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In the present work we examine a slightly dilleren situation. | In the present work we examine a slightly different situation. |
As in Pocllewska&Szuszkiewicz(2008) planets form a close pair and are embedded: in the gaseous disc. but this time the Super-Earth lies on the external orbit. | As in \citet{paperI} planets form a close pair and are embedded in the gaseous disc, but this time the Super-Earth lies on the external orbit. |
‘This case has been already studied by Thonumes(2005) and more recently bv Pierens&Nelson(2008). (hereafter PNOS). | This case has been already studied by \citet{thommes05}
and more recently by \citet{pierens}
(hereafter PN08). |
ποιος(2005) has found that a Jupiter mass planet can act. at least for à certain time. as a safety net Lor low-mass planets. capturing them into orbital commoensurabilities. | \citet{thommes05}
has found that a Jupiter mass planet can act, at least for a certain time, as a safety net for low-mass planets, capturing them into orbital commensurabilities. |
In his calculations. the low-mass planet. which is allowed. to accrete the mass. migrates towards the Jupiter and ends up in à 1:2 or 2:3 resonance depending on the surface density of the disc. | In his calculations, the low-mass planet, which is allowed to accrete the mass, migrates towards the Jupiter and ends up in a 1:2 or 2:3 resonance depending on the surface density of the disc. |
Contrary to his result. PNOS have noticed that a low-mass planet (in the range of 3.5 - 20 AL, ) can be trapped at the outer edge of the gap opened by the gas giant. | Contrary to his result, PN08 have noticed that a low-mass planet (in the range of 3.5 - 20 $M_{\oplus}$ ) can be trapped at the outer edge of the gap opened by the gas giant. |
Planets cannot therefore get close enough as it is necessary to attain a mean motion resonance. | Planets cannot therefore get close enough as it is necessary to attain a mean motion resonance. |
Such planet trapping mechanism is possible at the steep and. positive surface density. gradient in the radial profile of the gaseous disc where. the corotation orque compensates the dillerential Lindblad torque (Massetetal.2006). | Such planet trapping mechanism is possible at the steep and positive surface density gradient in the radial profile of the gaseous disc where, the corotation torque compensates the differential Lindblad torque \citep{masset}. |
. Alore recently Paardekooper&Papaloizou(2000) have studied the nonlinear cllects arising in the coorbital region of planets of a few Earth masses. | More recently \citet{paandpa}
have studied the nonlinear effects arising in the coorbital region of planets of a few Earth masses. |
They have ound that any. positive density gradient in the disc can act as à protoplanctary trap. | They have found that any positive density gradient in the disc can act as a protoplanetary trap. |
The investigations of Thonunes(2005) have been xrformed. using a hivbrid. code. that combines an N-bocly component with a one-dimensional viscous disc model. | The investigations of \citet{thommes05} have been performed using a hybrid code, that combines an N-body component with a one-dimensional viscous disc model. |
In his way the effects of Lindblad torques are well reproduced. »it the corotation torques acting on the low-mass planet are not taken into account. | In this way the effects of Lindblad torques are well reproduced, but the corotation torques acting on the low-mass planet are not taken into account. |
Emploving a 2D. hvedrodynamical code. PNOS have been able to include properly both types of torques. | Employing a 2D hydrodynamical code, PN08 have been able to include properly both types of torques. |
Lt has been shown by PNOS that the initially convergent migration of a Jupiter mass gas giant and an outer planet [ess massive than 20 M, stops when the Iow-mass planet approaches the outer edge of the gap formed bv the gas giant. | It has been shown by PN08 that the initially convergent migration of a Jupiter mass gas giant and an outer planet less massive than 20 $M_{\oplus}$ stops when the low-mass planet approaches the outer edge of the gap formed by the gas giant. |
Later on. the low-mass planets migrate outward. | Later on, the low-mass planets migrate outward. |
In the present work we confirm the results of PNOS in the case of a Super-Earth and a Jupiter-like planet. | In the present work we confirm the results of PN08 in the case of a Super-Earth and a Jupiter-like planet. |
The only cülference is that in the calculations of PNOS the low-mass planet was able to acercte matter from the clise and if its mass exceeded the value of 20 AL). the planets ended up in à mean-motion resonance. | The only difference is that in the calculations of PN08 the low-mass planet was able to accrete matter from the disc and if its mass exceeded the value of 20 $M_\oplus$, the planets ended up in a mean-motion resonance. |
In this paper we are interested in Super-Earths. so we did not take into account aceretion. | In this paper we are interested in Super-Earths, so we did not take into account accretion. |
As an extension. of the work of PNOS. we have investigated. the evolution of a Super-Earth also in the presence of Sub-Jupiter eas giants. whose masses are lower than that of Jupiter. | As an extension of the work of PN08, we have investigated the evolution of a Super-Earth also in the presence of Sub-Jupiter gas giants, whose masses are lower than that of Jupiter. |
For typical disc properties the gap opened by the gas giant. is very wide and the positions of all first order mean motion commoensurabilities are located inside the region allected by the gap. | For typical disc properties the gap opened by the gas giant is very wide and the positions of all first order mean motion commensurabilities are located inside the region affected by the gap. |
LE the eas giant. is assumed to be less massive than Jupiter (e.g. 0.5427). the gap opened by the planet is narrower. which gives a chance for attaining a first order mean motion resonance. | If the gas giant is assumed to be less massive than Jupiter (e.g. $0.5
M_J$ ), the gap opened by the planet is narrower, which gives a chance for attaining a first order mean motion resonance. |
However. in this situation the migration of the eas giant is faster than that of the low-mass planet causing the divergent relative motion of both planets. | However, in this situation the migration of the gas giant is faster than that of the low-mass planet causing the divergent relative motion of both planets. |
For this reason. in order to ect the commensurabilitv one needs to slow down the Sub-Jupiter or to speed up the Super-Earth. | For this reason, in order to get the commensurability one needs to slow down the Sub-Jupiter or to speed up the Super-Earth. |
Finally. we have achieved the 1:2 mean motion resonance for very thin clises and low surface density. | Finally, we have achieved the 1:2 mean motion resonance for very thin discs and low surface density. |
This configuration. however. has not been maintained till the end of the simulations. | This configuration, however, has not been maintained till the end of the simulations. |
This paper is organized as follows. | This paper is organized as follows. |
In. Section 2 we describe our. numerical set-up. | In Section 2 we describe our numerical set-up. |
In. Section. 3 we present the procedure. used. in order to achieve the convergent migration ofa Super-ISarth and a Jupiter-like planet. | In Section 3 we present the procedure used in order to achieve the convergent migration of a Super-Earth and a Jupiter-like planet. |
Section 4 ds dedicated. to the results obtained in the evolution of such a system of planets. | Section 4 is dedicated to the results obtained in the evolution of such a system of planets. |
We also discuss in this Section the eccentricity behaviour together with the analysis of the sensitivity of our results to numerical parameters. and | We also discuss in this Section the eccentricity behaviour together with the analysis of the sensitivity of our results to numerical parameters and |
events. bad pixels. and events registered too close to chip gaps by requiring "FLAGZO" and "PATTERN < 4. | events, bad pixels, and events registered too close to chip gaps by requiring “FLAG=0” and “PATTERN $\leq$ 4”. |
Inspection of lightcurves made from the data revealed no evidence of background flaring. and the entire 42 ksee was used to generate EPIC-pn spectra. | Inspection of lightcurves made from the data revealed no evidence of background flaring, and the entire 42 ksec was used to generate EPIC-pn spectra. |
Source and background spectra were made in the standard way by grouping PI channels 0-20479 by a factor of 5. | Source and background spectra were made in the standard way by grouping PI channels 0–20479 by a factor of 5. |
The source spectrum was extracted between 20-56 in RAWX. and using the full RAWY range. | The source spectrum was extracted between 20–56 in RAWX, and using the full RAWY range. |
Àn adjacent background region was extracted. and the spectra were properly normalized. | An adjacent background region was extracted, and the spectra were properly normalized. |
Custom redistribution matrix files (rmfs) and ancillary response files (arfs) for the spectra made using the SAS tasks "rmfgen" and "arfgzen". | Custom redistribution matrix files (rmfs) and ancillary response files (arfs) for the spectra made using the SAS tasks “rmfgen” and “arfgen”. |
We also made MOS-1 and MOS-2 event lists and spectra. | We also made MOS-1 and MOS-2 event lists and spectra. |
The MOS-I camera was operated in "timing" mode. which is seldom used. | The MOS-1 camera was operated in “timing” mode, which is seldom used. |
The MOS-2 camera was operated in "full-frame" mode. and therefore suffered photon pile-up. | The MOS-2 camera was operated in “full-frame” mode, and therefore suffered photon pile-up. |
While results from both MOS cameras confirm the pn results we report below. we regard them as less reliable and do not consider them in this work. | While results from both MOS cameras confirm the pn results we report below, we regard them as less reliable and do not consider them in this work. |
RXTE observed SWIFT J1753.5-0127 on 2006 March 24. | observed SWIFT $-$ 0127 on 2006 March 24, starting at 17:22:24 UT. |
packages and tools available in HEASOFT version 6.0. | This observation was reduced using the packages and tools available in HEASOFT version 6.0. |
After standard screening (e.g.. against SAA intervals). net PCA and HEXTE exposures of 2.3 ksec and 0.8 ksee were obtained. | After standard screening (e.g., against SAA intervals), net PCA and HEXTE exposures of 2.3 ksec and 0.8 ksec were obtained. |
PCU-2 is the best calibrated PCU in the RXTE/PCA. and so we extracted "Standard2" events (129 channels covering 2--60 keV. obtained every 16 seconds) from this PCU. | PCU-2 is the best calibrated PCU in the /PCA, and so we extracted “Standard2” events (129 channels covering 2--60 keV, obtained every 16 seconds) from this PCU. |
Data from all of the Xe gas layers in PCU-2 were combined. | Data from all of the Xe gas layers in PCU-2 were combined. |
Background spectra were made using the FTOOL "peabackest" using the latest "bright source" model. | Background spectra were made using the FTOOL “pcabackest” using the latest “bright source” model. |
An instrument response file was generated using the tool "pearsp". | An instrument response file was generated using the tool “pcarsp”. |
We added systematic errors to the full PCU-2 spectrum using the ftool "grppha" (Miller et 22006). | We added systematic errors to the full PCU-2 spectrum using the ftool “grppha” (Miller et 2006). |
We reduced "archive" mode data from the HEXTE-B cluster: these data have a time resolution of 32 s and cover the 10.0-250.0 keV band with 61 channels. | We reduced “archive” mode data from the HEXTE-B cluster; these data have a time resolution of 32 s and cover the 10.0–250.0 keV band with 61 channels. |
We extracted source and background files. and generated an instrument response file. using the standard procedures. | We extracted source and background files, and generated an instrument response file, using the standard procedures. |
All spectra considered in this paper were grouped to require at least 10 counts per bin using the ftool "grppha to ensure valid results using 4 statistical analysis. | All spectra considered in this paper were grouped to require at least 10 counts per bin using the ftool “grppha” to ensure valid results using $\chi^{2}$ statistical analysis. |
The spectra were analyzed using XSPEC version. 11.3.2 (Arnaud. Dorman 2000). | The spectra were analyzed using XSPEC version 11.3.2 (Arnaud Dorman 2000). |
Fits made to the EPIC-pn spectrum were restricted to the 0.5-10.0 keV range by calibration uncertainies. | Fits made to the EPIC-pn spectrum were restricted to the 0.5-10.0 keV range by calibration uncertainies. |
Similarly. fits to the PCU-2 and HEXTE-B spectra were restricted to the 2.8-25.0 keV and 20.0-100.0 keV bands. respectively. | Similarly, fits to the PCU-2 and HEXTE-B spectra were restricted to the 2.8–25.0 keV and 20.0–100.0 keV bands, respectively. |
All of the error measurements reported in this work are confidence errors. obtained by allowing all fit parameters to vary simultaneously. | All of the error measurements reported in this work are confidence errors, obtained by allowing all fit parameters to vary simultaneously. |
Using standard FTOOLS. we made fast Fourier transforms of theRXTE lighteurves of SWIFT J1753.5-0127 taken in PCA event modes. | Using standard FTOOLS, we made fast Fourier transforms of the lightcurves of SWIFT $-$ 0127 taken in PCA event modes. |
The resulting power spectra show strong. band-limited variability that is typical of the low—hard state in accreting black holes. | The resulting power spectra show strong, band-limited variability that is typical of the low–hard state in accreting black holes. |
The rms noise amplitude in. the 0.01-100 Hz band is30%. | The rms noise amplitude in the 0.01–100 Hz band is. |
. No QPOs were detected in this observation, | No QPOs were detected in this observation. |
Initial spectral fits were jointly made to the PCA and HEXTE-B spectra with a simple absorbed power-law model. | Initial spectral fits were jointly made to the PCA and HEXTE-B spectra with a simple absorbed power-law model. |
A normalizing constant was allowed to vary between the spectra. and the column density was fixed at the expected value (Nj;=1.7«107! em™). | A normalizing constant was allowed to vary between the spectra, and the column density was fixed at the expected value $N_{H} = 1.7\times
10^{21}~{\rm cm}^{-2}$ ). |
This fit gave a power-law index of T=1.65(2). and was in fact a formally acceptable result: 7/7=58.8/76 (see Figure 1). | This fit gave a power-law index of $\Gamma =
1.65(2)$, and was in fact a formally acceptable result: $\chi^{2}/\nu
= 58.8/76$ (see Figure 1). |
RXTE is not sensitive to variations in low column densities. given that its effective lower energy threshold is 3 keV. We note that variations m the column density as large as a factor of 2 only produced changes in the power-law index within the error range quoted above. and also resulted in statistically acceptable fits. | is not sensitive to variations in low column densities, given that its effective lower energy threshold is 3 keV. We note that variations in the column density as large as a factor of 2 only produced changes in the power-law index within the error range quoted above, and also resulted in statistically acceptable fits. |
The power-law index measured withRXTE. then. is a constraint robust against plausible variations in the absorbing column. | The power-law index measured with, then, is a constraint robust against plausible variations in the absorbing column. |
We next made fits to the EPIC-pn spectrum. using a simple power-law with the column density fixed at 1.7«107!ση”. | We next made fits to the EPIC-pn spectrum, using a simple power-law with the column density fixed at $1.7\times 10^{21}~{\rm cm}^{-2}$. |
This model yielded an unacceptable fit (47/7=4855.2/1903) and strong residuals below 3 keV in the data/model ratio. | This model yielded an unacceptable fit $\chi^{2}/\nu = 4855.2/1903$ ) and strong residuals below 3 keV in the data/model ratio. |
We next allowed the column density to vary: this step yielded an improved but unacceptable fit (47/7=3852.5/1901). | We next allowed the column density to vary; this step yielded an improved but unacceptable fit $\chi^{2}/\nu = 3852.5/1901$ ). |
The addition of a disk component to this model yields significantly improved fits. | The addition of a disk component to this model yields significantly improved fits. |
With the addition of a disk component. the following parameters are obtained Ny=2.301)«107!em. ΚΤ=0.2241) keV. Norm,a;=1200+200. P=1.6601) (consistent with RXTE). and Norm,25.5005)«107 ΟΥ= 2227.0/1899). | With the addition of a disk component, the following parameters are obtained $N_{H} = 2.3(1) \times 10^{21}~{\rm cm}^{-2}$, $kT =
0.22(1)$ keV, ${\rm Norm}_{disk} = 1200\pm 200$, $\Gamma = 1.66(1)$ (consistent with ), and ${\rm Norm}_{pow} = 5.50(5)\times
10^{-2}$ $\chi^{2}/\nu = 2227.0/1899$ ). |
The soft excess in this spectrum is shown in Figure 2. and the total fit is shown in Figure 3. | The soft excess in this spectrum is shown in Figure 2, and the total fit is shown in Figure 3. |
The disk component is required at more than the8c level of confidence. as determined by an F test. | The disk component is required at more than the$\sigma$ level of confidence, as determined by an F test. |
This two-component model gives an unabsorbed flux of 3.9«107!ereenvs! (0.5-10.0 keV) and | This two-component model gives an unabsorbed flux of $3.9\times
10^{-10}~{\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}$ (0.5-10.0 keV) and |
The maguitude-redshift formulae are derived in the Appendix. | The magnitude-redshift formulae are derived in the Appendix. |
We focus on the magnitude residual οτι or difference in apparent magnitude relative to a fiducial model. which we take here as the staudard fat ACDM . model with WAIAP values of Qu. and O,,. | We focus on the magnitude residual $\Delta m(z)$, or difference in apparent magnitude relative to a fiducial model, which we take here as the standard flat $\Lambda$ CDM model with WMAP values of $\Omato$ and $\Olamo$. |
Predictions are plotted asx curves (for various values of £) in Fig. | Predictions are plotted as curves (for various values of $L$ ) in Fig. |
3. where they are compared with measurements for 92 medimnu-redslift SNIa at 20.1 by Toury et al. ( | 3, where they are compared with measurements for 92 medium-redshift SNIa at $z>0.1$ by Tonry et al. ( |
2003) and 23 lieh+vedshitt SNIa at 2~1 as compiled by Riess et al. ( | 2003) and 23 high-redshift SNIa at $z\sim1$ as compiled by Riess et al. ( |
2006). | 2006). |
The heavy solid line in Fig. | The heavy solid line in Fig. |
3 indicates the fiducial or standard AC DAL model (straight ine Aun= 0). which overlaps with the present theory in the case L=1,vil and all cases with £o>300 Cpc (to within the precision of the plot). | 3 indicates the fiducial or standard $\Lambda$ CDM model (straight line $\Delta m=0$ ), which overlaps with the present theory in the case $L=\Lcrit$ and all cases with $L>300$ Gpc (to within the precision of the plot). |
For simaller values of £. ie theory beeins to depart frou standard cosmology with maxima deviations near ~|. confixiuug the usefuluess of SNIa as probes of the theory. | For smaller values of $L$, the theory begins to depart from standard cosmology with maximum deviations near $z\sim1$, confirming the usefulness of SNIa as probes of the theory. |
For £ ucar (or greater iu) the critical value £0,rit=1LO Gpc. the experiucutal uncertainties are too large o discriminate usefully between heoretical values of £. | For $L$ near (or greater than) the critical value $\Lcrit=4.9$ Gpc, the experimental uncertainties are too large to discriminate usefully between theoretical values of $L$. |
The data are. however. good rough to disfavor snaller values « tL. iurproviug significantly ou the age constraint aud ightcning observational bounds oi the theory to £L>L3 Gpc. | The data are, however, good enough to disfavor smaller values of $L$, improving significantly on the age constraint and tightening observational bounds on the theory to $L>4.3$ Gpc. |
We have taken the basic extension of ecucral relativity frou 1: to 5 dimensions aud asked what observational cousequences follow from its decaying cosmological "constaut. or density of dark energy. | We have taken the basic extension of general relativity from 4 to 5 dimensions and asked what observational consequences follow from its decaying cosmological “constant,” or density of dark energy. |
The four main consequences involve the age of the universe. structure formatio- imcleosvuthesis aud the maeguitude-redshitt relation for Type Ia superuovae. | The four main consequences involve the age of the universe, structure formation, nucleosynthesis and the magnitude-redshift relation for Type Ia supernovae. |
There are. of course. large Literatures on all four of these subjects; | There are, of course, large literatures on all four of these subjects. |
We lave therefore preseuted our results as possible departures from the current staudard model. | We have therefore presented our results as possible departures from the current standard model. |
The theory is consistent with all four classes of data at prescut. | The theory is consistent with all four classes of data at present. |
The best way to separate LD and 5Dcostuology by observational niens in the future would appear to be by use of better supernovae data at z21. | The best way to separate 4D and 5Dcosmology by observational means in the future would appear to be by use of better supernovae data at $z\gtrsim1$. |
Another possible test of the theory might come from analysis of the augular power spectrum of fluctuations in the cosmic microwave backerouud (CAIB). | Another possible test of the theory might come from analysis of the angular power spectrum of fluctuations in the cosmic microwave background (CMB). |
Qualitative considerations. however. sugeest that the sensitivity. of such a test would not be colpctitive with those discussed above for the kiud of theory considered here. | Qualitative considerations, however, suggest that the sensitivity of such a test would not be competitive with those discussed above for the kind of theory considered here. |
The main feature of the CAIB power spectrum is the aneularOo position of the first acoustic peak. (uus | The main feature of the CMB power spectrum is the angular position of the first acoustic peak, $\lpeak$. |
This quantity depeuds only weakly on dark-cnergy density |see Fig. | This quantity depends only weakly on dark-energy density [see Fig. |
1 of White (1998) or the analytic approximation in Cornish (20100]. | 1 of White (1998) or the analytic approximation in Cornish (2000)]. |
Wha (ay really measures is the of matter and dark-cucrey densities. 16. spatial curvature. | What $\lpeak$ really measures is the of matter and dark-energy densities, i.e. spatial curvature. |
We have assumed throughout that O,,,|O,,=IE (ie. &2 0). as in the standard ACDAL model. so we would not expect a siguificaut shift in m 6(,,,,. | We have assumed throughout that $\Omato+\Olamo=1$ (i.e. $k=0$ ), as in the standard $\Lambda$ CDM model, so we would not expect a significant shift in $\lpeak$ . |
Fig. | Fig. |
2 (bottom) shows that dark-energy | 2 (bottom) shows that dark-energy |
constraints on the amount of heavy elements within a planet's interior. | constraints on the amount of heavy elements within a planet's interior. |
Sammon computed detailed interior models for Jupiter aud Saturni (hat were consistent wilh all available observational constraints. | \citet{Saumon04} computed detailed interior models for Jupiter and Saturn that were consistent with all available observational constraints. |
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