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Since he universe does contain eravitationally collapsed structures. however. tle metric that describes space-time Is one step more complicated — it iust include the contribution [rom the structures. | Since the universe does contain gravitationally collapsed structures, however, the metric that describes space-time is one step more complicated — it must include the contribution from the structures. |
If the universe is already starting to accelerate. as observations tudicate. then structure formation is virtually finishecl. | If the universe is already starting to accelerate, as observations indicate, then structure formation is virtually finished. |
In the relatively near future. the universe will approach a state of exponential expausion aud growiug cosmological perturbatious will freeze out on all scales. | In the relatively near future, the universe will approach a state of exponential expansion and growing cosmological perturbations will freeze out on all scales. |
Existing structures will erow Isolated. | Existing structures will grow isolated. |
Because the parameters of our universe are now relatively well kuowan. this future evolution of cosmological structure can now be predicted with a high degree of confidence. | Because the parameters of our universe are now relatively well known, this future evolution of cosmological structure can now be predicted with a high degree of confidence. |
Several recent papers have begun to explore the possible future effects of vacuum energy density [1-6]. and demoustrate that the universe will indeed break up into a collection of "island. uuiverses. each contaiulug oue gravitational bouud structure. | Several recent papers have begun to explore the possible future effects of vacuum energy density [4–6], and demonstrate that the universe will indeed break up into a collection of “island universes”, each containing one gravitational bound structure. |
Iu this essay. we present the results of a recent series ofnumerical simulationsE. that describe the evolution of structure in a universe dominated by dark vacuum euergy (with O4 = 0.7 at the present epoch). | In this essay, we present the results of a recent series of numerical simulations that describe the evolution of structure in a universe dominated by dark vacuum energy (with $\vac$ = 0.7 at the present epoch). |
These numerical experimeuts show that each gravitationally bound halo structure erows isolated aud that its density profile always approaches the same general form. | These numerical experiments show that each gravitationally bound halo structure grows isolated and that its density profile always approaches the same general form. |
After describing the nunerical simulations in greater detail aud specifying the form of this ceusity profile. we construct the metric for each isolated. patch of space-time. | After describing the numerical simulations in greater detail and specifying the form of this density profile, we construct the metric for each isolated patch of space-time. |
Each island. universe attaius the saine eeometry aud we find the universal form for the metric that describes these patches of space-time. | Each island universe attains the same geometry and we find the universal form for the metric that describes these patches of space-time. |
As part of a more compreheusive study of structure formation in he future of an accelerating universe. we have performed a series of numerical simulations [7]. | As part of a more comprehensive study of structure formation in the future of an accelerating universe, we have performed a series of numerical simulations [7]. |
This set of cosnological simulations used the GADGET numerical package [8] and was run on an Intel j»arallel cluster (at U. Michigan. Center for Academic Computing). | This set of cosmological simulations used the GADGET numerical package [8] and was run on an Intel parallel cluster (at U. Michigan Center for Academic Computing). |
The simulations were set up wing a standard suite of initial conditions starting at scale factor a = 0.05 [9]. and. were evolved orward into the future uutil the scale factor had grown to « = 100. | The simulations were set up using a standard suite of initial conditions starting at scale factor $a$ = 0.05 [9], and were evolved forward into the future until the scale factor had grown to $a$ = 100. |
The cosmology was chosen to lave the standard parameters described above. with Quin = 0.3. Quy = 0.7. and Hy = 70 kms | IF. | The cosmology was chosen to have the standard parameters described above, with $\om$ = 0.3, $\vac$ = 0.7, and $H_0$ = 70 km $^{-1}$ $^{-1}$. |
All of the work reported here uses this choice of cosmological parameters. | All of the work reported here uses this choice of cosmological parameters. |
The simulatious followed the evolutionof a cubic. periodic region with comoving linear size 366 | The simulations followed the evolutionof a cubic, periodic region with comoving linear size 366 |
on UT 2004 January 16 in the 3.6. 4.5. 5.8 and 8.0y/m channels. | on UT 2004 January 16 in the 3.6, 4.5, 5.8 and ${\mu}{\rm m}$ channels. |
Here we discuss the two shortest wavelength. more sensitive. observations. | Here we discuss the two shortest wavelength, more sensitive, observations. |
Twelve and eighteen 200-second exposures were accumulated at 3.6j/m and 4.5j/m respectively. using the small-step cycling dither pattern. | Twelve and eighteen 200-second exposures were accumulated at $3.6{\mu}{\rm m}$ and $4.5{\mu}{\rm m}$ respectively, using the small-step cycling dither pattern. |
The Basic Calibrated Data (BCD) were combined using custom routines to produce the final stacked frame with a pixel scale of 0.6"/pixel. | The Basic Calibrated Data (BCD) were combined using custom routines to produce the final stacked frame with a pixel scale of $0.6''/{\rm pixel}$. |
We re-binned the data back to the original pixel scale of 1.2"/pixel to eliminate correlations in the background noise. | We re-binned the data back to the original pixel scale of $1.2''/{\rm pixel}$ to eliminate correlations in the background noise. |
Visual inspection of the final frames again indicates that there is no flux at the position of #11916 (Fig. 1). | Visual inspection of the final frames again indicates that there is no flux at the position of 1916 (Fig. \ref{fig:nir}) ). |
To quantify this non-detection we follow the same procedure as ΡΟΗ. as described in refhubble.. | To quantify this non-detection we follow the same procedure as P04, as described in \\ref{hubble}. |
We used 5.1" diameter apertures. 3« the seeing disk of the IRAC observations to obtain 3c sensitivity limits. of: F(3.65/m)z0.75jJy. απά F(4.5pim)=0.75pry respectively. | We used $5.1''$ diameter apertures, $3{\times}$ the seeing disk of the IRAC observations to obtain $3{\sigma}$ sensitivity limits of: $F(3.6{\mu}{\rm m}){=}0.75{\mu}{\rm Jy}$ and $F(4.5{\mu}{\rm m}){=}0.75{\mu}{\rm Jy}$ respectively. |
The objective of this section Is to answer the three questions posed in refintro:: (0) is #11916 at z—-2—37?: ( | The objective of this section is to answer the three questions posed in \\ref{intro}: (i) is 1916 at $z{\sim}2{-}3$ ?; ( |
1) is #11916 intrinsically variable?: ( | ii) is 1916 intrinsically variable?; ( |
111) does #11916 exist? | iii) does 1916 exist? |
Preliminary inspection of the data in refdata indicates that no flux is detected at the position of #11916 at any wavelength to date. | Preliminary inspection of the data in \\ref{data} indicates that no flux is detected at the position of 1916 at any wavelength to date. |
Combining this with Bremer et al | Combining this with Bremer et al. |
s more sensitive non-detection of H(3c)>26.0. it is tempting to leap to the third question and reply "no. | 's more sensitive non-detection of $H(3{\sigma}){>}26.0$, it is tempting to leap to the third question and reply “no”. |
We adopt a more conservative approach. | We adopt a more conservative approach. |
This test concentrates on the optical data because the detection of any flux shortward of the putative Lyman limit of a galaxy at zz10 would immediately discount that interpretation. | This test concentrates on the optical data because the detection of any flux shortward of the putative Lyman limit of a galaxy at $z{\simeq}10$ would immediately discount that interpretation. |
The red observed optical/near-infrared spectral energy distribution described by PO4 could then be naturally explained by a dusty galaxy at z—-2—3. perhaps associated with the SMGs that lie within ~30” (-—200—300kpc in projection at z—2—3) of #11916 (Ivison et 22000; Smail et 22005). | The red observed optical/near-infrared spectral energy distribution described by P04 could then be naturally explained by a dusty galaxy at $z{\sim}2{-}3$, perhaps associated with the SMGs that lie within ${\sim}30''$ ${\sim}200{-}300{\rm kpc}$ in projection at $z{\sim}2{-}3$ ) of 1916 (Ivison et 2000; Smail et 2005). |
Our new non-detection of 411916 with LRIS refkeck)). coupled with confirmation of PO4's non-detection with HST//WFPC2 and Lehnert et al | Our new non-detection of 1916 with LRIS \\ref{keck}) ), coupled with confirmation of P04's non-detection with /WFPC2 and Lehnert et al. |
/s non-detection in the V-band with VLT/FORS are mutually consistent in the sense that no optical flux has been detected at this position. to date. | 's non-detection in the $V$ -band with VLT/FORS are mutually consistent in the sense that no optical flux has been detected at this position to date. |
However these non-detections are consistent with all of the following: «Ξ10. extreme dust obscuration at z--2—3. an intrinsically variable source. and non-existence. | However these non-detections are consistent with all of the following: $z{=}10$, extreme dust obscuration at $z{\sim}2{-}3$, an intrinsically variable source, and non-existence. |
The result of this test 1s therefore inconclusive. | The result of this test is therefore inconclusive. |
The objective of this section is to. test. Bremer. et al | The objective of this section is to test Bremer et al. |
/s (2004) proposal that #11916 is intrinsically variable. | 's (2004) proposal that 1916 is intrinsically variable. |
If PO4Zs photometry (7=25.00+0.25 and K=25.51-40.51) is reproducible using our independent reduction of their near-infrared data. then the variable hypothesis would be supported. | If P04's photometry $H{=}25.00{\pm}0.25$ and $K{=}25.51{\pm}0.51$ ) is reproducible using our independent reduction of their near-infrared data, then the variable hypothesis would be supported. |
If not. then the idea that #11916 does not exist would gain credibility refq3)). | If not, then the idea that 1916 does not exist would gain credibility \\ref{q3}) ). |
We attempt to reproduce PO4s analysis using SExtractor (Bertin Arnouts 1996). | We attempt to reproduce P04's analysis using SExtractor (Bertin Arnouts 1996). |
SExtractor was configured to locate all sources with at least 7 pixels that are 70.756. per pixel above the background — aa signal-to-noise ratio of 2 per resolution element. based on the H-band seeing disk of FWHM=0.45+0.017 refisaac)) and the 0.15/pix scale of the ISAAC pixels. | SExtractor was configured to locate all sources with at least 7 pixels that are ${\ge}0.75{\sigma}$ per pixel above the background – a signal-to-noise ratio of ${\gs}2$ per resolution element, based on the $H$ -band seeing disk of ${\rm
FWHM}{=}0.45{\pm}0.01''$ \\ref{isaac}) ) and the $0.15''/{\rm pix}$ scale of the ISAAC pixels. |
We also smoothed the data with a gaussian filter that matched the FWHM of the observed point sources. aa gaussian of FWHME=3 pixels. | We also smoothed the data with a gaussian filter that matched the FWHM of the observed point sources, a gaussian of ${=}3$ pixels. |
In thisconfiguration SExtractor failed to detect a source at the position of #11916. | In thisconfiguration SExtractor failed to detect a source at the position of 1916. |
We therefore experimented with different smoothing schemes. both increasing and decreasing the full width of the gaussian filter. | We therefore experimented with different smoothing schemes, both increasing and decreasing the full width of the gaussian filter. |
A "detection" was only possible with the smallest available filter - FWHMzI.5 pixels. hhalf the width of the seeing disk — yielding H=25.3+0.6. | A “detection” was only possible with the smallest available filter – ${=}1.5$ pixels, half the width of the seeing disk – yielding $H{=}25.3{\pm}0.6$. |
Experimentation with block filters produced similar results in that a "detection" was not possible with any of the standard SExtractor block filters: 34.3. 54.5. 7«7 pixels. | Experimentation with block filters produced similar results in that a “detection” was not possible with any of the standard SExtractor block filters: $3{\times}3$, $5{\times}5$, $7{\times}7$ pixels. |
We also analyzed the K-band data in exactly the same manner and failed to detect anything at the position of #11916 with any gaussian or block filter. | We also analyzed the $K$ -band data in exactly the same manner and failed to detect anything at the position of 1916 with any gaussian or block filter. |
The H-band segmentation map produced when smoothing with the FWHMzI.5 pixel gaussian reveals that the "detection" is very elongated. with a width of 1—2 pixels and a length of —5 pixels. | The $H$ -band segmentation map produced when smoothing with the ${=}1.5$ pixel gaussian reveals that the “detection” is very elongated, with a width of $1{-}2$ pixels and a length of ${\sim}5$ pixels. |
The orientation of these pixels is consistent with the orientation of #11916 reported by ΡΟΗ. | The orientation of these pixels is consistent with the orientation of 1916 reported by P04. |
It is important to stress that the motivation for filtering data with a kernel that matches the resolution element of the data is to suppress false detections. | It is important to stress that the motivation for filtering data with a kernel that matches the resolution element of the data is to suppress false detections. |
The collection of pixels identified by SExtractor at the position of #11916 was only "detectable" with à smoothing kernel that has a linear scale half that of the resolution element of the data. | The collection of pixels identified by SExtractor at the position of 1916 was only “detectable” with a smoothing kernel that has a linear scale half that of the resolution element of the data. |
It is therefore instructive to consider how many such —26 blobs exist within the ISAAC data. | It is therefore instructive to consider how many such ${\sim}2{\sigma}$ blobs exist within the ISAAC data. |
In a single 1.5" diameter aperture mmatching that used for the photometry described above) placed randomly in these H-band data. there is a 5% chance of detecting a 20 noise fluctuation — aa spurious detection. | In a single $1.5''$ diameter aperture matching that used for the photometry described above) placed randomly in these $H$ -band data, there is a $5\%$ chance of detecting a $2{\sigma}$ noise fluctuation – a spurious detection. |
However the ISAAC array (1024.IO24pixels. each pixel 0.15”<0.15’) contains of order 101 independent photometric apertures of 1.5" diameter. | However the ISAAC array $1024{\times}1024{\rm pixels}$, each pixel $0.15''{\times}0.15''$ ) contains of order $10^4$ independent photometric apertures of $1.5''$ diameter. |
The H-band frame therefore contains —-500 noise fluctuations of 2σ significance. | The $H$ -band frame therefore contains ${\sim}500$ noise fluctuations of $2{\sigma}$ significance. |
Sadly. the only reasonable conclusion to draw from this analysis is that #11916 is not detected in our independent reduction of PO4's data. | Sadly, the only reasonable conclusion to draw from this analysis is that 1916 is not detected in our independent reduction of P04's data. |
We therefore place 3c limits on the flux at this position of: H725.0 and Κ225.0(5 refisaac)). | We therefore place $3{\sigma}$ limits on the flux at this position of: $H{\ge}25.0$ and $K{\ge}25.0$ \\ref{isaac}) ). |
The only wavelength at which two directly comparable observations are available is in. the. H-band. | The only wavelength at which two directly comparable observations are available is in the $H$ -band. |
Combining our non-detection with that of Bremer et ((2004). we conclude that there is no evidence for variability of 411916. and that (if it exists) its H-band flux is fainter than H=26 at 3o significance (Bremer et 22004). | Combining our non-detection with that of Bremer et (2004), we conclude that there is no evidence for variability of 1916, and that (if it exists) its $H$ -band flux is fainter than $H{=}26$ at $3{\sigma}$ significance (Bremer et 2004). |
The results of the preceding two sections were derived from non-detection of #11916 across the broadest wavelength range to date: 0.35A445; m. | The results of the preceding two sections were derived from non-detection of 1916 across the broadest wavelength range to date: $0.35{\le}{\lambda}_{\rm obs}{\le}5{\mu}{\rm m}$ . |
We now combine all of these non-detections to address the question of whether #11916 exists. | We now combine all of these non-detections to address the question of whether 1916 exists. |
The data force us to conclude that there is no statistically sound evidence that #11916 exists. | The data force us to conclude that there is no statistically sound evidence that 1916 exists. |
The balance of probability 1s that #11916 was a false detection in PO4's | The balance of probability is that 1916 was a false detection in P04's |
according to a Gaussian prolile: where (he scale height of the vorticity was the same as (le pressure scale height. | according to a Gaussian profile: where the scale height of the vorticity was the same as the pressure scale height. |
For an anlicvelone with Ro<1. the inward Coriolis force is somewhat more dominant than than the outward centrifugal force. aid (he vortex must be a region of high pressure for horizontal equilibrium (see Figure 2)). | For an anticyclone with $Ro\lesssim 1$, the inward Coriolis force is somewhat more dominant than than the outward centrifugal force, and the vortex must be a region of high pressure for horizontal equilibrium (see Figure \ref{F:force_balance}) ). |
The hieh-pressure core extends only over a finite height. so that (here is à vertical pressure force away [rom the midplane. | The high-pressure core extends only over a finite height, so that there is a vertical pressure force away from the midplane. |
In order for the vortex to be in vertical ecuilibrium. there must be cool. dense lids which provide a buovancy force directed toward (he midplane. | In order for the vortex to be in vertical equilibrium, there must be cool, dense lids which provide a buoyancy force directed toward the midplane. |
Figures 4 and 5 show the time evolution of (he z-component of the vorlicily in vertical slices yor al r=O0 ancl r—2 at y=O0. | Figures \ref{F:wz_yz} and \ref{F:wz_xz} show the time evolution of the $z$ -component of the vorticity in vertical slices $y\!-\!z$ at $x\!=\!0$ and $x\!-\!z$ at $y\!=\!0$. |
Figure 6 shows the z-component of the vorlicily in two different horizontal slices τν at 2—0 (first column) and z—2 (second column). | Figure \ref{F:wz_xy} shows the $z$ -component of the vorticity in two different horizontal slices $x\!-\!y$ at $z\!=\!0$ (first column) and $z\!=\!2$ (second column). |
Figure 7 shows vertical slices y-2 at 7-0 of the temperature perturbation. | Figure \ref{F:temp_yz} shows vertical slices $y\!-\!z$ at $x\!=\!0$ of the temperature perturbation. |
The time between frames in all these figures is A//7,,,2 GO. | The time between frames in all these figures is $\Delta t/\tau_{orb}\approx 60$ . |
These results were computed with the inlinite vertical domain version of the simulation: the horizontal dimensions were (L,.L,)=(2.8). and the vertical mapping parameter was £L.=4. | These results were computed with the infinite vertical domain version of the simulation: the horizontal dimensions were $(L_x,L_y) = (2,8)$, and the vertical mapping parameter was $L_z = 4$. |
The numbers of spectral modes along each direction οV.)Ne,=(64.256.256). | The numbers of spectral modes along each direction were $(N_x,N_y,N_z) = (64,256,256)$. |
The three components of the momentun equation were exaclly satislied initiallv. but the energy equation was out of equilibrium from (he start. | The three components of the momentum equation were exactly satisfied initially, but the energy equation was out of equilibrium from the start. |
The temperature field slowly evolved. generating a small vertical velocity which then coupled the horizontal lavers together. | The temperature field slowly evolved, generating a small vertical velocity which then coupled the horizontal layers together. |
After approximately a few dozen 7,54. the vertically truncated vortex settled into a new. quasi-equilibrium (see Irames 2-4 in Figures + 7)) that changed very little over (he course of a couple hundred orbits through (he disk. | After approximately a few dozen $\tau_{orb}$, the vertically truncated vortex settled into a new, quasi-equilibrium (see frames 2-4 in Figures \ref{F:wz_yz}- \ref{F:temp_yz}) ) that changed very little over the course of a couple hundred orbits through the disk. |
Figure 8 shows vortex lines for (he initial condition and for the euasi-equilibrium steady-state at {τον=110. | Figure \ref{F:vortex_lines_sim} shows vortex lines for the initial condition and for the quasi-equilibrium steady-state at $t/\tau_{orb}=170$. |
We thought we had indeed found a stable steady-state. but. surprisingly the vortex suffered a dramatic instability which ultimately resulted in the complete destruction of the vortex in (he micplane (see lame 5 in Figures + 7)). | We thought we had indeed found a stable steady-state, but surprisingly the vortex suffered a dramatic instability which ultimately resulted in the complete destruction of the vortex in the midplane (see frame 5 in Figures \ref{F:wz_yz}- \ref{F:temp_yz}) ). |
The initial condition was svuunetric with respect to the midplane. audthe equations of motion should have preserved (his symmetry. | The initial condition was symmetric with respect to the midplane, andthe equations of motion should have preserved this symmetry. |
However. (he instability clearly had an antisvinnietric component. | However, the instability clearly had an antisymmetric component. |
We decomposecl (he flow into its svaumetric ancl antisviunmetric parts. | We decomposed the flow into its symmetric and antisymmetric parts. |
Figure 9 shows the maximum absolute value of the antisvinnmetric part of the z-component of vorlicily as a [uncetion of time. | Figure \ref{F:growth} shows the maximum absolute value of the antisymmetric part of the $z$ -component of vorticity as a function of time. |
Initially. it was very close to zero. but grew from numerical round-olf errors. | Initially, it was very close to zero, but grew from numerical round-off errors. |
Eventually. a linear eigenmode emerged out of (his numerical antisvinmetric noise. | Eventually, a linear eigenmode emerged out of this numerical antisymmetric noise. |
The structure of the mode preserved its spatial form for over (en orders of magnitude of evowlth. proving that itis indeed a linear instability. | The structure of the mode preserved its spatial form for over ten orders of magnitude of growth, proving that itis indeed a linear instability. |
The e-folding time of the exponential growth was a few 754 | The $e$ -folding time of the exponential growth was a few $\tau_{orb}$ . |
the victim of tidal disruption is a main sequence star. | the victim of tidal disruption is a main sequence star. |
We estimate here both the thermal enussion ol the disk and the jet power. | We estimate here both the thermal emission of the disk and the jet power. |
The first is estimated using standard accretion disk theory. | The first is estimated using standard accretion disk theory. |
The latter is estimated in terms of the Blandlord-Znajek mechanism. using the disk pressure near the ISCO as a measure of the black hole's magnetic field. | The latter is estimated in terms of the Blandford-Znajek mechanism, using the disk pressure near the ISCO as a measure of the black hole's magnetic field. |
Although a tidal disruption of a main sequence star lakes place on a much larger lengtühscale than the disruption of a white dwarf. for most of the relevant parameter space a simular situation holds: the accretion is super-Edclington. thermal radiation is suppressed. ancl conditions for emergence of a strong jet are established. | Although a tidal disruption of a main sequence star takes place on a much larger lengthscale than the disruption of a white dwarf, for most of the relevant parameter space a similar situation holds: the accretion is super-Eddington, thermal radiation is suppressed, and conditions for emergence of a strong jet are established. |
Our work is complementary (o two related efforts. | Our work is complementary to two related efforts. |
Giannios&Metzger(2011) investigated. possible radio emission [rom a jet receiving a fixed. (small) fraction of the accretion energy released by accreting (idally disrupted matter. | \cite{giannios11} investigated possible radio emission from a jet receiving a fixed (small) fraction of the accretion energy released by accreting tidally disrupted matter. |
Lei&Zhane(2011) have suggested a similar picture. but. approach it rather dillerently. | \cite{leizhang11} have suggested a similar picture, but approach it rather differently. |
In particular. (ey. use thin disk approximations for both the sub- and super-Eddineton regimes. their scaling with black hole mass does not include the relation between disk thickness and accretion rate in the racliation-dominated sub-Eddington phase. and they do not discuss the luminosity of the thermal disk. | In particular, they use thin disk approximations for both the sub- and super-Eddington regimes, their scaling with black hole mass does not include the relation between disk thickness and accretion rate in the radiation-dominated sub-Eddington phase, and they do not discuss the luminosity of the thermal disk. |
We begin in 2 with a brief discussion of tidal disruption physics. | We begin in \ref{sec:tidal}
with a brief discussion of tidal disruption physics. |
We (hen discuss accretion ονπας in (his context and the jet and disk outputs in 3.. | We then discuss accretion dynamics in this context and the jet and disk outputs in \ref{sec:jet_disk}. |
In d. we show how this approach can be used to constrain a number of otherwise-unknown parameters of tidal clisruptions aud apply this method to Swift J2058 (Cenkoοἱal.2011).. a second example of a jet-dominated tidal disruption. | In \ref{sec:j2058}, we show how this approach can be used to constrain a number of otherwise-unknown parameters of tidal disruptions and apply this method to Swift J2058 \citep{cenko11}, a second example of a jet-dominated tidal disruption. |
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