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In particular. we would like to understand theoretically the modification of the maguetic field measurement through inverse Compton and rotation measure methods. as the ecometiy of the magnetic field changes from isotropic to racially-biased. | In particular, we would like to understand theoretically the modification of the magnetic field measurement through inverse Compton and rotation measure methods, as the geometry of the magnetic field changes from isotropic to radially-biased. |
With a theoretical undoerstaudiug. we could compute exact IC aud rotation measure maps from a Ισ]οποίο- simulated cluster for comparison with observational data. | With a theoretical understanding, we could compute exact IC and rotation measure maps from a high-resolution simulated cluster for comparison with observational data. |
Iu short. clusters of galaxies provide a rich physics laboratory for testing Dragiuski-MIID. the MI. and mauv other phenomena. | In short, clusters of galaxies provide a rich physics laboratory for testing Braginskii-MHD, the MTI, and many other phenomena. |
We have developed analytical and computational tools for understanding these phenomena. aud we will coutinue to apply these extended— AIITD inocdels to iuproviug our understanding of clusters of ealaxies. | We have developed analytical and computational tools for understanding these phenomena, and we will continue to apply these extended MHD models to improving our understanding of clusters of galaxies. |
We thank Eliot Quataert. Prateck Sharma. and Ben Chaudran for αμα useful conversations. | We thank Eliot Quataert, Prateek Sharma, and Ben Chandran for many useful conversations. |
We also acknowledge useful sugeestions from Chris Revuolds. Eve Ostriker. aud especially Jack Unehes. | We also acknowledge useful suggestions from Chris Reynolds, Eve Ostriker, and especially Jack Hughes. |
I. J. P. is supported by NASA through the Chandra Postdoctoral Fellowship erant PE?-80019 awarded by the N-Rav Center. which is operated by the Samüthsoniau| Astroplivsical Observatory for NASA under contract NASS-03060, | I. J. P. is supported by NASA through the Chandra Postdoctoral Fellowship grant PF7-80049 awarded by the X-Ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. |
TJ. P. was previously supported by the Departinent of Energy. Computational Science Graduate Fellowship. | I. J. P. was previously supported by the Department of Energy Computational Science Graduate Fellowship. |
J. M. S. acknowledges support by the DOE through eraut DE-ECG52-06NA26217. | J. M. S. acknowledges support by the DOE through grant DE-FG52-06NA26217. |
This research was supported in part bv the National Science. Foundation through TeraCiid resources provided by the Natioual Center for Atmospheric Research aud the Pittsburgh Supercomputing Center. | This research was supported in part by the National Science Foundation through TeraGrid resources provided by the National Center for Atmospheric Research and the Pittsburgh Supercomputing Center. |
Parts of this work were also performed on the Oraugeua aud Della supercompiuters at Princeton University. | Parts of this work were also performed on the Orangena and Della supercomputers at Princeton University. |
are drawn in Section 6.. | are drawn in Section \ref{concs}. |
Phroughout the paper. cosmological parameters of OQ= 1. X=0 and 44,=TOkkmss !Mpe. t are assumed. | Throughout the paper, cosmological parameters of $\Omega = 1$ , $\Lambda = 0$ and $H_{0}= 70$ $^{-1}$ $^{-1}$ are assumed. |
With a redshift of z=0.83. 03 is the highest redshift cluster in the Extended Mecium Sensitivity Survey (I2MSS) Xray selected. cluster sample (2)... and also one of the most luminous in Xravs with a kkeV Xrav luminosity of 9«10! eergss.+. | With a redshift of $z=0.83$, $-$ 03 is the highest redshift cluster in the Extended Medium Sensitivity Survey (EMSS) X–ray selected cluster sample \cite{gio90}, and also one of the most luminous in X–rays with a keV X--ray luminosity of $9 \times 10^{44}$ $^{-1}$. |
On account of its high redshift and richness (Abell class 3). a deep 5 by 5 arcminute mosaic was mace of the field around the cluster using the wideΠοια planetary camera 2 (WEDPC2) on the Hubble Space Telescope (ST). in two filters (E606. and ESI4M: van Dokkum 22000). | On account of its high redshift and richness (Abell class 3), a deep 5 by 5 arcminute mosaic was made of the field around the cluster using the wide–field planetary camera 2 (WFPC2) on the Hubble Space Telescope (HST), in two filters (F606W and F814W; van Dokkum 2000). |
This has subsequently. been supplemented. by. deep nearinfrared. imaging of the cluster in the J. ff and A wavebands. using the NT'T. and C. D. V. imagine using FORS on the VLT. to provide galaxy colours across a long wavelength baseline (Franx iin preparation). | This has subsequently been supplemented by deep near–infrared imaging of the cluster in the $J$, $H$ and $K$ wavebands using the NTT, and $U$, $B$, $V$ imaging using FORS on the VLT, to provide galaxy colours across a long wavelength baseline (Franx in preparation). |
These images show a conspicuous overdensity of red cluster galaxies with a somewhat irregular and elongated cistribution (2).. probably consisting of three sub-clumps of galaxies at the same radial velocity: this is consistent with the detection of substructure in the Nray image (7:?).. | These images show a conspicuous overdensity of red cluster galaxies with a somewhat irregular and elongated distribution \cite{dok00}, probably consisting of three sub-clumps of galaxies at the same radial velocity; this is consistent with the detection of substructure in the X–ray image \cite{don98,jel01}. |
Alultiobject. spectroscopy carried. out on. the Keck Telescope has enabled: redshifts to be determined. for over 200 objects in this field. with more than 130 of these being confirmed as cluster members (van Dokkum 22000. Tran iin preparation) | Multi–object spectroscopy carried out on the Keck Telescope has enabled redshifts to be determined for over 200 objects in this field, with more than 130 of these being confirmed as cluster members (van Dokkum 2000, Tran in preparation). |
"These authors found that the fraction of all carly tvpe galaxies in the central regions of the cluster is much lower than that at. low recshift. (~ SOUL). | These authors found that the fraction of all early type galaxies in the central regions of the cluster is, much lower than that at low redshift $\sim 80$ ). |
Further. à very high fraction 9 of cluster. galaxies are classified as "merger/peculiar" on the basis of double nuclei (separations lOkpc). tidal tails. and cistorted morphologics (?7).. | Further, a very high fraction ) of cluster galaxies are classified as “merger/peculiar” on the basis of double nuclei (separations $\ll 10\,$ kpc), tidal tails, and distorted morphologies \cite{dok99a}. |
This high fraction strongly argues against monolithic collapse models of galaxy. formation. | This high fraction strongly argues against monolithic collapse models of galaxy formation. |
Interestingly.e many of the mergingo OOgalaxies are red. bulgeὃνdominated galaxies with no detected nebular line emission. and: colours offset. from the carlytype (0DB). colour magnitude relation bv only 0.07 magnitudes. | Interestingly, many of the merging galaxies are red, bulge--dominated galaxies with no detected nebular line emission, and colours offset from the early–type $(U-B)_z$ colour magnitude relation by only 0.07 magnitudes. |
The fraction of blue galaxies in the cluster. calculated. in a manner equivalent to that. defined. by Butcher. Oemler (?).. is (7).. comparable to the mean value determined for clusters at redshifts 0.3«z0.5. | The fraction of blue galaxies in the cluster, calculated in a manner equivalent to that defined by Butcher Oemler \shortcite{but78}, is $0.22 \pm 0.05$ \cite{dok00}, comparable to the mean value determined for clusters at redshifts $0.3 < z < 0.5$. |
03 is clearly an interesting rich cluster with a wealth of observations over à wide varicty of wavelengths and. crucially. with spectroscopic redshifts for the majority of the objects. towards the cluster. centre: currently. spectroscopic redshifts have been. measured. for of all galaxies with 19.0<122.0 (the brightest cluster galaxy has L~ 19.5) within the bounds of the HIST. mosaic. | $-$ 03 is clearly an interesting rich cluster with a wealth of observations over a wide variety of wavelengths and, crucially, with spectroscopic redshifts for the majority of the objects towards the cluster centre: currently, spectroscopic redshifts have been measured for of all galaxies with $19.0 < {\rm I} <22.0$ (the brightest cluster galaxy has ${\rm I} \sim 19.5$ ) within the bounds of the HST mosaic. |
As such. AISLO54 03 is an ideal target for a deep cluster racio survey. | As such, $-$ 03 is an ideal target for a deep cluster radio survey. |
Indeed. it was one of the high redshift clusters in the L4GGllz survey of Stocke shortcitesto99b.. who detected three radio sources within the cluster down to a [lux density limit of 0.20]. | Indeed, it was one of the high redshift clusters in the GHz survey of Stocke \\shortcite{sto99b}, who detected three radio sources within the cluster down to a flux density limit of 0.2mJy. |
These are discussed later. together with the weaker sources identified in the eurrent observations. | These are discussed later, together with the weaker sources identified in the current observations. |
03 was observed using the Very Large. Array (VLA) at 5CGGllz in € array configuration during three 10-hour runs on April 3. 6 and 7 2000. | $-$ 03 was observed using the Very Large Array (VLA) at GHz in C array configuration during three 10-hour runs on April 3, 6 and 7 2000. |
The total on- integration time was 06270 seconds. | The total on-source integration time was 96270 seconds. |
The observations were carried out simultaneously. at two frequencies. 4835 and MMlIz. cach with two circular polarisations and AAILI banedwieth. | The observations were carried out simultaneously at two frequencies, 4835 and MHz, each with two circular polarisations and MHz bandwidth. |
With this setup. the fullwidthhalf»ower of the antenna primary beam is about 9 areniins and he angular resolution about 4 aresec. | With this set–up, the full--width--half--power of the antenna primary beam is about 9 arcmins and the angular resolution about 4 arcsec. |
The observations were carried out using standard VLA procedures. | The observations were carried out using standard VLA procedures. |
Short observations of the primary (lux calibrator 3C286 (13311305) were used to calibrate the flux density scale. assumüng Lux densities of 7.46 and 7.51 Jv at the wo observing [requencies: these are the most. recently determined VLA values. ancl are approximately above he flux density scale of Baars shorteitehaaT7.. | Short observations of the primary flux calibrator 3C286 (1331+305) were used to calibrate the flux density scale, assuming flux densities of 7.46 and 7.51 Jy at the two observing frequencies; these are the most recently determined VLA values, and are approximately above the flux density scale of Baars \\shortcite{baa77}. |
Observations of ὃς286 separated. in time » about 6 hours were used to determine the absolute »olarisation position angle and to estimate the uncertainty in this calibration (42°) from the dillerence between he solutions for the two cillerent. scans. | Observations of 3C286 separated in time by about 6 hours were used to determine the absolute polarisation position angle and to estimate the uncertainty in this calibration $\pm
2^{\circ}$ ) from the difference between the solutions for the two different scans. |
The secondary calibrator 10581015. olfset 5 degrees from MSI054. 03. was observed at. 30 minute intervals throughout the runs o provide accurate phase calibration. | The secondary calibrator 1058+015, offset 5 degrees from $-$ 03, was observed at 30 minute intervals throughout the runs to provide accurate phase calibration. |
"The wide range of xwallactic angles at which this calibrator was observed enabled the on-axis antenna polarisation response ternis to xf accurately determined. | The wide range of parallactic angles at which this calibrator was observed enabled the on-axis antenna polarisation response terms to be accurately determined. |
After first. ciscarcing data [from any antenna or baseline showing excessive noise (very little for the first run. about of the data from the second run and of the data rom the third run). the data were ed using the taskIMAGR. | After first discarding data from any antenna or baseline showing excessive noise (very little for the first run, about of the data from the second run and of the data from the third run), the data were ed using the task. |
. Then. the presence of a just sullicientIx brig= (7mJv) point source towards the centre of the field. enable wo eveles of phase selfcalibration to be carried out. which reduced the map rms by15%. | Then, the presence of a just sufficiently bright (7mJy) point source towards the centre of the field, enabled two cycles of phase self–calibration to be carried out, which reduced the map rms by. |
. Finalmaps of the fie were then produced in the Stokes parameters LQ and U w further eLEgANing the datasets. | Finalmaps of the field were then produced in the Stokes parameters I, Q and U, by further ing the datasets. |
Phe maps were produce using an intermediate data weighting between those of natural and uniform weighting. bv setting the data weightine | The maps were produced using an intermediate data weighting between those of natural and uniform weighting, by setting the data weighting |
to the atmosphere. | to the atmosphere. |
We can rewrite Eq. (2)) | We can rewrite Eq. \ref{e:enthalpy}) ) |
in terms of teniperature: where e is the specific heat at coustaut pressure. | in terms of temperature: where $c_{\mathrm{p}}$ is the specific heat at constant pressure. |
Duriug the atmospheric path. as the Mach umuber is large. the aeteoroid’s speed is close to the imaxiumn value corresponding to the stagnation temperature. | During the atmospheric path, as the Mach number is large, the meteoroid's speed is close to the maximum value corresponding to the stagnation temperature. |
Changes iu the stream properties are mainly due to changes in the stagnation temperature Zy. which is a direct measure of the amount of heat trausfer. | Changes in the stream properties are mainly due to changes in the stagnation temperature $T_{0}$, which is a direct measure of the amount of heat transfer. |
This argunient stresses the inuportance of the stagnation femiperature iu lwpersouic flow. since it is related to the maxinuun speed of the stream. which in turn is close to the speed of the cosmic body. | This argument stresses the importance of the stagnation temperature in hypersonic flow, since it is related to the maximum speed of the stream, which in turn is close to the speed of the cosmic body. |
According to Shapiro (1951)). the relationship between stagnation temperature and maxima speed of the stream cau be expressed im the following wav: where 5 is the ratio of specific heats; | According to Shapiro \cite{SHAPIRO}) ), the relationship between stagnation temperature and maximum speed of the stream can be expressed in the following way: where $\gamma$ is the ratio of specific heats. |
Dy meaus of the equation of state for the air. Vias can be expressed as a function of the stagnation pressure aud deusity: Tn order to obtain a condition. for the imeteoroicd breakup. the stagnation pressure py niust be set equal to the mechanical streneth S of the body. | By means of the equation of state for the air, $V_{\mathrm{max}}$ can be expressed as a function of the stagnation pressure and density: In order to obtain a condition for the meteoroid breakup, the stagnation pressure $p_0$ must be set equal to the mechanical strength $S$ of the body. |
As for the stagnation density. we have PoPas)/Pair71 (Landau Lifshitz 1987)). where pair is the uncisturbed air density at the airburst height. | As for the stagnation density, we have $(\rho_{0}-\rho_{\mathrm{air}})/\rho_{\mathrm{air}}\approx 1$ (Landau Lifshitz \cite{LANDAU}) ), where $\rho_{\mathrm{air}}$ is the undisturbed air density at the airburst height. |
Finally. bv expressing pair as a function of atmospheric height 2aud py. like iu Eq. ( | Finally, by expressing $\rho_{\mathrm{air}}$ as a function of atmospheric height $h$and $\rho_{\mathrm{sl}}$, like in Eq. ( |
1). we obtain a new equation to estimate Vias Which is close to the speed of the cosmic body at breakup V: For 5 we can use a value of about 1.7.resulting from. experinoenutal studies on plasina developed iu lypervelocity iupacts (Ikadono Fujiwara 1996). | 1), we obtain a new equation to estimate $V_{\mathrm{max}}$ , which is close to the speed of the cosmic body at breakup $V$: For $\gamma$ we can use a value of about $1.7$,resulting from experimental studies on plasma developed in hypervelocity impacts (Kadono Fujiwara \cite{KADONO}) ). |
Comparing Eq. (6)) | Comparing Eq. \ref{e:velo2}) ) |
to Eq. (1)). | to Eq. \ref{e:velo}) ), |
we see an additional factor of about 1.6. | we see an additional factor of about $1.6$. |
This comes from the fact that Eq. (6)) | This comes from the fact that Eq. \ref{e:velo2}) ) |
derives from Eq. CL). | derives from Eq. \ref{e:vmax}) ), |
according to which the stagnation temperature cdepe1cs on speed when a body is travelling at Lypersonic velocity. | according to which the stagnation temperature depends on speed when a body is travelling at hypersonic velocity. |
Eq. (6)) | Eq. \ref{e:velo2}) ) |
shows that the airburst occurs thanks to f16 combined thermal aud mechanical effects acting on the neteoroid. | shows that the airburst occurs thanks to the combined thermal and mechanical effects acting on the meteoroid. |
In other words. thermodvuamic processes decrease the effective pressure crushing the body i a significaut way. so the same body can reach a lower altitude. or for a given airburst altitude a lower strength is required. | In other words, thermodynamic processes decrease the effective pressure crushing the body in a significant way, so the same body can reach a lower altitude, or for a given airburst altitude a lower strength is required. |
By means of Eq. (6)) | By means of Eq. \ref{e:velo2}) ) |
we cau replace Table 1 with a new able for the breakup speeds of different types of cosmic xdv (see Tab. 23). | we can replace Table 1 with a new table for the breakup speeds of different types of cosmic body (see Tab. \ref{speed-new}) ). |
Note that jw the inferred speed or an ion body would be too lugh. aud stony bodies xovide the most plausible solution. | Note that now the inferred speed for an iron body would be too high, and stony bodies provide the most plausible solution. |
This i$ consisteut with the results of a detailed analysis of several hundreds ucteors carried out by Ceplecha AlcCrosky (1976)) aud Ceplecha (199 1). who found tha a height around 10 kin is fairly typical for stony objects. | This is consistent with the results of a detailed analysis of several hundreds meteors carried out by Ceplecha McCrosky \cite{JGR}) ) and Ceplecha \cite{CEPLECHA}) ), who found that a height around 10 km is fairly typical for stony objects. |
We can now calculate other data for the Tuuguska eveut solving the equations of motion and the luminosity equation. according to the procedure described in Foschini (1995)). | We can now calculate other data for the Tunguska event solving the equations of motion and the luminosity equation, according to the procedure described in Foschini \cite{FOSCHINI}) ). |
The results are sununarizec in Table 3.. | The results are summarized in Table \ref{summary}. |
The following assumptions have been made: (4) the Iuniuous eficicney 7 is D (i) the diameter of the object is calculated assimnuius a spherical shape and a deusityv of 3500 117. typical for a stoux object. | The following assumptions have been made: (i) the luminous efficiency $\tau$ is $5\%$; (ii) the diameter of the object is calculated assuming a spherical shape and a density of $3500$ $^{3}$, typical for a stony object. |
Comparing these results to previous ones and to the available data (for a review see Vasilvey 1998)). we note a generally eood agreement. except for the trajectory inclination over the horizon. | Comparing these results to previous ones and to the available data (for a review see Vasilyev \cite{VASILYEV}) ), we note a generally good agreement, except for the trajectory inclination over the horizon. |
The value obtained here is about 3°. while Vasilveyreported that the most likely inclination angle was about 157. | The value obtained here is about $3\degr$ , while Vasilyevreported that the most likely inclination angle was about $15\degr$ . |
ILoxcever. he also noted the possibility. of a good acrodvuamic shape of the | However, he also noted the possibility of a good aerodynamic shape of the |
In this section. we describe these simulations. and the relevant assumptions that go into our modeling. | In this section, we describe these simulations, and the relevant assumptions that go into our modeling. |
This involves combining a large number of simulation codes. | This involves combining a large number of simulation codes. |
In light of this. to guide the reader through the numerical details and equations in this section. we first summarise them more generally here. | In light of this, to guide the reader through the numerical details and equations in this section, we first summarise them more generally here. |
We first simulate the hydrodynamic evolution of both dise galaxies and mergers. | We first simulate the hydrodynamic evolution of both disc galaxies and mergers. |
It is from these simulations that we know the global distribution of stars. gas and metals in the galaxy. and their physical properties. | It is from these simulations that we know the global distribution of stars, gas and metals in the galaxy, and their physical properties. |
The radiative transfer occurs in post-processing. | The radiative transfer occurs in post-processing. |
We project the physical conditions of the particles onto an adaptive mesh using the SPH smoothing kernel. | We project the physical conditions of the particles onto an adaptive mesh using the SPH smoothing kernel. |
The base mesh is 5 spanning a 200 kpe box. | The base mesh is $^3$ spanning a 200 kpc box. |
The cells refine recursively into 2° subcells based on the refinement criteria the relative density variations of metals (7,,,/.<p, 2) should be less than 0.1. and the V -band optical depth across a cell be less than unity. | The cells refine recursively into $^3$ subcells based on the refinement criteria the relative density variations of metals $\sigma_{\rho m}/<\rho_m>$ ) should be less than 0.1, and the $V$ -band optical depth across a cell be less than unity. |
The maximum refinement level was L1. such that the smallest cells in this mesh are of order ~70 pe across. | The maximum refinement level was 11, such that the smallest cells in this mesh are of order $\sim70$ pc across. |
The surface density of and velocity dispersion within the GMCs are set by the physical conditions in the hydrodynamic galaxy evolution simulations. | The surface density of and velocity dispersion within the GMCs are set by the physical conditions in the hydrodynamic galaxy evolution simulations. |
A subgrid prescription comes into play when GMCs are unresolved (i.e. when cells in the adaptive mesh are very large). | A subgrid prescription comes into play when GMCs are unresolved (i.e. when cells in the adaptive mesh are very large). |
We assume that all of the mmass in the cell is in the GMC and we calculate the bbalance via analytic models (described below). | We assume that all of the mass in the cell is in the GMC and we calculate the balance via analytic models (described below). |
From this. the complete physical conditions (except for the temperature) of the GMCs are described by the hydrodynamic galaxy evolution simulations. | From this, the complete physical conditions (except for the temperature) of the GMCs are described by the hydrodynamic galaxy evolution simulations. |
The temperatures of the clouds are calculated by assuming thermal equilibrium between gas heating (by the grain photoelectric effect and cosmic rays). gas cooling (via molecular and atomic line cooling). dust heating (from the ambient radiation field). thermal dust cooling. and some energy exchange between gas and dust. | The temperatures of the clouds are calculated by assuming thermal equilibrium between gas heating (by the grain photoelectric effect and cosmic rays), gas cooling (via molecular and atomic line cooling), dust heating (from the ambient radiation field), thermal dust cooling, and some energy exchange between gas and dust. |
With the physical properties of the galaxies and GMCs known. we then proceed to calculate the emergent CO emission from the clouds. | With the physical properties of the galaxies and GMCs known, we then proceed to calculate the emergent CO emission from the clouds. |
We calculate the CO line emission from the GMCs utilising an escape probability formalism. | We calculate the CO line emission from the GMCs utilising an escape probability formalism. |
The radiation from these clouds then interacts with other clouds in the galaxy. and the level populations of CO are calculated by the balance of radiative absorptions. stimulated emission. spontaneous emission. and collisions with aand He. | The radiation from these clouds then interacts with other clouds in the galaxy, and the level populations of CO are calculated by the balance of radiative absorptions, stimulated emission, spontaneous emission, and collisions with and He. |
At this point. the general reader should be equipped to understand the general results of this paper. | At this point, the general reader should be equipped to understand the general results of this paper. |
For the remainder of this section. we elaborate on this abbreviated. description. | For the remainder of this section, we elaborate on this abbreviated description. |
Throughout. we assume /=0.7. | Throughout, we assume $h=0.7$. |
We simulate the hydrodynamic evolution of both idealised isolated dise galaxies. and mergers between these dises. | We simulate the hydrodynamic evolution of both idealised isolated disc galaxies, and mergers between these discs. |
The purpose of the ivdrodynamie simulations is to calculate the spatial distribution of ye neutral ISM. stars and metals. | The purpose of the hydrodynamic simulations is to calculate the spatial distribution of the neutral ISM, stars and metals. |
It is from the neutral ISM that we will calculate the molecular gas properties. and. as we will discuss. ye radiation from the stars and dust in the metals that determine ye IR. radiation field. | It is from the neutral ISM that we will calculate the molecular gas properties, and, as we will discuss, the radiation from the stars and dust in the metals that determine the IR radiation field. |
Here. we describe the components of the model most pertinent to this study. namely the physics of the ISM and star formation preseriptions. | Here, we describe the components of the model most pertinent to this study, namely the physics of the ISM and star formation prescriptions. |
For a more full understanding of ye underlying algorithms inGADGET-3.. please refer to and. | For a more full understanding of the underlying algorithms in, please refer to and. |
processors... The galaxies are simulated with a moditied version of the publicly available SPH code.citepsprOSb. | The galaxies are simulated with a modified version of the publicly available SPH code,. |
. The ISM is modeled as two-phase. with cold clouds embedded in a hot. pressure-contining medium2003). | The ISM is modeled as two-phase, with cold clouds embedded in a hot, pressure-confining medium. |
. Numerically. this is realised via hybrid SPH particles. | Numerically, this is realised via hybrid SPH particles. |
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