Stop, Drop, and Roll: TDE Photons and Their Misleading Spectra

Title: The X-Ray through Optical Fluxes and Line Strengths of Tidal Disruption Events
Authors: Nathaniel Roth, Daniel Kasen, James Guillochon, and Enrico Ramirez-Ruiz
First Author’s Institution: UC Berkeley
Status: Open access in The Astrophysical Journal

This guest post was written by Lindsay DeMarchi, an astronomy PhD student at Northwestern University. Lindsay uses gravitational waves and the whole of the electromagnetic spectrum to study the role of gravity in stellar deaths. Lindsay is also heavily involved in outreach at Northwestern, and enjoys finding creative ways to present data.

An astronomer’s favorite tool is optical spectroscopy; it allows us to peer directly into the unknown and gather a census of elements along our line of sight. Familiar combinations and patterns of emission and absorption that appear consistently among similar sources are a handy way for astronomers to identify subclasses of stars, galaxies, and transients. For example, supernovae subdivide into categories of hydrogen and helium abundance.

A puzzling aspect of tidal disruption events (TDEs), stars decomposed and devoured by black hole companions, are that their spectra reveal excess flux at UV/optical wavelengths orders of magnitude higher than predictions. Even more confounding, stars of solar metallicities are torn apart, yet reveal barely any hydrogen in their spectra! How do they silence themselves so effectively?

Roth et al. highlight the chilling implication that when we “look directly” at an object, we could be grossly underestimating the amount of hydrogen or helium actually present due to other emission processes affecting the spectra.

Choosing Your Own Adventure
When a black hole rips apart an orbiting star, the debris forms a spherical cloud as shown in Figure 1. Soft x-rays (20-100 eV— energy and wavelength are interchangeable) are born in the hot, radiative, luminosity-giving environment near the black hole at the inner radius of the envelope.

Figure 1: Map of TDE envelope photospheres. You can think of these as effective 
layers of material. Figure 1 of the paper.

X-rays must survive the journey through the rest of the envelope to reach us, and their energies determine their potential paths.

The largest obstacle for soft x-rays is absorption by HeII, plentiful in stars of solar metallicity. At a threshold energy of 54.4 eV, HeII photoionizes to HeIII. This means photons 54.4 eV or greater are absorbed by HeII and evict an electron upon collision. 54.4 eV is well within the bounds of the UV/soft x-ray regime, so it’s why the authors focus on this element! 

If the luminosity seeded by the black hole’s radiation is sufficiently higher than this value, the entire environment is effectively composed of HeIII. Roth et. al. define this critical luminosity, Lion, as a function of envelope mass, energy, and radius. Environments greater than Lion are best for soft x-rays because HeIII cannot ionize any further. Consequently, the photons sneak past their atomic enemies unnoticed and unaltered.

The path becomes much more perilous in an environment less than or equal to Lion. For example, larger envelope radii have temperatures cool enough for HeIII to recombine with free electrons and return to HeII. In such an instance, the photons see a long path of HeII hungry to devour and photoionize.

To make matters worse, a bath of rogue mercenary electrons await. While the photons attempt to random-walk their way out of the cloud, electrons pickpocket their energy as they collide. As a result, photons that began as energetic, soft x-rays reprocess to lower-energy (longer wavelength) UV/optical photons.

Building the Boss-Level
Roth et. al. adjust three knobs: the envelope’s inner radius, mass, and luminosity at the center. These are tweaked in Figure 2; each panel has the other two quantities held fixed.

Figure 2: First panel: changing the inner radius. Dotted lines show uninterrupted x-ray photons. Solid lines show the excess of optical flux from reprocessing. Second panel: changing the envelope mass. Increased mass causes similar excess in optical flux. Third panel: changing source luminosity. The x-ray peak moves to higher energies, but does not greatly contribute to excess optical flux. The grey line is a luminosity too weak to photoionize HeII, dooming photons to absorption. Figures 4-6 of the paper.

The wear and tear of this journey are most obvious in the first panel of Figure 2. Rugged x-ray photons struggle against HeII and free electrons, eventually emerging as reprocessed optical photons. This is the cause of the puzzling flux excess. 

X-ray photons similarly reprocess as we increase envelope mass and hold the radius fixed (increasing density, middle panel of Figure 2). This is akin to increasing the possible encounters a photon can experience leaving the TDE envelope. As a result, x-rays are more likely to fall prey to a free electron or HeII atom.

Turning up the luminosity at the center creates an environment of majority HeIII. In the third panel of Figure 2, larger luminosity values migrate the flux peak to higher energies as x-rays escape the cloud relatively unscathed. To convince yourself of this, compare their profile to the dotted lines of the first panel!

Bittersweet Victory
By following the path of the photon, we understand how x-ray reprocessing produces mysterious excess flux at optical wavelengths. This same explanation also applies to the second mystery: why hydrogen shows up in such small quantities, even for solar-metallicity stars.

Figure 3 summarizes the different endings of our photons. Even if there is much hydrogen in the envelope, it is possible for the continuum of reprocessed x-rays to almost completely drown out hydrogen line emission. You can think of reprocessed x rays like a rising tide in your spectrum (Figure 2, panel 1 is helpful), while specific elements resemble a mountain. You cannot know how deep underwater the mountain truly extends. In other words: you cannot be certain how much hydrogen exists, washed out by the continuum! 

Figure 3: The resulting spectra of a solar mass star with varying envelope densities. Notice for high densities, the hydrogen disappears! Figure 7 of the paper.

Following common practice and fitting the continuum to a single blackbody, the average astronomer makes a dangerous assumption: taking their spectra at face value, they conclude their TDE emits heavily at optical wavelengths. But, if these photons could confess the details of their journey, they would reveal they were born as x-rays, not optical photons at all! To emit x-rays, a source must be far more energetic and luminous than one producing the same spectra with natively optical photons.

Instead, the authors advise to fit multiple blackbodies to TDE spectra. Doing so more accurately chronicles the adventures of each photon escaping the envelope, accounts for the true peak in x-ray emission, and explains the puzzling presence of excess optical emission and startling lack of hydrogen.

Astrobite edited by Ali Crisp
Featured image credit: NASA / Chandra X-ray Center / M. Weiss

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