Taiji: China’s Space-based Gravitational-Wave Program

He WANG

On behave of Taiji Scientific Collaboration

International Centre for Theoretical Physics Asia-Pacific (ICTP-AP)
University of Chinese Academy of Sciences (UCAS)

@The University of Maryland, Washington, DC

From Taiji-1 heritage to full-mission development and data-analysis preparation

Taiji: China’s Space-based Gravitational-Wave Program

He WANG

International Centre for Theoretical Physics Asia-Pacific (ICTP-AP)
University of Chinese Academy of Sciences (UCAS)

@The University of Maryland, Washington, DC

From Taiji-1 heritage to full-mission engineering and data-analysis preparation

Section 0 — Opening

1. Taiji/TJ: China’s Space-borne Gravitational-Wave Program and Science Readiness
2. A brief history: from early studies to Taiji-1 in-orbit heritage
3. Three scientific frontiers: astrophysics, cosmology, and fundamental physics

Section 1 — Science and mission concept

1. The millihertz window: source classes and discovery space
2. Taiji/TJ full-mission concept
3. From Taiji-1 heritage to full-mission preparation

Section 2 — Taiji-1 heritage

1. Taiji-1: in-orbit technology demonstration
2. Taiji-1 beyond technology: global gravity-field output

Section 3 — Key enabling technologies

1. Eight key technology areas for full-mission readiness
2. Optical metrology and inter-satellite laser link
3. Inertial reference, micro-propulsion, and drag-free control
4. Ultra-stable platform and environmental coupling
5. System integration: MOSA, drag-free semi-physical verification, and three-arm interferometry

Section 4 — Data-analysis readiness

1. Why data challenges are mission-critical
2. Taiji Data Challenge: full-chain simulation and mock datasets
3. Data preprocessing: TDI, calibration, and detector characterization
4. Science data analysis: source pipelines, global fit, and population products

Section 5 — Science examples

1. Galactic compact binaries: verification sources, foreground, and Milky Way structure
2. Massive black holes: seeds, growth, and assembly history
3. EMRIs/IMRIs and strong-field gravity
4. Stochastic backgrounds, cosmology, and fundamental physics

【如果时间紧，这四页 science examples 可以压缩成两页。】

Section 6 — Network science

1. From Taiji/TJ to network science: LISA-Taiji-TianQin synergies
2. Network science as population inference: the origin of SMBHs
3. Summary and outlook

1. Taiji: China’s Space-based Gravitational-Wave Program
2. The millihertz window: sources and science questions
3. Primary science targets of Taiji/TJ
    
4. Mission concept: a heliocentric triangular constellation
5. A staged roadmap: from Taiji-1 to a full three-satellite mission
6. Taiji-1: in-orbit technology-demonstration heritage
7. Toward Taiji-2 and full mission readiness
    
8. The measurement chain: from test masses to science data
9. Inter-satellite interferometry and laser-link development
10. Acquisition, tracking and pointing over million-kilometer baselines
11. Inertial sensing, micro-thrusters and drag-free control
12. Stable platform and environmental coupling
13. Ground-based equivalent verification and system integration
     
14. Why data challenges are mission-critical
15. Taiji Data Challenge: full-chain simulation pipeline
16. Mock datasets: from L0 raw data to source-level products
17. The global-fit challenge: multi-source, multi-noise, high-dimensional inference
18. Prototype analysis modules: MBHB, GB, SGWB/noise
     
19. From Taiji to network science: LISA-Taiji-TianQin synergies
20. Open interfaces for international collaboration
21. Summary and outlook

A brief history: from early studies to Taiji-1 in-orbit heritage

Wen-Rui Hu , Yue-Liang Wu, Natl. Sci. Rev. Vol 4 (2017)

Yue-Liang Wu et al., Commun. Phys. 4, 34 (2021)

2008

—   CAS initiated early studies on space-based gravitational-wave          detection.

2010

—   Early national proposal for space-based GW observation.

—   Taiji was publicly introduced to the international community.

2016

—   Taiji-1 was approved and launched as an in-orbit                  technology demonstrator.

2018-2019

—   Overall mission design and development roadmap              were published.

2021

—   Current focus: engineering preparation, system-level verification, data challenges, and science-pipeline development.

2025-2026

Taiji/TJ has evolved from early conceptual studies to in-orbit technology heritage and is now moving toward full-mission engineering and science-data readiness.

Three Scientific Frontiers

Astrophysics, cosmology, and fundamental physics in the mHz band

Astrophysics

• Massive black holes and host-galaxy co-evolution
• Black-hole seeds and intermediate-mass black holes
• Galactic compact binaries and Milky Way structure
• Environments of massive black holes

Cosmology

• Cosmic expansion history and standard sirens
• Hubble constant tension
• Early-universe phase transitions
• Dark matter and stochastic backgrounds

Fundamental Physics

• Strong-field dynamics of black holes
• No-hair theorem and ringdown tests
• Tests of gravity beyond general relativity
• Black-hole horizons and exotic compact objects

Taiji/TJ is motivated by three broad frontiers: black-hole astrophysics, cosmology, and fundamental physics.

The millihertz window

From Galactic binaries to massive black holes, stochastic backgrounds, and unknown sources

HW, Minghui Du et al., Sci Sin-Phys Mech Astron 54, 270403 (2024)

Taiji/TJ targets a broad range of mHz sources: Galactic compact binaries, MBHB/IMBH mergers, EMRIs/IMRIs, stellar-mass BBHs, stochastic backgrounds, and unknown sources.

Galactic Compact Binaries

Verification binaries,
DWDs, and the
Milky Way foreground

Massive & Intermediate BHs

EMRIs / IMRIs

Stellar-Mass Compact Binaries

Stochastic Backgrounds

Unknown Sources

MBHB mergers,
black-hole seeds, and
galaxy co-evolution

Precision probes of
massive BHs and
strong-field gravity

Long inspirals before
LVK; multiband GW astronomy

Astrophysical
foregrounds and
early-universe phase
transitions

Discovery space for
unmodeled and
unexpected signals

Baseline full-mission concept

• Three drag-free spacecraft forming a near-equilateral triangular constellation
• Arm length: \(3\times 10^6\) km
• Heliocentric orbit, leading/trailing the Earth by  ~\(20^\circ\)
• Laser displacement sensitivity: \(8\,\mathrm{pm}/\sqrt{\mathrm{Hz}}\)
• Test-mass acceleration noise: \(3 \times 10^{-15}\,\mathrm{m\,s^{-2}}/\sqrt{\mathrm{Hz}}\)

Taiji/TJ Full-Mission Concept

A heliocentric triangular constellation for mHz gravitational-wave astronomy

Credit: Shucheng Yang

Mission idea: use million-kilometer laser interferometry to measure differential optical-path changes between free-falling test masses.

Ground-based drag-free spacecraft simulator for semi-physical verification

2008-2016

2018-2019

2020-2023

2024-2026

From Taiji-1 heritage to full-mission preparation

Early studies and
mission formulation

Taiji-1 in-orbit
heritage

Key technology
maturation

Full-mission
engineering
preparation

concept · proposal ·
public introduction

technology demo ·
launch · in-orbit
validation

drag-free · laser
interferometry ·
phasemeter ·
grav. reference sensor

integration · verification · data challenges

1. Taiji-1 (2019)

发射“太极一号”单星
目标：验证技术路线可行性
干涉测距指标：100pm/Hz1/2量级
加速度噪声指标：3×10-9ms-2/Hz1/2

Stage 2 — Taiji-1 in-orbit heritage

2019: Taiji-1 technology demonstration and geodetic output

* single-satellite technology demonstration；
* laser interferometry, GRS, micro-thrusters, drag-free control, thermal control；
* global gravity field / geoid model as a scientific-geodetic output.

2. Taiji-2 (202x)
发射“太极二号”卫星
目标：日心轨道高精度控制与星间高精度干涉测量关键技术
干涉测距指标：xx pm/Hz1/2量级
加速度噪声指标：xx m s-2/Hz1/2量级

The historical Taiji-1/2/3 roadmap has evolved into a more engineering-oriented path toward a full three-satellite science mission. The current emphasis is no longer simply the next technology demonstrator, but system-level design, integration, verification, and data-analysis readiness for the full mission concept.

    From Taiji-1 heritage to full-mission preparation

1. Taiji-1 (2019)

发射“太极一号”单星
目标：验证技术路线可行性
干涉测距指标：100pm/Hz1/2量级
加速度噪声指标：3×10-9ms-2/Hz1/2

• Launched in 2019 as a technology demonstrator for space-based GW detection.

Taiji-1: in-orbit technology demonstration

Single-satellite validation of key payload and control technologies

Drag-free test: residual acceleration before/after control-loop closure

Source: Taiji Scientific Collaboration, Communications Physics 4, 34 (2021)

Take-away: Taiji-1 was not a full GW detector, but it provided in-orbit heritage for the measurement and control technologies required by Taiji/TJ.

Yue-Liang Wu et al., Microgravity Sci., Technol. 34, 77 (2022). arXiv:2203.05876

Taiji-1 observations enabled the construction of a global gravity-field model: TJGM-r1911

Taiji-1 beyond technology: global gravity-field output

From in-orbit precision measurement to geodetic science

Geoid height anomalies from TJGM-r1911

Geoid height differences relative to EGM2008

PUBLISHED GEODETIC RESULT

GLOBAL GRAVITY-FIELD MODEL

COMPARISON WITH REFERENCE MODEL

Global Gravity Field Model from Taiji-1 Observations

Model: TJGM-r1911

Take-away: Taiji-1 demonstrated broader precision-measurement capability beyond technology validation, producing a concrete geodetic science output.

Toward Taiji-2 and full mission readiness

• Progress: Taiji-2
  • Taiji-2 just finished phase A study, all technologies is now TRL 5 or above according to 《ISO 16290》.  Ready to be approved to enter phase B1。Helio-centric, millions of kilometers arm
  • The engineering model of payloads（ATP、interferometer、inertial sensor、drag-free、SC…）were experimentally tested。

TJ-1 比较重要的科学产出（如技术验证+全球重力场）

• Target: Taiji-3
  • 白皮书

The measurement chain: from test masses to science data

L0: 原始激光干涉测量数据

TDI处理

L1: TDI科学数据

L2,3: 波源及参数目录

Inter-satellite interferometry and laser-link development

Interferometer

• Optical bonding
• Precise positioning
• Two 1:1 models
• Establishing laser link and test
• Phase-meter

• Deviation: 42 μrad, 9 μm

• Noise PSD: 6pm/Hz\(^{1/2}\)

• Phase meter: 1μrad/Hz\(^{1/2}\)

• Laser head, amplifier, FP locking
  

• 6Hz/Hz\(^{1/2}\), 4W, 10\(^{-4}\)/Hz\(^{1/2}\)

• Mirror
• Structure
• Invar steel, silicon carbide ……

• λ/100, 10pm/Hz\(^{1/2}\)

Acquisition, tracking and pointing over million-kilometer baselines

Taiji R&D progress —— ATP

• Acquisition with camera
• Pointing with DWS
• Archimedes spiral

• Acquisition 0.1μrad
• Pointing 20.25 nrad/Hz\(^{1/2}\)

• Field (out of telescope 100×) 6.23μrad (1d), 5.4μrad (2d); θ deviation (out of telescope 100×) 4.4 nrad(1d), 6.8nrad(2d); longitudinal noise 8.3pm/Hz\(^{1/2}\) (1d), 8.5pm/Hz\(^{1/2}\) (2d)

• Pointing ahead angle mechanism (1 dimensional & 2 dimensional)

Technologies: phase-locking amplification

• Millions of Kilometers、nano radian tracking & pointing
• Uncertain cone (mrad), precision (nrad), 6 orders of magnitude
• Multi-steps: star tracking, acquisition with camera, DWS

Inertial sensing, micro-thrusters and drag-free control

Technologies: drag-free

• Solar wind and radiation, need to be compensated
• Drag free——measure、feed back，net force zero on SC
• Core payload——inertial sensor

Technologies: inertial sensor

• Component：TM+Cage、capacitive sensing+electrostatic actuation、charge management、locking and releasing mechanism
  
• Locking and releasing (lock during launch，release on orbit，5μm/s，100μrad/s)；various noises to deal with
• obstacles：electrostatic force very small、surface adhesion
  

Stable platform and environmental coupling

Technologies: stable platform

• The spacecraft highly coupled to the payloads。
• Stable platform（self gravity、thermal、residue magnetic field…）。
• Self gravity：gravitational stiffness and gravitational bias around TMs

Ground-based equivalent verification and system integration

From key technologies to full-mission engineering​ readiness

One mission-design track and three system-verification tracks

SUPPORTING KEY TECHNOLOGY

TRL 5

TRL 6

TRL 5

TRL 5

TRL 5

under validation

TRL 6-7

under validation

Scientific interferometer full-chain verification

Three-arm interferometry · inertial reference · ranging / optical-path simulation · TDI-related noise suppression · long-duration stability

FULL-CHAIN VERIFICATION

Core measurement-system integration

MOSA-level integration of GRS, optical metrology, laser-link acquisition, and pointing subsystems

PAYLOAD INTEGRATION

Mission and engineering design

Launch · orbit · transfer · TT&C · spacecraft–payload interfaces · science operations · data-processing design

MISSION DESIGN

Take-away: System-level verification is the bridge from key-technology maturity to full-mission readiness.

Spacecraft / payload system

1. Inter-satellite laser interferometry
2. Acquisition, tracking and pointing
3. Gravitational reference sensor
4. Micro-propulsion
5. Drag-free control
6. Ultra-clean / ultra-precise / ultra-stable platform

Science application system
7. Noise suppression and signal inversion
8. End-to-end dynamic simulation

Optical metrology and laser-link acquisition

From component performance to link-level measurement stability

Interferometer noise: representative ground-test result

Interferometer optical bench (engineering model)

ATP acquisition and tracking experiment platform

Engineering-model and ground-test results. Full mission performance requires integrated system-level verification.

Take-away: Optical metrology is being developed toward a coupled laser-link measurement chain.

Optical metrology and laser link

Optical metrology is being developed not only as a set of components, but as a link-level measurement chain involving laser stability, phasemeter performance, acquisition/tracking/pointing, and pointing-noise control.

• 超稳激光器：采用光纤延长线+超稳腔结合的技术稳频，采用MOPA技术进行光放大；完成工程样机研制及环境实验，频稳达到6Hz/Hz1/2（ 30Hz/Hz1/2 ），输出功率大于4W（2W）
• 干涉仪：采用光粘及高精度装调技术完成全功能工程样机研制，开展力、热环境实验；平台内干涉精度1pm/Hz1/2（1pm/Hz1/2），十米平台间50nm/Hz1/2，TDI后1.6pm /Hz1/2（5pm/Hz1/2）
• 相位计：采用数字锁相环（DPLL）技术和峰值查找算法，研制完成具有频率信息捕获功能的工程样机，在2-20MHz内可自动捕获和测量，精度达到1μrad/Hz1/2（ 6μrad/Hz1/2 ）

• 捕获跟瞄：采用扫描-捕获-跟瞄多级捕获策略，在十米平台上完成捕获跟瞄双平台搭建和全流程调试，捕获精度达到0.1μrad/Hz1/2（ 1μrad/Hz1/2 ），跟瞄精度21nrad/Hz1/2（ 30nrad/Hz1/2 ）
• 超前瞄准机构：利用新型柔性铰链实现无光程差镜面偏转；基于新型可伸缩压电堆叠和电容传感实现低噪声压电驱动；研制工程样机，光程噪声实测小于8pm/Hz1/2（1pm/Hz1/2）
• 指向噪声评估：基于超前指向静态偏差和激光指向抖动的实测结果，评估激光指向稳定性噪声2.1pm/Hz1/2（2pm/Hz1/2）

Inertial reference and drag-free spacecraft control

From test-mass sensing to closed-loop spacecraft control

GRAVITATIONAL REFERENCE SENSOR

COLD-GAS MICRO-PROPULSION

DRAG-FREE CONTROL

Axis coupling coefficient:

Electrode symmetry:

Displacement readout:

Drive-voltage stability:

Release residual velocity:

Release angular velocity:

\(< 9  \times10^{-5}\)  (req. \(10^{-4}\))

\(< 15  \mu\mathrm{m}\)  (req. \(150  \mu\mathrm{m}\))

\(1.7  \mathrm{nm}/\sqrt{\mathrm{Hz}}\)  (req. \(3  \mathrm{nm}/\sqrt{\mathrm{Hz}}\))

\(3.3  \mathrm{ppm}/\sqrt{\mathrm{Hz}}\)

\(4  \mu\mathrm{m}/s\)  (req. \(20  \mu\mathrm{m}/s\))

\(86  \mu\mathrm{rad}/s\)  (req.  \(400  \mu\mathrm{rad}/s\))

Thrust noise:

Thrust resolution:

Response time:

\(0.02  \mu \mathrm{N}/\sqrt{\mathrm{Hz}}\)  (req. \(0.1  \mu \mathrm{N}/\sqrt{\mathrm{Hz}}\))

\(0.05  \mu\mathrm{N}\)  (req.  \(0.1  \mu\mathrm{N}\))

\(<120  \mathrm{ms}\)  (req.  \(150  \mathrm{ms}\))

SENSING & ACTUATION

FAST-RESPONSE ACTUATION

CLOSED-LOOP VERIFICATION

Engineering-model and ground-test results. Residual acceleration figure refers to numerical simulation; full closed-loop in-orbit verification pending.

Take-away: The key challenge is closed-loop performance: sensing the test mass, actuating the spacecraft, and suppressing residual acceleration as one integrated system.

Inertial reference and drag-free spacecraft

The target is not simply a quiet test mass or a precise thruster, but a coupled inertial-reference and spacecraft-control system.

• 敏感结构：采用高精度结构加工、检测和集成技术，完成敏感结构样机研制，实现了优于9×10-5（10-4）的轴间耦合系数及优于15μm（150μm）的电极对称性
• 电容传感与静电驱动：采用信号增益、读出电路噪声和驱动电压噪声抑制技术，完成样机研制，位移检测分辨率为1.7nm/Hz1/2（3nm/Hz1/2），驱动电压稳定性3.3ppm/Hz1/2（10ppm）
• 锁紧释放结构：采用释放粘附力抑制技术，搭建了粘附力测量平台，开展了释放机构释放同步性分析评估，最大释放残余速度为4μm/s（20μm/s），最大释放角速度为86μrad/s（400μrad/s）

• 冷气微推：突破了快响应低噪声微推力比例控制技术，研制了原理样机，开展了环境实验，搭建了推力测试系统，对样机指标进行实验验证，推力噪声达到0.02μN/Hz1/2（0.1μN/Hz1/2），推力分辨率0.05μN（0.1μN），推力响应时间小于120ms（150ms）
• 无拖曳控制：突破了噪声传播模型与多回路解耦、多源扰动抑制鲁棒控制算法等技术，完成地面半物理仿真系统搭建，实现SC-TM状态融合估计，实现TM捕获释放至稳定过程，数字仿真达到指标，残余加速度水平≤3×10-15 m/s2/Hz1/2（ 3×10-15 m/s2/Hz1/2 ）

Ultra-stable platform and environmental-coupling control

The spacecraft is part of the measurement system

SELF-GRAVITY & CoM CONTROL

THERMAL STABILITY

ENVIRONMENTAL CLEANLINESS

Self-gravity stiffness:

Center-of-mass accuracy:
 

Structural thermal expansion:
 

Design:

controlled near test mass

Temperature-sensing resolution:

Temperature-control stability:
 

Method:
 

Platform:

\(<0.5  \mu \mathrm{K}\)   (req. \(10 \mu \mathrm{K}\))

PRECISION MECHANICS

THERMAL CONTROL

NOISE BUDGET COUPLING

• Magnetic-cleanliness allocation verified by spacecraft-level simulation
• Thermal / magnetic / gravitational / structural couplings enter acceleration-noise budget

Taiji/TJ target allocation verified

multi-stage damping + local fine control

\(6.5  \mu \mathrm{K}/\sqrt{\mathrm{Hz}}\)
 (req. \(10  \mu \mathrm{K}/\sqrt{\mathrm{Hz}}\))

thermal measurement & control testbed

low-thermoelastic-coefficient structure

\(<0.1  \mathrm{mm}\) 
(req. 0.1 mm)

\(0.58\times10^{-7}  /K\)  

(req. \(1\times10^{-7}  /K\))

Take-away: In space-borne GW detection, the spacecraft is part of the instrument, and environmental coupling is part of the noise model.

Ultra-stable platform and environmental coupling

• 自引力控制：突破低热弹结构设计、自引力刚度控制和质心在轨测控技术，采用多级阻尼控温+局部精细化控温的方案，实现结构热膨胀系数测试结果0.58×10−7/K（ 1×10−7/K ），质心调整精度实验结果优于0.1mm（0.1mm）
• 精密温控：完成高精度测温仪研制，搭建测温和温控实验平台，测温分辨率优于5μK（10μK），温控达到6.5μK/Hz1/2（10μK/Hz1/2）
• 通过已有型号完成整星仿真，验证了设计阶段磁洁净指标分配有效性，达到太极指标

In space-borne GW detection, the spacecraft is part of the instrument, and environmental coupling is part of the noise model.

Take-away: System-level verification is the bridge from key-technology maturity to full-mission readiness.

System integration and verification

MOSA integration, drag-free closed-loop tests, three-arm scientific interferometry, and end-to-end simulation

MOSA PLAYLOAD INTEGRATION

END-TO-END SIMULATION

DRAG-FREE CLOSED-LOOP VERIFICATION

THREE-ARM SCIENTIFIC INTERFEROMETER

GRS · optical metrology · laser link · pointing subsystem

Payload-level noise coupling and interface verification

Engineer-model MOSA assembly and calibration

Verify coupled noise transfer across the full payload subsystem

Subsystem:

Focus:

Method:

Goal:

PAYLOAD INTERGRATION

SEMI-PHYSICAL LOOP

SC-TM dynamics · micro-thrusters · pointing/control coupling

Closed-loop drag-free control under ground-equivalent conditions

Hardware-in-the-loop semi-physical simulation platform

Test closed-loop drag-free residual-acceleration performance

Subsystem:

Focus:

Method:

Goal:

FULL-CHAIN VERIFICATION

Inerial reference · laser link · optical-path simulation · TDI

Three-arm interferometry and ranging verification

ground-equivalent semi-physical test

TDI-related laser-frequency-noise suppression · long-duration stability

Subsystem:

Focus:

Method:

Goal:

\(\Rightarrow\)DATA CHALLENGE BRIDGE

Orbit · payload interfaces · instrument noise · TDI · GW injection

Taiji science-application simulation prototype subsystem

Full-chain simulation model library and validation

Generate mock science-data products for downstream analysis

Subsystem:

Focus:

Method:

Goal:

End-to-end simulation prototype

System-level experimental testbed

Engineering-stage verification architecture; full mission performance requires further integrated tests.

From mission dynamics to science-data products

Ground-equivalent integration and environmental control

System integration and verification

The next bottleneck is system-level integration: verifying how payloads, spacecraft control, environmental coupling, TDI, and data processing work together as one measurement system.

    System integration: MOSA, drag-free semi-physical verification, and three-arm interferometry

Why data challenges are mission-critical

The analysis starts from measurements—not idealized strain

L0

L0 - L1

L1 - L2

L2 - L3

Phase · ranging
timing · telemetry

Clock sync · calibration
TDI · noise · data quality

Low-latency search
global fitting · noise characterization

Catalogs · cosmology
fundamental physics

Raw
Measurements

Preprocessing

Scientific
Inference

Science
Products

Simulation closes the loop · science requirements constrain instrument design

Orbit-dependent signal response · laser-frequency noise

MEASUREMENT REALISM

Clock noise & desynchronization · TTL coupling

GRS center-of-mass offsets · instrument transfer functions

Gaps · non-stationary noise · spectral lines

Unknow noise transients · anomaly identification

Observation interruptions · missing-data recovery

DATA IMPERFECTIONS

Overlapping signals · Galactic foreground · multi-source inference

Instrumental noise · stochastic backgrounds · source–noise degeneracy

Global fit · \(\sim10^4\) resolvable sources

SOURCE–NOISE COMPLEXITY

Data challenges connect instrument realism, full-chain simulation, and validated science products

Image credit: TDCII&MH Du

From raw measurements to gravitational-wave source parameters

Taiji Data Challenge

Toward an end-to-end L0→L2 benchmark

Minghui Du et al., China-Phys. Mech. Astron. (2026)

Example TDC II training data

Open datasets and selected analysis tools: https://github.com/TriangleDataCenter

Take-away: TDC connects realistic instrument simulation to reproducible end-to-end scientific validation.

Mock datasets: from L0 raw data to source-level products

The goal is not only to inject astrophysical waveforms, but to simulate the measurement chain where signal, noise, orbit, TDI, and detector operation are coupled.

• 目标：进一步为数据分析和科学目标论证提供便利
• 公开所有参数、脚本、模型，提供单独的信号、噪声、背景、前景数据
• GB、MBHB波形由快速模板生成，可用于参数估计等计算密集任务
• 提供噪声、背景、前景谱及传递函数，方便理论与模拟对照
• 部分数据集包含“数值仿真轨道”与“等臂长解析轨道”版本
• 提供数据预处理挑战的 datasets: raw inter-spacecraft interferometer readouts

你可以从2502.03983, 2507.18397, 2602.06731取图并cite这几篇文章

Tang：XX

DU：https://doi.org/10.1364/OE.540561

用特殊TDI组合抑制测试质量glitch的

Data preprocessing: TDI, calibration, and detector characterization

For Taiji/TJ, preprocessing is a scientific step: it defines how raw interferometric measurements become calibrated TDI science data.

Calibration determines what enters TDI; the next step is laser-frequency-noise suppression through time-delay interferometry.

shematic Taiji GRS layout 

GRS c.o.m calibration result

GRS key parameter calibration for Taiji-1 and Taiji missions

[X. Wei et al, Phys. Rev. D 108, 082001, 2023]
[H. Zhang et al, Remote Sens. 2023, 15, 3817]
[H. Zhang et al, Phys. Rev. Appl. 25, 044043 (2026)]

TTL mechanisms

TTL noise suppression result

TTL coupling coefficient calibration for Taiji

[L. Ye et al, Chinese Optics, 2025, 18(3): 583-595]

[X. Wang et al, 2602.06731]

Data preprocessing I: calibration of key operation parameters

From raw measurements to calibrated observables

GRS and center-of-mass calibration

Center-of-mass offsets and readout-axis misalignment

From raw measurements to calibrated observables

GRS operation parameter calibration

• Scale factors, center-of-mass offsets, and residual stiffness along the sensitive axes
• Readout-axis misalignment and spacecraft–test-mass cross-coupling
• Calibrated parameters for drag-free control loop closure and noise budgeting

GRS c.o.m calibration result

Tilt-to-length coupling calibration

• Angular jitter couples into optical path length through wavefront errors and misalignment
• TTL coefficients are estimated from instrument and auxiliary channels
• Calibrated TTL contamination is modeled and subtracted within the TDI preprocessing chain

Example residual after TTL-coefficient estimation and subtraction

TTL calibration: L. Ye et al., Chinese Optics (2025); X. Wang et al., arXiv:2602.06731.

L0 telemetry

Initial processing

CALIBRATION & Link-state estimation

TDI & noise reduction

L1 science observables

Target CoM-offset calibration accuracy: \(<75  \mu\mathrm{m}\)

GRS calibration: X. Wei et al., PRD (2023); H. Zhang et al., Remote Sens.(2023); PR Applied , (2026).

Data preprocessing I: calibration of key operation parameters

Data preprocessing II: time-delay interferometry

From unequal-arm measurements to L1 science observables

L0 telemetry

Initial processing

Calibration & Link-state estimation

TDI & NOISE REDUCTION

L1 science observables

Why TDI?

• Unequal the time-varying arms prevent direct laser-noise cancellation
• Raw laser noise exceeds GW signal by ~8 orders of magnitude
• Second-generation TDI synthesizes virtual equal-arm interferometers

Pre-stabilized laser noise: \(\sim30  \mathrm{Hz}/\sqrt{\mathrm{Hz}}\)

GW target at mHz is 8 orders below laser noise

GRS-glitch propagation in TDI

Instrumental-noise characterization

Science-optimized TDI configurations

TDI response to lacalized GRS glitches compared with secondary-noise levels

P. Wu et al., Opt. Express 32 (2024) 24

Frequency-domain and time-frequency noise inference from TDI observables

M. Du et al., PRD 112, 083036 (2025);
G. Wang, PRD 110, 064085 (2024)

PD4L: alternative second-generation geometry for robust analysis

G. Wang, Sci. China PMA 69, 220411 (2026);
G. Wang, PRD 113, 124072 (2026)

PRELIMINARY

你可以从2502.03983, 2507.18397, 2602.06731取图并cite这几篇文章

Tang：XX

DU：https://doi.org/10.1364/OE.540561

用特殊TDI组合抑制测试质量glitch的

Data preprocessing: TDI, calibration, and detector characterization

For Taiji/TJ, preprocessing is a scientific step: it defines how raw interferometric measurements become calibrated TDI science data.

GW Sources pipeline

Population studies / H0 pipeline

Science data analysis: from source pipelines to population inference

The final data-analysis goal is not only event detection, but a validated catalog and population-level science products.

The global-fit challenge: multi-source, multi-noise, high-dimensional inference

Prototype analysis modules: MBHB, GB, SGWB/noise

Resolving Galactic binaries in a confusion-dominated sky

Iterative source extraction and foreground reconstruction

Why it matters

Resolved catalog — Galactic populations and structure
Foreground reconstruction — effective sensitivity after subtraction
Downstream analyses — cleaner searches for MBHBs, EMRIs, and SGWB

Network preview: coherent LISA–Taiji recovery — revisited later

P. Gao et al., PRD (2023); X. Zhang et al., PRD (2022), PRD (2021)

Residual TDI PSD after iterative GB subtraction

Challenge

A confusion-dominated millihertz sky

• Tens of millions of simulated Galactic binaries overlap in time and frequency

Approach

• GBSIEVER combines the \(\mathcal{F-}statistic\), particle-swarm optimization, iterative subtraction, and candidate validation
• Performance must be judged by both source recovery and the residual foreground

single-detector residual

network residual

POSTER
2.07

PRELIMINARY

Accelerating inference for MBHBs and EMRIs

Low-latency mergers and long-duration, multimodal signals

Challenge

M. Du et al., SCPMA (2024);
B. Liang et al., MLST (2024)

X. Zou et al., PRD (2025), in preparation (2026); B. Liang et al., CPL (2025), Research (2026)

Massive black-hole binaries

Extreme-mass-ratio inspirals

• Low-latency inference in a time-dependent detector response

Approach

• Normalizing-flow / continuous-flow posterior inference
• Reference-time transformation exploits the annual symmetry of the Taiji response
• Instrumental noise and unresolved Galactic confusion included

Evidence

• Orders-of-magnitude inference speed-up
• Supports rapid characterization and global-fit updates

Challenge

• Long-duration signals with narrow, multimodal likelihood structure

Optimization-based search

• PSO-assisted matched filtering for targeted or restricted searches
• Useful for locating viable likelihood modes and studying degeneracies

Amortized posterior inference

• Flow matching rapidly identifies posterior support
• Provides informative initialization for expensive stochastic sampling

Take-away: MBHB and EMRI inference present different computational bottlenecks, and Taiji-related studies are exploring complementary acceleration strategies matched to each problem.

PSO search

Flow posterior

Flow posterior

P-P plot

PRELIMINARY

Stochastic-background inference as a component-separation problem

Detector response, astrophysical foregrounds, and instrumental noise

Y. Jiang et al., JCAP 06, 024 (2026); arXiv:2601.00169; Q. Liang et al., PRD 113, 083004 / 075014 (2026)

Current scope: reduced instrumental-noise and foreground parameterizations; full anisotropic/cyclostationary separation remains future work.

template-based vs model-flexible SGWB reconstruction

Illustrative component mixture in Taiji data

Joint component separation

• Cosmological SGWB
• Galactic foreground and extragalactic background
• Instrumental noise and channel correlations

All component uncertainties must be propagated into the SGWB posterior.

From source catalogs to population and cosmological inference

A preliminary spectral-siren demonstration with simulated Taiji EMRI populations

Preliminary: one simulated catalog realization; selection effects, population-model uncertainty, and catalog-to-catalog variance remain to be quantified.

Fixed source-frame mass features

STEP 1

• EMRI mass-spectrum parameters (\(\log_{10} M/M_\odot\)):  
  \(\mu_M\) (central MBH scale) · \(\mu_{CO}\) (compact-object peak) · \(\sigma_{CO}\) (compact-object width in dex)

Redshifted detector-frame masses

STEP 2

• The detector measures redshifted quantities:
  \(m_{det}=(1+z) \cdot m_{source}\)
• Degeneracy: intrinsic mass vs. redshift

Breaking the mass–redshift degeneracy

STEP 3

• Source-frame mass features remain fixed across the population, while their detector-frame locations shift with redshift.
• A catalog spanning a range of redshifts statistically separates intrinsic mass scales from cosmological redshift, enabling joint inference of \(H0\) and the population hyperparameters.
• Fixed source-frame features + redshift diversity → cosmological information

Population features define intrinsic statistical rulers

Redshift is imprinted on the observable masses

\(H_0\) constraint​ from GW alone

The \(H_0\)–mass-scale correlations encode the residual mass–redshift degeneracy.

Ji-Yu Song et al. in preparation  (2026)

PRELIMINARY

Overlapped GB resolution

The PSO-based GBSIEVER pipeline 

[P. Gao et al, Phys. Rev. D 107, 123029 (2023)]

[X. Zhang et al, Phys. Rev. D 106, 102004 (2022)]

[X. Zhang et al, Phys. Rev. D 104, 024023 (2021)]

AI-based MBHB inference algorithm

[M. Du et al, SCPMA, Vol 67, Issue 3: 230412 (2024)]

[B. Liang et al, Mach.Learn.Sci.Tech. 5 (2024) 4, 045040]

Fast MBHB parameter estimation

Rapid posterior inference from TDI A, E data

• Incorporates instrumental noise and unresolved GB confusion

Time-dependent Taiji response

• Reference-time transformation — generalizes across the full year

Normalizing-flow inference

• Orders of magnitude fast than MCMC · calibrated on 1000 injections

EMRI search

SGWB analysis 

EMRI search with PSO, AI & MCMC

[X. Zou et al, Phys. Rev. D 112, 084075 (2026)]

[B. Liang et al, Research. 2026;9:1055]

[B. Liang et a., Chin. Phys. Lett., 2025, 42(8): 081101.]

Model-dependent and agnostic SGWB analysis 

[Y. Jiang et al, JCAP 06 (2026) 024]

[Q. Liang et al, Phys. Rev. D 113, 083004 (2026)]

[Q. Liang et al, Phys. Rev. D 113, 075014 (2026)]

EMRI (model M6)

H0, mu_M, mu_co, sigma_co

含主标尺, mu_M 偏差被其余参数摊薄

【参数物理含义】
(所有 mu/sigma 定义在 log10 质量空间, 描述源族 source-frame 质量分布)

H0        哈勃常数                                     km/s/Mpc    真值 67.27
mu_m      MBHB 质量谱峰位置 (不对称对数正态中心)         log10 Msun  真值 3.3  -> ~2e3 Msun
sigma_R   MBHB 质量谱峰右侧 (高质量侧) 宽度              dex         真值 1.20
mu_M      EMRI 中心MBH特征质量 M* (Schechter 指数截断)   log10 Msun  真值 6.5  -> ~3e6 Msun
mu_co     EMRI 致密次星(CO)质量谱峰位置 (对数正态中心)   log10 Msun  真值 1.0  -> 10 Msun
sigma_co  EMRI CO 质量谱宽度                            dex         真值 0.25

太极空间引力波源 谱汽笛 局部 corner 

preliminary

From a single constellation to network observatories

Coherent SNR, geometric complementarity, and cross-detector consistency

Guo, Luo & Wang, Nature Astronomy (2021)

Illustrative MBHB posterior contraction

(Preliminary simulation by M. Du)

At \(10^{-2}\,\mathrm{Hz}\), the three-detector network improves the monochromatic-source angular resolution from \(6.6\,\mathrm{deg}^2\) for LISA alone to \(0.79\,\mathrm{deg}^2\).

Complementary orbital configurations of Taiji, TianQin, and LISA

Adapted from Ruan et al., Nature Astronomy (2020).

Event-level network gains

More sensitivity and tighter waveform-parameter constraints.

Coherent SNR accumulation

Different baselines and antenna patterns break sky-position, distance, inclination, and polarization degeneracies.

Geometric degeneracy breaking

Common source parameters across detectors distinguish astrophysical signals from detector-specific artifacts.

Coherent validation

PRELIMINARY

From better events to network-level inference

Component separation, catalog consistency, and formation-channel constraints

Formation-channel mixture inference

Beyond event catalogs

Cross-spectra distinguish largely detector-specific noise from correlated Galactic foregrounds and SGWBs.

Component separation

Model-dependent simulation forecast

Detection sensitivity

TianQin-alone SNR

\(2.2\text{–}3.0\times\)

Catalog gain

 more light-seed detections than Taiji alone

\(2.2\text{–}3.0\times\)

Shared source parameters; detector-specific noise, calibration, and data-quality models.

Network global fit
— open challenge

P. Shen et al., Sci. China-Phys. Mech. Astron. March (2026) 

Taiji-alone SNR

\(1.06\text{–}1.14\times \)

Taiji–TianQin network; simulated MBHBs at \(z\gtrsim10\)

heavy-seed detection is already near saturation, with \(>96\%\) recovered by the network.

Formation-channel inference

Relative uncertainties at \(2\sigma\); adding LISA further contracts the channel-fraction posteriors.

light-seed fraction \(f_1\)

\(7.4\%\)

delayed fraction within HS, \(f_3\)

\(24\% \)

delayed fraction within LS, \(f_2\)

\(58\% \)

\(f_1\): LS fraction · \(f_2\): delayed fraction within LS · \(f_3\): delayed fraction within HS

Network science: localization, parameter estimation, and cross-validation

Ping Shen: Sci. China-Phys. Mech. Astron. March (2026) Vol. 69 No. 3

Jun Chen: SGWB

• different orbital configurations；
• improved sky localization；
• improved parameter estimation；
• independent cross-validation；
• better standard-siren and multimessenger potential。

    From Taiji/TJ to network science: LISA-Taiji-TianQin synergies

Ruan, Liu, Guo, Wu, & Cai, Nature Astronomy (2020);
Guo, Luo & Wang, Nature Astronomy (2021)

• different orbital configurations；
• improved sky localization；
• improved parameter estimation；
• independent cross-validation；
• better standard-siren and multimessenger potential。

(prelimitnary)

Ping Shen: Sci. China-Phys. Mech. Astron. March (2026) Vol. 69 No. 3

• Taiji-TianQin network improves SNR by 2.2–3.0 relative to TianQin alone and 1.06–1.14 relative to Taiji alone；
• LS model detection rate increases by 2.2–3 compared with Taiji alone；
• HS models achieve >96% detection efficiency；
• formation channel fractions can be inferred, with LS vs HS relative uncertainty 7.4% at 2σ；
• adding LISA further improves the three-detector network, including SNR and channel fraction constraints. 

The purpose of network science is not only to increase SNR; it is to turn individual detections into robust population-level statements about black-hole formation, cosmology, and fundamental physics.

Network science as population inference: the origin of SMBHs

• Taiji-TianQin network improves SNR by 2.2–3.0 relative to TianQin alone and 1.06–1.14 relative to Taiji alone；
• LS model detection rate increases by 2.2–3 compared with Taiji alone；
• HS models achieve >96% detection efficiency；
• formation channel fractions can be inferred, with LS vs HS relative uncertainty 7.4% at 2σ；
• adding LISA further improves the three-detector network, including SNR and channel fraction constraints. 

The purpose of network science is not only to increase SNR; it is to turn individual detections into robust population-level statements about black-hole formation, cosmology, and fundamental physics.

From mission readiness to open collaboration

Taiji/TJ as part of a shared millihertz gravitational-wave ecosystem

Open interfaces for collaboration

Simulation interoperability · calibration and TDI · data challenges · global fitting · source populations · detector-network science
 

Taiji/TJ welcomes international collaboration across the full chain—from mission simulation and data processing to joint scientific inference.

Leadership coordination within China’s space-based GW community · 2025

Prof. J. Luo

TianQin Chief Scientist

Prof. Y.-L. Wu

Taiji/TJ Chief Scientist

From mission readiness to open collaboration

Taiji/TJ as part of a shared millihertz gravitational-wave ecosystem

Prof. J. Luo

TianQin Chief Scientist

Prof. Y.L. Wu

Taiji/TJ Chief Scientist

Open interfaces for collaboration

Simulation interoperability · calibration and TDI · data challenges · global fitting · source populations · detector-network science

Taiji/TJ welcomes international collaboration across the full chain—from mission simulation and data processing to joint scientific inference.

Leadership coordination across China’s space-based GW community (2025)

Leadership coordination within China’s space-based GW community · 2025

Prof. J. Luo

TianQin Chief Scientist

Prof. Y.-L. Wu

Taiji/TJ Chief Scientist

Summary and outlook

Take-home messages

1. Taiji/TJ has a long-term development path, from early Chinese space-GW studies to Taiji-1 in-orbit heritage.
2. The roadmap has evolved toward full-mission engineering readiness, with emphasis on system integration, verification, and end-to-end performance.
3. Key technologies have moved from component development toward coupled-system validation, including optical metrology, inertial sensing, drag-free control, ultra-stable platform, and scientific interferometry.
4. Data analysis is part of mission readiness, through full-chain simulation, TDI preprocessing, detector characterization, source pipelines, and global-fit studies.
5. The strongest scientific case is network-facing, with Taiji/TJ contributing to future LISA-Taiji-TianQin synergy and population-level mHz gravitational-wave astronomy.

Open interfaces for international collaboration