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As the mass of circulating eas slowly increases. the circulation flow AL is also expected to increase and the amount of heating / mmst decrease to maintain the circulation.
As the mass of circulating gas slowly increases, the circulation flow ${\dot M}$ is also expected to increase and the amount of heating $h$ must decrease to maintain the circulation.
Ultimately. a cooling event is expected (Equation 22).
Ultimately, a cooling event is expected (Equation 22).
When the central Mis stronelv reduced in our nuuerical simulations of centrally heated cooling flows. the flow cools episodically at larger radii iu he dow (Brighenuti Mathews 2002: 2003).
When the central ${\dot M}$ is strongly reduced in our numerical simulations of centrally heated cooling flows, the flow cools episodically at larger radii in the flow (Brighenti Mathews 2002; 2003).
It remains o be determined if iutermittent cooliug eveuts ean agree with the N-rav observations. but the observatious we have so far are consistent with no cooling at all.
It remains to be determined if intermittent cooling events can agree with the X-ray observations, but the observations we have so far are consistent with no cooling at all.
Finally. the iof bubbles also carry Type Ia supermovae (SNIa) mon enrichment out to ον broadening the ion abunudauce xofile relative to the stars. which agrees qualitatively with observations.
Finally, the hot bubbles also carry Type Ia supernovae (SNIa) iron enrichment out to $r_c$, broadening the iron abundance profile relative to the stars, which agrees qualitatively with observations.
The iron from SNIa acts like tracer particles hat can reveal the direction and maecuitucde of the radial How of hot eas (Alathews Drigheuti 2003).
The iron from SNIa acts like tracer particles that can reveal the direction and magnitude of the radial flow of hot gas (Mathews Brighenti 2003).
.lin Studies of the evolution of hot eas iu elliptical ealaxies at UC Sauta Cruz are supported by NASA erauts NAG 5-8109 ATP02-0122-0079 aud NSF erants AST- AST-0098351 for which we are very erateful.
.4in Studies of the evolution of hot gas in elliptical galaxies at UC Santa Cruz are supported by NASA grants NAG 5-8409 ATP02-0122-0079 and NSF grants AST-9802994 AST-0098351 for which we are very grateful.
We therefore convert to the proper distance 7=eg. which trausforiis equation (8)) iuto For siiall values of the first terii on the right-hand side. equation (9)) is identical with the correspouding equations derived by Newtouian methods (by wav of equations (5))).
We therefore convert to the proper distance $r=ay$, which transforms equation \ref{eq:flatgeo}) ) into For small values of the first term on the right-hand side, equation \ref{eq:geonewton}) ) is identical with the corresponding equations derived by Newtonian methods (by way of equations \ref{eq:reldyn}) )).
The solutious are. therefore. identical. and the behavior of free test particles is the sue as already set out as long as the coordinate speeds are mach «λαο than that of liebt.
The solutions are, therefore, identical, and the behavior of free test particles is the same as already set out as long as the coordinate speeds are much smaller than that of light.
This does not mean we have merely recovered the Newtonian limit of a relativistic situation. aud so have approximated away auvtling interesting.
This does not mean we have merely recovered the Newtonian limit of a relativistic situation, and so have approximated away anything interesting.
If a particle is to rejoin the Wubble flow by sole property of space-time. it should do so at any speed: and iu particular should do so when it is close to the flow.
If a particle is to rejoin the Hubble flow by some property of space-time, it should do so at any speed; and in particular should do so when it is close to the flow.
Now consider even relativistic speeds.
Now consider even relativistic speeds.
If a particle's speed is. sav. ereater than the Hubble flow at ---s position. the pareuthesis of equation (9)) Is positive: in an expanding universe. 6/« is positive: so the relativistic correction to its acceleration is also positive. that is. it tends to ect even further from the flow.
If a particle's speed is, say, greater than the Hubble flow at its position, the parenthesis of equation \ref{eq:geonewton}) ) is positive; in an expanding universe, $\dot{a}/a$ is positive; so the relativistic correction to its acceleration is also positive, that is, it tends to get even further from the flow.
The couclusiou of the previous section is reinforced: there is no sign of a flow of space. carrving objects with --- Saud bodies disturbed from their places iu the Dubble flow do not return to it.
The conclusion of the previous section is reinforced: there is no sign of a flow of space, carrying objects with it; and bodies disturbed from their places in the Hubble flow do not return to it.
Iu fact. if the relativistic ternis are included. even the oue case im which a particledid eventually join the flow is found to be inexact.
In fact, if the relativistic terms are included, even the one case in which a particle eventually join the flow is found to be inexact.
From thei expressious for free particle wotion. Davis et alt? conclude that it is not the motiou of the backeround universe which causes the decay of peculiar velocity and thus (n their view) the eveutual rejoining of the ITubble Sow. but the of that flow.
From their expressions for free particle motion, Davis et $^{10}$ conclude that it is not the motion of the background universe which causes the decay of peculiar velocity and thus (in their view) the eventual rejoining of the Hubble flow, but the of that flow.
This is a difficult thing to understand physically.
This is a difficult thing to understand physically.
Tow cau the acceleration of a coordinate svsteni have a physical effect?
How can the acceleration of a coordinate system have a physical effect?
But recall that this coordinate syste is tied to a set of masses: so perhaps it is from the acceleration of the backeround mass of the universe that the effect proceeds.
But recall that this coordinate system is tied to a set of masses; so perhaps it is from the acceleration of the background mass of the universe that the effect proceeds.
There might be an analogy with clectromaguetisi (in the clementary. nourclativistic formulation). in which the velocity of a charee causes a maeuetic field which may exert a force: and an accelerating charge radiates. thus potentially affecting other objects.
There might be an analogy with electromagnetism (in the elementary, nonrelativistic formulation), in which the velocity of a charge causes a magnetic field which may exert a force; and an accelerating charge radiates, thus potentially affecting other objects.
But we are not dealing with electromagnetisin here.
But we are not dealing with electromagnetism here.
Iu General Relativity. some motions cau cause gravitational radiation and thus move other bodies: but a homogeneous. isotropic situation. such as we have here. produces none.
In General Relativity, some motions can cause gravitational radiation and thus move other bodies; but a homogeneous, isotropic situation, such as we have here, produces none.
Have Davis et al.i9 discovered a previously uususpected effect iu cosmoloey. or perliaps plivsics?
Have Davis et $^{10}$ discovered a previously unsuspected effect in cosmology, or perhaps physics?
Not in any general seuse.
Not in any general sense.
Suppose we take &=Af in Equation (51). that is. au expaudiug but universe.
Suppose we take $a=kt$ in Equation \ref{eq:flatgeo}) ), that is, an expanding but non-accelerating universe.
Then the solution for 5 is with eq an arbitrary coustant.
Then the solution for $\dot{y}$ is with $c_1$ an arbitrary constant.
This peculiar velocity should be identically zero if its source is the acceleration of the IIubble flow: clearly it is not.
This peculiar velocity should be identically zero if its source is the acceleration of the Hubble flow; clearly it is not.
Davis et aL" did uot look at situatious like this. confining theniselves to muiverses witli more conventional dynamics. all of which have accelerating scale factors.
Davis et $^{10}$ did not look at situations like this, confining themselves to universes with more conventional dynamics, all of which have accelerating scale factors.
The appearance of @ in their expression for frec-particle motion suggested to them a causal relationship.
The appearance of $\ddot{a}$ in their expression for free-particle motion suggested to them a causal relationship.
In fact. as far as plivsics goes. the acceleration of e is caused by a matter density (plus. perhaps. a cosmological constant). the same thine which causes free particle acceleration: @ is an effect. not a cause.
In fact, as far as physics goes, the acceleration of $a$ is caused by a matter density (plus, perhaps, a cosmological constant), the same thing which causes free particle acceleration; $\ddot{a}$ is an effect, not a .
For comparison of the velocity structure of the simulations we will use the observational data and results from ?:: IRAM 30m telescope observations of CO J21—0.
For comparison of the velocity structure of the simulations we will use the observational data and results from : IRAM 30m telescope observations of $^{18}$ O $\rightarrow$ 0.
We also refer to the analysis of Serpens molecular data from the JCMT GBS HARP data of C0 J23—52(?)..
We also refer to the analysis of Serpens molecular data from the JCMT GBS HARP data of $^{18}$ O $\rightarrow$ 2.
For H» column density comparisons. we used the SCUBA 850 um emission from JCMT(?)..
For $_{2}$ column density comparisons, we used the SCUBA 850 $\mu$ m emission from JCMT.:
comparison: In order to compare with the observations. we first constructed à datacube from the simulated 3D cloud collisions.
In order to compare with the observations, we first constructed a datacube from the simulated 3D cloud collisions.
of the simulations where the first sink particle is formed. we created a datacube of column density for a space-space-velocity 3D grid.
of the simulations where the first sink particle is formed, we created a datacube of column density for a space-space-velocity 3D grid.
In the spatial planes we convolved the models with a Gaussian of FWHM of 10 pix (0.02 pe) which corresponds to the 22" spatial resolution of the IRAM-30m telescope observations of C'5O J21—0 at the distance of Serpens.
In the spatial planes we convolved the models with a Gaussian of FWHM of 10 pix (0.02 pc) which corresponds to the 22” spatial resolution of the IRAM-30m telescope observations of $^{18}$ O $\rightarrow$ 0 at the distance of Serpens.
While to reproduce the thermal velocity dispersion of Serpens. the velocity space was convolved with a normalised Gaussian of 0.4 kms”! full width half maximum (FWHM). correspondent to the thermal line width of H» at 10 K. Gas temperature. density and abundance all atfect the relationship. between the true column density of a cloud and the emission seen in a molecular line.
While to reproduce the thermal velocity dispersion of Serpens, the velocity space was convolved with a normalised Gaussian of 0.4 $^{-1}$ full width half maximum (FWHM), correspondent to the thermal line width of $_{2}$ at 10 K. Gas temperature, density and abundance all affect the relationship between the true column density of a cloud and the emission seen in a molecular line.
However as discussed in and in Serpens the CO appears to be a faithful tracer of the overall velocity structure of the cloud and not significantly affected by outflow or infall motions. while globally the 850 uim emission traces the mass distribution 1n. the region.
However as discussed in and in Serpens the $^{18}$ O appears to be a faithful tracer of the overall velocity structure of the cloud and not significantly affected by outflow or infall motions, while globally the 850 $\mu$ m emission traces the mass distribution in the region.
To assess the success of the simulations in modeling Serpens. we therefore compare the models with the velocity structure of the C'O and the overall column density distribution from the dust emission.
To assess the success of the simulations in modeling Serpens, we therefore compare the models with the velocity structure of the $^{18}$ O and the overall column density distribution from the dust emission.
The presence of dark matter in early (vpe galaxies is clear on large scales. based on both weak lensing (e.g. IXleinheinriceh et al.
The presence of dark matter in early type galaxies is clear on large scales, based on both weak lensing (e.g. Kleinheinrich et al.
2006. Mandelbaim et al.
2006, Mandelbaum et al.
2006) and X-ray (e.g. ]lunphnrev et al.
2006) and X-ray (e.g. Humphrey et al.
2006) studies.
2006) studies.
The distribution of the dark matter and (he mass fraction represented by (he stars are less well-determined because of the difficulties in measuring galaxy structure in (he (transition region between the stars ancl the dark matter.
The distribution of the dark matter and the mass fraction represented by the stars are less well-determined because of the difficulties in measuring early-type galaxy structure in the transition region between the stars and the dark matter.
Stellar
Stellar
lunes: ealaxies
nes: galaxies
(heir formation is an outcome of a much later stage in (he evolution of planetary svstenis.
their formation is an outcome of a much later stage in the evolution of planetary systems.
In order to test this possibility. it is essential to perform much more long-term dynamical studies of resonant svstems. lasting a few Civrs and more.
In order to test this possibility, it is essential to perform much more long-term dynamical studies of resonant systems, lasting a few Gyrs and more.
In order to further explore the issue of survivability of mean-moltion resonances. we need also to reline our knowledge of mulüplanetary systems.
In order to further explore the issue of survivability of mean-motion resonances, we need also to refine our knowledge of multiplanetary systems.
Specilicallv. we should compile a more comprehensive dataset of stellar ages for the multiplanetary svstems.
Specifically, we should compile a more comprehensive dataset of stellar ages for the multiplanetary systems.
Hopefully. with the advent of the recent planet [imdineg missions. such data will become more abundant.
Hopefully, with the advent of the recent planet finding missions, such data will become more abundant.
The results we presented in (his Letter are only a preliminary attempt to test whether (he issue of survival of mean-moltion resonsnces is worth exploring with the tools of stellar age estimates.
The results we presented in this Letter are only a preliminary attempt to test whether the issue of survival of mean-motion resonsnces is worth exploring with the tools of stellar age estimates.
Apparently. the existing data partly corroborate the hypothesis we presented in Section l.. and the 2/1 PC indeed tends to be found in younger svstems.
Apparently, the existing data partly corroborate the hypothesis we presented in Section \ref{intro}, and the $2/1$ PC indeed tends to be found in younger systems.
This may. very well be another window into the understanding of planetary. orbital evolution.
This may very well be another window into the understanding of planetary orbital evolution.
This research was supported by the ISRAEL SCIENCE FOUNDATION | The Adler Foundation for Space Research (grant No.
This research was supported by the ISRAEL SCIENCE FOUNDATION – The Adler Foundation for Space Research (grant No.
119/07).
119/07).
This research has mace use of the Exoplanet Orbit Database and the Exoplanet Data Explorer al exoplanets.org.
This research has made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org.
continuity between the galaxy population at z<1 and that at z>2, we have embarked on a campaign to measure c and Maynfor a large sample of field spheroidals at 1<z1.7.
continuity between the galaxy population at $z<1$ and that at $z>2$, we have embarked on a campaign to measure $\sigma$ and for a large sample of field spheroidals at $1<z<1.7$.
This has recently become practical using multi-object optical spectrographs equipped with deep depletion red-sensitive CCDs.
This has recently become practical using multi-object optical spectrographs equipped with deep depletion red-sensitive CCDs.
Our goal is to extend the earlier work at z<1 (T05, vdW08) to within ~1 Gyr of the sample of ultracompact galaxies at z~2.3.
Our goal is to extend the earlier work at $z<1$ (T05, vdW08) to within $\simeq$ 1 Gyr of the sample of ultracompact galaxies at $z\simeq2.3$.
In this first analysis, we present new results spanning the redshift range 1.05«2<1.60.
In this first analysis, we present new results spanning the redshift range $1.05<z<1.60$.
We adopt a ACDM cosmology with =(0.3,0.7, 0.7); all magnitudes are in the AB(Qm,Qv,h) system.
We adopt a $\Lambda$ CDM cosmology with $(\Omega_m, \Omega_v, h) = (0.3, 0.7, 0.7)$ ; all magnitudes are in the AB system.
A Chabrier IMF is assumed where necessary.
A Chabrier IMF is assumed where necessary.
Our targets were selected from archival HST//ACS data in the EGS (GO 10134, PI: Davis), SSA22 (GO 9760, PI: Abraham GO 10403, PI: Chapman), and GOODS-N (PI: Giavalisco) fields.
Our targets were selected from archival /ACS data in the EGS (GO 10134, PI: Davis), SSA22 (GO 9760, PI: Abraham GO 10403, PI: Chapman), and GOODS-N (PI: Giavalisco) fields.
For the EGS, we used the ? catalog which matches CFHT (BRI, ?;; ugriz, CFHTLS) and Palomar (JK,) photometry.
For the EGS, we used the \citet{Bundy2006} catalog which matches CFHT $BRI$, \citealt{Coil2004}; $ugriz$ , CFHTLS) and Palomar $JK_s$ ) photometry.
Photometric redshifts are supplemented by spectroscopic redshifts from the DEEP2 survey.
Photometric redshifts are supplemented by spectroscopic redshifts from the DEEP2 survey.
For SSA22, we used a photometric redshift catalog based on Subaru (BV RIz) and UH 2.2m (JH K,) imaging kindly provided by P. ?..
For SSA22, we used a photometric redshift catalog based on Subaru $BVRIz$ ) and UH 2.2m $JHK_s$ ) imaging kindly provided by P. \citet{Capak2004}.
In GOODS-N, we used the ? catalog which matches ACS and Subaru K, photometry.
In GOODS-N, we used the \citet{Bundy2009} catalog which matches ACS and Subaru $K_s$ photometry.
Galactic extinction corrections were based on the dust maps of ?..
Galactic extinction corrections were based on the dust maps of \citet{Schlegel1998}.
The parent sample for spectroscopic study in EGS and SSA22 was defined by I—K,>2, I«23.5, and z>1; in GOODS-N, the photometric criteria were F850LP—K,>1.5 and F850LP<23.5.
The parent sample for spectroscopic study in EGS and SSA22 was defined by $I-K_s > 2$, $I < 23.5$, and $z > 1$; in GOODS-N, the photometric criteria were ${\rm F850LP} - K_s > 1.5$ and ${\rm F850LP} < 23.5$.
All galaxies satisfying these criteria were visually inspected in the ACS images by one of us (RSE) and those with E/SO0 or early-disk morphology retained.
All galaxies satisfying these criteria were visually inspected in the ACS images by one of us (RSE) and those with E/S0 or early-disk morphology retained.
Keck I LRIS observations were made for 14 EGS and SSA22 targets on 2009 June 26-28 in median seeing of 0"9.
Keck I LRIS observations were made for 14 EGS and SSA22 targets on 2009 June 26–28 in median seeing of $0\farcs9$.
The 600 mm-! grating blazed at 1 jim was used, providing a velocity resolution of oinst=58 km s! at 9000À.
The 600 ${}^{-1}$ grating blazed at 1 $\mu$ m was used, providing a velocity resolution of $\sigma_{\rm inst} = 58$ km ${}^{-1}$ at 9000.
. The total integration times were 40.8 ks and 32.4 ks in the EGS and SSA22 fields, respectively.
The total integration times were 40.8 ks and 32.4 ks in the EGS and SSA22 fields, respectively.
On 2010 April 5-6 LRIS observations were made of 7 GOODS-N targets with 34.8 ks of integration in 0/8 seeing.
On 2010 April 5–6 LRIS observations were made of 7 GOODS-N targets with 34.8 ks of integration in $0\farcs8$ seeing.
One additional GOODS-N spectrum was secured with Keck II DEIMOS observations on 2010 April 11--12 using the 831 mm-! grating.
One additional GOODS-N spectrum was secured with Keck II DEIMOS observations on 2010 April 11--12 using the 831 ${}^{-1}$ grating.
The LRIS data were reduced using the code developed by ?..
The LRIS data were reduced using the code developed by \citet{Kelson2003}.
Spectra were extracted using optimal weighting based on Gaussian fits to the spatial profile.
Spectra were extracted using optimal weighting based on Gaussian fits to the spatial profile.
Telluric absorption correction and relative flux calibration were provided by a DA star observed at matching airmass at the end of each night.
Telluric absorption correction and relative flux calibration were provided by a DA star observed at matching airmass at the end of each night.
We measured stellar velocity dispersions, c, by fitting broadened stellar templates using the PPXF code of ?..
We measured stellar velocity dispersions, $\sigma$, by fitting broadened stellar templates using the PPXF code of \citet{Cappellari2004}.
The instrumental resolution was measured using unblended sky lines; their variation with wavelength was well fit by a low-order polynomial.
The instrumental resolution was measured using unblended sky lines; their variation with wavelength was well fit by a low-order polynomial.
The template collection comprised 348 stars of type F0-G9 from the Indo-US coudé library (?) with a range of metallicities and luminosities (classes III-V).
The template collection comprised 348 stars of type F0–G9 from the Indo-US coudé library \citep{Valdes2004} with a range of metallicities and luminosities (classes III–V).
We verified that including A star templates does not affect our measurements.
We verified that including A star templates does not affect our measurements.
For each galaxy, PPXF constructed an optimal template as a linear combination of these stellar spectra, although our results do not significantly differ if the best-fitting single template is used.
For each galaxy, PPXF constructed an optimal template as a linear combination of these stellar spectra, although our results do not significantly differ if the best-fitting single template is used.
To avoid systematic errors, we masked pixels contaminated by OH emission.
To avoid systematic errors, we masked pixels contaminated by OH emission.
Based on tests with the continuum filtering, Sky masking threshold, and stellar template choices, we assigned a systematic uncertainty to each velocity dispersion, typically 5—1096.
Based on tests with the continuum filtering, sky masking threshold, and stellar template choices, we assigned a systematic uncertainty to each velocity dispersion, typically $5 - 10\%$.
We were able to secure a reliable dispersion for 17/22 galaxies (see Figs.
We were able to secure a reliable dispersion for 17/22 galaxies (see Figs.
1 and 2)).
\ref{fig:spectra} and \ref{fig:spectra2}) ).
Velocity dispersions were corrected to an effective circular aperture of radius R,/8 as described in ?;; the mean correction factor is 1.13.
Velocity dispersions were corrected to an effective circular aperture of radius $R_e/8$ as described in \citet{Treu1999}; the mean correction factor is 1.13.
Surface photometry was measured in the images using GALFIT (?) with a PSF determined from a nearby isolated star.
Surface photometry was measured in the images using GALFIT \citep{Peng2002} with a PSF determined from a nearby isolated star.
F814W imaging was used in EGS and SSA22, while F850LP data were adopted in GOODS-N.
F814W imaging was used in EGS and SSA22, while F850LP data were adopted in GOODS-N.
For consistency with the local SDSS sample, we fit de Vaucouleurs profiles and determine circularized radii.
For consistency with the local SDSS sample, we fit de Vaucouleurs profiles and determine circularized radii.
We also fit Sérrsic profiles but found that the mean Séeersic index n is consistent with 4 (i.e., de Vaucouleurs).
We also fit Sérrsic profiles but found that the mean Séeersic index $n$ is consistent with 4 (i.e., de Vaucouleurs).
We estimate uncertainties of ~1096 in Πε based on testing the background level, simulating therecovery of synthetic de Vaucouleur profiles placed in blank sky patches, and comparing with the independent measurements of vdW08 for the T05 subsample.
We estimate uncertainties of $\sim10\%$ in $R_e$ based on testing the background level, simulating therecovery of synthetic de Vaucouleur profiles placed in blank sky patches, and comparing with the independent measurements of vdW08 for the T05 subsample.
We convert the observed ACS magnitude to the rest DB magnitude by matching the observed J—K, color to a grid of ? single-burst models of varying age and metallicity.
We convert the observed ACS magnitude to the rest $B$ magnitude by matching the observed $I-K_s$ color to a grid of \citet{BC03} single-burst models of varying age and metallicity.
The uncertainty in this k-correction is ~ 4%.
The uncertainty in this $k$ -correction is $\sim 4\%$ .
Based on the optical and NIR photometry discussed in §22, stellar masses were estimated using the Bayesian stellar population analysis code developed
Based on the optical and NIR photometry discussed in 2, stellar masses were estimated using the Bayesian stellar population analysis code developed
Eastman.Schmidt&Wirshner(1996). (hereafter E96) have shown. | mag uncertainty in ον results in only δα error in the derived: distance.
\citet*{E96} (hereafter E96) have shown, 1 mag uncertainty in $A_V$ results in only $\sim 8$ error in the derived distance.
However. the assumption hat the SN atmosphere radiates as a blackhock diluted »w electron. scattering raised. some concerns.
However, the assumption that the SN atmosphere radiates as a blackbody diluted by electron scattering raised some concerns.
These led. to he development of the applications of full. NLTIS mocel atmospheres. like the PHOENIX code in. the. "Spectral- Expanding Atmosphere Method" (SIZAM). 2004).. or the CAIPFGEN code by Dessart&Llillier (2005a.b).
These led to the development of the applications of full NLTE model atmospheres, like the PHOENIX code in the ``Spectral-fitting Expanding Atmosphere Method” (SEAM) \citep{baron99em}, or the CMFGEN code by \citet*{dessart2005a, dessart2005b}.