# How does one measure velocities of far-off, bright objects

As the title already says, I want to know how one measures velocities of far-off, bright objects, e.g. when the mean parallax drift isn't measurable with current apparatus (this means when there is only a "non-moving" picture of that object available)

I know that one can measure the redshift of spectral lines and correct them for gravitational redshifting if the distance is already known. But then the relation between source-frequency $f_S$ and observed frequency $f_O$ is $$f_O = f_S frac{sqrt{1-frac{v^2}{c^2}}}{1+frac{v}{c}cos(alpha)}$$, where $alpha$ is the angle between line of sight and the velocity vector.

If one only has a "non-moving" picture of the object, there is no way to determine this angle $alpha$ and therefore no way to get the velocity by means of redshift.

As an addition: At which distance does the mean parallax drift become unmeasurble with current apparatus?

The "redshift" of a distant galaxy is defined in terms of its line of sight velocity. In our model of the expanding universe, once we move away from the local group of galaxies (which have their own peculiar motions), distant galaxies follow the Hubble flow and to first order have a line of sight velocity tht is proportional to their distance way (it gets more complicated for very distant galaxies).

Distant galaxies may well have a "tangential" velocity too, but for galaxies outside the local group these velocities will be be negligible compared with the redshift. i.e. The line of sight velocity due to the expansion of the universe is dominant.

I guess by "parallax drift" you actually mean proper motion - which is the rate at which a star's position changes with respect to the celestial coordinate system. This proper motion depends on how far away the star is and how fast it is moving tangentially with respect to the solar system.

Thus to estimate a tangential velocity you need both the proper motion and the distance to the star.

I think the most distant object for which a proper motion has been determined with any accuracy is the Andromeda galaxy, which is a couple of million light years away. This was achieved by studying the position of many stars in Andromeda over a 7 year period using the Hubble Space Telescope. The details can be found in Sohn et al. (2012); but the headline numbers are that the proper motion is a mere $sim 0.05$ milli-arcseconds per year(!) , implying a tangential velocity (with respect to the solar system) of about 150 km/s.

Another candidate is measuring the velocities of material in the jet of the active galaxy M87 by Meyer et al. (2013). This galaxy is at 50 million light years, but the motion of the jet is only detectable here because it is moving relativistically.

These are quite special cases. In general, the tangential velocities of stars in our Galaxy are small and large-scale susrveys of proper motions are generally inaccurate beyond a few thousand light years. The upcoming Gaia results will improve this dramatically meaning we have good proper motions for objects out to tens of thousands of light years.

In general the total velocity of a faraway object is not obtainable, only the component along the line of sight. However, if a star is not too far away, and its position on the sky is measured very accurately with an interval of some years, the velocity component perpendicular to the line of sight can be determined, yielding together with the redshift the total velocity. The recently launched Gaia spacecraft is expected to be measure the proper motion of millions of stars in this way.

In distant galaxies, this is not possible. If one is interested in, say, the 3D velocity dispersion of the gas, the 1D dispersion is measured, and assuming (fairly) an isotropic dispersion, this number is then multiplied by $sqrt{3}$ to get the total velocity.

The distance to which parallax is measurable depends on the angular resolution of your instrument. For milliarcsec resolution, parallax measurements are good out to roughly 1 kpc. If you wait long enough, the motion around the galactic center increases your baseline such that larger distance can be probed.

## Dr. Aaron J. Romanowsky University of California Observatories

"Galaxies are to astronomy as ecosystems are to biology." - James Binney & Scott Tremaine, Galactic Dynamics

If you've ever looked up on a dark clear night, you've probably seen the Milky Way, a faint, hazy stream stretching across the sky. Familiar to humankind since ancient times, its nature wasn't known until Galileo turned his telescope toward it and discovered that it is composed of countless faint stars.

In fact, the Milky Way is the visible marker of a great system in which our solar system is located: a galaxy made up of 100 billion stars and vast amounts of gas, while the 500 or so individual stars visible to the naked eye represent just a handful of our closest neighbors. Our galaxy is shaped something like a pizza, and our own star, the Sun, is located in a piece of pepperoni halfway out toward the crusty edge. This is why from our perspective, we see a band of light wrapped around the sky.

In the early 20th century, it was discovered that the Milky Way is not all there is to the universe. Beginning nearby, and stretching into the distance as far as can be seen, there are billions of other galaxies, which are the patchwork quilt making up the universe. These galaxies come in many shapes and sizes, but there are two major general types:

Spiral galaxies are like our own Milky way: flat, gas-rich systems with prominent spiral arms. Examples include the nearby Andromeda Galaxy, the Sombrero Galaxy, M74, M83, NGC 1232, NGC 4622, M33, NGC 6946, NGC 7331, NGC 1365, M51, NGC 3310, M95, NGC 3184, NGC 2841, M64, NGC 891, NGC 1300, M100, M96, NGC 2336, NGC 3627, and M101.

Elliptical galaxies are rounded, featureless balls of stars. Some examples are M87, NGC 1316, and NGC 4365. An elliptical galaxy and a spiral galaxy next to each other can be seen here. A group of two ellipticals and one spiral are here. On a larger scale is the Coma Cluster, a huge swarming mass of hundreds of ellipticals and spirals.

One of the more astounding findings of late 20th century astronomy was that there is much more to the universe that meets the eye. All the visible matter we can see (stars, gas, dust) makes up only about 10% of the material in the universe. The rest, dark matter, is a material (or several different kinds of materials) of a nature still quite unknown. Being "dark", it has so far never been directly seen, but its existence is inferred--mainly from its gravitational effects.

One of the first places dark matter was detected was around spiral galaxies. The cold gas in the outer parts of these galaxies was found to move too quickly to be explained by the gravitational force of the visible galaxy. It turns out that around all spiral galaxies, there is a vast reservoir of dark matter: the dark halos. (See here for a more detailed explanation of how the presence of dark matter is inferred in spiral galaxies, or here or here for more general information about dark matter.)

We now think that dark matter is not only pervasive, but essential. In the paradigm known as "cold dark matter" or "hierarchical structure formation", it is the collapse of great blobs of dark matter under their own gravity that has led to the condensation of ordinary gaseous matter into the visible galaxies, stars, planets, and ultimately life that we see today. (A more recent discovery is "dark energy", but that's another matter. Ahem.)

But what about elliptical galaxies? Do they have dark halos? And if so, are they similar to spirals' dark halos? Yes, according to the theoretical picture above, but empirically, these questions have been unanswerable because ellipticals don't have cold gas which can be measured. Some other way is needed to probe for dark matter.

There are in fact some objects around elliptical galaxies which can be studied, albeit much more difficult than it is with cold gas. These include globular clusters and planetary nebulae. If one can measure the velocities of such objects in sufficient numbers, one can tell how strong the gravitational forces are around the galaxy, and thus how much dark matter there is.

Globular Clusters

Around every galaxy, including our own Milky Way, there are numerous smaller stellar systems called globular clusters. These are dense balls of "only" about a million stars each, and are the oldest known objects in the universe.

Some examples of globulars lurking around our galaxy are NGC 6093 Omega Centauri (also with close-up), M92, NGC 6397, 47 Tucanae (close-up here), M15 (also with close-up), NGC 1916, and NGC 5904.

(To take a virtual tour of the Milky Way's globular cluster system, see here. For more information about globulars, see here.) These dense collections of stars are visible in distant galaxies when indiviual stars are not. See M87, where most of the "stars" in the image are not stars at all but globular clusters swarming around the central galaxy. It is possible to measure the velocities of such globulars given a large enough telescope.

Planetary Nebulae

The name planetary nebula is misleading -- these nebulae have nothing to do with planets (when first discovered with small telescopes, their typically round appearance made them look like planets, hence the name). They are the cast-off remnants of aged, dying stars -- shells of gas lit up fluorescently by the central ember's fading rays. For a more detailed explanation, see here or here. For observing information, see Planetary Nebulae Observer's Home Page.

An example of a planetary nebula (PN) is the Eskimo Nebula You can see the remarkable difference in resolution between this spaced-based telescope image and this ground-based telescope image. Others include the Cat's Eye Nebula (also with X-ray and optical emission superimposed), the Hourglass Nebula, the Dumbbell Nebula, the Ring Nebula, the Ant Nebula, the Southern Ring Nebula, the Spirograph Nebula, NGC 6751, the Retina Nebula, the Red Spider Nebula, the Helix Nebula, (also here, with close-up of "cometary knots" here), M2-9, the Rotten Egg Nebula, NGC 2440, the Snowball Nebula, Abell 39, the Butterfly Nebula, the Stingray Nebula, and NGC 7027. A whole gallery of PN images from Hubble Space Telescope can be found here, and a ground-based gallery here, and a false-color one here. Three examples of a "proto-PN" are the Egg Nebula, CRL 618, and Gomez's Hamburger.

Because these PNe fluoresce, they emit their light with a few well-defined colors, and so with the use of appropriate color filters, the contrast between a PN and the background light can be increased, and thus they can be observed in distant galaxies, and have their velocities measured.

I have made many trips to some of the world's largest telescopes to measure the velocities of extragalactic PNe. Two such "observing runs" are described here and here. I am also heavily involved with a new instrument specially built for this purpose, the Planetary Nebula Spectrograph.

In addition to observing the velocities (kinematics) of these "halo tracer" objects, I also work on the dynamical modeling necessary to interpret the data. That is, I calculate how much dark matter there is, try to understand the internal motions of the galaxies, make inferences about their formational histories, etc. If you want to know the gory details, you can see here.

Now for the bottom line: what about results?? Our work on bright elliptical galaxies like M87 and M49 has turned up a lot of dark matter, as expected. However, with some of the first studies ever of "ordinary" ellipticals like NGC 3379, we got a bit of a shock. In these galaxies, we've found that the PN velocities fall off quickly with radius, as though there are no extra gravitational forces at work - and thus no dark matter!

Below are some images that show this. First is NGC 3379, with PN velocities shown around it. Blue dots show PNe which are moving toward us (Doppler blueshift) and red dots are moving away (redshift). The dot sizes are larger for larger velocities you can see by eye that the dots (and velocities) get smaller away from the galaxy center. Second is a plot of the velocities with radius for four different galaxies, superimposed on the same plot. The yellow dotted line shows the prediction if there's no dark matter, which matches up quite well with the data.

So in these cases the "missing mass" is missing: what you see is what you get. Since these systems aren't enveloped by the "normal" cloak of dark matter, we call them "naked galaxies" - although they might not actually be naked, but only scantily clad, since we can't rule out a small amount of dark matter.

Why are these galaxies naked? There are lots of ideas (e.g., they've lost their dark halos through interactions with other galaxies), but none of them seems to work so far. At this point, we'll continue gathering data on different galaxies, and analyzing them, so stay tuned.

If you'd like to know still more about the history of the universe, see Ned Wright's Cosmology Tutorial.
For an entire basic astronomy overview online, see Astronomy Notes.
For still more spectacular astronomical photos, see the Anglo-Australian Observatory or the Hubble Space Telescope.

## Astronomers unveil most detailed 3D map yet of Milky Way

Astronomers have unveiled the most precise 3D map yet of the Milky Way, an achievement that promises to shed fresh light on the workings of the galaxy and the mysteries of the broader universe.

The vast electronic atlas was compiled from data gathered by the European Space Agency’s Gaia observatory which has been scanning the heavens since it blasted off in 2013 from Kourou in French Guiana.

The map contains enough detail for astronomers to measure the acceleration of the solar system and calculate the mass of the galaxy. These in turn will provide clues as to how the solar system formed and the rate at which the universe has expanded since the dawn of time.

Nicholas Walton, a member of the ESA Gaia science team at the Institute of Astronomy in Cambridge, compared the effort to filling in the blanks on ancient maps that marked unknown regions with the assertion that “here be dragons”.

“What we’re really doing here is getting a very detailed map of the local universe that’s in three dimensions for stars out to a few hundred light years,” he said.

Animation shows orbits of the nearby stars around centre of the galaxy – video

By charting the positions and movements of the stars, the probe has uncovered destructive processes beyond the edge of the Milky Way. A faint stream of stars spotted between two nearby galaxies is evidence that the more massive Large Magellanic Cloud is steadily devouring the more diminutive Small Magellanic Cloud.

A 3D map showing the Large Magellanic Cloud (left) and the Small Magellanic Cloud made by astronomers using data from Gaia. Photograph: ESA/Gaia/DPAC/PA

Many of the bodies Gaia observes are quasars, extremely distant and intensely bright objects powered by black holes a billion times the mass of the sun. By measuring the solar system’s movement relative to these, Gaia data shows the solar system is falling towards the centre of the Milky Way with an acceleration of about 7mm a second each year.

Known as the Galaxy Surveyor, Gaia orbits the planet from a gravitationally stable position known as a Lagrange point 930,000 miles from Earth in the opposite direction to the sun. For the past seven years, the probe has measured the positions and velocities of nearly 2bn stars. Besides revealing trails of cosmic consumption, the data allow astronomers to piece together the distribution of matter in the Milky Way, from which they will directly estimate its mass.

Lagrange points are regions in space where gravitational forces tend to make objects stay put. For the Gaia observatory, this means a minimum of fuel is needed to maintain its location. The distant orbit has another advantage: it is far enough from Earth to avoid light pollution spoiling its view of the stars.

Floor van Leeuwen, who manages data processing for Gaia at the Institute for Astronomy, said the trove of data let astronomers “forensically analyse our stellar neighbourhood, and tackle crucial questions about the origin and future of our galaxy”.

Caroline Harper, the head of space science at the UK Space Agency, said: “For thousands of years, we have been preoccupied with noting and detailing the stars and their precise locations as they expanded humanity’s understanding of our cosmos.

“Gaia has been staring at the heavens for the past seven years, mapping the positions and velocities of stars. Thanks to its telescopes we have in our possession today the most detailed billion-star 3D atlas ever assembled.”

## Astronomers measure enormous planet lurking far from its star

Artist's rendering of a 10-million-year-old star system with a gas-giant planet like Jupiter. Credit: NASA/JPL-Caltech/T. Pyle

Scientists aren't usually able to measure the size of gigantic planets, like Jupiter or Saturn, which are far from the stars they orbit. But a UC Riverside-led team has done it.

The planet is roughly five times heavier than Jupiter, hence its nickname GOT 'EM-1b, which stands for Giant Outer Transiting Exoplanet Mass. Though it is nearly 1,300 light years away from Earth, GOT 'EM-1b, or Kepler-1514b as it is officially known, is still considered part of what researchers call our "solar neighborhood."

"This planet is like a stepping stone between the giant planets of our own solar system, which are very far from our sun, and other gas giants that are much closer to their stars," said UCR astronomer Paul Dalba, who led the research.

The discovery of GOT 'EM-1b has been detailed in a paper accepted for publication in the Astronomical Journal, and is being presented Jan. 11 at the 2021 meeting of the American Astronomical Society.

NASA's Kepler space telescope originally identified an object, which turned out to be this planet, in 2010. That mission then spotted periodic decreases in the brightness of a star, a clue that orbiting planets are nearby.

Dalba and his team then used W.M. Keck Observatory in Hawaii to determine the planet's size and density.

Dalba said it was surprising to find a planet such as GOT 'EM-1b.

"Taking 218 days to orbit a star is an order of magnitude longer than most giant exoplanets we've measured," Dalba said. "Kepler discovered thousands of planets, and only a few dozen had orbits of a couple hundred days or longer."

Giant planets tend to form farther from their stars, then migrate inward over time. The discovery of one that hasn't moved closer may serve as an analog, offering new insights into our own solar system.

Earth enjoys a lot of relative stability, and astronomers believe Jupiter may be protecting our planet from other objects in space that would impact us. But because they are so massive, planets such as Jupiter have the potential to disturb the orbits, architecture, and development of other nearby planets.

"Giant planets far from their stars can help us answer age-old questions about whether our solar system is normal or not in its stability and development," explained UCR planetary astrophysicist Stephen Kane, who participated in the research.

"We don't know of many analogs to Jupiter and Saturn—it's really hard to find those kinds of planets very far away, so this is exciting," Kane said.

Dalba explained that data from giant planets closer to their stars is often more difficult to interpret, since radiation from the star puffs them up.

"You first have to account for the inflation in size before investigating the composition and other aspects of planets near stars," Dalba said. "This planet doesn't have that radius problem, so it's more straightforward to study."

For these reasons, the discovery of Kepler-1514b is helpful to future NASA missions, such as the Nancy Grace Roman Space Telescope, which will attempt direct imaging of giant planets.

Dalba is also hoping to learn whether the planet has a moon or system of moons.

"We've never found a moon outside our solar system," Dalba said. "But if we did, it would let us know that moons can form around planets that are experiencing substantial migration, and teach us more about giant planets as a whole."

## How does one measure velocities of far-off, bright objects - Astronomy

I have a Ph.D in physics from Caltech (1948). I am living in a retirement community in Redlands, CA. By request, I am giving lectures on astronomy every two weeks. A question that I am asked but cannot answer satisfactorily is "How do they determine the age of the universe and the distance in light-years (or kilometers) to distant galaxies?"

I understand that the redshift determines the recession velocity, but I do not understand the relation of this to the distance.

There is a simple answer and a not-so-simple complication to it.

The simple answer is that it has been known for some time that the distance to a galaxy is proportional to its recessional velocity: this is called Hubble's Law, and it was demonstrated observationally by Hubble in the late 1920s. It turns out that if you assume that the Universe is homogeneous and isotropic (which we think is the case), then Hubble's Law can also be predicted by theory. The constant of proportionality between the recessional velocity of galaxies and their distance is called Hubble's constant. Astronomers have tried to measure Hubble's constant ever since the term was coined: the simplest way is to look at the recessional velocities of galaxies for which the distances are known by other means (like looking at the period of variable stars). The current best estimate of Hubble's constant today is about 20 km/s per Mly, so that a galaxy with a recessional velocity of 2000 kilometres per second is 100 mega-light-years away, and so on.

We can therefore use Hubble's law to tell us distances to galaxies by simply measuring their redshifts, which is a relatively easy thing to do even for very distant objects. We can also estimate the age of the Universe: you'll notice that the units of Hubble's constant are actually 1/time, so one over Hubble's constant must be the characteristic age of the Universe. From the Hubble constant above, we therefore calculate that the Universe is about 14 billion years old.

Now for the complications: it turns out that for *very* distant objects (at redshifts of, say, 2 and greater) Hubble's Law doesn't quite hold, because at very great distances we have to start taking the (4-dimensional) curvature of the Universe into account. A more important effect is that in most cosmologies, Hubble's constant isn't really a constant: it actually increases as you look back in time, so that its value was different for galaxies at redshifts of 5 than it is today. So, to get estimates of the distances to galaxies and the age of the Universe, astronomers must assume a set of cosmological parameters for the Universe (for instance, the total amount of "normal" matter it contains) and model its age and the distances of galaxies as a function of redshift by integrating the equations of motion for cosmological evolution. The answers they get are not that different from what we estimated above, but can be crucial to learning about galaxies at high redshift (for instance, the extraction of their sizes depends linearly on their distance, and their masses on the distance squared).

For all intents and purposes, however, Hubble's law is a very powerful tool for getting distances from velocities (and you may want to stop at that in your lectures).

#### Kristine Spekkens

Kristine studies the dynamics of galaxies and what they can teach us about dark matter in the universe. She got her Ph.D from Cornell in August 2005, was a Jansky post-doctoral fellow at Rutgers University from 2005-2008, and is now a faculty member at the Royal Military College of Canada and at Queen's University.

## How do astronomers calculate the size and distances of celestial bodies?

I’ve been watching videos on YT about astronomy for years now. It’s fascinating. I never really ask questions and just believe what the experts have to say. But today I have decided to ask this question… A question that I’ve often ignored before.

So yesterday, I was watching this video and it mentioned a star/some celestial body. I don’t remember exactly, sorry. It said that the astronomers have calculated that this celestial body is about *13 billion lightyears* away from us and this many billions-something-huge.

It’s just so baffling to me. How do they do it? They’re calculating masses and distances of bodies that are supposedly soo sooo huge and far away, when we haven’t even actually managed to step on mars, yet. My point is, how are we capable of determining all this accurately when on a universal scale, we’re capable of pretty much nothing. How do these calculations work?

For distance: Trigonometry!

They use a method called stellar parallax. The look at the position of the star at one point in the year, and then view that same stars position at a different point in the year. By comparing position, we can triangulate the distance of the star from Earth. It isn’t dissimilar to how cartographers made maps centuries ago – if you have two angles of a triangle and the distance between them, you can calculate the other two sides of the triangle.

For mass, the calculations are complicated, but since we know the mass of the Earth, and the speed/distance of our orbit, we can look at the orbital radiuses and speed of other objects and plug those into our equations to determine their mass.

First, we need a point of reference and the best reference point we have is the Sun. While ancient astronomers attempt to determine the distance to the Sun, they lacked the appropriate tools to make precise enough measurements, or knowledge of orbital mechanics to determine this with any reasonable degree of accuracy.

By the 17th century, we had a much better understanding of the orbits of planets, and were able to make connections about the orbits of the planets relative to each other. All we needed now was to know one of them.

The “one” was Venus. Occasionally, Venus will make a “transit.” That is, it’ll pass between the Earth and the Sun in a way that is visible. By measuring how long this transit lasts, we were able to, in the 18th century, calculate Venus’ orbit and, hence, Earth’s orbit, including our distance to the Sun.

Second, now that we know the distance to the Sun, we can use something called parallax to measure the distance from Earth to other stars. What you do is pick a star and measure the angle from Earth to that star. Then you wait 6 months and measure the angle to that star again. These two angles, plus the known distance between the position of the Earth (6 months apart, on opposite sides of the sun), uniquely defines a triangle whose apex is the chosen star. Once you know those three pieces of information, you can derive all the other information about that star, including the distance to it.

However, the further away something is, the more accurate you have to measure to get a good distance. Given our current tools, parallax only really works for things up to 100 light years away from Earth.

In the early 1900’s we discovered a type of star known as a Cepheid star. The cool thing about them is they dim and brighten in regular intervals. The interval depends only on the stars absolute brightness. A thing about luminosity is, the further away something is, the dimmer it appears. So if you look at one of these Cepheid stars and measure the period of its intervals, you can determine how bright it really is. If you compare how bright it really is with how bright it appears, you can determine how far away it is (since the rate at which things appear dimmer is mathematically related to how far away it is).

Cepheid stars are fairly common and fairly bright over all, allowing us to measure distances up to millions of light-years away.

We can use similar methods for other phenomenon with known brightnesses, such as supernovae, to measure distances even further away, up to a billion light years.

Lastly, is that the universe is expanding. The further two objects are away from each other, the faster they are moving away. When light is emitted from an object moving away from you, this “stretches out” the light which makes it appear “redder” than it really is^(*). So if you look at a kind of object whose brightness is known, you can measure how red-shifted its light is which tells you how fast it is moving away from you. Since the speed at which the object is moving away from you is related to its distance from you, you can then calculate its distance.

* – Not necessarily *literally* redder (though possibly so) but rather its wavelengths are longer (having been stretched out). This is in contrast to objects moving towards each other, whose wavelengths are squashed up and therefore smaller which makes it bluer. The terms red and blue refer to the fact that red and blue occupy the long and short wavelengths of our visible light spectrum, respectively.

For planets that are really far away, we look at the movement of the star they’re orbiting. When one body orbits another, although it seems like the star is stationary and the planet goes around it, they’re actaully orbiting around one another. This means that the star will “wiggle” ever so slightly. You can see how this works in [this](https://spaceplace.nasa.gov/review/barycenter/doppspec-above.en.gif) and [this](https://spaceplace.nasa.gov/barycenter/en/dopspec-inline.en.gif) gif. We can detect this wiggling by looking at tiny yet periodic changes in a star’s light. The wavelength will vary ever so slightly due to the movement of the star. This technique, called doppler spectroscopy, can give us an astounding amount of information when combined with a few other techniques and measurements, even letting us determine the mass and orbital period of the planet, and sometimes even the temperature on that planet.

For stars we can usually determine the size by looking at the type of light they emit. The mass of the star is partly determined by the temperature of the star, and the light emitted by the star can tell us the temperature of the star. So we can use this to get an idea of the size and mass of a star.

We use parallax. Hold your finger out in front of you at arms length. Look at the background just behind the finger as you move your head from side to side. Try to avoid moving your finger. You should notice that the background moves too, which is to be expected. Now, do the same trick but the first time hold your finger up in a way that the background is quite close to you. You should notice that when you move your head the background moves more than if the background is far away. This phenomenon is also noticable when you look out of one of the passenger windows of a car while driving. If you look at trees right next to the road, you’ll see them whizz by, but if you look at a tree that’s a long way away it seems to move slower. This effect is called parallax and we use it to measure how far away stars are. In astronomy we use stars that are far away as a reference and we make the star in question the “finger”. [Here](https://javalab.org/en/stellar_parallax_en/) is a good example of how this works. Instead of moving our heads we let the Earth orbit the sun, and then we use basic trigonometry to figure out what the distance is.

For planets this doesn’t really work because they don’t emit light, so what we usually do is look at the star it’s orbiting, and see how far away that is. This then gives us a decent idea of the distance to that planet.

The reason we’re so good at this is because the physics involved is really well understood. The laws describing how planets orbit stars are really well known, and this means that we can extract a shitload of information out of what few things we can measure. I always see it as milking every single drop of information we get for everything it can tell us about the star it came from. One of the people in my calculus classes always used to call it “interrogation of data” and he honestly wasn’t that far off, because we get so much data out of so little data.

## What Do Spectra Tell Us?

Most bright astronomical objects shine because they are hot. In such cases, the continuum they emit tells us what the temperature is. Here is a very rough guide.

Temperature
(in Kelvin)
Predominant
Astronomical examples
600Infrared Planets, warm dust
6,000Optical The photosphere of Sun and other stars
60,000UV The photosphere of very hot stars
600,000Soft X-rays The corona of the Sun
6,000,000X-rays The coronae of active stars

We can learn a lot more from the spectral lines than from the continuum.

## The chemical composition of stars

The studies of the solar spectrum (Joseph Fraunhofer is the most famous and probably also the most important early contributor to this field), however, revealed absorption lines (dark lines against the brighter continuum). The precise origin of these 'Fraunhofer lines', as we call them today, remained in doubt for many years, until Gustav Kirchhoff, in 1859, announced that the same substance can either produce emission lines (when a hot gas is emitting its own light) or absorption lines (when a light from a brighter, and usually hotter, source is shone through it). Now scientists had the means to determine the chemical composition of stars through spectroscopy!

One of the most dramatic triumphs of astrophysical spectroscopy during the 19th century was the discovery of helium. An emission line at 587.6 nm was first observed in the solar corona during the eclipse of August 18, 1868, although the precise wavelength was difficult to establish at the time (due to the short observation using temporary set-ups of instruments transported to Asia). Two months later, Norman Lockyer used a clever technique and managed to observe solar prominences without waiting for an eclipse. He noted the precise wavelength (587.6 nm) of this line, and saw that no known terrestrial elements had a line at this wavelength. He concluded that this must be a newly discovered element and called it 'helium'. Helium was discovered on Earth eventually (1895) and showed the same 587.6 nm line. Today, we know that helium is the second most abundant element in the Universe.

We also know today that the most abundant element is hydrogen. However, this fact was not obvious at first. Many years of both observational and theoretical works culminated in 1925, when Cecilia Payne published her PhD thesis entitled 'Stellar Atmospheres'. (Footnote: this was the first ever PhD awarded at Harvard it was also praised as "undoubtedly the most brilliant PhD thesis ever written in astronomy" nearly 40 years later. She later turned to studies of variable stars, and coined the term 'cataclysmic variables'.) In this early work, she utilized many excellent spectra taken by Harvard observers, and measured the intensities of 134 different lines from 18 different elements. She applied the up-to-date theory of spectral line formation and found that the chemical compositions of stars were probably all similar, with the temperature being the important factor in creating their diverse appearances. She was then able to estimate the abundances of 17 of the elements relative to the 18th, silicon. Hydrogen appeared to be more than a million times more abundant than silicon, a conclusion so unexpected that it took many years to become widely accepted.

## The motion of stars and galaxies

If the spectrum of a star is red or blue shifted, then you can use that to infer its velocity along the line of sight. Such 'radial velocity' studies have had at least three important applications in astrophysics.

The first is the study of binary star systems. The component stars in a binary revolve around each other. You can measure the radial velocities for one cycle (or more!) of the binary, then you can relate that back to the gravitational pull using Newton's equations of motion (or their astrophysical applications, Kepler's laws). If you have additional information, such as from observations of eclipses (see Light Curve), then you can sometimes measure the masses of the stars accurately. Eclipsing binaries, in which you can see the spectral lines of both stars, have played a crucial role in establishing the masses and the radii of different types of stars.

The second is the study of the structure of our Galaxy. Stars in the Galaxy revolve around its center, just like planets revolve around the Sun. It's more complicated, because the gravity is due to all the stars in the Galaxy combined, in this case. (In the Solar System, the Sun is such a dominant source that you can ignore the pull of the planets --- more or less). So, radial velocity studies of stars (binary or single) have played a major role in establishing the shape of the Galaxy. It is still an active field today. For example, one of the evidences for dark matter comes from the study of the distribution of velocities at different distances from the center of the Galaxy. Another exciting development is the radial velocity studies of stars very near the Galactic center, which strongly suggest that our Galaxy contains a massive black hole.

The third is the expansion of the Universe. Edwin Hubble established that more distant galaxies tended to have more redshifted spectra. Although not predicted even by Einstein, such an expanding universe is a natural solution for his general relativity theory. Today, for more distant galaxies, the redshift is used as a primary indicator of their distances. The ratio of the recession velocity to the distance is called the Hubble constant, and the precise measurement of its value has been one of the major accomplishments of astrophysics today, using such tools as the Hubble Space Telescope.

## How does one measure velocities of far-off, bright objects - Astronomy

The wave nature of light means there will be a shift in the spectral lines of an object if it is moving. This effect is known as the doppler effect. You have probably heard the doppler effect in the change of the pitch of the sound coming from something moving toward you or away from you (eg., a train whistle, a police siren, an ice cream truck's music, a mosquito buzzing). Sounds from objects moving toward you are at a higher pitch because the sound waves are compressed together, shortening the wavelength of the sound waves. Sounds from objects moving away from you are at a lower pitch because the sound waves are stretched apart, lengthening the wavelength. Light behaves in the same way.

Motion of the light source causes the spectral lines to shift positions. An object's motion causes a wavelength shift = new - rest that depends on the speed and direction the object is moving. The amount of the shift depends on the object's speed: = rest × Vradial / c, where c is the speed of light, rest is the wavelength you would measure if the object was at rest and Vradial is the speed along the line of sight.

There is a lot of information stored in that little formula! First, it says that the faster the object moves, the greater the doppler shift . For example, a particular emission line of hydrogen from nearby galaxies is shifted by a smaller amount than the same line from faraway galaxies. This means that the faraway galaxies are moving faster than the nearby galaxies. The radar guns'' used by police officers operate on this principle too. They send out a radio wave of a set wavelength (or frequency) that reflects off a car back to the radar gun''. The device determines the car's speed from the difference in the wavelength (or frequency) of the transmitted beam and reflected beam.

Second, the term Vradial means that only the object's motion along the line of sight is important. If object moves at an angle with respect to the line of sight, then the doppler shift () tells you only about the part of its motion along the line of sight. You must use other techniques to determine how much of an object's total velocity is perpendicular to the line of sight.

Finally, which way the spectral lines are shifted tells you if the object is moving toward or away from you. If the object is moving toward you, the waves are compressed, so their wavelength is shorter. The lines are shifted to shorter (bluer) wavelengths---this is called a blueshift. If the object is moving away from you, the waves are stretched out, so their wavelength is longer. The lines are shifted to longer (redder) wavelengths---this is called a redshift.

This explanation also works if you are moving and the object is stationary or if both you and the object are moving. The doppler effect will tell you about the relative motion of the object with respect to you. The spectral lines of nearly all of the galaxies in the universe are shifted to the red end of the spectrum. This means that the galaxies are moving away from the Milky Way galaxy and is evidence for the expansion of the universe.

The doppler effect will not affect the overall color of an object unless it is moving at a significant fraction of the speed of light (VERY fast!). For an object moving toward us, the red colors will be shifted to the orange and the near-infrared will be shifted to the red, etc. All of the colors shift. The overall color of the object depends on the combined intensities of all of the wavelengths (colors). The first figure below shows the continuous spectra for the Sun at three speeds (zero, a fast 0.01c, a VERY fast 0.1c). The Hydrogen-alpha line (at 656.3nm) is shown too. Objects in our galaxy move at speeds much less than 0.01c. The doppler-shifted continuous spectrum for the Sun moving at 0.01c is almost indistinguishable from the Sun at rest even when you zoom in to just the optical wavelengths (second figure). However, the doppler shift of the spectral line is easy to spot for the slow speed. By zooming in even further, you can detect spectral line doppler shifts for speeds as small as 1 km/sec or lower (less than 3.334吆 -6 c).

## Recent Projects

### Deciphering the Kinematic Structure of the Small Magellanic Cloud through its Red Giant Population

In Zivick, Kallivayalil, and van der Marel 2020, we present a new kinematic model for the Small Magellanic Cloud (SMC), using data from the gaia Data Release 2 catalog. We identify a sample of astrometrically well-behaved red giant (RG) stars belonging to the SMC and cross-match with publicly available radial velocity (RV) catalogs. We create a 3D spatial model for the RGs, using RR Lyrae for distance distributions, and apply kinematic models with varying rotation properties and a novel tidal expansion prescription to generate mock proper motion (PM) catalogs. When we compare this series of mock catalogs to the observed RG data, we find a combination of moderate rotation (with a magnitude of ∼10−20∼10−20 km s−1−1 at 1 kpc from the SMC center, inclination between ∼50−80∼50−80 degrees, and a predominantly north-to-south line of nodes position angle of ∼180∼180 degrees) and tidal expansion (with a scaling of ∼10∼10 km s−1−1 kpc−1−1) is required to explain the PM signatures. The exact best-fit parameters depend somewhat on whether we assess only the PMs or include the RVs as a qualitative check, leaving some small tension remaining between the PM and RV conclusions. In either case, the parameter space preferred by our model is different both from previously inferred rotational geometries, including from the SMC H gas and from the RG RV-only analyses, and new SMC PM analyses which conclude that a rotation signature is not detectable. Taken together this underscores the need to treat the SMC as a series of different populations with distinct kinematics.

### The Orbital Histories of Magellanic Satellites Using Gaia DR2 Proper Motions

With the release of Gaia DR2, it is now possible to measure the proper motions (PMs) of the lowest mass, ultra-faint satellites in the Milky Way’s (MW) halo for the first time. Many of these faint satellites are posited to have been accreted as satellites of the Magellanic Clouds (MCs). In Patel, Kallivayalil, Garavito-Camargo, et al. 2020, using their 6D phase space information, we calculate the orbital histories of 13 ultra-faint satellites and five classical satellites in a combined MW+LMC+SMC potential to determine which galaxies are dynamically associated with the LMC/SMC. We identify three classes of galaxies that have recently interacted with the MCs: i.) MW satellites on high-speed orbits that made a close approach (< 100 kpc) to the MCs < 1 Gyr ago (Sculptor 1, Tucana 3, Segue 1) ii.) short-term Magellanic satellites that have completed one recent, close pericentric passage (Reticulum 2, Phoenix 2) and iii.) long-term Magellanic satellites that have completed two consecutive recent, close passages (Carina 2, Carina 3, Horologium 1, Hydrus 1). Results are reported for a range of MW and LMC masses. Contrary to previous work, we find no dynamical association between Carina, Fornax, and the MCs. We find that Aquarius 2, Canes Venatici 2, Crater 2, Draco 1, Draco 2, Hydra 2, and Ursa Minor are not members of the Magellanic system. Finally, we determine that the addition of the SMC’s gravitational potential affects the longevity of satellites as members of the Magellanic system (short-term versus long-term satellites), but it does not change the total population of Magellanic satellites.

### The Proper Motion Field Along the Magellanic Bridge: a New Probe of the LMC-SMC Interaction

In Zivick, Kallivayalil, Besla, et al. 2019 we present the first detailed kinematic analysis of the proper motions (PMs) of stars in the Magellanic Bridge, from both the Gaia Data Release 2 catalog and from Hubble Space Telescope Advanced Camera for Surveys data. For the Gaia data, we identify and select two populations of stars in the Bridge region, young main sequence (MS) and red giant stars. The spatial locations of the stars are compared against the known H gas structure, finding a correlation between the MS stars and the HI gas. In the Hubble Space Telescope fields our signal comes mainly from an older MS and turn-off population, and the proper motion baselines range between ∼4 and 13 years. The PMs of these different populations are found to be consistent with each other, as well as across the two telescopes. When the absolute motion of the Small Magellanic Cloud is subtracted out, the residual Bridge motions display a general pattern of pointing away from the Small Magellanic Cloud towards the Large Magellanic Cloud. We compare in detail the kinematics of the stellar samples against numerical simulations of the interactions between the Small and Large Magellanic Clouds, and find general agreement between the kinematics of the observed populations and a simulation in which the Clouds have undergone a recent direct collision.

#### News Articles

The Missing Satellites of the Magellanic Clouds? Gaia Proper Motions of the Recently Discovered Ultra-Faint Galaxies

In Kallivayalil, Sales, Zivick, Fritz et al. 2018 we present proper motion measurements for 13 of the 32 newly discovered dwarf galaxy candidates using Gaia data release 2. All 13 also have radial velocity measurements. We compare the measured 3D velocities of these dwarfs to those expected at the corresponding distance and location for the debris of an LMC analog in a numerical simulation. We conclude that 4 of these galaxies (Hor1, Car2, Car3 and Hyd1) have come in with the Magellanic Cloud system, constituting the first confirmation of the type of satellite infall predicted by LCDM. Ret2, Tuc2 and Gru1 have some velocity components that are not consistent within 3 sigma of our predictions and are therefore less favorable. Hyd2 and Dra2 could be associated with the LMC and merit further attention. We rule out Tuc3, Cra2, Tri2 and Aqu2 as potential members. Of the dwarfs without measured PMs, 6 of them are deemed unlikely on the basis of their positions and distances alone which put them too far from the orbital plane expected for LMC debris (Eri2, Ind2, Cet2, Tri2, Cet3 and Vir1). For the remaining sample, we use the simulation to predict proper motions and radial velocities, finding that Phx2 has an overdensity of stars in DR2 consistent with this PM prediction. If its radial velocity is confirmed at ∼−15 km s -1 , it is also likely a member.

### The Proper Motion Field of the Small Magellanic Cloud: Kinematic Evidence for its Tidal Disruption

In Zivick, Kallivayalil, van der Marel et al. 2018 we present a new measurement of the systemic proper motion of the Small Magellanic Cloud (SMC), based on an expanded set of 30 fields containing background quasars and spanning a ∼3 year baseline, using the Hubble Space Telescope Wide Field Camera 3 (HST WFC3). Combining this data with our previous 5 HST fields, and an additional 8 measurements from the Gaia-Tycho Astrometric Solution Catalog, brings us to a total of 43 SMC fields. We measure a systemic motion of μW = −0.82 ± 0.02 (random) ± 0.10 (systematic) mas yr -1 and μN = −1.21 ± 0.01 (random) ± 0.03 (systematic) mas yr -1 . After subtraction of the systemic motion, we find little evidence for rotation, but find an ordered mean motion radially away from the SMC in the outer regions of the galaxy, indicating that the SMC is in the process of tidal disruption. We model the past interactions of the Clouds with each other based on the measured present-day relative velocity between them of 103±26 km s -1 . We find that in 97% of our considered cases, the Clouds experienced a direct collision 147±33 Myr ago, with a mean impact parameter of 7.5±2.5 kpc.

### The Orbit and Origin of the Ultra-faint Dwarf Galaxy Segue 1

In Fritz, Lokken, Kallivayalil et al. 2018 we present the first proper motion measurement for an ultra-faint dwarf spheroidal galaxy, Segue 1, using SDSS and LBC data as the first and second epochs separated by a baseline of ∼10 years. We obtain a motion of μαcos(δ)=−0.37±0.57 mas yr -1 and μδ=−3.39±0.58 mas yr -1 . Combining this with the known line-of-sight velocity, this corresponds to a Galactocentric Vrad=84±9 and Vtan=164 +66 −55 km s -1 . Applying Milky Way halo masses between 0.8 to 1.6×1012 M results in an apocenter at 33.9 +21.7 −7.4 kpc and pericenter at 15.4 +10.1 −9.0 kpc from the Galactic center, indicating Segue

1 is rather tightly bound to the Milky Way. Since neither the orbital pole of Segue 1 nor its distance to the Milky Way is similar to the more massive classical dwarfs, it is very unlikely that Segue 1 was once a satellite of a massive known galaxy. Using cosmological zoom-in simulations of Milky Way-mass galaxies, we identify subhalos on similar orbits as Segue 1, which imply the following orbital properties: a median first infall 8.1 +3.6 −4.3 Gyrs ago, a median of 4 pericentric passages since then and a pericenter of 22.8 +4.7 −4.8 kpc. This is slightly larger than the pericenter derived directly from Segue 1 and Milky Way parameters, because galaxies with a small pericenter are more likely to be destroyed. Of the surviving subhalo analogs only 27% were previously a satellite of a more massive dwarf galaxy (that is now destroyed), thus Segue 1 is more likely to have been accreted on its own.

### The Proper Motion of Pyxis: the first use of Adaptive Optics in tandem with HST on a faint halo object:

In Fritz, Linden, Zivick, Kallivayalil et al. 2017 we present a proper motion measurement for the halo globular cluster Pyxis, using HST/ACS data as the first epoch, and GeMS/GSAOI Adaptive Optics data as the second, separated by a baseline of ∼ 5 years. Our inertial reference frame consists of background galaxies. This is both the first measurement of the proper motion of Pyxis, as well as the first calibration and use of Multi-Conjugate Adaptive Optics data to measure an absolute proper motion for a faint, distant halo object. We use the obtained three-dimensional velocity of Pyxis and dynamical modeling to show that Pyxis is not plausibly a progenitor of the ATLAS stream. We use a cosmological numerical simulation of the Milky Way with an LMC analog to show that Pyxis is very unlikely to be associated with the Magellanic system. The eccentric orbit strengthens the case for an extragalactic origin of Pyxis. The metallicity and age of Pyxis points to an origin from a rather massive former host, at least the mass of Leo II. This work was highlighted in a Gemini Press Release.

### The shape of the inner Milky Way halo from observations of the Pal 5 and GD-1 stellar streams:

In Bovy, Bahmanyar, Fritz & Kallivayalil 2016 we constrain the shape of the Milky Way's halo by dynamical modeling of the observed phase-space tracks of the Pal 5 and GD-1 tidal streams. We find that the only information about the potential gleaned from the tracks of these streams are precise measurements of the shape of the gravitational potential---the ratio of vertical to radial acceleration---at the location of the streams, with weaker constraints on the radial and vertical accelerations separately. The latter will improve significantly with precise proper-motion measurements from Gaia. We measure that the overall potential flattening is 0.95 +/- 0.04 at the location of GD-1 ([R,z]

[12.5,6.7] kpc) and 0.94 +/- 0.05 at the position of Pal 5 ([R,z]

[8.4,16.8] kpc). Combined with constraints on the force field near the Galactic disk, we determine that the axis ratio of the dark-matter halo's density distribution is 1.05 +/- 0.14 within the inner 20 kpc, with a hint that the halo becomes more flattened near the edge of this volume. The halo mass within 20 kpc is 1.1 +/- 0.1 x 10^ <11>M_sun. A dark-matter halo this close to spherical is in tension with the predictions from numerical simulations of the formation of dark-matter halos.

### Identifying true satellites of the Magellanic Clouds:

In Sales, Navarro, Kallivayalil & Frenk 2016 we explore which of the newly found low mass satellites might have been brought in by the Magellanic System. The hierarchical nature of LCDM suggests that the Magellanic Clouds must have been surrounded by a number of satellites before their infall into the Milky Way. Many of those satellites should still be in close proximity to the Clouds, but some could have dispersed ahead/behind the Clouds along their Galactic orbit. Either way, prior association with the Clouds results in strong restrictions on the present-day positions and velocities of candidate Magellanic satellites: they must lie close to the nearly-polar orbital plane of the Magellanic stream, and their distances and radial velocities must follow the latitude dependence expected for a tidal stream with the Clouds at pericenter. We use a cosmological numerical simulation of the disruption of a massive subhalo in a Milky Way-sized LCDM halo to test whether any of the 20 low mass satellites recently-discovered in the DES, SMASH, Pan-STARRS, and ATLAS surveys are truly associated with the Clouds. Of the 6 systems with kinematic data, only Hydra II and Hor 1 have distances and radial velocities consistent with a Magellanic origin. Of the remaining low mass satellites, six (Hor 2, Eri 3, Ret 3, Tuc 4, Tuc 5, and Phx 2) have positions and distances consistent with a Magellanic origin, but kinematic data are needed to substantiate that possibility. Conclusive evidence for association would require proper motions to constrain the orbital angular momentum direction, which, for true Magellanic satellites, must coincide with that of the Clouds. We use this result to predict radial velocities and proper motions for all new low mass satellites. Our results are relatively insensitive to the assumption of first or second pericenter for the Clouds.

### Astrometry with MCAO at Gemini and at ELTs:

In Fritz et al. 2016 we present a first analysis of the astrometric error budget of absolute astrometry relative to background galaxies using adaptive optics. We use for this analysis multi-conjugated adaptive optics (MCAO) images obtained with GeMS/GSAOI at Gemini South. We find that it is possible to obtain 0.3 mas reference precision in a random field with 1 hour on source using faint background galaxies. Systematic errors are correctable below that level, such that the overall error is approximately 0.4 mas. Because the reference sources are extended, we find it necessary to correct for the dependency of the PSF centroid on the used aperture size, which would otherwise cause an important bias. This effect needs also to be considered for Extremely Large Telescopes (ELTs). When this effect is corrected, ELTs have the potential to measure proper motions of dwarf galaxies around M31 with 10 km/s accuracy over a baseline of 5 years.

### The Proper Motion of Palomar 5:

We used UVa’s Large Binocular Telescope in tandem with the Sloan Digital Sky Survey to measure the first CCD (charge coupled device)-based proper motion for the globular cluster Palomar 5 which is being tidally disrupted by the Milky Way. Subsequent modeling of this disruption shows surprising evidence that the Milky Way dark halo is adequately described by a spherical potential, rather than a triaxial one.

### Probing the dark halo of the Milky Way with GeMS/GSAOI

We are developing the use of Adapative Optics (AO) methods to measure proper motions (PMs) for a wide variety of tracers in the Local Group, too faint for GAIA astrometry. The main scientific goals of this program are to definitively constrain the dark halo shape, orientation, radial profile and total mass of the Milky Way. PMs are difficult to measure. The size of the subtended motion in the plane of the sky at typical halo distances (50 kpc) is very small compared to the precisions achievable with normal ground-based telescopes. With Hubble Space Telescope (HST) techniques, 10 km/s accuracy has been achieved at such distances. However, the continued use of HST is obviously limited by its lifetime, and only a fraction of Local Group substructure has been investigated. AO techniques are the most promising long-term avenue. The aim here is to develop multi-conjugate AO methods for measuring high accuracy PMs within the context of a recently approved Long/Large Gemini program. This will also serve as an anchor point of HST optical to K-band AO, which can be applied to much of the substantial HST archive, including M31 substructures, with potential for very high accuracy when extended with extremely large telescopes in the future.

#### Research Papers

Images of Pyxis (left) and Carina (right) taken using the GeMS/GSAOI system on Gemini South.

## Calculating Parallax

An astronomer might measure an angle of 2 arc seconds for the star he is observing, and he wants to calculate the distance to the star. Parallax is so tiny, it is measured in seconds of arc, equal to one-sixtieth of one minute of arc, which in turn is one-sixtieth of a degree of rotation.

The astronomer also knows that the Earth has moved 2 AU between observations. In other words, the right-angled triangle formed by the Earth, the sun and the star has a length of 1 AU for the side between the Earth and the sun, while the angle at the star, inside the right-angled triangle, is half the measured angle or 1 arc second. Then, the distance to the star equals 1 AU divided by the tangent of 1 arc second or 206,265 AU.

To make it easier to handle the units of parallax measurement, the parsec is defined as the distance to a star that has a parallax angle of 1 arc second, or 206,265 AU. To give some idea of the distances involved, one AU is about 93 million miles, one parsec is about 3.3 light years, and a light year is about 6 trillion miles. The closest stars are several light years away.

## The Death of Dark Matter’s #1 Competitor

“The discrepancy between what was expected and what has been observed has grown over the years, and we’re straining harder and harder to fill the gap.” -Jeremiah P. Ostriker

If you have any sort of interest in outer space, the Universe and just what this entire existence is made up of, you’ve probably heard of dark matter — or at least the dark matter problem — before. In brief, let’s take a look at what you might see if you looked out at the Universe with the greatest telescope technology we’ve ever developed as a species.

Not this image, of course. This is what you’d see to the significantly aided human eye: a small region of space that contains just a handful of dim, faint stars present within our own galaxy, and apparently nothing beyond it.

What we’ve done is look at not only this region in particular, but many others like it, with incredibly sensitive instruments. Even in a region like this, devoid of bright stars, galaxies, or known clusters or groups, all we have to do is point our cameras at it for arbitrarily long stretches of time. If we let enough go by, we start to collect photons from incredibly faint, distant sources. That tiny box marked “XDF” above is the location of the Hubble eXtreme Deep Field, a region so small it would take 32,000,000 of them to cover the entire night sky. And yet, here’s what Hubble saw.

There are 5,500 unique galaxies identified in this image, meaning that there are at least 200 billion galaxies in the entire Universe. But as impressive as that number is, it’s not even the most impressive thing we’ve learned about the Universe from studying the huge number and diversity of galaxies, groups and clusters within it.

Think about what’s making these galaxies shine, whether right next door to us or tens of billions of light-years away.

It’s the stars shining within them! Over the past 150 years or so, one of the greatest achievements of astronomy and astrophysics has been our understanding of how stars form, live, die, and shine while they’re alive. When we measure the starlight coming from any one of these galaxies, we can immediately infer exactly how what types of stars are present within it, and what the total mass of the stars inside is.

Hold this in your mind as we move forward: the light we observe from the galaxies, groups and clusters we see tells us how much mass is in that galaxy’s, group’s or cluster’s stars. But starlight isn’t the only thing we can measure!

We can also measure how these galaxies are moving, how quickly they’re rotating, what their velocities are relative to one another, and so on. This is incredibly powerful, because based on the laws of gravity, if we measure the velocities of these objects, we can infer how much mass-and-matter there must be inside of them!

Think about that for a moment: the law of gravitation is universal, meaning it’s the same everywhere in the Universe. The law that governs the Solar System must be the same as the law that governs the galaxies. And so here we have two different ways of measuring the mass of the largest structures in the Universe:

1. We can measure the starlight coming from them, and because we know how stars work, we can infer how much mass there is in stars in these objects.
2. We can measure how they’re moving, knowing whether-and-how they’re gravitationally bound. From gravitation, we can infer how much total mass there is in these objects.

So now we ask the crucial question: do these two numbers match?

Not only do they not match, they’re not even close! If you compute the amount of mass present in stars, you get a number, and if you compute the amount of mass that gravitation tells us must be there, you get a number that’s 50 times greater. This is true regardless of whether you look at small galaxies, large galaxies or groups or clusters of galaxies.

Well, that tells us something important: either whatever’s making up 98% of the mass of the Universe isn’t stars, or our understanding of gravitation is wrong. Let’s take a look at the first option, because we have a lot of data there.

There could be lots of other things out there besides stars that make up the mass of galaxies and clusters, including:

• clumps of non-luminous matter like planets, moons, moonlets, asteroids, iceballs, etc.,
• neutral and ionized interstellar gas, dust, and plasma,
• black holes,
• stellar remnants like white dwarfs and neutron stars
• and very dim stars or dwarf stars.

The thing is, we’ve measured the abundance of these objects and — in fact — the total amount of normal (i.e., made of protons, neutrons and electrons) matter in the Universe from a variety of independent lines, including the abundance of the light elements, the cosmic microwave background, the large scale structure of the Universe, and from astrophysical surveys. We’ve even tightly constrained the contribution of neutrinos here’s what we’ve learned.

About 15-16% of the total amount of matter in the Universe is made up of protons, neutrons and electrons, the majority of which is in interstellar (or intergalactic) gas and plasma. There’s maybe about another 1% in the form of neutrinos, and the rest must be some type of mass that’s not made up of any particles present in the Standard Model.

That’s the dark matter problem. But it’s possible that postulating some unseen, new form of matter isn’t the solution, but that the laws of gravity on the largest scales are simply wrong. Let me walk you through a brief history of the dark matter problem, and what we’ve learned about it as time has gone on.

Large-scale structure formation — at least initially — was poorly understood. But starting in the 1930s, Fritz Zwicky began measuring the starlight coming from galaxies present in clusters, as well as how quickly the individual galaxies were moving relative to one another. He noted the huge discrepancy mentioned above between the mass present in stars and the mass that must be present to keep these large clusters bound to one another.

This work went largely ignored for about 40 years.

When we started making large cosmological surveys in the 1970s, such as PSCz, their results started to indicate that in addition to Zwicky’s cluster-dynamics problems, the structure we were seeing on even larger-scales required an unseen, non-baryonic source of mass to reproduce the structures observed. (This has since been improved by surveys like 2dF, above, and SDSS.)

Also in the 1970s, Vera Rubin’s original and hugely influential work brought new attention to rotating galaxies, and the dark matter problem they showcased so thoroughly.

Based on what was known about the law of gravity and what was observed about the density of normal matter in galaxies, you would have expected that as you moved farther away from the center of a spinning, spiral galaxy, the stars orbiting it would slow down. This should be very similar to the phenomenon seen in the Solar System, where Mercury has the highest orbital speed, followed by Venus, then by Earth, then by Mars, etc. But what spinning galaxies show instead is that the rotational speed appears to remain constant as you move out to larger and larger distances, which tells us that either there’s more mass than can be accounted for by normal matter, or that the law of gravity needs to be modified.

Dark matter was the leading proposed solution to these problems, but no one knew whether it was all baryonic or not, what its temperature properties were, and whether/how it interacted with both normal matter and itself. We had some limits and constraints on what it couldn’t do, and some early simulations that seemed promising, but nothing concretely convincing. And then the first major alternative came along.

MOND — short for MOdified Newtonian Dynamics — was proposed in the early 1980s as a phenomenological, empirical fit to explain the rotating galaxies. It worked very well for small-scale structure (galaxy-scale), but failed on large scales in all models. It couldn’t explain galaxy clusters, it couldn’t explain large-scale structure, and it couldn’t explain the abundance of the light elements, among others.

While the galaxy dynamics people latched on to MOND because it is more successful at predicting galactic rotation curves than dark matter is, everyone else was highly skeptical, and for good reason.

In addition to its failures on all scales larger than that of individual galaxies, it wasn’t a viable theory of gravity. It wasn’t relativistic, meaning it couldn’t explain things like the bending of starlight due to intervening mass, gravitational time dilation or redshift, the behavior of binary pulsars, or any other relativistic, gravitational phenomena verified to occur in agreement with Einstein’s predictions. The holy grail of MOND — and what many vocal proponents of dark matter demanded, including myself — was a relativistic version that could explain the rotation curves of galaxies along with all the other successes of our current theory of gravity.

Meanwhile, as the years went on, dark matter started having a huge number of cosmological successes. As the large-scale structure of the Universe went from poorly-understood to well-understood, and as the matter power spectrum (above) and fluctuations in the cosmic microwave background (below) became precisely measured, dark matter was found to work wonderfully on the largest scales.

In other words, these new observations — just like those for Big Bang Nucleosynthesis — were consistent with a Universe that was composed of about five times as much dark (non-baryonic) matter as normal matter.

And then, in 2005, the supposed “smoking gun” was observed. We caught two galaxy clusters in the act of colliding, meaning that if dark matter was correct, we’d see the baryonic matter — the interstellar/intergalactic gas — colliding and heating up, while the dark matter, and hence the gravitational signal, should pass right through without slowing down. Below, you can see the X-ray data of the Bullet cluster in pink, with the gravitational lensing data overlaid in blue.

This was a huge victory for dark matter, and an equally huge challenge to all models of modified gravity. But small-scales still posed a problem for dark matter it still isn’t as good at explaining the rotation of individual galaxies as MOND is. And thanks to TeVeS, a relativistic version of MOND formulated by Jacob Bekenstein, it looked like MOND would finally get a fair shot.

Gravitational lensing and some relativistic phenomena could be explained, and there was finally a clear-cut way to distinguish between the two: find an observational test where the predictions of TeVeS and the predictions of General Relativity differed from one another! Amazingly, such a setup already exists in nature.

Spinning neutron stars — stellar remnants from ultramassive stars that have gone supernova and left a solar-mass atomic nucleus behind — are tiny things, only a few kilometers in diameter. Imagine that if you will: an object 300,000 times as massive as our planet, compressed down into a volume just one-hundred-millionth the size of our world! As you can imagine, gravitational fields near these guys get really intense, providing some of the most stringent strong-field tests of relativity ever.

Well, there are some instances where neutron stars have their axial “beams” pointed directly at us, so the “pulse” at us every time the neutron star completes an orbit, something that can happen up to 766 times a second for objects this small! (When this happens, the neutron stars are known as pulsars.) But in 2004, an even rarer system was discovered: a double pulsar!

Over the past decade, this system has been observed in its very tight gravitational dance, and Einstein’s General theory of Relativity has been put to the test like never before. You see, as massive bodies orbit one another in very strong gravitational fields, they ought to emit a very specific amount of gravitational radiation. Although we don’t have the technology to measure these waves directly, we do have the ability to measure how the orbits are decaying due to this emission! Michael Kramer of the Max Planck Institute for Radio Astronomy was one of the scientists working on this, and here’s what he had to say about the orbits of this system (emphasis mine):

“We discovered that this causes the orbit to shrink by 7.12 millimeters a year, with an uncertainty of nine-thousandths of a millimeter.”