Recipe for a Dusty Torus

Title: VLTI/GRAVITY Interferometric Measurements of Innermost Dust Structure Sizes around AGNs

Authors: GRAVITY Collaboration – A. Amorim, G. Bourdarot, W. Brandner, Y. Cao, Y. Clénet et al.

First Author’s Institution: Universidade de Lisboa – Faculdade de Ciências, Campo Grande, 1749-016 Lisboa, Portugal

Status: Accepted for publication in A&A [open access]

Step 1: Take a supermassive black hole and add a sprinkle of dust

Today we’re going to bake a cosmic donut, the so-called dusty torus. First, you need to gather your ingredients: a supermassive black hole and, as the name suggests, a handful of dust. This age-old recipe has been around for billions of years and is a key element of an active galactic nucleus (AGN), which harbors a supermassive black hole gobbling down material from its surroundings through a process called accretion. Smaller black holes are thought to grow into the supermassive black holes we see and love today through accretion. However, the accretion process is a messy one, with many moving parts, including both the inflow and outflow of gas! We astronomers are still working on understanding the details of how gas funnels down onto the black hole from larger scales and how this is connected to outflows and the surrounding galaxy. 

One of the reasons that these are difficult systems to study is because we can’t easily take a picture of an AGN and see its structure. Instead, we have to get creative to map the central most regions around the supermassive black hole! For example, combining spectroscopy with polarization (which allows us to peer through the dust in the torus) revealed that the AGN with and without broad emission lines are really just the same system viewed from different angles. Those with broad lines are viewed nearly face on, whereas those without are viewed directly through the dusty torus we’re baking today (which blocks our view of the broad lines). In addition to highlighting the importance of combining various observational techniques, this breakthrough also emphasizes the importance of the dusty torus in how we see AGN!

Step 2: Stir in a few observational techniques

Now, these two techniques are not the only ones we can use to learn about the detailed structure of AGN. Today’s paper combines two other techniques – interferometry and reverberation mapping – to map the structure of the dusty torus. These two techniques are both used to estimate the size of the dusty torus, and yet they often give different answers. First, the authors use a technique called interferometry, which combines light from different telescopes to effectively build a bigger telescope that can resolve smaller spatial scales. Interferometry is commonly done at radio wavelengths, but can also be done in the optical and infrared (where the torus emits most of its light). Doing interferometry at shorter wavelengths of light requires actually physically combining the light (rather than electronically combining them, like is done at radio wavelengths), and only a handful of instruments are able to overcome this major technological challenge. In today’s paper, the authors analyze data from the state-of-the-art near-infrared interferometry instrument called GRAVITY, which combines light from four 8m telescopes that are part of the Very Large Telescope Interferometer (VLTI). GRAVITY can resolve scales down to 3 milliarcsec, which is like being able to see a car on the moon! 

The second measurement in this paper uses a technique called reverberation mapping, which maps the size of the torus by measuring how it responds to the light coming from close to the supermassive black hole. Essentially this technique is like the echolocation that bats use, just instead of using sound waves, we use light! Since we know the speed of light, we can measure the time delay between the light from close to the black hole and light from the torus to infer the distance between them. The authors compiled the reverberation mapping estimates of the torus sizes from the literature to compare to their interferometry results. 

Figure 1 shows both the optical/infrared interferometry (OI) measurements and reverberation mapping (RM) measurements of the dusty torus sizes as a function of the total amount of light (luminosity) emitted by the AGN. Because the size of the torus is set by the distance at which dust can survive the intense luminosity of the AGN, we expect the size of the torus and the luminosity of the AGN to be related by R ∝ L0.5. Both OI and RM measurements are consistent with this theory! However, these measurements use the bolometric luminosity of the AGN (i.e. all of the light from all wavelengths, summed up). The authors show that comparing the radius to only the optical luminosity, for example, does not produce consistency with the theory. This tells us that we need to account for all of the light from the AGN when looking for correlations with the torus size! 

Measurements of the radius of the dusty torus as a function of the bolometric luminosity of the AGN. Both the OI (red) and RM (blue) measurements show consistency with the expected theory.
Figure 1: Radius of the dusty torus versus the total luminosity emitted by the AGN. The red shows the interferometry results, whereas the blue shows the reverberation mapping results. Both show a clear correlation with luminosity, as expected from theory, but the reverberation mapping gives consistently smaller torus sizes. Adopted from Figure 2 of today’s paper.

Step 3: Add a little flare and bake!

Another important finding from Figure 1 is that the RM measurements are consistently smaller than the OI measurements. This can naturally be explained with different torus geometries since the OI measurement is sensitive to projected torus distribution on the sky, whereas the RM measurement depends on the response of the dust at a range of radii. One way to produce a smaller radius with RM is a flared torus model, which is shown in the top right panel of Figure 2. In this geometry, the light from the center will (on average) hit the torus at a smaller radius than in a flat geometry, therefore producing a smaller measured RM radius relative to the OI measurement! The authors take this a step further and predict the OI and RM results for different assumptions about the torus shape. They find that this flared, bowl-like structure can match the average observed ratio of ROI/RRM ~ 2 with reasonable values for the radial and vertical distributions of material!

Top panels show two different geometries for the dusty torus, a thin disk on the left and a flared disk on the right. The bottom panel shows color for how the distribution of gas/dust affects the measurement of R_OI/R_RM
Figure 2: Modeling of the torus to produce the observed OI/RM signals. The top panels show two different example geometries for the torus. The left geometry, a thin disk, will produce an RM signal that roughly matches the OI signal. The right geometry, a flared disk, will produce an RM signal that is smaller than the OI signal because the central light will hit the flared torus at a smaller radius. The bottom panel shows the expected value or ROI/RRM for different assumptions about the vertical (β) and radial (α) distribution of material in the torus. This model can produce the observed ratio of ~2 for a relatively flared disk geometry (β > 0.5). Adapted from Figures 4 and 5 of today’s paper.

Bonus Step: Bake it again, but add another ingredient!

Want to make this recipe a bit more complex? The authors recommend adding in another ingredient: the rate of accretion onto the black hole (i.e. how quickly the black hole is gobbling down material). There is evidence from other techniques that the dusty torii around more rapidly accreting black holes covers less of the sky – is this consistent with their ROI/RRM ratios? More data is needed to assess this question, since most of the results here are from AGN with similar accretion rates, but keep your eyes peeled for an updated recipe with this new ingredient involved!

Astrobite edited by Nathalie Korhonen Cuestas

Featured image credit: modified from ESA/Hubble 

About Megan Masterson

I'm a 5th year PhD student at MIT studying transient accretion events around supermassive black holes, including tidal disruption events and changing-look AGN. I use a variety of telescopes across the electromagnetic spectrum to study these events, from ground-based optical telescopes to space-based X-ray and infrared telescopes! In my free time, you'll find me hiking, reading, and watching women's soccer.

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