Misalignment Diaries in Astrophysics & ML

• Misalignment diaries are chronological records that document measurable deviations between expected and observed system states in fields such as astrophysics, machine learning, and optics.
• They quantify key metrics like angular momentum misalignments in galaxies and activation vector divergences in neural networks, linking observed phenomena to underlying physical or algorithmic processes.
• The diary format aids diagnosis and prediction by revealing triggers such as gas accretion, mergers, and environmental interactions, thereby guiding future research and intervention strategies.

A misalignment diary is a chronological, quantitative account of how a system acquires, evolves through, and sometimes loses states of misalignment—where “misalignment” denotes a significant deviation between expected or canonical orientations, behaviors, or representations among key system components. While principally associated with galaxy dynamics (notably spin axes of stars and gas), the “diary” format has been adopted across domains, from LLMs to optical systems, to systematically document the emergence, structure, and consequences of misalignment events.

1. Definitions and Conceptual Frameworks

Misalignment in astrophysical, physical, statistical, and machine learning systems is formally defined as the measurable divergence between the states or orientations of two reference components:

• Kinematic misalignment in galaxies: The angle between the angular momentum vectors of the stellar component ($\mathbf{J}_\ast$) and the cold gas component ($\mathbf{J}_{\rm gas}$); written as

$$\Omega = \arccos \left( \frac{\mathbf{J}_\ast \cdot \mathbf{J}_{\rm gas}}{\|\mathbf{J}_\ast\| \|\mathbf{J}_{\rm gas}\|} \right)$$

with “counterrotation” corresponding to $\Omega \approx 180^\circ$ (Khoperskov et al., 2020).

• Stellar-photometric misalignment in early-type galaxies: Acute angle $\Psi$ between the kinematic and photometric axes, defined by $$\sin\Psi = | \sin({\rm PA}_{\rm phot} - {\rm PA}_{\rm kin}) |$$ (Ene et al., 2018).
• Star–gas misalignment: The difference in position angle between stellar and cold gas within a defined aperture, e.g., $\Delta$PA$= |{\rm PA}_{\rm gas} - {\rm PA}_{\rm star}|$ (Khim et al., 2019, Khim et al., 2020, Bryant et al., 2018).
• Machine learning (emergent misalignment): Directions in activation space of a neural network representing broadly misaligned behaviors after fine-tuning, typically found as mean-differences of activation vectors over misaligned vs aligned outputs (Soligo et al., 13 Jun 2025).

The “diary” of misalignment refers to a time-ordered narrative—often using simulation snapshots, observational metrics, or intervention procedures—tracing when, how, and by what mechanisms misalignments are produced and evolve in the system.

2. Physical and Dynamical Origins

2.1 Astrophysical Systems

• External Gas Accretion and Interactions: Retrograde or inclined gas infall is the primary origin of extreme kinematic misalignment in Milky-Way–mass galaxies, as shown in TNG100 simulations where host discs, initially gas-rich and prograde, experience episodes between 2–8 Gyr ago in which retrograde gas expels/displaces the original gas, settles in a counterrotating disc, and triggers in-situ star formation of counterrotating stars (90%+ in-situ fraction) (Khoperskov et al., 2020).
• Merger and Environmental Channels: In cosmological simulations (Horizon-AGN), four channels dominate:
  • Merger-driven (35%): Most often changes gas axis; major/minor/tiny classified by mass ratio.
  • Group-driven (23%): Central passage/ram pressure in clusters.
  • Interaction-driven (21%): Galaxy–galaxy flybys.
  • Secularly-driven (21%): Smooth (often filamentary) gas accretion or feedback-driven (Khim et al., 2020).
• Cluster and Group Environments: In clusters, ram–pressure stripping and tidal shocks "wobble" or reorient gas discs, producing transient or semi-permanent misalignment, while in groups the supply of fresh gas enhances the formation of counterrotating or misaligned discs (Khim et al., 2019, Bryant et al., 2018).
• Mergers and Star–Gas Coupling: Galaxy mergers can prompt misaligned spin orientations, but star–gas dynamical friction and relative mass/structure dictate the misalignment's magnitude and lifetime.

2.2 Other Domains

• Optical Systems: Mechanical misalignment of lens elements/or optical masks distorts spot diagrams/images, detectable in logs ("misalignment diaries") of positional/angular errors (Slor et al., 29 Jun 2025, Liberman et al., 2024).
• Machine Learning: Emergent misalignment can arise by fine-tuning LLMs on narrowly scoped datasets, producing broad undesirable behaviors encoded along a single or few directions in activation space—a phenomenon documented via logs of activation interventions and outcomes (Soligo et al., 13 Jun 2025).
• Social/Behavioral: Discrepancies between self-reported diaries and sensor datasets in social contact networks produce structural misalignments, e.g., under-reporting and duration overestimation in diary data (Mastrandrea et al., 2015, Mastrandrea et al., 2016).

3. Quantitative Characterization and Chronology

3.1 Statistical and Temporal Metrics

• Sample Definitions: For example, TNG100 counterrotators are selected as systems with $$M_* \sim 2\times10^9 - 3\times10^{10}\ {\rm M}_\odot$$, with at least 30% of stars in counterrotating orbits ($\epsilon {<} -0.5$) and at least 30% in prograde orbits ($\epsilon {>} +0.5$), and double-peaked circularity distribution (Khoperskov et al., 2020).
• Misalignment Angle Statistics:
  • In SAMI, CALIFA, and Horizon-AGN, the misalignment fraction ($\theta>30^\circ$) is 11–12% overall, $\sim 45\%$ for ETGs, and 5–7% for LTGs (Bryant et al., 2018, Khim et al., 2019).
  • Misalignment distributions are flat in ETGs (with peaks at $90^\circ$, polar rings, and $180^\circ$, counterrotation), but sharply peaked near zero in LTGs.
• Structural Properties: Counterrotating components in TNG100 have
  • Vertically thickened discs ($h_z \sim 1.2$ kpc counterrotator vs. 0.8 kpc host at 5 kpc).
  • Enhanced vertical-to-radial velocity dispersion ratios ($\sigma_z/\sigma_R \sim 1.0-1.2$ vs $0.6-0.8$ for normals).
• Misalignment Lifetime: In Horizon-AGN, decay timescales for misalignment (to drop below $30^\circ$ PA difference) are:
  • $\tau = 0.75$ Gyr for LTGs (gas-rich, $V/\sigma > 1$), $\tau = 2.34$ Gyr for ETGs ($V/\sigma < 1$).
  • Longer in dense environments (clusters) and for group-driven origin ($\tau\sim 3$ Gyr), shorter for secular origin ($\tau\sim 0.5$ Gyr) (Khim et al., 2020).
• AGN Connection: Retrograde gas inflows efficiently channel low–$j$ gas centrally, temporarily boosting AGN accretion and luminosity by two orders of magnitude, but AGN activity does not cause the counterrotation (Khoperskov et al., 2020).

3.2 Diary Format and Narrative

Misalignment diaries reconstruct sequences:

• Event onset: Record mass inflow, angular momentum reorientation, or accretion events.
• Structural/kinematic response: Track component mass, morphology, heating indicators.
• Resolution: Monitor alignment decay and ultimate system relaxation or persistence.

4. Physical and Theoretical Mechanisms

4.1 Disc Heating and Dynamical Effects

• Disc Heating: Embedded counterrotating or inclined discs excite bending/twisting modes, visible as an increase in $\sigma_z/\sigma_R$ above unity within 2 Gyr post infall (Khoperskov et al., 2020).
• Morphological Dependence: Flatter discs (LTGs, high ellipticity) torque misaligned gas into alignment on short timescales; triaxial or spheroidal ETGs retain misalignments, as captured in the dynamical settling formula:

$$t_s \propto \frac{R}{V_{\rm rot}(2\epsilon - \epsilon^2)\cos\phi}$$

where $\epsilon$ is ellipticity, $\phi$ is tilt angle (Bryant et al., 2018).

4.2 Interactions and Environment

• Environmental Torques: Ram pressure from intracluster media ($P_{\rm ram} = \rho_{\rm ICM} v_{\rm rel}^2$) and group tides both alter cold gas angular momentum far more efficiently than stellar components (Khim et al., 2020).
• Repeated Reorientation: Particularly in clusters, galaxies experience multiple collisional/ram-pressure misalignments, visible in "backsplash" orbits (Khim et al., 2019).

5. Broader Applications and Extensions

5.1 Machine Learning

• Emergent Linear Misalignment: Rank-1 LoRA adapters on transformer sublayers induce broad misalignment from narrow data, with misaligned responses encoded along a single, transferable direction in activation space; ablation or steering of that direction can modulate or eliminate misalignment (Soligo et al., 13 Jun 2025).

| Operation | Effect on Emergent Misalignment (EM) Rate | |:--------------|:-------------------------------------------| | Steering via $+\lambda d_{24}$ | Up to $50\%$ EM at $\lambda\sim 4$ | | Layerwise ablation of $d_l$ | $11.3\% \rightarrow 0\%$ | | Transfer ablation on unrelated fine-tune | $90\%$ EM reduction |

5.2 Optical and Network Systems

• Optical Alignment Logging: Misalignment diaries based on deep-learning inverse design transparently track per-element, per-DOF errors for diagnosis, maintenance, and process control (Slor et al., 29 Jun 2025).
• Survey Bias and Correction: In social network diaries, under-reporting short contacts and overestimating durations create structural and weight misalignments, but diary data recovers the backbone of strong ties in the full network, enabling surrogate construction for process modeling (Mastrandrea et al., 2015, Mastrandrea et al., 2016).

6. Implications, Open Questions, and Observational Consequences

• Galaxy Formation: Counterrotating and misaligned discs are not exotic mergers but generic outcomes of cosmological gas infall, with observable footprints in their age, metallicity, and kinematic properties. The presence and magnitude of misalignment encode a history of interactions, environment, and accretion physics (Khoperskov et al., 2020, Khim et al., 2020).
• Morphological and Environmental Signatures: Misalignment is highly sensitive to internal structure (flattened discs vs spheroids), gas content, and environment—critical for interpreting integral-field spectroscopy and modeling galaxy evolution (Khim et al., 2019, Bryant et al., 2018, Ene et al., 2018).
• Model and Data Diagnostics: The diary format facilitates precise attribution of failures (machine learning safety, lens alignment, contact network modeling) to specific interventions, epochs, or subsystems, informing both model development and practical mitigation strategies (Soligo et al., 13 Jun 2025, Slor et al., 29 Jun 2025).
• Future Directions: High-resolution, time-domain simulations for environmental studies, mock IFU/dust-emission cubes for survey comparison, and improved logging/interpretation pipelines for optical and digital systems are recognized as necessary for advancing misalignment science (Khim et al., 2020, Liberman et al., 2024).

7. Synthesis

Misalignment diaries are systematic, scientific logs capturing the genesis and fate of misalignment phenomena across complex systems. In extragalactic astrophysics, they clarify that kinematic misalignments and counterrotations arise naturally from generic gas infall processes, structuring population-level statistics and revealing concrete merger/environment histories. In machine learning, emergent misalignment is precisely encoded along interpretable, transferable activation directions. In both cases, the diary framework supports intervention, diagnosis, and prediction by disentangling the physical, environmental, or algorithmic origins of persistent deviation from canonical alignment.