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The model of 0.8M& and Z=0 in FIIOO is based on those of Fujimotoetal.(1995) (hereafter F95) and the comparable results are given in their Table 1. | The model of $0.8 \msun$ and $Z=0$ in FII00 is based on those of \citet{fuj95} (hereafter F95) and the comparable results are given in their Table 1. |
In F95, the values of MI??*, Macs, and logLEX(Lo) are 0.5116Mo, 0.3705Mo, and 9.983, respectively. | In F95, the values of $M_{1} \ups{max}$, $M_{\rm BCS}$, and $\lhe \ups{max} (L_\odot) $ are $0.5116 \msun$, $0.3705 \msun$, and 9.983, respectively. |
This core mass M; coincides with our 08nac very closely despite the differences in the input physics; F95 took into account only the resonant rreactions (Austin,Trentelman&Kashy1971),, which is smaller by a factor of ~2.4 than the NACRE rate at the relevant temperature range (logT~ 7.94). | This core mass $M_1$ coincides with our 08nac very closely despite the differences in the input physics; F95 took into account only the resonant reactions \citep{aus71}, which is smaller by a factor of $\sim 2.4$ than the NACRE rate at the relevant temperature range $\log T \simeq 7.94$ ). |
The smaller helium burning rate tends to delay the ignition of helium core flash. | The smaller helium burning rate tends to delay the ignition of helium core flash. |
On the other hand, the I83 formulae adopted here give larger conductivity than the Iben's fitting formulae used by F95 in the region of coulomb-liquid regime where the maximum temperature in the helium zone occurs (see fig. 1)), | On the other hand, the I83 formulae adopted here give larger conductivity than the Iben's fitting formulae used by F95 in the region of coulomb-liquid regime where the maximum temperature in the helium zone occurs (see fig. \ref{fig:cop}) ), |
which works to delay the helium ignition due to the enhanced cooling of helium zone through the inward heat conduction in our model. | which works to delay the helium ignition due to the enhanced cooling of helium zone through the inward heat conduction in our model. |
These two effects compensate for each other, while the effect of larger conduction is manifest in inner ignition (or in smaller Mpcs) in the 08nac model. | These two effects compensate for each other, while the effect of larger conduction is manifest in inner ignition (or in smaller $M_{\rm BCS}$ ) in the 08nac model. |
In actuality, the O8cf model with the same input physics as the 08nac model except for the nuclear reaction rates results in a larger core mass than the 08nac model. | In actuality, the 08cf model with the same input physics as the 08nac model except for the nuclear reaction rates results in a larger core mass than the 08nac model. |
This is because the cf88 rrate is smaller by 20% than the NACRE rrate around the temperature relevant here. | This is because the cf88 rate is smaller by $20 \%$ than the NACRE rate around the temperature relevant here. |
In any case, the dependence of M on the nuclear reaction rate is very small because of strong temperature dependence of rrate. | In any case, the dependence of $M_1$ on the nuclear reaction rate is very small because of strong temperature dependence of rate. |
It is also worth noting that the non-resonant | It is also worth noting that the non-resonant |
distributions given from the nested sampling algorithm are shown in Figure 4... | distributions given from the nested sampling algorithm are shown in Figure \ref{f:paramspl}. |
It is apparent from this that the estimated 7 (and z,) are biased high in the instantaneous reionization model. | It is apparent from this that the estimated $\tau$ (and $z_{\rm r}$ ) are biased high in the instantaneous reionization model. |
The bias goes away in the two-parameter model. as it should since that model can describe the true behaviour of the data. | The bias goes away in the two-parameter model, as it should since that model can describe the true behaviour of the data. |
Accordingly. to avoid a possible bias in measuring 7 one should consider both the one-parameter and two-parameter models. and Bayesian model average as in Liddle et al. ( | Accordingly, to avoid a possible bias in measuring $\tau$ one should consider both the one-parameter and two-parameter models, and Bayesian model average as in Liddle et al. ( |
2006b) to obtain constraints on 7 (the cost being a slightly increased uncertainty in. 7). | 2006b) to obtain constraints on $\tau$ (the cost being a slightly increased uncertainty in $\tau$ ). |
Similar conclusions have been reported in other papers teg. | Similar conclusions have been reported in other papers (eg. |
Kaplinghat et al. | Kaplinghat et al. |
2003: Holder et al. | 2003; Holder et al. |
2003). | 2003). |
We have made some assumptions about the true (fiducial) model that we are not certain about. | We have made some assumptions about the true (fiducial) model that we are not certain about. |
In practice we don't know the fiducial 24,44 when reionization started. | In practice we don't know the fiducial $z_{\rm
max}$ when reionization started. |
This has been assumed to be 30 in the fidueial model. | This has been assumed to be 30 in the fiducial model. |
A different su... corresponds to a different reionization history. hence z,,44 could be treated as an additional reionization parameter. but we don't go into a third reionization parameter here. | A different $z_{\rm max}$ corresponds to a different reionization history, hence $z_{\rm max}$ could be treated as an additional reionization parameter, but we don't go into a third reionization parameter here. |
Instead we ask what outcome arises if we analyze data so simulated (with a suns Of 30) with a z,— d, model with suas=20. | Instead we ask what outcome arises if we analyze data so simulated (with a $z_{\rm max}$ of 30) with a $z_{\rm
r}$ $d_\eta$ model with $z_{\rm max}=20$. |
Such an ‘incorrect’ model would not be distinguishable from the true model by Planck. | Such an `incorrect' model would not be distinguishable from the true model by Planck. |
Further. if our incorrect model was not a smooth transition model but one involving a step function. again with only two parameters. corresponding to 24,44 (prior range 7-30). with reionizationending at redshift 6. and with a constant reionization fraction in between these two redshifts of μη (prior range 0-1). such a model would again not be distinguishable from. the assumed true model by Planck. | Further, if our incorrect model was not a smooth transition model but one involving a step function, again with only two parameters, corresponding to $z_{\rm max}$ (prior range 7–30), with reionizationending at redshift 6, and with a constant reionization fraction in between these two redshifts of $x_e$ (prior range 0–1), such a model would again not be distinguishable from the assumed true model by Planck. |
These results are borne out of numbers presented in the next subsection for a cosmic variance limited hypothetical experiment. | These results are borne out of numbers presented in the next subsection for a cosmic variance limited hypothetical experiment. |
For a cosmic variance limited hypothetical experiment. the corresponding results are shown in the lower panel of Table | and in Figure 5.. | For a cosmic variance limited hypothetical experiment, the corresponding results are shown in the lower panel of Table \ref{table1} and in Figure \ref{f:paramscvl}. |
Again only TE and EE spectra are considered out to a maximum multipole of 100. | Again only TE and EE spectra are considered out to a maximum multipole of 100. |
This time the evidence favours the smooth and gradual transition z;—d,, model decisively over the instantaneous reionization model. | This time the evidence favours the smooth and gradual transition $z_{\rm
r}$ $d_\eta$ model decisively over the instantaneous reionization model. |
These results also show that. as before. a simpler model leads to a biased 7. a bias that disappears upon using a complicated | These results also show that, as before, a simpler model leads to a biased $\tau$ , a bias that disappears upon using a complicated |
? “CO & § 3. 58 4. 5$ 6.. | \citet{Banerji:timescales} $^{12}$ $\S$ \ref{sec:model} $\S$ \ref{sec:CO} $\S$ \ref{sec:abundances} $\S$ \ref{sec:disc}. |
1.5" at OS. 1.10. and 2.05 pan. respectively. | $1.5\arcsec$ at 0.8, 1.10, and 2.05 $\mu$ m, respectively. |
Using the same criteria as above. the uarrow-band. 2.15 fan image of the arc subteuds an angle of ~61" relative o the primary leusing ealaxy. auc is thus 1.37 in leueth. | Using the same criteria as above, the narrow-band, 2.15 $\mu$ m image of the arc subtends an angle of $\sim61^{\rm o}$ relative to the primary lensing galaxy, and is thus $1.3\arcsec$ in length. |
As expected. the are is unresolved in width at 2.15 ju. Tu he 2.12 jin continuun image. the are is relatively faint. inclicating that continu cussion comprises only a stall raction of the 2.15 jan flux. | As expected, the arc is unresolved in width at 2.15 $\mu$ m. In the 2.12 $\mu$ m continuum image, the arc is relatively faint, indicating that continuum emission comprises only a small fraction of the 2.15 $\mu$ m flux. |
Further. aside from the lensed quasar. there appear to be no stroug (245<18.3 mag) cluission-line sources at the redshift of Source 1 preseut iu he field. | Further, aside from the lensed quasar, there appear to be no strong $m_{2.15} < 18.3$ mag) emission-line sources at the redshift of Source 1 present in the field. |
Figure 3 shows close-up. contour plots of Source 1. | Figure 3 shows close-up, contour plots of Source 1. |
As roted by E96. the 0.5 gan image of Source 1 is asvinmectric. VINE a primary casteru peak separated fou a secondary western peak by ~0.21" (Figure 3a). | As noted by E96, the 0.8 $\mu$ m image of Source 1 is asymmetric, having a primary eastern peak separated from a secondary western peak by $\sim0.24\arcsec$ (Figure 3a). |
The 1.10 pan (Le. rest-frame 3300A)) cinission from the are has an asyhunetric appearance similar to the 0.5 jn. (vest-frame Jemission: thearchasanasyannetricappoarance, withamB yong oie Ria ΜΟΛΙΣ d from a faint. miner peak (P2) ou the western eud. | The 1.10 $\mu$ m (i.e., rest-frame ) emission from the arc has an asymmetric appearance similar to the 0.8 $\mu$ m (rest-frame $~$ ) emission; the arc has an asymmetric appearance, with a major peak (P1) on the eastern end of the arc separated by $\sim0.27\arcsec$ from a faint, minor peak (P2) on the western end. |
Iu coutrast to the 0.5 aud 1.10 sau cmiission. the 2.05 jaa Grest-franmie 62004.) emission has a nearly πιοτς appearance. with a single peak at the ceuter of the arc. | In contrast to the 0.8 and 1.10 $\mu$ m emission, the 2.05 $\mu$ m (rest-frame ) emission has a nearly symmetric appearance, with a single peak at the center of the arc. |
The position of the primary 1.10 juu aud the 2.05 san peaks differ by. 0.107, | The position of the primary 1.10 $\mu$ m and the 2.05 $\mu$ m peaks differ by $\arcsec$. |
Figure 3f shows the ratio of the 1.10 aud 2.05 jan images. | Figure 3f shows the ratio of the 1.10 and 2.05 $\mu$ m images. |
The image consists of a two-component arc with fainter cluission bridgie the componuecuts. | The image consists of a two-component arc with fainter emission bridging the components. |
The primary peak of the nuage is mareimally shifted (0.017)) eastward of the primary 1.10 yan peak (P1). and the secondary peaksis shifted a similar amount frou the secondary 1.10 jan peak (P2). | The primary peak of the image is marginally shifted ) eastward of the primary 1.10 $\mu$ m peak (P1), and the secondary peakis shifted a similar amount from the secondary 1.10 $\mu$ m peak (P2). |
Fieve 3e aud 3h show the contour plots of the 2.15 jan nuage and the difference of the 2.15 and 2.12 san images (ie. Πα ||[N Tj). | Figure 3g and 3h show the contour plots of the 2.15 $\mu$ m image and the difference of the 2.15 and 2.12 $\mu$ m images (i.e., $\alpha$ +[N II]). |
Because the peak of the 2.12 ju image appears shifted ~O10 west of the 2.05 juu peak. an additional check of the structure of the Πα |[N I| euuission was douc by scaling the 2.05 jan image to the flux of the 2.12 gan nuage. then subtracting it from the 2.15 gan nuage: the resultant are showed ouly margiual changes from the subtraction using the 2.12 pau image. | Because the peak of the 2.12 $\mu$ m image appears shifted $\sim0.10\arcsec$ west of the 2.05 $\mu$ m peak, an additional check of the structure of the $\alpha$ +[N II] emission was done by scaling the 2.05 $\mu$ m image to the flux of the 2.12 $\mu$ m image, then subtracting it from the 2.15 $\mu$ m image; the resultant arc showed only marginal changes from the subtraction using the 2.12 $\mu$ m image. |
The similarities between the images shown in Figure 2g and 2h are due to the large contribution of line cussion to the overall flux density aud structure of the 2.15 jan enission. | The similarities between the images shown in Figure 2g and 2h are due to the large contribution of line emission to the overall flux density and structure of the 2.15 $\mu$ m emission. |
Table 1 lists the magnitudes derived from the images in Figure 1. as well as magnitudes in the wavelength rauge 0.72.2 jun compiled frou the literature. | Table 1 lists the magnitudes derived from the images in Figure 1, as well as magnitudes in the wavelength range 0.7–2.2 $\mu$ m compiled from the literature. |
The magnitudes for all of the sources are consistent with previous eromud-based measurements. | The magnitudes for all of the sources are consistent with previous ground-based measurements. |
Both of the wide-band NICALOS Πμασος of Source 1. are composed of continua and ine Cluission: strong Ne V aud Ne TT emission have beeu detected in the wavelength range 1.11.3 jan (Soifer ct al. | Both of the wide-band NICMOS images of Source 1 are composed of continuum and line emission; strong Ne V and Ne III emission have been detected in the wavelength range 1.1–1.3 $\mu$ m (Soifer et al. |
1995: Dwinunuro et al. | 1995; Iwamuro et al. |
1995). aud Πα L[N II] cmiission has been observed at 2.15 pau (Elston et al. | 1995), and $\alpha$ +[N II] emission has been observed at 2.15 $\mu$ m (Elston et al. |
1991: Soifer et al. | 1994; Soifer et al. |
1995). | 1995). |
The percentage of Hue contribution to the 2.05 jan flux of Source 1 can be calculated frou the narrow-baud iuages. | The percentage of line contribution to the 2.05 $\mu$ m flux of Source 1 can be calculated from the narrow-band images. |
Subtracting the 2.12 pau countiuumu mage frou the 2.15 san and mcasuring the flux of the resultaut cinissiou-line image. the Ho |[N ΤΠ) &ux is calculated to be 00.&10.15 Wan 7. lower than the values of G.10 τα7? aud το]0D τα? determined bv Matthews et al. ( | Subtracting the 2.12 $\mu$ m continuum image from the 2.15 $\mu$ m and measuring the flux of the resultant emission-line image, the $\alpha$ +[N II] flux is calculated to be $(\pm0.4)\times10^{-18}$ W $^{-2}$, lower than the values of $\times10^{-18}$ W $^{-2}$ and $\times10^{-18}$ W $^{-2}$ determined by Matthews et al. ( |
1991) and Elston et al. ( | 1994) and Elston et al. ( |
1991). respectively, | 1994), respectively. |
Thus. Ho |[NX Π comprises ~12% of the 2.05 gan flux of Source 1. | Thus, $\alpha$ +[N II] comprises $\sim$ of the 2.05 $\mu$ m flux of Source 1. |
This percentage is consisteut with the approximate value of calculated from the ucarinfrared spectrum of FSCL0211)£221 by Soiter et al. ( | This percentage is consistent with the approximate value of calculated from the near-infrared spectrum of FSC10214+4724 by Soifer et al. ( |
1995). | 1995). |
Similarly using the Ho |[N IT] fux in combination with the Ne V aud Ne III to Παν ΤΗ flux ratio of 1.1 determined by Soifer et al. ( | Similarly, using the $\alpha$ +[N II] flux in combination with the Ne V and Ne III to $\alpha$ +[N II] flux ratio of 1.1 determined by Soifer et al. ( |
1995). the Neon emission nes are calculated to comprise 8 of the 1.10 qiu flux. | 1995), the Neon emission lines are calculated to comprise $\sim$ of the 1.10 $\mu$ m flux. |
Both the leneth aud structure of the continuum aud LBie cChussion of Source 1 cau be explained im terms of he relative sizes of the enussion regious. the structure the enuüssion regions. aud their location near the cusp of a caustic (1νο, line of infinite maenification: see | Both the length and structure of the continuum and line emission of Source 1 can be explained in terms of the relative sizes of the emission regions, the structure of the emission regions, and their location near the cusp of a caustic (i.e., line of infinite magnification: see Blandford Narayan 1992). |
gedust cushrouded quasar (81). it is very likely that a substautial yaction of the luninosity from Source 1. especially at ducer waveleneths. is scattered/reprocessed ACN light. | Given that Source 1 is a dust enshrouded quasar 1), it is very likely that a substantial fraction of the luminosity from Source 1, especially at bluer wavelengths, is scattered/reprocessed AGN light. |
The leneth of the wide-band continu emission has been shown to increase as a function of waveleneth (83.1). indicatiug that the light eiuitted at longer wavelengths is closer to the caustic than the shorter waveleusth ποτ, | The length of the wide-band continuum emission has been shown to increase as a function of wavelength 3.1), indicating that the light emitted at longer wavelengths is closer to the caustic than the shorter wavelength light. |
Physically, this can be understood if the 0.5.1.10 gan light cluanates predominantly from regions of scattered AGN ight. aud the 2.05 pin light emauates from the underlying. red stellar population of Source 1 which is more extended hau the scattered Πο region and bas a substantial cross-section on or near the caustic. | Physically, this can be understood if the 0.8–1.10 $\mu$ m light emanates predominantly from regions of scattered AGN light, and the 2.05 $\mu$ m light emanates from the underlying, red stellar population of Source 1 which is more extended than the scattered light region and has a substantial cross-section on or near the caustic. |
By comparison. the Παν ΤΠ emission. which traces light from the narrow-iue regions (e.g. Osterbrock 1989). has a leneth in between hat of the 0.8.1.10 san and 2.05 san cinission. indicating hat the uarrow-line region is more extended than the scattered ACN lieht region. but not as extended as the stellar region traced by the 2.05 gan emission. | By comparison, the $\alpha$ +[N II] emission, which traces light from the narrow-line regions (e.g. Osterbrock 1989), has a length in between that of the 0.8–1.10 $\mu$ m and 2.05 $\mu$ m emission, indicating that the narrow-line region is more extended than the scattered AGN light region, but not as extended as the stellar region traced by the 2.05 $\mu$ m emission. |
The change in the structure along the arc is indicative of variatious in the morphology of Source 1 as a function of wavelength. | The change in the structure along the arc is indicative of variations in the morphology of Source 1 as a function of wavelength. |
While the 0.8 and 1.10. san emission have an eastern and western peak. the fact that the 2.05 jan enission has ouly one peak at the center of the arc iav be a result of the red stellar cussion beime more extended than or displaced relative to the 0.8.1.10. ru. cutission. | While the 0.8 and 1.10 $\mu$ m emission have an eastern and western peak, the fact that the 2.05 $\mu$ m emission has only one peak at the center of the arc may be a result of the red stellar emission being more extended than or displaced relative to the 0.8–1.10 $\mu$ m emission. |
Further. the two-component morphology of the euission-lines is similar to the ratio of the 1.10 aud 2.05 jan eniüssion. | Further, the two-component morphology of the emission-lines is similar to the ratio of the 1.10 and 2.05 $\mu$ m emission. |
Normalizing the 1.10 san enudssion by the 2.05 jaa emission removes structure at 1.10. gan caused by. the red stellar population. | Normalizing the 1.10 $\mu$ m emission by the 2.05 $\mu$ m emission removes structure at 1.10 $\mu$ m caused by the red stellar population. |
Thus. the similarities between the structure of the line cussion aud the 1.10 juu / 2.05 jan ratio may coufirm that the 1.10 gun enüssiou is a superposition of a blue component associated with the enission-liue enüssiou and a red stellar component that dominates at 2.05 an. Such superpositious have also beeu modeled in radio galaxies at z 1. where the images of the ealaxies at bluer wavelength appear to be comprised of au clongated component. as well as à svuunetrie coniponenut simular iu shape to the svuuuetric inages of the ealaxies at redder waveleusths (Rieler et al. | Thus, the similarities between the structure of the line emission and the 1.10 $\mu$ m / 2.05 $\mu$ m ratio may confirm that the 1.10 $\mu$ m emission is a superposition of a blue component associated with the emission-line emission and a red stellar component that dominates at 2.05 $\mu$ m. Such superpositions have also been modeled in radio galaxies at $z\sim1$ , where the images of the galaxies at bluer wavelength appear to be comprised of an elongated component, as well as a symmetric component similar in shape to the symmetric images of the galaxies at redder wavelengths (Rigler et al. |
1992). | 1992). |
Figure { shows 0.5. 1.10. aud 2.05 jiu contour plots of Source 2 and the couuterimage (Source 5). | Figure 4 shows 0.8, 1.10, and 2.05 $\mu$ m contour plots of Source 2 and the counterimage (Source 5). |
There appears | There appears |
equation, but now use instead of equation (A6) from ?.. | equation, but now use instead of equation (A6) from \citet{vanEerten2009c}. |
This equation can be derived as usual from combining the continuity equation and the kinetic equation. | This equation can be derived as usual from combining the continuity equation and the kinetic equation. |
Also we now no longer explicitly inject hot electrons at the shock front during the simulation, but do this implicitly via the initial conditions of the simulation. | Also we now no longer explicitly inject hot electrons at the shock front during the simulation, but do this implicitly via the initial conditions of the simulation. |
We do this by setting yh, initially equal to 1019 everywhere outside the shock. | We do this by setting $\gamma'_M$ initially equal to $10^{10}$ everywhere outside the shock. |
Because the unshocked material is very cold, and the magnetic field strength is linked to the thermal energy density via cp, synchrotron cooling will not change y4; outside of the shock. | Because the unshocked material is very cold, and the magnetic field strength is linked to the thermal energy density via $\epsilon_B$, synchrotron cooling will not change $\gamma'_M$ outside of the shock. |
Once a shock passes, the fluid is heated and electron cooling automatically sets in directly. | Once a shock passes, the fluid is heated and electron cooling automatically sets in directly. |
If we now ignore unshocked parts of the fluid grid (i.e. cold, nonmoving areas that are resolved with only a few refinement levels) when calculating emission, we have an algorithm to calculate synchrotron radiation including electron cooling, but where we do not need to worry about seeking out the shock front during each iteration of the RHD simulation. | If we now ignore unshocked parts of the fluid grid (i.e. cold, nonmoving areas that are resolved with only a few refinement levels) when calculating emission, we have an algorithm to calculate synchrotron radiation including electron cooling, but where we do not need to worry about seeking out the shock front during each iteration of the RHD simulation. |
With these alterations, our method has moved closer to that implemented by ? 'To show the numerical validity of our results and check the resolution, we have performed calculations at different refinement levels. | With these alterations, our method has moved closer to that implemented by \citet{Downes2002} To show the numerical validity of our results and check the resolution, we have performed calculations at different refinement levels. |
In figure ΑΙ we show light curves at observer frequency 5.10!" Hz for a spherical explosion. | In figure \ref{res_lightcurve_figure} we show light curves at observer frequency $5 \cdot 10^{17}$ Hz for a spherical explosion. |
We show this high frequency because the hot region that dictates the spectrum above the cooling break is the hardest to resolve. | We show this high frequency because the hot region that dictates the spectrum above the cooling break is the hardest to resolve. |
This is illustrated by figure A2,, which shows the spectrum for a spherical explosion at observer time 0.5 days, the earliest time used in plots in this paper. | This is illustrated by figure \ref{res_spectrum05_figure}, which shows the spectrum for a spherical explosion at observer time 0.5 days, the earliest time used in plots in this paper. |
Because the blast wave width is smaller at earlier times, this is therefore also where any resolution issues should be most apparent. | Because the blast wave width is smaller at earlier times, this is therefore also where any resolution issues should be most apparent. |
The light curve in fig; | The light curve in fig. |
ΑΙ shows that the simulations quickly converge for the different refinement levels at later times. | \ref{res_lightcurve_figure} shows that the simulations quickly converge for the different refinement levels at later times. |
When the jet breaks occur, around a few days or so depending on the chosen jet opening angle, the convergence of the light curves is sufficient to show that the results of this paper remain unaltered under further increase in resolution. | When the jet breaks occur, around a few days or so depending on the chosen jet opening angle, the convergence of the light curves is sufficient to show that the results of this paper remain unaltered under further increase in resolution. |
We also note that convergence is achieved at an earlier time for frequencies below the cooling break, as can be seen from the spectrum, which confirms that electron cooling and fluid evolution occur on different spatial and temporal scales (as one would theoretically expect). | We also note that convergence is achieved at an earlier time for frequencies below the cooling break, as can be seen from the spectrum, which confirms that electron cooling and fluid evolution occur on different spatial and temporal scales (as one would theoretically expect). |
We have also tested the temporal resolution of the simulations by comparing light curves from a datasets with 1000 snapshots to light curves from a dataset with 10,000 snapshots. | We have also tested the temporal resolution of the simulations by comparing light curves from a datasets with 1000 snapshots to light curves from a dataset with 10,000 snapshots. |
For 1000 snapshots the temporal resolution is 3.7104 | For 1000 snapshots the temporal resolution is $3.7 \cdot 10^4$ |
i0n-independeut bius among the four slightly different analyses of the 1.5-12 keV baud). and the nuuber of sources (571). | non-independent bins among the four slightly different analyses of the 1.5-12 keV band), and the number of sources (571). |
The neglect of the oversample factor aud he immltiple similar analyses of the suu baud does not appear to have led to sienificaut macderestimates of the detection thresholds. aud. thus. this procedure appears o be jt«tified. | The neglect of the oversampling factor and the multiple similar analyses of the sum band does not appear to have led to significant underestimates of the detection thresholds, and, thus, this procedure appears to be justified. |
We have chosen a detection. threshold 2,5, for xeviouxlv unknown periodicities to limit the expected nuuber of false detectious produced by statistical Huctuatious (based on the Nia,assumption that the powers are exponentially distributed) iu the power spectra calculated using a eiven smoothing time parameter. | We have chosen a detection threshold $P_{thr}$ for previously unknown periodicities to limit the expected number of false detections $N_{exp}$ produced by statistical fluctuations (based on the assumption that the powers are exponentially distributed) in the power spectra calculated using a given smoothing time parameter. |
Thus we lave so that The values of £55,thi areogiven in Table 2. for Αν/=0.1. | Thus we have so that The values of $P_{thr}$ aregiven in Table \ref{tbl:tmscls} for $N_{exp} = 0.1$. |
As can seen 1‘ Figs. | As canbe seen in Figs. |
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