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We analyzed the Swift/XRT data of GRB 050904, taking special care to estimate the flare unbiased afterglow flux level at the epochs of interest and to extrapolate the flux where no data are available. | We analyzed the Swift/XRT data of GRB 050904, taking special care to estimate the flare unbiased afterglow flux level at the epochs of interest and to extrapolate the flux where no data are available. |
A spectral power-law model was fitted to the extracted SEDs, setting the spectral index and normalization at the dust-unbiased X-ray emission values. | A spectral power-law model was fitted to the extracted SEDs, setting the spectral index and normalization at the dust-unbiased X-ray emission values. |
No spectral breaks or chromatic temporal breaks between X-rays and optical wavelengths are expected at these epochs, according to past broad band modeling results for this burst (e.g.??).. | No spectral breaks or chromatic temporal breaks between X-rays and optical wavelengths are expected at these epochs, according to past broad band modeling results for this burst \citep[e.g.][]{Frail2006,Gou2007}. |
Indeed, this predicts that the synchrotron cooling frequency v. is already below the optical range at the time of interest, thus an identical afterglow decay law at X-ray and optical wavelengths is expected. | Indeed, this predicts that the synchrotron cooling frequency $\nu_c$ is already below the optical range at the time of interest, thus an identical afterglow decay law at X-ray and optical wavelengths is expected. |
We investigated any presence of dust extinction in the GRB afterglow by using the SMC extinction curve and the Calzetti attenuation law. | We investigated any presence of dust extinction in the GRB afterglow by using the SMC extinction curve and the Calzetti attenuation law. |
Wealso used the MEC at 4.0<z<6.4 inferred by ? from the analysis of 33 quasars, and the associated attenuation curve (MEC,,,). | Wealso used the MEC at $<$ $<$ 6.4 inferred by \cite{Gallerani2010} from the analysis of 33 quasars, and the associated attenuation curve $_{att}$ ). |
The SN-type extinction curve, proposed by ?,, which reproduces the dust extinction observed in a BAL QSO at z=6.2 (??) | The SN-type extinction curve, proposed by \cite{Todini2001}, , which reproduces the dust extinction observed in a BAL QSO at z=6.2 \citep{Maiolino2004,Gallerani2010} |
an optical spectrum of the secondary. the presence (absence) of in the spectrum would set a upper (lower) limit on the mass and. hence. the age of the system. in this case 1.8Gyr (21.1 Gyr). | an optical spectrum of the secondary, the presence (absence) of in the spectrum would set a upper (lower) limit on the mass and, hence, the age of the system, in this case $\lesssim$ 1.8Gyr $\gtrsim$ 1.1 Gyr). |
The likely proximity of the mass of the secondary to the LDB ts motivation to obtain an optical spectrum of this component. | The likely proximity of the mass of the secondary to the LDB is motivation to obtain an optical spectrum of this component. |
The absence of emission in the optical spectrum of 4445A and lack of UV or X-ray flux—the system is not detected in the GALEX (?) or the ROSAT (?) All-Sky Surveys—indicates that the system is not particularly active and. hence. not likely to be à very young system. | The absence of emission in the optical spectrum of A and lack of UV or X-ray flux—the system is not detected in the GALEX \citep{Martin2005b} or the ROSAT \citep{Voges1999} All-Sky Surveys—indicates that the system is not particularly active and, hence, not likely to be a very young system. |
This absence indicates that 4445AB ts probably older than 1-100 Myr. as such emission has been detected in brown dwarfs in the Orion Nebula Cluster (isochronal ?).. Taurus (~3Myr:?).. & Orionis (2-7Myr: λεν à Persei (~80Myr:?).. Pleiades (~100Myr:??).. and Blanco | (~100 Myr; P. A. Cargile et al.. | This absence indicates that AB is probably older than 1–100 Myr, as such emission has been detected in brown dwarfs in the Orion Nebula Cluster \citep[isochronal age $\sim$1~Myr;][]{Peterson2008}, , Taurus \citep[$\sim$3~Myr;][]{Guieu2006}, $\sigma$ Orionis \citep[2--7~Myr;][]{Zapatero-Osorio2002}, $\alpha$ Persei \citep[$\sim$80~Myr;][]{Stauffer1999}, Pleiades \citep[$\sim$100~Myr;][]{Stauffer1998, Martin2000}, and Blanco 1 $\sim$ 100 Myr; P. A. Cargile et al., |
in prep.). | in prep.). |
However. activity signatures might not be reliable age indicators in the VLM regime. | However, activity signatures might not be reliable age indicators in the VLM regime. |
Both and X-ray emission drop precipitously across the M dwarf/L dwarf transition (e.g..2222)., likely the result of reduced magnetic field coupling with increasingly neutral photospheres (e.g..?2).. | Both and X-ray emission drop precipitously across the M dwarf/L dwarf transition \citep[e.g.,][]{Kirkpatrick2000, Gizis2000, West2004,
Stelzer2006}, likely the result of reduced magnetic field coupling with increasingly neutral photospheres \citep[e.g.,][]{Gelino2002,
Mohanty2002}. |
Extreme youth can also be ruled out based on the the NIR spectra of these sources. which do not exhibit the triangular H-band peaks seen in ~100 Myr Pleiades M and L dwarfs (?) and young field L dwarfs (e.g..?).. | Extreme youth can also be ruled out based on the the NIR spectra of these sources, which do not exhibit the triangular H-band peaks seen in $\sim$ 100 Myr Pleiades M and L dwarfs \citep{Bihain2010}
and young field L dwarfs \citep[e.g.,][]{Kirkpatrick2006}. |
It is notable that 4445B ts somewhat red compared to typical Lo dwarfs οIN, = 1.82+0.07:2). as red sources have been shown to exhibit smaller velocity dispersions and. hence. younger ages (??).. | It is notable that B is somewhat red compared to typical L6 dwarfs \citep[$\langle{J-K_s} = $\pm$, as red sources have been shown to exhibit smaller velocity dispersions and, hence, younger ages \citep{Faherty2009, Schmidt2010}. |
However. 4445A is not unusually red for its spectral type (7)A)= 1.12+0.10): and the red color of the secondary may reflect an unusually dusty atmosphere (e.g..?).. | However, A is not unusually red for its spectral type $\langle{J-K_s}\rangle =$ $\pm$ 0.10); and the red color of the secondary may reflect an unusually dusty atmosphere \citep[e.g.,][]{Looper2008a}. |
Also. neither NIR spectra nor the optical spectrum of 4445A show high gravity signatures. 1.e.. unusually blue colors form enhancedH». or evidence of the system being metal-poor. making it unlikely that the system is as old as ~10 Gyr (??).. | Also, neither NIR spectra nor the optical spectrum of A show high gravity signatures, i.e., unusually blue colors form enhanced, or evidence of the system being metal-poor, making it unlikely that the system is as old as $\sim$ 10 Gyr \citep{Burgasser2003b, Reid2007}. |
Considering the kinematics of the system. the tangential velocity of 4445A. 192-3 is similar to the median velocities of the L dwarfs in the SDSS sample (28425kms+:2). the M9 dwarfs in the BDKP sample (23423kms1:2). and the M7-L8 dwarfs in the 2MASS sample (25421kms!::?) with the quoted errors being the Io dispersions. | Considering the kinematics of the system, the tangential velocity of A, $\pm$ 3 is similar to the median velocities of the L dwarfs in the SDSS sample \citep[28$\pm$25~{\kms};, the M9 dwarfs in the BDKP sample \citep[23$\pm$23~{\kms};, and the M7–L8 dwarfs in the 2MASS sample \citep[25$\pm$21~{\kms};, with the quoted errors being the $\sigma$ dispersions. |
The low tangential velocity suggests that 4445AB ts part of the thin disk. although we note that we cannot rule out a higher space velocity for the binary system. | The low tangential velocity suggests that AB is part of the thin disk, although we note that we cannot rule out a higher space velocity for the binary system. |
Kinematic studies have found that late-M and L dwarfs with average kinematics are typically ~2-4 Gyr old (?2).. | Kinematic studies have found that late-M and L dwarfs with average kinematics are typically $\sim$ 2–4 Gyr old \citep{Wielen1977, Faherty2009}. |
In conclusion. based on the absence of in the primary. we can place a (model-dependent) hard limit on the minimum age of 4445AB to be ~250 Myr while its kinematics indicate a preferred age of ~2-4 Gyr. | In conclusion, based on the absence of in the primary, we can place a (model-dependent) hard limit on the minimum age of AB to be $\sim$ 250 Myr while its kinematics indicate a preferred age of $\sim$ 2–4 Gyr. |
Spectral features for both components are in agreement with these ages. | Spectral features for both components are in agreement with these ages. |
For the ages of 0.25-10 Gyr. based on the ? and ? models. the estimated masses for 4445A and 4445B are 0.055-0.083 and 0.032-0.076 ... respectively. and the mass ratio is 0.57-0.92. | For the ages of 0.25–10 Gyr, based on the \citet{Burrows1993} and \citet{Burrows1997} models, the estimated masses for A and B are 0.055–0.083 and 0.032--0.076 , respectively, and the mass ratio is 0.57–0.92. |
For kinematics-based age limits of 2—4 Gyr. the estimated masses for 4445A and 4445B are 0.082—0.083 and 0.066-0.073 ... respectively. and the mass ratio is 0.81—0.89 (Table 4)). | For kinematics-based age limits of 2–4 Gyr, the estimated masses for A and B are 0.082–0.083 and 0.066–0.073 , respectively, and the mass ratio is 0.81–0.89 (Table \ref{Tab: model_props}) ). |
Hence.M the components straddle the hydrogen-burning mass limit: and this system ts likely composed of a very low mass star and (massive) brown dwarf pair. | Hence, the components straddle the hydrogen-burning mass limit; and this system is likely composed of a very low mass star and (massive) brown dwarf pair. |
With a projected separation of 130450 AU. 4445AB is one of only ten VLM systems wider than 100 AU. with six of them in the field. | With a projected separation of $\pm$ 50 AU, AB is one of only ten VLM systems wider than 100 AU, with six of them in the field. |
All of these systems have been identified relatively recently: prior to their discovery. it was believed that VLM field systems were nearly all tight. a possible consequence of dynamic ejection early on. | All of these systems have been identified relatively recently; prior to their discovery, it was believed that VLM field systems were nearly all tight, a possible consequence of dynamic ejection early on. |
Based onthis idea and the VLM binary population known at the time. two relations to define the largest possible separation of VLM binaries were proposed. | Based onthis idea and the VLM binary population known at the time, two relations to define the largest possible separation of VLM binaries were proposed. |
First. ? suggested that the maximum separation of a system was dependent on its mass: eua (AU) = 1400 ..?. | First, \citet{Burgasser2003a} suggested that the maximum separation of a system was dependent on its mass: $a_{\rm max}$ (AU) $=$ 1400 $^2$ . |
Second. ? proposed that the stability of binary systems was contingent on their bindingenergy—a criterion. based on the product rather than thesum of component masses: thus. only systems with binding energy =>104° erg would exist in the field'".. | Second, \citet{Close2003} proposed that the stability of binary systems was contingent on their bindingenergy—a criterion based on the product rather than thesum of component masses; thus, only systems with binding energy $\geq
10^{42.5}$ erg would exist in the . |
For the (age-dependent) estimated mass of | For the (age-dependent) estimated mass of |
Figure 5 and, for simplicity. we do not plot the perturbations again. | Figure \ref{fig:eigen1} and, for simplicity, we do not plot the perturbations again. |
The order of the solutions can be easily identified by the number of extrema (maxima and minima) of their temperature perturbation. | The order of the solutions can be easily identified by the number of extrema (maxima and minima) of their temperature perturbation. |
Thus, the most unstable mode has one maximum only, the second most unstable mode has one maximum and one minimum, and so on. | Thus, the most unstable mode has one maximum only, the second most unstable mode has one maximum and one minimum, and so on. |
The position of the largest extremum is shifted toward larger values of r/R às the order of the mode increases. | The position of the largest extremum is shifted toward larger values of $r/R$ as the order of the mode increases. |
In addition, the growth rate (indicated at the top of the panels of Fig. 5)) | In addition, the growth rate (indicated at the top of the panels of Fig. \ref{fig:eigen1}) ) |
decreases with the order of the mode. | decreases with the order of the mode. |
These two results are represented together in Figure 6,, which displays the growth rate of the 20 most unstable modes as a function of the position of their lareest extremum. | These two results are represented together in Figure \ref{fig:growth20}, which displays the growth rate of the 20 most unstable modes as a function of the position of their largest extremum. |
In comparison with the thermal continuum, slightly smaller values of the growth rate are obtained for the quasi-continuum modes. | In comparison with the thermal continuum, slightly smaller values of the growth rate are obtained for the quasi-continuum modes. |
The displacement of the largest extremum of the discrete modes toward larger values of r/R às their growth rate decreases is consistent with the behavior of the thermal continuum. | The displacement of the largest extremum of the discrete modes toward larger values of $r/R$ as their growth rate decreases is consistent with the behavior of the thermal continuum. |
From Figure 6 we also see that the solutions are closer to cach other as their order increases. | From Figure \ref{fig:growth20} we also see that the solutions are closer to each other as their order increases. |
This result can be explained by taking into account that theperpendicular thermal conductivity (Equation (7))) σκι-num7 | This result can be explained by taking into account that theperpendicular thermal conductivity (Equation \ref{eq:ionskappa}) )) is $\kappa_{\perp} \sim \rho_0^2 T^{-1/2}_0$. |
As we move toward larger r/R, Ty increases and po decreases in the equilibrium, meaning that κι gets smaller. | As we move toward larger $r/R$ , $T_0$ increases and $\rho_0$ decreases in the equilibrium, meaning that $\kappa_{\perp}$ gets smaller. |
Thus, the characteristic perpendicular spatial-scale decreases, causing the modes to cluster as r/R increases. | Thus, the characteristic perpendicular spatial-scale decreases, causing the modes to cluster as $r/R$ increases. |
To shed more light on the behavior of the eigenfunctions with κι. we perform the substitution kK,Ax, in the basic equations, with tan enhancing factor. | To shed more light on the behavior of the eigenfunctions with $\kappa_\perp$, we perform the substitution $\kappa_\perp \to \lambda \kappa_\perp$ in the basic equations, with $\lambda$ an enhancing factor. |
We can artificially increase the value Of x, by means of ,L and assess its influence on the eigenfunctions. | We can artificially increase the value of $\kappa_\perp$ by means of $\lambda$ and assess its influence on the eigenfunctions. |
We restrict ourselves to the most unstable mode. | We restrict ourselves to the most unstable mode. |
Figure 7((a) shows the temperature cigenfunction of the most unstable mode for different values of αἱ. | Figure \ref{fig:growth202}( (a) shows the temperature eigenfunction of the most unstable mode for different values of $\lambda$. |
Ast grows, the temperature cigenfunction becomes broader. | As $\lambda$ grows, the temperature eigenfunction becomes broader. |
To quantify this effect, we compute the width 6 of the maximum of the temperature perturbation measured at its half height. | To quantify this effect, we compute the width $\delta$ of the maximum of the temperature perturbation measured at its half height. |
The parameter 6 is related to the thickness of the conductive layer. | The parameter $\delta$ is related to the thickness of the conductive layer. |
Following the method by Sakuraietal.(1991) originally used for Alfvénn and slow resonances, VanderLinden(1993) obtained that the thickness of the conductive layer is proportional to Ky*. | Following the method by \citet{SGH91} originally used for Alfvénn and slow resonances, \citet{vanderlinden93} obtained that the thickness of the conductive layer is proportional to $\kappa_\perp^{1/3}$. |
In order to compare the analytical result of VanderLinden(1993) with our numerical computations, Figure 7((b) shows Ó/R versus the enhancing parameter 44.We see that the dependence of 6/R with Jt is consistent with a scaling law of .'34, pointing out that our numerical code works properly and recovers the behavior analytically predicted by VanderLinden(1993). | In order to compare the analytical result of \citet{vanderlinden93} with our numerical computations, Figure \ref{fig:growth202}( (b) shows $\delta/R$ versus the enhancing parameter $\lambda$.We see that the dependence of $\delta/R$ with $\lambda$ is consistent with a scaling law of $\lambda^{1/3}$, pointing out that our numerical code works properly and recovers the behavior analytically predicted by \citet{vanderlinden93}. |
We have also computed the cigenfunctions for other values of the azimuthal wavenumber in.We do not hàve obtained variations of the spectrum of quasi-continuum modes for different values of η. | We have also computed the eigenfunctions for other values of the azimuthal wavenumber $m$.We do not have obtained variations of the spectrum of quasi-continuum modes for different values of $m$. |
It is worth noting that for a= 0. the perturbations v; andB, are decoupled trom the remaining perturbations. while for mz0 all perturbations are coupled. | It is worth noting that for $m = 0$ , the perturbations $v_\varphi$ and$B_\varphi$ are decoupled from the remaining perturbations, while for $m \ne 0$ all perturbations are coupled. |
The temperature perturbation is independent of 1η. The effect of ini on the growth rate is studied in Section 5.. | The temperature perturbation is independent of $m$ The effect of $m$ on the growth rate is studied in Section \ref{sec:param}. |
the fact that the intrinsic CP in such a case is indeed close to zero. some additional CP can be produced by conversion of linear polarization (Sazonov1969:No-erdlinger 19758). | the fact that the intrinsic CP in such a case is indeed close to zero, some additional CP can be produced by conversion of linear polarization \citep{saz69,noe78}. |
. Iu terms of the Poincaré sphere. this situation corresponds to the normal modes axis pointing close to but not exactly iu the equatorial plane. | In terms of the Poincaré sphere, this situation corresponds to the normal modes axis pointing close to but not exactly in the equatorial plane. |
Therefore sole conversion of iutriusic linear polarization may occur provided that there is some imbalance in the number of electrons aud positrons. | Therefore some conversion of intrinsic linear polarization may occur provided that there is some imbalance in the number of electrons and positrons. |
Strong departures from node circularity. occur onlv when radiation propagates within a sinall anele ~vy,fv ofthe direction perpendicular to the magnetic field. where vpοόπιο. | Strong departures from mode circularity occur only when radiation propagates within a small angle $\sim\nu_{L}/\nu$ of the direction perpendicular to the magnetic field, where $\nu_{L}=eB/2\pi m_{e}c$. |
Therefore radiative. transfer is often performed in the quasi-lougitudinal (QL) approximation. | Therefore radiative transfer is often performed in the quasi-longitudinal (QL) approximation. |
Tf the normal modes are highly elliptical then the opposite. quasi-transverse (QT). limit applies (CiuzburgL961). | If the normal modes are highly elliptical then the opposite, quasi-transverse (QT), limit applies \citep{gin61}. |
Iu a typical observational situation it is usually assumed hat Faraday rotation within the source cannot be too aree. as this will lead to the suppression of linear larization. | In a typical observational situation it is usually assumed that Faraday rotation within the source cannot be too large, as this will lead to the suppression of linear polarization. |
However. this constraint does not preveut rotativitv from achieving large values locally as long as he mean rotativitv. Le. averaged over all directions of naenetic field along the line of sight. is indeed relatively σα], | However, this constraint does not prevent rotativity from achieving large values locally as long as the mean rotativity, i.e., averaged over all directions of magnetic field along the line of sight, is indeed relatively small. |
Such a situation may happen iu a turbulent plasma. | Such a situation may happen in a turbulent plasma. |
Sole effects of turbulence on polarization were discussed w Jones(1988) who neglected. a uniforin maguetic field component and by Wardleetal.(1998).. who xeseuted results for the case of a suall svuchrotrou depth. | Some effects of turbulence on polarization were discussed by \citet{jon88} who neglected a uniform magnetic field component and by \citet{war98}, who presented results for the case of a small synchrotron depth. |
Technically. the strong rotativity regime is equivalent to he QL limit aud in this paper we build our model ou this approxiuation. | Technically, the strong rotativity regime is equivalent to the QL limit and in this paper we build our model on this approximation. |
We consider a highly tangled magnetic field with a very πα. nies component which is required to determine the sign of circular polarization. | We consider a highly tangled magnetic field with a very small mean component which is required to determine the sign of circular polarization. |
Frou a theoretical view-point. we would expect some net poloidal maguetic field. either originating from the ceutral black hole or from the accretion disk. to be aligned prefercutially along the[um jet axis. | From a theoretical view-point, we would expect some net poloidal magnetic field, either originating from the central black hole or from the accretion disk, to be aligned preferentially along the jet axis. |
Specifically. from equipartition aud flux freezing arguments applied to a conical jet (BlaucdfordaudI&óniel1979) we eot fu2(pi2SDasxr |where p is the distance along the svuchrotrou cutting source aud the svinbols | and iL refer to magnetic fields parallel and perpendicular to the jet axis. respectively. | Specifically, from equipartition and flux freezing arguments applied to a conical jet \citep{bla79} we get $\langle B^{2}_{\|}\rangle^{1/2}\sim\langle
B^{2}_{\bot}\rangle^{1/2}\sim B_{\rm rms}\propto r^{-1}$ where $r$ is the distance along the synchrotron emitting source and the symbols $\|$ and $\bot$ refer to magnetic fields parallel and perpendicular to the jet axis, respectively. |
From the fiux- argument applied to the all parallel bias iu the inaguetie feld we obtain (Bi;~0 aud (By;xrey Dau where 0=B,/Bay.<1 is the ratio of the uniform and fluctuating components of the magnetic field. | From the flux-freezing argument applied to the small parallel bias in the magnetic field we obtain $\langle B_{\bot}\rangle\sim 0$ and $\langle B_{\|}\rangle\propto
r^{-2}\propto\delta B_{\rm rms}$ , where $\delta\equiv B_{u}/B_{\rm rms}\ll
1$ is the ratio of the uniform and fluctuating components of the magnetic field. |
We solve the radiative traustfer ofpolarized radiation im a turbulent plasiua by adopting transfer equatious for a piecewise homogeueous medium with a weakly anisotropic dielectric tensor (Sazonov1969:JonesaudODell. 1977a). | We solve the radiative transfer ofpolarized radiation in a turbulent plasma by adopting transfer equations for a piecewise homogeneous medium with a weakly anisotropic dielectric tensor \citep{saz69,jon77a}. . |
. Details of the trausfer equations are given iu the Appendix. | Details of the transfer equations are given in the Appendix. |
We asstune that the mean rotativitv por unit svuchrotron optical depth (Q2)=ὃς aud that (n20;=0 and fcos2a}=2pl. where 0<pxLois a parameter describing the polarization direction aud degree of order in the field. | We assume that the mean rotativity per unit synchrotron optical depth $\langle\zeta_{v}^{*}\rangle\equiv\delta\zeta$ and that $\langle\sin2\phi\rangle =
0$ and $\langle\cos2\phi\rangle =2p-1$ , where $0\leq p\leq 1$ is a parameter describing the polarization direction and degree of order in the field. |
We also asstme that circular absorptivity ος and circular emissivitv e, are both negligible. | We also assume that circular absorptivity $\zeta_{v}$ and circular emissivity $\epsilon_{v}$ are both negligible. |
Averaging the trausfer equations over orientatious of the magnetic feld. we obtain the following asvuiptotic expressions for large svuchrotrou optical Note that ος is not statistically independent frou [7 and Q due to the eradieut iu Faraday rotation across cach cell. | Averaging the transfer equations over orientations of the magnetic field, we obtain the following asymptotic expressions for large synchrotron optical Note that $\zeta_{v}^{*}$ is not statistically independent from $U$ and $Q$ due to the gradient in Faraday rotation across each cell. |
The correlation in eq. ( | The correlation in eq. ( |
2) then where ος and C denotes the fluctuating part of ο aud U. | 2) then where $\widetilde{\zeta}_{v}^{*}$ and $\widetilde{U}$ denotes the fluctuating part of $\zeta_{v}^{*}$ and $U$. |
An analogous relation holds for Q iu eq. ( | An analogous relation holds for $Q$ in eq. ( |
3). | 3). |
We ucelect the term (550) m eq. ( | We neglect the term $\langle\widetilde{\zeta}_{q}^{*}\widetilde{U}\rangle$ in eq. ( |
E) as convertibility is a 1uucli wealer function of plasmid piarzuneters than rotativitv. | 4) as convertibility is a much weaker function of plasma parameters than rotativity. |
It will be shown in Section L1.3 that the correlations (QU, aud (CQ teud to zero as the nuuberof field reversals aloug the line of sight increases aud This implies that the mean levels of circular aud linearpolarizations will also depend onthe nuuber of the field reversals along the line of sight. | It will be shown in Section 4.1.3 that the correlations $\langle\widetilde{\zeta}_{v}^{*}\widetilde{U}\rangle$ and $\langle\widetilde{\zeta}_{v}^{*}\widetilde{Q}\rangle$ tend to zero as the numberof field reversals along the line of sight increases and This implies that the mean levels of circular and linearpolarizations will also depend onthe number of the field reversals along the line of sight. |
Setting 7,=O/T. *,—UI md a, 2V/T. we eet mean normalized Stokes piriuneters from equations where Note | Setting $\overline{\pi}_{q}=\overline{Q}/\overline{I}$ , $\overline{\pi}_{u}=\overline{U}/\overline{I}$ and $\overline{\pi}_{v}=\overline{V}/\overline{I}$ , we get mean normalized Stokes parameters from equations where Note |
Due to the limited coverage of UINIDSS. only 198 have J- and Ix-band. photometry in 2ALASS and UIKIDSS. from which ISS are unalfected by saturation (/2 11. A7 9). | Due to the limited coverage of UKIDSS, only 198 have J- and K-band photometry in 2MASS and UKIDSS, from which 188 are unaffected by saturation $J>11$ , $K>9$ ). |
With LH and Ix the numbers are even lower. | With H and K the numbers are even lower. |
As can be seen in Fig. 3.. | As can be seen in Fig. \ref{f3}, |
left panel. three sources are strongly variable with di 0.5mmag. | left panel, three sources are strongly variable with $dK>0.5$ mag. |
Two of them show this level of variability in two bands: they are listed in Table 1.. | Two of them show this level of variability in two bands; they are listed in Table \ref{var}. |
Note that no band transformation was carried. out. for the UIXIDSS photometry in Fig. 3.. | Note that no band transformation was carried out for the UKIDSS photometry in Fig. \ref{f3}, |
because not all objects in this plot have the required colour information. | because not all objects in this plot have the required colour information. |
This causes some aclelitional scatter around the zeropoint in the diagram. but does not allect the selection of strongly variable objects. | This causes some additional scatter around the zeropoint in the diagram, but does not affect the selection of strongly variable objects. |
151 objects have usable J- and. Ix-band. photometry in PALASS ancl DIZNIS. which is plotted in Fig. 3.. | 151 objects have usable J- and K-band photometry in 2MASS and DENIS, which is plotted in Fig. \ref{f3}, , |
right panel. | right panel. |
4 of them exceed dA=0.5 mmae. 2 of them have also 0.5 and are included in Table 1L.. | 4 of them exceed $dK=0.5$ mag, 2 of them have also $dJ>0.5$ and are included in Table \ref{var}. |
The ONC is a crowded area. ancl all of the objects listed in Table 1. might. be allecteck by close neighbours. particularly in the 24LASS ancl DENIS images. | The ONC is a crowded area, and all of the objects listed in Table \ref{var} might be affected by close neighbours, particularly in the 2MASS and DENIS images. |
Thus. some of these objects might not be variable. | Thus, some of these objects might not be variable. |
Re-obscrvations with eood resolution are necessary to clarify their nature. | Re-observations with good resolution are necessary to clarify their nature. |
For the ONC we cannot probe the mid-infrared. excess for the sample. | For the ONC we cannot probe the mid-infrared excess for the sample. |
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