# Posts Tagged accurate mass

## Recent Postings from accurate mass

### Refining our knowledge of the white dwarf mass-radius relation

The presence of a white dwarf in a resolved binary system, such as Sirius, provides an opportunity to combine dynamical information about the masses, from astrometry and spectroscopy, with a gravitational red-shift measurement and spectrophotometry of the white dwarf atmosphere to provide a test of theoretical mass-radius relations of unprecedented accuracy. We demonstrated this with the first Balmer line spectrum of Sirius B to be obtained free of contamination from the primary, with STIS on HST. However, we also found an unexplained discrepancy between the spectroscopic and gravitational red-shift mass determinations. With the recovery of STIS, we have been able to revisit our observations of Sirius B with an improved observation strategy designed to reduce systematic errors on the gravitational red-shift measurement. We provide a preliminary report on the refined precision of the Sirius B mass-radius measurements and the extension of this technique to a larger sample of white dwarfs in resolved binaries. Together these data can provide accurate mass and radius determinations capable of testing the theoretical mass-radius relation and distinguishing between possible structural models.

### Precise mass and radius measurements for the components of the bright solar-type eclipsing binary star V1094 Tau

V1094 Tau is bright eclipsing binary star with an orbital period close to 9 days containing two stars similar to the Sun. Our aim is to test models of Sun-like stars using precise and accurate mass and radius measurements for both stars in V1094 Tau. We present new spectroscopy of V1094 Tau which we use to estimate the effective temperatures of both stars and to refine their spectroscopic orbits. We also present new, high-quality photometry covering both eclipses of V1094 Tau in the Stroemgren uvby system and in the Johnson V-band. The masses, radii and effective temperatures of the stars in V1094 Tau are found to be M$_A$ = 1.0964 $\pm$ 0.0040 M$_{\odot}$, R$_A$ = 1.4129 $\pm$ 0.0058 R$_{\odot}$, T$_{\rm eff,A}$ = 5850 $\pm$ 100 K, and M$_B$ = 1.0120 $\pm$ 0.0028 M$_{\odot}$, R$_B$ = 1.0913 $\pm$ 0.0066 R$_{\odot}$, T$_{\rm eff,B}$ = 5700 $\pm$ 100 K. An analysis of the times of mid-eclipse and the radial velocity data reveals apsidal motion with a period of 14500 $\pm$ 3700 years. The observed masses, radii and effective temperatures are consistent with stellar models for an age $\approx$ 6 Gyr if the stars are assumed to have a metallicity similar to the Sun. This estimate is in reasonable agreement with our estimate of the metallicity derived using Stroemgren photometry and treating the binary as a single star ([Fe/H] $= -0.09 \pm 0.11$). The rotation velocities of the stars suggest that V1094 Tau is close to the limit at which tidal interactions between the stars force them to rotate pseudo-synchronously with the orbital motion.

### Precise mass and radius measurements for the components of the bright solar-type eclipsing binary star V1094 Tau [Replacement]

V1094 Tau is bright eclipsing binary star with an orbital period close to 9 days containing two stars similar to the Sun. Our aim is to test models of Sun-like stars using precise and accurate mass and radius measurements for both stars in V1094 Tau. We present new spectroscopy of V1094 Tau which we use to estimate the effective temperatures of both stars and to refine their spectroscopic orbits. We also present new, high-quality photometry covering both eclipses of V1094 Tau in the Stroemgren uvby system and in the Johnson V-band. The masses, radii and effective temperatures of the stars in V1094 Tau are found to be M$_A$ = 1.0965 $\pm$ 0.0040 M$_{\odot}$, R$_A$ = 1.4109 $\pm$ 0.0058 R$_{\odot}$, T$_{\rm eff,A}$ = 5850 $\pm$ 100 K, and M$_B$ = 1.0120 $\pm$ 0.0028 M$_{\odot}$, R$_B$ = 1.1063 $\pm$ 0.0066 R$_{\odot}$, T$_{\rm eff,B}$ = 5700 $\pm$ 100 K. An analysis of the times of mid-eclipse and the radial velocity data reveals apsidal motion with a period of 14500 $\pm$ 3700 years. The observed masses, radii and effective temperatures are consistent with stellar models for an age $\approx$ 6 Gyr if the stars are assumed to have a metallicity similar to the Sun. This estimate is in reasonable agreement with our estimate of the metallicity derived using Stroemgren photometry and treating the binary as a single star ([Fe/H] $= -0.09 \pm 0.11$). The rotation velocities of the stars suggest that V1094 Tau is close to the limit at which tidal interactions between the stars force them to rotate pseudo-synchronously with the orbital motion.

### An accurate mass and radius measurement for an ultracool white dwarf

Studies of cool white dwarfs in the solar neighbourhood have placed a limit on the age of the Galactic disk of 8-9 billion years. However, determining their cooling ages requires the knowledge of their effective temperatures, masses, radii, and atmospheric composition. So far, these parameters could only be inferred for a small number of ultracool white dwarfs for which an accurate distance is known, by fitting their spectral energy distributions (SEDs) in conjunction with a theoretical mass-radius relation. However, the mass-radius relation remains largely untested, and the derived cooling ages are hence model-dependent. Here we report direct measurements of the mass and radius of an ultracool white dwarf in the double-lined eclipsing binary SDSS J013851.54-001621.6. We find M(WD)=0.529+/-0.010Msol and R(WD)=0.0131+/-0.0003Rsol. Our measurements are consistent with the mass-radius relation and we determine a robust cooling age of 9.5 billion years for the 3570K white dwarf. We find that the mass and radius of the low mass companion star, M(sec)=0.132+/-0.003Msol and R(sec)=0.165+/-0.001Rsol, are in agreement with evolutionary models. We also find evidence that this >9.5 Gyr old M5 star is still active, far beyond the activity lifetime for a star of its spectral type. This is likely caused by the high tidally-enforced rotation rate of the star. The companion star is close to filling its Roche lobe and the system will evolve into a cataclysmic variable in only 70 Myr. Our direct measurements demonstrate that this system can be used to calibrate ultracool white dwarf atmospheric models.

### Toward an accurate mass function for precision cosmology

Cosmological surveys aim to use the evolution of the abundance of galaxy clusters to accurately constrain the cosmological model. In the context of LCDM, we show that it is possible to achieve the required percent level accuracy in the halo mass function with gravity-only cosmological simulations, and we provide simulation start and run parameter guidelines for doing so. Some previous works have had sufficient statistical precision, but lacked robust verification of absolute accuracy. Convergence tests of the mass function with, for example, simulation start redshift can exhibit false convergence of the mass function due to counteracting errors, potentially misleading one to infer overly optimistic estimations of simulation accuracy. Percent level accuracy is possible if initial condition particle mapping uses second order Lagrangian Perturbation Theory, and if the start epoch is between 10 and 50 expansion factors before the epoch of halo formation of interest. The mass function for halos with fewer than ~1000 particles is highly sensitive to simulation parameters and start redshift, implying a practical minimum mass resolution limit due to mass discreteness. The narrow range in converged start redshift suggests that it is not presently possible for a single simulation to capture accurately the cluster mass function while also starting early enough to model accurately the numbers of reionisation era galaxies, whose baryon feedback processes may affect later cluster properties. Ultimately, to fully exploit current and future cosmological surveys will require accurate modeling of baryon physics and observable properties, a formidable challenge for which accurate gravity-only simulations are just an initial step.

### Cheap Space-Based Microlens Parallaxes for High-Magnification Events

We show that for high-magnification (Amax > 100) microlensing events, accurate microlens parallaxes can be obtained from three or fewer photometric measurements from a small telescope on a satellite in solar orbit at ~1 AU from Earth. This is 1–2 orders of magnitude less observing resources than are required for standard space-based parallaxes. Such microlens parallax measurements would yield accurate mass and distance measurements to the lens for all cases in which finite-source effects were observed from the ground over peak. This would include virtually all high-magnification events with detected planets and a substantial fraction of those without. Hence it would permit accurate estimates of the Galactic distribution of planets.

### CLASH: Mass Distribution in and around MACS J1206.2-0847 from a Full Cluster Lensing Analysis

We derive an accurate mass distribution of the galaxy cluster MACS J1206.2-0847 (z=0.439) from a combined weak-lensing distortion, magnification, and strong-lensing analysis of wide-field Subaru BVRIz’ imaging and our recent 16-band Hubble Space Telescope observations taken as part of the Cluster Lensing And Supernova survey with Hubble (CLASH) program. We find good agreement in the regions of overlap between several weak and strong lensing mass reconstructions using a wide variety of modeling methods, ensuring consistency. The Subaru data reveal the presence of a surrounding large scale structure with the major axis running approximately north-west south-east (NW-SE), aligned with the cluster and its brightest galaxy shapes, showing elongation with a \sim 2:1 axis ratio in the plane of the sky. Our full-lensing mass profile exhibits a shallow profile slope dln\Sigma/dlnR\sim -1 at cluster outskirts (R>1Mpc/h), whereas the mass distribution excluding the NW-SE excess regions steepens further out, well described by the Navarro-Frenk-White form. Assuming a spherical halo, we obtain a virial mass M_{vir}=(1.1\pm 0.2\pm 0.1)\times 10^{15} M_{sun}/h and a halo concentration c_{vir} = 6.9\pm 1.0\pm 1.2 (\sim 5.7 when the central 50kpc/h is excluded), which falls in the range 4< <7 of average c(M,z) predictions for relaxed clusters from recent Lambda cold dark matter simulations. Our full lensing results are found to be in agreement with X-ray mass measurements where the data overlap, and when combined with Chandra gas mass measurements, yield a cumulative gas mass fraction of 13.7^{+4.5}_{-3.0}% at 0.7Mpc/h (\approx 1.7r_{2500}), a typical value observed for high mass clusters.

### CLASH: Mass Distribution in and around MACS J1206.2-0847 from a Full Cluster Lensing Analysis [Replacement]

We derive an accurate mass distribution of the galaxy cluster MACS J1206.2-0847 (z=0.439) from a combined weak-lensing distortion, magnification, and strong-lensing analysis of wide-field Subaru BVRIz’ imaging and our recent 16-band Hubble Space Telescope observations taken as part of the Cluster Lensing And Supernova survey with Hubble (CLASH) program. We find good agreement in the regions of overlap between several weak and strong lensing mass reconstructions using a wide variety of modeling methods, ensuring consistency. The Subaru data reveal the presence of a surrounding large scale structure with the major axis running approximately north-west south-east (NW-SE), aligned with the cluster and its brightest galaxy shapes, showing elongation with a \sim 2:1 axis ratio in the plane of the sky. Our full-lensing mass profile exhibits a shallow profile slope dln\Sigma/dlnR\sim -1 at cluster outskirts (R>1Mpc/h), whereas the mass distribution excluding the NW-SE excess regions steepens further out, well described by the Navarro-Frenk-White form. Assuming a spherical halo, we obtain a virial mass M_{vir}=(1.1\pm 0.2\pm 0.1)\times 10^{15} M_{sun}/h and a halo concentration c_{vir} = 6.9\pm 1.0\pm 1.2 (\sim 5.7 when the central 50kpc/h is excluded), which falls in the range 4< <c> <7 of average c(M,z) predictions for relaxed clusters from recent Lambda cold dark matter simulations. Our full lensing results are found to be in agreement with X-ray mass measurements where the data overlap, and when combined with Chandra gas mass measurements, yield a cumulative gas mass fraction of 13.7^{+4.5}_{-3.0}% at 0.7Mpc/h (\approx 1.7r_{2500}), a typical value observed for high mass clusters.

### Applying scale-free mass estimators to the Local Group in Constrained Local Universe Simulations

We use the recently proposed scale-free mass estimators to determine the masses of the Milky Way (MW) and Andromeda (M31) galaxy in a dark matter only Constrained Local UniversE Simulation (CLUES). While these mass estimators work rather well for isolated spherical host systems, we examine here their applicability to a simulated binary system with a unique satellite population similar to the observed satellites of MW and M31. We confirm that the scale-free estimators work also very well in our simulated Local Group galaxies with the right number of satellites which follow the observed radial distribution. In the isotropic case and under the assumption that the satellites are tracking the total gravitating mass, the power-law index of the radial satellite distribution $N(<r)\propto r^{3-\gamma}$ is directly related to the host's mass profile $M(<r)\propto r^{1-\alpha}$ as $\alpha=\gamma-2$. The use of this relation for any given $\gamma$ leads to highly accurate mass estimations which is a crucial point for observer, since they do not know a priori the mass profile of the MW and M31 haloes. We discuss possible bias in the mass estimators and conclude that the scale-free mass estimators can be satisfactorily applied to the real MW and M31 system.

### Masses of subgiant stars from asteroseismology using the coupling strengths of mixed modes

Since few decades, asteroseismology, the study of stellar oscillations, enables us to probe the interiors of stars with great precision. It allows stringent tests of stellar models and can provide accurate radii, masses and ages for individual stars. Of particular interest are the mixed modes that occur in subgiant solar-like stars since they can place very strong constraints on stellar ages. Here we measure the characteristics of the mixed modes, particularly the coupling strength, using a grid of stellar models for stars with masses between 0.9 and 1.5 M_{\odot}. We show that the coupling strength of the $\ell = 1$ mixed modes is predominantly a function of stellar mass and appears to be independent of metallicity. This should allow an accurate mass evaluation, further increasing the usefulness of mixed modes in subgiants as asteroseismic tools.

### Masses of subgiant stars from asteroseismology using the coupling strengths of mixed modes [Replacement]

Since few decades, asteroseismology, the study of stellar oscillations, enables us to probe the interiors of stars with great precision. It allows stringent tests of stellar models and can provide accurate radii, masses and ages for individual stars. Of particular interest are the mixed modes that occur in subgiant solar-like stars since they can place very strong constraints on stellar ages. Here we measure the characteristics of the mixed modes, particularly the coupling strength, using a grid of stellar models for stars with masses between 0.9 and 1.5 M_{\odot}. We show that the coupling strength of the $\ell = 1$ mixed modes is predominantly a function of stellar mass and appears to be independent of metallicity. This should allow an accurate mass evaluation, further increasing the usefulness of mixed modes in subgiants as asteroseismic tools.

### Absolute dimensions of eclipsing binaries. XXIX. The Am-type systems SW Canis Majoris and HW Canis Majoris

CONTEXT: Accurate physical properties of eclipsing stars provide important constraints on models of stellar structure and evolution, especially when combined with spectroscopic information on their chemical composition. Empirical calibrations of the data also lead to accurate mass and radius estimates for exoplanet host stars. Finally, accurate data for unusual stellar subtypes, such as Am stars, also help to unravel the cause(s) of their peculiarities. AIMS: We aim to determine the masses, radii, effective temperatures, detailed chemical composition and rotational speeds for the Am-type eclipsing binaries SW CMa (A4-5m) and HW CMa (A6m) and compare them with similar normal stars. METHODS: Accurate radial velocities from the Digital Speedometers of the Harvard-Smithsonian Center for Astrophysics were combined with previously published uvby photometry to determine precise physical parameters for the four stars. A detailed abundance analysis was performed from high-resolution spectra obtained with the Nordic Optical Telescope (La Palma). RESULTS: We find the masses of the (relatively evolved) stars in SW CMa to be 2.10 and 2.24 solar masses, with radii of 2.50 and 3.01 solar radii, while the (essentially zero-age) stars in HW CMa have masses of 1.72 and 1.78 solar masses, radii of 1.64 and 1.66 solar radii — all with errors well below 2%. Detailed atmospheric abundances for one or both components were determined for 14 elements in SW CMa ([Fe/H] = +0.49/+0.61 dex) and 16 in HW CMa ([Fe/H] = +0.33/+0.32 dex); both abundance patterns are characteristic of metallic-line stars. Both systems are well fit by current stellar evolution models for assumed bulk abundances of [Fe/H] = +0.05 and +0.23, respectively ([alpha/Fe] = 0.0), and ages of about 700 Myr and 160 Myr.

### Predictions for mass-loss rates and terminal wind velocities of massive O-type stars

Mass loss forms an important aspect of the evolution of massive stars, as well as for the enrichment of the surrounding ISM. Our goal is to predict accurate mass-loss rates and terminal wind velocities. These quantities can be compared to empirical values, thereby testing radiation-driven wind models. One specific issue is that of the “weak-wind problem”, where empirically derived mass-loss rates fall orders of magnitude short of predicted values. We employ an established Monte Carlo model and a recently suggested new line acceleration formalism to solve the wind dynamics consistently. We provide a new grid of mass-loss rates and terminal wind velocities of O stars, and compare the values to empirical results. Our models fail to provide mass-loss rates for main-sequence stars below a luminosity of log(L/Lsun) = 5.2, where we run into a fundamental limit. At luminosities below this critical value there is insufficient momentum transferred in the region below the sonic point to kick-start the acceleration. This problem occurs at the location of the onset of the weak-wind problem. For O dwarfs, the boundary between being able to start a wind, and failing to do so, is at spectral type O6/O6.5. The direct cause of this failure is a combination of the lower luminosity and a lack of Fe V lines at the wind base. This might indicate that another mechanism is required to provide the necessary driving to initiate the wind. For stars more luminous than log(L/Lsun) = 5.2, our new mass-loss rates are in excellent agreement with the mass-loss prescription by Vink et al. 2000. This implies that the main assumption entering the method of the Vink et al. prescriptions – i.e. that the momentum equation is not explicitly solved for – does not compromise the reliability of the Vink et al. results for this part of parameter space (Abridged).

### Remodel the Envelope Around the 21 micrometer PPN IRAS 07134+1005

Recently, the CO J=3-2 observational result of the envelope of the 21 micrometer PPN IRAS 07134+1005 has been reported. Assuming that the CO J=3-2 line was optically thin, the mass-loss rate of the superwind in this PPN was found to be at least 2 orders of magnitude lower than the typical range. In order to obtain a more accurate mass-loss rate, we reexamine this data and construct a radiative transfer model to compare with the data. Also, in order to better resolve the superwind, we adopt a different weighting on the data to obtain maps at higher resolution. Our result shows that the CO J=3-2 emission is located slightly further away from the central source than the mid-IR emission, probably because that the material is cooler in the outer part and thus better traced by the CO emission. At lower resolution, however, the CO emission appeared to be spatially coincident with the mid-IR emission. Our model has two components, an inner ellipsoidal shell-like superwind with an equatorial density enhancement and an outer spheroidal AGB wind. The thick torus in previous model could be considered as the dense equatorial part of our ellipsoidal superwind. With radiative transfer, our model reproduces more observed features than previous model and obtains an averaged superwind mass-loss rate of ~ 1.8 x 10^-5 solar mass per year, which is typical for a superwind. The mass-loss rate in the equatorial plane is 3 x 10^-5 solar mass per year, also the same as that derived before from modeling CO J=1-0 emission.

### L-band spectroscopy of Galactic OB-stars

Context. Mass-loss, occurring through radiation driven supersonic winds, is a key issue throughout the evolution of massive stars. Two outstanding problems are currently challenging the theory of radiation-driven winds: wind clumping and the weak-wind problem. Aims. We seek to obtain accurate mass-loss rates of OB stars at different evolutionary stages to constrain the impact of both problems in our current understanding of massive star winds. Methods. We perform a multi-wavelength quantitative analysis of a sample of ten Galactic OB-stars by means of the atmospheric code CMFGEN, with special emphasis on the L-band window. A detailed investigation is carried out on the potential of Br\alpha\ and Pf\gamma\ as mass-loss and clumping diagnostics. Results. For objects with dense winds, Br\alpha\ samples the intermediate wind while Pf\gamma\ maps the inner one. In combination with other indicators (UV, H\alpha, Br\gamma) these lines enable us to constrain the wind clumping structure and to obtain “true” mass-loss rates. For objects with weak winds, Br\alpha\ emerges as a reliable diagnostic tool to constrain the mass-loss rates. The emission component at the line Doppler-core superimposed on the rather shallow Stark absorption wings reacts very sensitively to mass loss already at very low mass-loss values. On the other hand, the line wings display similar sensitivity to mass loss as H\alpha, the classical optical mass loss diagnostics. Conclusions. Our investigation reveals the great diagnostic potential of L-band spectroscopy to derive clumping properties and mass-loss rates of hot star winds. We are confident that Br\alpha\ will become the primary diagnostic tool to measure very low mass-loss rates with unprecedented accuracy

### On a novel approach using massive clusters at high redshifts as cosmological probe [Replacement]

In this work we propose a novel method for testing the validity of the fiducial LCDM cosmology by measuring the cumulative distribution function of the most massive haloes in a sample of subvolumes of identical size tiled on the sky at a fixed redshift. The fact that the most massive clusters probe the high-mass tail of the mass function, where the difference between LCDM and alternative cosmological models is strongest, makes our method particularly interesting as a cosmological probe. We utilise general extreme value statistics (GEV) to obtain a cumulative distribution function of the most massive objects in a given volume. We sample this distribution function according to the number of patches covered by the survey area for a range of different “test cosmologies” and for differently accurate mass estimations of the haloes. By fitting this sample with the GEV distribution function, we can study which parameters are the most sensitive with respect to the test cosmologies. We find that the peak of the probability distribution function of the most massive halo is well suited to test the validity of the fiducial LCDM model, once we are able to establish a sufficiently complete large-area survey with M_lim=10^14.5 M_sun/h (M_lim=10^14 M_sun/h) at redshifts above z=1 (z=1.5). Being of cumulative nature the proposed measure is robust and an accuracy of 20-30% in the cluster masses would be sufficient to test for alternative models. Since one only needs the most massive system in each angular patch, this method would be ideally suited as a first fast consistency check before going into a more complex statistical analysis of the observed halo sample.

### Planetary systems in close binary stars: the case of HD196885

Planets can form and survive in close binaries, although dynamical interactions with the secondary component can actually significantly impact the giant planet formation and evolution. Rare close binaries hosting giant planets offer therefore an ideal laboratory to explore the properties and the stability of such extreme planetary systems. In the course of our CFHT and VLT coronographic imaging survey dedicated to the search for faint companions of exoplanet host stars, a close (about 20 AU) secondary stellar companion to the exoplanet host HD196885 A was discovered. For more than 4 years, we have used the NaCo near-infrared adaptive optics instrument to monitor the astrometric position of HD196885 B relative to A. The system was observed at five different epochs from August 2005 to August 2009 and accurate relative positions were determined. Our observations fully reject the stationary background hypothesis for HD196885 B. The two components are found to be comoving. The orbital motion of HD196885 B is well resolved and the orbital curvature is even detected. From our imaging data combined with published radial velocity measurements, we refine the complete orbital parameters of the stellar component. We derive for the first time its orbital inclination and its accurate mass. We find also solutions for the inner giant planet HD196885 Ab compatible with previous independent radial velocity studies. Finally, we investigate the stability of the inner giant planet HD196885 Ab due to the binary companion proximity. Our dynamical simulations show that the system is currently and surprisingly more stable in a high mutual inclination configuration that falls in the Kozai resonance regime. If confirmed, this system would constitute one of the most compact non-coplanar systems known so far. It would raise several questions about its formation and stability

### A Detailed Model Atmosphere Analysis of Cool White Dwarfs in the Sloan Digital Sky Survey

We present optical spectroscopy and near-infrared photometry of 126 cool white dwarfs in the Sloan Digital Sky Survey (SDSS). Our sample includes high proper motion targets selected using the SDSS and USNO-B astrometry and a dozen previously known ultracool white dwarf candidates. Our optical spectroscopic observations demonstrate that a clean selection of large samples of cool white dwarfs in the SDSS (and the SkyMapper, Pan-STARRS, and the Large Synoptic Survey Telescope datasets) is possible using a reduced proper motion diagram and a tangential velocity cut-off (depending on the proper motion accuracy) of 30 km/s. Our near-infrared observations reveal eight new stars with significant absorption. We use the optical and near-infrared photometry to perform a detailed model atmosphere analysis. More than 80% of the stars in our sample are consistent with either pure hydrogen or pure helium atmospheres. However, the eight stars with significant infrared absorption and the majority of the previously known ultracool white dwarf candidates are best explained with mixed hydrogen and helium atmosphere models. The age distribution of our sample is consistent with a Galactic disk age of 8 Gyr. A few ultracool white dwarfs may be as old as 12-13 Gyr, but our models have problems matching the spectral energy distributions of these objects. There are only two halo white dwarf candidates in our sample. However, trigonometric parallax observations are required for accurate mass and age determinations and to confirm their membership in the halo.

### High precision orbital and physical parameters of double-lined spectroscopic binary stars - HD78418, HD123999, HD160922, HD200077 and HD210027

We present high precision radial velocities (RVs) of double-lined spectroscopic binary stars HD78418, HD123999, HD160922, HD200077 and HD210027. They were obtained based on the high resolution echelle spectra collected with the Keck I/Hires, Shane/CAT/Hamspec and TNG/Sarge telescopes/spectrographs over the years 2003-2008 as a part of TATOOINE search for circumbinary planets. The RVs were computed using our novel iodine cell technique for double-line binary stars. The precision of the RVs is of the order of 1-10 m/s. Our RVs combined with the archival visibility measurements from the Palomar Testbed Interferometer allow us to derive very precise spectroscopic/astrometric orbital and physical parameters of the binaries. In particular, we derive the masses, the absolute K and H band magnitudes and the parallaxes. The masses together with the absolute magnitudes in the K and H bands enable us to estimate the ages of the binaries. These RVs allow us to obtain some of the most accurate mass determinations of binary stars. The fractional accuracy in m*sin(i) only and hence based on the RVs alone ranges from 0.02% to 0.42%. When combined with the PTI astrometry, the fractional accuracy in the masses ranges in the three best cases from 0.06% to 0.5%. Among them, the masses of HD210027 components rival in precision the mass determination of the components of the relativistic double pulsar system PSRJ0737-3039. In the near future, for double-lined eclipsing binary stars we expect to derive masses with a fractional accuracy of the order of up to ~0.001% with our technique. This level of precision is an order of magnitude higher than of the most accurate mass determination for a body outside the Solar System – the double neutron star system PSRB1913+16.

### Accurate masses for dispersion-supported galaxies [Replacement]

We derive an accurate mass estimator for dispersion-supported stellar systems and demonstrate its validity by analyzing resolved line-of-sight velocity data for globular clusters, dwarf galaxies, and elliptical galaxies. Specifically, by manipulating the spherical Jeans equation we show that the dynamical mass enclosed within the 3D deprojected half-light radius r_1/2 can be determined with only mild assumptions about the spatial variation of the stellar velocity dispersion anisotropy. We find M_1/2 = 3 \sigma_los^2 r_1/2 / G ~ 4 \sigma_los^2 R_eff / G, where \sigma_los^2 is the luminosity-weighted square of the line-of-sight velocity dispersion and R_eff is the 2D projected half-light radius. While deceptively familiar in form, this formula is not the virial theorem, which cannot be used to determine accurate masses unless the radial profile of the total mass is known a priori. We utilize this finding to show that all of the Milky Way dwarf spheroidal galaxies (MW dSphs) are consistent with having formed within a halo of mass approximately 3 x 10^9 M_sun in Lambda CDM cosmology. The faintest MW dSphs seem to have formed in dark matter halos that are at least as massive as those of the brightest MW dSphs, despite the almost five orders of magnitude spread in luminosity. We expand our analysis to the full range of observed dispersion-supported stellar systems and examine their I-band mass-to-light ratios (M/L). The M/L vs. M_1/2 relation for dispersion-supported galaxies follows a U-shape, with a broad minimum near M/L ~ 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to M/L ~ 1,600 for ultra-faint dSphs, and a more shallow rise to M/L ~ 800 for galaxy cluster spheroids.

### Accurate masses for dispersion-supported galaxies [Replacement]

We derive an accurate mass estimator for dispersion-supported stellar systems and demonstrate its validity by analyzing resolved line-of-sight velocity data for globular clusters, dwarf galaxies, and elliptical galaxies. Specifically, by manipulating the spherical Jeans equation we show that the dynamical mass enclosed within the 3D deprojected half-light radius r_1/2 can be determined with only mild assumptions about the spatial variation of the stellar velocity dispersion anisotropy. We find M_1/2 = 3 \sigma_los^2 r_1/2 / G ~ 4 \sigma_los^2 R_eff / G, where \sigma_los^2 is the luminosity-weighted square of the line-of-sight velocity dispersion and R_eff is the 2D projected half-light radius. While deceptively familiar in form, this formula is not the virial theorem, which cannot be used to determine accurate masses unless the radial profile of the total mass is known a priori. We utilize this finding to show that all of the Milky Way dwarf spheroidal galaxies (MW dSphs) are consistent with having formed within a halo of mass approximately 3 x 10^9 M_sun in Lambda CDM cosmology. The faintest MW dSphs seem to have formed in dark matter halos that are at least as massive as those of the brightest MW dSphs, despite the almost five orders of magnitude spread in luminosity. We expand our analysis to the full range of observed dispersion-supported stellar systems and examine their I-band mass-to-light ratios (M/L). The M/L vs. M_1/2 relation for dispersion-supported galaxies follows a U-shape, with a broad minimum near M/L ~ 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to M/L ~ 1,600 for ultra-faint dSphs, and a more shallow rise to M/L ~ 800 for galaxy cluster spheroids.

### Accurate masses for dispersion-supported galaxies [Replacement]

We derive an accurate mass estimator for dispersion-supported stellar systems and demonstrate its validity by analyzing resolved line-of-sight velocity data for globular clusters, dwarf galaxies, and elliptical galaxies. Specifically, by manipulating the spherical Jeans equation we show that the dynamical mass enclosed within the 3D deprojected half-light radius r_1/2 can be determined with only mild assumptions about the spatial variation of the stellar velocity dispersion anisotropy. We find M_1/2 = 3 \sigma_los^2 r_1/2 / G ~ 4 \sigma_los^2 R_eff / G, where \sigma_los^2 is the luminosity-weighted square of the line-of-sight velocity dispersion and R_eff is the 2D projected half-light radius. While deceptively familiar in form, this formula is not the virial theorem, which cannot be used to determine accurate masses unless the radial profile of the total mass is known a priori. We utilize this finding to show that all of the Milky Way dwarf spheroidal galaxies (MW dSphs) are consistent with having formed within a halo of mass approximately 3 x 10^9 M_sun in Lambda CDM cosmology. The faintest MW dSphs seem to have formed in dark matter halos that are at least as massive as those of the brightest MW dSphs, despite the almost five orders of magnitude spread in luminosity. We expand our analysis to the full range of observed dispersion-supported stellar systems and examine their I-band mass-to-light ratios (M/L). The M/L vs. M_1/2 relation for dispersion-supported galaxies follows a U-shape, with a broad minimum near M/L ~ 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to M/L ~ 3,200 for ultra-faint dSphs, and a more shallow rise to M/L ~ 800 for galaxy cluster spheroids.

### The Mass Structure of the Galaxy Cluster Cl0024+1654 from a Full Lensing Analysis of Joint Subaru and ACS/NIC3 Observations [Replacement]

We derive an accurate mass distribution of the rich galaxy cluster Cl0024+1654 (z=0.395) based on deep Subaru BR_{c}z’ imaging and our recent comprehensive strong lensing analysis of HST/ACS/NIC3 observations. We obtain the weak lensing distortion and magnification of undilted samples of red and blue background galaxies by carefully combining all color and positional information. Unlike previous work, the weak and strong lensing are in excellent agreement where the data overlap. The joint mass profile continuously steepens out to the virial radius with only a minor contribution \sim 10% in the mass from known subcluster at a projected distance of \sim 700kpc/h. The projected mass distribution for the entire cluster is well fitted with a single Navarro-Frenk-White model with a virial mass, M_{vir} = (1.2 \pm 0.2) \times 10^{15} M_{sun}/h, and a concentration, c_{vir} = 9.2^{+1.4}_{-1.2}. This model fit is fully consistent with the depletion of the red background counts, providing independent confirmation. Careful examination and interpretation of X-ray and dynamical data strongly suggest that this cluster system is in a post collision state, which we show is consistent with our well-defined mass profile for a major merger occurring along the line of sight, viewed approximately 2-3Gyr after impact when the gravitational potential has had time to relax in the center, before the gas has recovered and before the outskirts are fully virialized. Finally, our full lensing analysis provides a model-independent constraint of M_{2D}(<r_{vir}) = (1.4 \pm 0.3) \times 10^{15} M_{sun}/h for the projected mass of the whole system, including any currently unbound material beyond the virial radius, which can constrain the sum of the two pre-merger cluster masses when designing simulations to explore this system.

### The Mass Structure of the Galaxy Cluster Cl0024+1654 from a Full Lensing Analysis of Joint Subaru and ACS/NIC3 Observations

We derive an accurate mass distribution of the rich galaxy cluster Cl0024+1654 (z=0.395) based on deep Subaru BR_{c}z’ imaging and our recent comprehensive strong lensing analysis of HST/ACS/NIC3 observations. We define an undiluted background population of red and blue galaxies by carefully combining all color and positional information. Unlike previous work, the weak and strong lensing are in excellent agreement where the data overlap. The joint mass profile continuously steepens out to the virial radius, 2300kpc/h, with only a minor contribution, \sim 10% in the mass, from known subcluster at a projected distance of \sim 700kpc/h. The projected mass distribution for the entire cluster is well fitted with a single Navarro-Frenk-White model with a virial mass, M_{vir} = (1.2 \pm 0.2) \times 10^{15} M_{sun}/h, and a concentration, c_{vir} = 9 \pm 1. Careful examination and interpretation of X-ray and dynamical data, based on recent high-resolution cluster collision simulations, strongly suggest that this cluster system is in a post collision state, which we show is consistent with our well-defined mass profile for a major merger occurring along the line of sight, viewed approximately 2-3Gyr after impact when the gravitational potential has had time to relax in the center, before the gas has recovered and before the outskirts are fully virialized. Finally, our full lensing analysis provides a model-independent constraint of M_{2D}(<r_{vir}) = (1.4 \pm 0.3) \times 10^{15} M_{sun}/h for the projected mass of the whole system, including any currently unbound material beyond the virial radius, which can constrain the sum of the two pre-merger cluster masses when designing simulations to explore this system.

### The Mass Structure of the Galaxy Cluster Cl0024+1654 from a Full Lensing Analysis of Joint Subaru and ACS/NIC3 Observations [Replacement]

We derive an accurate mass distribution of the rich galaxy cluster Cl0024+1654 (z=0.395) based on deep Subaru BR_{c}z’ imaging and our recent comprehensive strong lensing analysis of HST/ACS/NIC3 observations. We obtain the weak lensing distortion and magnification of undilted samples of red and blue background galaxies by carefully combining all color and positional information. Unlike previous work, the weak and strong lensing are in excellent agreement where the data overlap. The joint mass profile continuously steepens out to the virial radius, 2300kpc/h, with only a minor contribution, \sim 10% in the mass, from known subcluster at a projected distance of \sim 700kpc/h. The projected mass distribution for the entire cluster is well fitted with a single Navarro-Frenk-White model with a virial mass, M_{vir} = (1.2 \pm 0.2) \times 10^{15} M_{sun}/h, and a concentration, c_{vir} = 9 \pm 1. This model fit is fully consistent with the depletion of the red background counts, providing independent confirmation. Careful examination and interpretation of X-ray and dynamical data strongly suggest that this cluster system is in a post collision state, which we show is consistent with our well-defined mass profile for a major merger occurring along the line of sight, viewed approximately 2-3Gyr after impact when the gravitational potential has had time to relax in the center, before the gas has recovered and before the outskirts are fully virialized. Finally, our full lensing analysis provides a model-independent constraint of M_{2D}(<r_{vir}) = (1.4 \pm 0.3) \times 10^{15} M_{sun}/h for the projected mass of the whole system, including any currently unbound material beyond the virial radius, which can constrain the sum of the two pre-merger cluster masses when designing simulations to explore this system.

### Dynamic masses for the close PG1159 binary SDSSJ212531.92-010745.9

SDSSJ212531.92-010745.9 is the first known PG1159 star in a close binary with a late main sequence companion allowing a dynamical mass determination. The system shows flux variations with a peak-to-peak amplitude of about 0.7 mag and a period of about 6.96h. In August 2007, 13 spectra of SDSSJ212531.92-010745.9 covering the full orbital phase range were taken at the TWIN 3.5m telescope at the Calar Alto Observatory (Alm\’{e}ria, Spain). These confirm the typical PG1159 features seen in the SDSS discovery spectrum, together with the Balmer series of hydrogen in emission (plus other emission lines), interpreted as signature of the companion’s irradiated side. A radial velocity curve was obtained for both components. Using co-added radial-velocity-corrected spectra, the spectral analysis of the PG1159 star is being refined. The system’s lightcurve, obtained during three seasons of photometry with the G\"ottingen 50cm and T\"ubingen 80cm telescopes, was fitted with both the NIGHTFALL and PHOEBE binary simulation programs. An accurate mass determination of the PG1159 component from the radial velocity measurements requires to first derive the inclination, which requires light curve modelling and yields further constraints on radii, effective temperature and separation of the system’s components. From the analysis of all data available so far, we present the possible mass range for the PG1159 component of SDSSJ212531.92-010745.9.

### Hadrons As Kerr-Newman Black Holes [Replacement]

The scale invariance of the source-free Einstein field equations suggests that one might be able to model hadrons as "strong gravity" black holes, if one uses an appropriate rescaling of units or a revised gravitational coupling factor. The inner consistency of this hypothesis is tested by retrodicting a close approximation to the mass of the proton from an equation that relates the angular momentum and mass of a Kerr black hole. More accurate mass and radius values for the proton are then retrodicted using the geometrodynamics form of the full Kerr-Newman solution of the Einstein-Maxwell equations. The radius of an alpha particle is calculated as an additional retrodictive test. In a third retrodictive test of the "strong gravity" hypothesis, the subatomic particle mass spectrum in the 100 MeV to 7,000 MeV range is retrodicted to a first approximation using the Kerr solution of General Relativity. The particle masses appear to form a restricted set of quantized values of the Kerr solution: n^1/2 M, where values of n are a set of discrete integers and M is the revised Planck mass. The accuracy of the 27 retrodicted masses averages 98.4%. Finally, the new atomic scale gravitational coupling constant suggests a radical revision of the assumptions governing the Planck scale, and leads to a natural explanation for the fine structure constant.