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Αν value of αμ that is not excessively large or small (within a few powers of ten of unity) has uo significaut ellect except in regions that are both couvective aud uouaciabatic.
Any value of $\gml$ that is not excessively large or small (within a few powers of ten of unity) has no significant effect except in regions that are both convective and nonadiabatic.
An estimate of gayp in terms of the size of a convective "element" or “blob” is given in Table 1 above. which we repeat here: gary=(6/ο where rj is the “blob” radius.
An estimate of $g_{ML}$ in terms of the size of a convective "element" or "blob" is given in Table \ref{tablemlp} above, which we repeat here: $g_{ML} = ( \ell/\sqrt{3} r_b )^2$, where $r_b$ is the "blob" radius.
In MLT. 0.5770. forcing two independent length scales. { aud V/3ry. to be the same.
In MLT, $r_b \equiv \ell/\sqrt{3} \approx 0.577 \ell$ , forcing two independent length scales, $\ell$ and $\sqrt{3} r_b$, to be the same.
Adjustment of gayp allows the super-aciabatic region to have the correct entropy jump. for auy reasonable value of the mixiug leugth parameter aayp: that is. αλ may be chosen to be hydrodyuanmiueally consistent.
Adjustment of $\gml$ allows the super-adiabatic region to have the correct entropy jump, for any reasonable value of the mixing length parameter $\aml$ ; that is, $\aml$ may be chosen to be hydrodynamically consistent.
This does provide a consistent. couvective theory if other important effects. such as entrainment aud wave generation.are ignored.
This does provide a consistent convective theory if other important effects, such as entrainment and wave generation,are ignored.
escape between these accretion streams, resulting in more prompt re-ionization.
escape between these accretion streams, resulting in more prompt re-ionization.
The rate of production of ionizing photons be co-moving Mpc? can be calculated using the density of halos as a function of mass and redshift given by, for example, the simulations ofMo&White(2002) or Jenkinsetal. (2001).
The rate of production of ionizing photons be co-moving $^{3}$ can be calculated using the density of halos as a function of mass and redshift given by, for example, the simulations of\citet{Mo02} or \citet{Jenkins01}.
. Equation 2 gives the photon production rate for a halo of a given mass.
Equation \ref{photons} gives the photon production rate for a halo of a given mass.
We have computed two cases - that in which the UV photon production in shocks is contemporaneous with the formation of the halo and the case in which this photon production is delayed by 50 Myr, related to the free-fall collapse time.
We have computed two cases - that in which the UV photon production in shocks is contemporaneous with the formation of the halo and the case in which this photon production is delayed by 50 Myr, related to the free-fall collapse time.
The photon production rate is summed over the space density of halos given by Mo&White(2002) to give theproduction rate of photons per co-moving Mpc?.
The photon production rate is summed over the space density of halos given by \citet{Mo02} to give theproduction rate of photons per co-moving $^{3}$.
We then compute the time dependent ionization of the universe using a photon diffusion approximation.
We then compute the time dependent ionization of the universe using a photon diffusion approximation.
In this, the ionization fronts move rapidly to ionize the least-dense phases first, and the denser HI in the halos is ionized more slowly and at later times.
In this, the ionization fronts move rapidly to ionize the least-dense phases first, and the denser HI in the halos is ionized more slowly and at later times.
This provides a reasonable approximation to this complex process (Ilievetal.2009).
This provides a reasonable approximation to this complex process \citep{Iliev09}.
. The photons needed to maintain the ionization in the ionized volume are included in the calculation.
The photons needed to maintain the ionization in the ionized volume are included in the calculation.
The appropriate densities have been computed for us using a more recent (higher resolution) version of the cosmological simulation by Kobayashi,Springe]&White (2007).
The appropriate densities have been computed for us using a more recent (higher resolution) version of the cosmological simulation by \citet{Kobayashi07}.
The result is shown in Figure 3..
The result is shown in Figure \ref{fig_3}.
We find that with the Mo&White(2002) cosmological parameters, ~50% by volume (and by mass) of the universe is ionized by z<8, and that re-ionization is complete by zZ5.8.
We find that with the \citet{Mo02} cosmological parameters, $\sim 50$ by volume (and by mass) of the universe is ionized by $z \lesssim 8$, and that re-ionization is complete by $z\gsim 5.8$.
Note that the effect of more prompt escape of UV photons would be to markedly increase the degree of ionization at early times.
Note that the effect of more prompt escape of UV photons would be to markedly increase the degree of ionization at early times.
At a redshift of z—10 the photon density is increased by more than a factor of three by this prompt escape.
At a redshift of $z =10$ the photon density is increased by more than a factor of three by this prompt escape.
Note that the space density of massive halos given by the equations of Jenkinsetal.(2001) and the models of Mo&White(2002) assume the cosmological parameter og.
Note that the space density of massive halos given by the equations of \citet{Jenkins01} and the models of \citet{Mo02} assume the cosmological parameter $\sigma_8$.
This is related to the mean mass density fluctuations on scales of 8h-! Mpc today, and is = 0.9.
This is related to the mean mass density fluctuations on scales of $8h^{-1}$ Mpc today, and is $\approx 0.9$ .
'This enters exponentially into the overall collapse fraction.
This enters exponentially into the overall collapse fraction.
There is some uncertainty in this value and the more recent estimates Komatsuetal(2011) suggest og©0.8.
There is some uncertainty in this value and the more recent estimates \citet{Komatsu11} suggest $\sigma_8 \approx 0.8$.
If one assumes this latter value, the fraction of baryons in massive halos at high redshift will be reduced by approximately a factor of 4.5 compared to those estimated using Mo&White(2002).
If one assumes this latter value, the fraction of baryons in massive halos at high redshift will be reduced by approximately a factor of 4.5 compared to those estimated using \citet{Mo02}.
. As a consequence, the rate of production of ionizing photons will be reduced by a similar factor.
As a consequence, the rate of production of ionizing photons will be reduced by a similar factor.
However, the effect on the epoch of re-ionization is much smaller, as we now show.
However, the effect on the epoch of re-ionization is much smaller, as we now show.
As described above, only themost massive halos are important as sources of ionizing photons.
As described above, only themost massive halos are important as sources of ionizing photons.
We estimate that dominant halos for production of UV photon s have masses in the range 1011Η:5 Mo.
We estimate that dominant halos for production of UV photon s have masses in the range $10^{11-11.5}$ $_\odot$.
The photon production by accretion shocks increases very rapidly with decreasing redshift, thanks to the rapid increase in space density of halos, and the increasing importance of the more massive halos.
The photon production by accretion shocks increases very rapidly with decreasing redshift, thanks to the rapid increase in space density of halos, and the increasing importance of the more massive halos.
At z~ 8, it is increasing (with decreasing redshift) ος(1+2) 19.
At $z \sim 8$ , it is increasing (with decreasing redshift) $\propto (1+z)^{-10}$ .
At the same time the number of photons needed to ionize the universe decreases c(1+ z)?.
At the same time the number of photons needed to ionize the universe decreases $\propto (1+z)^{3}$ .
These factors serve to “lock
These factors serve to “lock
(Ikewleyctal.
\citep{kewley06}.
2δα), More specifically we constructed the diagrams hat compare the|O Πλ Π) ratio with |N |A6583/Tla. [S TUAAGTLO.6731/Tla and [ο YAG36L/Tla shown in Fig. l.
More specifically we constructed the diagrams that compare the[O $\lambda$ $/$ $\beta$ ratio with [N $\lambda$ $/$ $\alpha$ , [S $\lambda\lambda$ $/$ $\alpha$ and [O $\lambda$ $/$ $\alpha$ shown in Fig. \ref{dd}.
Ratios involving line upper lnmits are rot considered.
Ratios involving line upper limits are not considered.
Iu the left haid panels of this feure. the 3CR sources are dudicated by circles with sizes proportional to the O TI] huninosity. in the central panels the errors on the Ine ratios are stown and iu the right pancls the 3CR πα ALC COMPwed with the SDSS cussion line galaxies rou IKKO06..
In the left hand panels of this figure, the 3CR sources are indicated by circles with sizes proportional to the [O III] luminosity, in the central panels the errors on the line ratios are shown and in the right panels the 3CR sources are compared with the SDSS emission line galaxies from \citetalias{kewley06b}.
The xid Lines divide sources iuto star-forming ealaxies (lower kft reeion of the diagram). Sevterts (top oft region) and LINERs (bottom right region) according o TIxt6..
The solid lines divide sources into star-forming galaxies (lower left region of the diagram), Seyferts (top left region) and LINERs (bottom right region) according to \citetalias{kewley06b}. .
Tn the first diagnostic diagram (first row) of Fig.
In the first diagnostic diagram (first row) of Fig. \ref{dd},
og |O > νιvsus log [N H[/TIIo. all 3CR sources are Ocatec iu the AGN reeion with only a few exceptions: one object (3C 1987)) falls among the star-forming galaxies.
log [O $/$ $\beta$ versus log [N $/$ $\alpha$, all 3CR sources are located in the AGN region with only a few exceptions: one object (3C ) falls among the star-forming galaxies.
Two objects (3€ 028 and 3€ 3111) are located in he couposite region and. together with 3€ 318. have extremely low |O /ILJ ratio (ον 0.5): however. they are well inο the AGN region in the other two diagrams.
Two objects (3C 028 and 3C 314.1) are located in the composite region and, together with 3C 348, have extremely low [O $/$ $\beta$ ratio $\sim 0.5$ ); however, they are well into the AGN region in the other two diagrams.
The ocatioi of the remaining sources appears to be related o their line himinosity.
The location of the remaining sources appears to be related to their line luminosity.
Powerful sources (LigZ104 Creyes s ) are mostly ound along a horizontal strip around og|O ΠΠ) .
Powerful sources $L_{\rm [OIII]}\gtrsim10^{41.5}$ erg $^{-1}$ ) are mostly found along a horizontal strip around log[O $/$ $\sim1$ .
Wenπο οe that all 83CR ealaxies in which we detected a broad ccomponent belongo this 3ub-group.
We also note that all 3CR galaxies in which we detected a broad component belongto this sub-group.
Iu coutrast. fainter sources (LtJxj(H cre ‘) are justead ecnuerally
In contrast, fainter sources $L_{\rm [OIII]}\lesssim10^{41.5}$ erg $^{-1}$) are instead generally
We review the main results of the Near-LR SO ealaxy Survey (NLRSOS) obtained so far+.
We review the main results of the Near-IR S0 galaxy Survey (NIRS0S) obtained so far.
. NIRSOS is a magnitude (mg 12.5r mag) and inclinaion (less than 65°) Limited sample of ~ 200 nearby. galaxies. mainly SOs. but include also Sa spirals and 25 [ate-tvpe ellipticals.
NIRS0S is a magnitude $_B$$\leq$ 12.5 mag) and inclination (less than $^o$ ) limited sample of $\sim$ 200 nearby galaxies, mainly S0s, but include also Sa spirals and 25 late-type ellipticals.
Late-type ellipticals were included for not to miss any potentially misclassified SOs.
Late-type ellipticals were included for not to miss any potentially misclassified S0s.
“Phe observations were done in the A band. carried out using 3-4 meter sized ground-based telescopes with sub-areseconcd pixel resolution.
The observations were done in the $K_s$ -band, carried out using 3-4 meter sized ground-based telescopes with sub-arcsecond pixel resolution.
The images are ¢cep. tvpically reaching a surface brightnesses of 23.5 mag 7 in azimuthally averaged. profiles (~ 2 mag deeper than the 2\LASS images). thus allowing the detection of the faint outer disks in SOs.
The images are deep, typically reaching a surface brightnesses of 23.5 mag $^{-2}$ in azimuthally averaged profiles $\sim$ 2 mag deeper than the 2MASS images), thus allowing the detection of the faint outer disks in S0s.
Our main emphasis was to acleress possible secular evolutionary processes in galaxies by comparing the photometric properties of SOs and spirals. based on similarly seleced samples. with similar image quality.
Our main emphasis was to address possible secular evolutionary processes in galaxies by comparing the photometric properties of S0s and spirals, based on similarly selected samples, with similar image quality.
We present a method to calculate small stationary [fluctuations around static solutions describing bound states in a (1+ l)-dimensional Ao".+ theory in a finite domain.
We present a method to calculate small stationary fluctuations around static solutions describing bound states in a $(1+1)$ -dimensional $\lambda \phi^{n+1}$ theory in a finite domain.
We also calculate explicitlv fluctuations for the Ao!.
We also calculate explicitly fluctuations for the $\lambda \phi^4$.
These solutions are written in terms of Jacobi Elliptic functions ancl are obtained from both linear and nonlinear equations.
These solutions are written in terms of Jacobi Elliptic functions and are obtained from both linear and nonlinear equations.
For (he linear case we get eigenvalues of a Lameé tvpe Equation and the nonlinear one relies on Iirota's Method.
For the linear case we get eingenvalues of a Lamé type Equation and the nonlinear one relies on Hirota's Method.
0.60cm llt is well known that. for some applications. quantum fields can be thought as c]assical fields upon which are added quantum corrections [1]..
0.60cm It is well known that, for some applications, quantum fields can be thought as classical fields upon which are added quantum corrections \cite{jack}.
In addition non-linear field theories are nowadays powerlull tools to describe fundamental physical theories including cosmology. mainly for Che inflationary model of the universe 2.3]..
In addition non-linear field theories are nowadays powerfull tools to describe fundamental physical theories including cosmology, mainly for the inflationary model of the universe \cite{lind, kolb}.
On the other hand it is also well known that quantum systems when placed in finite domains (cavities) can present significant alterations on their behaviour.
On the other hand it is also well known that quantum systems when placed in finite domains (cavities) can present significant alterations on their behaviour.
A step further is the study. of interacting fields in finite domains 4].
A step further is the study of interacting fields in finite domains ${\cite{carr01}}$.
A modern paradigm is the famous Casimir Effect [5.6]..
A modern paradigm is the famous Casimir Effect \cite{casim, casim1}.
In particular since these corrections are sensitive to boundary conditions an effect. could expected on bound states of (he physical svstem under In a previous work Carrillo [Y]. obtained a number of solutions of a (141- Ao!-Theory in a finite domain in terms of Jacobi Elliptic functions.
In particular since these corrections are sensitive to boundary conditions an effect could expected on bound states of the physical system under In a previous work Carrillo \cite{nl:a1} obtained a number of solutions of a $(1+1)$ -dimensional $\lambda \phi^4$ -Theory in a finite domain in terms of Jacobi Elliptic functions.
In this work we (ake a step further in the direction of a semi-clasical approach of the theory by studying small fInctuations around one of the above mentioned solutions describing its bound states.
In this work we take a step further in the direction of a semi-clasical approach of the theory by studying small fluctuations around one of the above mentioned solutions describing its bound states.
We think this is enough to exemplify our approach to this
We think this is enough to exemplify our approach to this
We thank the releree for helpful suggestions which have improved (his paper significantlv.
We thank the referee for helpful suggestions which have improved this paper significantly.
We acknowledge the technical help provided by Joan Wrobel in scheduling the VLBA observations.
We acknowledge the technical help provided by Joan Wrobel in scheduling the VLBA observations.
This work is partially supported by NASA grant GOS-9103X. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Administration.
This work is partially supported by NASA grant G08-9108X. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
M.J.IHI. thanks the Roval Society for support.
M.J.H. thanks the Royal Society for support.
extended emission in M82 ts resolved out.
extended emission in M82 is resolved out.
Flux densities were extracted by fitt5 two-dimensional Gaussians to the images.
Flux densities were extracted by fitting two-dimensional Gaussians to the images.
The measured flux densities of 220081z and two other supernova remnants that could be easily separated from the diffuse background emission are listed in Table 1..
The measured flux densities of 2008iz and two other supernova remnants that could be easily separated from the diffuse background emission are listed in Table \ref{tab:vla}.
The errors are estimated by adding in quadrature the formal error from the fit to the images. the difference between peak and integrated flux densities. and an 5% error allown5 for an error in the overall flux density scale.
The errors are estimated by adding in quadrature the formal error from the fit to the images, the difference between peak and integrated flux densities, and an $\%$ error allowing for an error in the overall flux density scale.
Furthermore. we added an additional 55€ error at 1.4. 4.8. and 8.4 GHz since we have more confusion from the extended emission at these frequencies.
Furthermore, we added an additional $\%$ error at 1.4, 4.8, and 8.4 GHz since we have more confusion from the extended emission at these frequencies.
Note that the flux density at 4.8 GHz is in good agreement with the flux densities reported by ?.. obtained with MERLIN a few days later (28.54 2 mJy).
Note that the flux density at 4.8 GHz is in good agreement with the flux densities reported by \cite{BeswickMuxlowPedlar2009}, obtained with MERLIN a few days later $\pm$ 2 mJy).
The spectrum of 22008iz is shown in Fig. 2..
The spectrum of 2008iz is shown in Fig. \ref{fig:vla}.
First. we fitted a single power-law spectrum to the data.
First, we fitted a single power-law spectrum to the data.
This gives a spectral index of —0.8840.07.
This gives a spectral index of $-0.88\pm$ 0.07.
However. the fit has a large reduced y value of 2.6. since the 1.4 GHz value is too low.
However, the fit has a large reduced $\chi^2$ value of 2.6, since the 1.4 GHz value is too low.
Thus. we fitted the spectra also with a broken power-law. where a and ó are the spectral indices of the optically thin and thick parts of the spectrum.
Thus, we fitted the spectra also with a broken power-law, where $\alpha$ and $\delta$ are the spectral indices of the optically thin and thick parts of the spectrum.
So and vo represent the maximum flux density and the peak frequency of the fitted spectrum.
$S_0$ and $\nu_0$ represent the maximum flux density and the peak frequency of the fitted spectrum.
Since one data point in the optically thick part of the spectrum is 1ot enough to fit the spectral index there. we made two fits. one with a value for a synchrotron self-absorbed spectrum (6 =2.5). and a steeper free-free absorbed spectrum (024.5).
Since one data point in the optically thick part of the spectrum is not enough to fit the spectral index there, we made two fits, one with a value for a synchrotron self-absorbed spectrum $\delta=$ 2.5), and a steeper free-free absorbed spectrum $\delta$ =4.5).
The reduced y values in both cases are now 0.9.
The reduced $\chi^2$ values in both cases are now 0.9.
The fit (using 0= 4.5) gives a spectral index in the optically thin part of «=—1.08+0.08 and a turnover frequency of vo=1:51+0.09 GHz.
The fit (using $\delta=4.5$ ) gives a spectral index in the optically thin part of $\alpha=-1.08\pm0.08$ and a turnover frequency of $\nu_0=1.51\pm0.09$ GHz.
While the spectral index « 1s not affected by the choice of 0. vo changes slightly to 1.55 for 0=2.5.
While the spectral index $\alpha$ is not affected by the choice of $\delta$, $\nu_0$ changes slightly to 1.55 for $\delta=2.5$.
This indicates that the source was still optically thick. and brightening at the lowest frequencies in April 2009 (foraftertheexplosion: ?)..
This indicates that the source was still optically thick, and brightening at the lowest frequencies in April 2009 \cite[for comparision: SN\,1993J reached it's peak at 1.4 GHz $\sim$500 days after the explosion;][]{Weiler2002}.
The off-axis configuration. and consequently the degraded angular resolution. as well as the diffuse background. have largely decreased the sensitivity of the Chandra measurements.
The off-axis configuration and consequently the degraded angular resolution, as well as the diffuse background, have largely decreased the sensitivity of the Chandra measurements.
The detection limit of these observations is estimated from the total emission around the radio position in a region with the same size as the point spread function.
The detection limit of these observations is estimated from the total emission around the radio position in a region with the same size as the point spread function.
220081z is located close to several variable ultraluminous X-ray sources.
2008iz is located close to several variable ultraluminous X-ray sources.
However. no emission was detected at the position. of the supernova.
However, no emission was detected at the position of the supernova.
? and ? report the discovery of a second radio transient in M82. with the MERLIN telescope.
\cite{MuxlowBeswickPedlar2009} and \cite{MuxlowBeswickGarrington2010} report the discovery of a second radio transient in M82 with the MERLIN telescope.
This source appeared between 2009 April 24 and 2009 May 5 and is located at a position with a diffuse emission background.
This source appeared between 2009 April 24 and 2009 May 5 and is located at a position with a diffuse emission background.
It is surrounded by a few point-like sources.
It is surrounded by a few point-like sources.
There i$ no enhanced X-ray emission at the location of this second radio transient. neithey on 2009 April 17. nor on 2009 April 29.
There is no enhanced X-ray emission at the location of this second radio transient, neither on 2009 April 17, nor on 2009 April 29.
To compare our limits with the emission from 11993J. we assume spectral properties that are similar to the ones of 11993J at a similar age. Le.. a thermal bremsstrahlung spectrum with a temperature of 1.05 keV. abundances from Table 2. Column 4 of ?.. and an absorption colunn density of 5.4x1077 em7 (see Sect. 5.1).
To compare our limits with the emission from 1993J, we assume spectral properties that are similar to the ones of 1993J at a similar age, i.e., a thermal bremsstrahlung spectrum with a temperature of 1.05 keV, abundances from Table 2, Column 4 of \cite{ZimmermannAschenbach2003}, and an absorption column density of $\times10^{22}$ $^{-2}$ (see Sect. \ref{coldens}) ).
Then we get an 3 « upper limit of 15x10? erg s! in the energy range 0.3-2.4 keV. This is consistent with the X-ray luminosity of 11993J at à similar age (?) in the same energy range.
Then we get an 3 $\sigma$ upper limit of $\times 10^{39}$ erg $^{-1}$ in the energy range 0.3-2.4 keV. This is consistent with the X-ray luminosity of 1993J at a similar age \citep{ZimmermannAschenbach2003} in the same energy range.
The 3 c sensitivity at the location of the MERLIN transient. assuming a column density of 107 em and a photon law index of 1.7 (anapproximationtoathermal ?).. is found to be about 1.2 107? erg s7! in 0.3-2.4 keV. which we take as the upper limit of the X-ray luminosity.
The 3 $\sigma$ sensitivity at the location of the MERLIN transient, assuming a column density of $^{22}$ $^{-2}$ and a photon power-law index of 1.7 \citep[an approximation to a thermal bremsstrahlung spectrum with a temperature of 10 keV, as seen in SN1995N;][]{FoxLewinFabian2000}, is found to be about $\times$ $^{38}$ erg $^{-1}$ in 0.3–2.4 keV, which we take as the upper limit of the X-ray luminosity.
The resultant countrates in the Swift XRT data (0.5-8.0 keV) are 0.6040.02. 0.5940.02. and 0.6820.02 s! on 2007 January 26. 2008 May 1. and 2009 April 25. respectively.
The resultant countrates in the Swift XRT data (0.5-8.0 keV) are $\pm$ 0.02, $\pm$ 0.02, and $\pm$ 0.02 $^{-1}$ on 2007 January 26, 2008 May 1, and 2009 April 25, respectively.
There is no clear rise in total flux from the pre-SNe observation to the May 2008 post-explosion epoch at 75 days. and while a ~ increase in count rate is seen in the final observation. this is consistent with BeppoSAX observations of the central region of M82 showing variations on the order of (2-10 keV) on hour time-seales (?)..
There is no clear rise in total flux from the pre-SNe observation to the May 2008 post-explosion epoch at $\sim$ 75 days, and while a $\sim$ increase in count rate is seen in the final observation, this is consistent with BeppoSAX observations of the central region of M82 showing variations on the order of (2-10 keV) on hour time-scales \citep{CappiPalumboPellegrini1999}. .
Indeed. such intrinsic variations are also seen over the course of each epoch in the XRT
Indeed, such intrinsic variations are also seen over the course of each epoch in the XRT
and regular gaps in the light curve when only Uag=zero points are used.
and regular gaps in the light curve when only flag=zero points are used.
The llag algorithm was therefore. not used to exclude measurements. and the light curve was instead cleaned manually from outlving points.
The flag algorithm was therefore not used to exclude measurements, and the light curve was instead cleaned manually from outlying points.
The final data set is composed of 20983 useful points. vielding the very high duty evele of 86 per A Fourier analysis of the data was performed using the PeriodO4 software package developed. by Lenz&Dreger (2005).
The final data set is composed of 20983 useful points, yielding the very high duty cycle of 86 per A Fourier analysis of the data was performed using the Period04 software package developed by \citet{len}.