This paper deals with fundamental properties of Poincaré half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincaré half-maps, their ...series expansions (Taylor and Newton–Puiseux) at the tangency point and at infinity, the relative position between the graph of Poincaré half-maps and the bisector of the fourth quadrant, and the sign of their second derivatives. All these properties are essential to understand the dynamic behavior of planar piecewise linear systems. Accordingly, we also provide some of their most immediate, but non-trivial, consequences regarding periodic orbits.
Abstract
In the third paper from the COOL–LAMPS Collaboration, we report the discovery of COOL J0542-2125, a gravitationally lensed quasar at
z
= 1.84, observed as three images due to an intervening ...massive galaxy cluster at
z
= 0.61. The lensed quasar images were identified in a search for lens systems in recent public optical imaging data and have separations on the sky up to 25.″9, wider than any previously known lensed quasar. The galaxy cluster acting as a strong lens appears to be in the process of merging, with two subclusters separated by ∼1 Mpc in the plane of the sky, and their central galaxies showing a radial velocity difference of ∼1000 km s
−1
. Both cluster cores show strongly lensed images of an assortment of background sources, as does the region between them. A preliminary strong lens model implies masses of
M
<
250
k
p
c
=
1.79
−
0.01
+
0.16
×
10
14
M
⊙
and
M
<
250
k
p
c
=
1.48
−
0.10
+
0.04
×
10
14
M
⊙
for the east and west subclusters, respectively. This line of sight is also coincident with an ROSAT ALL-sky Survey source, centered between the two confirmed cluster halos reminiscent of other major cluster-scale mergers. Archival and new follow-up imaging show flux variability in the quasar images of up to 0.4 mag within ∼1 yr, and new multicolor imaging data reveal a 2
σ
detection of the underlying quasar host. A lens system with this configuration offers rare opportunities for a range of future studies of both the lensed quasar and its host and the foreground cluster merger causing the lensing.
Numerical methods are often used to put in evidence the existence of global connections in differential systems. The principal reason is that the corresponding analytical proofs are usually very ...complicated. In this work we give an analytical proof of the existence of a pair of homoclinic connections in a continuous piecewise linear system, which can be considered to be a version of the widely studied Michelson system. Although the computations developed in this proof are specific to the system, the techniques can be extended to other piecewise linear systems.
We demonstrate the feasibility of determining magnitudes of stars on archival photographic plates using a commercially available scanner. We describe one photometric approach that could serve as a ...useful example for other studies. In particular, we measure and calibrate stellar magnitudes from a 1903 photographic plate from the Yerkes Observatory collection, and demonstrate that the overall precision from our methods is better than 0.10 mag. Notably, these measurements are dominated by intrinsic plate noise, rather than noise introduced through the scanning/digitization process. The low expense of this approach expands the scientific potential to study variable stars in the archives of observatory plate collections. We use the serendipitous discovery of a candidate transient at photographic magnitude pg = 16.60 in the spiral galaxy NGC 7331 to illustrate our photometric methods. If this unknown source is a supernova, it would represent the fourth known supernova in NGC 7331.
Abstract
We demonstrate the feasibility of determining magnitudes of stars on archival photographic plates using a commercially available scanner. We describe one photometric approach that could ...serve as a useful example for other studies. In particular, we measure and calibrate stellar magnitudes from a 1903 photographic plate from the Yerkes Observatory collection, and demonstrate that the overall precision from our methods is better than 0.10 mag. Notably, these measurements are dominated by intrinsic plate noise, rather than noise introduced through the scanning/digitization process. The low expense of this approach expands the scientific potential to study variable stars in the archives of observatory plate collections. We use the serendipitous discovery of a candidate transient at photographic magnitude
pg
= 16.60 in the spiral galaxy NGC 7331 to illustrate our photometric methods. If this unknown source is a supernova, it would represent the fourth known supernova in NGC 7331.
Abstract
We present COOL J1323+0343, an early-type galaxy at
z
= 1.0153 ± 0.0006, strongly lensed by a cluster of galaxies at
z
= 0.353 ± 0.001. This object was originally imaged by DECaLS and noted ...as a gravitational lens by COOL-LAMPS, a collaboration initiated to find strong-lensing systems in recent public optical imaging data, and confirmed with follow-up data. With ground-based
grzH
imaging and optical spectroscopy from the Las Campanas Observatory and the Nordic Optical Telescope, we derive a stellar mass, metallicity, and star formation history from stellar-population synthesis modeling. The lens modeling implies a total magnification, summed over the three images in the arc, of
μ
∼ 113. The stellar mass in the source plane is
M
*
∼ 10.64
M
⊙
and the 1
σ
upper limit on the star formation rate (SFR) in the source plane is SFR ∼ 3.75 × 10
−2
M
⊙
yr
−1
(log sSFR = −12.1 yr
−1
) in the youngest two age bins (0–100 Myr), closest to the epoch of observation. Our measurements place COOL J1323+0343 below the characteristic mass of the stellar mass function, making it an especially compelling target that could help clarify how intermediate-mass quiescent galaxies evolve. We reconstruct COOL J1323+0343 in the source plane and fit its light profile. This object is below the expected size evolution of an early-type galaxy at this mass with an effective radius r
e
∼ 0.5 kpc. This extraordinarily magnified and bright lensed early-type galaxy offers an exciting opportunity to study the morphology and star formation history of an intermediate-mass early-type galaxy in detail at
z
∼ 1.
Abstract
We report the discovery of COOL J1241+2219, a strongly lensed galaxy at redshift
z
= 5.043 ± 0.002 with observed magnitude
z
AB
= 20.47, lensed by a moderate-mass galaxy cluster at
z
... = 1.001 ± 0.001. COOL J1241+2219 is the brightest lensed galaxy currently known at optical and near-infrared wavelengths at
z
≳ 5; it is ∼5 times brighter than the prior record-holder lensed galaxy, and several magnitudes brighter than the brightest unlensed galaxies known at these redshifts. It was discovered as part of COOL-LAMPS, a collaboration initiated to find strongly lensed systems in recent public optical imaging data. We characterize the lensed galaxy, as well as the central galaxy of the lensing cluster using ground-based
grizJH
imaging and optical spectroscopy. We report model-based magnitudes, and derive stellar masses, dust content, metallicity, and star-formation rates via stellar-population synthesis modeling. Our lens mass modeling, based on ground-based imaging, implies a median source magnification of ∼30, which puts the stellar mass and star-formation rate (in the youngest age bin, closest to the epoch of observation) at log
M
*
=
10.11
−
0.26
+
0.21
and SFR =
27
−
9
+
13
M
⊙
yr
−1
, respectively. We constrain a star-formation history for COOL J1241+2219 consistent with constant star formation across ∼1 Gyr of cosmic time, and that places this galaxy on the high-mass end of the star-forming main sequence. COOL J1241+2219 is two to four times more luminous than a galaxy with the characteristic UV luminosity at these redshifts. The UV continuum slope
β
= −2.2 ± 0.2 places this galaxy on the blue side of the observed distribution of galaxies at
z
= 5, although the lack of Ly
α
emission indicates dust sufficient to suppress this emission.
We report the discovery of COOL J1241+2219, a strongly lensed galaxy at redshift z = 5.043 0.002 with observed magnitude zAB = 20.47, lensed by a moderate-mass galaxy cluster at z = 1.001 0.001. COOL ...J1241+2219 is the brightest lensed galaxy currently known at optical and near-infrared wavelengths at z 5; it is ∼5 times brighter than the prior record-holder lensed galaxy, and several magnitudes brighter than the brightest unlensed galaxies known at these redshifts. It was discovered as part of COOL-LAMPS, a collaboration initiated to find strongly lensed systems in recent public optical imaging data. We characterize the lensed galaxy, as well as the central galaxy of the lensing cluster using ground-based grizJH imaging and optical spectroscopy. We report model-based magnitudes, and derive stellar masses, dust content, metallicity, and star-formation rates via stellar-population synthesis modeling. Our lens mass modeling, based on ground-based imaging, implies a median source magnification of ∼30, which puts the stellar mass and star-formation rate (in the youngest age bin, closest to the epoch of observation) at logM* = and SFR = M yr−1, respectively. We constrain a star-formation history for COOL J1241+2219 consistent with constant star formation across ∼1 Gyr of cosmic time, and that places this galaxy on the high-mass end of the star-forming main sequence. COOL J1241+2219 is two to four times more luminous than a galaxy with the characteristic UV luminosity at these redshifts. The UV continuum slope β = −2.2 0.2 places this galaxy on the blue side of the observed distribution of galaxies at z = 5, although the lack of Ly emission indicates dust sufficient to suppress this emission.
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