---
title: "Interstellar Radio Propagation Interactive Lab | Sandbox Physics"
description: "Why does one cosmic radio flash arrive at different times and with a rotated polarization? Free electrons delay lower radio frequencies more strongly."
canonical_url: "https://sandboxphysics.com/labs/interstellar-radio-propagation/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/interstellar-radio-propagation/"
last_modified: "2026-10-28"
---

AC06 · A pulse crosses the plasma

# Interstellar Radio Propagation

**Why does one cosmic radio flash arrive at different times and with a rotated polarization?** Free electrons delay lower radio frequencies more strongly. A magnetic field along the path also rotates linear polarization. Unequal paths through density fluctuations spread the pulse into a tail, so its timing and polarization reveal different parts of the intervening plasma.

Drag an electron screen and reverse its magnetic field. Watch a pulse disperse, grow a scattering tail and rotate its polarization, then recover the rotation from recorded detector samples.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

The detector records synthetic Stokes intensity and linear polarization in an observer-frame cold-plasma screen model. A prescribed causal exponential tail represents an isotropic thin scattering screen, with a chosen inverse-fourth-power frequency scaling. Electron column and signed field set dispersion and Faraday rotation independently of that scattering prescription. Gaussian detector noise and rectangular frequency-channel averaging are included. Plasma cutoff, collisions, intrinsic spectral evolution, instrumental calibration, absorption and cosmological propagation are omitted. The scene compresses travel distance and enlarges differential delays. The companion CHIME tutorial uses measured intensity only.

Receiver brightness and polarization marks use the same saved synthetic I/Q/U record as these plots.

A synthetic pulse at the receiver

Align the frequency channels

Recorded linear polarization

Find the rotation measure

Gray profiles precede correction and mint profiles use the selected DM; Q is blue, U pink, and the response-aware RM fit gold, with secondary peaks from sampling aliases.

Readout and fit scope

The scene compresses distance and enlarges differential delay; blue, violet and pink mark high, middle and low frequencies. Receiver brightness uses saved intensity and its direction marks use integrated Q/U; all panels share one frozen synthetic record.

Waterfall brightness uses recorded intensity above zero with a fixed asinh stretch and a blue-white display palette. Replaying the scene preserves the acquired noise samples.

The delay and 600-MHz tail are prescribed model quantities. RM and linear fraction are recovered from time-integrated recorded Q/U, using equal Gaussian channel noise, one Faraday-thin component, and a common intrinsic polarization spectrum. The search spans minus 330 to plus 330 radians per square meter in steps of a quarter. Integration includes the saved window; its exponentially small missing tail is not rescaled. The finite-step scattering kernel gives sub-sample timing uncertainty. The display sample interval adapts to the pulse window.

Physics tutorial

## Three changes to one pulse

**Background** Interstellar space contains free electrons. The pulse drives them back and forth, and their response changes its propagation. A magnetic field adds a different response for the two circular polarization components.

**Why it matters** Arrival times probe an electron column. Polarization probes its magnetic weighting. A scattering tail adds information about uneven paths through the medium.

Start with the essentials

- **Focus question**: Which changes when the field reverses: arrival time, polarization or both?
- **One-sentence intuition**: Dispersion measures electron column; signed Faraday rotation measures the field weighted by that column.

### Core mathematical model

#### Relative group delay

$$
\Delta t=4.149\,\mathrm{ms}\,\frac{\mathrm{DM}}{\mathrm{pc\,cm^{-3}}}\left[\left(\frac{\nu}{\mathrm{GHz}}\right)^{-2}-\left(\frac{\nu_{\rm ref}}{\mathrm{GHz}}\right)^{-2}\right]
$$

Lower frequencies arrive later. The coefficient is rounded, and frequencies are observed frequencies.

#### Faraday rotation

$$
P=Q+iU=L e^{2i\chi},\qquad \chi=\chi_0+\mathrm{RM}\lambda^2,\qquad \mathrm{RM}=0.812\int n_e B_\parallel\,dl
$$

Electron density is in inverse cubic centimeters, field in microgauss and path length in parsecs. Positive field points toward the observer; RM is in radians per square meter.

#### A causal scattering tail

$$
h(t)=\frac{e^{-t/\tau}}{\tau}H(t),\qquad I_{\rm out}(t)=\int I_{\rm in}(t-u)h(u)\,du
$$

The normalized response redistributes fluence toward later times. Its shape assumes an isotropic thin screen.

### Common difficulties

#### A polarization angle repeats

**Typical misconception** A straight line through the displayed angles always gives the rotation measure.

**Better mental model** An angle repeats after a half-turn. Fitting Q and U together avoids choosing an angle unwrap, though finite frequency sampling still creates competing RM peaks.

### Run the experiment

1. 01

   #### Change one sign

   Predict the result, then choose Reverse the field.

   **What to observe:** The rotation-measure peak changes sign. Dispersion follows the same electron column.

2. 02

   #### Spread the arrival paths

   Choose A long scattering tail and compare the dispersed and dedispersed profiles.

   **What to observe:** Removing the frequency delay aligns the leading pulse, but a tail remains within each channel.

3. 03

   #### Average a rotating vector

   Choose Coarse channels lose polarization. Reduce only Frequency channel width.

   **What to observe:** Opposing polarization vectors cancel within wide channels. Narrowing them restores the observed Q and U oscillations.

Physical conclusion

A pulse carries several independent clues about the path. A broad pulse alone cannot determine an electron density or a source mechanism.

## Related experiments and articles

Continue exploring

### Measuring the sky

What do positions, colors, interference and radio delays reveal about the sky?

1. [Lab **Observing Cadence and Aliases** Move exposures and compare the rhythms that survive the sampling.](https://sandboxphysics.com/labs/observing-cadence-aliases/)
2. [Lab **Supernova Distances and the Distance Ladder** Move a geometric distance anchor and follow its shared calibration error.](https://sandboxphysics.com/labs/supernova-distance-expansion/)
3. [Lab **Stellar Parallax and Proper Motion** Change the stellar distance and follow its annual motion.](https://sandboxphysics.com/labs/stellar-parallax-proper-motion/)
4. [Lab **Crowded-star Photometry** Move the aperture and compare the light admitted from neighbouring stars.](https://sandboxphysics.com/labs/crowded-star-photometry/)
5. [Lab **Stellar Absorption Lines** Change the gas temperature and velocity, then compare the absorption lines.](https://sandboxphysics.com/labs/stellar-absorption-lines/)
6. [Lab **Galaxy Colors and Photometric Redshift** Compare redshift, dust and stellar-population effects in the same five bands.](https://sandboxphysics.com/labs/galaxy-colors-photometric-redshift/)
7. [Lab **Stellar Interferometry and Sparse Imaging** Move a telescope and compare images fitted to the same sparse signals.](https://sandboxphysics.com/labs/stellar-interferometer/)
8. [You are here **Interstellar Radio Propagation** Change the electron column and field, then follow the arriving radio pulse.](https://sandboxphysics.com/labs/interstellar-radio-propagation/)

Radio pulses through interstellar space · Reading path

### Radio pulses through interstellar space

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why low radio frequencies arrive late**](https://sandboxphysics.com/stories/interstellar-radio/late-radio/)
2. [Article **From electron motion to a radio delay**](https://sandboxphysics.com/stories/interstellar-radio/electron-column/)
3. [Article **Fit the rotating polarization vector**](https://sandboxphysics.com/stories/interstellar-radio/polarization-vectors/)
4. [Article **Replay a measured CHIME radio flash offline**](https://sandboxphysics.com/stories/interstellar-radio/chime-intensity/)
5. [Article **Read a Faraday spectrum without turning it into a distance map**](https://sandboxphysics.com/stories/interstellar-radio/faraday-depth/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)