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Things are different if we consider an extended-Yang monopole. | Things are different if we consider an extended-Yang monopole. |
As shown in [9],, imposing spherical symmetry to a SO(4) bundle over R?—0 leaves four homotopically different possibilities. | As shown in \cite{DL}, imposing spherical symmetry to a $SO(4)$ bundle over $R^5-{0}$ leaves four homotopically different possibilities. |
So the number of charges is 4 in this case. | So the number of charges is 4 in this case. |
This is intimately related to the fact that the algebra of SO(4) is isomorphic to the Cartesian product of two copies of su(2), as can be visualized in its Dynkin diagram. | This is intimately related to the fact that the algebra of $SO(4)$ is isomorphic to the Cartesian product of two copies of $\mathfrak{su(2)}$, as can be visualized in its Dynkin diagram. |
In the brane picture, the isomorphism of the algebras together with the geometric engineering mechanism we have used along subsection (??)), suggests that the construction of the SO(4)- involves two vanishing 2-cycles on K3. | In the brane picture, the isomorphism of the algebras together with the geometric engineering mechanism we have used along subsection \ref{sec:SCOTYM}) ), suggests that the construction of the $SO(4)$ -monopole involves two vanishing 2-cycles on K3. |
Recall that in the ALE space, each vanishing cycle is an A, singularity where the D2-brane is wrapped. | Recall that in the ALE space, each vanishing cycle is an $A_1$ singularity where the D2-brane is wrapped. |
Now, two wrap a shrinking cycle each, and geometrically engineer a su(2) factor. | Now, two D2-branes wrap a shrinking cycle each, and geometrically engineer a $\mathfrak{su(2)}$ factor. |
The singularities are well and disconnected. | The singularities are well and disconnected. |
They are distinguishable. | They are distinguishable. |
Now, as in the Yang case, we wrap them with a D4-brane (see figure), which also wraps the of the K3 surface. | Now, as in the Yang case, we wrap them with a D4-brane (see figure), which also wraps the of the K3 surface. |
As before, the"one-way" wrap of the D4-brane is identified with the "other-way" wrap of the D4-antibrane, so only branes are considered. | As before, the“one-way” wrap of the D4-brane is identified with the “other-way” wrap of the $4$ -antibrane, so only branes are considered. |
Now, the fact that A; singularities are distinguishable rises the number of possible inequivalent configurations to 4. | Now, the fact that $A_1$ singularities are distinguishable rises the number of possible inequivalent configurations to 4. |
The homotopy group which labels the homotopically inequivalent | The homotopy group which labels the homotopically inequivalent |
corresponding to a virial temperature of 10* K or the local Jeans mass, whichever is higher. | corresponding to a virial temperature of $10^4$ K or the local Jeans mass, whichever is higher. |
In the neutral regions, since the Jeans mass is always low, the cut-off mass always corresponds to the virial temperature of 103 K. The minimum mass corresponds to the circular velocity of where µ is the mean molecular weight. | In the neutral regions, since the Jeans mass is always low, the cut-off mass always corresponds to the virial temperature of $10^4$ K. The minimum mass corresponds to the circular velocity of where $\mu$ is the mean molecular weight. |
For a temperature of £z104 K, the minimum circular velocity is +25 km s~*. | For a temperature of $\approx 10^4$ K, the minimum circular velocity is $\approx 25$ km $^{-1}$. |
Note that this value is comparable to values obtained in simulations (?) but is somewhat higher than that taken in the semi-analytic prescription of ?.. | Note that this value is comparable to values obtained in simulations \citep{2000ApJ...542..535G} but is somewhat higher than that taken in the semi-analytic prescription of \citet{2007MNRAS.377..285S}. |
We find that Mmin(z) increases with time taking values of =10° Mo at z©10 and &10° Mo at zc7. | We find that $M_\mathrm{min}(z)$ increases with time taking values of $\approx 10^7$ $_\odot$ at $z\approx 10$ and $\approx 10^8$ $_\odot$ at $z\approx 7$. |
In overdense regions the minimum mass is enhanced to about 1015 Mo. | In overdense regions the minimum mass is enhanced to about $10^{10}$ $_\odot$. |
Figure 5 shows the evolution of the minimum mass. | Figure \ref{mmin} shows the evolution of the minimum mass. |
The results for reionization and thermal histories within overdense regions are presented in this section. | The results for reionization and thermal histories within overdense regions are presented in this section. |
We first consider the effect of overdensity on reionization history for our fiducial model. | We first consider the effect of overdensity on reionization history for our fiducial model. |
As is well known, reionization proceeds differently in overdense regions. | As is well known, reionization proceeds differently in overdense regions. |
The solid lines in Figure 1 show the evolution of the photoionisation rate, temperature in ionised regions, star formation rate density and the volume filling factor of ionised regions in an overdense region with size Ry=1.482 Mpc and linearly extrapolated overdensity 6=8.86. | The solid lines in Figure \ref{BestFitReionizationModel} show the evolution of the photoionisation rate, temperature in ionised regions, star formation rate density and the volume filling factor of ionised regions in an overdense region with size $R_L=1.482$ Mpc and linearly extrapolated overdensity $\delta=8.86$. |
This corresponds to the HUDF WFC3/IR field centred at the brightest source in ?.. ( | This corresponds to the HUDF WFC3/IR field centred at the brightest source in \citet{2010ApJ...709L.133B}. . ( |
See Section 2.2..) | See Section \ref{biassec}. .) |
Clearly while the average region is completely ionised at z&6, the biased region is ionised much earlier, at 2.ο7.5. | Clearly while the average region is completely ionised at $z\approx 6$, the biased region is ionised much earlier, at $z\approx 7.5$. |
This result agrees with ?,, although note that unlike that work, here we calculate the clumping factor from a physical model for inhomogeneities. | This result agrees with \citet{2007MNRAS.375.1034W}, although note that unlike that work, here we calculate the clumping factor from a physical model for inhomogeneities. |
The reason for early reionization in overdense regions is the enhanced number of sources, which is clear from the plots of photoionisation rate and the star-formation rate, both of which are 5 times higher than the corresponding globally averaged values. | The reason for early reionization in overdense regions is the enhanced number of sources, which is clear from the plots of photoionisation rate and the star-formation rate, both of which are $\sim 5$ times higher than the corresponding globally averaged values. |
However, these overdense regions have more recombinations, which results in enhanced temperatures as is clear from the top right panel. | However, these overdense regions have more recombinations, which results in enhanced temperatures as is clear from the top right panel. |
This results in enhanced negative radiative feedback which will suppress star formation in low mass galaxies and hence affect the shape of the luminosity function. | This results in enhanced negative radiative feedback which will suppress star formation in low mass galaxies and hence affect the shape of the luminosity function. |
In fact, for the average case, haloes in ionised regions with masses below 10° Mo cannot form stars, whereas this cutoff mass rises to close to 10!?Mo in the overdense case. | In fact, for the average case, haloes in ionised regions with masses below $10^8$ $_\odot$ cannot form stars, whereas this cutoff mass rises to close to $10^{10}$$_\odot$ in the overdense case. |
Clearly feedback is enhanced in overdense regions. | Clearly feedback is enhanced in overdense regions. |
These values are based on fits to data for a sample of 19 Taurus fiekl stars in the extinction range 5«Ay<24 mag (see. e.g. Figure 4 of Whittet 22007). | These values are based on fits to data for a sample of 13 Taurus field stars in the extinction range $5<\av<24$ mag (see, e.g, Figure 4 of Whittet 2007). |
The majority of stars in our sample lack the spectral data that would enable direct measurement of ice column densities: in these cases. we use Equation (3) with the above values of q and A," to estimate the contributions of solid CO and (to the total column density in Equation (2) from the ly values for field stars. | The majority of stars in our sample lack the spectral data that would enable direct measurement of ice column densities: in these cases, we use Equation (3) with the above values of $q$ and $\av^{~0}$ to estimate the contributions of solid CO and to the total column density in Equation (2) from the $\av$ values for field stars. |
Resulting values are listed in Table 1. | Resulting values are listed in Table 1. |
We consider the well-established Nice versus dy correlations to be sufficiently strong to justilv this approach for field stars. but it may not be appropriate for YSOs. | We consider the well-established $N_{\rm \,ice}$ versus $\av$ correlations to be sufficiently strong to justify this approach for field stars, but it may not be appropriate for YSOs. |
For this reason. total CO column densities are caleulated for YSOs onlv in cases where direct measurements of both. N(COJ; and N(COs);4 are available [rom the literature: only (wo out of ten in our sample (J043955144-2545020 ancl JOJ4400800-2-2605253) satisfy this requirement (Cook 22010). | For this reason, total CO column densities are calculated for YSOs only in cases where direct measurements of both $N({\rm CO})_{\rm ice}$ and $N({\rm CO}_2)_{\rm ice}$ are available from the literature: only two out of ten in our sample (J04395574+2545020 and J04400800+2605253) satisfy this requirement (Cook 2010). |
The resulting plot of IN(CO), versus Ao is shown in 2. | The resulting plot of $N({\rm CO})_{\rm total}$ versus $\av$ is shown in 2. |
The overall distribution ol points is clearly consistent wilh the linear least-scquares fit (solid line). vielding a correlation only marginally different. from that predicted. by Equation (1). | The overall distribution of points is clearly consistent with the linear least-squares fit (solid line), yielding a correlation only marginally different from that predicted by Equation (1). |
This corresponds to an abundance Noo/Ny~5.3x10.7 at extinctions above the threshold. assuming the canonical value of NuAve&19x1074emπας! for the total hydrogen gas to extinction ratio (Bohlin 11973). | This corresponds to an abundance $N_{\rm CO}/N_{\rm H} \sim 5.3\times 10^{-5}$ at extinctions above the threshold, assuming the canonical value of $N_{\rm H}/\av \approx 1.9\times 10^{21}~{\rm cm^{-2}\,mag^{-1}}$ for the total hydrogen gas to extinction ratio (Bohlin 1978). |
The CO depletion factor is defined such that 0ος)<1. the lower and upper bounds corresponding to all CO in easeous and solid forms. respectively. | The CO depletion factor is defined such that $0\le\delta({\rm CO})\le 1$, the lower and upper bounds corresponding to all CO in gaseous and solid forms, respectively. |
This quantitv was calculated [or each line of sight in our sample from the data used to construct Figures 1 and 2. and the results plotted against ely linin 3. | This quantity was calculated for each line of sight in our sample from the data used to construct Figures 1 and 2, and the results plotted against $\av$ in 3. |
The curveeurve iis caleulated]culated in t1(he same1 wav bvby ratioing the sigmoidal fit [rotLom 1l with the linear fit fom 2. | The curve is calculated in the same way by ratioing the sigmoidal fit from 1 with the linear fit from 2. |
In 5general. the data in 3 are consistent with a monotonic increase in 0(CO) from zero at low extinction (lyS 5) to ~0.6 at the hieh end of the observed range. | In general, the data in 3 are consistent with a monotonic increase in $\delta({\rm CO})$ from zero at low extinction $\av \la 5$ ) to $\sim 0.6$ at the high end of the observed range. |
The scatter appears somewhat asvimnmneltric because il arises primarily in (he denominator of Equation (6): outliers well above the trend arise because a few lines of sieht with intermediate extinction have unexpectedly low gaseous CO column densities for their ον. values. | The scatter appears somewhat asymmetric because it arises primarily in the denominator of Equation (6); outliers well above the trend arise because a few lines of sight with intermediate extinction have unexpectedly low gaseous CO column densities for their $\av$ values. |
National Natural Science Foundation Nos 10473012. 10573020. 10633020. 10673012 and 10603006: and by National Basic Research Program of China (973 Program) No. | National Natural Science Foundation Nos 10473012, 10573020, 10633020, 10673012 and 10603006; and by National Basic Research Program of China (973 Program) No. |
2007CB815403. | 2007CB815403. |
RdG acknowledges partial financial support from the Royal Society in the form of a UK-China International Joint Project. | RdG acknowledges partial financial support from the Royal Society in the form of a UK-China International Joint Project. |
Speetroscopic. surveys of. radio. sources at [ux density. levels lower than those of the 3€ catalogue. and its various. .LIL (e.g.. Rileyκ &: 1983.. hereafter. .steep are essential to. provide coverage⋅ of the∢⋅ redshift-racdio ».inaged plane. | Spectroscopic surveys of radio sources at flux density levels much lower than those of the 3C catalogue and its various revisions Laing, Riley Longair 1983, hereafter LRL) are essential to provide coverage of the redshift-radio luminosity plane. |
. Such coverage. is required. to. establish thehave . cosmic evolution of these sources both in number density and physical properties such as size ancl structure. | Such coverage is required to establish the cosmic evolution of these sources both in number density and physical properties such as size and structure. |
Over the past two decades. several [ux-limited. samples selected. at low radio frequency. (ancl hence directly comparable with in being. selected.. primarily on. the basis of. unbeaumed⋅ much spectrum radio lobe.. emission) have⋅ been defined. aud↔ revisions in. the. radio and. optical. | Over the past two decades, several flux-limited samples selected at low radio frequency (and hence directly comparable with LRL in being selected primarily on the basis of unbeamed steep spectrum radio lobe emission) have been defined and imaged in the radio and optical. |
Only. recently. however. LRL) redshifts have. been obtained for. a⊲⋠⋅ significant fraction⋅⋠ IuminosityMEN the. radio sources. | Only recently, however, have redshifts have been obtained for a significant fraction of the radio sources. |
mE This .paper describes spectroscopic. of observations of the 38-MlIz SC North Ecliptie Cap (NEC) sample of Lacy. Hawlings Warner (1992: hereafter Paper 1) and Lacy et 11993. 1999a (hereafter. Papers LL and | This paper describes spectroscopic observations of the 38-MHz 8C North Ecliptic Cap (NEC) sample of Lacy, Rawlings Warner (1992; hereafter Paper I) and Lacy et 1993, 1999a (hereafter Papers II and |
special interest is the ealactie center region. in which it was clearly proven (hat its flat raclio spectrum is not due to self absorption (Leschetal.1988:Yusel-Zaclel1989). | special interest is the galactic center region, in which it was clearly proven that its flat radio spectrum is not due to self absorption \citep{lesch88, yus89}. |
. The evidence for flat. optically. (hin radio spectra in several active galactic nuclei has been presented by Ilughesetal.(1989);Melrose(1996);Wang(1997). | The evidence for flat, optically thin radio spectra in several active galactic nuclei has been presented by \citet{hugh89, mel96, wang97}. |
.. All these authors consider different Fermi-like acceleration schemes (either multiple shocks or second order Fermi mechanism) to be responsible for the hardness of the electron energy spectra. | All these authors consider different Fermi-like acceleration schemes (either multiple shocks or second order Fermi mechanism) to be responsible for the hardness of the electron energy spectra. |
In the present contribution it is suggested that optically thin svnchrotron emission due to hard electron spectra produced in magnetic reconnection regions can explain (he nature of the flat/inverted spectrum radio sources. | In the present contribution it is suggested that optically thin synchrotron emission due to hard electron spectra produced in magnetic reconnection regions can explain the nature of the flat/inverted spectrum radio sources. |
Anv acceleration model of charged particles must ultimately be based on the energy gain of the particles in electric fields. | Any acceleration model of charged particles must ultimately be based on the energy gain of the particles in electric fields. |
Llowever. the dvnamics of the respective plasma processes involved can be «uite dillerent. | However, the dynamics of the respective plasma processes involved can be quite different. |
The principal acceleration scenarios (reviews are given. e.g. bv Schlickeiser(1986):Kirk(1994):Ixuijpers (1996))) maa be divided in the Fermi I and Fermi H mechanisms. shock-drilt acceleration (which in fact can be considered as an example of Fermi I acceleration). dilfusive shock acceleration. plasma wave acceleration. electrostatic double lavers and the energization of particles in reconnection events. | The principal acceleration scenarios (reviews are given, e.g., by \citet{sch86, kir94, kui96}) ) may be divided in the Fermi I and Fermi II mechanisms, shock-drift acceleration (which in fact can be considered as an example of Fermi I acceleration), diffusive shock acceleration, plasma wave acceleration, electrostatic double layers and the energization of particles in reconnection events. |
Inn contrast to the other classic mechanisms it was only more recently that reconnection was discussed as a process that does not only convert magnetic fiekl energv to plasma bulk motion and heating but also plavs an important role in (he context of fast particle acceleration 19990).. | In contrast to the other 'classic' mechanisms it was only more recently that reconnection was discussed as a process that does not only convert magnetic field energy to plasma bulk motion and heating but also plays an important role in the context of fast particle acceleration \citep{sch91,
vek95, lesch98, sch98, lit97, lit99}. |
In the context of shock acceleration much elaborated work has been done concerning the shape and evolution of the energy distribution of the accelerated particles (e.g. KuijpersAehterberg(2000) ancl ref. | In the context of shock acceleration much elaborated work has been done concerning the shape and evolution of the energy distribution of the accelerated particles (e.g. \citet{kui96,
ach00} and ref. |
therein). | therein). |
One may note that in the diffusive shock scenarios the injection problem appears. ie. one has (o assume a hieh-enerev electrons {ο start with. | One may note that in the diffusive shock scenarios the injection problem appears, i.e. one has to assume a high-energy electrons to start with. |
Within many applications only the moclilication of power law spectra by shocks which are assumed [or the injected. particle population in the first place are investigated. | Within many applications only the modification of power law spectra by shocks which are assumed for the injected particle population in the first place are investigated. |
What is more. verv [lat spectra are verv hard to explain in the context of simple shock acceleration (Melrose1996). | What is more, very flat spectra are very hard to explain in the context of simple shock acceleration \citep{mel96}. |
. Nothing comparable to the detailed studies on the energy spectra of shock accelerated parücles has been done for the reconnection scenario. | Nothing comparable to the detailed studies on the energy spectra of shock accelerated particles has been done for the reconnection scenario. |
In this contribution we analvze the enerev spectra (that can be expected to be caused by high-energv particles accelerated in de | In this contribution we analyze the energy spectra that can be expected to be caused by high-energy particles accelerated in dc |
in order o define the filters. it nüeht not be that easy in practice since we can not separate the sigual frou the noise. | in order to define the filters, it might not be that easy in practice since we can not separate the signal from the noise. |
We will herefore ai at making a joint estimation of the signal aud the noise. | We will therefore aim at making a joint estimation of the signal and the noise. |
This has been pioneered] recently by (FerreiraandJaffe2000) and uplemented independentlyby (Prunetetal.2000). | This has been pioneered recently by \cite{FeJa00} and implemented independentlyby \cite{PrNe00}. |
. The latter imuplenieutation is rather straightforwu in our particular case since it just implies reevaluatiug the filters after a uuuber of iterations. giveu the (current) estimation of the signal map aud thus of the signal data stream. | The latter implementation is rather straightforward in our particular case since it just implies reevaluating the filters after a number of iterations, given the (current) estimation of the signal map and thus of the signal data stream. |
Nevertheless its non-obvious convergence properties have to be studied carefully through. simulations. | Nevertheless its non-obvious convergence properties have to be studied carefully through simulations. |
Maláug use of (16)) our evaluation of the noise timeline »" at the at” iteration aud at level max is “TE Pd. | Making use of \ref{noisedef}) ) our evaluation of the noise timeline $\hat{n}^n$ at the $n^{th}$ iteration and at level max is ^n = d + P d). |
Then we compute its spectrum aud (re) define the required filters. | Then we compute its spectrum and (re-) define the required filters. |
We then eo through several nmulti-egrid eveles (5 in the above demonstrated case) before re-evaluating the noise stream. | We then go through several multi-grid cycles (5 in the above demonstrated case) before re-evaluating the noise stream. |
Very few evaluations of he noise are needed before getting a couverged power spectitun (around 2). | Very few evaluations of the noise are needed before getting a converged power spectrum (around 2). |
Iu such an implementation. no i0ise priors at all are assumed. | In such an implementation, no noise priors at all are assumed. |
This is illustrated ou one articular worked out example iu the case of a { hours ARCTIIEOPS like flight (110re detailed considerations will ος cliscusseclL somewhere else). | This is illustrated on one particular worked out example in the case of a 4 hours ARCHEOPS like flight (more detailed considerations will be discussed somewhere else). |
To reduce the παο of deerees of freedom we bin the evaluated noise power spectra using a coustant logarithmic biuniug (Aluf=A15 iu our case) for f.x2μμ and a constaut inear biuniug (Af=0.08Tz iu our case) for üeher frequency. | To reduce the number of degrees of freedom we bin the evaluated noise power spectrum using a constant logarithmic binning $\Delta \ln f=0.15$ in our case) for $f \leq 2~f_{knee}$ and a constant linear binning $\Delta~f~=~0.08~\mathrm{Hz}$ in our case) for higher frequency. |
The figure & shows the eeuuine aud evaluated noise power spectrum. | The figure \ref{noise_eval_1} shows the genuine and evaluated noise power spectrum. |
The initial noise power spectrun was a realistic one POF)x(1GeuccéFY) o Which we added some all perturbations (the two visible mns) to test the method. | The initial noise power spectrum was a realistic one $P(f)~\propto~(1+({f_{knee}/f})^{\alpha}) \displaystyle$ to which we added some small perturbations (the two visible bumps) to test the method. |
Note the small bias ALOTwound the elescopescope spin frequency.frequency atat. faisfei,=0.05ITz0.05IIz: his is illustrative of the difficulties we fuudiueutallv face o separate signal and noise at this particular frequency hrough equation 16)) | Note the small bias around the telescope spin frequency at $f_{spin} = 0.05 \mathrm{Hz}$: this is illustrative of the difficulties we fundamentally face to separate signal and noise at this particular frequency through equation \ref{noisedef}) ). |
Naturally. this bias was not xesent in the case demoustrated on figure 5 where weassunied a prior knowledge of the spectrim. | Naturally, this bias was not present in the case demonstrated on figure \ref{spec_rec}
where weassumed a prior knowledge of the spectrum. |
This possible vias forced us to work with a coarser binning (Alnf=1.) in the 1/f xwt of the spectrum till the convergence is reached. we evaluate the noise power spectrum with he previousv meutioned binning only at the las step. | This possible bias forced us to work with a coarser binning $\Delta \ln f=1.$ ) in the $1/f$ part of the spectrum till the convergence is reached, we evaluate the noise power spectrum with the previously mentioned binning only at the last step. |
Procecding us way. the convergeuce towards the cOrrect spectrin is |oth. fast (3 noise evaluations) aud stale. | Proceeding this way, the convergence towards the correct spectrum is both fast $3$ noise evaluations) and stable. |
Secoud. the output of any map-making should coutaim as well au evaluation of the map noise covariance matrix (APN14)t, | Second, the output of any map-making should contain as well an evaluation of the map noise covariance matrix $(A^T N^{-1}
A)^{-1}$. |
Civeu such a fast algorithi and given an evaluation of the power spectrum. it is natural to obtain it through a Monte-Carlo algonritlun fueled with various realizatious of the noise timeline generated usimg the evaluated power spectrum. | Given such a fast algorithm and given an evaluation of the power spectrum, it is natural to obtain it through a Monte-Carlo algorithm fueled with various realizations of the noise timeline generated using the evaluated power spectrum. |
This part will be preseuted iu a future work. | This part will be presented in a future work. |
However we illustrate it very briefly by a very rough C, determination (which is iu no wav iu appropriate C; estimate). | However we illustrate it very briefly by a very rough $C_{\ell}$ determination (which is in no way an appropriate $C_{\ell}$ estimate). |
To this purpose we perform a oue dav ToplIat like simulation including only the CAIB signal plus the noise. | To this purpose we perform a one day TopHat like simulation including only the CMB signal plus the noise. |
From this data stream we obtain an “optimal” signal map as well as an evaluation of the noise power spectrum using the previously described algoritlin. | From this data stream we obtain an “optimal” signal map as well as an evaluation of the noise power spectrum using the previously described algorithm. |
With the help of the routine of the TEAL?ALDPix packageιο we calculatelculate tlthis way a roughgh €,C7"gral | With the help of the routine of the HEALPix package we calculate this way a rough $C_{\ell}^{signal}$. |
"Ung he estimated noise power spectrum we generate LO realisations of the noise aud get couscquently LO “optimal” noise maps. | Using the estimated noise power spectrum we generate $10$ realisations of the noise and get consequently $10$ “optimal” noise maps. |
For cach of them we measure as before C, and average them to obtain C"nois . | For each of them we measure as before $C_{\ell}$ and average them to obtain $C_{\ell}^{noise}$ . |
In order to debiase the signal )ower spectrum recovered in this wav. we substract CPO to 6"signalt . | In order to debiase the signal power spectrum recovered in this way, we substract $C_{\ell}^{noise}$ to $C_{\ell}^{signal}$ . |
The power spectrum obtained im this | The power spectrum obtained in this |
most of these objects are less than half the radius of Jupiter. which indicates that they. are al most Neptunesize (Dorucki et al. | most of these objects are less than half the radius of Jupiter, which indicates that they are at most Neptune–size (Borucki et al. |
2011). | 2011). |
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