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We adopt a perfectly edec-on orbital geometry in all cases. but otherwise use the appropriate orbital parameters (a. c. (ο). planetary radius ΟΠ). aud. stellar parameters (2... Ta. logy. [Fe/T). | We adopt a perfectly edge-on orbital geometry in all cases, but otherwise use the appropriate orbital parameters $a$, $e$, $\omega$ ), planetary radius $R_{p}$ ), and stellar parameters $R_{*}$, $T_{\rm eff}$, $\log g$, [Fe/H]). |
We can run the caleulatious for arbitrary waveleneths but only present here the leht curves for TRAC chamucl | (8 sau). | We can run the calculations for arbitrary wavelengths but only present here the light curves for IRAC channel 4 (8 $\mu$ m). |
Since ours is a one-laver model. the shape of the phase variations is essentialv unchauged if one adopts a different wavehbaud. | Since ours is a one-layer model, the shape of the phase variations is essentialy unchanged if one adopts a different waveband. |
The only free model parameters are lL. Taq. aud wage in practice we set cA=0 since the albedo does uot significantly affect the of the thermal phase varlatious and it appears that hot Jupiters have low albedos (Roweetal.2008:Cowan&Agol2010.andref-erencestherein). | The only free model parameters are $A$, $\tau_{\rm rad}$, and $\omega_{\rm rot}$; in practice we set $A=0$ since the albedo does not significantly affect the of the thermal phase variations and it appears that hot Jupiters have low albedos \citep[][and references therein]{Rowe_2008, Cowan_2010}. |
All stelhuü and planetary data are taken from exoplauct.cu. maintained by Jean Schneider: using uunubers from exoplanets.org did not perceptibly chauge our results. | All stellar and planetary data are taken from exoplanet.eu, maintained by Jean Schneider; using numbers from exoplanets.org did not perceptibly change our results. |
When the stellar data are not available. we have asstuned typical parameters for the appropriate spectral class. aud solar mictallicity. | When the stellar data are not available, we have assumed typical parameters for the appropriate spectral class, and solar metallicity. |
Iusofar as we are ouly concerned with the broadband mid-IR. brightuesses of the stars. our results should not depend sensitively on the input stellar parameters. | Insofar as we are only concerned with the broadband mid-IR brightnesses of the stars, our results should not depend sensitively on the input stellar parameters. |
Using the stars Tg. logg aud [Fe/TI]. we use the PHOENIX/NextGen stellar spectrum erids (auschildtctal.1999) to determine their brightness temperatures at the observed frequencies. | Using the stars' $T_{\rm eff}$, $\log g$ and [Fe/H], we use the PHOENIX/NextGen stellar spectrum grids \citep{Hauschildt_1999} to determine their brightness temperatures at the observed frequencies. |
For cach svaveband. we determine the ratio of the stellar flix to the blackbody flux at that eid stars Tig. | For each waveband, we determine the ratio of the stellar flux to the blackbody flux at that grid star's $T_{\rm eff}$. |
We then apply this factor to the Tig of the actual observed star. | We then apply this factor to the $T_{\rm eff}$ of the actual observed star. |
There are many computational shortcuts that oue cau use with this analytic model. | There are many computational shortcuts that one can use with this analytic model. |
The orbits are treated as edee-on and the planetary obliquity is assumed to be zero (this is strictly true for the core: for the atimosphere it simply means that the equatorial jet-stream flows in the East-West direction). so the D.E. need ouly he solved at one latitude on the cay-side (c.g.. the equator) aud those day-side heating curves are casily adjusted for other latitudes via Ty. | The orbits are treated as edge-on and the planetary obliquity is assumed to be zero (this is strictly true for the core; for the atmosphere it simply means that the equatorial jet-stream flows in the East-West direction), so the D.E. need only be solved at one latitude on the day-side (e.g., the equator) and those day-side heating curves are easily adjusted for other latitudes via $T_{0}$. |
The D.E. can then be solved analytically ou the planets wielt-side. | The D.E. can then be solved analytically on the planet's night-side. |
The observed flux ratio depends on a combination of orbital factors (e. 6). planetary factors (A. Taq. wu) and viewiug ecometry (we and a. the usual phase angele: a=0 at eclipse; a=x at transit), | The observed flux ratio depends on a combination of orbital factors $a$, $e$ ), planetary factors $A$, $\tau_{\rm rad}$, $\omega_{\rm rot}$ ), and viewing geometry $\omega$ and $\alpha$, the usual phase angle: $\alpha=0$ at eclipse, $\alpha=\pi$ at transit). |
We show schematically in Figure 5 how we combine the orbital. anetaryv and viewing factors to obtain discdntegrated iecnmal light curves. | We show schematically in Figure 5 how we combine the orbital, planetary and viewing factors to obtain disc-integrated thermal light curves. |
The top pauel simply shows the dlanet’s distance from its host star: the second pancl VArows the planets orbital angular velocity: the third xuiel shows the equilibrium temperature at the sub-y.cllay point (solid line) and the highest temperature ou 1e model plauet (dotted line). | The top panel simply shows the planet's distance from its host star; the second panel shows the planet's orbital angular velocity; the third panel shows the equilibrium temperature at the sub-stellar point (solid line) and the highest temperature on the model planet (dotted line). |
The fourth panel slows ιο total absorbed flux (solid line) and the total emitted Hux (dotted line). | The fourth panel shows the total absorbed flux (solid line) and the total emitted flux (dotted line). |
The fifth panel shows the planets ---Thuninated fraction. f£=$(11cosa). | The fifth panel shows the planet's illuminated fraction, $f = \frac{1}{2}(1+\cos\alpha)$. |
The bottom panel shows the planet/star flux ratio at 8 juu as seeu from Earth. | The bottom panel shows the planet/star flux ratio at 8 $\mu$ m as seen from Earth. |
We start the calculations with all of the parcels at T— Jy. but the planet reaches a periodic equilibrium iu a couple e-foldiug times (a few τας). | We start the calculations with all of the parcels at $T = T_{0}$ , but the planet reaches a periodic equilibrium in a couple e-folding times (a few $\tau_{\rm rad}$ ). |
If the planet had no heat capacity. the dotted nes would perfectly track the solid lines in the third and fourth paucls of Figure 5. | If the planet had no heat capacity, the dotted lines would perfectly track the solid lines in the third and fourth panels of Figure 5. |
The effect of a non-zero plauctary leat capacity | The effect of a non-zero planetary heat capacity |
orbits. | orbits. |
On the shorter time scales of a typical observation the hardness ratios in the low state appear to be nearly constant. | On the shorter time scales of a typical observation the hardness ratios in the low state appear to be nearly constant. |
There is a general slight tendency for the hardness ratios to get smaller with increasing count rate. | There is a general slight tendency for the hardness ratios to get smaller with increasing count rate. |
In the high state orbit 34] there are strong indications of a hardening of the spectrum when the source brightens. | In the high state orbit 341 there are strong indications of a hardening of the spectrum when the source brightens. |
NLS] galaxies are generally characterized by very steep spectra in the soft energy band (Boller et al. | NLS1 galaxies are generally characterized by very steep spectra in the soft energy band (Boller et al. |
1996). | 1996). |
From observations of Gliozzi et al. ( | From observations of Gliozzi et al. ( |
2000) find a steep power law with T~3 in the 0.1—2.4 keV energy range: in the 0.6-10 keV band Vaughan et al. ( | 2000) find a steep power law with $\Gamma \sim 3$ in the $-$ 2.4 keV energy range; in the $-$ 10 keV band Vaughan et al. ( |
1999) obtain Γ=2.26+0.03. | 1999) obtain $\Gamma = 2.26 \pm0.03$. |
The XMM-Newton data (O'Brien et al. | The $-$ Newton data (O'Brien et al. |
2001) clearly show a strong soft excess below ~2 keV over a harder power law at higher energies. | 2001) clearly show a strong soft excess below $\sim $ 2 keV over a harder power law at higher energies. |
The PN data with their outstanding signal to noise ratio and their wide bandpass are ideally suited for a detailed spectral study of the source. | The PN data with their outstanding signal to noise ratio and their wide bandpass are ideally suited for a detailed spectral study of the source. |
For the spectral analysis we used the latest available response matrices (version 6.3) issued in December 2002. | For the spectral analysis we used the latest available response matrices (version 6.3) issued in December 2002. |
We extracted single and double events with quality flag = 0 from a rectangular region of 30x30 RAW pixels around the source position. | We extracted single and double events with quality flag = 0 from a rectangular region of $\times$ 30 RAW pixels around the source position. |
The region includes ~ of the source photons but avoids the gap between the detector chips. | The region includes $\sim$ of the source photons but avoids the gap between the detector chips. |
The background was taken on the same chip at distances as close to the source position as possible. avoiding contamination, | The background was taken on the same chip at distances as close to the source position as possible, avoiding contamination. |
With a count rate of 2 20 counts s! in the high state the PN detector. operated in Full Window mode. showed strong indications of pile-up. clearly apparent from the XMMSAS task epatplot. | With a count rate of $\gta$ 20 counts $^{-1}$ in the high state the PN detector, operated in Full Window mode, showed strong indications of pile-up, clearly apparent from the XMMSAS task $epatplot$. |
We therefore discarded photons from the innermost (typically 2x3) RAW pixels at the core of the point spread function from the spectral analysis. | We therefore discarded photons from the innermost (typically $2\times3$ ) RAW pixels at the core of the point spread function from the spectral analysis. |
In Fig. | In Fig. |
5 we show the power law fit in the 2-10 keV energy range to the data of orbit 153 (E22.13€0.03;Vg=0.90/303 d.o.f with a galactic Nj,=4.4x10-" cm7 ). | \ref{figure:powl} we show the power law fit in the $-$ 10 keV energy range to the data of orbit 153 $\Gamma = 2.13\pm0.03;
\chi_{\rm red}^2 = 0.90 / 303$ d.o.f with a galactic $_H = 4.4\times 10^{20}$ $^{-2}$ ). |
The fitted model is extrapolated to lower energies and the ratio between data and model. given in the lower panel. clearly demonstrates the presence of a large soft X-ray excess over the hard power law. | The fitted model is extrapolated to lower energies and the ratio between data and model, given in the lower panel, clearly demonstrates the presence of a large soft X-ray excess over the hard power law. |
The spectrum of appears to be a carbon copy of that of the NLSI galaxy PG 084424349 (Brinkmann et al. | The spectrum of appears to be a carbon copy of that of the NLS1 galaxy PG 0844+349 (Brinkmann et al. |
2003) even with respect to the δις blue bump' seen in both objects (O'Brien et al. | 2003) even with respect to the `big blue bump' seen in both objects (O`Brien et al. |
2001) and it is very similar to that of 1H 0419-577 (Page et al. | 2001) and it is very similar to that of 1H 0419-577 (Page et al. |
2002) and the other NLS] galaxy Mrk 896 (Page et al. | 2002) and the other NLS1 galaxy Mrk 896 (Page et al. |
2003) studied with XMM-Newton. | 2003) studied with XMM-Newton. |
The upper limits given for an iron line are rather low (O'Brien et al. | The upper limits given for an iron line are rather low (O'Brien et al. |
2001) and the soft banc spectral excess is far too broad to be fitted by a single black body component. | 2001) and the soft band spectral excess is far too broad to be fitted by a single black body component. |
A multiple blackbody (in the soft band) plus a power law at higher energies provides acceptable fits to the data. however. the physical nature of these different components remains obscure. | A multiple blackbody (in the soft band) plus a power law at higher energies provides acceptable fits to the data, however, the physical nature of these different components remains obscure. |
While a model with two Comptonization components gives an accurate description of the spectra. two power law models require absorption in excess of the galactic value and yield slightly worse fits. | While a model with two Comptonization components gives an accurate description of the spectra, two power law models require absorption in excess of the galactic value and yield slightly worse fits. |
For example. for the above mentioned orbit 153 (see as well Tab. | For example, for the above mentioned orbit 153 (see as well Tab. |
2) we obtain an Nj=7.79x107 em™. Doon=3.28£0.08. F4=1.62£0.10 with a -=1.163/578 d.of.. | 2) we obtain an $_H = 7.79\times10^{20}$ $^{-2}$, $\Gamma_{\rm soft}=3.28\pm0.08$, $\Gamma_{\rm hard}=1.62\pm0.10$ with a $\chi_{\rm red}^2 = 1.163 / 578$ d.o.f., |
values. which are representative for the other orbits as well. | values, which are representative for the other orbits as well. |
The relatively long RGS observation of orbit 84 provides a sufficient number of photons for an accurate fit. | The relatively long RGS observation of orbit 84 provides a sufficient number of photons for an accurate fit. |
We have reprocessed the RGS data using XMMSAS version 5.3.3 and the RGS response matrices were created with the SAS package resrmfgen. | We have reprocessed the RGS data using XMMSAS version 5.3.3 and the RGS response matrices were created with the SAS package $rgsrmfgen$ . |
The spectral data were binned to contain at least 30 photons per energy channel. | The spectral data were binned to contain at least 30 photons per energy channel. |
We fitted the RGS data with a single comp7T Comptonization model. available in Xspec (Titarchuk 1994). assuming galacticabsorption plus | We fitted the RGS data with a single $compTT$ Comptonization model, available in $Xspec$ (Titarchuk 1994), assuming galacticabsorption plus |
2.3-n Bok telescopes. | 2.3-m Bok telescopes. |
We describe the results of these observations below. | We describe the results of these observations below. |
The SPOL CCD hnagine/Spectropolarimetcr (Schunidtetal.1992a)— mounted ou the Steward Observatory 2.314 Dok telescope (INitt Peak. AZ) and the 1.51 Kuiper telescope BBieclow. AZ) was used to obtain spectropolarimetiy of SN 201110 over 10 welts. | The SPOL CCD Imaging/Spectropolarimeter \citep{schmidt92a} mounted on the Steward Observatory 2.3-m Bok telescope (Kitt Peak, AZ) and the 1.54 Kuiper telescope Bigelow, AZ) was used to obtain spectropolarimetry of SN 2011fe over 10 nights. |
We have grouped the 10 nights of observations into four Epochs in Table 1. | We have grouped the 10 nights of observations into four Epochs in Table 1. |
Observatious covered aat a resolution of ~20 ((GO00 line 1 erating in first order. using a 571 «51 sslit and a Tova L3s blocking filter). | Observations covered at a resolution of $\sim$ 20 (600 line $^{-1}$ grating in first order, using a $\farcs$ $\times$ $\arcsec$ slit and a Hoya L38 blocking filter). |
À rotatable senuachromatic halfwave plate was used to modulate incident polarization and a Wollaston priuu iu the collimated beam separated the orthogonally polarized spectra onto a thinned. autirefiection-coated 800 «1200 SITe CCD. | A rotatable semiachromatic half-wave plate was used to modulate incident polarization and a Wollaston prism in the collimated beam separated the orthogonally polarized spectra onto a thinned, anti-reflection-coated $\times$ 1200 SITe CCD. |
The cfficieney of the wave plate as a function of waveleneth is measured by inserting a fully-polarizing Nicol prin iuto the beam above the slit. | The efficiency of the wave plate as a function of wavelength is measured by inserting a fully-polarizing Nicol prism into the beam above the slit. |
À series of four separate exposures that xuuple 16 orientations of the wave plate vields two independent. background-subtraeted measures of each of the normalized luecar Stokes parameters. q aud | A series of four separate exposures that sample 16 orientations of the wave plate yields two independent, background-subtracted measures of each of the normalized linear Stokes parameters, $q\/$ and $u\/$. |
Each night. several such sequences of observations of SN 2011fe were obtained aud combined. with the weighting of the individual measurements based on photon statistics. | Each night, several such sequences of observations of SN 2011fe were obtained and combined, with the weighting of the individual measurements based on photon statistics. |
The polavization results for September 15 aud 16 were iudistinguishable. so they were combined to vield the final result for the third observational epoch. | The polarization results for September 15 and 16 were indistinguishable, so they were combined to yield the final result for the third observational epoch. |
Similarly, the polarization spectra from the six observations obtained between September 26 and October 6 (Epoch 1) were averaged together. since we detected no inter-nieht variations in (Q or C over this time period. | Similarly, the polarization spectra from the six observations obtained between September 26 and October 6 (Epoch 4) were averaged together, since we detected no inter-night variations in $Q$ or $U$ over this time period. |
We confirmed that the instrumental polarization of SPOL mounted on the Dok and dEuiper telescopes is nmch less than through observations of the unpolarized standard stars 1211 and WD 212311 (Schinidtetal.1992b) during each epoch. | We confirmed that the instrumental polarization of SPOL mounted on the Bok and Kuiper telescopes is much less than through observations of the unpolarized standard stars $^{\circ}$ 4211 and HD 212311 \citep{schmidt92b} during each epoch. |
The linear polarization position angle on the sky (0) was determined bv observing the interstellar polarization standards Illtuer 960 and VI (νο #112 (Sclunidtetal.19905210) during all epochs. | The linear polarization position angle on the sky $\theta\/$ ) was determined by observing the interstellar polarization standards Hiltner 960 and VI Cyg 12 \citep{schmidt92b} during all epochs. |
Additional observations of the polarization standard stars 59°389 and 61°106 were nade during the third epoch (Table 1). | Additional observations of the polarization standard stars $^{\circ}$ 389 and $^{\circ}$ 106 were made during the third epoch (Table 1). |
The adopted correction from the instrmucutal to the standi equatorial fraane for 0 for all epochs was determunc: from the average position angle offset of Wiltner 960 anc VI Cre | The adopted correction from the instrumental to the standard equatorial frame for $\theta\/$ for all epochs was determined from the average position angle offset of Hiltner 960 and VI Cyg 12. |
Differences between the measured ane expected polarization position aueles were <073 for al of the standard stars. | Differences between the measured and expected polarization position angles were $< 0\farcs3$ for all of the standard stars. |
During the first epoch. two field) stars within ~2! oof SN 201fc (2MASS J11031367|5115131 ane 2NTASS. J11025112]1Galactic5116288). were measured to check for siguificaut interstellar polarization (ISP) along the line-of-sight to the SN. | During the first epoch, two field stars within $\sim$ of SN 2011fe (2MASS J14031367+5415431 and 2MASS J14025413+5416288) were measured to check for significant Galactic interstellar polarization (ISP) along the line-of-sight to the SN. |
These stars vicldec a consistent estimate for Calactic ISP. with Pawo= at Ü=Ill—7 for 2\0ASS J11031367|5115131 aud Pag=O1640.0 at 0=109"t6" for 2MASS J1102511315116288. assiuniug that Àj,,,;. the waveleugth where the interstellar polarization is at a maxi (Pig) is5550À.. | These stars yielded a consistent estimate for Galactic ISP, with $P_{max} = 0.11 \pm 0.03$ at $\theta = 114^{\circ} \pm 7^{\circ}$ for 2MASS J14031367+5415431 and $P_{max} = 0.16 \pm 0.03$ at $\theta = 109^{\circ} \pm
6^{\circ}$ for 2MASS J14025413+5416288, assuming that $\lambda_{max}$, the wavelength where the interstellar polarization is at a maximum $P_{max}$ ) is. |
The results for the field stars were averaged aud ων=0.134 at 0=112° was adopted as the Galactic ISP in the sighthue to SN 2011te. | The results for the field stars were averaged and $P_{max} = 0.13$ at $\theta = 112^{\circ}$ was adopted as the Galactic ISP in the sightline to SN 2011fe. |
This low value for the Galactic ISP is consistent witli the high Calactic latitude of MIOL aud the very low estimated amount of extinction for the supernova. | This low value for the Galactic ISP is consistent with the high Galactic latitude of M101 and the very low estimated amount of extinction for the supernova. |
The polarization spectra of SN 20111ο have been corrected for this level of Galactic ISP assiuniug that it is fit well by a Serkowski law (Willàugetal.1980:Serkowski.\lath-ewson. | The polarization spectra of SN 2011fe have been corrected for this level of Galactic ISP assuming that it is fit well by a Serkowski law \citep{wilking80,serkowski}. |
&Ford 1975).. No estimate or correction for ISP within ΑΠΟ at the location of SN 2011fe has been mace (although see 833). | No estimate or correction for ISP within M101 at the location of SN 2011fe has been made (although see 3). |
Our reported values for the degree of polarization. 2. have been corrected for statistica bias Den(Wardle&I&rouberg1971). | Our reported values for the degree of linear polarization, $P\/$, have been corrected for statistical bias \citep{wardle74}. |
. Our sequence of spectra are shown in the top pane ofFigure 1l.. displaviug the emergeuce of absorption features typical of SNe Ia. The contiuuu cussion is polarized with the red waveleueths wore highly poluizec than the blue waveleugths at carly epochs. reaching up to ~O.1%.. | Our sequence of spectra are shown in the top panel ofFigure \ref{fig:spec-seq}, displaying the emergence of absorption features typical of SNe Ia. The continuum emission is polarized with the red wavelengths more highly polarized than the blue wavelengths at early epochs, reaching up to $\sim$. |
The polarization of the red coutiuuua THOOA)) exhibits a slight decrease with time. from about down to0.2%.. while contimmun polarization in the irange mereases from undetected up to | The polarization of the red continuum ) exhibits a slight decrease with time, from about down to, while continuum polarization in the range increases from undetected up to. |
The polarization of absorption lues is clearly present in blueshifted Si A6355À aabsorptiou. and it changes markedly with tine. | The polarization of absorption lines is clearly present in blueshifted Si $\lambda$ absorption, and it changes markedly with time. |
This lue polarization of SiΗ is shown in velocity space in Figure 2.. | This line polarization of Si is shown in velocity space in Figure \ref{fig:si2-vel}. |
Before παπα at Epoch 1. Sii1 AG355A sshows polarization at the same position angle(PA) as the continuum. but is roughlv stronecr than the adjacent continuum in polarization degree. | Before maximum at Epoch 1, Si $\lambda$ shows polarization at the same position angle (PA) as the continuum, but is roughly stronger than the adjacent continuum in polarization degree. |
In the subsequent two epochs near maxiuun (Epochs 2 aud 3). however. Si A6355À aabsorptiou has ~0.2% polarization than the contiuuuu. and the absorption-line PA changes by about | In the subsequent two epochs near maximum (Epochs 2 and 3), however, Si $\lambda$ absorption has $\sim$ polarization than the continuum, and the absorption-line PA changes by about |
compatible with that observed by Fermi LAT. | compatible with that observed by Fermi LAT. |
The discussion about the SSC from the ES scenario in was also restricted to noting that the SSC peak frequency may be in the GeV range for reasonable parameter values. | The discussion about the SSC from the ES scenario in was also restricted to noting that the SSC peak frequency may be in the GeV range for reasonable parameter values. |
Here we have shown that a reasonable set of parameters can be found that also implies a flux level at | GeV compatible with the one observed by Fermi LAT. | Here we have shown that a reasonable set of parameters can be found that also implies a flux level at 1 GeV compatible with the one observed by Fermi LAT. |
Moreover. we have considered two additional scenarios (1. | Moreover, we have considered two additional scenarios (1. |
and 3.). | and 3.). |
We have shown that scenarios 2. ( | We have shown that scenarios 2. ( |
SSC) and 4. | SSC) and 4. |
are viable explanations of the observed tail for a burst located at z~0.1. | are viable explanations of the observed tail for a burst located at $z\sim 0.1$. |
To reproduce the high energy tail in a delayed IS scenario. the lately emitted shells should have a time variability of about | ms and a Lorentz factor of about F=300. | To reproduce the high energy tail in a delayed IS scenario, the lately emitted shells should have a time variability of about $1$ ms and a Lorentz factor of about $\Gamma=300$. |
In the ES shock scenario. the high energy tail can be explained by assuming a flat spectrum. Le. p=2.05. and that the short GRB is powered by a fireball with ar isotropic energy of about 10°! erg. expanding in an ISM with density ?=5 em7*. | In the ES shock scenario, the high energy tail can be explained by assuming a flat spectrum, i.e. $p=2.05$, and that the short GRB is powered by a fireball with an isotropic energy of about $10^{51}$ erg, expanding in an ISM with density $n=5$ $^{-3}$. |
These values of the parameters are order-of-magnitude estimates due to the uncertainties in the early-time afterglow flux. which was not observed for this burst. | These values of the parameters are order-of-magnitude estimates due to the uncertainties in the early-time afterglow flux, which was not observed for this burst. |
In particular. the fast cooling conditior (fio22.5 8). which is reasonable to expect at the early times we consider here. depends linearly on the chosen value of12 anc almost linearly on the early-time afterglow flux value. | In particular, the fast cooling condition $t_{cool}\gtrsim 2.5$ s), which is reasonable to expect at the early times we consider here, depends linearly on the chosen value of $n$ and almost linearly on the early-time afterglow flux value. |
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