# Why is sun's photosphere a million times less dense than air at the surface of the Earth?

Sun's photosphere is about 19 times as hot as Earth's surface. (Source: http://solar-center.stanford.edu/vitalstats.html)

But Solar surface gravity is about 28 times terrestrial surface gravity.

So, shouldn't the density of gases at the photosphere of the sun be comparable to that on the surface of the Earth?

Why is the density of Sun's photosphere a million times lesser? (Source: http://solar-center.stanford.edu/vitalstats.html)

Essentially, what I am asking has been aptly worded in userLTK's answer, "how can the photosphere be so light and almost vacuum like under such high gravity (28 earth gravity)"?

Some of the answers have suggested that this may be because the Sun's photosphere is ionised. This doesn't seem to be accurate. The Hydrogen ionisation at optical depth = 1 is only 0.04%. (Source: http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1968SoPh....3....5G&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf)

• The question still doesn't make sense. Why do you think it is at all valid to compare the Sun's quite warm (4400 kelvins or more) photosphere with the Earth's much cooler atmosphere? – David Hammen Feb 19 '18 at 21:58
• What's with the downvotes? Isn't curiosity welcome in this community? I don't understand what part of my question makes it so bad that it is better to delete it than to ask it? – Ritesh Singh Feb 20 '18 at 10:41
• @Alchimista Since I don't have a strong mathematical basis for claiming 1.5, I have replaced it with the word "comparable" in the original question. – Ritesh Singh Feb 20 '18 at 14:46
• One thing I would consider is the velocity of the hydrogen molecules at photosphere temperature, and compare that to the solar escape velocity. I'd also look at how far each molecule moves before colliding with another molecule, perhaps it's like the Earth's exosphere en.wikipedia.org/wiki/Exosphere where the atmosphere is no longer behaving like a gas due to lack of collision with other molecules (a property of a gas). There's a good question in here, but it gets tricky, there's a fair bit of physics in it. I'm not sure I'd get it right if I tried to work it out. – userLTK Feb 21 '18 at 0:11
• The hydrogen is not ionised but other things are - sodium, lithium, potassium for example. There are enough free electrons to produce H- ions, and it is these that provide the dominant opacity source. – ProfRob Feb 21 '18 at 0:38

In addition to the two answers above, I'll add that, first, your estimate of a million times seems wrong. These numbers are rough approximations of a fluid, not fixed volume, and I'd take them with a grain of salt too, but Wikipedia gives the density of the photosphere as about 2×10−4 kg/m^3. That's about 1/6,000 (not a millionth) of Earth's atmospheric density at the surface (1.2 kg/m^3).

It's not clear if that density figure is an average for the entire photosphere or closer to the surface where we can measure, but if we measure the entire Earth's atmosphere, the density of our atmosphere drops significantly (how much depends on where you determine the top of the atmosphere is), but that's a problem, there's no absolute boundary, so comparing density is a futile exercise, but the ratio drops to far less than 6,000 to 1, when you take the density of Earth's entire atmosphere. You could also compare the photosphere to Earth's Mesosphere and the photosphere probably becomes more dense, but no matter how you compare, it's always going to be apples to oranges and rather pointless.

The photosphere is about 500 km thick. I don't trust the numbers enough to calculate the pressure at the bottom of the photosphere with any accuracy. If you take a 500,000 meter column at the above density, .0002 kg/m^3, that's 100 kg or 220 lbs per column, worked out to square inches (PSI), .14 psi - 1/100th the pressure on the surface of Earth - but these numbers are terrible and prone to high inaccuracy. I just put this out there to show that the pressure and density at the bottom of the photosphere is still low, but not as low as 1 part in 6000 of Earth's surface.

The gist of your question is, how can the photosphere be so light and almost vacuum like over 500 km thickness under such high gravity (28 earth gravity), and that's a fair question. The answer, as others have pointed out is due to the high temperature and content that's mostly ionized hydrogen in a plasma state. Plasma is a different state of matter than gas and it tends to be much more spread out. The outward pressure of photons may be a key factor too (I'm not 100% sure on that point).

• Thanks userLTK for your answer! I don't think ionisation should play a major role since the Hydrogen ionisation at optical depth = 1 is only 0.04%. (Source: articles.adsabs.harvard.edu/cgi-bin/…). Also, thanks for aptly rewording the question. I have added it to the original question with due credits to you. – Ritesh Singh Feb 20 '18 at 10:44
• I have also added the source for my data about the density of the photosphere being about a million times less than that of air on Earth's surface. – Ritesh Singh Feb 20 '18 at 10:50
• The data mentioned in Wikipedia is incorrect even as per the cited source. I have corrected it and added my source. – Ritesh Singh Feb 20 '18 at 11:03
• I appreciate the vote up, but since I didn't actually answer your question, if someone does, feel free to vote them up. – userLTK Feb 21 '18 at 0:14

I think there is a misconception underlying your question. You write

But Solar surface gravity is about 28 times terrestrial surface gravity.

So, shouldn't the density of gases at the photosphere of the sun be comparable to that on the surface of the Earth?

It does sound natural that a stronger gravity would imply a thicker atmosphere, but no matter how strong the gravity is, there is a point where the atmosphere fades away almost to nothing. At the height of the ISS, earth's gravity is around 80% of the gravity at sea level. But yet the ISS is orbiting in the vacuum of space. Similarly, above Jupiter's atmosphere, the gravity is still more than twice that of earth, but there is still vacuum. With the sun, it just so happens that the part of the atmosphere that produces the light we see is close enough to the (imprecisely defined) edge of space that its density has gone down almost to nothing.

Certainly, if it were cooler, it would be denser. But some day the sun will be a white dwarf, about the size of the earth but with not that much less mass than it has now. Its gravity will be hugely strong, but there will still be a top of the atmosphere were it is less than a millionth of earth's atmosphere. As it cools, that atmosphere will cool so that it is no warmer than earth's atmosphere, but there will still be a point where the atmosphere is that thin. And even above that height, gravity will be much higher than even at the current surface of the sun.

• Thank you for your excellent insightful answer! Why does it happen? Why wasn't Earth able to retain more of atmosphere and why has it retained what it has? When the gravity at the top and the bottom of the atmosphere is similar, what led the bottom of the atmosphere to remain attached to the Earth, while the atmosphere at the top slowly slipped away? – Ritesh Singh Feb 21 '18 at 15:24
• If you think about it, how else could it be? There is only so much matter in the solar system, and most of it is in the sun. Most of the rest is in planets that are moving so fast they don't fall into the sun. Because of gravity, the sun's material squeezes together as much as it can, but since there is only so much material, there is a point where it fades away. If it is warm enough to be a gas, it fades away by roughly the same percentage for every unit of distance until it is indistinguishable from the interplanetary medium. – Mark Foskey Feb 22 '18 at 17:04
• @RiteshSingh The bottom of the atmosphere is compressed by the weight of the top of the atmosphere. Nothing is slipping away to space (well, not much, anyway) – Steve Linton Sep 29 '18 at 18:42

Where the photosphere lies is not only a function of density $\rho$, but also of opacities $\kappa$. One will find it at a particular wavelength wherever the integral optical depth integral $\tau = \int \rho \; \kappa \; dz$ along the line of sight $z$ becomes one.
As the opacities are a strong function of the composition of the atmosphere, it is insufficient to just take gravity and temperature and try to predict the location of the photosphere.

• Thanks AtmosphericPrisonEscape for your answer! I just want to clarify that I am not trying to predict the location of the photosphere. I am just trying to get an explanation for its counter-intuitively low density in an environment of very high gravity (even after accounting for the high temperatures). – Ritesh Singh Feb 20 '18 at 10:47
• @RiteshSingh: I wanted to point out that the density at optical depth is not a meaningful quantity. It becomes meaningful if you take atmospheric opacities into account and compare them to Earth's. Our atmosphere after all also has photospheres in nearly all wavelengths, optical being an important exception. – AtmosphericPrisonEscape Feb 20 '18 at 12:59

The Sun's photosphere is roughly a 400 km thick layer below which almost photons do not escape and above which almost all photons with an outward direction do escape the Sun. Even a fairly diffuse plasma (compared to Earth surface pressure) does a fairly good job of absorbing thermal photons. A somewhat diffuse plasma (e.g., the bottom of the photosphere) does an exceptionally good job of absorbing thermal photons.

The somewhat high temperatures (4400 kelvins or more) in the Sun's photosphere means that a good portion of the gas (mostly hydrogen and helium, plus some trace elements) is ionized. The much lower temperatures (~300 kelvins) in Earth's troposphere means that essentially none of the gas (mostly molecular nitrogen and oxygen, plus some trace compounds) is ionized. The very different temperatures and very different makeup mean that the Sun's photosphere and the Earth's troposphere are incomparable.

• Thanks David for your answer! I don't think ionisation should play a major role since the Hydrogen ionisation at optical depth = 1 is only 0.04%. (Source: articles.adsabs.harvard.edu/cgi-bin/…). – Ritesh Singh Feb 20 '18 at 10:43

The density of the solar atmosphere decreases with radius. The position of the solar photosphere is defined by where the optical depth (measured inwards) reaches unity. There is no direct connection between pressure/density and gravity; only between the pressure gradient and gravity. $$\frac{dP}{dr}= -\rho g$$ A larger gravity merely increases the pressure and density gradient over what it would be in a lower gravitational field at the same density.

The photosphere occurs at the density and temperature it does, because that is where the optical depth reaches unity. The species that dominates the opacity at these temperatures is the H$^{-}$ ion (hydrogen with an extra electron).

The Earth's atmosphere is largely neutral and even at higher densities has a much lower opacity at visible wavelengths.