The Science of Interstellar

Gargantua’s disk looks quite different from the pictures of thin disks that you see on the web or in astrophysicists’ technical publications, because those pictures omit a key feature: the gravitational lensing of the disk by its black hole. Not so in Interstellar, where Chris insisted on visual accuracy.

Eugénie von Tunzelmann was charged with putting an accretion disk into Oliver James’ gravitational lensing computer code, the code I described in Chapter 8. As a first step, just to see what the lensing does, Eugénie inserted a disk that was truly infinitesimally thin and lay precisely in Gargantua’s equatorial plane. For this book she has provided a more pedagogical version of that disk, made of equally spaced color swatches (Inset in Figure 9.7).

If there had been no gravitational lensing, the disk would have looked like the inset. The lensing produced huge changes from this (body of Figure 9.7). You might have expected the back portion of the disk to be hidden behind the black hole. Not so. Instead, it is gravitationally lensed to produce two images, one above Gargantua and the other below; see Figure 9.8. Light rays emitted from the disk’s top face, behind Gargantua, travel up and over the hole to the camera, producing the disk image that wraps over the top of Gargantua’s shadow in Figure 9.7; and similarly for the disk image that wraps under the bottom of Gargantua’s shadow.

^{Fig. 9.7. An infinitesimally thin disk in Gargantua’s equatorial plane, gravitationally lensed by Gargantua’s warped space and time. Here Gargantua spins very fast. Inset: The disk in the absence of the black hole. [From Eugénie von Tunzelmann’s artistic team at Double Negative.]}

^{Fig. 9.8. Light rays (red) bring to the camera images of the back part of the accretion disk, behind Gargantua: one image above the hole’s shadow, the other below the hole’s shadow.}

Inside these primary images, we see thin secondary images of the disk, wrapping over and under the shadow, near the shadow’s edge. And if the picture were made much larger, you would see tertiary and higher-order images, closer and closer to the shadow.

Can you figure out why the lensed disk has the form you see? Why is the primary image wrapping under the shadow attached to the thin secondary image wrapping over it? Why are the paint swatches on the over-wrapping and under-wrapping images widened so greatly, and those on the sides squeezed?…

Gargantua’s space whirl (space moving toward us on the left and away on the right) distorts the disk images. It pushes the disk away from the shadow on the left and toward the shadow on the right, so the disk looks a bit lopsided. (Can you explain why?)

To get further insight, Eugénie von Tunzelmann and her team replaced their variant of the color-swatch disk (Figure 9.7) with a more realistic thin accretion disk: Figure 9.9. This was much more beautiful, but it raised problems. Chris did not want his mass audience to be confused by the lopsidedness of the disk and black-hole shadow, and the shadow’s flat left edge, and the complicated star-field patterns near that edge (discussed in Chapter 8). So he and Paul slowed Gargantua’s spin to 0.6 of the maximum, making these weirdnesses more modest. (Eugénie had already omitted the Doppler shift caused by the disk’s motion toward us on the left and away on the right. It would have made the disk far more lopsided: bright blue on the left and dim red on the right—totally confusing to a mass audience!)

^{Fig. 9.9 Gargantua with the infinitesimally thin paint-swatch disk (Fig. 9.7) replaced by a more realistic, infinitesimally thin accretion disk. [From Eugénie von Tunzelmann’s artistic team at Double Negative.]}