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rtm-sgt-ocr-v1

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These probabilities do not change significantly when errors on (Qy, or σαι are taken into account.
These probabilities do not change significantly when errors on $Q_b$ or $\sigma_{\mbox{\scriptsize sm}}$ are taken into account.
In (he event that the (wo samples intersect. we exclude the shared ealaxies [rom both samples in order to do the comparison.
In the event that the two samples intersect, we exclude the shared galaxies from both samples in order to do the comparison.
In the few cases where both sample sizes small we use the Wilcoxon rank-sum test instead of the IX-8 test.
In the few cases where both sample sizes small, we use the Wilcoxon rank-sum test instead of the K-S test.
The Wilcoxon test compares two samples A and D of size .N4 and Ny. with VyXNy. where the “tue” mean values of A and D are sry and sry. respectively.
The Wilcoxon test compares two samples A and B of size $N_A$ and $N_B$, with $N_A \le N_B$, where the “true” mean values of A and B are $\mu_A$ and $\mu_B$, respectively.
Letting the sum of the ranks in sample A be i. the probability that poy>fry is equal to the probability that the sum of the ranks of N4 randomly. chosen elements (from a set of size Nat Ny) is Xτον while the probability that poy<pay is equal to the probability that the sium of ranks is >INí4CV47Ng+1)—ac.
Letting the sum of the ranks in sample A be $w$, the probability that $\mu_A > \mu_B$ is equal to the probability that the sum of the ranks of $N_A$ randomly chosen elements (from a set of size $N_A + N_B$ ) is $\le w$, while the probability that $\mu_A < \mu_B$ is equal to the probability that the sum of ranks is $\ge N_A (N_A + N_B + 1) - w$.
Our Classifications and measurements of o,, are summarized in Table 1..
Our classifications and measurements of $\sigma_{\mbox{\scriptsize sm}}$ are summarized in Table \ref{tbl:data}.
There is a probability that the tightly wound (TW) nuclear dust spirals have the same underlying distribution of barstrength as the rest of the sample.
There is a probability that the tightly wound (TW) nuclear dust spirals have the same underlying distribution of barstrength as the rest of the sample.
As shown in Figure 4.. TW nuclear spirals are found primarilyalthough not exclusivelyin weakly barred galaxies.
As shown in Figure \ref{fig:tw}, TW nuclear spirals are found primarily—although not exclusively—in weakly barred galaxies.
As the TW class is defined to be those dust spirals with pileh angle <107.. (his is consistent wilh the idea that a galaxy. which is axisvimimetric al large scales (1.e.. has a small Q,) will either have high differential rotation or simply that the central regions of these galaxies cannol
As the TW class is defined to be those dust spirals with pitch angle $\le$, this is consistent with the idea that a galaxy which is axisymmetric at large scales (i.e., has a small $Q_b$ ) will either have high differential rotation or simply that the central regions of these galaxies cannot
NS oscillations ancl instabilities.
NS oscillations and instabilities.
This requires further investigation.
This requires further investigation.
The requirement on GW enerev level could be lower if more signals are emitted near (he most sensitive frequency band of grounud-based detectors (~40—200 Iz).
The requirement on GW energy level could be lower if more signals are emitted near the most sensitive frequency band of ground-based detectors $\sim 40-200$ Hz).
Through reasonable assumptions of average source spectra. the lowest detectable (in terms of stochastic background) GW energy for individual source will be LO*M.c? for third generation detectors like ET (Zhuοἱal.2010)..
Through reasonable assumptions of average source spectra, the lowest detectable (in terms of stochastic background) GW energy for individual source will be $10^{-7} \hspace{1mm} M_{\odot} c^2$ for third generation detectors like ET \cite{SN_limit}.
Overall. for the detection of SGWD [from NS instabilies. more ellicient emitters are required (see. e.g. Andersson οἱ al.
Overall, for the detection of SGWB from NS instabilities, more efficient emitters are required (see, e.g., Andersson et al.
2010 for reviews of GW emission from NSs and Ixastaun et al.
2010 for reviews of GW emission from NSs and Kastaun et al.
2010 for details of a possible more efficient mechanism - [-mode).
2010 for details of a possible more efficient mechanism - f-mode).
While the SGWB from NS r-mode instability is difficult to detect. the associated GW signal is still detectable in terms of single events (Owen2010).. although this possibility also depends stronely on (he saturation amplitude.
While the SGWB from NS r-mode instability is difficult to detect, the associated GW signal is still detectable in terms of single events \cite{owen}, although this possibility also depends strongly on the saturation amplitude.
For instance. initially it was believed that GWs from r-mode instability in a newborn NS could be detected by advanced. LIGO out to a distauce o£ 20 Alpe (Owen&Lindblom2002).
For instance, initially it was believed that GWs from r-mode instability in a newborn NS could be detected by advanced LIGO out to a distance of 20 Mpc \cite{Owen2002}.
. ILowever even for the most optimistic case in Dondarescu et al. (
However even for the most optimistic case in Bondarescu et al. (
2009). the detectable distance For advanced LIGO is only 1 Mpc.
2009), the detectable distance for advanced LIGO is only 1 Mpc.
The LIGO Scientilic Collaboration and. Virgo Collaboration have already performed many searches for periodic GWs Iron rapidly rotating NSs including the first search (argetine ihe voungest known NS - Cassiopeia A (Abaclieetal.2010).
The LIGO Scientific Collaboration and Virgo Collaboration have already performed many searches for periodic GWs from rapidly rotating NSs including the first search targeting the youngest known NS - Cassiopeia A \cite{ns}.
. Although no GWs have been detected. direct upper limits on GW emission [rom known pulsars like (he Crab pulsar have beaten down the indirect spin-down limits (Abbottetal.2003).
Although no GWs have been detected, direct upper limits on GW emission from known pulsars like the Crab pulsar have beaten down the indirect spin-down limits \cite{crab}.
. This work was supported by the National Natural Science Foundation of China under the Distinguished Young Scholar Grant 10825313 and Grant 11073005. and by the Ministry ol Science and Technology national basic science Program (Project 973) under Grant No.
This work was supported by the National Natural Science Foundation of China under the Distinguished Young Scholar Grant 10825313 and Grant 11073005, and by the Ministry of Science and Technology national basic science Program (Project 973) under Grant No.
2007CD815401.
2007CB815401.
We thank the anonymous referee for valuable comments and useful suggestions which improved (is work very much.
We thank the anonymous referee for valuable comments and useful suggestions which improved this work very much.
ZXJ is erateful to Yun Chen. Eric Howell. David Blair and Luciano Rezzolla for helpful discussions. and to Tania Reeimbau lor providing data of ET sensitivity and > function.
ZXJ is grateful to Yun Chen, Eric Howell, David Blair and Luciano Rezzolla for helpful discussions, and to Tania Regimbau for providing data of ET sensitivity and $\gamma$ function.
may together be enough to explain the differences in number count predictions between our analysis and that of CBS06, this issue must be more carefully examined in subsequent work.
may together be enough to explain the differences in number count predictions between our analysis and that of CBS06, this issue must be more carefully examined in subsequent work.
We have uncovered many degeneracies among the scalings of radio power with cluster mass and turbulent pressure and the mass-dependence of cluster magnetic fields.
We have uncovered many degeneracies among the scalings of radio power with cluster mass and turbulent pressure and the mass-dependence of cluster magnetic fields.
These degeneracies can be broken by several methods.
These degeneracies can be broken by several methods.
For example, a better understanding of the relationship between cluster mass and magnetic field will constrain our (B) (?).. (??),,
For example, a better understanding of the relationship between cluster mass and magnetic field will constrain our $\aveb$ \citep{Brunetti2009a}. \citep{Cassano2006,Brunetti2008},
\nocite{*}
orbit ISCO) when the central black hole is sufiicieuthly simall ia mass.
orbit (ISCO) when the central black hole is sufficiently small in mass.
For this to happen. canonical estimates provide a botnd of 3.7AL. on nonotatije black holes and a bouud of 28M.. on rapidly rot:inue black holes.
For this to happen, canonical estimates provide a bound of $3.7M_\odot$ on non-rotating black holes and a bound of $28M_\odot$ on rapidly rotating black holes.
This uxicates a substantially wider wineow of mass for the xXtaine case.
This indicates a substantially wider window of mass for the rotating case.
It follows tlat a torus is more Likev to form around a Kerr blewk. nP The colapsar. failed SHpeOrnowva or hyper10Và scenario envisonst 1ο collapse of he center of a vou1οo assive star with hieh augular ΠΟΙΟΙitin.
It follows that a torus is more likely to form around a Kerr black \cite{pac91} The collapsar, failed supernova or hypernova scenario envisions the collapse of the center of a young massive star with high angular momentum.
The origin of the aueular 110nent is most likely orbital angular momeitiua from the progenlor binary svstei.
The origin of the angular momentum is most likely orbital angular momentum from the progenitor binary system.
While the! details of orbital aueular uxneti traister iut» the collapsing star are somewhat uncertain. collapse oa rapidly rotating object Is expeced ο result in à compact core surrounded by matter stalled agaiist an auguar moment xurier.
While the details of orbital angular momentum transfer into the collapsing star are somewhat uncertain, collapse of a rapidly rotating object is expected to result in a compact core surrounded by matter stalled against an angular momentum barrier.
Hf the core forms a black hole 11 xonipt. collapse the rthenuore. the black hole will have ᾱ lass. sufficient to accotut for the auear momentum 4 in view of the Ker constraint+ 77,U€M7Di (in+ geonetrical uuis. With AY denoting the Sclavarzsclild radius- “4JDGanjc. where Gis Nowtou's c)ustant. a the mass of the black hole aud e the velociv of light) "..
If the core forms a black hole in prompt collapse then, furthermore, the black hole will have a mass, sufficient to account for the angular momentum $J_H$ in view of the Kerr constraint $J_H^2\le M^2$ (in geometrical units, with $M$ denoting the Schwarzschild radius $Gm/c^2$, where $G$ is Newton's constant, $m$ the mass of the black hole and $c$ the velocity of light) \cite{mvp01a}.
For exa1.iple; a Laue-Emden relationship with polvtropic 1idex n=3 for the progen1or star gives AMc104... cousistcut with the observed rouge of 3LIAL. i1 SNTs shown in Fig.
For example, a Lane-Emden relationship with polytropic index $n=3$ for the progenitor star gives $M\ge 10M_\odot$, consistent with the observed range of $3-14M_\odot$ in SXTs shown in Fig.
2.
2.
Iu both SCOjuios. a magnetized icutron star or voung lassive star represen by a nmaenetie nonient ¢(ΠΙΟ. will τος] iu a disk or torus endowed. wi ha uct poloidal fux.
In both scenarios, a magnetized neutron star or young massive star - represented by a magnetic moment density – will result in a disk or torus endowed with a net poloidal flux.
It nay be appreciated that the nass in the disk o tons n finite in a auch nore stricter sense than in analogous configuratioas hxJieved to exist in active ealactic nuclei.
It may be appreciated that the mass in the disk or torus a finite in a much more stricter sense than in analogous configurations believed to exist in active galactic nuclei.
Wi 1inagnetic regulated accretion. accretion of OLAS. becomes arly rapid ou a tire-scale of a second Or less «ito onto a 10A, mass black hole.
With magnetic regulated accretion, accretion of $0.1M_\odot$ becomes fairly rapid on a time-scale of a second or less onto onto a $10M_\odot$ mass black hole.
Depleting 10 SULTOULudings of xuwvolnic uatter inevitably preveuts any further activity of he black role.
Depleting the surroundings of baryonic matter inevitably prevents any further activity of the black hole.
This sugeests---- hat additional physical processes should accouit for he relatively ong duraion iu long bursts.
This suggests that additional physical processes should account for the relatively long duration in long bursts.
Iu a recent proposal. the magnetic nioneit density of the surrounding torus is believed to periit a suspende-aceretion state for he duratiou of spin-down of the central black hole.
In a recent proposal, the magnetic moment density of the surrounding torus is believed to permit a suspended-accretion state for the duration of spin-down of the central black hole.
A bianoda dcistribution of duratiouns then occurs when the ratio of black hole-to-disk or OYUs Lüüss ls arge? The black hole will be surrounded by a torus magnetosphere. supported by the accretion disk.
A bi-modal distribution of durations then occurs when the ratio of black hole-to-disk or torus mass is \cite{mvp01a} The black hole will be surrounded by a torus magnetosphere, supported by the accretion disk.
The black hole will adjust to a lowest cucrey state by developing au equilibrimu macuetic moment?
The black hole will adjust to a lowest energy state by developing an equilibrium magnetic \cite{mvp01b}
authors. who used various datasets and methods: redshift survey of galaxies. ?:: PSCz.. ? and reanalvsis by τν X-ray selected clusters. οτι reconstructed. velocity field of PAIRS. ?..
authors, who used various datasets and methods: redshift survey of galaxies, \cite{Strauss}; , \cite{Schmoldt} and reanalysis by \cite{BP06}; X-ray selected clusters, \cite{KE06}; reconstructed velocity field of 2MRS, \cite{Lav10}.
On the other hand. they contradict claims of convergence al scales even as small as GO Ape/h: optical sample of ον redshift sample ofAbell/ACO clusters. 2:PSCz.. ?:: and DTP. ?: 2AIRS. ?..
On the other hand, they contradict claims of convergence at scales even as small as 60 – $\Mpch$: optical sample of \cite{Hudson}; redshift sample ofAbell/ACO clusters, \cite{Tini};, \cite{RR2000}; and BTP, \cite{DMSa}; 2MRS, \cite{Erdogdu}.
Our analysis also suggests a different interpretation of the results of ? cata presentation as in our Figure 2 instead of figure 1 (therein would possibly point to similar lack of convergence.
Our analysis also suggests a different interpretation of the results of \cite{Maller03} — data presentation as in our Figure \ref{Fig:growth.r} instead of figure 1 therein would possibly point to similar lack of convergence.
On the other hand. in order to ba able to compare our results with those of ?.. we would have to apply the same weighting as was done for the 2MBRS sample. namely by the inverse ol the fIux-weighted selection function.
On the other hand, in order to ba able to compare our results with those of \cite{Erdogdu}, we would have to apply the same weighting as was done for the 2MRS sample, namely by the inverse of the flux-weighted selection function.
We are unable to do it. not knowing distances nor redshifts for the whole sample.
We are unable to do it, not knowing distances nor redshifts for the whole sample.
Apart from galaxy. weighting. the discrepancies between the above listed results most probably stem from the different nature of catalogs and methods used for the caleulation. ancl in particular may be due to distinct.
Apart from galaxy weighting, the discrepancies between the above listed results most probably stem from the different nature of catalogs and methods used for the calculation, and in particular may be due to distinct.
windows.. Such a window lor a given survey describes the sample: it may be interpreted as a filter (in real or Fourier space) through which we observe the Universe.
Such a window for a given survey describes the sample: it may be interpreted as a filter (in real or Fourier space) through which we observe the Universe.
Ixnowledge of the observational windows. necessary (o correctly confront results as those given above. is also essential if we want (o make comparisons with theoretical expectations.
Knowledge of the observational windows, necessary to correctly confront results as those given above, is also essential if we want to make comparisons with theoretical expectations.
We would now like to check if the behavior of the 2\TASS [his dipole is consistent with the predictions of the currently favorecl cosmological model. namely Lambda-Cold-Dark-Aatter (ACDAI).
We would now like to check if the behavior of the 2MASS flux dipole is consistent with the predictions of the currently favored cosmological model, namely Lambda-Cold-Dark-Matter $\Lambda$ CDM).
We start bv. presenting the theoretical framework for such a comparison.
We start by presenting the theoretical framework for such a comparison.
It was first derived in the context of then-popular models like cold-darkanatter ancl isocurvature barvon. as described in detail in (wo classic papers: ? and ?..
It was first derived in the context of then-popular models like cold-dark-matter and isocurvature baryon, as described in detail in two classic papers: \cite{JVW} and \cite{LKH}.
More recently. this approach was taken by 2.. who reconstructed the local peculiar velocity field (up to ~150 Mpc/h). applving the data [rom the 2MBRS.
More recently, this approach was taken by \cite{Lav10}, who reconstructed the local peculiar velocity field (up to $\sim150\Mpch$ ), applying the data from the 2MRS.
The basic quantity for these comparisons is the joint probabilitydistribution funcüon for & ancl g. assumed to be a multivariate Gaussian.
The basic quantity for these comparisons is the joint probabilitydistribution function for $\bmv$ and $\bmg$ , assumed to be a multivariate Gaussian.
with the optimal time step size for each phase of light curve evolution.
with the optimal time step size for each phase of light curve evolution.
Therefore. we implemented an adaptive time step routine to determine the optimal time step size for the current time step.
Therefore, we implemented an adaptive time step routine to determine the optimal time step size for the current time step.
The energy change Ae of the energy of the material e may be approximated by where Q is the energy change of the interaction with the radiation. and € is the energy deposition by the gamma rays.
The energy change $\Delta e$ of the energy of the material $e$ may be approximated by where Q is the energy change of the interaction with the radiation, and $\epsilon$ is the energy deposition by the gamma rays.
The energy change due to the expansion is ignored imn this case.
The energy change due to the expansion is ignored in this case.
On the one hand. this energy change depends on the new matter density after the time step. which is unknown because it depends on the size of the time step itself.
On the one hand, this energy change depends on the new matter density after the time step, which is unknown because it depends on the size of the time step itself.
Furthermore. the energy change because of the expansion is small compared to the changes caused by the energy transport and the energy deposition by y-rays.
Furthermore, the energy change because of the expansion is small compared to the changes caused by the energy transport and the energy deposition by $\gamma$ -rays.
The idea of the adaptive time step procedure is to limit the energy change to a prescribed amount of the energy of the material.
The idea of the adaptive time step procedure is to limit the energy change to a prescribed amount of the energy of the material.
Thus. rewriting equation 10.. we obtain the time step size Ar for the current time step by where x is the introduced limiting energy change factor.
Thus, rewriting equation \ref{eq:adapt}, we obtain the time step size $\Delta t$ for the current time step by where $x$ is the introduced limiting energy change factor.
The factor x ranges between vx,; and ρω. Which mark the largest and smallest allowed energy change.
The factor $x$ ranges between $x_{min}$ and $x_{max}$, which mark the largest and smallest allowed energy change.
These are input parameters for the adaptive time step procedure.
These are input parameters for the adaptive time step procedure.
The time step size is calculated for every layer. and the minimum time step size of all layers is used for the energy solver.
The time step size is calculated for every layer, and the minimum time step size of all layers is used for the energy solver.
Each time the adaptive time step procedure is called. it checks if the energy changes of the time step before were too big or could have been bigger.
Each time the adaptive time step procedure is called, it checks if the energy changes of the time step before were too big or could have been bigger.
If the minimum time step size is in a different layer. the same value of x is kept for the next time step.
If the minimum time step size is in a different layer, the same value of $x$ is kept for the next time step.
If the minimum is in the same layer and the sign of the energy change does not change. the previous time step might have been too small.
If the minimum is in the same layer and the sign of the energy change does not change, the previous time step might have been too small.
Thus. the factor x is increased for the following time step.
Thus, the factor $x$ is increased for the following time step.
If the sign changes. the last time step might have been too large. therefore. the factor x 1s decreased.
If the sign changes, the last time step might have been too large, therefore, the factor $x$ is decreased.
This means that for each time step. the allowed energy change is adapted and the factor x 1s updated to get the optimal time step during the whole evolution of the SN Ia atmosphere.
This means that for each time step, the allowed energy change is adapted and the factor $x$ is updated to get the optimal time step during the whole evolution of the SN Ia atmosphere.
All new implemented physical processes of the simple energy solver have to be tested.
All new implemented physical processes of the simple energy solver have to be tested.
For the test atmosphere. the atmosphere structure and abundances of the W7 deflagration model (?) are used.
For the test atmosphere, the atmosphere structure and abundances of the W7 deflagration model \citep{nomoto84} are used.
The atmosphere structure is expanded to a point in time of 10 days after the explosion.
The atmosphere structure is expanded to a point in time of 10 days after the explosion.
The densities and radii are determined by free homologous expansion and can be computed easily.
The densities and radii are determined by free homologous expansion and can be computed easily.
To perform the test calculations. we obtained an initial temperature structure with the ttemperature correction. procedure (2)..
To perform the test calculations, we obtained an initial temperature structure with the temperature correction procedure \citep{phhtc03}.
This temperature structure is the result of a simple approach that does not represent the temperature structure of an SN Ia precisely.
This temperature structure is the result of a simple approach that does not represent the temperature structure of an SN Ia precisely.
However. for the test calculations for our energy solver. this simple temperature structure is sufficient.
However, for the test calculations for our energy solver, this simple temperature structure is sufficient.
With this initial atmosphere structure. the energy solver is applied for different test cases.
With this initial atmosphere structure, the energy solver is applied for different test cases.
All contributions to the energy change are tested separately.
All contributions to the energy change are tested separately.
In this section. the energy transport through the atmosphere ts tested.
In this section, the energy transport through the atmosphere is tested.
The energy solver considers only the energy change caused by emission and absorption of radiation. where the result of the radiative transfer equation is needed.
The energy solver considers only the energy change caused by emission and absorption of radiation, where the result of the radiative transfer equation is needed.
All other influences are neglected.
All other influences are neglected.
As a first test. we check how the initial temperature structure changes if the energy solver is changing the SN Ia envelope.
As a first test, we check how the initial temperature structure changes if the energy solver is changing the SN Ia envelope.
As the initial. atmosphere structure ts already in radiative equilibrium. the energy solver should not change the temperature structure significantly. because it also pushes the atmosphere towards a radiative equilibrium state.
As the initial atmosphere structure is already in radiative equilibrium, the energy solver should not change the temperature structure significantly, because it also pushes the atmosphere towards a radiative equilibrium state.
In Fig. 1..
In Fig. \ref{fig:lc_test_tcor},
à comparison of the temperature structure of the energy solver to the result of the temperature correction procedure is shown.
a comparison of the temperature structure of the energy solver to the result of the temperature correction procedure is shown.
The differences in. the temperature structure for most layers are less than1%.
The differences in the temperature structure for most layers are less than.
. But the temperature differences of the inner layers are clearly higher.
But the temperature differences of the inner layers are clearly higher.
These differences arise in the ttemperature correction result which produces a spike in the temperature structure.
These differences arise in the temperature correction result which produces a spike in the temperature structure.
This is likely due to the boundary condition in the temperature correction.
This is likely due to the boundary condition in the temperature correction.
Hence. the resulting temperature structure obtained with the energy solver is more accurate.
Hence, the resulting temperature structure obtained with the energy solver is more accurate.
Here. the temperature structure is smooth.
Here, the temperature structure is smooth.