascade time. | In the weak cascades, the cascade time is longer than the waveperiod, and a wave experiences multiple, randomly-phased perturbations during its cascade time. |
In the strong cascades. the cascade time is comparable to (or shorter than) the waveperiod. aud a wave suffers a coherent strain as it cascades. | In the strong cascades, the cascade time is comparable to (or shorter than) the waveperiod, and a wave suffers a coherent strain as it cascades. |
Furthermore. weak turbulence subunits to perturbation theory but strong turbulence does not. | Furthermore, weak turbulence submits to perturbation theory but strong turbulence does not. |
Iu the | ve wave cascade: We contend that the [ve wave cascade is strong because the second aud third items have dynamical sjeuificauce whereas the first does not. | In the $+$ ve wave cascade: We contend that the $+$ ve wave cascade is strong because the second and third items have dynamical significance whereas the first does not. |
The cimensiouless paralmcter that iudicates whether the |ve waves are strouely cascaded. is and not ὧν. | The dimensionless parameter that indicates whether the $+$ ve waves are strongly cascaded is and not $\chi_\lambda^-$. |
Strong cascades. corresponi toy, ~EH. and weals ones to ὧν<1. | Strong cascades correspond to $\hat{\chi}_\lambda^{-}\sim 1$, and weak ones to $\hat{\chi}_\lambda^{-}<1$. |
For the νο wave cascade. W=l. since the correlation time of | vo waves iu the frame of the ve ones is A/Va. | For the $-$ ve wave cascade, $\hat{\chi}_\lambda^+={\chi}_\lambda^+\sim 1$, since the correlation time of $+$ ve waves in the frame of the $-$ ve ones is $\Lambda_\lambda/\va$. |
We call the criterion WI] "modified critical balance; to distinguish it frou critical balance (which would incorrectly imply WI~ i). | We call the criterion $\hat{\chi}_\lambda^\pm\sim 1$ “modified critical balance,” to distinguish it from critical balance (which would incorrectly imply $\chi_\lambda^\pm\sim 1$ ). |
We lave deduced the behavior of mibalauced. strong ΑΠΟ turbulence. | We have deduced the behavior of imbalanced strong MHD turbulence. |
Its salicut properties are: 1, | Its salient properties are: 1. |
The | ve aud ve waves carry unequalenergy fluxes. el #2. whilethey bothundergo cascades. | The $+$ ve and $-$ ve waves carry unequalenergy fluxes, $\varepsilon^+\neq \varepsilon^-\,$ , whilethey bothundergo cascades. |
2. | 2. |
In the inertialrange. the rans. | In the inertial–range, the r.m.s. |
Elsasser amplitudes are proportional to the one.third power of the transverse scale: TNx AU]. | Elsasser amplitudes are proportional to the one–third power of the transverse scale: $w^{\pm}_\lambda\propto
\lambda^{1/3}\,$ . |
This is similar to the balanced. strong cascade. | This is similar to the balanced, strong cascade. |
Moreover. their ratio. uuTSalfs is independent of A. | Moreover, their ratio, $\wpluslam/\wminuslam \sim
\varepsilon^+/\varepsilon^-$ is independent of $\lambda$ . |
3.The parallel scales of the | ve aud νο waves are equal. | 3.The parallel scales of the $+$ ve and $-$ ve waves are equal. |
The conunon parallel scale of eddies of transverse seale AL isAyxATO μή] to the balanced. strong cascade. | The common parallel scale of eddies of transverse scale $\lambda$ , is$\Lambda_\lambda \propto\lambda^{2/3}$ , similar to the balanced, strong cascade. |
phase. | phase. |
This 1iechauisui should also produce shorter more svuuuetrie bursts than in crustal fracture. | This mechanism should also produce shorter more symmetric bursts than in crustal fracture. |
2? states that the harduess-fuence anticorrclation found in SCGRs is consistent with magnetic reconnection. | \citet{lyu03} states that the hardness-fluence anticorrelation found in SGRs is consistent with magnetic reconnection. |
For the surtace-cooling model. the opposite is expected. | For the surface-cooling model, the opposite is expected. |
As diseussed by δν, both miechliuisius could easily be at work. | As discussed by \citet{lyu03}, both mechanisms could easily be at work. |
? suggested that observationallv. there are two types of magnetar bursts. | \citet{wkg+05} suggested that observationally, there are two types of magnetar bursts. |
Type A bursts are nearly sviunetric and are typical of SCR bursts. | Type A bursts are nearly symmetric and are typical of SGR bursts. |
Type D bursts have cen observed in ANPs aud are characterized by a short spike followed by a long tail. typically much longer hau the rotational period of the pulsar. | Type B bursts have been observed in AXPs and are characterized by a short spike followed by a long tail, typically much longer than the rotational period of the pulsar. |
Pulsatious have οσα observed iu these tails. | Pulsations have been observed in these tails. |
Since the Type B bursts observed in ANPs occur prefercutially in phase and exhibit a harduess-fiueuce correlation. and the Type A musts in SGBs are distributed raucomly m phase aud je a harduess-flucuce auti-correlation. 7? suggest the naenetic reconnection mcchanisin for tvpe A bursts aud he surtace-cooling model for Type D bursts. | Since the Type B bursts observed in AXPs occur preferentially in phase and exhibit a hardness-fluence correlation, and the Type A bursts in SGRs are distributed randomly in phase and have a hardness-fluence anti-correlation, \citet{wkg+05} suggest the magnetic reconnection mechanism for type A bursts and the surface-cooling model for Type B bursts. |
For LE 51058. none of the bursts detected bySwift NRT could be classified as Type D. However. the two nursts with lone pulsating tails found in data by 2 and ? have typical Type B morphology. | For 1E $-$ 5408, none of the bursts detected by XRT could be classified as Type B. However, the two bursts with long pulsating tails found in data by \citet{snb+10} and \citet{mgw+09} have typical Type B morphology. |
For the bursts in this work. over half of the bursts were classified as svuuuetric. which nonünallv corresponds o Type A (see topaight pauecl of Figure 13. for example). | For the bursts in this work, over half of the bursts were classified as symmetric, which nominally corresponds to Type A (see top-right panel of Figure \ref{fig:burstex} for example). |
About of the bursts were classified as slow-fall bursts. which are actually closer to Type A in norpholoey than Type B. although they are not very svuuuetne. | About of the bursts were classified as slow-fall bursts, which are actually closer to Type A in morphology than Type B, although they are not very symmetric. |
Thus. the bursts from 1E 5108 are rot easilv classified into Types A and D as described o Y. | Thus, the bursts from 1E $-$ 5408 are not easily classified into Types A and B as described by \citet{wkg+05}. |
Moreover. for both the svuuuetric aud slow-fall musts. the folded photon arrival times exhibited a clear phase dependence. although for the slow-fall bursts this "pulse is auch strouger. | Moreover, for both the symmetric and slow-fall bursts, the folded photon arrival times exhibited a clear phase dependence, although for the slow-fall bursts this `pulse' is much stronger. |
That the svuumetric bursts slow sole pulse nodulation is sueecstive of a difference with ‘classical’ Type A bursts. or that pulse phase analyses of he latter should be attempted using all burst couuts. as hey too may be pulsed. | That the symmetric bursts show some pulse modulation is suggestive of a difference with `classical' Type A bursts, or that pulse phase analyses of the latter should be attempted using all burst counts, as they too may be pulsed. |
That the burst counts are pulsed indicates that burst enussion comes from a preferred region in rotational phase. be it on or near the surface or high in the magnetosphere. even if the burst peaks arrive randomly iu phase. | That the burst counts are pulsed indicates that burst emission comes from a preferred region in rotational phase, be it on or near the surface or high in the magnetosphere, even if the burst peaks arrive randomly in phase. |
The offset between the burst counts pulse peak aud the persistent pulse peak secu when comparing Figures Th aud το denmoustrates that the preferred burst cinissiou region has location and ecolctry similar to. but distinct from. that producimg the persistent pulsations. | The offset between the burst counts pulse peak and the persistent pulse peak seen when comparing Figures 7b and 7e demonstrates that the preferred burst emission region has location and geometry similar to, but distinct from, that producing the persistent pulsations. |
The total οποιον released iu the Suiff-detected bursts was ~τν10/9 ore in the 1-10 keV range. | The total energy released in the -detected bursts was $\sim
1 \times 10^{40}$ erg in the 1-10 keV range. |
This is much lower than the 1-10 keV energv released frou the persistent enission between 2009 January 22 and 2009 September 30 of ~9«10! ore. | This is much lower than the 1-10 keV energy released from the persistent emission between 2009 January 22 and 2009 September 30 of $\sim 9 \times 10^{41}$ erg. |
For reference. the energv released frou the spin-down in that same period is ~ὃν10! ore. | For reference, the energy released from the spin-down in that same period is $\sim 5 \times 10^{40}$ erg. |
2 find that for SCRs. the enerev released in the bursts is higher than that released in the persistent cussion. but for LE 2259|586. the opposite is true. | \citet{wkt+04} find that for SGRs, the energy released in the bursts is higher than that released in the persistent emission, but for 1E 2259+586, the opposite is true. |
Iu this regard. the 2009 outburst of LE 1517. 5108 is more like that of ANP 1E 2259|586. | In this regard, the 2009 outburst of 1E $-$ 5408 is more like that of AXP 1E 2259+586. |
We have presented an analysis of the persistent radiative evolution of the 2009 January outburst of 1E 5108 from NRT observations. | We have presented an analysis of the persistent radiative evolution of the 2009 January outburst of 1E $-$ 5408 from XRT observations. |
We found that —6 hr after the 2009 DAT trigger the observed persisteut 110 keV unabsorbed fux reached a peak of —S10P? eres 72 1; au increase of more than 500 times the quiesceut flux leadiug up to the outburst. | We found that $\sim6$ hr after the 2009 BAT trigger the observed persistent 1–10 keV unabsorbed flux reached a peak of $\sim8 \times 10^{-9}$ ergs $^{-2}$ $^{-1}$, an increase of more than 500 times the quiescent flux leading up to the outburst. |
This flux evolution is not due solely to the source: in the first dav. there is also emission from dust scattering rues that is delaved eiission from an energtie event near the ousct of the outburst. | This flux evolution is not due solely to the source; in the first day, there is also emission from dust scattering rings that is delayed emission from an energtic event near the onset of the outburst. |
There was significant spectral hardening at the outburst as secu in other maguctar outbursts. | There was significant spectral hardening at the outburst as seen in other magnetar outbursts. |
Note that the absence of spectral variation reported by ? is consistent with our results. as thev uissed the bulk of the spectal changes which occured iu the first dav of the outburst aud their observations did not beein until the next day. | Note that the absence of spectral variation reported by \citet{nkd+10} is consistent with our results, as they missed the bulk of the spectal changes which occured in the first day of the outburst and their observations did not begin until the next day. |
The pulsed fraction showed au auti-correlatiou with the phase-averaged fux for both the previous 2008 aud 2009 outbursts. with both sets of data following the same trend. ?.. | The pulsed fraction showed an anti-correlation with the phase-averaged flux for both the previous 2008 and 2009 outbursts, with both sets of data following the same trend. \citet{wkg+05}. |
? | \citet{bis+11} |
sky are expected to be confusiou-limited by these sources. | sky are expected to be confusion-limited by these sources. |
The anisotropies are the result of variations in the nuuber of verv fait sources with fluxes around 0.5 12Js. | The anisotropies are the result of variations in the number of very faint sources with fluxes around 0.5 mJy. |
À linJw point source will produce an increment of 20 pl in the APEN-SZ map. | A 1 mJy point source will produce an increment of 20 $\mu$ K in the APEX-SZ map. |
The APEN-SZ map of the AMALLSS field is too shallow to pick out these sub-niJv sources. and we see no evidence of reaching the confusion-limüt iu the current observations. | The APEX-SZ map of the XMM-LSS field is too shallow to pick out these sub-mJy sources, and we see no evidence of reaching the confusion-limit in the current observations. |
The dusty ealaxy coutribution to the APEN-SZ baud powers is predicted by the model presented in? to be C, = 1.1 «1ο pS? (LT Jy? sy 4) iu the absence of clustering. which is in good aerecment with the measured poiut source power in Table 2.. | The dusty galaxy contribution to the APEX-SZ band powers is predicted by the model presented in \citet{negrello2007} to be $C_\ell$ = 1.1 $\times 10^{-5}$ $\mu$ $^2$ (1.7 $^2$ $^{-1}$ ) in the absence of clustering, which is in good agreement with the measured point source power in Table \ref{tab:params}. |
The predicted power from dusty ealaxies is nearly indepeudent of the flux cut level above liuJs. | The predicted power from dusty galaxies is nearly independent of the flux cut level above 1 mJy. |
Dusty galaxies are expected to account for most of the power in the APEX-SZ maps. | Dusty galaxies are expected to account for most of the power in the APEX-SZ maps. |
The BLAST collaboration veceutly released measurements of the power spectrum of the— cosmic farunfrared background at frequencies of 600 CIIz to 1.2 THz (?).. | The BLAST collaboration recently released measurements of the power spectrum of the cosmic far-infrared background at frequencies of 600 GHz to 1.2 THz \citep{viero2009}. |
BLAST incasured a Poisson contribution frou star-forming galaxies with an amplitude of 2.68340.1«10° Ίντα | at 600 ο. | BLAST measured a Poisson contribution from star-forming galaxies with an amplitude of $2.63 \pm 0.1 \times 10^3$ $^2$ $^{-1}$ at 600 GHz. |
A clustering term is detected as well on aneular scales larger than those probed by APEX-SZ. | A clustering term is detected as well on angular scales larger than those probed by APEX-SZ. |
Expressing the frequency dependence of the source fuses as οί)xrÜ. we can derive an effective spectral iudex. a. by comparing the power measured by BLAST at 600 GIIz to the point source power likelihooc function of the APEN-SZ maps at 150 CGIIz. | Expressing the frequency dependence of the source fluxes as $S(\nu) \propto \nu^\alpha$, we can derive an effective spectral index, $\alpha$, by comparing the power measured by BLAST at 600 GHz to the point source power likelihood function of the APEX-SZ maps at 150 GHz. |
This iudex will depend ou the the spectra of the iudividual galaxies and their redshift distribution. | This index will depend on the the spectra of the individual galaxies and their redshift distribution. |
We find that a spectra index. of à=2.61105 scales the BLAST power to match the best-fit C, = «107 pK? (7S Jv? sv !) of the APEN-SZ data. | We find that a spectral index of $\alpha=2.64^{+0.4}_{-0.2}$ scales the BLAST power to match the best-fit $C_\ell$ = $^{+0.9}_{-0.8} \times 10^{-5}$ $\mu$ $^2$ $^{+1.4}_{-1.3}$ $^2$ $^{-1}$ ) of the APEX-SZ data. |
This inferred spectra index agrees well with previous estinates for sub-uuu bright ealaxics. | This inferred spectral index agrees well with previous estimates for sub-mm bright galaxies. |
2 examined nearby galaxy data a found 5,xp29*9?.Iu an alternative approach. ? conrpared the flux of sources in overlapping regions observed by MAMBO (1.2 nimi) and SCUBA (850 jan) and fouud the fuxes scaled as 5,xv2. | \citet{knox2004} examined nearby galaxy data and found $S_\nu \propto \nu^{2.6 \pm 0.3}$.In an alternative approach, \citet{greve2004} compared the flux of sources in overlapping regions observed by MAMBO (1.2 mm) and SCUBA (850 $\mu$ m) and found the fluxes scaled as $S_\nu \propto \nu^{2.65}$. |
The poiut source power in the APEN-SZ data set at 150 GIIz is consistent with beiug eutirelv. due to a population of dusty subnmuu-hbresht galaxies such as those observed by BLAST. | The point source power in the APEX-SZ data set at 150 GHz is consistent with being entirely due to a population of dusty submm-bright galaxies such as those observed by BLAST. |
We also consider radio sources as a potential foreground. in the APEN-SZ maps. | We also consider radio sources as a potential foreground in the APEX-SZ maps. |
? and ?/— have modeled the uuuber counts of several classes of racio sources at tens of GIIz. | \cite{granato2004} and \cite{zotti2005} have modeled the number counts of several classes of radio sources at tens of GHz. |
We derive Cio frou their modeled παο counts at 150 GIIz. | We derive ${\it C}_\ell^{\rm radio}$ from their modeled number counts at 150 GHz. |
The radio source power is dependent on the brightest objects and is expected to scale approximately lincarly with the source cut threshold. | The radio source power is dependent on the brightest objects and is expected to scale approximately linearly with the source cut threshold. |
At the 2 mJy source cut threshold of APEN-SZ. CP should be X5% of the dusty ealaxy contribution. | At the 2 mJy source cut threshold of APEX-SZ, ${\it C}_\ell^{\rm radio}$ should be $\lesssim 5\%$ of the dusty galaxy contribution. |
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