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We find that the error bean of JCAL is substantial at this wavelength. as predicted. with only ~15% of the power appearing in the central 14 arcsec.
We find that the error beam of JCMT is substantial at this wavelength, as predicted, with only $\sim$ of the power appearing in the central 14 arcsec.
We note that a telescope with a greater surface accuracy would. improve upon this number. and that other observing sites in even higher or
We note that a telescope with a greater surface accuracy would improve upon this number, and that other observing sites in even higher or
are mostly averaged out, leaving a clean Gaussian statistics.
are mostly averaged out, leaving a clean Gaussian statistics.
Indeed, it must be noted that the y? values are close to unity in both cases, which confirms that error bars have been properly evaluated by the data reduction software and which suggests that systematic errors do not dominate the overall error budget.
Indeed, it must be noted that the $\chi^2_r$ values are close to unity in both cases, which confirms that error bars have been properly evaluated by the data reduction software and which suggests that systematic errors do not dominate the overall error budget.
A quick inspection of the best y? maps shows relatively high uniformity of the best y? (narrow range of avalues), and the absence of particularly outstanding minima.
A quick inspection of the best $\chi^2_r$ maps shows a relatively high uniformity of the best $\chi^2_r$ (narrow range of values), and the absence of particularly outstanding minima.
To properly assess the presence of significant minima in the maps, we renormalise the y? cube so that y?=1 for the best- model, as described in Section 3.2..
To properly assess the presence of significant minima in the maps, we renormalise the $\chi^2_r$ cube so that $\chi^2_r=1$ for the best-fit model, as described in Section \ref{sub:search}.
The single-star model is then associated with a y? of 1.05 for Fomalhaut and 1.14 for tau Cet.
The single-star model is then associated with a $\chi^2_r$ of 1.05 for Fomalhaut and 1.14 for tau Cet.
The corresponding probability for the single-star model to reproduce the data is (or 1.60) and (or 2.70, respectively.
The corresponding probability for the single-star model to reproduce the data is (or $1.6\sigma$ ) and (or $2.7\sigma$ ), respectively.
The minima of the y? maps can therefore not be considered as significant, and we conclude that no firm detection is reported around these two stars.
The minima of the $\chi^2_r$ maps can therefore not be considered as significant, and we conclude that no firm detection is reported around these two stars.
Following Eq. 4,,
Following Eq. \ref{eq:sensmap},
we derive the 3σ upper limits on the flux of off-axis companions within the search region around both stars.
we derive the $3\sigma$ upper limits on the flux of off-axis companions within the search region around both stars.
The resulting sensitivity maps are illustrated in Fig.
The resulting sensitivity maps are illustrated in Fig.
2 (top and middle left).
\ref{fig:sensitivity} (top and middle left).
They show sensitivity limits in the range for Fomalhaut and in the case of tau Cet, suggesting that companions as faint as 1:1000 of the stellar flux would be detectable at some particular positions within the search region.
They show sensitivity limits in the range for Fomalhaut and in the case of tau Cet, suggesting that companions as faint as 1:1000 of the stellar flux would be detectable at some particular positions within the search region.
The cumulated histogram of the sensitivity level across the whole search region is illustrated by the solid curves in the left-hand side plots of Fig. 5..
The cumulated histogram of the sensitivity level across the whole search region is illustrated by the solid curves in the left-hand side plots of Fig. \ref{fig:blind_test}.
The median and percentile sensitivity limits are 2.3x107? and 2.8x10? (Fomalhaut) and 3.5x10? and 4.5x10? (tau Cet), respectively.
The median and percentile sensitivity limits are $2.3\times10^{-3}$ and $2.8\times10^{-3}$ (Fomalhaut) and $3.5\times10^{-3}$ and $4.5\times10^{-3}$ (tau Cet), respectively.
Another, more conventional way to represent the sensitivity of our observations is to consider concentric annuli, in which cumulated sensitivity histograms can be inspected to search for, e.g., median and completeness levels.
Another, more conventional way to represent the sensitivity of our observations is to consider concentric annuli, in which cumulated sensitivity histograms can be inspected to search for, e.g., median and completeness levels.
This is illustrated on the right-hand side of Fig.
This is illustrated on the right-hand side of Fig.
2 (top and middle).
\ref{fig:sensitivity} (top and middle).
The full dynamic range of PIONIER is achieved as close as mmas for Fomalhaut and mmas for tau Cet, and is maintained all the way to the edge of the search zone mmas), where the effect of the Gaussian profile of the fibre transmission starts to be noticeable.
The full dynamic range of PIONIER is achieved as close as mas for Fomalhaut and mas for tau Cet, and is maintained all the way to the edge of the search zone mas), where the effect of the Gaussian profile of the fibre transmission starts to be noticeable.
helore the cluster contains a fair sample of the cosmic mass budget.
before the cluster contains a fair sample of the cosmic mass budget.
Fig. shows the median gas fraction inside the virial radius as a function of temperature (still using 7;,, inside A500): Che virial overdensity is 97 (mes critical lor our chosen cosmology.
$.$ \\ref{fig:gfrac} shows the median gas fraction inside the virial radius as a function of temperature (still using $T_{ew}$ inside $R_{500}$ ); the virial overdensity is 97 times critical for our chosen cosmology.
Even at this radius. it is only for the most massive clusters (kT;,,26keV) that the barvon fraction reaches (he cosmic mean: in smaller clusters feedback causes the eas (o expand. reducing the gas fraction by many tens of percent.
Even at this radius, it is only for the most massive clusters ${\rm k}T_{ew}\gtrsim 6$ keV) that the baryon fraction reaches the cosmic mean; in smaller clusters feedback causes the gas to expand, reducing the gas fraction by many tens of percent.
Attempts to determine the cosmic barvon density [rom elusters will need to take this effect into account.
Attempts to determine the cosmic baryon density from clusters will need to take this effect into account.
Fie. relfig:efrac also demonstrates how the median gas fraction changes in the maximum feedback case if we also add a relativistic component with 0,4,=0.20 (there is little change in the spread around the median).
$.$ \\ref{fig:gfrac} also demonstrates how the median gas fraction changes in the maximum feedback case if we also add a relativistic component with $\delta_{rel}=0.20$ (there is little change in the spread around the median).
With this component. a lower temperature is required to achieve pressure balance al a given density.
With this component, a lower temperature is required to achieve pressure balance at a given density.
This model behaves like the no feedback case at. higher masses. and like an intermediate feedback case al lower masses.
This model behaves like the no feedback case at higher masses, and like an intermediate feedback case at lower masses.
This behavior also holds for all the other relationships (AMsoj—T4.Ly£4. etc.)
This behavior also holds for all the other relationships $M_{500}-T_{ew}, L_x-T_{ew}$, etc.)
explored in this paper: Cains il seenis a relativistic component will have little effect on thermal cluster observables.
explored in this paper; thus it seems a relativistic component will have little effect on thermal cluster observables.
While our implementation is quite simplified. similar results were found using full hydrodyvnanmic simulations by Pfrommeretal.(2006): thev found that including the ellects of cosmic ravs caused only small changes in the gas fraction and integrated SZ signal (hev found a larger change in L,. but this was related to cooling cores. which we do not implement).
While our implementation is quite simplified, similar results were found using full hydrodynamic simulations by \citet{PfrommerSJE06z}: they found that including the effects of cosmic rays caused only small changes in the gas fraction and integrated SZ signal (they found a larger change in $L_x$, but this was related to cooling cores, which we do not implement).
To summarize this section. we find that a WMAP 3-vear cosmological model coupled with a feedback parameter of ej;=3—5x10" (which corresponds to an input energy of roughly 2-3 keV per barvon) provides a &ood fit to the extant A-ray observations of hot gas in clusters.
To summarize this section, we find that a WMAP 3-year cosmological model coupled with a feedback parameter of $\epsilon_f=3-5\times 10^{-5}$ (which corresponds to an input energy of roughly 2-3 keV per baryon) provides a good fit to the extant X-ray observations of hot gas in clusters.
In (his paper we have presented a method [or determining (he gas distribution inside a fully three-dimensional potenüal: this method. assumes hydrostatic equilibrium. ancl a polvivopic equation of state. and also that the original gas energv per unit mass equals that of the DM.
In this paper we have presented a method for determining the gas distribution inside a fully three-dimensional potential; this method assumes hydrostatic equilibrium and a polytropic equation of state, and also that the original gas energy per unit mass equals that of the DM.
We then applied this method to az=0 catalog of DM cluster halos drawn Irom N-body simulations. and compared the resulüng ICM distributions to observations of nearby clusters.
We then applied this method to a $z=0$ catalog of DM cluster halos drawn from N-body simulations, and compared the resulting ICM distributions to observations of nearby clusters.
The main result is that (his simple gas prescription can reproduce many of the observed bulk properties of the ICM. including the temperature distribution and the relationships between temperature and mass. X-ray luminosity. or gas fraction.
The main result is that this simple gas prescription can reproduce many of the observed bulk properties of the ICM, including the temperature distribution and the relationships between temperature and mass, X-ray luminosity, or gas fraction.
The main drawback is that in nearby X-ray clusters (here is significantly more scatter seen in (lese relationships (han is produced in our method.
The main drawback is that in nearby X-ray clusters there is significantly more scatter seen in these relationships than is produced in our method.
This could be due to a number of factors.
This could be due to a number of factors,
Alost of the known galaxies are cwarls.
Most of the known galaxies are dwarfs.
"They. span mass ranges from a few 10"M... (or Mycm18 mag: 10" L.) like NGC 205. 10 10" (Myc12 mag: 10 L.)). like Fornax anc Sculptor galaxies. satellites— of the Milky Way. and. probably down to 107 (Myc3 mae: 1000 L.)) for the fainter Milky Way satellites found from the SDSS (7)..
They span mass ranges from a few $10^9$, (or ${\rm M}_V \simeq -18$ mag; $10^9$ ) like NGC 205, to $10^7$ ${\rm M}_V \simeq -12$ mag; $10^6$ ), like Fornax and Sculptor galaxies, satellites of the Milky Way, and probably down to $10^5$ ${\rm M}_V \simeq -3$ mag; 1000 ) for the fainter Milky Way satellites found from the SDSS \citep{koposov09}.
Dwarls vary considerably in their eas content ancl morphology. between dwarf. irregular galaxies (dev) and «ναι elliptical or spheroidal galaxies (cll/elSph).
Dwarfs vary considerably in their gas content and morphology, between dwarf irregular galaxies (dIrr) and dwarf elliptical or spheroidal galaxies (dE/dSph).
Environmental effects. likely drive. the evolution of star forming dwarf galaxies to the quiescent ones after gas removal and/or exhaustion.
Environmental effects likely drive the evolution of star forming dwarf galaxies to the quiescent ones after gas removal and/or exhaustion.
Among the quiescent objects. the fainter ones are traditionally called. dSph while the more massive are named dk (diffuse or cdwarl ellipticals: e.g. 2)).
Among the quiescent objects, the fainter ones are traditionally called dSph while the more massive are named dE (diffuse or dwarf ellipticals; e.g. \citealp{grebel99}) ).
The bound is often set at My&14 mag.
The bound is often set at ${\rm M}_V \simeq -14$ mag.
However. the physical distinction between these two classes is unclear.
However, the physical distinction between these two classes is unclear.
Dwarf. spheroidals are. generally companions of massive galaxies (20 of them were identified around the Milky. Way ancl 15 around. Anclromeca: ?)) while dls are ound in clusters (1141. of them are [listed in the Virgo Cluster Catalogue: 2)). but NGC 205. prototype of ces. is also a companion of AL331. and fnt. dl/dSph are now ouncl in nearby clusters (????)..
Dwarf spheroidals are generally companions of massive galaxies (20 of them were identified around the Milky Way and 15 around Andromeda; \citealp{irwin08}) ) while dEs are found in clusters (1141 of them are listed in the Virgo Cluster Catalogue; \citealp{bst85}) ), but NGC 205, prototype of dEs, is also a companion of 31, and faint dE/dSph are now found in nearby clusters \citep{trentham02,mieske07,adami07,derijcke09}.
Phe nearby dSphs are often ound to be dominated by dark matter (2).. while the more massive. cles are apparently similar to the massive elliptical ealaxies: the stellar content of NGC 147. NGC 155 and GC 205 account for hall of their dynamical masses (?)..
The nearby dSphs are often found to be dominated by dark matter \citep{mateo98}, while the more massive, dEs are apparently similar to the massive elliptical galaxies: the stellar content of NGC 147, NGC 185 and NGC 205 account for half of their dynamical masses \citep{derijcke06}.
Other properties. like the Sérrsic index. n. characterizing he shape of the photometric profile. seems to form a continuum over all the mass range.
Other properties, like the Sérrsic index, n, characterizing the shape of the photometric profile, seems to form a continuum over all the mass range.
?.— proposes that the Sérrsic index is independent of the luminosity for Alyο14 mag. nzQ.T. and increases with the luminosity above this limit.
\cite{derijcke09} proposes that the Sérrsic index is independent of the luminosity for ${\rm M}_V \gtrsim -14$ mag, $n \approx 0.7$, and increases with the luminosity above this limit.
The change in the photometric scaling relation may rellect the different nature of cles and dSphs. but both the measurement uncertainties and the cosmic dispersion. are still large enough to dispute such a dichotomy.
The change in the photometric scaling relation may reflect the different nature of dEs and dSphs, but both the measurement uncertainties and the cosmic dispersion are still large enough to dispute such a dichotomy.
ere the heating may occtr: however. oir previous work iucicated that euough of the heating may take place deep enougl in the atinosplie‘eto contribute to radius inflation (Pernaetal.2010b).
where the heating may occur; however, our previous work indicated that enough of the heating may take place deep enough in the atmosphere to contribute to radius inflation \citep{Perna2010b}.
. hough it is uot clear if tle weak-drag 11oclel would produce enough olunic heating be significai efliciency. fou nc our imediuim-dra:[n]) model should be able o inflate the plajetary raclit ile the efficiency. of our strone-crag model is so high tha this heating may be able ipletely evaporate tie. planet (accordiigtothemocelsofBatyelleal.2011).
Although it is not clear if the weak-drag model would produce enough ohmic heating be significant, the efficiency found in our medium-drag model should be able to inflate the planetary radius, while the efficiency of our strong-drag model is so high that this heating may be able to completely evaporate the planet \citep[according to the models of][]{Batygin2011}.
. I ls importa tote that οw strong drag model is not self-cousisteu.in that the oljc heatiug is Lol explicit uced and 1t would likely have a large ellect ou the circulatiou patteru aud therefore tle alot of siuetic ene‘oy dissipated by drag.
It is important to note that our strong drag model is not self-consistent, in that the ohmic heating is not explicitly included and it would likely have a large effect on the circulation pattern and therefore the amount of kinetic energy dissipated by drag.
A better analysis of the correlation beweeu the easiwar shit of tUe hottest region of the atmosphere aud the amount of raclius inflatic)l nius wail [or an improved --modeling scheme which accotuts for magjetic drag and its associate oluui€ heating selí-coisistently.
A better analysis of the correlation between the eastward shift of the hottest region of the atmosphere and the amount of radius inflation must wait for an improved modeling scheme which accounts for magnetic drag and its associated ohmic heating self-consistently.
Fially. we calculate the rate of nume‘ical kinetic euergy loss in each of oas dag models.
Finally, we calculate the rate of numerical kinetic energy loss in each of our drag models.
For our fidCl:il mocel the rate of kinetic energy loss was found by comparing the uou-zero global let racdiative heating to the rate of energy inout to the atmosphere. assumiug tlat he uet heating Was aucing the net numerical loss.
For our fiducial model the rate of kinetic energy loss was found by comparing the non-zero global net radiative heating to the rate of energy input to the atmosphere, assuming that the net heating was balancing the net numerical loss.
The magneic drag is an explicit sink o. kinetic enerey ancl We 5ract this value from the net radiaive heating. assuming that the remajucder is balancing nunmerk‘al dissipation.
The magnetic drag is an explicit sink of kinetic energy and we subtract this value from the net radiative heating, assuming that the remainder is balancing numerical dissipation.
As we report in Tadle 2.. he amount of numerical loss issl ular between our [i|Clal. wealk-. aud 1jecliuuisdrag models. but is zero (to within )) in our sroug-drag moel.
As we report in Table \ref{tab:energy}, the amount of numerical loss is similar between our fiducial, weak-, and medium-drag models, but is zero (to within ) in our strong-drag model.
An exact identification of the source of numerical oss in our moclels (e.g.. whether it is localized or distribted uuilormly) is bevoud the scope of this paper: however. the lack of aly Seuilicant loss in our strong-drag mode seems to iudicate that tje numerical loss is related to tμοι juchli strouger wind syeeds in our other models.
An exact identification of the source of numerical loss in our models (e.g., whether it is localized or distributed uniformly) is beyond the scope of this paper; however, the lack of any significant loss in our strong-drag model seems to indicate that the numerical loss is related to the much stronger wind speeds in our other models.
It may be tha we can substautially reduce junmerical loss by correcty including all sowces of drag in our models. be it maguetic or relatedto subgrid processes (see.e.g..Li&(οὐια 2010)..
It may be that we can substantially reduce numerical loss by correctly including all sources of drag in our models, be it magnetic or relatedto subgrid processes \citep[see, e.g.,][]{Li2010}. .
With these three equations. we create a diagnostic η, namely the ratio of the theoretical duration D (derived above) and the observed duration. Duy (obtained from photometric observations).
With these three equations, we create a diagnostic $\eta$, namely the ratio of the theoretical duration $D$ (derived above) and the observed duration, $D_{\rm obs}$ (obtained from photometric observations).
There are still unknowns: the [actor Z. known to be constrained (o lie between 0 and 1. and one of 2, or A.
There are still unknowns: the factor $Z$, known to be constrained to lie between 0 and 1, and one of $R_\star$ or $R_{\rm p}$.
The latter duality leads to (wo dillerent formis of the exoplanet diagnostic. y and i. each of which is useful in different circumstances.
The latter duality leads to two different forms of the exoplanet diagnostic, $\eta_{\rm p}$ and $\eta_{\star}$, each of which is useful in different circumstances.
adii of stars that are thought to have a reasonable chance of harboring an exoplanet. namely main sequence spectral types F through late IX. can vary. by a factor of three or so. while the tvpical planetary radius that can produce a detectable transit [rom ground. varies by about a factor of (wo.
Radii of stars that are thought to have a reasonable chance of harboring an exoplanet, namely main sequence spectral types F through late K, can vary by a factor of three or so, while the typical planetary radius that can produce a detectable transit from ground varies by about a factor of two.
Therelore. ground-based transit searches would be better served by a diagnostic (75) that takes the unknown Zi to be constant. while satellite missions. which are sensilive Lo a much wider range of 725. would be better served using a diagnostic (ην) tha assumed f, was constant.
Therefore, ground-based transit searches would be better served by a diagnostic $\eta_{\rm p}$ ) that takes the unknown $R_{\rm p}$ to be constant, while satellite missions, which are sensitive to a much wider range of $R_{\rm p}$ , would be better served using a diagnostic $\eta_\star$ ) that assumed $R_\star$ was constant.
We stress. however. (hat for any primaries for which the radius can be estimated (from spectral classification. for example). ap. should be used.
We stress, however, that for any primaries for which the radius can be estimated (from spectral classification, for example), $\eta_\star$ should be used.
These two exoplanet diagnostics. easily derivable from the above equations. are: and Note that 1, is independent of 2, and i is independent of Z4,.
These two exoplanet diagnostics, easily derivable from the above equations, are: and Note that $\eta_{\rm p}$ is independent of $R_\star$ and $\eta_\star$ is independent of $R_{\rm p}$.
The one remaining unknown left in (hese equations. Z. will not critically affect the viability of these diagnostics.
The one remaining unknown left in these equations, $Z$, will not critically affect the viability of these diagnostics.
In what follows. we take Z=I andl describe the consequences of (his assumption.
In what follows, we take $Z = 1$ and describe the consequences of this assumption.
Looking at Eqs.
Looking at Eqs.
4 and 7. one would expect the (vpical binary. (rausil to last longer than the (vpical exoplanet (ransil. as the radius of a transiting star would [ar exceed (hat of a (ransiling planet. unless it was an extreme grazing eclipse.
4 and 7, one would expect the typical binary transit to last longer than the typical exoplanet transit, as the radius of a transiting star would far exceed that of a transiting planet, unless it was an extreme grazing eclipse.
The Ay+2, for an exoplanetary transit becomes £2,4—iyo for a stellar eclipsing binary a large increase in (his term.
The $R_{\rm p}+R_\star$ for an exoplanetary transit becomes $R_{\star,1}+R_{\star,2}$ for a stellar eclipsing binary – a large increase in this term.
A more in-depth examination of thesediagnostics gives greater insight into the situation.
A more in-depth examination of thesediagnostics gives greater insight into the situation.
Hp scales as
$\eta_{\rm p}$ scales as
The nucleosynthesis products from intermediate mass stars (IMS) (1.5Sm/M.5) are of special interest here since the IME for Population Ill stars mieht peak in (his mass range.
The nucleosynthesis products from intermediate mass stars (IMS) $1.5\la m/M_\odot\la 8$ ) are of special interest here since the IMF for Population III stars might peak in this mass range.
Note that a star with initial mass around 7-8 M. has a lifetime (~10* ντ) onlv slightly larger (han that of a tvpical SNII progenitor and therefore will contribute to IGM enrichment shortly alterwiuds.
Note that a star with initial mass around 7-8 $_\odot$ has a lifetime $\sim 10^7$ yr) only slightly larger than that of a typical SNII progenitor and therefore will contribute to IGM enrichment shortly afterwards.
Due to the peculiarity of the Z=0 stellar evolution. appropriate vields are highly necessary.
Due to the peculiarity of the $Z=0$ stellar evolution, appropriate yields are highly necessary.
Previous calculations of the stellar vields in metal-poor IMS were obtained from stellar models with no primordial composition. Z~10!Z. (Marigo.Bressan&Chiosi1998:VandenΠουGroenewegen1997).
Previous calculations of the stellar yields in metal-poor IMS were obtained from stellar models with no primordial composition, $Z\sim 10^{-4} Z_\odot$ \citep{mar98, van97}.
Aloreover. these vields were obtained [rom synthetic approximations alter the end οἱ Ile-burning without having taken into account the evolution during the TP-AGD phase.
Moreover, these yields were obtained from synthetic approximations after the end of He-burning without having taken into account the evolution during the TP-AGB phase.
In fact. the existence of third dredge-up (TDU) episodes and thermal pulses (TP) in Chis phase plays a crucial role in determining the stellar vields [rom IMS.
In fact, the existence of third dredge-up (TDU) episodes and thermal pulses (TP) in this phase plays a crucial role in determining the stellar yields from IMS.
Recently. performed a detailed analvsis of the evolution of zero metal IMS.
Recently, \citet{chi01} performed a detailed analysis of the evolution of zero metal IMS.
Using the evolutionary code FRANEC (Chielli.Limonei&Straniero1998) these authors found. at variance with previous studies. that these stars do experience TP during the AGB phase.
Using the evolutionary code FRANEC \citep{chi98} these authors found, at variance with previous studies, that these stars do experience TP during the AGB phase.
As a consequence. TDU episodes occur and the stellar envelope may be enriched with fresh PC. UN and PO during this phase.
As a consequence, TDU episodes occur and the stellar envelope may be enriched with fresh $^{12}$ C, $^{14}$ N and $^{16}$ O during this phase.
The most important result [rom this study is that these stars become C-rich (1.6. carbon stars) and N-rich and can eject important amounts of these elements at the end of their evolution.
The most important result from this study is that these stars become C-rich (i.e. carbon stars) and N-rich and can eject important amounts of these elements at the end of their evolution.
The vields from these stars are. however. sensitive to ihe modeling of the mass-loss rate during the AGB phase.
The yields from these stars are, however, sensitive to the modeling of the mass-loss rate during the AGB phase.
In fact. it is the mass-loss rate that finally determines the duration of the AGB phase since it limits the munber of TPs and. therefore. the nmmber of TDU episodes.
In fact, it is the mass-loss rate that finally determines the duration of the AGB phase since it limits the number of TPs and, therefore, the number of TDU episodes.
Both mass loss aud dredge up efficiency. could be deduced by the observed properties of the disk AGB population. but little is known of (hese phenomena in very metal-poor stars.
Both mass loss and dredge up efficiency could be deduced by the observed properties of the disk AGB population, but little is known of these phenomena in very metal-poor stars.
We note. however. that the increase of the heavy elements in the envelope. caused by the TDU in Population HI AGB stars. could reduce the difference with respect to the more metal-rich AGB stars.
We note, however, that the increase of the heavy elements in the envelope, caused by the TDU in Population III AGB stars, could reduce the difference with respect to the more metal-rich AGB stars.
The vields of intermediate mass
The yields of intermediate mass
Both SPH andrpSPH simulations have a final linear momentum corresponding to 4.1 and 3.2 km per second per gas particle, respectively.
Both SPH and simulations have a final linear momentum corresponding to 4.1 and 3.2 km per second per gas particle, respectively.
The difference vector between the final gas momenta of the simulation has a magnitude of 2.6 km/s per gas particle.
The difference vector between the final gas momenta of the simulation has a magnitude of 2.6 km/s per gas particle.
This is a difference of order one half of a percent of the mass weighted mean r.m.s.
This is a difference of order one half of a percent of the mass weighted mean r.m.s.
velocity of ~400 km/s. Obviously, giving up the strict linear momentum conservation in our equation of motion has not lead to any noticeable difference in this measure but has improved the comparison with results from adaptive mesh refinement codes.
velocity of $\sim 400$ km/s. Obviously, giving up the strict linear momentum conservation in our equation of motion has not lead to any noticeable difference in this measure but has improved the comparison with results from adaptive mesh refinement codes.
However, this particular application is relatively easy as dark matter dominates the gravitational potential.
However, this particular application is relatively easy as dark matter dominates the gravitational potential.
As we will show further belowrpSPH is quite easy to break with self-gravitating fluids.
As we will show further below is quite easy to break with self-gravitating fluids.
Next we demonstrate that using our pressure force discretisation give another very important advantage.
Next we demonstrate that using our pressure force discretisation give another very important advantage.
Simulations with drastically varying particle masses continue to give correct results.
Simulations with drastically varying particle masses continue to give correct results.
This is markedly different compared to previous SPH simulations employing particle splitting.
This is markedly different compared to previous SPH simulations employing particle splitting.
The latter only worked reasonably as long as different particle masses were very well separated spatially.
The latter only worked reasonably as long as different particle masses were very well separated spatially.
As an explicit example we revisit the Rayleigh-Taylor problem from above.
As an explicit example we revisit the Rayleigh–Taylor problem from above.
This time we initialize particles on a uniform lattice and model the density contrast by changing the particle masses according to the density profile.
This time we initialize particles on a uniform lattice and model the density contrast by changing the particle masses according to the density profile.
We employ a density at the top ten times the one of the one at the bottom fluid to demonstrate that this is not just a marginally better aspect ofrpSPH.
We employ a density at the top ten times the one of the one at the bottom fluid to demonstrate that this is not just a marginally better aspect of.