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we can model the secular evolution at this location (Fig. 11,
we can model the secular evolution at this location (Fig. \ref{fig:dampmig},
top two rows).
top two rows).
When this ratio is small (“fast” migration), Neptune effectively damps at its final position and we can model the secular evolution there (Fig. 11,,
When this ratio is small (“fast" migration), Neptune effectively damps at its final position and we can model the secular evolution there (Fig. \ref{fig:dampmig},
bottom two rows).
bottom two rows).
When the ratio is order unity modeling the secular evolution at the location Neptune reaches after half a damping time is a decent approximation (Fig. 11,,
When the ratio is order unity, modeling the secular evolution at the location Neptune reaches after half a damping time is a decent approximation (Fig. \ref{fig:dampmig},
middle row).
middle row).
However, we have not explored the regime in which ΤαΤε Or Τα~Τι in detail.
However, we have not explored the regime in which $\tau_a \sim \tau_e$ or $\tau_a \sim \tau_i$ in detail.
Typically, we expect the damping and migration to occur in either the fast or slow regime, for reasons we will now state.
Typically, we expect the damping and migration to occur in either the fast or slow regime, for reasons we will now state.
The models in which Neptune is scattered from its location of formation to close to its current location (e.g.?) can be considered fast migration.
The models in which Neptune is scattered from its location of formation to close to its current location \citep[e.g.][]{2008L} can be considered fast migration.
For extensive migration in a planetesimal disk, we expect the migration timescale to be significantly longer than the
For extensive migration in a planetesimal disk, we expect the migration timescale to be significantly longer than the
These seven facts can be used to consider the time evolution in the twisted geometry of KDJ that results in the type I field line topology in Figure 1.
These seven facts can be used to consider the time evolution in the twisted geometry of KDJ that results in the type I field line topology in Figure 1.
Figure 2 simulates the most plausible scenario based on these seven results above which is used as a surrogate for actual fine time scale data sampling.
Figure 2 simulates the most plausible scenario based on these seven results above which is used as a surrogate for actual fine time scale data sampling.
The left hand frame shows a typical twisted accretion disk coil in white being approached by a coronal hairpin in red near the black hole.
The left hand frame shows a typical twisted accretion disk coil in white being approached by a coronal hairpin in red near the black hole.
Notice that the coronal hairpin is azimuthally twisted in KDJ.
Notice that the coronal hairpin is azimuthally twisted in KDJ.
Reconnection is very complicated in a twisted 3-D environment and is not well understood (Pontinetal2011).
Reconnection is very complicated in a twisted 3-D environment and is not well understood \citep{pon11}.
. However, the configuration as drawn forms a natural reconnection site (an X-point).
However, the configuration as drawn forms a natural reconnection site (an X-point).
We expect both types of field lines in Figure 2 to exist from points 1, 4 and 5 above.
We expect both types of field lines in Figure 2 to exist from points 1, 4 and 5 above.
The elements required for the pre-reconnection geometry in the left hand frame of Figure 2, commonly occur in this family of simulations.
The elements required for the pre-reconnection geometry in the left hand frame of Figure 2, commonly occur in this family of simulations.
Thus, it is reasonable to expect that these field configurations coexist in proximity at various times and these potential reconnection sites should not be rare.
Thus, it is reasonable to expect that these field configurations coexist in proximity at various times and these potential reconnection sites should not be rare.
However, the reconnection rate in such a complicated geometry that does not proceed by a physical mechanism, but through numerical diffusion, is very uncertain.
However, the reconnection rate in such a complicated geometry that does not proceed by a physical mechanism, but through numerical diffusion, is very uncertain.
By points 2, 3 and 6 above, reconnection must have occurred in KDJ as depicted in the right hand frame of Figure 2.
By points 2, 3 and 6 above, reconnection must have occurred in KDJ as depicted in the right hand frame of Figure 2.
The white curve in the right hand frame is poloidal flux through the equatorial plane of the ergosphere in one hemisphere in analogy to the left hand frame of Figure 1 and the red curve would be a buoyant hairpin field line that moves out in the corona consistent with point 7.
The white curve in the right hand frame is poloidal flux through the equatorial plane of the ergosphere in one hemisphere in analogy to the left hand frame of Figure 1 and the red curve would be a buoyant hairpin field line that moves out in the corona consistent with point 7.
A significant difference between the topology resulting from the reconnection in Figure 2 compared to that in Figure 11 of Beckwithetal(2009),, is that in Figure 2 the reconnection is happening before the hairpin penetrates the event horizon and in Figure 11 of Beckwithetal(2009) it occurs after the hairpin penetrates the horizon.
A significant difference between the topology resulting from the reconnection in Figure 2 compared to that in Figure 11 of \citet{bec09}, is that in Figure 2 the reconnection is happening before the hairpin penetrates the event horizon and in Figure 11 of \citet{bec09} it occurs after the hairpin penetrates the horizon.
This indicates that the coherent flux transport rate combined with the reconnection rate and twisted 3-D field line geometry (which affects the reconnection rate) might determine if a field line penetrates the event horizon or the inner accretion flow when and if reconnection occurs.
This indicates that the coherent flux transport rate combined with the reconnection rate and twisted 3-D field line geometry (which affects the reconnection rate) might determine if a field line penetrates the event horizon or the inner accretion flow when and if reconnection occurs.
The final field line topology depends on the balancing of reaction rates (reconnection and transport) as well as internal dynamics (that affect field line shape) that are determined by the numerical simulation.
The final field line topology depends on the balancing of reaction rates (reconnection and transport) as well as internal dynamics (that affect field line shape) that are determined by the numerical simulation.
The Letter shows that the "coronal mechanism” for flux transport in simulations of black hole accretion provides a plausible explanation for the one sided ergospheric disk field lines in the high spin 3-D simulation KDJ.
The Letter shows that the "coronal mechanism" for flux transport in simulations of black hole accretion provides a plausible explanation for the one sided ergospheric disk field lines in the high spin 3-D simulation KDJ.
It therefore explains the strange phenomenon observed in KDJ that the black hole driven jet Poynting flux was very one sided, jumping from side to side and emanating primarily from the ergospheric disk.
It therefore explains the strange phenomenon observed in KDJ that the black hole driven jet Poynting flux was very one sided, jumping from side to side and emanating primarily from the ergospheric disk.
An otherwise almost identical simulation to KDJ that includes additional artificial diffusion terms in the equations of continuity, energy conservation, and momentum conservation (as described in DeVilliers (2006))) do not show these one sided ergospheric disk structures Punsly(2011).
An otherwise almost identical simulation to KDJ that includes additional artificial diffusion terms in the equations of continuity, energy conservation, and momentum conservation (as described in \citet{dev07}) ) do not show these one sided ergospheric disk structures \citet{pun11}.
. This is seems to indicate a change in the the reconnection process that is driven either directly or indirectly by the numerical diffusion.
This is seems to indicate a change in the the reconnection process that is driven either directly or indirectly by the numerical diffusion.
In support of this interpretation, the force-free simulations of an initially uniform field in Komissarov(2004) show magnetic flux threading the ergospheric equatorial plane near the black hole, yet the same initial state that is time evolved in a different force-free code with a slower ansatz for the reconnection rate shows no magnetic flux threading the equatorial plane near the black hole (McKinney2006a)..
In support of this interpretation, the force-free simulations of an initially uniform field in \citet{kom04} show magnetic flux threading the ergospheric equatorial plane near the black hole, yet the same initial state that is time evolved in a different force-free code with a slower ansatz for the reconnection rate shows no magnetic flux threading the equatorial plane near the black hole \citep{mck05}.
The implication is that the global topology of the black hole
The implication is that the global topology of the black hole
a given X-ray spectral index. the Compton parameter. v=47.7. is approximately constant.
a given X-ray spectral index, the Compton parameter, $y=4 T_{\rm e}\tau_{\rm T}$, is approximately constant.
Also. A7. is anticorrelated with τι for a given local dissipation rate in a hot flow. reflecting the varying power per electron.
Also, $kT_{\rm e}$ is anticorrelated with $\tau_{\rm T}$ for a given local dissipation rate in a hot flow, reflecting the varying power per electron.
Fits of the one-zone thermal-Compton model yield ry~| (e.g. Yuan Zdziarski 2004) whereas the vertical optical depths of the flow are ry«I. see reffig:OSedd((b). which expresses the same discrepancy as 7, of the flow being too high.
Fits of the one-zone thermal-Compton model yield $\tau_{\rm T}\sim 1$ (e.g., Yuan Zdziarski 2004) whereas the vertical optical depths of the flow are $\tau_{\rm T}\ll 1$, see \\ref{fig:05edd}( (b), which expresses the same discrepancy as $T_{\rm e}$ of the flow being too high.
As stated above. taking into account the GR effects in the global-Compton model improves the agreement significantly (pointing to the inadequacy of Comptonization models neglecting GR). but not sutficientlv.
As stated above, taking into account the GR effects in the global-Compton model improves the agreement significantly (pointing to the inadequacy of Comptonization models neglecting GR), but not sufficiently.
On the face of it. this discrepancy might indicate that the hot flow model is not applicable to the hard state of black hole binaries and Seyfert galaxies.
On the face of it, this discrepancy might indicate that the hot flow model is not applicable to the hard state of black hole binaries and Seyfert galaxies.
However. we note that the present calculations assume a very strong outflow. equation (3)) with s= 0.3. motivated by the modelling of the Galactic Centre. (Yuan et 22003).
However, we note that the present calculations assume a very strong outflow, equation \ref{eq:outflow}) ) with $s=0.3$ , motivated by the modelling of the Galactic Centre (Yuan et 2003).
On the other hand. our assumed. dimensionless accretion rate is >> that of the Galactic Centre source. whereas the relative strength of outflows appears to decrease with the increasing accretion rate (Gallo. Fender Pooley 2003: Fender. Belloni Gallo 2004). as also indicated by a relatively small change of the X-ray bolometric luminosity during hard/soft state transitions (e.g Zadziarski et 22004).
On the other hand, our assumed dimensionless accretion rate is $\gg$ that of the Galactic Centre source, whereas the relative strength of outflows appears to decrease with the increasing accretion rate (Gallo, Fender Pooley 2003; Fender, Belloni Gallo 2004), as also indicated by a relatively small change of the X-ray bolometric luminosity during hard/soft state transitions (e.g., Zdziarski et 2004).
This is plausible from a theoretical point of view because the Bernoulli parameter becomes smaller with the increasing accretion rates (Yuan, Cui Narayan 2005: Bu Yuan in preparation).
This is plausible from a theoretical point of view because the Bernoulli parameter becomes smaller with the increasing accretion rates (Yuan, Cui Narayan 2005; Bu Yuan in preparation).
Thus. it is likely that the fractional strength of the outflow. 82 per cent for our assumed s. οι and Mo (with 18 per cent of My crossing the horizon). may in reality be much weaker.
Thus, it is likely that the fractional strength of the outflow, 82 per cent for our assumed $s$, $R_{\rm out}$ and $\dot M_0$ (with 18 per cent of $\dot M_0$ crossing the horizon), may in reality be much weaker.
Setting s=0 leads to τι being a few times higher and 7. about a factor of two lower. see reftig:outflow..
Setting $s=0$ leads to $\tau_{\rm T}$ being a few times higher and $T_{\rm e}$ about a factor of two lower, see \\ref{fig:outflow}.
Although the calculations in reffigcoutflow are done with the local analytical treatment of Comptonization. and are thus not self-consistent. they correctly predict the direction of the changes of the flow parameter.
Although the calculations in \\ref{fig:outflow} are done with the local analytical treatment of Comptonization, and are thus not self-consistent, they correctly predict the direction of the changes of the flow parameter.
If the characteristic 7, of the self-consistent flow were reduced by the same factor of two with respect the model with s=0.3. the peak of the EdL/dE spectrum would also go down by a similar factor. bringing it to the observed range and resolving the discrepancy with the data.
If the characteristic $T_{\rm e}$ of the self-consistent flow were reduced by the same factor of two with respect the model with $s=0.3$, the peak of the $E {\rm d}L/{\rm d}E$ spectrum would also go down by a similar factor, bringing it to the observed range and resolving the discrepancy with the data.
Our second assumption has been of a strong viscous heating of electrons. 6=0.5.
Our second assumption has been of a strong viscous heating of electrons, $\delta=0.5$.
As seen in reftig:outflow.. this has a relatively minor effect on 7. and τι.
As seen in \\ref{fig:outflow}, this has a relatively minor effect on $T_{\rm e}$ and $\tau_{\rm T}$.
We ulso note that the half-depth Thomson optical depth of a slab is the quantity closest to that of the half-depth of the flow. and should preferably be used when comparing accretion flow models with one-zone thermal Comptonization models.
We also note that the half-depth Thomson optical depth of a slab is the quantity closest to that of the half-depth of the flow, and should preferably be used when comparing accretion flow models with one-zone thermal Comptonization models.
For a given. spectral index. the optical depth is somewhat lower for a slab geometry than for spherical one.
For a given X-ray spectral index, the optical depth is somewhat lower for a slab geometry than for spherical one.
We note that there is à number of additional effects that can further reduce 7. and increase r4. possibly allowing the hot flow model to be in agreement with the full range of the observed hard- spectra.
We note that there is a number of additional effects that can further reduce $T_{\rm e}$ and increase $\tau_{\rm T}$, possibly allowing the hot flow model to be in agreement with the full range of the observed hard-state spectra.
First. an increase of the black-hole spin reduces the radial velocity and increases the density of the flow.
First, an increase of the black-hole spin reduces the radial velocity and increases the density of the flow.
The effect is rather strong. as can be seen. e.g.. in 55 of Gammie Popham (1998).
The effect is rather strong, as can be seen, e.g., in 5 of Gammie Popham (1998).
Global Comptonization in the Kerr metric will be studied in detail in our forthcoming work.
Global Comptonization in the Kerr metric will be studied in detail in our forthcoming work.
Second. the presence of moderate large-scale toroidal magnetic fields in the accretion flow significantly reduces 7... as shown by Bu. Yuan Xie (2009).
Second, the presence of moderate large-scale toroidal magnetic fields in the accretion flow significantly reduces $T_{\rm e}$, as shown by Bu, Yuan Xie (2009).
Third. electron cooling will also be significantly enhanced in either a two-phase flow. with cold clouds mixed with the hot flow. or. fourth. at presence of an inner collapsed dise. with both effects wppening above some critical accretion rate (Section ὃς, see also YOI. Yuan 2003).
Third, electron cooling will also be significantly enhanced in either a two-phase flow, with cold clouds mixed with the hot flow, or, fourth, at presence of an inner collapsed disc, with both effects happening above some critical accretion rate (Section \ref{results}, see also Y01, Yuan 2003).
Furthermore. the cut-off energy in the hard state of black- binaries is observed to decrease with the increasing luminosity (Wardzinsski et 22002: Yamaoka et 22006: Yuan et 22007: Miyakawa et22008)!.
Furthermore, the cut-off energy in the hard state of black-hole binaries is observed to decrease with the increasing luminosity (Wardzińsski et 2002; Yamaoka et 2006; Yuan et 2007; Miyakawa et.
. Also. the hot-flow characteristic emperature goes down with the increasing accretion rate. in agreement with the observations.
Also, the hot-flow characteristic temperature goes down with the increasing accretion rate, in agreement with the observations.
In our case. the bolometric uminosity is only 0.0077, (Section 59). and. thus our model spectrum should. be compared with the hard state at the correspondingly low £ (which is somewhat below. e.g.. the state range of L of Cyg X-I of =0.01-0.02£,.. Zdziarski et 22002). which spectra are likely to have the cut-off energies 100 keV. This would be in agreement with our results. after the correction for the outflow discussed above.
In our case, the bolometric luminosity is only $0.007 L_{\rm E}$ (Section \ref{results}) ), and thus our model spectrum should be compared with the hard state at the correspondingly low $L$ (which is somewhat below, e.g., the hard-state range of $L$ of Cyg X-1 of $\simeq 0.01$ $0.02L_{\rm E}$, Zdziarski et 2002), which spectra are likely to have the cut-off energies $>100$ keV. This would be in agreement with our results, after the correction for the outflow discussed above.
Malzae Belmont (2009) have also pointed out that the ion temperatures implied by observations of the hard state are much lower than those typical for ADAF models.
Malzac Belmont (2009) have also pointed out that the ion temperatures implied by observations of the hard state are much lower than those typical for ADAF models.
However. the ratio of Ti/T.. calculated by Malzac Belmont (2009) directly from the formula for Coulomb energy transfer from ions to electrons. is approximately οτp and the discrepancy pointed out by those authors occurs at Tp.|.
However, the ratio of $T_{\rm i}/T_{\rm e}$, calculated by Malzac Belmont (2009) directly from the formula for Coulomb energy transfer from ions to electrons, is approximately $\propto \tau_{\rm T}^{-2}$, and the discrepancy pointed out by those authors occurs at $\tau_{\rm T}\sim 1$.
Tf we take instead the low values of τι obtained in ADAF models. there is an agreement between their estimate and the hot flow models.
If we take instead the low values of $\tau_{\rm T}$ obtained in ADAF models, there is an agreement between their estimate and the hot flow models.
On the other hand. we stress that using equation (3)) with does not weaken our conclusions related to the role of globa Comptonization.
On the other hand, we stress that using equation \ref{eq:outflow}) ) with $s=0.3$ does not weaken our conclusions related to the role of global Comptonization.
Instead. if the outflow is weaker for à given M. the radiation generated at small radii and subsequently received a large radii will be stronger. thus the global Comptonization effec will become even more important than for our chosen assumption.
Instead, if the outflow is weaker for a given $\dot M_0$, the radiation generated at small radii and subsequently received at large radii will be stronger, thus the global Comptonization effect will become even more important than for our chosen assumption.
This would further reduce the average photon energy of the emitted spectrum,
This would further reduce the average photon energy of the emitted spectrum.
Another related issue is our determination of the value of the critical aceretion rate. at which an inner part of the hot flow collapses.
Another related issue is our determination of the value of the critical accretion rate, at which an inner part of the hot flow collapses.
We tind it corresponds to a relatively low £L=0.011.
We find it corresponds to a relatively low $L\simeq 0.01\ledd$.
Luminosities of the hard state of black-hole binaries are commonly above this £L (e.g. Done et 22007: Zdziarski et 22002).
Luminosities of the hard state of black-hole binaries are commonly above this $L$ (e.g, Done et 2007; Zdziarski et 2002).
Again. our determination is for the assumed strong outflow. and relaxing this assumption may increase that critical luminosity.
Again, our determination is for the assumed strong outflow, and relaxing this assumption may increase that critical luminosity.
On the other hand. the presence of a collapsed geometrically thin dise close to the horizon would explain the tinding of relativistically broaden Fe Κα line in the hard state of black-hole binaries (e.g.. Miller et 22006: Miller 2007: but see Done Diaz Trigo 2009 for a critical view). whose origin would have otherwise been in conflict with the hot accretion flow model of the hard state.
On the other hand, the presence of a collapsed geometrically thin disc close to the horizon would explain the finding of relativistically broaden Fe $\alpha$ line in the hard state of black-hole binaries (e.g., Miller et 2006; Miller 2007; but see Done Diaz Trigo 2009 for a critical view), whose origin would have otherwise been in conflict with the hot accretion flow model of the hard state.
Finally. we note that alternative models for the hard state have been proposed.
Finally, we note that alternative models for the hard state have been proposed.
A very interesting recent model is non-thermal. in which the power supplied to electrons (with the optical depth of T,7 1) goes into their acceleration into a power-law distribution (Poutanen Vurm 2009: Malzac Belmont 2009).
A very interesting recent model is non-thermal, in which the power supplied to electrons (with the optical depth of $\tau_{\rm T}\ga 1$ ) goes into their acceleration into a power-law distribution (Poutanen Vurm 2009; Malzac Belmont 2009).
Then. synchrotron self-absorption and Coulomb interactions efficiently thermalize the electrons provided any blackbody emission 1s weak.
Then, synchrotron self-absorption and Coulomb interactions efficiently thermalize the electrons provided any blackbody emission is weak.
This radiative one-zone model fits the hard-state data. e.g. of Cyg X-l. very well.
This radiative one-zone model fits the hard-state data, e.g., of Cyg X-1, very well.
An important issue here is the location of the non- plasma.
An important issue here is the location of the non-thermal plasma.
It cannot be a corona as the model constrains any dise blackbody emission irradiating the plasma to be very weak.
It cannot be a corona as the model constrains any disc blackbody emission irradiating the plasma to be very weak.
If
If
we require a shapelet model of the relevant. kernel.
we require a shapelet model of the relevant kernel.
1n the radio image the restoring beam is exactly known. so the deconvolution process is relatively straightforward.
In the radio image the restoring beam is exactly known, so the deconvolution process is relatively straightforward.
As mentioned above. the restoring beam is a 0.4 arcsec circular Gaussian.
As mentioned above, the restoring beam is a 0.4 arcsec circular Gaussian.
Massey&Relreeicr(2005). describe the ensuing deconvolution step in detail: briellv.. the shapelets: are convolved with the PSE model. and the resulting Functions are least-squares fit to the data.
\citet{2005MNRAS.363..197M} describe the ensuing deconvolution step in detail; briefly, the shapelets are convolved with the PSF model, and the resulting functions are least-squares fit to the data.
The coellicients of the fit correspond to the deconvolvect model.
The coefficients of the fit correspond to the deconvolved model.
To estimate the ACS PSE. we also use SlExtractor to create a catalogue of stars using the SExtractor star/galaxy classifier index (see Bertin&Arnouts(1996). for details).
To estimate the ACS PSF, we also use SExtractor to create a catalogue of stars using the SExtractor star/galaxy classifier index (see \citet{1996A&AS..117..393B} for details).
We decompose cach stellar image into shapelet coefficients: for each shapelet mode. the mean cocllicient is used for the PSE model.
We decompose each stellar image into shapelet coefficients; for each shapelet mode, the mean coefficient is used for the PSF model.
Again. the methodology of Massey(2005) is used to deconvolve all galaxy images.
Again, the methodology of \citet{2005MNRAS.363..197M} is used to deconvolve all galaxy images.
3efore arriving at a final shear catalogue. various necessary cuts were applicd to the datasets.
Before arriving at a final shear catalogue, various necessary cuts were applied to the datasets.
Galaxies with failures in the shapelet modelling. due to poor 7 fits. have been removed.
Galaxies with failures in the shapelet modelling, due to poor $\chi^2$ fits, have been removed.
In the radio case we also removed all objects that were not resolved. ic. ΕΛΛΗΝΙΚΟ0.4. and. also applied. a Hux cut of Sy254yrJy to remove low level noise peaks.
In the radio case we also removed all objects that were not resolved, i.e. $<0.4''$, and also applied a flux cut of $S_{1.4}>54\mu\mbox{Jy}$ to remove low level noise peaks.
In the optical case we applied a magnitude cut of m.<25 in order to only work with objects with S/N6: this cut also removed all unresolved objects.
In the optical case we applied a magnitude cut of $m_{z}<25$ in order to only work with objects with $>6$; this cut also removed all unresolved objects.
We now nee to combine the shapelet coefficients of each object to estimate the weak shear they have experienced.
We now need to combine the shapelet coefficients of each object to estimate the weak shear they have experienced.
We use the simple Gaussian-weightecd shear estimator given by Masseyctal.(2007). Noteote that tlthe averageσ on the ddenominator[ is taktaken over the objects once the cuts described above have been mace.
We use the simple Gaussian-weighted shear estimator given by \citet{2007MNRAS.380..229M}, Note that the average on the denominator is taken over the objects once the cuts described above have been made.
La this fashion we calculate a two-component shear estimator for each useable galaxy in the survey.
In this fashion we calculate a two-component shear estimator for each useable galaxy in the survey.
We are now ready to examine the properties of weak lensing in the radio at current Dux limits.
We are now ready to examine the properties of weak lensing in the radio at current flux limits.
1n our final shear catalogue constructed as described above. we obtain number densities of 7=0.75aremin for the eold radio dataset. 7=3.76aremin for the silver racio dataset. and n=40.66arcmin7 for the optical data.
In our final shear catalogue constructed as described above, we obtain number densities of $n=0.75\mbox{ arcmin}^{-2}$ for the gold radio dataset, $n=3.76 \mbox{ arcmin}^{-2}$ for the silver radio dataset, and $n=40.66\mbox{ arcmin}^{-2}$ for the optical data.
lt can immediately be seen that currently. racio number densities are substantially lower than those available at optical wavelengths.
It can immediately be seen that currently, radio number densities are substantially lower than those available at optical wavelengths.
Llowever. it should also be noted how much » has increased in relation to Changetal.(2004).. where there were only &20 objects per square degree.
However, it should also be noted how much $n$ has increased in relation to \citet{2004ApJ...617..794C}, where there were only $\simeq20$ objects per square degree.
With the imminent arrival of e-\LERLIN and LOLFAR. racio number densities will begin to compare well with optical number densities: this is crucial for weak lensing 2-point statistics. where the noise is inversely proportional to the number clonsity.
With the imminent arrival of -MERLIN and LOFAR, radio number densities will begin to compare well with optical number densities; this is crucial for weak lensing 2-point statistics, where the noise is inversely proportional to the number density.
In addition. the noise on weak lensingin] 2-point statistics is proportional to the shear estimator variance. στ, so this is
In addition, the noise on weak lensing 2-point statistics is proportional to the shear estimator variance, $\sigma_\gamma^2$ , so this is
width of the last scattering laver aud the distortion of the CAIB spect.
width of the last scattering layer and the distortion of the CMB spectrum.
Though the amount of the residual ionization is uportaut for the further evolution of the Universe (Peebles 1995. Lepp Shull 1981). it cai not be measured directly.
Though the amount of the residual ionization is important for the further evolution of the Universe (Peebles 1993, Lepp Shull 1984), it can not be measured directly.
A possible observable consequence of the hydrogen recombination m the carly Universe is the distortion of the mucrowave backerotnd radiaion spectrüun.
A possible observable consequence of the hydrogen recombination in the early Universe is the distortion of the microwave background radiation spectrum.
[t was first calculated for the flat cosmological model by Peebles (196i.
It was first calculated for the flat cosmological model by Peebles (1968).
In this work we concentrate on the deernünnuation o[o this: distortiou for different cosmological models.
In this work we concentrate on the determination of this distortion for different cosmological models.