arXiv subjects

J. Morse

Publications and source records attributed to J. Morse.

12 recordsLinked to original sources

arXiv2026

LUnar-based Survey for Time-domain Exploration and Research network (LUSTER-net)

LUSTER-net is a lunar-surface UVOIR observatory network mission concept for time-domain astrophysics. The concept envisions a scalable array of approximately 6-12 commonly designed telescope nodes, with apertures in the $\sim0.5-1$ m class, distributed across the lunar surface to provide long-duration monitoring, rapid follow-up, and coordinated imaging and spectroscopy of transient and variable sources. By combining continuous observing windows from the lunar surface with adaptive network scheduling, LUSTER-net would provide persistent UVOIR characterization of discoveries from facilities such as Rubin, Roman, ULTRASAT, UVEX, and multi-messenger observatories. The science enabled includes exoplanet atmosphere studies, microlensing parallax, Solar System object characterization, fast transients, electromagnetic counterparts to multi-messenger events, and broader UVOIR variability studies. This white paper outlines the science motivation, notional architecture, implementation trades, and role of LUSTER-net as a step toward future lunar astrophysics facilities.

astro-ph.IM↗

arXiv2007

Collimation, Proper Motions, and Physical Conditions in the HH 30 Jet From HST Slitless Spectroscopy

We present Space Telescope Imaging Spectrograph (STIS) spectral images of the HH~30 stellar jet taken through a wide slit over two epochs. The jet is unresolved spectrally, so the observations produce emission-line images for each line in the spectrum. This rich dataset shows how physical conditions in the jet vary with distance and time, produces precise proper motions of knots within the jet, resolves the jet width close to the star, and gives a spectrum of the reflected light from the disk over a large wavelength range at several positions. We introduce a new method for analyzing a set of line ratios based on minimizing a quadratic form between models and data. The method generates images of the density, temperature and ionization fraction computed using all the possible line ratios appropriately weighted. In HH 30, the density declines with distance from the source in a manner consistent with an expanding flow, and is larger by a factor of two along the axis of the jet than it is at the periphery. Ionization in the jet ranges from ~ 5% to 40%, and high ionization/excitation knots form at about 100 AU from the star and propagate outward with the flow. These high-excitation knots are not accompanied by corresponding increases in the density, so if formed by velocity variations the knots must have a strong internal magnetic pressure to smooth out density increases while lengthening recombination times.

astro-ph↗

arXiv2006

The Expansion Asymmetry and Age of the Cassiopeia A Supernova Remnant

HST ACS images of the young SN remnant Cas A are used to explore the expansion and spatial distribution of its highest velocity debris. Proper motions of over 1800 outlying ejecta knots are reported. The distribution of transverse expansion velocities for these knots shows a striking bipolar asymmetry with the highest velocity knots confined to nearly opposing northeast and southwest `jets'. The jets appear kinematically and chemically distinct with respect to the remnant's highest velocity debris seen in other directions. Significant gaps in the spatial distribution of outlying ejecta lie in directions which are approximately perpendicular to the jets. Extrapolations of 9 month proper motions for all outer ejecta knots and a subsample of 72 bright and compact knots suggest explosion dates (assuming no knot deceleration) of 1662 +/- 27 and 1672 +/- 18, respectively. We find some evidence for non-uniform deceleration in different directions with knots located along the northwestern limb among the least decelerated ejecta suggesting a convergence date of 1681 +/-19. The remnant's central X-ray point source lies some $7''$ to the southeast of the estimated expansion center (PA = 169 deg) indicating a projected motion of ~350 km/s toward the middle of the broad southern outer ejecta knot gap.

astro-ph↗

arXiv2005

Discovery of Outlying, High-Velocity Oxygen-Rich Ejecta in Cassiopeia A

Hubble Space Telescope images of the young Galactic supernova remnant Cassiopeia A reveal a far larger population of outlying, high-velocity knots of ejecta with a broader range of chemical properties than previously suspected. We identify three main classes of outer ejecta: 1) Knots dominated by [N II] 6548,6583 emission; 2) Knots dominated by oxygen emission lines especially [O II] 7319,7330; and 3) Knots with emission line strengths similar to the [S II] strong FMK ejecta commonly seen in the main emission shell. The discovery of a significant population of O-rich ejecta situated in between the suspected N-rich outer photospheric layer and S-rich FMK-like ejecta suggests that the Cas A progenitor's chemical layers were not completely disrupted by the supernova explosion outside of the remnant's NE and SW high velocity `jet' regions. In addition, we find the majority of O-rich outer ejecta at projected locations out beyond (v = 6500 - 9000 km/s) the remnant's fastest moving Fe-rich X-ray emission material (6000 km/s) seen in Chandra and XMM data along the eastern limb. This suggests that penetration of Fe-rich material up through the S and Si-rich mantle did not extend past the progenitor's N or O-rich outer layers for at least this section of the remnant.

astro-ph↗

arXiv2005

Proper Motions of the HH 47 Jet Observed with the Hubble Space Telescope

We present a proper motion study of the shock waves within the classic stellar jet HH 47 based on Hubble Space Telescope H-alpha and [S II] images of the region taken over two epochs. Individual knots within the jet and in the bow shock/Mach disk working surface of HH 47A move significantly in the five years that separate the images, and the excellent spatial resolution of HST makes it possible to measure the proper motions with enough precision to easily observe differential motions throughout the flow. The bright portion of the jet emerges at 37.5 +/- 2.5 degrees from the plane of the sky with an average velocity of 300 km/s. Dynamical ages of the shock waves in the jet range from a few decades for knots recently ejected by the source to ~ 1300 years for the faint extended bow shock HH 47D. The jet curves, but motions of knots in the jet are directed radially away from the exciting source, and velocity variability in the flow drives the shock waves that heat the jet internally. The jet orientation angle varies with time by about 15 degrees, and currently points to the northwestern portion of a cavity outlined by a reflection nebula, where a quasi-stationary shock deflects the jet. The major working surface HH 47A is more complex than a simple bow shock/Mach disk, and contains numerous clumps that move relative to one another with velocities of ~ +/- 40 km/s. Small clumps or instabilities affect the Mach disk, and dense clumps may move all the way through the working surface to cause the bumpy morphology seen at the bow shock. A localized area between the bow shock and Mach disk varies significantly between the two sets of images.

astro-ph↗

arXiv2005

Quantum cohomology and the k-Schur basis

We prove that structure constants related to Hecke algebras at roots of unity are special cases of k-Littlewood-Richardson coefficients associated to a product of k-Schur functions. As a consequence, both the 3-point Gromov-Witten invariants appearing in the quantum cohomology of the Grassmannian, and the fusion coefficients for the WZW conformal field theories associated to \hat{su}(\ell) are shown to be k-Littlewood Richardson coefficients. From this, Mark Shimozono conjectured that the k-Schur functions form the Schubert basis for the homology of the loop Grassmannian, whereas k-Schur coproducts correspond to the integral cohomology of the loop Grassmannian. We introduce dual k-Schur functions defined on weights of k-tableaux that, given Shimozono's conjecture, form the Schubert basis for the cohomology of the loop Grassmannian. We derive several properties of these functions that extend those of skew Schur functions.

math.CO↗

arXiv2004

Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions

The $k$-Young lattice $Y^k$ is a partial order on partitions with no part larger than $k$. This weak subposet of the Young lattice originated from the study of the $k$-Schur functions(atoms) $s_λ^{(k)}$, symmetric functions that form a natural basis of the space spanned by homogeneous functions indexed by $k$-bounded partitions. The chains in the $k$-Young lattice are induced by a Pieri-type rule experimentally satisfied by the $k$-Schur functions. Here, using a natural bijection between $k$-bounded partitions and $k+1$-cores, we establish an algorithm for identifying chains in the $k$-Young lattice with certain tableaux on $k+1$ cores. This algorithm reveals that the $k$-Young lattice is isomorphic to the weak order on the quotient of the affine symmetric group $\tilde S_{k+1}$ by a maximal parabolic subgroup. From this, the conjectured $k$-Pieri rule implies that the $k$-Kostka matrix connecting the homogeneous basis $\{h_\la\}_{\la\in\CY^k}$ to $\{s_\la^{(k)}\}_{\la\in\CY^k}$ may now be obtained by counting appropriate classes of tableaux on $k+1$-cores. This suggests that the conjecturally positive $k$-Schur expansion coefficients for Macdonald polynomials (reducing to $q,t$-Kostka polynomials for large $k$) could be described by a $q,t$-statistic on these tableaux, or equivalently on reduced words for affine permutations.

math.CO↗

arXiv2001

Tableau atoms and a new Macdonald positivity conjecture

Let $Λ$ be the space of symmetric functions and $V_k$ be the subspace spanned by the modified Schur functions $\{S_λ[X/(1-t)]\}_{λ_1\leq k}$. We introduce a new family of symmetric polynomials, $\{A_λ^{(k)}[X;t]\}_{λ_1\leq k}$, constructed from sums of tableaux using the charge statistic. We conjecture that the polynomials $A_λ^{(k)}[X;t]$ form a basis for $V_k$ and that the Macdonald polynomials indexed by partitions whose first part is not larger than $k$ expand positively in terms of our polynomials. A proof of this conjecture would not only imply the Macdonald positivity conjecture, but would substantially refine it. Our construction of the $A_λ^{(k)}[X;t]$ relies on the use of tableaux combinatorics and yields various properties and conjectures on the nature of these polynomials. Another important development following from our investigation is that the $A_λ^{(k)}[X;t]$ seem to play the same role for $V_k$ as the Schur functions do for $Λ$. In particular, this has led us to the discovery of many generalizations of properties held by the Schur functions, such as Pieri and Littlewood-Richardson type coefficients.

math.QA↗

arXiv2001

Schur function analogs for a filtration of the symmetric function space

We consider a filtration of the symmetric function space given by $Λ^{(k)}_t$, the linear span of Hall-Littlewood polynomials indexed by partitions whose first part is not larger than $k$. We introduce symmetric functions called the $k$-Schur functions, providing an analog for the Schur functions in the subspaces $Λ^{(k)}_t$. We prove several properties for the $k$-Schur functions including that they form a basis for these subspaces that reduces to the Schur basis when $k$ is large. We also show that the connection coefficients for the $k$-Schur function basis with the Macdonald polynomials belonging to $Λ^{(k)}_t$ are polynomials in $q$ and $t$ with integral coefficients. In fact, we conjecture that these integral coefficients are actually positive, and give several other conjectures generalizing Schur function theory.

math.CO↗

arXiv2001

Schur function identities, their t-analogs, and k-Schur irreducibility

We obtain general identities for the product of two Schur functions in the case where one of the functions is indexed by a rectangular partition, and give their t-analogs using vertex operators. We study subspaces forming a filtration for the symmetric function space that lends itself to generalizing the theory of Schur functions and also provides a convenient environment for studying the Macdonald polynomials. We use our identities to prove that the vertex operators leave such subspaces invariant. We finish by showing that these operators act simply on the k-Schur functions, thus leading to a concept of irreducibility for these functions.

math.CO↗

arXiv1998

Tableaux statistics for two part Macdonald polynomials

The Macdonald polynomials expanded in terms of a modified Schur function basis have coefficients called the $q,t$-Kostka polynomials. We define operators to build standard tableaux and show that they are equivalent to creation operators that recursively build the Macdonald polynomials indexed by two part partitions. We uncover a new basis for these particular Macdonald polynomials and in doing so are able to give an explicit description of their associated $q,t$-Kostka coefficients by assigning a statistic in $q$ and $t$ to each standard tableau.

math.CO↗

arXiv1998

Determinantal expressions for Macdonald polynomials

We show that the action of classical operators associated to the Macdonald polynomials on the basis of Schur functions, S_λ[X(t-1)/(q-1)], can be reduced to addition in λ-rings. This provides explicit formulas for the Macdonald polynomials expanded in this basis as well as in the ordinary Schur basis, S_λ[X], and the monomial basis, m_λ[X].

math.CO↗