An extension of Wiener integration with the use of operator theory

With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for these stochastic integrals. In our extension, we circumvent some of the limitations of the more widely used stochastic integral due to Wiener and Ito, i.e., stochastic integration with respect to Brownian motion. Finally we discuss the connection between the two approaches, as well as a priori estimates and applications.Comment: 13 page

The Possible z=0.83 Precursors of z=0 M* Early-type Cluster Galaxies

We examine the distribution of stellar masses of galaxies in MS 1054-03 and RX J0152.7-1357, two X-ray selected clusters of galaxies at z=0.83. Our stellar mass estimates, from spectral energy distribution fitting, reproduce the dynamical masses as measured from velocity dispersions and half-light radii with a scatter of 0.2 dex in the mass for early-type galaxies. When we restrict our sample of members to high stellar masses, > 1e11.1 Msun (M* in the Schechter mass function for cluster galaxies), we find that the fraction of early-type galaxies is 79 +/- 6% at z=0.83 and 87 +/- 6% at z=0.023 for the Coma cluster, consistent with no evolution. Previous work with luminosity-selected samples finds that the early-type fraction in rich clusters declines from =~80% at z=0 to =~60% at z=0.8. The observed evolution in the early-type fraction from luminosity-selected samples must predominately occur among sub-M* galaxies. As M* for field and group galaxies, especially late-types, is below M* for clusters galaxies, infall could explain most of the recent early-type fraction growth. Future surveys could determine the morphological distributions of lower mass systems which will confirm or refute this explanation.Comment: 5 pages in emulate ApJ format with three color figures. Accepted for publication in ApJ Letters, v642n2. Updated to correct grammatical and typographic errors found by the journa

The Fundamental Plane at z=1.27: First Calibration of the Mass Scale of Red Galaxies at Redshifts z>1

We present results on the Fundamental Plane (FP) of early-type galaxies in the cluster RDCS J0848+4453 at z=1.27. Internal velocity dispersions of three K-selected early-type galaxies are determined from deep Keck spectra. Structural parameters are determined from HST NICMOS images. The galaxies show substantial offsets from the FP of the nearby Coma cluster, as expected from passive evolution of their stellar populations. The offsets from the FP can be expressed as offsets in M/L ratio. The M/L ratios of the two most massive galaxies are consistent with an extrapolation of results obtained at z=0.02-0.83. The evolution of early-type galaxies with masses >10^11 M_sun is well described by ln M/L(B) = (-1.06 +- 0.09) z, corresponding to passive evolution of -1.50 +- 0.13 mag at z=1.3. Ignoring selection effects, the best fitting stellar formation redshift is z*=2.6, corresponding to a luminosity weighted age at the epoch of observation of ~2 Gyr. The M/L ratios of these two galaxies are also in excellent agreement with predictions from models that include progenitor bias. The third galaxy is a factor ~10 less massive than the other two, shows strong Balmer absorption lines in its spectrum, and is offset from the Coma Fundamental Plane by 2.9 mag in rest-frame B. Despite their large range in M/L ratios, all three galaxies fall in the ``Extremely Red Object'' (ERO) class with I-H>3 and R-K>5, and our results show that it is hazardous to use simple models for converting luminosity to mass for these objects. Measurements of M/L ratios at high redshift can be considered first steps to empirically disentangle luminosity and mass evolution at the high mass end of the galaxy population, lifting an important degeneracy in the interpretation of evolution of the luminosity function. [SHORTENED]Comment: Accepted for publication in the Astrophysical Journa

Forming Galaxies with MOND

Beginning with a simple model for the growth of structure, I consider the dissipationless evolution of a MOND-dominated region in an expanding Universe by means of a spherically symmetric N-body code. I demonstrate that the final virialized objects resemble elliptical galaxies with well-defined relationships between the mass, radius, and velocity dispersion. These calculations suggest that, in the context of MOND, massive elliptical galaxies may be formed early (z > 10) as a result of monolithic dissipationless collapse. Then I reconsider the classic argument that a galaxy of stars results from cooling and fragmentation of a gas cloud on a time scale shorter than that of dynamical collapse. Qualitatively, the results are similar to that of the traditional picture; moreover, the existence, in MOND, of a density-temperature relation for virialized, near isothermal objects as well as a mass-temperature relation implies that there is a definite limit to the mass of a gas cloud where this condition can be met-- an upper limit corresponding to that of presently observed massive galaxies.Comment: 9 pages, 9 figures, revised in response to comments of referee. Table added, extended discussion, accepted MNRA

Mass-Selection and the Evolution of the Morphology-Density Relation from z=0.8 to z=0

We examined the morphology-density relations for galaxy samples selected by luminosity and by mass in each of five massive X-ray clusters from z=0.023 to 0.83 for 674 spectroscopically-confirmed members. Rest-frame optical colors and visual morphologies were obtained primarily from Hubble Space Telescope images. Morphology-density relations (MDR) are derived in each cluster from a complete, luminosity-selected sample of 452 galaxies with a magnitude limit M_V < M^{*}_{V} + 1. The change in the early-type fraction with redshift matches previous work for massive clusters of galaxies. We performed a similar analysis, deriving MDRs for complete, mass-selected samples of 441 galaxies with a mass-limit of 10^{10.6} M_{\sun}. Our mass limit includes faint objects, the equivalent of =~1 mag below L^{*} for the red cluster galaxies, and encompasses =~70% of the stellar mass in cluster galaxies. The MDRs in the mass-selected sample at densities of Sigma > 50 galaxies Mpc^{-2} are similar to those in the luminosity-selected sample but show larger early-type fractions. However, the trend with redshift in the fraction of elliptical and S0 galaxies with masses > 10^{10.6} M_{\sun} differs significantly between the mass- and luminosity-selected samples. The clear trend seen in the early-type fraction from z=0 to z=~ 0.8 is not found in mass-selected samples. The early-type galaxy fraction changes much less, and is consistent with being constant at 92% +/- 4% at \Sigma> 500 galaxies Mpc^{-2} and 83 +/- 3% at 50 < \Sigma < 500 galaxies Mpc^{-2}. This suggests that galaxies of mass lower than > 10^{10.6} M_{\sun} play a significant role in the evolution of the early-type fraction in luminosity-selected samples. (Abstract abridged)Comment: 18 pages in emulate ApJ format, with 10 color figures, Accepted to ApJ. Version updated to reflect published version, includes new references and a correction to table

Experimental aerodynamic characteristics for a cylindrical body of revolution with side strakes and various noses at angles of attack from 0 degrees to 58 degrees and Mach numbers from 0.6 to 2.0

For a body of revolution with afterbody side strakes, an experimental investigation was conducted in the Ames 6- by 6-Foot Wind Tunnel to determine the effects on the aerodynamic characteristics of forebody geometry, nose strakes, body side strakes, Reynolds number, Mach number, and angle of attack. Aerodynamic force and moment characteristics were measured for the straked cylindrical afterbody (cylinder fineness ratio of 7) with tangent ogive noses of fineness ratio 2.5 to 5.0. In addition, the straked cylinder afterbody was tested with an ogive nose having a rounded tip and an ogive nose with two different nose strake arrangements. The data demonstrate that the aerodynamic characteristics for a body of revolution with side strakes can be significantly affected by changes in nose fineness ratio, nose bluntness, Reynolds number, Mach number, and, of course, angle of attack. Removing the strakes from the cylindrical aftersection greatly decreased the lift, but this removal hardly changed the maximum magnitudes of the undesirable side forces that developed at angles of attack greater than about 25 deg for subsonic Mach numbers

Experimental aerodynamic characteristics for slender bodies with thin wings and tail at angles of attack from 0 deg to 58 deg and Mach numbers from 0.6 to 2.0

An experimental investigation was conducted by wind tunnel to measure the static aerodynamic characteristics for bodies of circular and elliptic cross section with various thin flat plate wings and a thin tail consisting of horizontal and vertical parts. The wings had aspect ratios of 4 and taper ratios of about 0, 0.25, and 0.5. Two additional wings, which had taper ratios near 0.25 and aspect ratios of about 3 and 5, were also tested in combination with the bodies and tail. All wings had about the same planform area. The exposed area of the horizontal portion of the tail was about 33 to 36 percent of the exposed area of the wings. The exposed area of the vertical tail fin was about 22 to 24 percent of the exposed area of the wings. The elliptic body, with an a/b = 2 cross section, had the same length and axial distribution of cross sectional area as the circular body. The circular body had a cylindrical aftersection of fineness ratio 7, and it was tested with the wings and tail in combination with tangent ogive noses that had fineness ratios of 2.5, 3.0, 3.5, and 5.0. In addition, an ogive nose with a rounded tip and an ogive nose with two different nose strake arrangements were used. Nineteen configuration combinations were tested at Mach numbers of 0.6, 0.9, 1.5, and 2.0 at angles of attack from 0 to 58 deg. The Reynolds numbers, based on body base diameter, were about 4.3 X 100,000

Experimental aerodynamics characteristics for bodies of elliptic cross section at angles of attack from 0 deg to 58 deg and Mach numbers from 0.6 to 2.0

An experimental investigation was conducted to measure the static aerodynamic characteristics for two bodies of elliptic cross section and for their equivalent body of revolution. The equivalent body of revolution had the same length and axial distribution of cross-sectional area as the elliptic bodies. It consisted of a tangent ogive nose of fineness ratio 3 followed by a cylinder with a fineness ratio of 7. All bodies were tested at Mach numbers of 0.6, 0.9, 1.2, 1.5, and 2.0 at angles of attack from 0 deg to 58 deg. The data demonstrate that the aerodynamic characteristics can be significantly altered by changing the body cross section from circular to elliptic and by rolling the body from 0 deg to 90 deg. For example, the first elliptic body (with a constant cross-sectional axis ratio of 2) developed at zero roll about twice the normal force developed by the equivalent body of revolution. At some angles of attack greater than about 25 deg, side forces and yawing moments were measured in spite of the fact that the bodies were tested at zero angle of sideslip. The side-force and yawing-moment coefficients decreased with an increase in Mach number and essentially disappeared for all the bodies at Mach numbers greater than 1.2. From the standpoint of reducing undesirable side forces at high angles of attack, it is best to have the flattest side of the nose of the elliptic bodies pitching against the stream crossflow. The effect of Reynolds number was also the least significant for both elliptic bodies when the flattest side of the nose was pitched against the stream crossflow

VLT and NTT Observations of Two EIS Cluster Candidates. Detection of the Early-Type Galaxies Sequence at z~1

Optical data from the ESO VLT-UT1 Science Verification observations are combined with near-infrared data from SOFI at the NTT to obtain optical-infrared color-magnitude diagrams for the objects in the fields of two EIS cluster candidates. In both cases, evidence is found for a well-defined sequence of red galaxies that appear to be significantly more clustered than the background population. These results suggest that the two systems are real physical associations. The (R-Ks), (I-Ks) and (J-Ks) colors of the red sequences are used, in conjunction with similar data for spectroscopically confirmed clusters, to obtain redshift estimates of z ~ 0.9 and z ~ 1.0 for these two systems. These results make these EIS cluster candidates prime targets for follow-up spectroscopic observations to confirm their reality and to measure more accurately their redshift.Comment: 6 pages, 5 figures, to appear in Astronomy & Astrophysics (Special Letters Edition on "First Science with the VLT"