cosmic-microwave-background - 2.7 degrees but does the Big Bang care? The Big Bang is a proposed answer to the beginning of the universe, and the Cosmic Microwave Background or CMB is a central part of the evidence for it.

Now suppose the measurement returned a different value than 2.7K.

What if it were 0.27K or 27K?  Would the Big Bang theory still work with a few minor adjustments or is the specific temperature of 2.7K critical evidence that the theory works?

Edit: I have removed a paragraph which was not mine asking about small changes in temperature. It is a fundamentally different question. I am more interested in how firm the evidence for the BB theory is, not its details. At least for this question.
However if uhoh who seems to have done the editing thinks it a fair question, I would certainly welcome it - in another post.

The expansion of the universe is described by a scale factor that we normally call $a(t)$. We take the scale factor to be equal to one right now, so if $a(t)$ is less than one that means the universe has contracted while if $a(t)$ is greater than one the universe has expanded.

General relativity allows us to calculate how the scale factor depends on time. If you're interested I do this in the question How does the Hubble parameter change with the age of the universe? on the Physics SE. This is what the results look like:

The point of this is that the CMB temperature is directly related to the scale factor so if we can calculate how the scale factor has changed with time then we can calculate the current CMB temperature.

But the way the scale factor changes with time depends on the density of matter and energy in the universe. Specifically it depends on how much light, matter (normal and dark) and dark energy is present. The matter/energy density could in principle have any values, that is there is no fundamental principle in physics that specifies what the densities of the of the various types of matter and energy have to be.

Our current best measurements of the matter/energy density come from the Planck experiment, and they suggest the total density has a value close to the critical density. This density gives us the form of the scale factor that I drew above, and it gives us the CMB temperature of 2.7K. If the density were lower than critical we would get a lower CMB temperature and if the density were higher than critical we get a higher CMB temperature. So the answer to your question is that the CMB temperature is not uniquely determined and it could be higher or lower. Ultimately the CMB temperature is an experimental parameter that we have to determine by making experimental measurements.

But we should note that there are excellent reasons why we would expect the matter/energy density to be equal to the critical density, so we would expect the CMB temperature to be what we observe. If the CMB temperature were different by a factor of ten that would be hard to explain theoretically.

Finally we should note that there are other independent constraints of the form of the scale factor function. Rob Jeffries describes some of these in his answer so I won't go through them again here, but for example the ratio of hydrogen to helium depends on how quickly $a(t)$ increased after the Big Bang. If the scale factor had increased significantly faster or more slowly it would have changed the hydrogen to helium ratio and we'd be able to measure this change.


Brightness, altitude & azimuth for satellites? I'm using the heavens-above website to identify a satellite I've seen several nights this week.

The question is related to how I can search the satellites table with the information I can provide.

The page has a table that has the satellite name, Brightness (mag), and Time, Altitude, and Azimuth for Start , Highest point and End. I don't know how brightness and altitude are measured, and I don't know how the start, highest, and end points are measured. In terms of azimuth, if I base it on this compass, and based on the time I saw it, I would have to say NNE.

With that said, last night I was sitting looking straight north. I first saw the satellite, literally moving directly over my head, at 7:33pm EST and stopped seeing it at a 7:36PM EST because it was too far. The satellite was going North and just a bit to the East.

My question: how can I use this information to search for the satellite in the table? Also, how do I know what's the Brightness (mag)? The satellite is so tiny that it's almost impossible to see with the naked eye.

Altitude is measured in degrees above the horizon, from 0° on the horizon to 90° directly overhead.
Your fist appears about 10° wide at arm's length away from your eye.

Azimuth is measured along the horizon, usually with north 0°, east 90°, south 180° west 270°, and other directions (e.g. NNE, ENE) interpolated as in the compass image.

Magnitude is a logarithmic scale in which the brightest stars are 0 or 1, and the faintest stars visible to the unaided eye are 4 or 5 (maybe 2 or 3 in a city, or 6 in a remote area).

Each row of Heavens-Above's table links to a sky chart showing their predicted path for that satellite pass.
The brightness listed in the main table is a maximum; the table under the sky chart shows a brightness for other points on the path.


What are evidences of stationarity of rotation of galaxies Recently I have found the article Does There Really Exist the Problem of the Dark Matter in Spiral Galaxies? which states that dark matter does not exist because astronomers are wrong assuming stationarity of galaxy rotation.

According to them Doppler measurements give only one component of speed which is insufficiebt to restore full three dimensional vector. So they claim that stars in galaxies are on escape tragectories but reproduce correst rotational curves if we assume stationarity of rotation.

What are evidences that this is not true, what about measurements of proper motions, not doppler shifts only?

If stars were actually about to escape, they would do so on a so-called dynamical timescale:
$$
t_\mathrm{dyn} \sim \sqrt{\frac{R^3}{8GM}},
$$
where $G$ is the gravitational constant, and $R$ and $M$ are the radius and the mass of the galaxy, respectively. For a Milky Way-sized galaxy, this is equates to roughly 30 million years$^\dagger$. But disk galaxies are observed over time spans of billions of years. If they had for some reason been gravitationally bound and then "unleashed", they would have to be so at times synchronized such that we, today, in all directions, observe them in a state that has a very short time span compared their lives throughout the history of the Universe. That is, distant galaxies (which are young because we look far back in time) were unleashed early in their lives, and nearby galaxies (which we see in the "old age" because we look less far back in time) were unleashed recently. This not only seems unlikely, but would also put us in a special place in the Universe.

Note also that the paper you link to is over 20 years old, non-refereed and has no citations (and that the author in general has very few citations). Of course this by no means implies that he's wrong, but it does give a hint that it's a good idea to be cautious of the conclusions of the paper. Since that paper was written, much more independent evidence for dark matter has been obtained.

$^\dagger$Since the roughly constant rotation speed of disk galaxies with galaxy mass (a few 100s of km/s) implies that $R$ grows approximately linearly with $R$ (and not with $R^3$ as one might expect), smaller galaxies — which exist in much larger numbers than large galaxies — have even shorter dynamical timescales.


Verifying refractor lens about scratches I found an used Skywatcher 70mm telescope for buying, but its lenses are a little suspect about harming. In one photo, it looks clearly a scratch, but in the another, it is not visible. Could it be an optical illusion or is it really a harm? If it's a scratch, should I discard the possibility of buying?

Pointing where I think there are scratches:

Price vs. quality.   You're unlikely to see any significant degradation in the final image if those are scratches.  However,  that is not how you should make your purchase decision.  You want to inspect the entire body for any evidence of dents, bends, etc. which indicate rough usage, not to mention misalignment of the optical elements.

If you can't try out the 'scope in person, make sure there's a 100% refund guarantee before having it shipped to you.


Conversion of matter into antimatter Is it possible that the intense gravity of a black hole converts matter into antimatter? Does this mean that matter or energy that goes inside the black hole is converted to antimatter?

It would be more accurate to say that a black hole eventually turns whatever falls in it into equal quantities of matter and antimatter.

The difference between matter and antimatter is defined by some conserved (or approximately conserved) quantum numbers. For example, matter baryons and quarks have positive baryon number, while antibaryons and antiquarks have negative baryon number. Leptons (e.g., electrons, neutrinos) and their antiparticles have a corresponding lepton number instead.

Semiclassically, a black hole evaporates through Hawking radiation. For astrophysically large black holes, this will be overwhelmingly be in terms of photons, which are their own antiparticles, but once the black hole evaporates to a small enough size, it will also radiate massive particles as well. Because there are no long-range forces that couple to baryon number or lepton number, a black hole is under no obligation to conserve them, and thus should radiate equal amounts of matter and antimatter, regardless of what fell into it.

This is unlike, say, energy-momentum, electric charge, and angular momentum, the presence of which makes a difference in the long-range gravitational and/or electromagnetic fields. Thus the total amount of charge the black hole will radiate should match the total amount that fell into it, etc.

Unless, of course, quantum gravity gives us more surprises, which is definitely possible.


Is there a spectrum of polarization? Does polarization vary depending on wavelength, from one and the same source? Is it possible, and does it occur naturally, that the light from the same source is simultaneously polarized differently at different wavelengths? Light can be polarized by interstellar magnetic fields. Could it polarize light of different wavelengths differently? Does a pair of polarized sunglasses polarize radio waves and UV in the same way as visible light?

Yes. Radiation may be polarized when it is scattered, and different media scatter different wavelengths differently.
For instance, neutral hydrogen scatters Lyman $\alpha$ radiation (i.e. photons coming from the $2$$\rightarrow$$1$ transition of hydrogen). The degree of polarization is coupled to the "phase function" which determines in which direction it is scattered. If a Ly$\alpha$ photon is close to the line center (which is at 1215.67 Ångström), it is scattered isotropically (i.e. equal probability of being scattered in any given direction), and will not be polarized, but if it is more than a few Doppler widths from the line center, it is scattered anisotropically, and will then be polarized. Maximum polarization occurs at 90º scattering, where $3/7 \simeq 43\%$ of the light will be polarized.
If the photons are even farther from the line center, they won't be scattered at all (because they're no longer in resonance with the $2$$\rightarrow$$1$ transition), and the radiation is hence unpolarized.
Example of polarization at a particular wavelength
The figure below, taken from Hayes et al. (2011), shows a so-called "Lyman $\alpha$ blob", which is a source of Lyman $\alpha$ that is quite a lot larger than a galaxy. There was some debate whether the radiation is created outside a central galaxy from gas accreting onto the galaxy and cooling — a signature of galaxy formation — or whether it is centrally produced (from stars) radiation that escapes the galaxy and subsequently scatters on the surrounding gas. If the latter scenario is true, you would expect the Lyman $\alpha$ to be polarized to some degree in sort of a ring around the center, because this light would be scattered at roughly 90º toward you. In the figure, the blue cross marks the center, and the red lines' direction mark the direction of polarization and their length mark the degree of polarization (if it were fully polarized, they would have the length of the red bar in the upper right corner).
Indeed it seems that the light is polarized around a central source.