نقدم محددات نظرية جزئية على الكمية الإجمالية للمادة الظلام في عقدة الرصاص المدمجة باستخدام الحوارات الزمنية لمجموعة المحلية التقليدية. نحن نعتبر أقواس الذرات في الأنظمة الجذرية التي تناسب بيانات الإشعاع. وتم العثور على أنظمة CDM متوافقة بشكل ضعيف في الجاذبية النيوتونية بإجمالي الشحنة M_{CDM} = 1 × 10 ^ {15} Msun من الظلام البارد: يمكن للشريحة الرصاصية التحرك بسرعة V_{DM} = 3000 كم / س، ويمكن لغاز الرصاص البارد التحرك بسرعة V_{gas} = 4200 كم / س. هذه هي تقريبًا أقصى سرعات التي يمكن تسارعها بواسطة الجاذبية لشريحتين من الظلام البارد في وقت هابل حتى بدون الضغط الشديد. وتنقض التوافق إذا اعتمدنا أعلى نهاية من مجموعات البيانات الخطأ لسرعة الغاز الرصاصي (5000-5400 كم / س)، ولن يكون الغاز الرصاصي مرتبطًا بشريحة العقدة لوقت هابل. وستطلب الأنظمة التي تحمل V_{DM} ~ 4500 كم / س ~ V_{gas} كمية غير واقعية كبيرة من CDM لعقدة تحتوي فقط على ~ 10 ^ {14} Msun من الغاز. يمكن تطبيق نتائجنا على أشياء أخرى بخارج الجاذبية العامة، على سبيل المثال، يمكن الحصول على سرعة $ 4500 كم / س بسهولة في نموذج الإشعاع الموندي المتأثر الفلاشي لأنجوس et al. (2007). ومع ذلك، يصعب التوافق مع بيانات الإشعاع والسرعة لنموذج MONDian مع قليل من الظلام البارد $ M_{HDM} le 0.6times 10 ^ {15} msun ونموذج CDM مع كتلة شريحة صغيرة $ le 1times 10 ^ {15} msun.
We present semi-analytical constraint on the amount of dark matter in the merging bullet galaxy cluster using the classical Local Group timing arguments. We consider particle orbits in potential models which fit the lensing data. {it Marginally consistent} CDM models in Newtonian gravity are found with a total mass M_{CDM} = 1 x 10^{15}Msun of Cold DM: the bullet subhalo can move with V_{DM}=3000km/s, and the bullet X-ray gas can move with V_{gas}=4200km/s. These are nearly the {it maximum speeds} that are accelerable by the gravity of two truncated CDM halos in a Hubble time even without the ram pressure. Consistency breaks down if one adopts higher end of the error bars for the bullet gas speed (5000-5400km/s), and the bullet gas would not be bound by the sub-cluster halo for the Hubble time. Models with V_{DM}~ 4500km/s ~ V_{gas} would invoke unrealistic large amount M_{CDM}=7x 10^{15}Msun of CDM for a cluster containing only ~ 10^{14}Msun of gas. Our results are generalisable beyond General Relativity, e.g., a speed of $4500kms$ is easily obtained in the relativistic MONDian lensing model of Angus et al. (2007). However, MONDian model with little hot dark matter $M_{HDM} le 0.6times 10^{15}msun$ and CDM model with a small halo mass $le 1times 10^{15}msun$ are barely consistent with lensing and velocity data.
We introduce in a reduced complex space, a new coherent sub-sheaf of the sheaf $omega_{X}^{bullet}$ which has the universal pull-back property for any holomorphic map, and which is in general bigger than the usual sheaf of holomorphic differential forms $Omega_{X}^{bullet}/torsion$. We show that the meromorphic differential forms which are sections of this sheaf satisfy integral dependence equations over the symmetric algebra of the sheaf $Omega_{X}^{bullet}/torsion$. This sheaf $alpha_{X}^{bullet}$ is also closely related to the normalized Nash transform. We also show that these $q-$meromorphic differential forms are locally square-integrable on any $q-$dimensional cycle in $X$ and that the corresponding functions obtained by integration on an analytic family of $q-$cycles are locally bounded and locally continuous on the complement of closed analytic subset.
In this work, we report on a detailed simulation of the Bullet Cluster (1E0657-56) merger, including magnetohydrodynamics, plasma cooling, and adaptive mesh refinement. We constrain the simulation with data from gravitational lensing reconstructions and 0.5 - 2 keV Chandra X-ray flux map, then compare the resulting model to higher energy X-ray fluxes, the extracted plasma temperature map, Sunyaev-Zeldovich effect measurements, and cluster halo radio emission. We constrain the initial conditions by minimizing the chi-squared figure of merit between the full 2D observational data sets and the simulation, rather than comparing only a few features such as the location of subcluster centroids, as in previous studies. A simple initial configuration of two triaxial clusters with NFW dark matter profiles and physically reasonable plasma profiles gives a good fit to the current observational morphology and X-ray emissions of the merging clusters. There is no need for unconventional physics or extreme infall velocities. The study gives insight into the astrophysical processes at play during a galaxy cluster merger, and constrains the strength and coherence length of the magnetic fields. The techniques developed here to create realistic, stable, triaxial clusters, and to utilize the totality of the 2D image data, will be applicable to future simulation studies of other merging clusters. This approach of constrained simulation, when applied to well-measured systems, should be a powerful complement to present tools for understanding X-ray clusters and their magnetic fields, and the processes governing their formation.
We estimate the expected distribution of displacements between the two dominant dark matter (DM) peaks (DM-DM displacements) and between DM and gaseous baryon peak (DM-gas displacements) in dark matter halos with masses larger than $10^{13}$ Msun/h. We use as a benchmark the observation of SL2S J08544-0121, which is the lowest mass system ($1.0times 10^{14}$ Msun/h) observed so far featuring a bi-modal dark matter distribution with a dislocated gas component. We find that $(50 pm 10)$% of the dark matter halos with circular velocities in the range 300 km/s to 700 km/s (groups) show DM-DM displacements equal or larger than $186 pm 30$ kpc/h as observed in SL2S J08544-0121. For dark matter halos with circular velocities larger than 700 km/s (clusters) this fraction rises to 70 $pm$ 10%. Using the same simulation we estimate the DM-gas displacements and find that 0.1 to 1.0% of the groups should present separations equal or larger than $87pm 14$kpc/h corresponding to our observational benchmark; for clusters this fraction rises to (7 $pm$ 3)%, consistent with previous studies of dark matter to baryon separations. Considering both constraints on the DM-DM and DM-gas displacements we find that the number density of groups similar to SL2S J08544-0121 is $sim 6.0times 10^{-7}$ Mpc$^{-3}$, three times larger than the estimated value for clusters. These results open up the possibility for a new statistical test of LCDM by looking for DM-gas displacements in low mass clusters and groups.
The analysis of the cluster environment is a valuable instrument to investigate the origin of AGN and star-forming galaxies gas fuelling and trigger mechanisms. To this purpose, we present a detailed analysis of the point-like X-ray sources in the Bullet cluster field. Thanks to $sim600$ ks Chandra observations, we produced a catalogue of 381 X-ray point sources up to a distance of $sim$1.5 virial radius and with flux limits $sim1times10^{-16}$ and $sim8times10^{-16}$ erg cm$^{-2}$ s$^{-1}$ in the 0.5-2 keV and 2-10 keV bands, respectively. We found a strong (up to a factor 1.5-2) and significant ($ge$4$sigma$) over-density in the full region studied $0.3R_{200}<R<1.5R_{200}$. We identified optical and infrared counterparts for $sim$84% and $sim$48% of the X-ray sources, respectively. We obtained new spectroscopic redshifts for 106 X-ray sources. Spectroscopic and photometric redshifts of optical and infrared sources have been also collected, and these sources were used as ancillary samples. We find that the over-density in the region $0.3R_{200}<R<R_{200}$ is likely due to X-ray AGN (mostly obscured) and star-forming galaxies both associated to the cluster, while in the more external region it is likely mostly due to background AGN. The fraction of cluster galaxies hosting an X-ray detected AGN is 1.0$pm$0.4$%$, nearly constant with the radius, a fraction similar to that reported in other clusters of galaxies at similar redshift. The fraction of X-ray bright AGN (L$_{2-10keV}$$>$10$^{43}$ ergs s$^{-1}$) in the region $0.3R_{200}<R<R_{200}$ is $0.5^{+0.6}_{-0.2}$$%$, higher than that in other clusters at similar redshift and more similar to the AGN fraction in the field. Finally, the spatial distributions of AGN and star-forming galaxies, selected also thanks to their infrared emission, appear similar, thus suggesting that both are triggered by the same mechanism.
The graded coherent sheaf $alpha_X^bullet$ constructed in [B.18] for any reduced pure dimensional complex space $X$ is stable by exterior product but not by the de Rham differential. We construct here a new graded coherent sheaf $alpha_X^bullet$ containing $alpha_X^bullet$ and stable both by exterior product and by the de Rham differential. We show that it has again the ``pull-back property for holomorphic maps $f : X to Y$ between irreducible complex spaces such that $f(X)$ is not contained in the singular set of $Y$. Moreover, this graded coherent sheaf $alpha_X^bullet$ comes with a natural coherent exhaustive filtration and this filtration is also compatible with the pull-back by such holomorphic maps. These sheaves define new invariants on singular complex spaces. We show on some simple examples that these invariants are new.