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

source stringlengths 1 2.05k ⌀	target stringlengths 1 11.7k
While the CIF simulations are not a perfect match to our satellite sample.this provides some support for the asstuptions we mace in deriving Equation 3.	While the GIF simulations are not a perfect match to our satellite sample, this provides some support for the assumptions we made in deriving Equation \ref{m260_def}.
A amore direct approach is to confirm that the data aud siuulatious show a consistent relationship between the observables: 9, aud luminosity.	A more direct approach is to confirm that the data and simulations show a consistent relationship between the observables: $\sigma_{r}$ and luminosity.
This comparison of the SDSS and CIF o, vs. Iuuinositv measurements is shown in Figure 2..	This comparison of the SDSS and GIF $\sigma_{r}$ vs. luminosity measurements is shown in Figure \ref{sdss_gif_comparison}.
The SDSS hnuuinositv measurenieuts are dmnἐν and the GIE huuinosities in Jolnsou L but as both are converted to solar luminosities the comparison roeniadus appropriate.	The SDSS luminosity measurements are in, and the GIF luminosities in Johnson I, but as both are converted to solar luminosities the comparison remains appropriate.
Both the SDSS aud CIF results are cousisteut with a simple model in which o,XLU?	Both the SDSS and GIF results are consistent with a simple model in which $\sigma_{r} \propto L^{0.5}$.
Since the CIF simulations provide values for the aassociated with each halo. we can compare neasures of daderived from galaxy. velocities to wwithin the simulations.	Since the GIF simulations provide values for the associated with each halo, we can compare measures of derived from galaxy velocities to within the simulations.
This comparison suggests that MM0.7	This comparison suggests that $\approx 0.7\times$.
It is essential to note that this relation is determined only for the most huninous galaxies. aud over onlv a factor of four in luminosity.	It is essential to note that this relation is determined only for the most luminous galaxies, and over only a factor of four in luminosity.
While this colmparison is limited. it provides some confidence that Equation 3\| seusiblv relates satellite velocities to masses,	While this comparison is limited, it provides some confidence that Equation \ref{m260_def} sensibly relates satellite velocities to masses.
A more detailed unuderstaudiug awaits simulations with lugher mass resolution. iu which more direct coniparisous can be mace.	A more detailed understanding awaits simulations with higher mass resolution, in which more direct comparisons can be made.
The meastrcments of. delerived frou satellite motions are shown in Figure 3..	The measurements of derived from satellite motions are shown in Figure \ref{mass_comparison}.
relationship between⋅ ALG) aud light in cach passbaudis well fit by a single power law.	The relationship between and light in each passband is well fit by a single power law.
As observed in M02. these relations are consistent with a power law mdex of one (constant. AZ/£)) iu all bands exceptu.. where a flatter relation. with a best fit power law iudex ~0.6 is observed.	As observed in M02, these relations are consistent with a power law index of one (constant ) in all bands except, where a flatter relation, with a best fit power law index $\sim$ 0.6 is observed.
To compare these results to the MO2 lensing mmoresults. we fix the power law iudex to oue. aud fit the ves. luminosity data in each baud to obtain values forAMfL.	To compare these results to the M02 lensing results, we fix the power law index to one, and fit the vs. luminosity data in each band to obtain values for.
. Values for these irafios are given in Fieure 3..	Values for these ratios are given in Figure \ref{mass_comparison}.
The dynamical vvalues are consistent with the leusiug values at the lo level iu iiost bands.	The dynamical values are consistent with the lensing values at the $\sigma$ level in most bands.
They differ most strongly iu u aud ο, where MO2 sugeests results will be very sensitive to the nux of host types.	They differ most strongly in u and g, where M02 suggests results will be very sensitive to the mix of host types.
The masses of galaxy halos are proportional to helt. and values vary strouely with color.	The masses of $_{*}$ galaxy halos are proportional to light, and values vary strongly with color.
More detailed quantitative comparison of the lensine aud dynamical results will oulv be possible when we cau measure more identical samples of hosts and lenses.	More detailed quantitative comparison of the lensing and dynamical results will only be possible when we can measure more identical samples of hosts and lenses.
This is difficult.	This is difficult.
The magnitude Linit of the SDSS spectroscopy biases dvuazuucal studies toward hosts at z<0.05. while lens econietries prefer lenses at z~O.15.	The magnitude limit of the SDSS spectroscopy biases dynamical studies toward hosts at $<$ 0.05, while lens geometries prefer lenses at $\sim$ 0.15.
Still. the vvalues derived by indepeudent imoethods agree reasonably. especially in the redder bands. where differences between the host aud leas samples are probably less inportaut.	Still, the values derived by independent methods agree reasonably, especially in the redder bands, where differences between the host and lens samples are probably less important.
Recent SDSS weals Ieusine results (MO2). revealed near relation between galaxy huuimositv and mass on halo scales.	Recent SDSS weak lensing results (M02) revealed a linear relation between galaxy luminosity and mass on halo scales.
To quautitatively test this result. we lave measured the velatiouship between galaxy Iuninosityv aud satellite αναος fora large sample of reasonably isolated host galaxies.	To quantitatively test this result, we have measured the relationship between galaxy luminosity and satellite dynamics for a large sample of reasonably isolated host galaxies.
ag We observe a highlv siguifcaut increase m satellite velocity with host Iuuinosity.	We observe a highly significant increase in satellite velocity with host luminosity.
To make direct comparisons to the weak lensing results. we apply a sinple mass estimator.. which is closely analogous to the mass modcling used in \L02.	To make direct comparisons to the weak lensing results, we apply a simple mass estimator, which is closely analogous to the mass modeling used in M02.
A first order test of the validity of this model is made by computing it within the CIF simulations.	A first order test of the validity of this model is made by computing it within the GIF simulations.
The relatiouship secu here between aan hiuinosityο matches reasonably the relation seen by cntirely independent weals lensing methods.	The relationship seen here between and luminosity matches reasonably the relation seen by entirely independent weak lensing methods.
This confinis the esseutial conclusious reached in M02.	This confirms the essential conclusions reached in M02.
The hnuuinous and dark components of galaxies are stronely coupled on 7200 kpc scales.	The luminous and dark components of $_{*}$ galaxies are strongly coupled on $\sim$ 200 kpc scales.
It is uuknown whether the scaling relatious observed here for eealaxies apply at lower huuinositv.	It is unknown whether the scaling relations observed here for galaxies apply at lower luminosity.
Perhaps the most iuportaut future extension of these studies will be to less luminous galaxies.	Perhaps the most important future extension of these studies will be to less luminous galaxies.
Additional comparison of lensing and dynamical mass estimates will require nieasuremoent of iore closely related host and Ileus samples. and more detailed study of the extraction of mass from the observable PMCTE aud satellite velocity structure.	Additional comparison of lensing and dynamical mass estimates will require measurement of more closely related host and lens samples, and more detailed study of the extraction of mass from the observable PMCF and satellite velocity structure.
The Sloan Digital Sky Survey (SDSS) is a thejoint project of The University of Chicago. Fermilab. Tustitute for Advanced Study. the Japan Participation Croup. The Johus Uopkins Universitv. Los Alamos National Laboratory. the Masx-Plauck-Institute for Απώμώιν (MPIA). the Alax-Plauck-Institute for Astroplivsics (AIPA). New Alexico State. Whiversity. Princeton University. the United States Naval Observatory. aud the University of Washineton.	The Sloan Digital Sky Survey (SDSS) is a joint project of The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Princeton University, the United States Naval Observatory, and the University of Washington.
Apache Point Observatory. site of the SDSS telescopes. is operated by the Astrophysical Research Consortimm (ARC).	Apache Point Observatory, site of the SDSS telescopes, is operated by the Astrophysical Research Consortium (ARC).
Funding for the project has been provided by the Alfred P. Sloan Foundation. the SDSS member institutions. the National Acronautics and Space Achuinistration. theNational Scicuce Foundation. the U.S. Departinent of Euergv. the Japanese Monbukagaklushlio.	Funding for the project has been provided by the Alfred P. Sloan Foundation, the SDSS member institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho,
Iu our 1D simulation.~(0.1.0.2)νY. for 100 aua <pE ory. where ry is the shockradius.	In our 1D simulation, $Y_{\bar\nu_e}\sim (0.1-0.2)\times Y_e$ for 100 km $\lesssim r\lesssim r_\mathrm{sh}$ , where $r_\mathrm{sh}$ is the shock.
Since this condition is barely satisfied. the collective oscillations in reality could modify the spectra to some extent between leavy-leptou neutrinos and electron/auti-electron ucutrinos. however the full swapping asstued in this study may be exaggerated.	Since this condition is barely satisfied, the collective oscillations in reality could modify the spectrum to some extent between heavy-lepton neutrinos and electron/anti-electron neutrinos, however the full swapping assumed in this study may be exaggerated.
Veryrecentht?.. Chakrabortycet}al.(2011a.b) pointed out that the matter effeét could fully suppress the spectral swapping in the} accretion phase using 1D neutrine-radiation bydvodyuamic simulation data of Fischeretal.(2010).	Very, \cite{chak11a,chak11b} pointed out that the matter effect could fully suppress the spectral swapping in the accretion phase using 1D neutrino-radiation hydrodynamic simulation data of \cite{fisc10}.
.. Mowevey. the απο understanding of the collective oscillathon is not completed aud calculations in this field cauplov several assimuptions (c.e.. single anele approximation) (butseealsoDaseuptactal.2011.formore}receutwork)...	However, the current understanding of the collective oscillation is not completed and calculations in this field employ several assumptions (e.g., single angle approximation) \citep[but see also][for more recent work]{dasg11}.
To draw a robust sivitVettermms. cos a ore detailed. sπαν including. the collective neutriub flavor oscillation to the ντοςπας simulations nu a ore self-consistent manner. which we are goie to challeuge as a sequel of this study.	To draw a robust conclusion, one needs a more detailed study including the collective neutrino flavor oscillation to the hydrodynamic simulations in a more self-consistent manner, which we are going to challenge as a sequel of this study.
We thank to IX. Sumivoshi. I. Suzuki. S. Yamiacla. T. Yoshida for stimmlating discussions.	We thank to K. Sumiyoshi, H. Suzuki, S. Yamada, T. Yoshida for stimulating discussions.
Numerical computations were in part carried on NT Lat CfCA of the National Astronomical Observatory of Japan.	Numerical computations were in part carried on XT4 at CfCA of the National Astronomical Observatory of Japan.
ML are supported by the Swiss National Scicuce Foundation under grant No.	ML are supported by the Swiss National Science Foundation under grant No.
PPOOP2-121879 and 200020-122287	PP00P2-124879 and 200020-122287.
This study was supported in part by the Japan Society for Promotion of Seieuce (JSPS) Research Fellowships (YS). the Cvauts-in-Aid for the Scicutifie Research from the Ministry of Education. Science and Culture of Japan (Nos.	This study was supported in part by the Japan Society for Promotion of Science (JSPS) Research Fellowships (YS), the Grants-in-Aid for the Scientific Research from the Ministry of Education, Science and Culture of Japan (Nos.
19101006. 195[0309 and 207LOL50). and UPCT Strategic Program of Japanese MEXT.	19104006, 19540309 and 20740150), and HPCI Strategic Program of Japanese MEXT.
Iu this section. we demonstrate the conservation of plivsical quautities using the spherical collapse model CNITI3).	In this section, we demonstrate the conservation of physical quantities using the spherical collapse model (NH13).
Figure A15 depicts the evolution of total binding cucrey by eravity (red liue). total internal οποιον (ereen). total kinetic euerev (blue). total trapped-neutrino enerev. Guagenta). total energy leaked by neutrinos (evan). aud variation of overall energy. (black dashed). respectively.	Figure \ref{fig:ensy_cnsv} depicts the evolution of total binding energy by gravity (red line), total internal energy (green), total kinetic energy (blue), total trapped-neutrino energy (magenta), total energy leaked by neutrinos (cyan), and variation of overall energy (black dashed), respectively.
The eravitational energv aud total euergv are negative aud absolute values are shown.	The gravitational energy and total energy are negative and absolute values are shown.
The eravitational cucrey aud interual energy dominate (with different sign) aud reach ~10° ere soou after bounce.	The gravitational energy and internal energy dominate (with different sign) and reach $\sim 10^{53}$ erg soon after bounce.
Despite such an cuormous energy change. the total euergv varies oulv within ~3«1019 ere so that the violation of energev conservation remains «0.03%.	Despite such an enormous energy change, the total energy varies only within $\sim 3\times10^{49}$ erg so that the violation of energy conservation remains $< 0.03\%$.
The eucrex of the trapped neutrinos decreases with the diffusion timescale. which leads to the PNS cooling.	The energy of the trapped neutrinos decreases with the diffusion timescale, which leads to the PNS cooling.
The kinetic energy rapidly drops because of the photodissociation of iron aud the clectrou capture (14. e1issiou) that is cousisteut with the shock stall.	The kinetic energy rapidly drops because of the photodissociation of iron and the electron capture $\nu_e$ emission) that is consistent with the shock stall.
We have monitoredthese values ina 2D sinulation aud obtained a similar level of energy. conservation.	We have monitoredthese values in a 2D simulation and obtained a similar level of energy conservation.
From the instrumental point of view. we have demonstrated that: Asan on-sky validation. we collected K-band interferometric fringes in the vicinity of the first visibility null of the bright starSer.	From the instrumental point of view, we have demonstrated that: As an on-sky validation, we collected K-band interferometric fringes in the vicinity of the first visibility null of the bright star.
. By fitting the visibility curves. we measured a diameter of 7.56+0.025 mmas in three directions simultaneously.	By fitting the visibility curves, we measured a diameter of $7.56\pm{}0.025$ mas in three directions simultaneously.
We reached such sub-percent accuracy without spending additional time on calibrators since the technique is independent from absolute calibration (at least for baselines that fully span the visibility null).	We reached such sub-percent accuracy without spending additional time on calibrators since the technique is independent from absolute calibration (at least for baselines that fully span the visibility null).
We show that. at this level of precision. several systematic error sources have to be taken into account. for example the spectral calibration of the instrument and the pupil lateral position.	We show that, at this level of precision, several systematic error sources have to be taken into account, for example the spectral calibration of the instrument and the pupil lateral position.
From the scientific point of view. this work opens several perspectives for the VLTI in the field of stellar	From the scientific point of view, this work opens several perspectives for the VLTI in the field of stellar
To proceed. we consider a nominal impactor radius of 10 m. on the understanding that (his size is probably slighilv too large but is in any case uncertain by a [actor of several as a result of the unknown impactor speed. density. incident angle and inpact parameter.	To proceed, we consider a nominal impactor radius of 10 m, on the understanding that this size is probably slightly too large but is in any case uncertain by a factor of several as a result of the unknown impactor speed, density, incident angle and impact parameter.
We used (he asteroid collision probabilities [rom Dottke οἱ al. (	We used the asteroid collision probabilities from Bottke et al. (
1994) in order (o estimate 7,. (he interval between impacts of 10 m projectiles onto a LOO km radius target. asteroid.	1994) in order to estimate $\tau_c$, the interval between impacts of 10 m projectiles onto a 100 km radius target asteroid.
These collision probabilities are based on measurements of asteroids larger than 1 km in size. requiring a factor of 100 extrapolation to reach the LO m scale of the projectiles implicated here.	These collision probabilities are based on measurements of asteroids larger than 1 km in size, requiring a factor of 100 extrapolation to reach the 10 m scale of the projectiles implicated here.
Unfortunately. knowledge of the size distribution of sub-kilometer asteroids in the is limited. because most such bodies are too faint to be directly observed.	Unfortunately, knowledge of the size distribution of sub-kilometer asteroids in the main-belt is limited because most such bodies are too faint to be directly observed.
We rely on crater counts Iron asteroid Gaspra to provide an indication of the size distribution of small projectiles.	We rely on crater counts from asteroid Gaspra to provide an indication of the size distribution of small projectiles.
There. impact craters from 0.4 km to 1.5 km in diameter are distributed as a power-law with a differential size index -3.7+40.5 (Bellon et al.	There, impact craters from 0.4 km to 1.5 km in diameter are distributed as a power-law with a differential size index $\pm$ 0.5 (Belton et al.
1992. while fresh craters may Follow a slishtlv steeper index according to Chapman οἱ al.	1992, while fresh craters may follow a slightly steeper index according to Chapman et al.
1996).	1996).
Craters in this size range result. [rom the impact of projectiles a few decameters in radius. again subject to significant uncertainties about the surface physical properties of Gaspra.	Craters in this size range result from the impact of projectiles a few decameters in radius, again subject to significant uncertainties about the surface physical properties of Gaspra.
Using this size distribution. we estimate that the timescale for impact onto Themis or Cybele-sized asteroids is 7.~ 10% vr.	Using this size distribution, we estimate that the timescale for impact onto Themis or Cybele-sized asteroids is $\tau_c \sim$ $^3$ yr.
This timescale is clearly very. uncertain because of the large extrapolation from the relatively well-samplecl asteroids at kilometer size-scales down to the 10 m sizes of the projectiles.	This timescale is clearly very uncertain because of the large extrapolation from the relatively well-sampled asteroids at kilometer size-scales down to the 10 m sizes of the projectiles.
For example. the estimated numbers of asteroids with r,> 5 m range from ~10M to ~10' (Davis et al.	For example, the estimated numbers of asteroids with $r_n \ge$ 5 m range from $\sim$ $^{10}$ to $\sim$ $^{12}$ (Davis et al.
2002). indicating a two order-of-iagnitude uncertainty in 7. al small projectile sizes.	2002), indicating a two order-of-magnitude uncertainty in $\tau_c$ at small projectile sizes.
With these caveats in mind. we consider the implications of a 10* vr timescale [or Προς,	With these caveats in mind, we consider the implications of a $^3$ yr timescale for impact.
First. we note that the number of non-overlapping craters (hat can be placed on the surface is roughly NV.cfd4r2/(r2).	First, we note that the number of non-overlapping craters that can be placed on the surface is roughly $N_c \sim 4 r_n^2/(r_c^2)$.
With r, = 100 km and r. = 130 m. we find Vy.~ 2x10". corresponding to the accumulation of impacts over ~2 ανν,	With $r_n$ = 100 km and $r_c$ = 130 m, we find $N_c \sim$ $\times$ $^6$, corresponding to the accumulation of impacts over $\sim$ 2 Gyr.
Buried ice could persist against repeated impact excavation over a large traction of (he age of (he solar svstem.	Buried ice could persist against repeated impact excavation over a large fraction of the age of the solar system.
We next determine the conditions which must prevail lor excavated ice to survive on the surface for 7.c 10* vr.	We next determine the conditions which must prevail for excavated ice to survive on the surface for $\tau_c \sim$ $^3$ yr.
The mass column density of a 1 mmn thick ice laver is pf = 1 kg m7.	The mass column density of a 1 mm thick ice layer is $\rho \ell$ = 1 kg $^{-2}$.
If this laver is to survive for 10* vr (3x 10! s). the mean loss rate cannot exceed pé/7.~ 3x10 ! ke ? +. setting an upper limit to the equilibrium sublimation temperature T.< 131 Ix from Equation (4)).	If this layer is to survive for $^3$ yr $\times$ $^{10}$ s), the mean loss rate cannot exceed $\rho \ell/\tau_c \sim$ $\times$ $^{-11}$ kg $^{-2}$ $^{-1}$, setting an upper limit to the equilibrium sublimation temperature $T_c \le$ 131 K from Equation \ref{sublimation}) ).
In the specific model considered here. with the Sun on the projected rotation axis. sufficiently low temperatures are found in a thin baud around the equator where cos(8) in Equation (4)) is suitably small.	In the specific model considered here, with the Sun on the projected rotation axis, sufficiently low temperatures are found in a thin band around the equator where $\cos(\theta)$ in Equation \ref{sublimation}) ) is suitably small.
By analogy. with the Moon. surface ice on Themis and Cybele might survive best in regions protected from Sunlight by local topography.	By analogy with the Moon, surface ice on Themis and Cybele might survive best in regions protected from Sunlight by local topography.
observation. we have extensively tested the results of this pipeline and we now describe these tests.	observation, we have extensively tested the results of this pipeline and we now describe these tests.
First we have taken the Images as they come out of the CASU pipeline (1e. dark-subtracted. flat-fielded. systematic noise removed. sky-corrected. and finally. registered. and stacked) and found centroids two ways: (1) fitting a two-dimensional gaussian to the object’s point source function (PSF) and (2) fitting a one-dimensional gaussian to the object’s marginal distributions above the sky background.	First we have taken the images as they come out of the CASU pipeline (i.e. dark-subtracted, flat-fielded, systematic noise removed, sky-corrected, and finally registered and stacked) and found centroids two ways: (1) fitting a two-dimensional gaussian to the object's point source function (PSF) and (2) fitting a one-dimensional gaussian to the object's marginal distributions above the sky background.
The two-dimensional gaussian fit is what is used in the Torino Observatory Parallax Program (?.hereafterTOPP) and the marginal distribution fit is what is suggested by Stone (1989) in the presence of a high background.	The two-dimensional gaussian fit is what is used in the Torino Observatory Parallax Program \citep[hereafter TOPP]{SMA99A} and the marginal distribution fit is what is suggested by Stone (1989) \nocite{1989AJ.....97.1227S} in the presence of a high background.
We use these centroids and those from the CASU pipeline to compare eight ULAS 0034 observations over the period 2005 to 2008. after à six-constant transform (translation. scale and rotation) to a common system.	We use these centroids and those from the CASU pipeline to compare eight ULAS 0034 observations over the period 2005 to 2008, after a six-constant transform (translation, scale and rotation) to a common system.
In Fig.	In Fig.
2 we plot the root-mean-square (rms) of the x coordinate from the CASU pipeline of common stars.	\ref{f4800792rwf_fortest0cx.eps} we plot the root-mean-square (rms) of the x coordinate from the CASU pipeline of common stars.
The median rms is 18 mas and using the other centroiding methods the rms was identical.	The median rms is 18 mas and using the other centroiding methods the rms was identical.
In the y coordinate the median rms was slightly larger. 20 mas. but the difference between the three centroiding methods was also negligible.	In the y coordinate the median rms was slightly larger, 20 mas, but the difference between the three centroiding methods was also negligible.
We have also tried recombining the original micro-stepped images using a drizzle (?) routine rather than the CASU standard routine.	We have also tried recombining the original micro-stepped images using a drizzle \citep{2002PASP..114..144F} routine rather than the CASU standard routine.
In the standard routine the 4+ micro-stepped images are interleaved. i.e. combined assuming a higher spatial resolution. to produce a combined image with pixel size 0.27 (half the 0.47 physical pixel size).	In the standard routine the 4 micro-stepped images are interleaved, i.e. combined assuming a higher spatial resolution, to produce a combined image with pixel size 0.2” (half the 0.4” physical pixel size).
This produces a spiky PSF as the seeing changes between the four images.	This produces a spiky PSF as the seeing changes between the four images.
The alternative approach is to combine the counts in pixels from the four images in an underlying higher resolution grid with appropriate weighting (1e. drizzling).	The alternative approach is to combine the counts in pixels from the four images in an underlying higher resolution grid with appropriate weighting (i.e. drizzling).
This gives a much smoother PSF and retains the signal-to-noise. while losing some of the resolution as adjacent pixels are correlated.	This gives a much smoother PSF and retains the signal-to-noise, while losing some of the resolution as adjacent pixels are correlated.
Using this process caused the ULAS 0034 median rms to increase slightly from 18 to 20 mas.	Using this process caused the ULAS 0034 median rms to increase slightly from 18 to 20 mas.
As a result of these tests we have decided to use positions coming directly out of the CASU pipeline. and work under the assumption that our median error is around 18 mas.	As a result of these tests we have decided to use positions coming directly out of the CASU pipeline, and work under the assumption that our median error is around 18 mas.
We assume the larger error found in the ULAS 0034 sequence compared to the two-epoch cluster test is due to the fact that we are comparing a wider range of observing conditions over a longer time span.	We assume the larger error found in the ULAS 0034 sequence compared to the two-epoch cluster test is due to the fact that we are comparing a wider range of observing conditions over a longer time span.
We note that the centroiding errors provided by the CASU pipeline are good indications of the errors found in our test.	We note that the centroiding errors provided by the CASU pipeline are good indications of the errors found in our test.

While the CIF simulations are not a perfect match to our satellite sample.this provides some support for the asstuptions we mace in deriving Equation 3.

While the GIF simulations are not a perfect match to our satellite sample, this provides some support for the assumptions we made in deriving Equation \ref{m260_def}.

A amore direct approach is to confirm that the data aud siuulatious show a consistent relationship between the observables: 9, aud luminosity.

A more direct approach is to confirm that the data and simulations show a consistent relationship between the observables: $\sigma_{r}$ and luminosity.

This comparison of the SDSS and CIF o, vs. Iuuinositv measurements is shown in Figure 2..

This comparison of the SDSS and GIF $\sigma_{r}$ vs. luminosity measurements is shown in Figure \ref{sdss_gif_comparison}.

The SDSS hnuuinositv measurenieuts are dmnἐν and the GIE huuinosities in Jolnsou L but as both are converted to solar luminosities the comparison roeniadus appropriate.

The SDSS luminosity measurements are in, and the GIF luminosities in Johnson I, but as both are converted to solar luminosities the comparison remains appropriate.

Both the SDSS aud CIF results are cousisteut with a simple model in which o,XLU?

Both the SDSS and GIF results are consistent with a simple model in which $\sigma_{r} \propto L^{0.5}$.

Since the CIF simulations provide values for the aassociated with each halo. we can compare neasures of daderived from galaxy. velocities to wwithin the simulations.

Since the GIF simulations provide values for the associated with each halo, we can compare measures of derived from galaxy velocities to within the simulations.

This comparison suggests that MM0.7

This comparison suggests that $\approx 0.7\times$.

It is essential to note that this relation is determined only for the most huninous galaxies. aud over onlv a factor of four in luminosity.

It is essential to note that this relation is determined only for the most luminous galaxies, and over only a factor of four in luminosity.

While this colmparison is limited. it provides some confidence that Equation 3| seusiblv relates satellite velocities to masses,

While this comparison is limited, it provides some confidence that Equation \ref{m260_def} sensibly relates satellite velocities to masses.

A more detailed unuderstaudiug awaits simulations with lugher mass resolution. iu which more direct coniparisous can be mace.

A more detailed understanding awaits simulations with higher mass resolution, in which more direct comparisons can be made.

The meastrcments of. delerived frou satellite motions are shown in Figure 3..

The measurements of derived from satellite motions are shown in Figure \ref{mass_comparison}.

relationship between⋅ ALG) aud light in cach passbaudis well fit by a single power law.

The relationship between and light in each passband is well fit by a single power law.

As observed in M02. these relations are consistent with a power law mdex of one (constant. AZ/£)) iu all bands exceptu.. where a flatter relation. with a best fit power law iudex ~0.6 is observed.

As observed in M02, these relations are consistent with a power law index of one (constant ) in all bands except, where a flatter relation, with a best fit power law index $\sim$ 0.6 is observed.

To compare these results to the MO2 lensing mmoresults. we fix the power law iudex to oue. aud fit the ves. luminosity data in each baud to obtain values forAMfL.

To compare these results to the M02 lensing results, we fix the power law index to one, and fit the vs. luminosity data in each band to obtain values for.

. Values for these irafios are given in Fieure 3..

Values for these ratios are given in Figure \ref{mass_comparison}.

The dynamical vvalues are consistent with the leusiug values at the lo level iu iiost bands.

The dynamical values are consistent with the lensing values at the $\sigma$ level in most bands.

They differ most strongly iu u aud ο, where MO2 sugeests results will be very sensitive to the nux of host types.

They differ most strongly in u and g, where M02 suggests results will be very sensitive to the mix of host types.

The masses of galaxy halos are proportional to helt. and values vary strouely with color.

The masses of $_{*}$ galaxy halos are proportional to light, and values vary strongly with color.

More detailed quantitative comparison of the lensine aud dynamical results will oulv be possible when we cau measure more identical samples of hosts and lenses.

More detailed quantitative comparison of the lensing and dynamical results will only be possible when we can measure more identical samples of hosts and lenses.

This is difficult.

The magnitude Linit of the SDSS spectroscopy biases dvuazuucal studies toward hosts at z<0.05. while lens econietries prefer lenses at z~O.15.

The magnitude limit of the SDSS spectroscopy biases dynamical studies toward hosts at $<$ 0.05, while lens geometries prefer lenses at $\sim$ 0.15.

Still. the vvalues derived by indepeudent imoethods agree reasonably. especially in the redder bands. where differences between the host aud leas samples are probably less inportaut.

Still, the values derived by independent methods agree reasonably, especially in the redder bands, where differences between the host and lens samples are probably less important.

Recent SDSS weals Ieusine results (MO2). revealed near relation between galaxy huuimositv and mass on halo scales.

Recent SDSS weak lensing results (M02) revealed a linear relation between galaxy luminosity and mass on halo scales.

To quautitatively test this result. we lave measured the velatiouship between galaxy Iuninosityv aud satellite αναος fora large sample of reasonably isolated host galaxies.

To quantitatively test this result, we have measured the relationship between galaxy luminosity and satellite dynamics for a large sample of reasonably isolated host galaxies.

ag We observe a highlv siguifcaut increase m satellite velocity with host Iuuinosity.

We observe a highly significant increase in satellite velocity with host luminosity.

To make direct comparisons to the weak lensing results. we apply a sinple mass estimator.. which is closely analogous to the mass modcling used in \L02.

To make direct comparisons to the weak lensing results, we apply a simple mass estimator, which is closely analogous to the mass modeling used in M02.

A first order test of the validity of this model is made by computing it within the CIF simulations.

A first order test of the validity of this model is made by computing it within the GIF simulations.

The relatiouship secu here between aan hiuinosityο matches reasonably the relation seen by cntirely independent weals lensing methods.

The relationship seen here between and luminosity matches reasonably the relation seen by entirely independent weak lensing methods.

This confinis the esseutial conclusious reached in M02.

This confirms the essential conclusions reached in M02.

The hnuuinous and dark components of galaxies are stronely coupled on 7200 kpc scales.

The luminous and dark components of $_{*}$ galaxies are strongly coupled on $\sim$ 200 kpc scales.

It is uuknown whether the scaling relatious observed here for eealaxies apply at lower huuinositv.

It is unknown whether the scaling relations observed here for galaxies apply at lower luminosity.

Perhaps the most iuportaut future extension of these studies will be to less luminous galaxies.

Perhaps the most important future extension of these studies will be to less luminous galaxies.

Additional comparison of lensing and dynamical mass estimates will require nieasuremoent of iore closely related host and Ileus samples. and more detailed study of the extraction of mass from the observable PMCTE aud satellite velocity structure.

Additional comparison of lensing and dynamical mass estimates will require measurement of more closely related host and lens samples, and more detailed study of the extraction of mass from the observable PMCF and satellite velocity structure.

The Sloan Digital Sky Survey (SDSS) is a thejoint project of The University of Chicago. Fermilab. Tustitute for Advanced Study. the Japan Participation Croup. The Johus Uopkins Universitv. Los Alamos National Laboratory. the Masx-Plauck-Institute for Απώμώιν (MPIA). the Alax-Plauck-Institute for Astroplivsics (AIPA). New Alexico State. Whiversity. Princeton University. the United States Naval Observatory. aud the University of Washineton.

The Sloan Digital Sky Survey (SDSS) is a joint project of The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Princeton University, the United States Naval Observatory, and the University of Washington.

Apache Point Observatory. site of the SDSS telescopes. is operated by the Astrophysical Research Consortimm (ARC).

Apache Point Observatory, site of the SDSS telescopes, is operated by the Astrophysical Research Consortium (ARC).

Funding for the project has been provided by the Alfred P. Sloan Foundation. the SDSS member institutions. the National Acronautics and Space Achuinistration. theNational Scicuce Foundation. the U.S. Departinent of Euergv. the Japanese Monbukagaklushlio.

Funding for the project has been provided by the Alfred P. Sloan Foundation, the SDSS member institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho,

Iu our 1D simulation.~(0.1.0.2)νY. for 100 aua <pE ory. where ry is the shockradius.

In our 1D simulation, $Y_{\bar\nu_e}\sim (0.1-0.2)\times Y_e$ for 100 km $\lesssim r\lesssim r_\mathrm{sh}$ , where $r_\mathrm{sh}$ is the shock.

Since this condition is barely satisfied. the collective oscillations in reality could modify the spectra to some extent between leavy-leptou neutrinos and electron/auti-electron ucutrinos. however the full swapping asstued in this study may be exaggerated.

Since this condition is barely satisfied, the collective oscillations in reality could modify the spectrum to some extent between heavy-lepton neutrinos and electron/anti-electron neutrinos, however the full swapping assumed in this study may be exaggerated.

Veryrecentht?.. Chakrabortycet}al.(2011a.b) pointed out that the matter effeét could fully suppress the spectral swapping in the} accretion phase using 1D neutrine-radiation bydvodyuamic simulation data of Fischeretal.(2010).

Very, \cite{chak11a,chak11b} pointed out that the matter effect could fully suppress the spectral swapping in the accretion phase using 1D neutrino-radiation hydrodynamic simulation data of \cite{fisc10}.

.. Mowevey. the απο understanding of the collective oscillathon is not completed aud calculations in this field cauplov several assimuptions (c.e.. single anele approximation) (butseealsoDaseuptactal.2011.formore}receutwork)...

However, the current understanding of the collective oscillation is not completed and calculations in this field employ several assumptions (e.g., single angle approximation) \citep[but see also][for more recent work]{dasg11}.

To draw a robust sivitVettermms. cos a ore detailed. sπαν including. the collective neutriub flavor oscillation to the ντοςπας simulations nu a ore self-consistent manner. which we are goie to challeuge as a sequel of this study.

To draw a robust conclusion, one needs a more detailed study including the collective neutrino flavor oscillation to the hydrodynamic simulations in a more self-consistent manner, which we are going to challenge as a sequel of this study.

We thank to IX. Sumivoshi. I. Suzuki. S. Yamiacla. T. Yoshida for stimmlating discussions.

We thank to K. Sumiyoshi, H. Suzuki, S. Yamada, T. Yoshida for stimulating discussions.

Numerical computations were in part carried on NT Lat CfCA of the National Astronomical Observatory of Japan.

Numerical computations were in part carried on XT4 at CfCA of the National Astronomical Observatory of Japan.

ML are supported by the Swiss National Scicuce Foundation under grant No.

ML are supported by the Swiss National Science Foundation under grant No.

PPOOP2-121879 and 200020-122287

PP00P2-124879 and 200020-122287.

This study was supported in part by the Japan Society for Promotion of Seieuce (JSPS) Research Fellowships (YS). the Cvauts-in-Aid for the Scicutifie Research from the Ministry of Education. Science and Culture of Japan (Nos.

This study was supported in part by the Japan Society for Promotion of Science (JSPS) Research Fellowships (YS), the Grants-in-Aid for the Scientific Research from the Ministry of Education, Science and Culture of Japan (Nos.

19101006. 195[0309 and 207LOL50). and UPCT Strategic Program of Japanese MEXT.

19104006, 19540309 and 20740150), and HPCI Strategic Program of Japanese MEXT.

Iu this section. we demonstrate the conservation of plivsical quautities using the spherical collapse model CNITI3).

In this section, we demonstrate the conservation of physical quantities using the spherical collapse model (NH13).

Figure A15 depicts the evolution of total binding cucrey by eravity (red liue). total internal οποιον (ereen). total kinetic euerev (blue). total trapped-neutrino enerev. Guagenta). total energy leaked by neutrinos (evan). aud variation of overall energy. (black dashed). respectively.

Figure \ref{fig:ensy_cnsv} depicts the evolution of total binding energy by gravity (red line), total internal energy (green), total kinetic energy (blue), total trapped-neutrino energy (magenta), total energy leaked by neutrinos (cyan), and variation of overall energy (black dashed), respectively.

The eravitational energv aud total euergv are negative aud absolute values are shown.

The gravitational energy and total energy are negative and absolute values are shown.

The eravitational cucrey aud interual energy dominate (with different sign) aud reach ~10° ere soou after bounce.

The gravitational energy and internal energy dominate (with different sign) and reach $\sim 10^{53}$ erg soon after bounce.

Despite such an cuormous energy change. the total euergv varies oulv within ~3«1019 ere so that the violation of energev conservation remains «0.03%.

Despite such an enormous energy change, the total energy varies only within $\sim 3\times10^{49}$ erg so that the violation of energy conservation remains $< 0.03\%$.

The eucrex of the trapped neutrinos decreases with the diffusion timescale. which leads to the PNS cooling.

The energy of the trapped neutrinos decreases with the diffusion timescale, which leads to the PNS cooling.

The kinetic energy rapidly drops because of the photodissociation of iron aud the clectrou capture (14. e1issiou) that is cousisteut with the shock stall.

The kinetic energy rapidly drops because of the photodissociation of iron and the electron capture $\nu_e$ emission) that is consistent with the shock stall.

We have monitoredthese values ina 2D sinulation aud obtained a similar level of energy. conservation.

We have monitoredthese values in a 2D simulation and obtained a similar level of energy conservation.

From the instrumental point of view. we have demonstrated that: Asan on-sky validation. we collected K-band interferometric fringes in the vicinity of the first visibility null of the bright starSer.

From the instrumental point of view, we have demonstrated that: As an on-sky validation, we collected K-band interferometric fringes in the vicinity of the first visibility null of the bright star.

. By fitting the visibility curves. we measured a diameter of 7.56+0.025 mmas in three directions simultaneously.

By fitting the visibility curves, we measured a diameter of $7.56\pm{}0.025$ mas in three directions simultaneously.

We reached such sub-percent accuracy without spending additional time on calibrators since the technique is independent from absolute calibration (at least for baselines that fully span the visibility null).

We show that. at this level of precision. several systematic error sources have to be taken into account. for example the spectral calibration of the instrument and the pupil lateral position.

We show that, at this level of precision, several systematic error sources have to be taken into account, for example the spectral calibration of the instrument and the pupil lateral position.

From the scientific point of view. this work opens several perspectives for the VLTI in the field of stellar

From the scientific point of view, this work opens several perspectives for the VLTI in the field of stellar

To proceed. we consider a nominal impactor radius of 10 m. on the understanding that (his size is probably slighilv too large but is in any case uncertain by a [actor of several as a result of the unknown impactor speed. density. incident angle and inpact parameter.

To proceed, we consider a nominal impactor radius of 10 m, on the understanding that this size is probably slightly too large but is in any case uncertain by a factor of several as a result of the unknown impactor speed, density, incident angle and impact parameter.

We used (he asteroid collision probabilities [rom Dottke οἱ al. (

We used the asteroid collision probabilities from Bottke et al. (

1994) in order (o estimate 7,. (he interval between impacts of 10 m projectiles onto a LOO km radius target. asteroid.

1994) in order to estimate $\tau_c$, the interval between impacts of 10 m projectiles onto a 100 km radius target asteroid.

These collision probabilities are based on measurements of asteroids larger than 1 km in size. requiring a factor of 100 extrapolation to reach the LO m scale of the projectiles implicated here.

These collision probabilities are based on measurements of asteroids larger than 1 km in size, requiring a factor of 100 extrapolation to reach the 10 m scale of the projectiles implicated here.

Unfortunately. knowledge of the size distribution of sub-kilometer asteroids in the is limited. because most such bodies are too faint to be directly observed.

Unfortunately, knowledge of the size distribution of sub-kilometer asteroids in the main-belt is limited because most such bodies are too faint to be directly observed.

We rely on crater counts Iron asteroid Gaspra to provide an indication of the size distribution of small projectiles.

We rely on crater counts from asteroid Gaspra to provide an indication of the size distribution of small projectiles.

There. impact craters from 0.4 km to 1.5 km in diameter are distributed as a power-law with a differential size index -3.7+40.5 (Bellon et al.

There, impact craters from 0.4 km to 1.5 km in diameter are distributed as a power-law with a differential size index $\pm$ 0.5 (Belton et al.

1992. while fresh craters may Follow a slishtlv steeper index according to Chapman οἱ al.

1992, while fresh craters may follow a slightly steeper index according to Chapman et al.

1996).

Craters in this size range result. [rom the impact of projectiles a few decameters in radius. again subject to significant uncertainties about the surface physical properties of Gaspra.

Craters in this size range result from the impact of projectiles a few decameters in radius, again subject to significant uncertainties about the surface physical properties of Gaspra.

Using this size distribution. we estimate that the timescale for impact onto Themis or Cybele-sized asteroids is 7.~ 10% vr.

Using this size distribution, we estimate that the timescale for impact onto Themis or Cybele-sized asteroids is $\tau_c \sim$ $^3$ yr.

This timescale is clearly very. uncertain because of the large extrapolation from the relatively well-samplecl asteroids at kilometer size-scales down to the 10 m sizes of the projectiles.

This timescale is clearly very uncertain because of the large extrapolation from the relatively well-sampled asteroids at kilometer size-scales down to the 10 m sizes of the projectiles.

For example. the estimated numbers of asteroids with r,> 5 m range from ~10M to ~10' (Davis et al.

For example, the estimated numbers of asteroids with $r_n \ge$ 5 m range from $\sim$ $^{10}$ to $\sim$ $^{12}$ (Davis et al.

2002). indicating a two order-of-iagnitude uncertainty in 7. al small projectile sizes.

2002), indicating a two order-of-magnitude uncertainty in $\tau_c$ at small projectile sizes.

With these caveats in mind. we consider the implications of a 10* vr timescale [or Προς,

With these caveats in mind, we consider the implications of a $^3$ yr timescale for impact.

First. we note that the number of non-overlapping craters (hat can be placed on the surface is roughly NV.cfd4r2/(r2).

First, we note that the number of non-overlapping craters that can be placed on the surface is roughly $N_c \sim 4 r_n^2/(r_c^2)$.

With r, = 100 km and r. = 130 m. we find Vy.~ 2x10". corresponding to the accumulation of impacts over ~2 ανν,

With $r_n$ = 100 km and $r_c$ = 130 m, we find $N_c \sim$ $\times$ $^6$, corresponding to the accumulation of impacts over $\sim$ 2 Gyr.

Buried ice could persist against repeated impact excavation over a large traction of (he age of (he solar svstem.

Buried ice could persist against repeated impact excavation over a large fraction of the age of the solar system.

We next determine the conditions which must prevail lor excavated ice to survive on the surface for 7.c 10* vr.

We next determine the conditions which must prevail for excavated ice to survive on the surface for $\tau_c \sim$ $^3$ yr.

The mass column density of a 1 mmn thick ice laver is pf = 1 kg m7.

The mass column density of a 1 mm thick ice layer is $\rho \ell$ = 1 kg $^{-2}$.

If this laver is to survive for 10* vr (3x 10! s). the mean loss rate cannot exceed pé/7.~ 3x10 ! ke ? +. setting an upper limit to the equilibrium sublimation temperature T.< 131 Ix from Equation (4)).

If this layer is to survive for $^3$ yr $\times$ $^{10}$ s), the mean loss rate cannot exceed $\rho \ell/\tau_c \sim$ $\times$ $^{-11}$ kg $^{-2}$ $^{-1}$, setting an upper limit to the equilibrium sublimation temperature $T_c \le$ 131 K from Equation \ref{sublimation}) ).

In the specific model considered here. with the Sun on the projected rotation axis. sufficiently low temperatures are found in a thin baud around the equator where cos(8) in Equation (4)) is suitably small.

In the specific model considered here, with the Sun on the projected rotation axis, sufficiently low temperatures are found in a thin band around the equator where $\cos(\theta)$ in Equation \ref{sublimation}) ) is suitably small.

By analogy. with the Moon. surface ice on Themis and Cybele might survive best in regions protected from Sunlight by local topography.

By analogy with the Moon, surface ice on Themis and Cybele might survive best in regions protected from Sunlight by local topography.

observation. we have extensively tested the results of this pipeline and we now describe these tests.

observation, we have extensively tested the results of this pipeline and we now describe these tests.

First we have taken the Images as they come out of the CASU pipeline (1e. dark-subtracted. flat-fielded. systematic noise removed. sky-corrected. and finally. registered. and stacked) and found centroids two ways: (1) fitting a two-dimensional gaussian to the object’s point source function (PSF) and (2) fitting a one-dimensional gaussian to the object’s marginal distributions above the sky background.

First we have taken the images as they come out of the CASU pipeline (i.e. dark-subtracted, flat-fielded, systematic noise removed, sky-corrected, and finally registered and stacked) and found centroids two ways: (1) fitting a two-dimensional gaussian to the object's point source function (PSF) and (2) fitting a one-dimensional gaussian to the object's marginal distributions above the sky background.

The two-dimensional gaussian fit is what is used in the Torino Observatory Parallax Program (?.hereafterTOPP) and the marginal distribution fit is what is suggested by Stone (1989) in the presence of a high background.

The two-dimensional gaussian fit is what is used in the Torino Observatory Parallax Program \citep[hereafter TOPP]{SMA99A} and the marginal distribution fit is what is suggested by Stone (1989) \nocite{1989AJ.....97.1227S} in the presence of a high background.

We use these centroids and those from the CASU pipeline to compare eight ULAS 0034 observations over the period 2005 to 2008. after à six-constant transform (translation. scale and rotation) to a common system.

We use these centroids and those from the CASU pipeline to compare eight ULAS 0034 observations over the period 2005 to 2008, after a six-constant transform (translation, scale and rotation) to a common system.

In Fig.

2 we plot the root-mean-square (rms) of the x coordinate from the CASU pipeline of common stars.

\ref{f4800792rwf_fortest0cx.eps} we plot the root-mean-square (rms) of the x coordinate from the CASU pipeline of common stars.

The median rms is 18 mas and using the other centroiding methods the rms was identical.

In the y coordinate the median rms was slightly larger. 20 mas. but the difference between the three centroiding methods was also negligible.

In the y coordinate the median rms was slightly larger, 20 mas, but the difference between the three centroiding methods was also negligible.

We have also tried recombining the original micro-stepped images using a drizzle (?) routine rather than the CASU standard routine.

We have also tried recombining the original micro-stepped images using a drizzle \citep{2002PASP..114..144F} routine rather than the CASU standard routine.

In the standard routine the 4+ micro-stepped images are interleaved. i.e. combined assuming a higher spatial resolution. to produce a combined image with pixel size 0.27 (half the 0.47 physical pixel size).

In the standard routine the 4 micro-stepped images are interleaved, i.e. combined assuming a higher spatial resolution, to produce a combined image with pixel size 0.2” (half the 0.4” physical pixel size).

This produces a spiky PSF as the seeing changes between the four images.

The alternative approach is to combine the counts in pixels from the four images in an underlying higher resolution grid with appropriate weighting (1e. drizzling).

The alternative approach is to combine the counts in pixels from the four images in an underlying higher resolution grid with appropriate weighting (i.e. drizzling).

This gives a much smoother PSF and retains the signal-to-noise. while losing some of the resolution as adjacent pixels are correlated.

This gives a much smoother PSF and retains the signal-to-noise, while losing some of the resolution as adjacent pixels are correlated.

Using this process caused the ULAS 0034 median rms to increase slightly from 18 to 20 mas.

As a result of these tests we have decided to use positions coming directly out of the CASU pipeline. and work under the assumption that our median error is around 18 mas.

As a result of these tests we have decided to use positions coming directly out of the CASU pipeline, and work under the assumption that our median error is around 18 mas.

We assume the larger error found in the ULAS 0034 sequence compared to the two-epoch cluster test is due to the fact that we are comparing a wider range of observing conditions over a longer time span.

We note that the centroiding errors provided by the CASU pipeline are good indications of the errors found in our test.