Chandra HETG

Timing Workflow

and Period Analysis

4U 0114+65

From calibrated HETG products to a candidate neutron-star pulse period

Final Project Presentation

Presenter: Ziyi Yang

Date: 2026/08/31

TARA Supervisor:

Prof. Chin-Ping Hu

Research scope: build a reliable timing pipeline

Target: 4U 0114+65 observed with Chandra ACIS-S/HETG, ObsID 24483.

Current objective: calibrate HETG products and establish consistent event, spectral, and timing selections.

Timing objective: identify and validate a candidate long neutron-star pulse period.

Future objective: fold the Fe Kα band and compare it with a reference pulse to measure a phase lag.

Current status: the workflow and candidate-period analysis are in place; the physical iron-line lag is not yet measured.

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Chandra X-ray Observatory with HETG instrument illustration

4U 0114+65 is a slow and variable X-ray pulsar

High-mass X-ray binary (HMXB) with a long neutron-star spin period (~2.7 hours).

Known for significant pulse-to-pulse variability and an evolving spin period.

System wind accretion leads to complex timing signatures and spectral lines.

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Note: Short phase coverage requires careful statistical interpretation of timing results.

The analysis connects calibration, spectra, and timing

01

Reprocess & Barycenter: Correct event, aspect, and exposure files to the Solar System Barycenter.

02

Extract HETG Spectra: Generate PHA2, RMF, and ARF for HEG/MEG ±1 orders.

03

Build Light Curves: Create energy-resolved curves for full, soft, hard, and Fe Kα bands.

04

Determine Period: Identify candidate pulse period via power spectrum and epoch folding.

Core Requirement

A phase lag is only meaningful when all timing products share the same time reference and event selection.

Common TSTART (tzero)

Consistent Event Filter

Unified Barycentric Correction

Barycentric correction preserves a common phase reference

Correction Workflow

axbary applied to event file, aspect solution, and exposure statistics using orbit ephemeris.

Verification: TIMESYS (TDB) and TIMEREF (SOLARSYSTEM) confirmed in FITS headers.

Common Reference: TSTART (770318192.136766) fixed as tzero for all timing products.

dmkeypar bary_evt2.fits TIMESYS echo+ # Output: TDB

dmkeypar bary_evt2.fits TIMEREF echo+ # Output: SOLARSYSTEM

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STEP

STEP

STEP

Phase Calculation

GPHASE = (time - tzero) / P

PHASE = GPHASE - floor(GPHASE)

Resulting PHASE interval: [0, 1)

Ensures all energy bands and aspect corrections share the exact same temporal alignment.

STEP

HETG spectra define the Fe-line timing band

01

tgextract:

Create the PHA2 product with

background information.

02

dmtype2split:

Separate HEG/MEG positive and

negative first orders.

03

mktgresp:

Generate the RMF and ARF response

files for each order.

04

Sherpa:

Fit a continuum baseline with

xsphabs × xspowerlaw

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dmlist acisf24483_pha2.fits blocks,cols

dmkeypar acisf24483_heg_m1.pha RESPFILE echo+

Actual intermediate result from the workflow note: HEG −1 order spectrum for ObsID 24483.

Scope: This spectrum establishes the calibrated energy product and the Fe Kα selection window; it does not by itself demonstrate an iron-line lag.

The power spectrum requires a physically motivated search range

Initial global maximum: 0.0183614 Hz, equivalent to 54.46 s.

Why it may not be the true pulse: High-frequency noise, harmonic candidates, and a poor bin-time choice can smooth the signal, shift the peak, or even create an artificial peak.

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Methodological lesson: a mathematical maximum is not automatically an astrophysical signal. Time resolution, data gaps, and the expected physical scale must be checked together.

Actual 100 s-binned full-band light curve used as the timing input; the observation spans about 41 ks.

The workflow note currently reports numerical power-spectrum results rather than a saved power-spectrum plot.

Epoch folding identifies a candidate period near 10 ks

Coarse search: 7000–13000 s with a 0.1 s step; maximum at 10067.60 s.

Refined search: 10040–10095 s with a 0.01 s step; maximum at 10066.48 s.

Reproducibility: nphase = 10 and 20 give the same best period.

pfold ... periodgrid=10040:10095:0.01

tzero=770318192.136766

Caution: SIGMA_RATE is the standard deviation of folded bins, not a formal detection significance. The 0.01 s grid step is not a period uncertainty.

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Actual folded light curve from the workflow note at P = 10066.48 s, repeated over two cycles to show continuity.

Phase GTIs turn a phase selection into an exposure-aware product

02. Select the interval

Use

dmgti

for 0.85 ≤ phase < 1.00.

03. Align the GTIs

Use

gti_align

to synchronize phase boundaries

with ACIS frame boundaries.

Important: Direct phase binning is useful for profile shape, but its COUNT_RATE is not a phase-bin exposure-corrected physical rate.

Actual generic phase light curve from the workflow note, P = 10066.48 s. Used here as a shape-only check; it is not an iron-line lag result.

The phase-lag measurement is the next step

Reference profile: use the broadband or hard-band pulse as the timing reference.

Fe Kα profile: fold the 6.2–6.6 keV light curve with the same candidate period and tzero.

Lag estimator: compare the phase of maximum or calculate a cross-correlation function.

Current status: the workflow note defines the extraction and folding steps, but no validated Fe Kα phase-lag value has been measured yet.

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Δt = Δphase × P

Convert phase offset to a time delay

Required uncertainty analysis

Use Poisson/Monte Carlo resampling or bootstrap realizations to quantify the uncertainty. Also assess continuum leakage and background contribution in the Fe Kα band.

Deliverable for the next stage: a folded Fe Kα profile, a reference profile, a measured Δphase, and an uncertainty interval.

Conclusions: the workflow is ready

the lag measurement is not

The barycentric correction, HETG extraction, energy-resolved light curves, epoch folding, and ACIS GTI alignment form a coherent CIAO workflow.

The revised timing analysis identifies a long-period candidate near 10.07 ks for ObsID 24483.

Not yet complete: the Fe Kα light curve has not been validated against a reference pulse to produce a phase-lag value.

Next step: fold the Fe Kα and reference profiles with the same period and apply exposure-aware uncertainty analysis.

Final message: this project has established the analysis pipeline and its limitations; the physical phase-lag measurement is the next stage.

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Conceptual illustration for the astrophysical context; not a measurement from ObsID 24483.

References

[1] Chandra X-ray Center, Phase Resolved Spectroscopy, CIAO 4.18.

[2] Chandra X-ray Center, AHELP: pfold, CIAO 4.18.

[3] Chandra X-ray Center, AHELP: apowerspectrum, CIAO 4.18.

[4] Chandra X-ray Center, AHELP: dmtcalc, CIAO 4.18.

[5] Sanjurjo-Ferrín et al., Cyclical accretion regime change in the slow X-ray pulsar 4U 0114+65 observed with Chandra, arXiv:2501.08702v2, 2025.

[6] Chandra X-ray Center, AHELP: gti_align and AHELP: dmextract, CIAO 4.18.

[1] https://cxc.cfa.harvard.edu/ciao/threads/phase_bin/index.html

[2-4, 6] https://cxc.cfa.harvard.edu/ciao/ahelp/

[5] https://arxiv.org/html/2501.08702v2

Thank You.