arXiv subjects

Martijn de Vries

Publications and source records attributed to Martijn de Vries.

15 recordsLinked to original sources

arXiv2022

Chandra measurements of gas homogeneity and turbulence at intermediate radii in the Perseus Cluster

We present a Chandra study of surface brightness fluctuations in the diffuse intracluster medium of the Perseus Cluster. Our study utilizes deep, archival imaging of the cluster core as well as a new mosaic of 29 short 5 ks observations extending in 8 different directions out to radii of r_500 ~ 2.2r_2500. Under the assumption that the distribution of densities at a given radius is log-normally distributed, two important quantities can be derived from the width of the log-normal density distribution on a given spatial scale: the density bias, which is equal to the square root of the clumping factor C; and the one-component turbulent velocity, v_(k, 1D). We forward-model all contributions to the measured surface brightness, including astrophysical and particle background components, and account for the Poisson nature of the measured signal. Measuring the distribution of surface brightness fluctuations in 1 arcmin^2 regions, spanning the radial range 0.3-2.2 r_2500 (7.8-57.3 arcmin), we find a small to moderate average density bias of around 3% at radii below 1.6r_2500. We also infer an average turbulent velocity at these radii of v_1D <400 km s^-1. Direct confirmation of our results on turbulent velocities inferred from surface brightness fluctuations should be possible using the X-ray calorimeter spectrometers to be flown aboard the XRISM and Athena. observatories.

astro-ph.HE↗

arXiv2022

A Quarter Century of Guitar Nebula/Filament Evolution

We have collected a new deep {\it Chandra X-ray Observatory} ({\it CXO}) exposure of PSR B2224+65 and the `Guitar Nebula', mapping the complex X-ray structure. This is accompanied by a new {\it HST} H$α$ image of the head of the Guitar. Comparing the {\it HST} and {\it CXO} structures in 4 epochs over 25 years, we constrain the evolution of the TeV particles that light up the filament. Cross-field diffusion appears to be enhanced, likely by the injected particles, behind the filament's sharp leading edge, explaining the filament width and its evolving surface brightness profile.

astro-ph.HE↗

arXiv2022

Topology of univoque sets in real base expansions

Given a positive integer $M$ and a real number $q \in (1,M+1]$, an expansion of a real number $x \in \left[0,M/(q-1)\right]$ over the alphabet $A=\{0,1,\ldots,M\}$ is a sequence $(c_i) \in A^{\mathbb N}$ such that $x=\sum_{i=1}^{\infty}c_iq^{-i}$. Generalizing many earlier results, we investigate in this paper the topological properties of the set $U_q$ consisting of numbers $x$ having a unique expansion of this form, and the combinatorial properties of the set $U_q'$ consisting of their corresponding expansions. We also provide shorter proofs of the main results of Baker in [B] by adapting the method given in [EJK] for the case $M=1$.

math.CO↗

arXiv2022

The Long Filament of PSR J2030+4415

New X-ray and optical observations shed light on the remarkable X-ray filament of the Gamma-ray pulsar PSR~J2030+4415. Images of the associated H$α$ bow shock's evolution over the past decade compared with its velocity structure provide an improved kinematic distance of $\sim$0.5kpc. These velocities also imply that the pulsar spin axis lies $\sim 15^\circ$ from the proper motion axis which is close to the plane of the sky. The multi-bubble shock structure indicates that the bow shock stand-off was compressed to a small value $\sim 20-30$y ago when the pulsar broke through the bow shock to its present bubble. This compression allowed multi-TeV pulsar $e^\pm$ to escape to the external ISM, lighting up an external magnetic field structure as the `filament'. The narrow filament indicates excellent initial confinement and the full $15^\prime$ ($2.2$~pc=7~lt-y) projected length of the filament indicates rapid $e^\pm$ propagation to its end. Spectral variation along the filament suggests that the injected particle energy evolved during the break-through event.

astro-ph.HE↗

arXiv2020

PSR J1709-4429's Proper Motion and its Relationship to SNR G343.1-2.3

We have obtained a deep 670 ks CXO ACIS image of the remarkable pulsar wind nebula (PWN) of PSR J1709-4429, in 4 epochs during 2018-2019. Comparison with an archival 2004 data set provides a pulsar proper motion mu = 13 \pm 3 mas/yr at a PA of 86 \pm 9 degree (1 sigma combined statistical and systematic uncertainties), precluding birth near the center of SNR G343.1-2.3. At the pulsar's characteristic age of 17 kyr, the association can be preserved through a combination of progenitor wind, birth kick and PWN outflow. Associated TeV emission may, however, indicate explosion in an earlier supernova. Inter-epoch comparison of the X-ray images shows that the PWN is dynamic, but we are unable to conclusively measure flow speeds from blob motion. The pulsar has generated a radio/X-ray wind bubble, and we argue that the PWN's long narrow jets are swept back by shocked pulsar wind venting from this cavity. These jets may trace the polar magnetic field lines of the PWN flow, an interesting challenge for numerical modeling.

astro-ph.HE↗

arXiv2020

PSR J2030+4415's Remarkable Bow Shock, PWN and Filament

We report on new X-ray and optical observations of PSR J2030+4415, a Gamma-ray Pulsar with an H$α$ bow shock. These data reveal the velocity structure of the bow shock apex and resolve unusual X-ray structure in its interior. In addition the system displays a very long, thin filament, extending at least $5^\prime$ at $\sim 130^\circ$ to the pulsar motion vector. Careful astrometry, compared with a short archival exposure, detects the pulsar proper motion at 85 mas yr$^{-1}$. With the H$α$ velocity structure this allows us to estimate the distance as $0.75$ kpc.

astro-ph.HE↗

arXiv2020

The X-Ray Cavity Around Hotspot E in Cygnus A: Tunneled by a Deflected Jet

The powerful FR II radio galaxy Cygnus A exhibits primary and secondary hotspots in each lobe. A 2 Msec Chandra X-ray image of Cygnus A has revealed an approximately circular hole, with a radius of 3.9 kpc, centered on the primary hotspot in the eastern radio lobe, hotspot E. We infer the distribution of X-ray emission on our line-of-sight from an X-ray surface brightness profile of the radio lobe adjacent to the hole and use it to argue that the hole is excavated from the radio lobe. The surface brightness profile of the hole implies a depth at least 1.7 $\pm$ 0.3 times greater than its projected width, requiring a minimum depth of 13.3 $\pm$ 2.3 kpc. A similar hole observed in the 5 GHz VLA radio map reinforces the argument for a cavity lying within the lobe. We argue that the jet encounters the shock compressed intracluster medium at hotspot E, passing through one or more shocks as it is deflected back into the radio lobe. The orientation of Cygnus A allows the outflow from hotspot E to travel almost directly away from us, creating an elongated cavity, as observed. These results favor models for multiple hotspots in which an FR II jet is deflected at a primary hotspot, then travels onward to deposit the bulk of its power at a secondary hotspot, rather than the dentist drill model.

astro-ph.HE↗

arXiv2018

Simulations of the merging cluster of galaxies Cygnus A

The archetype FR-II galaxy Cygnus A lies in a moderately rich cluster about to undergo a major merger. We study the pre-merger Cygnus cluster environment using smoothed particle hydrodynamics simulations constrained by 2Ms of Chandra observations of the hot intracluster medium. The observations constrain the total gravitating mass and concentration parameter, and the simulations provide the quiescent and merger-enhanced temperature profiles of the pre- and post merger of the cluster excluding the central active galactic nucleus. We present the first detailed model of the sub cluster north west of Cygnus A, named CygNW. We find a lower baryon fraction and higher concentration parameter for CygA than expected from known scaling relations in the literature. The model suggests the Cygnus cluster hosts a pre-merger with a progenitor mass ratio of about 1.5:1 at the virial radius. We notice that the intra cluster medium is heated as a result of the merger, but we find no evidence for a (pre-)merger shock in the interstitial region between both cluster haloes. We attribute the merger-induced heating to compression of the cluster outskirts. The smooth model obtained from our simulations is subtracted from the observed cluster state and shows residual temperature structure that is neither hydrostatic nor merger-heated cluster gas. We speculate that this residual heating may result from previous AGN activity over the last ~100 Myr.

astro-ph.HE↗

arXiv2018

Signatures of multiple episodes of AGN activity in the core of Abell 1795

In this paper we analyze AGN activity signatures in the rich nearby galaxy cluster Abell 1795 aiming to confirm and characterize the long-term feedback history in the system. We combine radio observations at 610 and 235 MHz from the Giant Metrewave Radio Telescope (GMRT) with 3.4 Msec X-ray data from the Chandra Observatory. Extracting radial temperature profiles, as well as X-ray and radio surface brightness profiles in three directions showing major morphological disturbances, we highlight the signatures of activity in the system. For the first time we observe radio emission corresponding to the NW X-ray depression, which provides evidence in favor of the classification of the depression as a cavity. We identify two other X-ray cavities situated NW and SW of the AGN. While the central radio emission corresponding to the inner cavities shows flatter spectral index, the radio extensions associated with the furthest X-ray cavities consist of aged plasma. All observed signatures both in radio and X-ray are consistent with several consecutive episodes of AGN activity, which gave rise to the observed morphology NW and SW from the core. In the southern region, we confirm the cooling wake hypothesis for the origin of the long tail. The deep X-ray data also allows us to distinguish significant distortions in the tail's inner parts, which we attribute to the activity of the AGN.

astro-ph.GA↗

arXiv2018

The Cocoon Shocks of Cygnus A: Pressures and Their Implications for the Jets and Lobes

We use 2.0 Msec of Chandra observations to investigate the cocoon shocks of Cygnus A and some implications for its lobes and jet. Measured shock Mach numbers vary in the range 1.18-1.66 around the cocoon. We estimate a total outburst energy of $\simeq 4.7\times10^{60}\rm\ erg$, with an age of $\simeq 2 \times 10^{7}\rm\ yr$. The average postshock pressure is found to be $8.6 \pm 0.3 \times 10^{-10}\rm\ erg\ cm^{-3}$, which agrees with the average pressure of the thin rim of compressed gas between the radio lobes and shocks, as determined from X-ray spectra. However, average rim pressures are found to be lower in the western lobe than in the eastern lobe by $\simeq 20\%$. Pressure estimates for hotspots A and D from synchrotron self-Compton models imply that each jet exerts a ram pressure $\gtrsim$ 3 times its static pressure, consistent with the positions of the hotspots moving about on the cocoon shock over time. A steady, one-dimensional flow model is used to estimate jet properties, finding mildly relativistic flow speeds within the allowed parameter range. Models in which the jet carries a negligible flux of rest mass are consistent with with the observed properties of the jets and hotspots. This favors the jets being light, implying that the kinetic power and momentum flux are carried primarily by the internal energy of the jet plasma rather than by its rest mass.

astro-ph.HE↗

arXiv2017

Univoque bases and Hausdorff dimension

Given a positive integer $M$ and a real number $q >1$, a \emph{$q$-expansion} of a real number $x$ is a sequence $(c_i)=c_1c_2\cdots$ with $(c_i) \in \{0,\ldots,M\}^\infty$ such that \[x=\sum_{i=1}^{\infty} c_iq^{-i}.\] It is well known that if $q \in (1,M+1]$, then each $x \in I_q:=\left[0,M/(q-1)\right]$ has a $q$-expansion. Let $\mathcal{U}=\mathcal{U}(M)$ be the set of \emph{univoque bases} $q>1$ for which $1$ has a unique $q$-expansion. The main object of this paper is to provide new characterizations of $\mathcal{U}$ and to show that the Hausdorff dimension of the set of numbers $x \in I_q$ with a unique $q$-expansion changes the most if $q$ "crosses" a univoque base. Denote by $\mathcal{B}_2=\mathcal{B}_2(M)$ the set of $q \in (1,M+1]$ such that there exist numbers having precisely two distinct $q$-expansions. As a by-product of our results, we obtain an answer to a question of Sidorov (2009) and prove that \[\dim_H(\mathcal{B}_2\cap(q',q'+δ))>0\quad\textrm{for any}\quad δ>0,\] where $q'=q'(M)$ is the Komornik-Loreti constant.

math.NT↗

arXiv2011

Optimal expansions in non-integer bases

For a given positive integer $m$, let $A=\set{0,1,...,m}$ and $q \in (m,m+1)$. A sequence $(c_i)=c_1c_2 ...$ consisting of elements in $A$ is called an expansion of $x$ if $\sum_{i=1}^{\infty} c_i q^{-i}=x$. It is known that almost every $x$ belonging to the interval $[0,m/(q-1)]$ has uncountably many expansions. In this paper we study the existence of expansions $(d_i)$ of $x$ satisfying the inequalities $\sum_{i=1}^n d_iq^{-i} \geq \sum_{i=1}^n c_i q^{-i}$, $n=1,2,...$ for each expansion $(c_i)$ of $x$.

math.NT↗

arXiv2010

A two-dimensional univoque set

Let $\mathbf{J} \subset \mathbb{R}^2$ be the set of couples $(x,q)$ with $q>1$ such that $x$ has at least one representation of the form $x=\sum_{i=1}^{\infty} c_i q^{-i}$ with integer coefficients $c_i$ satisfying $0 \leq c_i < q$, $i \ge 1$. In this case we say that $(c_i)=c_1c_2...$ is an expansion of $x$ in base $q$. Let $\mathbf{U}$ be the set of couples $(x,q) \in \mathbf{J}$ such that $x$ has exactly one expansion in base $q$. In this paper we deduce some topological and combinatorial properties of the set $\mathbf{U}$. We characterize the closure of $\mathbf{U}$, and we determine its Hausdorff dimension. For $(x,q) \in \mathbf{J}$, we also prove new properties of the lexicographically largest expansion of $x$ in base $q$.

math.NT↗

arXiv2009

On the number of unique expansions in non-integer bases

Let $q > 1$ be a real number and let $m=m(q)$ be the largest integer smaller than $q$. It is well known that each number $x \in J_q:=[0, \sum_{i=1}^{\infty} m q^{-i}]$ can be written as $x=\sum_{i=1}^{\infty}{c_i}q^{-i}$ with integer coefficients $0 \le c_i < q$. If $q$ is a non-integer, then almost every $x \in J_q$ has continuum many expansions of this form. In this note we consider some properties of the set $\mathcal{U}_q$ consisting of numbers $x \in J_q$ having a unique representation of this form. More specifically, we compare the size of the sets $\mathcal{U}_q$ and $\mathcal{U}_r$ for values $q$ and $r$ satisfying $1< q < r$ and $m(q)=m(r)$.

math.NT↗

arXiv2008

Unique expansions of real numbers

It was discovered some years ago that there exist non-integer real numbers $q>1$ for which only one sequence $(c_i)$ of integers $c_i \in [0,q)$ satisfies the equality $\sum_{i=1}^\infty c_iq^{-i}=1$. The set of such "univoque numbers" has a rich topological structure, and its study revealed a number of unexpected connections with measure theory, fractals, ergodic theory and Diophantine approximation. In this paper we consider for each fixed $q>1$ the set $\mathcal{U}_q$ of real numbers $x$ having a unique representation of the form $\sum_{i=1}^\infty c_iq^{-i}=x$ with integers $c_i$ belonging to $[0,q)$. We carry out a detailed topological study of these sets. For instance, we characterize their closures, and we determine those bases $q$ for which $\mathcal{U}_q$ is closed or even a Cantor set. We also study the set $\mathcal{U}_q'$ consisting of all sequences $(c_i)$ of integers $c_i \in [0,q)$ such that $\sum_{i=1}^{\infty} c_i q^{-i} \in \mathcal{U}_q$. We determine the numbers $r >1$ for which the map $q \mapsto \mathcal{U}_q'$ (defined on $(1, \infty)$) is constant in a neighborhood of $r$ and the numbers $q >1$ for which $\mathcal{U}_q'$ is a subshift or a subshift of finite type.

math.NT↗