A. Bailey | Searcharxiv

arXiv2022

Type Ia Supernova cosmology combining data from the $Euclid$ mission and the Vera C. Rubin Observatory

The $Euclid$ mission will provide first-of-its-kind coverage in the near-infrared over deep (three fields, $\sim$10-20 square degrees each) and wide ($\sim$10000 square degrees) fields. While the survey is not designed to discover transients, the deep fields will have repeated observations over a two-week span, followed by a gap of roughly six months. In this analysis, we explore how useful the deep field observations will be for measuring properties of Type Ia supernovae (SNe Ia). Using simulations that include $Euclid$'s planned depth, area and cadence in the deep fields, we calculate that more than 3700 SNe between $0.0 0.8$. Furthermore, we predict how well additional $Euclid$ mock data can be used to constrain a key systematic in SN Ia studies - the size of the luminosity 'step' found between SNe hosted in high mass ($>10^{10} M_{\odot}$) and low mass ($>10^{10} M_{\odot}$) galaxies. This measurement has unique information in the rest-frame NIR. We predict that if the step is caused by dust, we will be able to measure its reduction in the NIR compared to optical at the 4$\sigma$ level. We highlight that the LSST and $Euclid$ observing strategies used in this work are still provisional and some level of joint processing is required. Still, these first results are promising, and assuming $Euclid$ begins observations well before the Nancy Roman Space Telescope (Roman), we expect this dataset to be extremely helpful for preparation for Roman itself.

astro-ph.CO↗

arXiv2010

Nonuniform sampling and recovery of multidimensional bandlimited functions by Gaussian radial-basis functions

Let $S\subset\R^d$ be a bounded subset with positive Lebesgue measure. The Paley-Wiener space associated to $S$, $PW_S$, is defined to be the set of all square-integrable functions on $\R^d$ whose Fourier transforms vanish outside $S$. A sequence $(x_j:j\kin\N)$ in $\R^d$ is said to be a Riesz-basis sequence for $L_2(S)$ (equivalently, a complete interpolating sequence for $PW_S$) if the sequence $(e^{-i\la x_j,\cdot\ra}:j\kin\N)$ of exponential functions forms a Riesz basis for $L_2(S)$. Let $(x_j:j\kin\N)$ be a Riesz-basis sequence for $L_2(S)$. Given $λ>0$ and $f\in PW_S$, there is a unique sequence $(a_j)$ in $\ell_2$ such that the function $$ I_λ(f)(x):=\sum_{j\in\N}a_je^{-λ\|x-x_j\|_2^2}, \qquad x\kin\R^d, $$ is continuous and square integrable on $\R^d$, and satisfies the condition $I_λ(f)(x_n)=f(x_n)$ for every $n\kin\N$. This paper studies the convergence of the interpolant $I_λ(f)$ as $λ$ tends to zero, {\it i.e.,\} as the variance of the underlying Gaussian tends to infinity. The following result is obtained: Let $δ\in(\sqrt{2/3},1]$ and $0<β<\sqrt{3δ^2 -2}$. Suppose that $δB_2\subset Z\subset B_2$, and let $(x_j:j\in\N)$ be a Riesz basis sequence for $L_2(Z)$. If $f\in PW_{βB_2}$, then $f=\lim_{λ\to 0^+} I_λ(f)$ in $L_2(\R^d)$ and uniformly on $\R^d$. If $δ=1$, then one may take $β$ to be 1 as well, and this reduces to a known theorem in the univariate case. However, if $d\ge2$, it is not known whether $L_2(B_2)$ admits a Riesz-basis sequence. On the other hand, in the case when $δ<1$, there do exist bodies $Z$ satisfying the hypotheses of the theorem (in any space dimension).

math.CA↗