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We create composite spectra using the method described in VandenBerketal. (2001).
We create composite spectra using the method described in \citet[][]{VandenBerk_etal_2001}.
. In short, each spectrum was shifted to restframe, rebinned onto a common dispersion of 1 pper bin, and normalized.
In short, each spectrum was shifted to restframe, rebinned onto a common dispersion of 1 per bin, and normalized.
The final composite spectrum was generated by taking the median (or geometric mean) flux density in each bin of the shifted, rebinned, and scaled
The final composite spectrum was generated by taking the median (or geometric mean) flux density in each bin of the shifted, rebinned, and scaled spectra.
An error was generated from the semi-interquantilespectra. range of the spectrumflux densities in each bin scaled by NV. where is the number of spectra contributing to that bin.
An error spectrum was generated from the semi-interquantile range of the flux densities in each bin scaled by $N_{\rm spec}^{1/2}$, where $N_{\rm spec}$ is the number of spectra contributing to that bin.
We refer the Nopecreader to VandenBerketal.(2001) for more details regarding generating the composite spectra.
We refer the reader to \citet{VandenBerk_etal_2001} for more details regarding generating the composite spectra.
The left panel of 33 shows composite spectra for the above quasar samples.
The left panel of 3 shows composite spectra for the above quasar samples.
AAL quasars have colors lying between normal quasars and the so-called β€œdust-reddened” quasars in SDSS (with color A(gβ€”i)>0.3; Richards et al.
AAL quasars have colors lying between normal quasars and the so-called β€œdust-reddened” quasars in SDSS (with color $\Delta(g-i)>0.3$; Richards et al.
2003).
2003).
The reddening of AAL quasars relative to the control quasars is well described by a SMC-like extinction curve, with E(Bβ€”V)~0.03, consistent with VandenBerketal. (2008).
The reddening of AAL quasars relative to the control quasars is well described by a SMC-like extinction curve, with $E(B-V)\sim 0.03$, consistent with \cite{Vanden_Berk_etal_2008}.
. The right panel shows flux ratios of the AAL quasar composites to that of the control quasars.
The right panel shows flux ratios of the AAL quasar composites to that of the control quasars.
The β€œredshifted” and β€œblueshifted” samples show a prominent excess of narrow eemission, which is absent in the case of the like” sample.
The β€œredshifted” and β€œblueshifted” samples show a prominent excess of narrow emission, which is absent in the case of the ``intervening-like'' sample.
The lack of eemission excess, the similar amount of reddening to classical intervening absorption systems (e.g., York et 22006), and the fact that they join the plateau of the velocity distribution (e.g., reffig:vdist)), suggest that AALs with voy>1500kms"! are in fact mostly classical interveningabsorbers’.
The lack of emission excess, the similar amount of reddening to classical intervening absorption systems (e.g., York et 2006), and the fact that they join the plateau of the velocity distribution (e.g., \\ref{fig:vdist}) ), suggest that AALs with $v_{\rm off}>1500\,{\rm km\,s^{-1}}$ are in fact mostly classical intervening.
. We note that the large-scale fluctuations seen in the composite ratios are due to correlated noise arising from variance in the shape of quasar continua.
We note that the large-scale fluctuations seen in the composite ratios are due to correlated noise arising from variance in the shape of quasar continua.
The correlation between the presence of absorbers with VorrΒ«1500 ss?! and eemission is of great interest.
The correlation between the presence of absorbers with $v_{\rm off}<1500$ $^{-1}$ and emission is of great interest.
While the composite aabsorption lines are, by construction, offset by hundreds of kms"! with respect to the quasars, the stacked excess eemission is found more or less at the quasar systemic velocity (see below).
While the composite absorption lines are, by construction, offset by hundreds of ${\rm km\,s^{-1}}$ with respect to the quasars, the stacked excess emission is found more or less at the quasar systemic velocity (see below).
velocity.. The central engine, i.e., the black hole radiation, appears to be similar in AAL quasars and in normal quasars: other than the reddening and aabsorption, no difference is seen in the continuum and broad emission lines between the two quasar populations.
The central engine, i.e., the black hole radiation, appears to be similar in AAL quasars and in normal quasars: other than the reddening and absorption, no difference is seen in the continuum and broad emission lines between the two quasar populations.
This suggests that dust-reddening is the explanation for the color difference seen in AAL quasars and normal quasars.
This suggests that dust-reddening is the explanation for the color difference seen in AAL quasars and normal quasars.
One might ask if this dust reddening might also cause the apparent eexcess seen in the flux ratio plot in Fig. 3..
One might ask if this dust reddening might also cause the apparent excess seen in the flux ratio plot in Fig. \ref{fig:composite}.
Dust reddening could occur on spatial scales much smaller than the eemission region but much larger than the continuum plus broad line region.
Dust reddening could occur on spatial scales much smaller than the emission region but much larger than the continuum plus broad line region.
In this case the continuum is attenuated while the eemission is not, an enhancement of sstrength relative to the causingunderlying apparentcontinuum.
In this case the continuum is attenuated while the emission is not, causing an apparent enhancement of strength relative to the underlying continuum.
Assuming an SMC-like extinction curve, we require E(Bβ€”V)~0.12 to achieve the level of eemission enhancement relative to the continuum, substantially larger than the inferred E(Bβ€”V)~0.03 from the composite spectra.
Assuming an SMC-like extinction curve, we require $E(B-V)\sim 0.12$ to achieve the level of emission enhancement relative to the continuum, substantially larger than the inferred $E(B-V)\sim 0.03$ from the composite spectra.
We now focus on the eemission excess.
We now focus on the emission excess.
To quantify it and estimate its significance, we create continuum-subtracted median composites around the eemission line.
To quantify it and estimate its significance, we create continuum-subtracted median composites around the emission line.
This is done by subtracting a running median
This is done by subtracting a running median
and variable couplings, as compared to ACDM, and the effect significantly grows with mass (the decreasing behavior found in ? can be explained in view of ?)).
and variable couplings, as compared to $\Lambda $ CDM, and the effect significantly grows with mass (the decreasing behavior found in \cite{Manera_Mota_2006} can be explained in view of \cite{Wintergerst_pettorino_2010}) ).
In particular, at zΒ©1.5 the halo number density at the high-mass end of our simulated mass functions exceeds the ACDM value by a factor ~10 and ~3 for constant and variable couplings, respectively.
In particular, at $z\approx 1.5$ the halo number density at the high-mass end of our simulated mass functions exceeds the $\Lambda $ CDM value by a factor $\sim 10$ and $\sim 3$ for constant and variable couplings, respectively.
In Fig.
In Fig. \ref{mass_corr_plot}) )
we plot the same quantities for our hydrodynamical @)high-resolution simulations, which confirm the trend found in the larger simulation box, although the
we plot the same quantities for our hydrodynamical high-resolution simulations, which confirm the trend found in the larger simulation box, although the
AGN and SD components do not seem to experience a strong evolution with redshift up to 2~0.35.
AGN and SB components do not seem to experience a strong evolution with redshift up to $z \sim 0.35$.
It is now possible to obtain a quantitative estimate of the AGN contribution to the bolometric Iuminosityv. by assuming &β€”RA?{Re2225; β†΄βŠΊβˆβ‰Όβ†²β‰€β†§β†΄βˆβ‰€β†§β†΄β†₯β‹‘βˆ–β†½βˆβ‰Ίβˆ’β‰€β†§β†΄β†₯βŠ³βˆ–β‡βˆ₯β†²β†•β†½β‰»βŠ³βˆ–βŠ½β‰Όβ‡‚β‰Όβ†²β‹βˆ–βŠ½β‰Ίβˆ’β†•β‹…β†•βˆ£β†½β‰»β‰Όβ†²β‰Όβ‡‚βŠ³βˆ–β‡βˆͺβ†“β‹Ÿβ‰€β†§β†΄β†•β‹…β‰€β‹―
It is now possible to obtain a quantitative estimate of the AGN contribution to the bolometric luminosity, by assuming $\kappa=R^\mathit{agn}/R^\mathit{sb}\sim$ 25: The analytical steps described so far are summarized in Fig. \ref{np},
β†²β‹βˆ–βŠ½βˆβˆβˆβŠ”β‰€β†§β†΄β†•β‹…β†•βˆ β‰Όβ†²β‰Όβ‡‚β†₯βˆβŠ‘β‰Έβ‰Ÿβ‹…βˆƒβ‹…β‹…β†•βˆβˆ–βˆ–β†½βˆβ†•β‰Ίβˆ’βˆβŠ”βˆβ†²βˆ£β†½β‰»β‰Όβ†²βŠ³βˆ–β‡β†₯∐β†₯βˆͺ↓≯ βˆͺβ†“β‰―βˆ£β†½βˆ£β†œβˆ£β‹―βˆ£β†“β‹Ÿβˆͺβ†•β‹…βŠ”βˆβ†²β†₯βˆβ‰Όβˆβˆ–β†½β†•β‹”β‹―β†₯βŠ³βˆ–β‡β‹―βˆβ‹…β‰Ίβˆ’β‰Όβ†²βŠ³βˆ–βŠ½β‰€β†§β†΄β†•β‹…β‰Όβ†²βˆβŠ³βˆ–βŠ½βˆ©β†²β‰ΌβŠ”βˆβ†΄βŠΊβ‰€β†§β†΄βˆ£β†½β‰»β†₯≼↲βŠ₯β‹…β‹…βˆ–βˆ–β†½β†•βŠ”β†₯βŠ”βˆβ†²βŠ₯βŠ”β‰Ίβˆ’βˆͺβˆβ‡‚βˆŽβˆβ‡‚β‰Όβ†²βˆβ‰Ίβˆ’β‰Όβ†²βˆβˆβ†“βˆβŠ³βˆ–βŠ½β‹…
in which the best fit of equation \ref{eq}) ) is shown as a function of $\alpha_\mathit{bol}$, that is $R=\alpha_\mathit{bol}R^\mathit{agn}+(1-\alpha_\mathit{bol})R^\mathit{sb}$.
β‰Όβ†•βŠ²βˆͺβˆβ‰Ίβˆ’β‰Όβ†²β†•β‹…βˆβ†•βˆβ‰Έβ†½β†”β†΄βŠ”βˆβ†²βŠ₯βŠ³βˆ«β‹‘βˆ–β†½β†§βŠΊβˆŸβˆβ‹©βŠ‚β†½βŠβ‹Ÿβˆ–βŠ½β‹…β‹―βˆβ‹…β†•β‹…β‰Όβ†²β‹Ÿβˆ–βŠ½βˆβˆβ‹Ÿβˆ–βŠ½β‰€β‹―β†²β†•βˆβ†–β‰Ίβ†½β†”β†΄βˆͺβ‹―β‡‚β‰€β†§β†΄β‰Έβ†½β†”β†΄β†•β‹…β‰Όβ†²β‰Όβ†²βˆβˆβ†²β†•βˆβˆ–βˆ–βŠ½β†•βŠ”β†₯βŠ”β†₯βˆͺβ‹Ÿβˆ–β‡β‰Όβ†²βˆͺβ†“β‹Ÿβˆ–βŠ½β‰Όβ†²β†•βˆβ‰Όβ†²βˆβ‡€β†Έ
The values of $\alpha_\mathit{bol}$ for the individual sources are listed in Table \ref{t1}, with the $\sigma$ confidence limits.
≼↲β†₯≀↕↴β†₯β‹…β‹œβ‹‘βˆƒβˆ©βˆ©β‰€βˆβ‰€β†§βˆβ‹βˆΆβŠ”βˆβ†²β†•β†•β‹…β‰Όβ†²βˆβ‹Ÿβˆ–β‡β‰Όβ†²βˆβ†“βˆ£β†½β‰»β†₯β‰Όβ†²β‰€β†§β†΄βˆβ‰Ίβ‡‚β†•βˆβ‰Ίβˆβˆ–β†½β†•β‰Όβ‡‚βˆβ‰€β†§β†΄β†₯β‰Όβ†²β‹Ÿβˆ–βŠ½βˆβˆβ†“β‰€β†§β†΄βˆ©β†²β‹Ÿβˆ–βŠ½β‰€β†§β†΄β†•β‹…β‰Όβ†²β†₯≀↧↴↕⋅
Concerning the 1 Jy ULIRGs, our results are in good agreement with those of Veilleux et al. (
β‰Έβ†½β†”β†΄β‰Όβ†²β†•β‹…βŠ”β†₯β‰€β†§β†΄βˆβˆͺβ‹―β‹…β‹Ÿβˆ–βŠ½βˆ£β†½β‰»β‹‘βˆ–β†½β†΄βˆΏβ†΄βˆβŠ“β†½β‰»β‰Όβ†²β†•β‹… cent. but this seems to be a small svstematic effect related to the AGN/SB (or. in other words. the [actor &).
2009a): their ensemble and individual estimates are larger than ours by $\sim$ 10 per cent, but this seems to be a small systematic effect related to the AGN/SB (or, in other words, the factor $\kappa$ ).
The work of Veilleux et al. (
The work of Veilleux et al. (
2009a) explores the connection between ULIBRGs and quasars. and provides six different methods based on the Spi/zer--RS spectra for computing the AGN contribution to the bolometrie luminosity of both kinds of sources.
2009a) explores the connection between ULIRGs and quasars, and provides six different methods based on the -IRS spectra for computing the AGN contribution to the bolometric luminosity of both kinds of sources.
The comparison among (hese six independent estimates gives a good measure ol the uncertainties involved when considering the individual sources. which sometimes can be rather huge with respect to the AGN contribution averaged over all methods.
The comparison among these six independent estimates gives a good measure of the uncertainties involved when considering the individual sources, which sometimes can be rather large with respect to the AGN contribution averaged over all methods.
Such discrepancies can be regarded as (he natural dispersion connected to the use of single indicators. whieh allects our narrow-band analvsis as well.
Such discrepancies can be regarded as the natural dispersion connected to the use of single indicators, which affects our narrow-band analysis as well.
The scatter around. the best lit of Fig.
The scatter around the best fit of Fig.
2 is in [act significantly larger than the statistical uncertaintv on the best values of RO" and R.
\ref{np} is in fact significantly larger than the statistical uncertainty on the best values of $R^\mathit{agn}$ and $R^\mathit{sb}$.
The actual lo dispersion is 0.18 dex. nearly independent of 05,4. and this should be considered the intrinsic dispersion of the 6 sau to bolometric ratios for the AGN and SB components.
The actual $\sigma$ dispersion is 0.18 dex, nearly independent of $\alpha_\mathit{bol}$, and this should be considered the intrinsic dispersion of the 6 $\mu$ m to bolometric ratios for the AGN and SB components.
An ecquivalent way of visualizing this point is shown in Fig. 3..
An equivalent way of visualizing this point is shown in Fig. \ref{pd},
where the total HR. Iuminosities inferred from our spectral analvsis. assuming (he best values of RO!” and 75 as the true bolometric corrections. are compared to the luminosities nieasured by according to equation (1)).
where the total IR luminosities inferred from our spectral analysis, assuming the best values of $R^\mathit{agn}$ and $R^\mathit{sb}$ as the true bolometric corrections, are compared to the luminosities measured by according to equation \ref{e1}) ).
The natural dispersion is clearly brought out once again. and (his limits the accuracy. with which the AGN and SB components can be assessed in individual objects.
The natural dispersion is clearly brought out once again, and this limits the accuracy with which the AGN and SB components can be assessed in individual objects.
We finally remind what are (he possible sources of svstematic error in our approach: 1) the selection of a narrow wavelength range for our analvsis prevents a complete understanding of the gas and dust properties. Chat could be better investigated by considering the whole
We finally remind what are the possible sources of systematic error in our approach: 1) the selection of a narrow wavelength range for our analysis prevents a complete understanding of the gas and dust properties, that could be better investigated by considering the whole
The interred geometry of the accretion disk in {0 50.55 (i.c.. truncated. and/or iuner parts covered bv corona) nav be conunon features of ACNs with powerful jets.
The inferred geometry of the accretion disk in 4C 50.55 (i.e., truncated and/or inner parts covered by corona) may be common features of AGNs with powerful jets.
Receut studies iudicate that radio galaxies also ave relatively narrow irou-Ix. enissionu lines e.g. ry,7 20 ry tefor 3€ 390.3 (Saubrunaetal.2009) and rg2 Ll re for 171.26 (Larssonetal.2008). from the sinele diskline fit. and rg,=(9x1) for 3€ 120 from the iultiple conrponeuts ft (INataokactal.2007).
Recent studies indicate that radio galaxies also have relatively narrow iron-K emission lines e.g., $r_{\rm in} >$ 20 $r_{\rm g}$ for 3C 390.3 \citep{Sam09} and $r_{\rm in} >$ 44 $r_{\rm g}$ for 4C +74.26 \citep{Lar08} from the single diskline fit, and $r_{\rm in} = (9\pm1) r_{\rm g}$ for 3C 120 from the multiple components fit \citep{Kat07}.
. This result is in accordance with an expectation from theories that jets are more easily produced by radiatively inefΓΌcieut accretion flow than by a standard cisk.
This result is in accordance with an expectation from theories that jets are more easily produced by radiatively inefficient accretion flow than by a standard disk.
Another key paramcter to understand the accretion How is the Eddington ratio. which is estimated to be Lyua/LgaacO.L for [€ 50.55 (section ??)).
Another key parameter to understand the accretion flow is the Eddington ratio, which is estimated to be $L_{\rm bol}/L_{\rm Edd} \sim 0.4$ for 4C 50.55 (section \ref{differ_SED}) ).
Similarly. we also estimate that of 3€ 120 to be Lig/Lpgq~0.5. using the 210 keV flux (Ikataokactal.2007). and the black hole mass of LO" citepPeto L.
Similarly, we also estimate that of 3C 120 to be $L_{\rm bol}/L_{\rm Edd} \sim 0.5$, using the 2–10 keV flux \citep{Kat07} and the black hole mass of $10^{7.7}$ \\citep{Pet04}.
. Thus. these two sources 11av belong to a very similar class of AGNs, except for the radio louduess to the N-rav flux (log Rx=2.1 for 3C 120 and ΞŠΞΏΟ… Rx=3.6 for IC 50.55). which could be partially explained bx the small inclination angle of 3€ 120 (/<1l: see Ikataokaetal. 2007)) couipired with LC 50.55 (/~ 357).
Thus, these two sources may belong to a very similar class of AGNs, except for the radio loudness to the X-ray flux (log $R_{\rm X} = -2.1$ for 3C 120 and log $R_{\rm X} = -3.6$ for 4C 50.55), which could be partially explained by the small inclination angle of 3C 120 $i<14^{\circ}$; see \citealt{Kat07}) ) compared with 4C 50.55 $i \sim 35^{\circ}$ ).
The physical reasou for the difference in their N-ray spectra that the reflection component and mon-kE lines are strouger in 3€ 120 (Iβ€” 0.7) is not clear at present.
The physical reason for the difference in their X-ray spectra that the reflection component and iron-K lines are stronger in 3C 120 $R\sim0.7$ ) is not clear at present.
1€ 50.55. and 3€ 120 are rare objects haviug distinctively hieh fractions of Eddington luuinositv compared with other typical BLRGs. for instance. Lyua/Lgg = 0.010.07 for 3€ 390.3 (Sambrunaetal.2009:Lewis&Eracleous 2006).. β€”0.01 for LC |71.26 (Larssonetal.2008). and 0.0010.002 for Arp 102D (Lewis&Eracleous2006).
4C 50.55 and 3C 120 are rare objects having distinctively high fractions of Eddington luminosity compared with other typical BLRGs, for instance, $L_{\rm bol}/L_{\rm Edd}$ = 0.01–0.07 for 3C 390.3 \citep{Sam09, Lew06}, $\sim 0.04$ for 4C +74.26 \citep{Lar08}, and 0.001–0.002 for Arp 102B \citep{Lew06}.
. By analogy to the Galactic dack holes. these low Eddiustou ratio sources likely correspond to the low/hard state. where the accretion disk is accompanied by steadyuh jets. while wormal Sevfert ealaxies may do to the lieh state. where the disk extends close to the ISCO with quenchedm jet activity.
By analogy to the Galactic black holes, these low Eddington ratio sources likely correspond to the low/hard state, where the accretion disk is accompanied by steady jets, while normal Seyfert galaxies may do to the high/soft state, where the disk extends close to the ISCO with quenched jet activity.
The accretion flows in IC 50.55 aud 3€ could be explained as a lieh Πιοτν eud of the low/hard state.
The accretion flows in 4C 50.55 and 3C 120 could be explained as a high luminosity end of the low/hard state.
Alternatively. they may be another state achieved witli even higher mass accretion rates than iu the hieh/soft state. where the disk structure is also simular to that found iu the loxΞ±Ξ½Ξ± state (.0.. truncated disk).
Alternatively, they may be another state achieved with even higher mass accretion rates than in the high/soft state, where the disk structure is also similar to that found in the low/hard state (i.e., truncated disk).
For this possibility. itf is iuterestiug to note the similarly to the hieh-Eddiugtouratio Galactic black hole CRS 1915|105. which exhibits a similarly narrow ΞΏΟ‚ cussion liue over a Comptonization clominated coutinuuu. implying that the tuner disk is fully covered by a corona (Uedaetal.2010): in GRS 1915|105. a compact jet is also detected in a steady state with a παντα spectrum. so-called in Class \ (seee.g..Feuder&Belloui2001)..
For this possibility, it is interesting to note the similarly to the high-Eddington ratio Galactic black hole GRS 1915+105, which exhibits a similarly narrow iron-K emission line over a Comptonization dominated continuum, implying that the inner disk is fully covered by a corona \citep{Ued10}; in GRS 1915+105, a compact jet is also detected in a steady state with a hard spectrum, so-called in Class $\chi$ \citep[see e.g.,][]{Fen04a}.
Iu sununaryv. the unified picture of accretion flows over a wide range of black hole mass is far frou established.
In summary, the unified picture of accretion flows over a wide range of black hole mass is far from established.
Further svstematic studies of the accretion disk structure of radio loud ACNs at various accretion rates based ou detailed N-ray spectroscopy and multi-waveleneths data are very iurportaut to reveal these fundamental problems.
Further systematic studies of the accretion disk structure of radio loud AGNs at various accretion rates based on detailed X-ray spectroscopy and multi-wavelengths data are very important to reveal these fundamental problems.
We thank Corry Skinner for providing the Suvff/BAT heht curve of 1€ 50.55. and the team for the calibration of the iustrmuents.
We thank Gerry Skinner for providing the /BAT light curve of 4C 50.55, and the team for the calibration of the instruments.
Part of this work was financially supported by Cwauts-in-Aid for Scicutific Research 20510230. (YU) aud 20710100. (YT). auc by the erant-inaid for the Clobal COE Program "The Next Generation of Physics. Spun from Universality aud Emergence” from the Ministry of Education. Culture. Sports. Science aud Technology (AIENT) of Japan.
Part of this work was financially supported by Grants-in-Aid for Scientific Research 20540230 (YU) and 20740109 (YT), and by the grant-in-aid for the Global COE Program β€œThe Next Generation of Physics, Spun from Universality and Emergence” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.
driving velocities.
driving velocities.
The triangle represents the "corrected" 7 value for the run "C4" and the star is the corrected value for "A3".
The triangle represents the β€œcorrected" $\eta$ value for the run β€œC4" and the star is the corrected value for β€œA3".
The scalings. corresponding to the lines plotted in the Figure. are = VV,=0.1. = 0.147: VV,-0.05 = VV,=0.05 -- Here one can see two different comparable fits for the slow (V,= 0.05) driving experiments. with the scaling based on the corrected value leading to aslightly stronger dependence of Jing 0n 3.
The scalings, corresponding to the lines plotted in the Figure, are = V_d=0.1, = V_d=0.05 - = V_d=0.05 - Here one can see two different comparable fits for the slow $V_d=0.05$ ) driving experiments, with the scaling based on the corrected value leading to aslightly stronger dependence of $J_{max}$ on $\eta$ .
However. the correction of the 77 value for the faster driver does not seem to lead to a linear scaling relation.
However, the correction of the $\eta$ value for the faster driver does not seem to lead to a linear scaling relation.
We now turn to the scaling of the peak current with the driving velocity. for a constant 77 value. which is investigated using the 7=107? experiments listed inΞ™.
We now turn to the scaling of the peak current with the driving velocity, for a constant $\eta$ value, which is investigated using the $\eta=10^{-3}$ experiments listed in.
. The result is shown 19.. where it is seen that while the peak current clearly depends on the imposed driving velocity. there is no simple (e.g. linear or exponential) relation that can be obtained to fit the data.
The result is shown in, where it is seen that while the peak current clearly depends on the imposed driving velocity, there is no simple (e.g. linear or exponential) relation that can be obtained to fit the data.
The dimensions and tilt angle of the current sheet have been measured for the same experiments.
The dimensions and tilt angle of the current sheet have been measured for the same experiments.
They are found to be independent of 7 for a constant driving velocity. to within our measurement accuracy.
They are found to be independent of $\eta$ for a constant driving velocity, to within our measurement accuracy.
On the other hand. varying the driving velocity while maintaining a constant value for 77. we find that there are significant changes of these dimensions. indicating that they are largely dependent on the amount of imposed stress.
On the other hand, varying the driving velocity while maintaining a constant value for $\eta$, we find that there are significant changes of these dimensions, indicating that they are largely dependent on the amount of imposed stress.
However. as discussed above. the present domain size and the extent of the driving region limit the current sheet from evolving freely. and thus with the present setup we are unable to provide scaling relations for these quantities.
However, as discussed above, the present domain size and the extent of the driving region limit the current sheet from evolving freely, and thus with the present setup we are unable to provide scaling relations for these quantities.
The top frame of shows the maximum outflow velocity as a function of time for different driving velocities Vj.
The top frame of shows the maximum outflow velocity as a function of time for different driving velocities $V_d$ .
This showsa significant variation both with time and
This showsa significant variation both with time and
It appears then that Lor large redshifts.
It appears then that for large redshifts.
Any model with a luminosity distance that grows slower than vields (miβ€”M)<0 (as SNLO97TID) bevond some z. Perhaps the simplest model one can construct wilh such a property is a flat space wilh a single (hud with constant equation of statew,.
Any model with a luminosity distance that grows slower than yields (m-M)<0 (as SN1997ff) beyond some z. Perhaps the simplest model one can construct with such a property is a flat space with a single fluid with constant equation of state.
. In (Bis case one has in and the lnminosity distance (lor /=2/3) β‹…β‹… β†“β‹Ÿβˆͺβ†•β‹…β‰€β†§β†΄βˆβˆ–β‡βˆ£βˆ£β‹…β†™βˆ•βˆ–βˆ•βˆ–βˆ©β‹…β‹…β‡€βˆ–β†•
In this case one has in and the luminosity distance (for =2/3) For <2/3 and large z we have.
βˆβˆβ‰Όβ†²β‹…βŠ³βˆ–βŠ½βˆβ†“β‹―β‡‚β‰Όβ†²β†₯βˆ©β†•βˆ–β†½β‰Όβ†²β‹βˆ–βŠ½β‰€β†§β†΄β†₯βˆ–βˆ–β†½β‰€β†§β†΄βˆ–β†½βŠ³βˆ–βŠ½β†₯β‰€β†§β†΄β†•β‹…βˆ©β‰Όβ†²β†•β‹…β‰ΊβˆβŠ³βˆ–β‡β†₯β‰€β†§β†΄βˆβ‰Ίβˆ’β‰Όβ†²βŠ³βˆ–βŠ½β‹œβ‰€β†§β†΄βˆβ‰Όβ‡‚βŠ”βˆβ†²β†•β‹…β‰Όβ†²β†“β‰―βˆͺβ†•β‹…β‰Όβ†²β‹Ÿβ‰€β†§β†΄β†•βˆβˆ©β†²β†•β‹… ↽ βŠŸβ‰»β†•β‹…βˆ£βˆ£β‹…β†™β†™βˆ–βˆ•βˆ–βˆ’β‰»βˆ•βˆ•βˆ£β‰‘βŠ°β‰€β†§β†΄β†•βˆβŠ”β‰€β†§β†΄β†•β‹…β‰Έβ‰Ÿβ‰Όβ†²βŠ³βˆΆβˆ–βˆ–β†½β‰Όβ†²βˆβ‰€β†§β†΄βˆ–β†½β‰Όβ†²β†™βˆ£βŠ₯βˆΎβŠ³βˆΆβˆ’βŠ”β†΄βˆ’β‹…β‹…βˆβ†“βˆͺ∐βˆͺβˆ–βˆ–βŠ½βŠ³βˆ–βŠ½βŠ”β‹―β†₯⋅≀↧↴β†₯β†₯β‰€β†§β†΄β†•β‹…β†–β†³β†΄β‰Όβ†²βŠ³βˆΆβ‰€β†§β†΄βˆβ‰Όβ‡‚ β†₯∏∐∐∐βˆͺβ‹βˆ–βŠ½βˆβˆ–β†½β‹…β†₯⋅≼↲⋅β†₯β‰€β†§β†΄β†•β‹…βˆ©β‰Όβ†²β†•β‹…β‰€β†§β†΄β†½β‰»β†½β‰»β‰€β†§β†΄β†•β‹…β‰Όβ†²βˆβ†₯βˆβ†“β‰€β†§β†΄βˆ©βˆβˆβ‹―β‡‚β‰Όβ†²β‹βˆ–βŠ½β‹βŠ”β‹―β†΄βˆβŠ”βˆβ†²βŠ³βˆ–β‡β†•βˆβˆ©β†₯β‰Όβ†²βˆ’βˆβˆβ†•β‰Ίβ‡‚βˆβ‰€β†§β†΄β†₯βˆ’β‹βˆ–βŠ½β†½β‰»β‰€β†§β†΄β‰Ίβˆ’β‰Όβ†²β‰Όβ†²βˆ–β†½βˆͺ∏∐βˆͺβˆβ‹… CΒ» .
It follows that, at large z and for any >0, Milne's model gives always larger distances (and therefore fainter luminosity, i.e. larger apparent magnitudes) than the single-fluid flat-space evolution.
J In Fig.
In Fig.
1Ξ· I plot AQ β€”M)for various values of wy...alone withmodel the reference [lat e ,, =0.65.
1 I plot (m-M) for various values of, along with the reference flat model =0.65.
.It appears clearly that values of te, 0.4 m are acceptable. as it will be confirmed by the likelihood analvsis below.
It appears clearly that values of around 0.1 are acceptable, as it will be confirmed by the likelihood analysis below.
llowever. according to (he observations. our universe is composed by a mixture oL ΞΊΞ±Ξ½. of clustered matter (which includes a
However, according to the observations, our universe is composed by a mixture of, say, of clustered matter (which includes a
tenth of a magnitude in the (H-K,) color.
tenth of a magnitude in the ) color.
These offsets were added to the zero-points calculated for our photometry.
These offsets were added to the zero-points calculated for our photometry.
The errors on these zero-point offsets to the magnitudes of the MKO system are smaller than the photometric An analysis to examine the internal photometric uncertainties calculated by ALLSTAR-DAOPHOT routine was made for each filter by means of adding artificial stars to the science images.
The errors on these zero-point offsets to the magnitudes of the MKO system are smaller than the photometric An analysis to examine the internal photometric uncertainties calculated by -DAOPHOT routine was made for each filter by means of adding artificial stars to the science images.
Our 6604 field was divided in two regions: the β€˜central region’ and the β€˜field region’.
Our 604 field was divided in two regions: the `central region' and the `field region'.
As the main cluster of 6604 does not stand out as an evident increase in the stellar density, the central region limit was set using a NIRI image obtained with the Pa narrow-band filter (details on narrow-band images and analysis will be included in a forthcoming paper).
As the main cluster of 604 does not stand out as an evident increase in the stellar density, the central region limit was set using a NIRI image obtained with the $\beta$ narrow-band filter (details on narrow-band images and analysis will be included in a forthcoming paper).
This is illustrated in Figure 4 where the smoothed Pa contours at 5c used to define the central region limit are shown.
This is illustrated in Figure \ref{fig:contornos} where the smoothed $\beta$ contours at $\sigma$ used to define the central region limit are shown.
The central region, enclosed by a ~150 pc radius circle, is centered at a=01347335.14and 6=--30?47'1."9 and its area (of 68000 pc?) encompasses the 6604 SOBA.
The central region, enclosed by a $\sim$ 150 pc radius circle, is centered at $\alpha=01^h34^m33^s.14$and $\delta=+30^{\circ}47\arcmin 1.\arcsec9$ and its area (of 68000 $^2$ ) encompasses the 604 SOBA.
The region outside the circle, the field region, has a surface of ~118000 pc? and was used to account for field star A histogram of magnitude distribution (0.5 mag bin width) was generated separately for each region.
The region outside the circle, the field region, has a surface of $\sim$ 118000 $^2$ and was used to account for field star A histogram of magnitude distribution (0.5 mag bin width) was generated separately for each region.
A new image was created by adding artificial stars to each region.
A new image was created by adding artificial stars to each region.
The number of added objects represented of the stars at each magnitude interval.
The number of added objects represented of the stars at each magnitude interval.
The artificial star magnitudes were measured following the same procedure employed for the natural stars.
The artificial star magnitudes were measured following the same procedure employed for the natural stars.
By comparing their measured magnitudes with their β€˜true’ magnitudes, we found that the differences are in the range of the magnitude uncertainties calculated by the routine.
By comparing their measured magnitudes with their `true' magnitudes, we found that the differences are in the range of the magnitude uncertainties calculated by the routine.
In Figure α½… we have plotted the difference between the β€˜true’ and measured magnitudes for the artificial stars for theJ,H, and filters in the top, middle, and bottom panels, respectively.
In Figure \ref{fig:error_j} we have plotted the difference between the `true' and measured magnitudes for the artificial stars for the, and filters in the top, middle, and bottom panels, respectively.
The bars represent the magnitude error calculated by for the measured magnitudes.
The bars represent the magnitude error calculated by for the measured magnitudes.
gas is in hwerostatic equilibrium.
gas is in hydrostatic equilibrium.
Using entropy rather than. for example. the gas density as the basic parametrization is motivated by the theoretical and observed. self-similarity of entropy. profiles in. cluster samples.
Using entropy rather than, for example, the gas density as the basic parametrization is motivated by the theoretical and observed self-similarity of entropy profiles in cluster samples.
This model can be constrained by SZ and X-ray data to give fitted. eas. and total matter properties of the cluster.
This model can be constrained by SZ and X-ray data to give fitted gas and total matter properties of the cluster.
The model has sensible convergence properties and can be used out to the virial radius of the cluster.
The model has sensible convergence properties and can be used out to the virial radius of the cluster.
By construction. the model does not allow unphysical or inconsistent properties of the cluster gas as can happen if. for example. a parametric fit to the eas density is combined with an unrelated parametric fit to the empoerature.
By construction, the model does not allow unphysical or inconsistent properties of the cluster gas as can happen if, for example, a parametric fit to the gas density is combined with an unrelated parametric fit to the temperature.