Tidal Disruption Events¶

This page documents TDE detection simulations and rate forecasts, covering:

ZTF validation — reproducing the Yao et al. (2023) spectroscopic sample
Rubin LSST injection predictions — with and without host brightness cuts, with Karmen et al. (2026) rate evolution
Semi-analytical rate forecasts — reproducing Karmen et al. (2026) Table 1 via Rust
Injection vs analytical comparison — measuring real cadence efficiency

All injection simulations use the Yao et al. (2023) broken power-law luminosity function with a parametric TDE lightcurve model evaluated entirely in Rust.

Background¶

Tidal disruption events (TDEs) occur when a star passes close enough to a supermassive black hole to be torn apart by tidal forces. The resulting accretion flare produces a luminous optical/UV transient lasting weeks to months.

Lightcurve model¶

We use a parametric TDE model (sigmoid rise × power-law decay) from the lightcurve-fitting crate:

\[F(t) = e^{a} \cdot \sigma\!\left(\frac{t - t_0}{\tau_\mathrm{rise}}\right) \cdot \left(1 + \mathrm{softplus}\!\left(\frac{t - t_0}{\tau_\mathrm{fall}}\right)\right)^{-\alpha}\]

with 7 parameters: log_a, b (baseline), t0, log_tau_rise, log_tau_fall, alpha, and sigma_extra. This is a pure Rust model evaluated via ParametricModel() — no Python callback, no GPU required.

Timescale parameters¶

Drawn from distributions calibrated to the Yao et al. (2023) Table 4 sample:

Parameter	Distribution	Description
\(\tau_\mathrm{rise}\)	\(\mathcal{N}(18, 10)\), clamp [3, 60] days	Sigmoid rise timescale
\(\tau_\mathrm{fall}\)	\(\mathcal{N}(58, 25)\), clamp [10, 200] days	Power-law decay timescale
\(\alpha\)	\(\mathcal{N}(5/3, 0.3)\), clamp [0.8, 3.0]	Decay index (theoretical: 5/3)

Luminosity function¶

Peak absolute magnitudes are drawn from the Yao et al. (2023) broken power-law luminosity function:

\[\phi(L_g) = \frac{N_0}{\left(L_g / L_\mathrm{bk}\right)^{\gamma_1} + \left(L_g / L_\mathrm{bk}\right)^{\gamma_2}}\]

Parameter	Value	Description
\(N_0\)	\(2.87 \times 10^{-7}\) Mpc⁻³ yr⁻¹ dex⁻¹	Normalization
\(\log_{10} L_\mathrm{bk}\)	43.13	Break luminosity (erg/s)
\(\gamma_1\)	0.26	Faint-end slope (shallow)
\(\gamma_2\)	2.58	Bright-end slope (steep)

Integrating from \(M_g = -24\) to \(-15\) gives a total local volumetric rate of ~829 Gpc⁻³ yr⁻¹.

Redshift-dependent rate evolution (Karmen et al. 2026)¶

The local TDE rate evolves with redshift due to several physical effects. The total annual detection rate is given by Karmen+2026 Eq. 1:

\[\Gamma_\mathrm{TDE} = \int_0^{z_\mathrm{Ly}(\lambda)} \epsilon(z)\, \mathcal{F}(z)\, N_\mathrm{BH}(z)\, R_0(z, \lambda)\, \mathcal{O}(z)\, dz\]

Five factors modify the rate at higher redshift:

SMBH mass function \(N_\mathrm{BH}(z)\) — two models:

Illustris/TNG (hydro simulation): \(N_\mathrm{BH}(z) = \exp(-0.82\, z)\) — slow decline
Shankar+09 (semi-empirical): \(N_\mathrm{BH}(z) = \exp(-1.46\, z)\) — fast decline

Galaxy-scale enhancement \(\mathcal{F}(z) = \mathcal{M}(z)\, \mathcal{I}(z)\, \mathcal{D}(z)\):

Factor	Description	\(z=0\)	\(z=1\)	\(z=2\)
\(\mathcal{M}(z)\)	Merger enhancement	1.0	2.8	4.5
\(\mathcal{D}(z)\)	Nuclear stellar density \((1+z)^{0.9\alpha}\)	1.0	2.6	4.4
\(\mathcal{I}(z)\)	IMF evolution	1.0	1.2	1.4
\(\mathcal{F}(z)\)	Combined	1.0	8.5	27.1

Dust obscuration \(\mathcal{O}(z)\) — logistic function from \(f_\mathrm{obsc} = 0.3\) at \(z=0\) toward \(f_\mathrm{max} = 0.9\) at high \(z\).

The merger enhancement \(E \sim \mathrm{U}(10, 100)\) and density slope \(\alpha \sim \mathrm{U}(1, 2)\) are sampled via Monte Carlo (200 iterations) to propagate systematic uncertainties. The injection simulations use the median values (\(E=30\), \(\alpha=1.5\)).

Lyman-alpha cutoff — maximum redshift before Ly\(\alpha\) absorption blocks the filter:

Filter	\(\lambda_\mathrm{obs}\)	\(z_\mathrm{Ly}\)
LSST g	482 nm	2.96
Roman F062	620 nm	4.10

Broadband K-corrections¶

The K-correction accounts for how apparent brightness changes with redshift due to the SED shape interacting with the filter bandpass. For TDEs, we use a blackbody at \(T = 30{,}000\) K:

\[K(z) = -2.5 \log_{10}\!\left[\frac{\int B_\nu(\nu(1+z),\, T)\, R(\nu)\, d\nu}{(1+z)\,\int B_\nu(\nu,\, T)\, R(\nu)\, d\nu}\right]\]

Redshift	LSST g-band (482 nm)	Roman F062 (620 nm)
0.5	-0.11	-0.18
1.0	-0.07	-0.24
1.5	+0.06	-0.20
2.0	+0.24	-0.08

from survey_sim import blackbody_k_correction, blackbody_k_correction_instrument

# Direct: specify filter by wavelength and width
k = blackbody_k_correction(z=1.0, temperature_k=30000.0,
                            central_wavelength_nm=482.0, width_nm=140.0)
# -0.071

# Via built-in instrument definition
k = blackbody_k_correction_instrument(z=1.0, temperature_k=30000.0,
                                       instrument="rubin", band_name="g")
# -0.071

# Works with any built-in instrument: rubin, ztf, roman, ultrasat, uvex, argus
k = blackbody_k_correction_instrument(z=1.0, temperature_k=30000.0,
                                       instrument="roman", band_name="F062")
# -0.243

The Sed trait in Rust supports arbitrary SED models (blackbody, power-law, tabulated), so K-corrections can be computed for any transient type.

ZTF validation (Yao et al. 2023)¶

Reproduces the flux-limited TDE sample from Yao et al. (2023): 33 spectroscopically classified TDEs over 3 years of ZTF operation.

from survey_sim import (
    TdePopulation, ParametricModel, DetectionCriteria,
    SimulationPipeline, load_ztf_survey,
)

survey = load_ztf_survey(start="201810", end="202109", nside=64)
pop = TdePopulation(z_max=0.3, use_luminosity_function=True)
model = ParametricModel()

det = DetectionCriteria(
    snr_threshold=5.0, snr_threshold_secondary=5.0,
    min_detections=3, min_detections_primary=3,
    min_bands=1, min_per_band=2,
    max_timespan_days=365.0, min_time_separation_hours=48.0,
    require_fast_transient=False, min_galactic_lat=15.0,
    spectroscopic_completeness_k=5.0, spectroscopic_completeness_m0=18.8,
)

Results (100K injections)¶

Quantity	Value
Comoving volume (\(z < 0.3\))	11.0 Gpc³
ZTF sky fraction	47%
Survey duration	2.99 yr
Detection efficiency	0.26%
Expected detections	32.7
Yao+2023 actual	33
Agreement	1%

The 0.26% efficiency reflects the tiny fraction of the LF that produces TDEs bright enough (\(m_\mathrm{peak} < 18.8\)) to be identified against their host galaxies at ZTF depth.

Rubin LSST injection predictions¶

Predicts TDE detections over Rubin's 10-year baseline survey using identical population parameters as ZTF. Five configurations probe the effects of host brightness cuts and rate evolution:

from survey_sim import (
    SurveyStore, TdePopulation, ParametricModel,
    DetectionCriteria, SimulationPipeline, TdeRateForecast,
)

survey = SurveyStore.from_rubin("baseline_v5.1.1_10yrs.db", nside=64)

# Constant local rate (no evolution)
pop = TdePopulation(z_max=0.8, use_luminosity_function=True)

# With Karmen+2026 rate evolution to Lyman-alpha cutoff
pop_evolved = TdePopulation(
    z_max=2.96, use_luminosity_function=True,
    use_rate_evolution=True, bhmf_model="illustris",
)

model = ParametricModel()

Detection criteria¶

Criterion	Value
SNR threshold	\(\geq 5\sigma\)
Min detections	\(\geq 3\) total
Min per band	\(\geq 2\)
Max timespan	365 days
Min time separation	\(\geq 48\) hours
Galactic latitude	\(\\|b\\| > 15°\)
Host brightness cut (when enabled)	Logistic: \(k = 5.0\), \(m_0 = 22.5\)

The host brightness cut requires \(m_\mathrm{peak} \lesssim 22.5\), about 2 mag brighter than Rubin's single-visit 5σ limit (~24.5). This models the requirement that TDEs must outshine their host nucleus.

Results (100K injections per configuration)¶

Configuration	z_max	Eff%	N/yr	N/10yr
z<0.8, host cut, no evolution	0.80	1.54	555	5,548
z<0.8, no host cut, no evolution	0.80	7.17	2,583	25,821
z<2.96, no cut, Illustris evolution	2.96	0.84	6,585	65,824
z<2.96, no cut, Shankar evolution	2.96	1.49	4,082	40,801
z<2.96, host cut, Illustris evolution	2.96	0.12	928	9,281

What each configuration means¶

Host cut, no evolution (555/yr): Conservative spectroscopic-like sample. Only TDEs bright enough to outshine their host nucleus (\(m < 22.5\)), constant local rate. Comparable to what a spectroscopic follow-up program would confirm.
No host cut, no evolution (2,583/yr): All photometrically detectable TDEs at \(z < 0.8\). The 4.7× increase over the host-cut case shows how many faint-end LF TDEs are lost to the brightness requirement.
No host cut, Illustris evolution (6,585/yr): Full photometric sample with Karmen+2026 rate evolution out to \(z_\mathrm{Ly} = 2.96\). Galaxy-scale enhancements (\(\mathcal{F}(z)\) up to ~27× at \(z=2\)) boost the high-redshift rate, partially offset by BHMF decline.
No host cut, Shankar evolution (4,082/yr): Same but with faster BHMF decline (\(\alpha = -1.46\) vs \(-0.82\)), giving ~40% fewer detections.
Host cut, Illustris evolution (928/yr): The realistic spectroscopic case — rate evolution extends the volume, but the host cut removes most faint TDEs. Only 928/yr survive both filters.

Semi-analytical rate forecasts (Karmen et al. 2026)¶

The TdeRateForecast class reproduces the predictions from Karmen et al. (2026, arXiv:2602.04947) entirely in Rust. These assume perfect survey efficiency (\(\epsilon = 1\)) for time-domain surveys.

Comparison with Karmen et al. (2026) Table 1¶

Computed with TdeRateForecast(temperature_k=30000, n_mc=200, seed=42):

Survey	BHMF	This work	Paper	Ratio
Rubin (LSST)	Illustris	21,383	26,873	0.80
Rubin (LSST)	Shankar	13,135	13,803	0.95
Rubin (DDF)	Illustris	66.7	61.9	1.08
Rubin (DDF)	Shankar	35.5	31.8	1.11
Roman wide	Illustris	58.9	72.3	0.81
Roman wide	Shankar	30.1	33.9	0.89
Roman deep	Illustris	35.3	36.0	0.98
Roman deep	Shankar	15.2	14.2	1.07

Six of eight values are within 15% of the paper. The remaining differences (Rubin Illustris at 0.80, Roman wide Illustris at 0.81) arise from:

Broadband K-correction: We use a top-hat filter approximation; the paper uses sncosmo with realistic filter curves
Lightcurve parameters: We average over the van Velzen (2021) parameter grid; the paper Monte Carlos over the full ZTF sample
Cosmology: We use Simpson's rule integration; the paper uses Romberg integration

Survey specifications¶

Survey	Area	Filter	Depth	\(\epsilon\)	Seasonal
Rubin (LSST)	18,000 deg²	g (482 nm)	25.0	1 (time-domain)	1.0
Rubin (DDF)	50 deg²	g (482 nm)	26.0	1 (time-domain)	0.5
Roman wide	19 deg²	F062 (620 nm)	25.95	1 (time-domain)	1.0
Roman deep	6 deg²	F062 (620 nm)	26.95	1 (time-domain)	1.0

Usage¶

from survey_sim import TdeRateForecast

forecast = TdeRateForecast(temperature_k=30000.0, n_mc=200, seed=42)

# Built-in survey names: rubin, rubin_ddf, roman_wide, roman_deep
result = forecast.compute_rate("rubin", bhmf_model="illustris")
print(f"Rubin Illustris: {result['N_median']:.0f} "
      f"[{result['N_16']:.0f}, {result['N_84']:.0f}] TDEs/yr")
# Rubin Illustris: 21383 [15276, 28091] TDEs/yr

# Custom survey
result = forecast.compute_rate_custom(
    name="ULTRASAT TDE survey",
    area_deg2=204.0, depth=22.5,
    central_wavelength_nm=260.0, width_nm=68.0,
    bhmf_model="illustris", is_time_domain=True,
)
print(f"{result['survey']}: {result['N_median']:.1f} TDEs/yr")

Injection vs analytical: measuring cadence efficiency¶

The injection and analytical approaches answer different questions:

Analytical (\(\epsilon = 1\)): How many TDEs are above the depth limit at any given time?
Injection: How many TDEs actually pass the detection criteria through the real survey cadence?

Rubin cadence efficiency¶

Comparing injection (no host cut, with evolution) to analytical at matched BHMF:

BHMF	Injection (N/yr)	Analytical (N/yr)	Cadence efficiency
Illustris	6,585	21,383	0.31
Shankar	4,082	13,135	0.31

The cadence efficiency of ~31% is consistent across both BHMF models, meaning Rubin's real cadence detects about one-third of TDEs that are above the depth limit. The remaining ~69% are lost to:

Cadence gaps: TDE peaks falling between visits
Detection threshold: Requiring \(\geq 3\) detections at \(\geq 5\sigma\) with \(\geq 48\)hr separation
Seasonal gaps: Some sky regions have months-long gaps between observations
Band coverage: Requiring detections in \(\geq 1\) band with \(\geq 2\) per band

This \(\epsilon \approx 0.31\) is the key result that injection simulations provide beyond analytical forecasts. It can be used to calibrate analytical predictions for realistic survey performance.

Effect of host brightness cut¶

The host brightness cut further reduces the sample by removing faint TDEs that cannot outshine their host nucleus:

Cut	Injection (N/yr)	Factor
No host cut, Illustris	6,585	1.0×
Host cut (\(m_0 = 22.5\)), Illustris	928	0.14×

The host cut removes ~86% of photometrically detectable TDEs — primarily faint events near the LF break that are too dim to stand out against their host galaxies.

Survey-independent population design¶

The population is survey-independent — both ZTF and Rubin use identical parameters:

pop = TdePopulation(z_max=..., use_luminosity_function=True)

The use_luminosity_function=True flag activates:

LF-based magnitude drawing: Peak \(M_g\) drawn from Yao+2023 via rejection sampling (\(M_g = -24\) to \(-15\))
Auto-computed rate: Volumetric rate from LF integration (~829 Gpc⁻³ yr⁻¹)

Adding use_rate_evolution=True further activates:

Evolved redshift sampling: \(dN/dz \propto dV/dz \times \mathcal{F}(z) \times N_\mathrm{BH}(z) \times \mathcal{O}(z) / (1+z)\)
BHMF model selection: bhmf_model="illustris" or "shankar"

The only survey-dependent parameter is the host brightness cut (\(m_0\)), which encodes how bright a TDE must be to outshine its host at the survey's depth.

Architecture¶

The computation is split across Rust modules:

Module	Purpose
`lightcurve::kcorrection`	General-purpose broadband K-corrections (`Sed` trait, `BlackbodySed`, `PowerLawSed`, `TopHatFilter`)
`efficiency::tde`	TDE rate forecast (`TdeLuminosityFunction`, `BhmfModel`, scaling factors, `compute_tde_rate`)
`population::generator`	`TdePopulation` with optional rate evolution (`sample_redshift_evolved`)
PyO3 bindings (`py_rates`)	`TdeRateForecast`, `blackbody_k_correction`, `blackbody_k_correction_instrument`

Performance¶

Implementation	Time (8 survey×BHMF combos)	Speedup
Python (astropy cosmology)	4.3 s	1×
Rust (survey_sim)	0.07 s	60×

The Rust implementation pre-computes cosmology, K-corrections, and the LF integration grid once, then runs the MC loop with minimal overhead.

Scripts¶

Script	Description
`python/scripts/run_tde_ztf.py`	ZTF Yao+2023 validation (100K injections)
`python/scripts/run_tde_rubin.py`	Rubin 10-year prediction (5 configs + analytical comparison)
`python/scripts/run_tde_rates_forecast.py`	Semi-analytical forecast for all surveys

References¶

Karmen et al. (2026), arXiv:2602.04947 — TDE rate forecasts for LSST, Roman, and JWST
Yao et al. (2023), arXiv:2303.06523 — ZTF TDE sample and g-band luminosity function
van Velzen (2021), ApJ 908 4 — TDE lightcurve parameterization
Shankar et al. (2009), ApJ 690 20 — SMBH mass function evolution
Bricman & Gomboc (2020), ApJ 890 73 — LSST TDE predictions