8,030 research outputs found
Connections and Metrics Respecting Standard Purification
Standard purification interlaces Hermitian and Riemannian metrics on the
space of density operators with metrics and connections on the purifying
Hilbert-Schmidt space. We discuss connections and metrics which are well
adopted to purification, and present a selected set of relations between them.
A connection, as well as a metric on state space, can be obtained from a metric
on the purification space. We include a condition, with which this
correspondence becomes one-to-one. Our methods are borrowed from elementary
*-representation and fibre space theory. We lift, as an example, solutions of a
von Neumann equation, write down holonomy invariants for cyclic ones, and ``add
noise'' to a curve of pure states.Comment: Latex, 27 page
On the Apparent Orbital Inclination Change of the Extrasolar Transiting Planet TrES-2b
On June 15, 2009 UT the transit of TrES-2b was detected using the University
of Arizona's 1.55 meter Kuiper Telescope with 2.0-2.5 millimag RMS accuracy in
the I-band. We find a central transit time of
HJD, an orbital period of days, and an
inclination angle of , which is consistent with our
re-fit of the original I-band light curve of O'Donovan et al. (2006) where we
find . We calculate an insignificant inclination
change of over the last 3 years, and as
such, our observations rule out, at the level, the apparent
change of orbital inclination to as
predicted by Mislis and Schmitt (2009) and Mislis et al. (2010) for our epoch.
Moreover, our analysis of a recently published Kepler Space Telescope light
curve (Gilliland et al. 2010) for TrES-2b finds an inclination of for a similar epoch. These Kepler results definitively
rule out change in as a function of time. Indeed, we detect no significant
changes in any of the orbital parameters of TrES-2b.Comment: 19 pages, 1 table, 7 figures. Re-submitted to ApJ, January 14, 201
A Search for Additional Bodies in the GJ 1132 Planetary System from 21 Ground-based Transits and a 100 Hour Spitzer Campaign
We present the results of a search for additional bodies in the GJ 1132
system through two methods: photometric transits and transit timing variations
of the known planet. We collected 21 transit observations of GJ 1132b with the
MEarth-South array since 2015. We obtained 100 near-continuous hours of
observations with the Space Telescope, including two transits of GJ
1132b and spanning 60\% of the orbital phase of the maximum period at which
bodies coplanar with GJ 1132b would pass in front of the star. We exclude
transits of additional Mars-sized bodies, such as a second planet or a moon,
with a confidence of 99.7\%. When we combine the mass estimate of the star
(obtained from its parallax and apparent band magnitude) with the stellar
density inferred from our high-cadence light curve (assuming zero
eccentricity), we measure the stellar radius of GJ 1132 to be
, and we refine the radius measurement of
GJ 1132b to . Combined with HARPS RV measurements, we
determine the density of GJ 1132b to be \ g cm, with the
mass determination dominating this uncertainty. We refine the ephemeris of the
system and find no evidence for transit timing variations, which would be
expected if there was a second planet near an orbital resonance with GJ 1132b.Comment: 29 pages, 4 Tables, 8 Figures, Submitted to ApJ. Comments welcom
The rotation and Galactic kinematics of mid M dwarfs in the Solar Neighborhood
Rotation is a directly-observable stellar property, and drives magnetic field
generation and activity through a magnetic dynamo. Main sequence stars with
masses below approximately 0.35Msun (mid-to-late M dwarfs) are
fully-convective, and are expected to have a different type of dynamo mechanism
than solar-type stars. Measurements of their rotation rates provide insights
into these mechanisms, but few rotation periods are available for these stars
at field ages. Using photometry from the MEarth transit survey, we measure
rotation periods for 387 nearby, mid-to-late M dwarfs in the Northern
hemisphere, finding periods from 0.1 to 140 days. The typical detected rotator
has stable, sinusoidal photometric modulations at a semi-amplitude of 0.5 to
1%. We find no period-amplitude relation for stars below 0.25Msun and an
anti-correlation between period and amplitude for higher-mass M dwarfs. We
highlight the existence of older, slowly-rotating stars without H{\alpha}
emission that nevertheless have strong photometric variability. The Galactic
kinematics of our sample is consistent with the local population of G and K
dwarfs, and rotators have metallicities characteristic of the Solar
Neighborhood. We use the W space velocities and established age-velocity
relations to estimate that stars with P<10 days are on average <2 Gyrs, and
that those with P>70 days are about 5 Gyrs. The period distribution is mass
dependent: as the mass decreases, the slowest rotators at a given mass have
longer periods, and the fastest rotators have shorter periods. We find a lack
of stars with intermediate rotation periods. [Abridged]Comment: Accepted to ApJ. Machine readable tables and additional figures are
available in the published article or on reques
Harmonic theta series and the kodaira dimension of a6
We construct a basis of the space S14(Sp12(ℤ)) of Siegel cusp forms of degree 6 and weight 14 consisting of harmonic theta series. One of these functions has vanishing order 2 at the boundary which implies that the Kodaira dimension of A6 is nonnegative
- …