# Paper Summaries

#### Polarimetry of Faint Sources with ALMA: a How-to Guide

We reanalyzed published Atacama Large Millimeter/Submillimeter Array (ALMA) linear polarization observations of a Gamma-ray burst, and demonstrated that the published detection suffered from instrumental systematics. We recommended the following series of tests while working with polarimetry of faint sources with ALMA and other radio interferometers:

1. Check that the residual polarization of the polarization calibrator after polarization calibration is consistent with noise.
2. Check that the ratio of the parallel hand gains (e.g. XX/YY) is uniform and low for all antennas after polarization calibration.
3. Check that the rms gain ratio is uniform across antennas.
4. Check the magnitude of the leakage (D-terms) is consistent with known values for the array.
5. Check the net (averaged over baselines) instrumental polarization is consistent with expectation for the array.
6. When self-calibrating, ensure that solutions are calculated only at intervals larger than the minimum theoretical solution interval.
7. When self-calibrating, keep the phase offset between the two polarizations fixed.
8. Test the source for time-variable polarization by dividing the data up into time bins (e.g., for ALMA, using the three executions of the scheduling block).
9. Test the source for frequency-dependent polarization by dividing the data up into frequency bins (e.g. by spectral window).
10. Image the gain calibrator, check that it appears as a point source, and verify that any secondary peaks in both Stokes Q and U images are consistent with noise.
11. Test the gain calibrator for time and frequency-dependent polarization by dividing the data into time and frequency bins.
12. Check Stokes V for spurious polarization signal in both the target and the gain calibrator
13. Repeat the calibration and all the above steps with a different reference antenna.
14. If feasible, employ a check source during the observations, and verify that it's polarization properties are (i) stable, and (ii) agree with published values.

We also surveyed linear polarization observations of GRBs at radio wavelengths and concluded that significant improvements in instrumental sensitivity are necessary for detecting polarized emission from Gamma-ray bursts routinely.

#### A Reverse Shock in GRB 181201A

We used the Atacama Large Millimeter/Submillimeter Array (ALMA) and NSF's Karl G. Jansky Very Large Array (VLA) to capture radio emission simultaneously from the reverse shock and forward shock in a GRB jet for the first time. The reverse shock propagates into the GRB jet, and the forward shock into the ambient environment. Capturing light from them both at the same time allows us to measure infer physical quantities about the jet, such as its speed, composition and the relative magnetization of the two shocks. This is because these quantities are related to the ratios of the peak brightness (and peak frequencies) of the emission from the two shocks. With this measurement, we were able to break the degeneracies and infer the initial speed of the jet at launch (Γ0), the time it took the jet to decelerate (tdec), and the shock magnetization ratio (RB).

We conducted this analysis with a modeling software I wrote using python for my dissertation at Harvard University.

The next steps are to measure these quantities for more events, and see whether there is any pattern in the relative shock magnetization with other properties of the gamma-ray burst.

#### First Detection of Radio Polarization from a Gamma-ray Burst

##### Laskar et al, The Astrophysical Journal Letters, 878, 26 [ADS, Journal]

We used the Atacama Large Millimeter/Submillimeter Array (ALMA) to capture linearly polarized light from the radio afterglow of a gamma-ray burst for the first time. By combining the ALMA data with observations from NSF's Karl G. Jansky Very Large Array (VLA), we showed that the polarized light came from a shock produced in the gamma-ray burst jet upon its collision with the pre-explosion environment.

Our research made it to the Editor's Pick on Physics World! From this discovery, we were able to measure the size of coherent magnetic field patches in the GRB jet: about 60 astronomical units, or about the diameter of Neptune's orbit. We found that the jet does not contain large-scale ordered magnetic fields, as previously thought. Instead, the field is broken up into many little patches, each with its own orientation.

Here's a video I produced together with physicist Kitty Yeung to describe this research.

#### A New Analytical Model for the Spreading of Relativistic Jets

We presented a new, semi-analytical model on the spreading of relativistic jets by performing relativistic numerical jet calculations. We derived the relationship between the Lorentz factor, opening angle, and shock radius. We then used the analytical model to calculate the Lorentz factor and jet opening angle as a function of the shock radius and calibrated our analytical model to the numerical solutions.

#### ALMA Creates Its First-ever Movie of a Cosmic Explosion

We produced the Atacama Large Millimeter/Submillimeter Array's (ALMA) first-ever time-lapse movie of a cosmic explosion! Our ALMA observations of GRB 161219B provided the first ALMA of a GRB, and revealed a surprisingly long-lasting reverse shock echoing back through the jet. The light from the reverse shock shines most brightly at the millimeter wavelengths on timescales of about a day, which is most likely why it has been so difficult to detect previously. As the reverse shock entered the jet, it slowly but continuously transferred the jet’s energy into the forward-moving blast wave, causing the X-ray and visible light to fade much slower than expected. We have always puzzled where this extra energy in the blast wave comes from. Thanks to ALMA, we know this energy – up to 85 percent of the total in the case of GRB 161219B – is hidden in slow-moving material within the jet itself.

We turned the light into sound! Hear the full data set below (the reverse shock in the ALMA band is audible as a series of double chimes at 16 - 17 seconds).

Here's an audio-only version. Check out the original blog post here.

#### Uncovering the Flash From a High-speed Shell Collision

We found a highly unusual radio spectrum in a Gamma-ray burst, which points to evidence of a high-speed collision between two relativistic shells travelling with the Lorentz factors of $$\Gamma_1 \approx 110$$ (99.992% of the speed of light) and  $$\Gamma_2 \approx 160$$ (99.996% of the speed of light), respectively. We see a flare in the X-ray brightness at about 2 minutes (in the frame of the galaxy where this event occurred) after the burst. If we associate that time with the ejection of the second shell, then the two shells collide about 30 minutes after the second shell was emitted. The collision results in a rebrightening in the X-rays as well as radio emission from (reverse) shocks that resound through both shells - and these double reverse shocks fully explain the unusual radio observations.
We also stressed the diagnostic power of millimeter-band observations. In this particular case, we found a high value of the forward shock partition parameters, $$\epsilon_e + \epsilon_B \approx 1$$; however, lower values are also allowed, and the difference could be discerned with deeper millimeter-band observations. It is possible that some previous works suffer from similar hidden degeneracies.