ReadingTimeMachine/rtm-sgt-ocr-v1 · Datasets at Hugging Face

The orbital solution is eiven in Table 1.

The orbital solution is given in Table 1.

Preliminary solutions included a velocity zero point offset between the

the accretion dise extends up to the tical radius ancl so the asymmetric brightness distribution in the accretion disc we observed can be explained. by the presence of a tically cistorted accretion disc.

the accretion disc extends up to the tidal radius and so the asymmetric brightness distribution in the accretion disc we observed can be explained by the presence of a tidally distorted accretion disc.

Naravan.AleClintock&Yi(1996).and Naravan.Barret&MeClintock(1997) have proposed an accretion [iow model to explain the observations of quiescent black hole X-rav transients.

\citet{Narayan96} and \citet{Narayan97} have proposed an accretion flow model to explain the observations of quiescent black hole X-ray transients.

Phe accretion disc has two components. an inner hot advection-dominated accretion Dow. CXDAT) that extends from the black hole horizon to a transition radius and a thin acerction disc that extends from the transition disc to the edge of the accretion disc.

The accretion disc has two components, an inner hot advection-dominated accretion flow (ADAF) that extends from the black hole horizon to a transition radius and a thin accretion disc that extends from the transition disc to the edge of the accretion disc.

Interactions between the hot inner ADAP ancl the cool. outer thin disc. at or near the transition radius could be a source of quasi-periodic variability.

Interactions between the hot inner ADAF and the cool, outer thin disc, at or near the transition radius could be a source of quasi-periodic variability.

The ADAP flow requires electrons in the gas to cool via svnehrotron. bremsstrahlung. and inverse Compton oocesses which predict the form of the spectrum from racio o hard. X-ravs.

The ADAF flow requires electrons in the gas to cool via synchrotron, bremsstrahlung, and inverse Compton processes which predict the form of the spectrum from radio to hard X-rays.

lt has been suggested that the [ares observed in aanel other quiescent X-ray transicnts arise. from the ransition radius (Zuritaetal.2003: Shahbazetal. 2003b)).

It has been suggested that the flares observed in and other quiescent X-ray transients arise from the transition radius \citealt{Zurita03}; \citealt{Shahbaz03b}) ).

Indeed. the mmllIz feature detected in CCve has oen used to determine the transition radius. assuming hat the periodicity. represents the Weplerian period. at he transition between the thin and advective disce regions (Shahbazetal.2003b).. and a possible low freequeney. breaks in the power spectrum of mmav have a related origin (Hlvnesctal.2003).

Indeed, the mHz feature detected in Cyg has been used to determine the transition radius, assuming that the periodicity represents the Keplerian period at the transition between the thin and advective disc regions \citep{Shahbaz03b}, and a possible low frequency break in the power spectrum of may have a related origin \citep{Hynes03}.

. In the original. ADA models the optical flux. is produced. by svnchrotron emission.

In the original ADAF models the optical flux is produced by synchrotron emission.

As pointed out in Shahbaz (2003hb).. it is difficult to explain the Dare spectrum in ternis of optically thin synchrotron emission. unless the electrons follow a much steeper power-law electron energy distribution compared to solar [lares: solar and stellar flares have a frequeney spectrum with a power-law index of a=0.5 and an electron energy. distribution with a power-law index of ~ 2.

As pointed out in \citet{Shahbaz03b}, it is difficult to explain the flare spectrum in terms of optically thin synchrotron emission, unless the electrons follow a much steeper power-law electron energy distribution compared to solar flares; solar and stellar flares have a frequency spectrum with a power-law index of $\alpha$ =–0.5 and an electron energy distribution with a power-law index of $\sim$ –2.

llowever. more recently the ADAE models have »en questioned. and substantial mocifications proposed.

However, more recently the ADAF models have been questioned, and substantial modifications proposed.

Blandford&Beegclman(1999) emphasised. that the Bernoulli constant of the gas is positive and henee outLlows are possible (as also noted by Naravan&Yi 1994)).

\citet{Blandford99} emphasised that the Bernoulli constant of the gas is positive and hence outflows are possible (as also noted by \citealt{Narayan94}) ).

In he adiabatic inflow outllow solution CXDIOS) mocdel. of DBlandford&Begelman(1999) most of the accretion energy hat is released near the black hole is used to drive a wind rom the surface of the accretion disc.

In the adiabatic inflow outflow solution (ADIOS) model of \citet{Blandford99} most of the accretion energy that is released near the black hole is used to drive a wind from the surface of the accretion disc.

Most of the gas that alls onto the outer edge of the accretion disc is carried. by his wind away from the black hole. with the result that the 1ole’s accretion rate is much smaller than the discs accretion rate.

Most of the gas that falls onto the outer edge of the accretion disc is carried by this wind away from the black hole, with the result that the hole's accretion rate is much smaller than the disc's accretion rate.

Advective [lows are also expected to be convectively unstable. as also remarked by Naravan&Y1(1994).

Advective flows are also expected to be convectively unstable, as also remarked by \citet{Narayan94}.

. In these models the central accretion rate can also be suppressed.

In these models the central accretion rate can also be suppressed.

For either of these cases. the elfect is to shift the source of cooling outwards. ancl the optical svnchrotron emission is reduced. (Quatacrt&Naravan1000 Ball.Naravan.&Quatacrt 2001)).

For either of these cases, the effect is to shift the source of cooling outwards, and the optical synchrotron emission is reduced \citealt{Quataert99}; \citealt{Ball01}) ).

In these more realistic cases optical Lares clirecthy from the inner How are less likely.

In these more realistic cases $optical$ flares directly from the inner flow are less likely.

Optical emission might still arise from the inner edge of the outer (thin) disc. or [rom reprocessing of X-ray variability.

Optical emission might still arise from the inner edge of the outer (thin) disc, or from reprocessing of X-ray variability.

lt was argued by Hvnesetal.(2002). that. since large (~ ew d) flares in. V404CCvg involve enhancements of both Xue and red wings of Hao. they must involve the whole disc.

It was argued by \citet{Hynes02} that since large $\sim$ few d) flares in Cyg involve enhancements of both blue and red wings of $\alpha$, they must involve the whole disc.

While these observations indicate. participation bv a wide range of azimuths. they leave open the possibility that only he inner disc is involved.

While these observations indicate participation by a wide range of azimuths, they leave open the possibility that only the inner disc is involved.

Using simultaneous multicolour Xhotometrv Shahbazetal.(2003b). determined the colour of similar larec [lares in V404CCve.

Using simultaneous multicolour photometry \citet{Shahbaz03b} determined the colour of similar large flares in Cyg.

Although the [lare xwameters. determined: are complicated by uncertainties in the interstellar reddening. the Hare temperature was estimated to be ~SOOO KIS. Flares on timescales similar to hose present in (i.c. tens of minutes) were also. observed. but no shysical parameters could. be determined given the large uncertainties in the colour.

Although the flare parameters determined are complicated by uncertainties in the interstellar reddening, the flare temperature was estimated to be $\sim$ K. Flares on timescales similar to those present in (i.e. tens of minutes) were also observed, but no physical parameters could be determined given the large uncertainties in the colour.

Vhe large (~ few hrs) Hares were observed. to arise from regions that cover at least 3 percent ol the discs surface area.

The large $\sim$ few hrs) flares were observed to arise from regions that cover at least 3 percent of the disc's surface area.

Shahbazetal.(2003b) have suggested that the laree (~ few hes) Uares in V404CCve are produced. in regions further out or further above the disc from a corona than the rapid (~0.5 hhr) and more rapic ( mmin) flares.

\citet{Shahbaz03b} have suggested that the large $\sim$ few hrs) flares in Cyg are produced in regions further out or further above the disc from a corona than the rapid $\sim$ hr) and more rapid $\sim$ min) flares.

Ifthe Dares in C'C'vg and hhave the same origin. then it is interesting to note tha the large Dares (~ few hrs) observed in οvg cover a larger surface area of the disc compared to the rapid. (tens of mins) Hares observed. in.00... which is consisten with the idea that the large Hares arise from regions tha extend. further out. into the disc compared. to the rapic Hares.

If the flares in Cyg and have the same origin, then it is interesting to note that the large flares $\sim$ few hrs) observed in Cyg cover a larger surface area of the disc compared to the rapid (tens of mins) flares observed in, which is consistent with the idea that the large flares arise from regions that extend further out into the disc compared to the rapid flares.

Although the flare temperatures derived suggest tha large fares are cooler than rapid Lares. the uncertainties are large and so no meaningful conclusion can be drawn a this stage.

Although the flare temperatures derived suggest that large flares are cooler than rapid flares, the uncertainties are large and so no meaningful conclusion can be drawn at this stage.

Accurate physical parameters for the Lares can only be obtained by resolving the Balmer jump and Paschen continuum.

Accurate physical parameters for the flares can only be obtained by resolving the Balmer jump and Paschen continuum.

For the data presented here on00.. there is evidence that some of the [lare events in the continuum lighteurve are correlated. with the Balmer emission line lightceurves. similar to what is observed in V404C€vg (Ilvnesetal. 2002).

For the data presented here on, there is evidence that some of the flare events in the continuum lightcurve are correlated with the Balmer emission line lightcurves, similar to what is observed in Cyg \citep{Hynes02}.

. The value for the Balmer decrement suggests that the persistent flux is optically thin and the decrease of the Jalmer clecrement during the Lares suggests a significant temperature increase.

The value for the Balmer decrement suggests that the persistent flux is optically thin and the decrease of the Balmer decrement during the flares suggests a significant temperature increase.

We find that the optically thin spectrum of the flare. which lasts tens of minutes. has a temperature of ~12000KI and covers 0.08. percent of the disc's projected surface area (see retE LAIUZ)).

We find that the optically thin spectrum of the flare, which lasts tens of minutes, has a temperature of $\sim$ K and covers 0.08 percent of the disc's projected surface area (see \\ref{FLARE}) ).

In many high inclination svstems the continuum light from the bright-spot. produces a single hump in the lighteurve. because the bright-spot is obscured by the disc when it is on the side of the disc facing away [rom the observer.

In many high inclination systems the continuum light from the bright-spot produces a single hump in the lightcurve, because the bright-spot is obscured by the disc when it is on the side of the disc facing away from the observer.

Since lis at an intermediate inclination angle (41°: Shahbazctal. and Gelinoetal. 2001)) where no strong obscuration

Since is at an intermediate inclination angle $^\circ$ ; \citealt{Shahbaz94} and \citealt{Gelino01}) ) where no strong obscuration

scattering processes|52].. In ourmodel. itisassumed. that

made out of valence spin-0 diquark and valence quark.

incidentbarvons aremainly

Consequently, the magnitude of

that have already occiured. we can nevertheless conduct meaningful tests and identily the natures of at least some of the lenses.

that have already occurred, we can nevertheless conduct meaningful tests and identify the natures of at least some of the lenses.

We should check existing multiwavelength: catalogs and data sets at the position of each event well-sampled enough (hat we are reasonably confident (a) il corresponds (o microlensing and (b) that the short duration is not due to blending.

We should check existing multiwavelength catalogs and data sets at the position of each event well-sampled enough that we are reasonably confident (a) it corresponds to microlensing and (b) that the short duration is not due to blending.

In at least some cases we should find evidence for an object that is not the lensed source. but which could instead be part of the lens svstem.

In at least some cases we should find evidence for an object that is not the lensed source, but which could instead be part of the lens system.

In cases where (here is a match. the possible contributions of additional observations. including some with LST. should be considered.

In cases where there is a match, the possible contributions of additional observations, including some with HST, should be considered.

It would be surprising if a comprehensive analvsis of alreacly-cliscoverecl short evenis does not reveal the presence of a set of interesting lenses.

It would be surprising if a comprehensive analysis of already-discovered short events does not reveal the presence of a set of interesting lenses.

The existing data sets are almost certainly minute in comparison with future data sets. which will discover more events per vear.

The existing data sets are almost certainly minute in comparison with future data sets, which will discover more events per year.

Column 6 of Table 1 shows that we can expect 150 short events among each 1000 events (Column 5) detected by monitoring programs sensitive to short events.

Column 6 of Table 1 shows that we can expect $150$ short events among each $1000$ events (Column 5) detected by monitoring programs sensitive to short events.

The challenge aliead is. therefore. to institute real-time recognition of events to immediately identify those (hat are promising candidates for additional observations. We discuss (his further in 86.

The challenge ahead is, therefore, to institute real-time recognition of short-duration events to immediately identify those that are promising candidates for additional observations, We discuss this further in 6.

For each type of lens defined bv a given mass range. the selection of short-duration evenis corresponds to a selection of lenses in one of (wo distance regimes.

For each type of lens defined by a given mass range, the selection of short-duration events corresponds to a selection of lenses in one of two distance regimes.

This is because the equation for Dj, is quadratic. generally admitting (wo solutions. D, and D,. For lenses that are brown clwarls. planets. and neutron stars. D, is shown as a function of vin Figures 1 through 3. respectively.

This is because the equation for $D_L$ is quadratic, generally admitting two solutions, $D_L^+$ and $D_L^-.$ For lenses that are brown dwarfs, planets, and neutron stars, $D_L$ is shown as a function of $v$ in Figures $1$ through $3$, respectively.

D, can be in the range of tens or hundreds of pe.

$D_L^-$ can be in the range of tens or hundreds of pc.

When the lens svstem is this close to us. the probability of being able to detect it is large.

When the lens system is this close to us, the probability of being able to detect it is large.

As discussed in the companion paper. the degeneracy inherent in lensing can therefore olten be broken.

As discussed in the companion paper, the degeneracy inherent in lensing can therefore often be broken.

In fact. for a given lens. there may be several different wavs of measuring the some Κον qualities. such as the mass of the planet-lens (see. e.g.. 83.2).

In fact, for a given lens, there may be several different ways of measuring the some key quantities, such as the mass of the planet-lens (see, e.g., 3.2).

Because nearby lenses can be so well studied. we can use them to make predictions for the population of distant lenses. with D,=D,. Nearby lenses producing short-duration evenis can be identified as planets. brown cdwarfs. or stellar remnants.

Because nearby lenses can be so well studied, we can use them to make predictions for the population of distant lenses, with $D_L=D_L^+.$ Nearby lenses producing short-duration events can be identified as planets, brown dwarfs, or stellar remnants.

If we assume that stellar populations in the dense source systems contain similar populations. we can predict the distributions of values of 7j; ancl also of values of 85. (85 is more likely to be measured for D,= ).

If we assume that stellar populations in the dense source systems contain similar populations, we can predict the distributions of values of $\tau_E$ and also of values of $\theta_E.$ $\theta_E$ is more likely to be measured for $D_L=D_L^+$ ).

Comparisons between the predicted and observed distributions will allow us to test models.

Note. in addition. (hat for a given lens mass and speed. (the requirement that D, be real. places an upper limit on the Einstein diameter crossing time.

Note, in addition, that for a given lens mass and speed, the requirement that $D_L$ be real, places an upper limit on the Einstein diameter crossing time.

As a starting point, we consider the evolution equation for CDM and baryon density perturbations óc)=δρειυ/βοι in the Newtonian limit and in the presence of a DE-CDM interaction as derived by ?,, in Fourier space and in cosmic time: The additional contribution appearing in the first term on the right hand side of Eq. (10))

As a starting point, we consider the evolution equation for CDM and baryon density perturbations $\delta _{c,b}\equiv \delta \rho _{c,b}/\rho _{c,b}$ in the Newtonian limit and in the presence of a DE-CDM interaction as derived by \citet{Amendola_2004}, in Fourier space and in cosmic time: The additional contribution appearing in the first term on the right hand side of Eq. \ref{gf_c}) )

is the extra friction associated with momentum conservation in cDE models (seee.g.?,foradiscus-sionontheeffectsoffrictionterm) and the factor I. defined as includes the effect of the fifth-force mediated by the DE scalar field for CDM density perturbations.

is the extra friction associated with momentum conservation in cDE models \citep[see \eg ][for a discussion on the effects of the friction term]{Baldi_2011b} and the factor $\Gamma _{c}$ defined as includes the effect of the fifth-force mediated by the DE scalar field for CDM density perturbations.

A few assumptions have to be made in order to derive Eqs. (10,,11)),

A few assumptions have to be made in order to derive Eqs. \ref{gf_c}, \ref{gf_b}) ),

besides the already mentioned Newtonian limit of small scales for the Fourier modes under consideration, A—aH/k< 1.

besides the already mentioned Newtonian limit of small scales for the Fourier modes under consideration, $\lambda \equiv aH/k \ll 1$ .

In particular, one has to assume the dimensionless mass of the scalar field $, defined as to be small compared to the Fourier modes at the scales of interest, such that If this condition is not fulfilled, the clustering of the DE scalar field ¢ might grow beyond the linear level at scales below 1/TR, and the fifth force of Eq. (12))

In particular, one has to assume the dimensionless mass of the scalar field $\phi $, defined as to be small compared to the Fourier modes at the scales of interest, such that If this condition is not fulfilled, the clustering of the DE scalar field $\phi $ might grow beyond the linear level at scales below $1/\hat{m}^{2}_{\phi }$ and the fifth force of Eq. \ref{Gamma_c_massless}) )

would then acquire a Yukawa suppression factor given by: Since both the linear treatment of density perturbations discussed in the present Section and the non-linear N-body algorithm used for the analysis presented in the next Section are based on the assumption of a small scalar mass, and therefore on a term like (12)) for the fifth-force implementation, it is important to clarify to which extent this assumption can be considered to hold.

would then acquire a Yukawa suppression factor given by: Since both the linear treatment of density perturbations discussed in the present Section and the non-linear N-body algorithm used for the analysis presented in the next Section are based on the assumption of a small scalar mass, and therefore on a term like \ref{Gamma_c_massless}) ) for the fifth-force implementation, it is important to clarify to which extent this assumption can be considered to hold.

In Fig.

4 we plot the quantity Tig? for several comoving wavenumbers k~1,0.1,0.01,0.001h/Mpce as a function of redshift.

\ref{fig:scalar_mass} we plot the quantity $\hat{m}^{2}_{\phi }\lambda ^{2}$ for several comoving wavenumbers $k\sim 1\,,0.1\,,0.01\,,0.001\, h/$ Mpc as a function of redshift.

As one can see from the plot, the scalar mass can start playing a significant role at z<10 only for scales close to the cosmic horizon, while for all scales below ~700 comoving Mpc/h (k~ 0.01h/Mpc) the influence of a non-zero scalar mass is negligible and Eqs. (10,,11,,12))

As one can see from the plot, the scalar mass can start playing a significant role at $z<10$ only for scales close to the cosmic horizon, while for all scales below $\sim 700$ comoving $/h$ $k\sim 0.01\, h/$ Mpc) the influence of a non-zero scalar mass is negligible and Eqs. \ref{gf_c}, \ref{gf_b}, \ref{Gamma_c_massless}) )

can be safely used.

For the N- results discussed in Sec.

For the N-body results discussed in Sec.

4 we will consider simulations with a box of 1 comoving Gpc/h aside, for which only the largest scales sampled by the initial power spectrum might be marginally affected by our massless field approximation, while we will concentrate on nonlinear structure formation processes occurring at much smaller scales.

\ref{sec:sims} we will consider simulations with a box of $1$ comoving $/h$ aside, for which only the largest scales sampled by the initial power spectrum might be marginally affected by our massless field approximation, while we will concentrate on nonlinear structure formation processes occurring at much smaller scales.

Having clarified the range of validity of the assumptions made in deriving Eqs. (10,,11,,12))

Having clarified the range of validity of the assumptions made in deriving Eqs. \ref{gf_c}, \ref{gf_b}, \ref{Gamma_c_massless}) )

we can now discuss one of the central results of the present work.

By numerically solving the system of Eqs. (1--5,,10,,11))

By numerically solving the system of Eqs. \ref{klein_gordon}- \ref{friedmann}, \ref{gf_c}, \ref{gf_b}) )

at subhorizon scales (k~0.1 /Mpc) we can compute the linear growth of density perturbations for all the different cosmological models under investigation and compare it to the standard ACDM growth factor.

at subhorizon scales $k\sim 0.1\, h$ /Mpc) we can compute the linear growth of density perturbations for all the different cosmological models under investigation and compare it to the standard $\Lambda $ CDM growth factor.

As boundary conditions for our integration we impose that the ratio of baryonic to CDM perturbations at zcwp takes the value 6/5.~3.0x1075 as computed by running the Boltzmann code CAMB (?) fora ACDM cosmology and for the WMAP7 parameters adopted in the present study as listed in Table 1..

As boundary conditions for our integration we impose that the ratio of baryonic to CDM perturbations at $z_{\rm CMB}$ takes the value $\delta _{b}/\delta _{c} \sim 3.0\times 10^{-3}$ as computed by running the Boltzmann code CAMB \citep{camb} for a $\Lambda {\rm CDM}$ cosmology and for the WMAP7 parameters adopted in the present study as listed in Table \ref{tab:parameters}. .

our data well.

We therefore provide a new and more accurate fitting formula for the relation between 65, and ój.

We therefore provide a new and more accurate fitting formula for the relation between $\delta_{\mathrm{m}}^{\mathrm{s}}$ and $\delta_{\mathrm{1}}^{\mathrm{s}}$.

The redshift range we can study is 0<z10 in 30 bins, logarithmically spaced in (1+z)!.

The redshift range we can study is $0 \leq z \leq 10$ in 30 bins, logarithmically spaced in $(1+z)^{-1}$.

For each redshift bin, we find that the parameterisation gives a very good fit for all values of 6}: the ratio of the fit residuals to the true value is less than 5 per cent for redshift 0 and lessthan 1 per cent for z>6.

For each redshift bin, we find that the parameterisation gives a very good fit for all values of $\delta_1^{\mathrm{s}}$: the ratio of the fit residuals to the true value is less than 5 per cent for redshift 0 and lessthan 1 per cent for $z>6$.

The functions A, B and C depend on z in the following way: In the limiting case z—oo, some of the fit coefficients do not show the right asymptotic behaviour (A—0, B—1, C— 0) as one would expect because 65,—67, so this fit should be used for redshifts outside the fitted range.

The functions $A$, $B$ and $C$ depend on $z$ in the following way: In the limiting case $z \rightarrow \infty$, some of the fit coefficients do not show the right asymptotic behaviour $A \rightarrow 0$, $B \rightarrow 1$, $C \rightarrow 0$ ) as one would expect because $\delta_{\mathrm{m}}^{\mathrm{s}} \rightarrow \delta_{\mathrm{1}}^{\mathrm{s}}$, so this fit should be used for redshifts outside the fitted range.

Both density fields were smoothed with R=12Mpc/h.

Both density fields were smoothed with $R=12\ \mathrm{Mpc}/h$.

The choice of R does not significantly influence the fitting parameters, but the agreement is worse when large values of 6; and ὃν, are allowed (i.e. R is small at low redshifts).

The choice of $R$ does not significantly influence the fitting parameters, but the agreement is worse when large values of $\delta_1^{\mathrm{s}}$ and $\delta_{\mathrm{m}}^{\mathrm{s}}$ are allowed (i.e. $R$ is small at low redshifts).

Another relation between the linear and non-linear density fields that is sometimes used is the lognormal transformation (e.g. ?,, ?)).

Another relation between the linear and non-linear density fields that is sometimes used is the lognormal transformation (e.g. \citealt*{1991MNRAS.248....1C}, \citealt*{1995ApJ...443..479B}) ).

This has proven to yield a PDF which agrees well with simulations.

However, this does not imply that it can be used as a point-by-point relation between the linear and non-linear density fields, as pointed out by ?..

However, this does not imply that it can be used as a point-by-point relation between the linear and non-linear density fields, as pointed out by \citet*{2001ApJ...561...22K}.

We follow their parameterisation, which can be rewritten as with Here, o? (02) is the variance of the smoothed linear (non-linear) density field.

We follow their parameterisation, which can be rewritten as with Here, $\sigma^2$ $\sigma^2_{\mathrm{m}}$ ) is the variance of the smoothed linear (non-linear) density field.

We calculate c? and leave "y as the fit parameter.

We calculate $\sigma^2$ and leave $\gamma$ as the fit parameter.

This fit yields values for dm which are systematically lower by zz30 per cent at redshift 0 and still 20 per cent at z>6.

This fit yields values for $\delta_{\mathrm{m}}$ which are systematically lower by $\approx 30$ per cent at redshift 0 and still 20 per cent at $z>6$.

So indeed the lognormal transformation can not be used to accurately predict the evolution of an initial Gaussian field into a non-linear field.

Again, this does not mean that the statistics of a non-linear density field can not be described by a lognormal field, just that one can not expect that, for a point-by-point comparison, the linear field used in the transformation corresponds to the initial conditions of that non-linear field.

After calculating the higher order density contrast, we now calculate the matter power spectra up to the 1-loop order.

We can do this in two ways: calculating the volume average of the SPT density contrast (Eq. 8))

We can do this in two ways: calculating the volume average of the SPT density contrast (Eq. \ref{pgen}) )

or integrating a given linear power spectrum Pii(k) (Eq. 10)),

or integrating a given linear power spectrum $P_{11}(k)$ (Eq. \ref{analyt}) ),

where Pii(k) is the same power spectrum that was used to set up the initial conditions of the simulation.

where $P_{11}(k)$ is the same power spectrum that was used to set up the initial conditions of the simulation.

This also serves as a consistency check for our grid-based calculation.

The results for the large box are shown in Fig. 5..

The results for the large box are shown in Fig. \ref{fig:p11theo}.

The small box is not shown because it is very similar.

The lines show the results from Eq. (10))

The lines show the results from Eq. \ref{analyt}) )

and the points show the numerical result, without smoothing, ie. R= 0.

and the points show the numerical result, without smoothing, i.e. $R=0$ .

The errors of the power spectra are calculated assuming that our fields are Gaussian: where ng is the number of modes in each k-bin.

The errors of the power spectra are calculated assuming that our fields are Gaussian: where $n_{\mathrm{B}}$ is the number of modes in each $k$ -bin.

'The linear power spectrum from the simulation agrees

The linear power spectrum from the simulation agrees

subcluster has lost its gas on approaching the cluster from the south and is currently located north to the main cluster.

The image shows an East-West elongated core on the small scale. while on the large scale it appears to be symmetric.

The image shows an East-West elongated core on the small scale, while on the large scale it appears to be symmetric.

The pressure map has two maxima and two elongations towards the south-west and south-east.