JetCurry I. Reconstructing Three-Dimensional Jet Geometry from Two-Dimensional Images

2025-05-05 0 0 2.16MB 10 页 10玖币

JetCurry I. Reconstructing Three-Dimensional Jet Geometry from

Two-Dimensional Images

Sailee M. Sawanta,1,Katie Kosaka,c,1,Kunyang Lia,d,1,Sayali S. Avachata,e,1,Eric S. Perlmanaand

Debasis Mitrab

aDepartment of Aerospace, Physics and Space Sciences, Florida Institute of Technology, 150 W. University Blvd., Melbourne, FL, 32901, USA

bDepartment of Computer Engineering and Sciences, Florida Institute of Technology, 150 W. University Blvd., Melbourne, FL, 32901, USA

cPhysics Department, University of Warwick, Coventry, CV4 7AL, UK

dCenter for Relativistic Astrophysics, School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, GA, 30332, USA

eInter-University Centre for Astronomy and Astrophysics, Pune, Maharashtra, 411007, India

ARTICLE INFO

Keywords:

galaxies: jets

galaxies: individual (M87)

methods: numerical

Applied computing: physical sciences

and engineering

Computing methodologies: modeling

and simulation

ABSTRACT

We present a three-dimensional (3-D) visualization of jet geometry using numerical methods based

on a Markov Chain Monte Carlo (MCMC) and limited memory Broyden–Fletcher–Goldfarb–Shanno

(BFGS) optimized algorithm. Our aim is to visualize the 3-D geometry of an active galactic nucleus

(AGN) jet using observations, which are inherently two-dimensional (2-D) images. Many AGN jets

display complex structures that include hotspots and bends. The structure of these bends in the jet’s

frame may appear quite diﬀerent than what we see in the sky frame, where it is transformed by our

particular viewing geometry. The knowledge of the intrinsic structure will be helpful in understanding

the appearance of the magnetic ﬁeld and hence emission and particle acceleration processes over the

length of the jet. We present the JetCurry algorithm to visualize the jet’s 3-D geometry from its 2-D

image. We discuss the underlying geometrical framework and outline the method used to decompose

the 2-D image. We report the results of our 3-D visualization of the jet of M87, using the test case

of the knot D region. Our 3-D visualization is broadly consistent with the expected double helical

magnetic ﬁeld structure of knot D region of the jet. We also discuss the next steps in the development

of the JetCurry algorithm.

1. Introduction

Relativistic jets transport mass and energy from sub-

parsec central regions to Mpc-scale lobes, with a kinetic

power comparable to that of their host galaxies and active

galactic nuclei (AGNs). This profoundly inﬂuences the evo-

lution of the hosts, nearby galaxies, and the surrounding in-

terstellar and intracluster medium (Silk et al.,2012;Fabian,

2012). The generation of such ﬂows is tied to the process

of accretion onto (likely) rotating black holes, where the

magneto-rotational instability can couple the black hole’s

spin and magnetic ﬁeld to the disk or ﬂow to produce high-

latitude outﬂows at speeds close to the speed of light (Meier

et al.,2001). While these jets have a dominant direction of

motion (i.e., outward from the black hole), they often have

bends and features (both stationary and moving) that are

either perpendicular or aligned relative to the jet at some

angle. Deciphering the true nature of these features and

their geometry, relation, and dynamical meaning within the

ﬂow is a diﬃcult problem, as any astronomical images we

acquire are of necessity two-dimensional (2-D) views of

three-dimensional (3-D) objects.

The problem of reconstructing 3-D information from 2-

D images is common to many ﬁelds, but it is particularly

critical in astronomy. In most other cases, e.g., medical

ssawant2011@my.fit.edu (S.M. Sawant)

ORCID(s): 0000-0002-7987-0310 (S.M. Sawant); 0000-0002-0867-8946

(K. Li); 0000-0002-5550-5693 (S.S. Avachat); 0000-0002-3099-1664 (E.S.

Perlman); 0000-0002-4351-1252 (D. Mitra)

1These authors contributed equally.

imaging, one may take images of a source from multiple

viewpoints to aid reconstruction. However, this is not pos-

sible in astronomy, so we must rely on other methods. For

instance, Steﬀen et al. (2011), Wenger et al. (2012), Wenger

et al. (2013), Cormier (2013), Sabatini et al. (2018), and

Lagattuta et al. (2019) used symmetries inherent in, respec-

tively, planetary nebulae and galaxies, plus 2-D images, to

infer and reconstruct 3-D visualizations of these objects.

This ﬁeld is, in fact, rapidly growing in astronomy, as can

be seen by the vast number of subjects explored on the

3DAstrophysics blog2.

In astrophysical jets, the problem is rather diﬀerent.

Unlike in galaxies or planetary nebulae, we cannot make

assumptions such as spherical, elliptical or disk symmetry,

or rotation. However, we can assume a dominant direction of

propagation. As an example of the typical knotted structure

of AGN jets, we show in Figure 1, a broad view of the M87

jet, one of the nearest of the class at 16.7 Mpc distance,

taken from Meyer et al. (2013). In every single image, the

M87 jet shows an amazing complexity of features, including

knots, helical undulations, shocks, and a variety of other

morphological structures, many of which are oriented at

some odd angles with respect to the overall jet direction. As

shown by Meyer et al. (2013), some of the features in the

M87 jet seem to move with apparent velocities up to about

6𝑐within the inner 12.

′′0of the jet, with a general decline

in apparent speed with increasing distance from the nucleus.

However, there are some nearly stationary components that

2https://3dastrophysics.wordpress.com/

Sawant, Kosak, Li, Avachat et al.: Preprint submitted to Elsevier. Accepted. Page 1 of 10

arXiv:2210.03033v1 [astro-ph.HE] 6 Oct 2022

Reconstructing 3-D Jet Geometry

Figure 1: Superluminal motion of the sub-components in

several of the knot regions (I, A, B, and C) of the M87

jet, spanning over 13.25 years of monitoring between 1995-

2008, with the Hubble Space Telescope. The westward direction

lies 20.5◦below the horizontal. The bottom panel depicts

the velocities as vectors from their positions in the jet. The

length of the vectors is proportional to the apparent speed.

Reproduction of Figure 3 from Meyer et al. (2013). Courtesy–

Eileen Meyer.

are largely located near the upstream ends of knots. Addi-

tionally, the polarimetric imaging of Avachat et al. (2016)

shows apparent helical winding structures to the inferred

magnetic ﬁeld vectors in several knots. These features are

clues to complex jet dynamics, but are diﬃcult to interpret

properly.

In this paper, we describe a geometrically based code

that attempts to reconstruct the 3-D structure of jets, starting

from 2-D images. This is an evolving project that in later

stages will attempt to use kinematic information as well as

incorporate special relativistic corrections so that foreshort-

ening, Doppler boosting, and superluminal motion can be

included. Our goal is to provide a ﬁrmer geometrical ground-

ing to these modeling eﬀorts by allowing reconstruction of

a jet’s structure in 3-D.

2. Geometrical Framework

To visualize the geometry of the jet in 3-D, the key

parameters to consider are the distance between any two

features and the apparent angle between them with respect to

the direction of the jet’s axis. The distance between the core

of the jet and the location of interest on the jet is deﬁned

as 𝑠, and the angle of the location to the core is 𝜂. Another

parameter is the line of sight (LOS).

We assumed that the 2-D projection of the jet’s axis

lies along the 𝑥-axis and measured the angles with respect

to the positive 𝑥direction. We considered 𝑠and 𝜂as our

known parameters, which can be directly measured from the

images, i.e., in the sky frame. A third parameter, assumed to

be known (albeit from other information such as a 𝛽vs. 𝜃

plot based on the observed superluminal motion, where 𝛽is

the space velocity and 𝜃is the viewing angle with respect to

the LOS) is the angle the jet’s propagation axis makes with

respect to the LOS.

Following Conway and Murphy (1993), Figure A-1

shows the relevant geometry for a single bend within a jet,

and speciﬁcally how the 2-D sky frame can be related to

the jet’s frame, which is inherently 3-D. All primed points

represent the observed, sky-frame projection we see, with

the components lying at A′and B′in that frame but at points

A and B in the jet’s frame. The point D′is the projection

of B′on the +𝑥axis, and the point D is projection of B on

(𝑥, 𝑧) plane. Angle 𝜂is the angle between segment A′B′and

the +𝑥axis. From point B draw a line BC perpendicular to

the jet axis (OC) and set the ∠CAB as 𝜉. Point C is then

where line BC crosses line OC perpendicularly, so ∠BCA

is 90◦. Segment BC makes an angle 𝜙with the (𝑥, 𝑧) plane

(i.e., ∠BCD = 𝜙). This way, ΔABC is raised oﬀ the (𝑥, 𝑧)

plane through angle 𝜙, while the segment AC still lies in

the (𝑥, 𝑧)plane. Segment AC makes an angle 𝜃with the

LOS, which is assumed to be along the +𝑧axis. The distance

between points A and B in the jet’s frame is 𝑑, while 𝑠is the

projection of 𝑑on the (𝑥, 𝑦) plane, i.e., the distance between

A′and B′. Angle 𝛼is the apex angle of ΔBAD, and 𝛽is the

angle between triangles BAD and FAE. Finally, ΔAGH is

the projection of ΔABD on the (𝑦, 𝑧) plane.

To simplify the algorithm both computationally and

physically, for now we assume that the jet is non-relativistic.

The LOS eﬀects in addition to various relativistic eﬀects can

enhance the intensity and shift the frequency observed, as

well as change the comparison between geometry in the jet

and observer frames (Böttcher,2012). These eﬀects will be

included in the next version of JetCurry.

2.1. Non-linear Parametrized Equations

We used a set of non-linear parametrized equations con-

taining the angles and distances described above. Assuming

the non-relativistic jet ﬂow and using the geometry in Fig-

ure A-1, we derived the following non-linear equations in-

cluding three known parameters (𝑠,𝜂,𝜃), and ﬁve unknown

parameters (𝛼,𝛽,𝜉,𝜙,𝑑).

If a local jet structure has a smaller bend; i.e., 𝜉 < (𝜋

2−𝜃),

the transformation is:

tan𝜂=sin𝜉sin𝜙

cos𝜉sin𝜃+ sin𝜉cos𝜙cos𝜃(1)

d= cos𝛽(2)

(tan𝛽

tan𝛼)2

= cos2𝜂(3)

dcos𝜉cos𝜃=scos𝜂tan𝛼+dsin𝜉cos𝜙sin𝜃(4)

Sawant, Kosak, Li, Avachat et al.: Preprint submitted to Elsevier. Accepted. Page 2 of 10

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

JetCurryI.ReconstructingThree-DimensionalJetGeometryfromTwo-DimensionalImagesSaileeM.Sawanta,1,KatieKosaka,c,1,KunyangLia,d,1,SayaliS.Avachata,e,1,EricS.PerlmanaandDebasisMitrabaDepartmentofAerospace,PhysicsandSpaceSciences,FloridaInstituteofTechnology,150W.UniversityBlvd.,Melbourne,FL,32901,USAbDep...

展开>> 收起<<

JetCurry I. Reconstructing Three-Dimensional Jet Geometry from Two-Dimensional Images.pdf

共10页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

JetCurry I. Reconstructing Three-Dimensional Jet Geometry from Two-Dimensional Images

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: