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

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

• 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.

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.

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.

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.

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.

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

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.

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

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

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 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

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