How loud would the Sun be?

Question

Sound can't travel through outer space. But if it could, how loud would the Sun be? Would the sound be dangerous to life on Earth, or would we barely hear it from this distance?

Answer 1

The Sun is immensely loud. The surface generates thousands to tens of thousands of watts of sound power for every square meter. That's something like 10x to 100x the power flux through the speakers at a rock concert, or out the front of a police siren. Except the "speaker surface" in this case is the entire surface of the Sun, some 10,000 times larger than the surface area of Earth.

Despite what "user10094" said, we do in fact know what the Sun "sounds" like -- instruments like SDO's HMI or SOHO's MDI or the ground-based GONG observatory measure the Doppler shift everywhere on the visible surface of the Sun, and we can actually see sound waves (well, infrasound waves) resonating in the Sun as a whole! Pretty cool, eh? Since the Sun is large, the sound waves resonate at very deep frequencies -- typical resonant modes have 5 minute periods, and there are about a million of them going all at once.

The resonant modes in the Sun are excited by something. That something is the tremendous broadband rushing of convective turbulence. Heat gets brought to the surface of the Sun by convection -- hot material rises through the outer layers, reaches the surface, cools off (by radiating sunlight), and sinks. The "typical" convection cell is about the size of Texas, and is called a "granule" because they look like little grains when viewed through a telescope. Each one (the size of Texas, remember) rises, disperses its light, and sinks in five minutes. That produces a heck of a racket. There are something like 10 million of those all over the surface of the Sun at any one time. Most of that sound energy just gets reflected right back down into the Sun, but some of it gets out into the solar chromosphere and corona. No one can be sure, yet, just how much of that sound energy gets out, but it's most likely between about 30 and about 300 watts per square meter of surface, on average. The uncertainty comes because the surface dynamics of the Sun are tricky. In the deep interior, we can pretend the solar magnetic field doesn't affect the physics much and use hydrodynamics, and in the exterior (corona) we can pretend the gas itself doesn't affect the physics much. At the boundary layers above the visible surface, neither approximation applies and the physics gets too tricky to be tractable (yet).

In terms of dBA, if all that leaked sound could somehow propagate to Earth, well let's see... Sunlight at Earth is attenuated about 10,000 times by distance (i.e. it's 10,000 times brighter at the surface of the Sun), so if 200 W/m2 of sound at the Sun could somehow propagate out to Earth it would yield a sound intensity of about 20 mW/m2. 0dB is about 1pW/m2 , so that's about 100dB. At Earth, some 150,000,000 kilometers from the sound source. Good thing sound doesn't travel through space, eh?

The good folks at the SOHO/MDI project created some sound files of resonant solar oscillations by speeding up the data from their instrument by 43,000 times. You can hear those here, at the Solar Center website. Someone else did the same thing with the SDO/HMI instrument, and superposed the sounds on first-light videos from SDO. Both of those sounds, which sound sort of like rubber bands twanging, are heavily filtered from the data -- a particular resonant spatial mode (shape of a resonant sound) is being extracted from the data, and so you hear mainly that particular resonant mode. The actual unfiltered sound is far more cacophonous, and to the ear would sound less like a resonant sound and more like noise.

Answer 2

While Sir Cumference's post is a very intriguing answer, but I'm afraid it's wrong. The sun's surface is clearly in motion, but that does not necessarily result in the radiation of audible sound, even if the sun and earth where in a fluid medium (such as a air) that would allow sound transfer.

To explain why, we can actually apply the same line of analysis to the earth's ocean. The surface moves a lot, so sound should be radiated. However, we hear nothing unless you are really close by and have breaking waves.

Let's run the math with rough numbers: The ocean has a surface area of about 510 million square kilometers. $150 \cdot 10^{12} m^2$. Let's say the average wave height is 1m and the average wave frequency is 0.1 Hz (1 wave every 10 s). If the ocean were a spherical source this would create a sound power of $5 \cdot 10^{24} W$ and the sound pressure at 1000 km away would be 240 dB SPL. That's obviously not the case, otherwise we'd all be dead.

So why not? In order for sound to actually radiate, the surface must move uniformly. For every ocean wave that moves air up there is a wave nearby that moves air down and so the contributions simply cancel. Technically speaking, we need to calculate the power by integrating the normal intensity over the entire surface, the intensity has equal amounts of positive and negative components and the sum over those is zero.

That's the same reason why you put a loudspeaker in a box: in open air, the air motion from the front of the cone and from the rear of the cone will simply cancel out, so you put it in a box to get rid of the sound from the rear.

So I think the real answer here is: you would hear absolutely nothing since the sound contributions from different parts of the sun's surface would cancel each other out. Sound radiation over that distance would only occur if the sun's surface moves uniformly, i.e. the whole sun expands or contracts. That does happen to some degree but only at very, very low frequencies which are inaudible and where sound radiation is a lot less efficient.

Answer 3

Along with the other answers, which differ, about the loudness of the Sun there is information available about what it actually sounds like. I would describe it as as varying humming with static.

Listen to the raw audio in this NASA video: "NASA | Sun Sonification (raw audio)", a narrated version by NASA Goddard: "Sounds of the Sun", or visit Goddard Media Studios' webpage: "Sounds of the Sun". The article says nothing about the "loudness".

Another webpage at NASA, with an identical name to the one at GMS: "Sounds of the Sun", provides some additional information:

"The Sun is not silent. The low, pulsing hum of our star's heartbeat allows scientists to peer inside, revealing huge rivers of solar material flowing around before their eyes — er, ears. NASA heliophysicist Alex Young explains how this simple sound connects us with the Sun and all the other stars in the universe. This piece features low frequency sounds of the Sun. For the best listening experience, listen to this story with headphones.

...

These are solar sounds generated from 40 days of the Solar and Heliospheric Observatory’s (SOHO) Michelson Doppler Imager (MDI) data and processed by A. Kosovichev. The procedure he used for generating these sounds was the following. He started with doppler velocity data, averaged over the solar disk, so that only modes of low angular degree (l = 0, 1, 2) remained. Subsequent processing removed the spacecraft motion effects, instrument tuning, and some spurious points. Then Kosovichev filtered the data at about 3 MHz to select clean sound waves (and not supergranulation and instrumental noise). Finally, he interpolated over the missing data and scaled the data (speeded it up a factor 42,000 to bring it into the audible human-hearing range (kHz)). For more audio files, visit the Stanford Experimental Physics Lab Solar Sounds page.​ Credits: A. Kosovichev, Stanford Experimental Physics Lab.".

As is explained on the Stanford webpage: "Solar Sound Speed Variations" they have been able to analyze these sounds to produce a density plot of the Sun. Further information is available on Stanford's webpage: "Helioseismology" where they explain:

"Waves
The primary physics in both seismology and helioseismology are wave motions that are excited in the body's (Earth or Sun) interior and that propagate through a medium. However, there are many differences in number and type of waves for both terrestrial and solar environments.

For the Earth, we usually have one (or a few) source(s) of agitation: earthquake(s).

For the Sun, no one source generates solar "seismic" waves. The sources of agitation causing the solar waves that we observe are processes in the larger convective region. Because there is no one source, we can treat the sources as a continuum, so the ringing Sun is like a bell struck continually with many tiny sand grains.

On the Sun's surface, the waves appear as up and down oscillations of the gases, observed as Doppler shifts of spectrum lines. If one assumes that a typical visible solar spectrum line has a wavelength of about 600 nanometers and a width of about 10 picometers, then a velocity of 1 meter per second shifts the line about 0.002 picometers [Harvey, 1995, pp. 34]. In helioseismology, individual oscillation modes have amplitudes of no more than about 0.1 meters per second. Therefore the observational goal is to measure shifts of a spectrum line to an accuracy of parts per million of its width.

Oscillation Modes
The three different kinds of waves that helioseismologists measure or look for are: acoustic, gravity, and surface gravity waves. These three waves generate p modes, g modes, and f modes, respectively, as resonant modes of oscillation because the Sun acts as a resonant cavity. There are about 10^7 p and f modes alone. [Harvey, 1995, pp. 33]. Each oscillation mode is sampling different parts of the solar interior. The spectrum of the detected oscillations arises from modes with periods ranging from about 1.5 minutes to about 20 minutes and with horizontal wavelengths of between less then a few thousand kilometers to the length of the solar globe [Gough and Toomre, p. 627, 1991].

The image below was generated by the computer to represent an acoustic wave ( p mode wave) resonating in the interior of the Sun.

The figure above shows one set of standing waves of the Sun's vibrations. Here, the radial order is n = 14, angular degree is l = 20, and the angular order is m = 16. Red and blue show element displacements of opposite sign. The frequency of this mode determined from the MDI data is 2935.88 +/- 0.2 microHz.

The wikipedia webpage on Helioseismology offers this power chart:

An analysis of the Sun's p-modes was offered in: "Activity-related variations of high-degree p-mode amplitude, width, and energy in solar active regions" (Jan 21 2014), by R. A. Maurya, A. Ambastha and J. Chae. In section 3 they provide a formula to convert the 3 dimensional resonance to amplitude:

...

"1. Introduction

Photospheric five-minute oscillations, probably first observed by Leighton et al. (1962), are caused by trapped acoustic waves (p-modes) inside the solar interior (Ulrich 1970; Leibacher & Stein 1971) and are well known and have been studied extensively. It is believed that the energy of p-modes is contributed by convective or radiative fluxes. A precise determination of the p-modes properties provides a powerful tool to probe the solar interior. High-degree ($ℓ$ > 200) acoustic oscillations are vertically trapped in a spherical shell with the photosphere as the upper boundary and the lower boundary depending on the horizontal wavenumber, $\small{k^2_h = \frac{l(l+1)}{r^2}}$, and the frequency ($ω$),

$$\frac{l(l+1)}{r^2_t} = \frac{w^2}{c^2_s(r_t)}, \tag{1}$$

where $r_t$ is depth of the lower turning point. Lifetimes of high-degree modes are much shorter than the sound travel time around the Sun, therefore local effects are more important for these modes than for the low-degree modes, which have longer horizontal wavelengths and longer lifetimes. It is likely that high-degree acoustic waves are not global modes, that is, they do not remain coherent while travelling over the circumference to interfere with themselves. Therefore, they can locally be considered as horizontally travelling, vertically trapped waves. These are observed as photospheric motions inferred from the Doppler shifts of photospheric spectral lines.

...

3. Analysis techniques
3.1. Ring diagrams and p-mode parameters

To estimate the p-mode parameters corresponding to a selected area over the Sun, the region of interest is tracked over time. This spatio-temporal area is defined by an array (or data cube) of dimension $N_x × N_y × N_t$. Here, first two dimension ($N_x,N_y$) correspond to the spatial size of the active region (AR) along $x$- and $y$-axes, representing zonal and meridional directions, and the third ($N_t$) to the time $t$ in minutes. The data cubes employed for the ring diagram analysis have typically duration of 1664 min and cover area of 16° × 16° centred around the location of interest. This choice of area is a compromise between the spatial resolution on the Sun, the range of depth and the resolution in spatial wavenumber of the power spectra. A larger size allows accessing the deeper sub-photospheric layers, but only with a coarser spatial resolution. On the other hand, a smaller size not only limits access to the deeper layers, but also renders the fitting of rings more difficult.

The spatial coordinates of pixels in tracked images are not always integer. To apply the three-dimensional Fourier transform on tracked data cube, we interpolated the coordinates of tracked images to integer values, for which we use the sinc interpolation method. Three-dimensional Fourier transformation of data cube truncates the rings near the edges due to the aliasing of higher frequencies toward lower side. To avoid the truncation effects, we apodized the data cube in both the spatial and temporal dimensions. The spatial apodization was obtained by a 2D-cosine bell method, which reduces the 16° × 16° area to a circular patch with a radius of 15° (Corbard et al. 2003).

The observed photospheric velocity signal $v(x,y,t)$ in the data cube is a function of position ($x,y$) and time ($t$). Let the velocity signal in frequency domain be $f(k_x,k_y,ω)$, where, $k_x$ and $k_y$ are spatial frequencies in $x$- and $y$- directions, respectively, and ω is the angular frequency of oscillations. Then the data cube $v(x,y,t)$ can be written as

$$v(x,y,t) = \int \int \int f(k_x,k_y,\omega)e^{i(k_x x + k_y y + \omega t)} dk_x dk_y d\omega.\tag{2} $$

The amplitude $f(k_x,k_y,ω)$ of p-mode oscillations is calculated using three-dimensional Fourier transformation of Eq. (2). The power spectrum is given by $$P(k_x,k_y,\omega) = \left | f(k_x,k_y,\omega) \right |^2. \tag{3} $$

5. Summary and conclusions

We studied the high-degree p-mode properties of a sample of several flaring and dormant ARs and associated QRs, observed during solar cycles 23 and 24 using the ring-diagram technique, assuming plane waves, and their association with magnetic and flare activities. The changes in p-mode parameters are the combined effects of duty cycles, foreshortening, magnetic and flare activities, and measurement uncertainties.

The p-mode amplitude ($A$) and background power ($b_0$) of ARs were found to be decreasing with their angular distances from the disc centre, while the width increases slowly. The effects of foreshortening on the mode amplitude and width are consistent with reports by Howe et al. (2004). The decrease in mode amplitude $A$ with distance arises because with increasing distance from the disc centre we measure only the cosine component of the vertical displacement. Moreover, foreshortening causes a decrease in spatial resolution of the Dopplergrams as we observe increasingly closer toward the limb. This reduces the spatial resolution determined on the Sun in the centre-to-limb direction, and hence leads to systematic observational errors.

The second-largest effects on p-mode parameters are caused by duty cycle. We found that the mode amplitude increases with increasing duty cycle, while the mode width and background power show the opposite trend. Similar results were reported previously for the global p-mode amplitude and width, for example by Komm et al. (2000a). These authors reported the strongest increase in mode width and reduction in amplitude with duty cycle when its values are lower. These changes in mode parameters may be caused by the increase in signal samples in data cubes. However, we found that for a few modes in the five-minute and in higher-frequency bands, the mode amplitudes do not increase significantly with duty cycle. The effect of the duty cycle decreases with increasing harmonic degree $ℓ$. To study the relation of mode parameters with magnetic and flare activities, we corrected the mode parameters of all the ARs and QRs for foreshortening. ...".

The exact loudness, as calculated above, is a function of where and when you measure.

The Wikipedia webpages: Chladni figures (flat), mechanical resonance and Helmholtz resonance (air-filled sphere) provide some related information about the difficulty and complexity of the calculations. The paper: "A review on Asteroseismology" (Nov 7 2017), by Maria Pia Di Mauro discusses standing waves travelling inside the star which interfere constructively with themselves giving rise to resonant modes.