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The ratio of the FUR emission and radio emission will also allow is to investigate the physical origin and spatial clistribution of the energy sources in the detected objects in the same way that VLA maps have been central to our understanding of the origin of LRAS SOULCCS. | The ratio of the FIR emission and radio emission will also allow is to investigate the physical origin and spatial distribution of the energy sources in the detected objects in the same way that VLA maps have been central to our understanding of the origin of IRAS sources. |
Finally. this survey. due to its cepth ancl extension. is very important also as radio survey in its own right. | Finally, this survey, due to its depth and extension, is very important also as radio survey in its own right. |
In fact. the selected. sample is large ancl deep enough to constitute a statistically significant sample of sub-mJv. raclio sources. whose nature and characteristics are still a major topic in observational cosmology (sce Winclhorst. Mathis Neuschaefer 1990. Fomalont et al. | In fact, the selected sample is large and deep enough to constitute a statistically significant sample of sub-mJy radio sources, whose nature and characteristics are still a major topic in observational cosmology (see Windhorst, Mathis Neuschaefer 1990, Fomalont et al. |
1991. Rowan-Robinson et al. | 1991, Rowan-Robinson et al. |
1993. Ciruppioni et al. | 1993, Gruppioni et al. |
1997) The VLA €configuration and the observing frequeney of 1 Giz give the optimum. resolution to acquire the kind of radio data that we need. | 1997) The VLA C–configuration and the observing frequency of 1.4 GHz give the optimum resolution to acquire the kind of radio data that we need. |
Whilst. less prone to surface rightness effects 16 VLA D configuration is imitecd at the [uxes we wish to attain (the 5 σ confusion imit in D configuration is 0.4 mv/beam) | Whilst less prone to surface brightness effects , the VLA D configuration is confusion-limited at the fluxes we wish to attain (the 5 $\sigma$ confusion limit in D configuration is 0.4 mJy/beam). |
With the C configuration and a frequency of 1.4 (αλ the synthesized xam size (Pull Width at Hal Power. FWILP) is 215 arcesec. | With the C configuration and a frequency of 1.4 GHz the synthesized beam size (Full Width at Half Power, FWHP) is $\sim$ 15 arcsec. |
"The well-defined svnthesized beam of the VLA should enable us to pinpoint optical identifications to 1 aresec. except for he asymmetric multi-components sources. | The well-defined synthesized beam of the VLA should enable us to pinpoint optical identifications to 1 arcsec, except for the asymmetric multi-components sources. |
The frequency of 1.4 Giz was chosen because at this frequency the ENCLIP of he VLA primary bean is 31 aremin. | The frequency of 1.4 GHz was chosen because at this frequency the FWHP of the VLA primary beam is 31 arcmin. |
This allow us to cover he ELAS field with a relative small number of pointing centers. | This allow us to cover the ELAIS field with a relative small number of pointing centers. |
In fact it is possible to obtain a mosaic map with nearly uniform sensitivity if the separation is 31 V3 22 arcmin. | In fact it is possible to obtain a mosaic map with nearly uniform sensitivity if the separation is 31 / $\sqrt{2}$ $\sim$ 22 arcmin. |
Moreover. at 1.4 Gllz there will be contributions from both the steep and flat spectrum population of radio SOULCCS. | Moreover, at 1.4 GHz there will be contributions from both the steep and flat spectrum population of radio sources. |
Our observations are mace in spectral line mode using two cdilferent. LF channels centered. at 1.3649. Cllz (1E1) and 1.4352 CGIIZ(1E2). | Our observations are made in spectral line mode using two different IF channels centered at 1.3649 GHz (IF1) and 1.4352 GHz(IF2). |
Each HE channel has a bandwidth of 18.75 MlIz. which is subcdivided into 7 spectral line channels evenly spaced in frequency across the bandwidth of the input Ik channel. | Each IF channel has a bandwidth of 18.75 MHz, which is subdivided into 7 spectral line channels evenly spaced in frequency across the bandwidth of the input IF channel. |
Pherefore. we have a total of 14 spectral line channels (7 for cach IE) with a bandwidth of 2.68 Mllz each. | Therefore, we have a total of 14 spectral line channels (7 for each IF) with a bandwidth of 2.68 MHz each. |
We decided to use the line moce in order to facilitate wide field mapping and avoid the elfect of interference. | We decided to use the line mode in order to facilitate wide field mapping and avoid the effect of interference. |
The total bancwidth available is thus 37.5 Mllz. narrower than the 50MLIz used in continuum moce. | The total bandwidth available is thus 37.5 MHz, narrower than the 50MHz used in continuum mode. |
A narrower bandwidth means à worse sensitivity. | A narrower bandwidth means a worse sensitivity. |
In our case we lose about ~25% in sensitivity or in signal to noise near the pointing centers because the total bandwidth. is of that. in the continuum mode. | In our case we lose about $\sim$ in sensitivity or in signal to noise near the pointing centers because the total bandwidth is of that in the continuum mode. |
However. we considerably recluce the chromatic aberration (bandwidth smearing). which reduces the area covered by cach pointing in continuum. mocle. | However, we considerably reduce the chromatic aberration (bandwidth smearing), which reduces the area covered by each pointing in continuum mode. |
In addition. the line mode is less susceptible to. narrow interference noise spikes. since one only. needs to excise thechannel that is allectecl rather than loosing the whole LF | In addition, the line mode is less susceptible to narrow interference noise spikes, since one only needs to excise thechannel that is affected rather than loosing the whole IF |
ol the values given in Table 1. | of the values given in Table 1. |
In the interest of clarity. however. the MOS data have not been plotted in Figure 1. | In the interest of clarity, however, the MOS data have not been plotted in Figure 1. |
Inspection of the distribution of the resulting net counts reveals a rather weak continuum. the possible emission line that prompted. the detection. and an excess of counts al high energies. | Inspection of the distribution of the resulting net counts reveals a rather weak continuum, the possible emission line that prompted the detection, and an excess of counts at high energies. |
All three sources seem (o be characterized by an X-ray spectrum consisting of a two component model: a “leaky absorbed” power law continuum plus an emission line. | All three sources seem to be characterized by an X-ray spectrum consisting of a two component model: a “leaky absorbed" power law continuum plus an emission line. |
This is twpical of absorbed. AGN and thus suggests that these three sources are indeed. ACN. | This is typical of absorbed AGN and thus suggests that these three sources are indeed AGN. |
Although this is not the first time that an AGN is recognized as such ancl classified cdirectlv from the X-ray data (e.g. ANJ22544-1146. Della Ceca et al.. | Although this is not the first time that an AGN is recognized as such and classified directly from the X-ray data (e.g. AXJ2254+1146, Della Ceca et al., |
2000). to our knowledge. it is (he first me that (his happens bevond the local universe. | 2000), to our knowledge, it is the first time that this happens beyond the local universe. |
In Figure 1 (a through c) we report the X-ray spectrum of the three sources ancl the distribution of the total counts (inset) in the 3-D cells. which has led to the line detection. | In Figure 1 (a through c) we report the X-ray spectrum of the three sources and the distribution of the total counts (inset) in the 3-D cells, which has led to the line detection. |
From the position of the emission line. and assuming (hat it is due to cold Fe at 6.4 keV. il is possible to derive. directly from the X-ray data. the redshift of (he sources. | From the position of the emission line, and assuming that it is due to cold Fe at 6.4 keV, it is possible to derive, directly from the X-ray data, the redshift of the sources. |
The values are reported in Table 1 where the basic X-ray. properties of these Ciree sources are summarize. | The values are reported in Table 1 where the basic X-ray properties of these three sources are summarized. |
We stress that the values derived should be considered as indicative given the very low statistics involved (the (11ος sources have of the order of 50 net counts each in the Epic-pn detector). | We stress that the values derived should be considered as indicative given the very low statistics involved (the three sources have of the order of 50 net counts each in the Epic-pn detector). |
In the fitting procedure. we did not apply Occam's razor. rather we have assumed aà reasonable model (see above). and determined a set of values that well describe the data. | In the fitting procedure, we did not apply Occam's razor, rather we have assumed a reasonable model (see above), and determined a set of values that well describe the data. |
This is why no formal errors are quoted on the derived cuantities. | This is why no formal errors are quoted on the derived quantities. |
Inspection of deep optical material reveals (he presence of 1-2 candidates consistent (on positional ground) with being (he optical counterparts of (he X-ray sources. | Inspection of deep optical material reveals the presence of $-$ 2 candidates consistent (on positional ground) with being the optical counterparts of the X-ray sources. |
Their magnitudes are in the range 22.0—22.5. | Their magnitudes are in the range $-$ 23.5. |
Considering. for each X-ray source. the brightest candidate. the resulting log(F,/ F,,,) are in the range 1.2—1.8. | Considering, for each X-ray source, the brightest candidate, the resulting $F_{x}/F_{opt}$ ) are in the range $\sim 1.2-1.8$. |
These values are typical of absorbed AGN (see. among others. Fiore et al. | These values are typical of absorbed AGN (see, among others, Fiore et al. |
2003 and Della Ceca et al. | 2003 and Della Ceca et al. |
2004) ancl thus further support our proposed identifications. | 2004) and thus further support our proposed identifications. |
Optical spectroscopy is of course needed to validate these results and has been proposed. together with follow up NMM-Newton observations. | Optical spectroscopy is of course needed to validate these results and has been proposed, together with follow up XMM-Newton observations. |
The results presented here are very preliminary. | The results presented here are very preliminary. |
We have no doubts about the reality of the sources and we are confident on the presence of the X-ray. emission line in (he source spectra. | We have no doubts about the reality of the sources and we are confident on the presence of the X-ray emission line in the source spectra. |
Three objects are too few to derive "general properties”. | Three objects are too few to derive “general properties". |
Also. we still have to determine the complex visibility function of our novel algorithm. the volume investigated for a given line luminositv/EW. (he sensitivity of our search as a functüon of the spectral | Also, we still have to determine the complex visibility function of our novel algorithm, the volume investigated for a given line luminosity/EW, the sensitivity of our search as a function of the spectral |
Iu this study we ideutifv for the first time the contributions to the misaliguiment of the maenetic field. in terms of optimized poteutial field) models. non-poteutialitv due to electric curents. and stereoscopic maneulation errors. | In this study we identify for the first time the contributions to the misalignment of the magnetic field, in terms of optimized potential field models, non-potentiality due to electric currents, and stereoscopic triangulation errors. |
These results open up a umber of new avenues to inprove theoretical iiodeliug of the coronal magnetic feld. | These results open up a number of new avenues to improve theoretical modeling of the coronal magnetic field. |
First of all. optimized potential Seld models can be found that represeut a suitable ower boundary condition at the base of the force-free corona. which provides a less computiug-expoeusive uethod than nonlinear force-free codes. | First of all, optimized potential field models can be found that represent a suitable lower boundary condition at the base of the force-free corona, which provides a less computing-expensive method than nonlinear force-free codes. |
Second. methods cau be developed that allow us to localize electric currents in the non-force-free photophere and chromosphere. | Second, methods can be developed that allow us to localize electric currents in the non-force-free photophere and chromosphere. |
Third. the iuisaligniieut angle can be used as a sensitive paraiucter to probe the evolution of current dissipation. energy. build-up im form of non-potenutial uaenetic enerev in different quiesceuct aud flaring zones of active regions. | Third, the misalignment angle can be used as a sensitive parameter to probe the evolution of current dissipation, energy build-up in form of non-potential magnetic energy in different quiescenct and flaring zones of active regions. |
The high-resolution maguctic field data from inode aud.Observatory provide excellent opportunities to obtain better heoretical models of the coronal magneticOo field usingOo our bootstrappingC» method. which is uot restricted to stereoscopic data oulv. but can also be applied to sinele-spacecratt observations. | The high-resolution magnetic field data from Hinode and provide excellent opportunities to obtain better theoretical models of the coronal magnetic field using our bootstrapping method, which is not restricted to stereoscopic data only, but can also be applied to single-spacecraft observations. |
Acknowledecments: We are grateful to helpful discussions with Mare. DeRosa and Allen Cuv. | Acknowledgements: We are grateful to helpful discussions with Marc DeRosa and Allen Gary. |
This work was partially supported by the NASA coutract NAS5-38099 of the TRACE mission aud by NASA STEREO under NRL contract NOOL73-02-C-2035. | This work was partially supported by the NASA contract NAS5-38099 of the TRACE mission and by NASA STEREO under NRL contract N00173-02-C-2035. |
The STEREO/SECCII data used here are produced by an international consortium of NRL. LAISAL. RAL. MPI. ISAS. aud NASA. | The STEREO/SECCHI data used here are produced by an international consortium of NRL, LMSAL, RAL, MPI, ISAS, and NASA. |
The MDI/SOoIIO data were produced by the MDI Team at Stanford Universit | The MDI/SoHO data were produced by the MDI Team at Stanford University and NASA. |
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|
that are either taken from the Millennium LE simulation (for haloes anc subhaloes with m10hAL. ). or generated using the Monte-Carlo method assuming a Sheth-Tormen mass function (for haloes with m:dh TALL). | that are either taken from the Millennium II simulation (for haloes and subhaloes with $m>10^8 h^{-1}M_{\odot}$ ), or generated using the Monte-Carlo method assuming a Sheth-Tormen mass function (for haloes with $m\geqslant10^6
h^{-1}M_{\odot}$ ). |
We use DU), the probability for the cusp-caustic relation. és. to be larger than or equal to 0.187 — the smallest. value of Afi measured. for euspecaustic svstenis o date (for the quasar D1422) over all realizations with Adx90 as a statistical measure of the. cusp-caustic violation probability. | We use $P^{90}(\Rcusp^{0.187})$, the probability for the cusp-caustic relation, $\Rcusp$, to be larger than or equal to 0.187 – the smallest value of $\Rcusp$ measured for cusp-caustic systems to date (for the quasar B1422) – over all realizations with $\Delta\theta
\leqslant 90^{\circ}$, as a statistical measure of the cusp-caustic violation probability. |
We have found that the mean violation obabilitv from. intervening haloes depends: strongly. on heir density. profiles. | We have found that the mean violation probability from intervening haloes depends strongly on their density profiles. |
7 assumed singular isothermal spheres for line-of-sight ialoes and find that they only contribute to 5104 of the otal perturbation. | \citet{Chen2003} assumed singular isothermal spheres for line-of-sight haloes and find that they only contribute to $\leqslant 10 \%$ of the total perturbation. |
Assuming the same halo density. profile. we find that the cusp-caustic violation probability caused w linc-ol-sight haloes with m2LO!TAL. is comparable ο that caused. by intrinsic substructures within the main ensing halo (PIgmzr vs. 10%. ?2)). which is in good agreement with ?.. | Assuming the same halo density profile, we find that the cusp-caustic violation probability caused by line-of-sight haloes with $m\geqslant 10^{6} h^{-1}M_{\odot}$ is comparable to that caused by intrinsic substructures within the main lensing halo $P^{90}(\Rcusp^{0.187})\approx8\%$ vs. $10\%$, \citealt{Dandan2010AqII}) ), which is in good agreement with \citet{Miranda2007}. |
The dilferent. results between ? and ours can be attributed to the drawbacks of their cross-section. method. which underestimates. cllects from. more sophisticated: perturbation scenarios (see ?)). | The different results between \citet{Chen2003}
and ours can be attributed to the drawbacks of their cross-section method, which underestimates effects from more sophisticated perturbation scenarios (see \citealt{Metcalf2005a}) ). |
When we assume truncated NEW profiles for the Iine-o[-sight. haloes Ga2:10" TALL). the violation probability. pUqme) increases to 23% if we adopt. the DOI-MO5 concentration-mass relation and to 1254 if we adopt our preferred relation. that by MOS. | When we assume truncated NFW profiles for the line-of-sight haloes $m\geqslant 10^{6} h^{-1}M_{\odot}$ ), the violation probability, $P^{90}(\Rcusp^{0.187})$, increases to $23\%$ if we adopt the B01-M05 concentration-mass relation and to $12\%$ if we adopt our preferred relation, that by M08. |
These values are larger than that due to the intrinsic subhalo populations alone. | These values are larger than that due to the intrinsic subhalo populations alone. |
A typical NEW profile has an Einstein radius 3—4 orders of magnitude smaller than a singular isothermal sphere with a same mass. | A typical NFW profile has an Einstein radius $3\sim4$ orders of magnitude smaller than a singular isothermal sphere with a same mass. |
However. NEW perturbers in the mass range from 10hTAL. to 107775.TAL. cause more cusp violations than their singular isothermal counterparts. | However, NFW perturbers in the mass range from $10^{6}
h^{-1}M_{\odot}$ to $10^{9\sim 10} h^{-1}M_{\odot}$ cause more cusp violations than their singular isothermal counterparts. |
This may be due to the fact that in this mass range. perturbation in magnification (ratios) is mainly [rom Iluetuations in the local density field that do not change the image positions. | This may be due to the fact that in this mass range, perturbation in magnification (ratios) is mainly from fluctuations in the local density field that do not change the image positions. |
When comparing an NEW with a singular isothermal sphere of the same mass. we notice that. the surface clensitv distribution of the former exceeds that ofthe latter from a raclius of 0.001765 outwards. which means the NEW profile is more effective in introducing Iuctuation to the convergence and thus causing Dux-ratio anomalies. | When comparing an NFW with a singular isothermal sphere of the same mass, we notice that the surface density distribution of the former exceeds that of the latter from a radius of $\sim0.001r_{200}$ outwards, which means the NFW profile is more effective in introducing fluctuation to the convergence and thus causing flux-ratio anomalies. |
On the other hand. the deflection angle of a pertρου om—107b.TAL. is always small C50.001" for a singular isothermal sphere locating at >= 0.6). until the perturber is massive: (mzLOLupfh1 WAL.) and compact enough (a singular: isothermal sphere) to have a deflection. angle 0.01") that can shift a nearby image to a new position with a different magnification from the primary lens (see ?2)). | On the other hand, the deflection angle of a perturber of $m\sim
10^{6-9} h^{-1}M_{\odot}$ is always small $\lesssim 0.001\arcsec$ for a singular isothermal sphere locating at $z=0.6$ ), until the perturber is massive $m \gtrsim 10^{10} h^{-1}M_{\odot}$ ) and compact enough (a singular isothermal sphere) to have a deflection angle $\gtrsim
0.01\arcsec$ ) that can shift a nearby image to a new position with a different magnification from the primary lens (see \citealt{Metcalf2005b}) ). |
Ehis can explain the larger violation probabilities (as shown in Table 4). caused by singular isothermal perturbers of mzdq0775OeLtFAL. than by their. NEWpaa counterparts which. are less ellective in causing llux-anomalies due to shifting image positions. | This can explain the larger violation probabilities (as shown in Table 4), caused by singular isothermal perturbers of $m\geqslant10^{9\sim10} h^{-1}M_{\odot}$ than by their NFW counterparts which are less effective in causing flux-anomalies due to shifting image positions. |
Another issue concerns the finite-souree effect. | Another issue concerns the finite-source effect. |
7 pointed out that. biased. results about substructures could be drawn due to the point source approximation. which is used in this work. | \citet{Metcalf2010FluxAnomaly} pointed out that biased results about substructures could be drawn due to the point source approximation, which is used in this work. |
The racio-emission regions of observed quasars are estimated to be 10 parsees in extent. (22)). corresponding ο 0.001" for a source at ος=2.0. | The radio-emission regions of observed quasars are estimated to be $\sim$ 10 parsecs in extent \citealt{Andreani1999,Wyithe2002}) ), corresponding to $\sim0.001\arcsec$ for a source at $z_s=2.0$. |
When the perturbing mass drops down below LO°TAL... the corresponding elective. perturbing area. decreases to <0.001". in radius or the perturber at zy=0.6. becoming smaller than an image with ο10.20 (around the tangential curve) of the radio emission region of a background quasar. | When the perturbing mass drops down below $10^6 h^{-1}M_{\odot}$, the corresponding effective perturbing area decreases to $\lesssim0.001\arcsec$ in radius for the perturber at $z_d=0.6$, becoming smaller than an image with $\mu\sim10-20$ (around the tangential curve) of the radio emission region of a background quasar. |
As a result. he induced. magnification Luctuation would be smoeared out (within the image area). and thus no significant image lux anomaly would be observed at radio wavelengths (but could still be seen in the optical/near-infrared. which comes rom much smaller physical regions. | As a result, the induced magnification fluctuation would be smeared out (within the image area), and thus no significant image flux anomaly would be observed at radio wavelengths (but could still be seen in the optical/near-infrared, which comes from much smaller physical regions. |
See ?. for spectroscopic eravitational lensing). | See \citealt{Moustakas2003} for spectroscopic gravitational lensing). |
This is why we do not consider the violation probability produced by perturbing haloes below 10°HAL. | This is why we do not consider the violation probability produced by perturbing haloes below $10^6 h^{-1}M_{\odot}$. |
As can be seen from Table 4. even if we neglect contributions from perturbers below 10b.tAL.. we still lind ~10 cusp-violation probability from. line-of-sight NEW-like perturbers adopting the MOS concentration-mass relation. | As can be seen from Table 4, even if we neglect contributions from perturbers below $10^7
h^{-1}M_{\odot}$, we still find $\sim10\%$ cusp-violation probability from line-of-sight NFW-like perturbers adopting the M08 concentration-mass relation. |
Several other points are worth noting. | Several other points are worth noting. |
Firstly. the violation probability depends. of course. —on. the concentration of the halo. and both large halo concentrations and a large scatter in concentration will result in higher Violation probabilities. | Firstly, the violation probability depends, of course, on the concentration of the halo, and both large halo concentrations and a large scatter in concentration will result in higher violation probabilities. |
Thus. it may be possible to use the statistics of [Lux-ratio clistributions (measured in the radio) from Large8 samples of lensed 1quasars to constrain the density profiles of low-mass dark matter halocs. | Thus, it may be possible to use the statistics of flux-ratio distributions (measured in the radio) from large samples of lensed quasars to constrain the density profiles of low-mass dark matter haloes. |
secondly. in ? we found that the violation probability is higher for svstems with larger Einstein radii because the mass [fraction in dark substructures increases with radius. | Secondly, in \citet{Dandan09AquI} we found that the violation probability is higher for systems with larger Einstein radii because the mass fraction in dark substructures increases with radius. |
Lere. the probability of a system. violating the cusp-caustic relation is also seen to increase with the Einstein radius but for a dilferent. reason: close triple images (with a given opening angle A@) that form at larger radii are more likely to be intercepted by linc-of-sight. perturbers. | Here, the probability of a system violating the cusp-caustic relation is also seen to increase with the Einstein radius but for a different reason: close triple images (with a given opening angle $\Delta\theta$ ) that form at larger radii are more likely to be intercepted by line-of-sight perturbers. |
Aclopting bie= 1.0". the mean Einstein radius for the observed sample. we find that the violation probability pUm) increases {ο ifthe MOS concentration-mass relation is adopted. | Adopting $b_{\rm SIE
}=1.0\arcsec$ , the mean Einstein radius for the observed sample, we find that the violation probability $P^{90}(\Rcusp^{0.187})$ increases to if the M08 concentration-mass relation is adopted. |
We also note that if. we use the DOI-MOS5 concentration-mass relation. the violation. probabilities for the representative cases in ?. can be reproduced. | We also note that if we use the B01-M05 concentration-mass relation, the violation probabilities for the representative cases in \citet{Metcalf2005a} can be reproduced. |
Third. the Rowp-A@ distribution varies with the | Third, the $\Rcusp$ $\Delta\theta$ distribution varies with the |
lt is also clear in this figure that the majority of candidates have verv low density ratios. | It is also clear in this figure that the majority of candidates have very low density ratios. |
This can be primarily attributed to (vo causes bevond the limitations of paxjo: giant stars and blends. which are eclipsing binaries whose light is accompanied by a bright (hire star. causing deep eclipses to be diluted and thus appear like planetary (ransit. | This can be primarily attributed to two causes beyond the limitations of $\rho_{\rm SMO}$: giant stars and blends, which are eclipsing binaries whose light is accompanied by a bright third star, causing deep eclipses to be diluted and thus appear like planetary transit. |
As already mentioned in Seager&Mallén-Ornelas(2003).. both blends and giant stars will have unusually low values of pao. the giants stars because their density is (uly much lower (han main sequence stars anc (he blends because the inclusion of the light of the third star leads the trapezoid fit to converge on a solution that is larger than the bright third star and with a higher impact parameter. | As already mentioned in \citet{sea2003}, both blends and giant stars will have unusually low values of $\rho_{\rm
SMO}$ – the giants stars because their density is truly much lower than main sequence stars and the blends because the inclusion of the light of the third star leads the trapezoid fit to converge on a solution that is larger than the bright third star and with a higher impact parameter. |
This overestimation of the radius leads in turn to an underestimation of the stellar density of the third star of up to504. | This overestimation of the radius leads in turn to an underestimation of the stellar density of the third star of up to. |
The known planets in this figure support the hypothesis that the distribution of densities ratios is due more to the insullicieney of pyy than the (transit densities. | The known planets in this figure support the hypothesis that the distribution of densities ratios is due more to the insufficiency of $\rho_{JK}$ than the transit densities. |
The precision of CoRoT data is extremely hieh. so the errors in (he transit parameters are dominated by uncertainties in the limb darkening rather (han limitations of the photometry. | The precision of CoRoT data is extremely high, so the errors in the transit parameters are dominated by uncertainties in the limb darkening rather than limitations of the photometry. |
Indeed. despite the fact that payjo is built upon more risky assumptions than p, and p» and therefore presumably less reliable. the distribution of the pao densities for the CoRoT planets are essentially indistinguiable from the distribution of the pj; and p,» densities for all exoplanets (including the ColtoT planets) while the individual values awe clillerent. the distribution is not. | Indeed, despite the fact that $\rho_{\rm SMO}$ is built upon more risky assumptions than $\rho_{t1}$ and $\rho_{t2}$ and therefore presumably less reliable, the distribution of the $\rho_{\rm
SMO}$ densities for the CoRoT planets are essentially indistinguiable from the distribution of the $\rho_{t1}$ and $\rho_{t2}$ densities for all exoplanets (including the CoRoT planets) – while the individual values are different, the distribution is not. |
The only exception is Coltol-Tb. for which (he extracted transit parameters are likely distorted by. magnetic activity or (rausil Ging variations. | The only exception is CoRoT-7b, for which the extracted transit parameters are likely distorted by magnetic activity or transit timing variations. |
This demonstrates (hat paxjo is actually quite useful in and of itself (particularly for more central transits) eiven the errors inherent in the extracted transit parameters. which may or may not include impossible-to-define uncertainties in limb darkening coefficients. | This demonstrates that $\rho_{\rm SMO}$ is actually quite useful in and of itself (particularly for more central transits) given the errors inherent in the extracted transit parameters, which may or may not include impossible-to-define uncertainties in limb darkening coefficients. |
surface density implies a continuum in vvalues. rather than a bimodality. | surface density implies a continuum in values, rather than a bimodality. |
Thus the relationship between our model results and he interpretation of oobservations by and will depend on the distribution of surface densities in their observed galaxies. among other issues. | Thus the relationship between our model results and the interpretation of observations by and will depend on the distribution of surface densities in their observed galaxies, among other issues. |
We note. jowever. that our work. like that of (2010)... is consistent with the idea that the observed behaviour in the star ormation rates and ecan be explained without the need to invoke a volumetric star formation law that is different in dises and mergers. | We note, however, that our work, like that of , is consistent with the idea that the observed behaviour in the star formation rates and can be explained without the need to invoke a volumetric star formation law that is different in discs and mergers. |
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