# Star density in- versus out- of the arms of the galactic pattern?

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What is the density difference in our galaxy (or in a typical spiral),

at A, B, C versus at a, b, c?

Consider the yellow track.

Do astronomers have a graph like this…

… which shows the shape of the density through and between the arms?

In short,

# Do we roughly know the density between-arms versus in-arms… is it 10%, 50% or 90%?

Further issues arising:

= I understand that one of the reasons the arms "appear real" is just that there are more bright young stars forming in the arms (due to the higher pressure). Perhaps the actual density difference is very low?

= Perhaps the density variation is dependent on the type of star, or other material - what about things like gasses?

= Let's say the percentage I am asking about is X% - at our radius. Is it X% at all radii? How does the "strengthiness" percentage vary with radius? This is not immediately intuitive from looking at images.

(original galaxy arm pattern diagram courtesy wikipedia)

I'm afraid there is no answer, yet… The problem is that you would have to know the star densities in the different regions (in the spiral arms and outside of the spiral arms). While it is certainly possible to have an accurate estimate of the density of massive stars because of their brightness, the density of low mass stars in different regions of the galaxy is much more difficult to estimate. And since low mass stars make up the vast majority of stars (see for instance the initial mass function which is a measure of the distribution of stars over the different masses), estimating the density of stars in different regions becomes very uncertain.

But, at the moment the Gaia satellite is measuring the position and distances of about a billion stars and other objects. A much more detailed three dimensional map will be created with that data, including distance data for dim stars whose distances we were as yet unable to measure. So there is hope ;-)

NB. The first data release of Gaia has been published in September. I haven't found any papers that were able to answer your question (my search was not extensive though), but they might be forthcoming. Of course if you have some programming skills, you might determine the density differences from the data (available here) yourself.

EDIT - Just took a look at the data, the parallax (and therefore the distance) is still lacking for many stars. Hopefully this will change with future data releases.

= I understand that one of the reasons the arms "appear real" is just that there are more bright young stars forming in the arms (due to the higher pressure). Perhaps the actual density difference is very low?

I would expect that the density difference of stars is quite small.

= Perhaps the density variation is dependent on the type of star, or other material - what about things like gasses?

The density variation is certainly different between different types of stars. High mass stars only occur near star forming regions (i.e. in spiral arms). Their lifespan is so short that they do not have the time to get very far from the region in which they were formed.

I'd expect that the density variation for gas and dust will be higher (but I have no knowledge to support this).

## Density wave theory

Density wave theory or the Lin-Shu density wave theory is a theory proposed by C.C. Lin and Frank Shu in the mid-1960s to explain the spiral arm structure of spiral galaxies. Their theory introduces the idea of long-lived quasistatic density waves (also called heavy sound), [1] which are sections of the galactic disk that have greater mass density (about 10–20% greater). [2] The theory has also been successfully applied to Saturn's rings.

## Star density in- versus out- of the arms of the galactic pattern? - Astronomy

Spiral galaxies are observed to exhibit a range of morphologies, in particular in the shape of spiral arms. A key diagnostic parameter is the pitch angle, which describes how tightly wound the spiral arms are. Observationally and analytically, a correlation between pitch angle and galactic shear rate has been detected. For the first time, we examine whether this effect is detected in N-body simulations by calculating and comparing pitch angles of both individual density waves and overall spiral structure in a suite of N-body simulations. We find that higher galactic shear rates produce more tightly wound spiral arms, both in individual mode patterns (density waves) and in the overall density enhancement. Although the mode pattern pitch angles by construction remain constant with time, the overall logarithmic spiral arm winds over time, which could help to explain the scatter in the relation between pitch angle versus shear seen from observations. The correlation between spiral arm pitch angle and galactic shear rate that we find in N-body simulations may also explain why late Hubble type of spiral galaxies tend to have more open arms.

## Astronomy Chapter 19 Module 19 HW2

Spiral arms are waves of [a] in the disk of a spiral galaxy.
Stars are widely separated and are not individually affected by the greater crowding in spiral arms.
The gas clouds are much larger and, relatively, closer. Thus they suffer from crowding in the spiral arms. The [b] waves of the spiral arms squeeze the gas and dust clouds and that promotes star formation.

Massive young stars that are formed are [c] (enter "bluer" or "redder" or 'the same color" without quotation marks) and brighter than the lower mass stars.

The massive stars have [d] (enter "longer" or "shorter" or 'the same length" without quotation marks) lifetimes and do not have time to spread out out across the galactic disk so they trace the location of the [e] arms.

Most stars in the halo are less luminous than the Sun.

Most stars in the halo contain a much lower percentage of heavy elements than the Sun.

Halo stars are no longer being formed at the current epoch.

All halo stars are less massive than our Sun.

****Halo stars are made entirely of hydrogen and helium with no heavy elements.

During a star's lifetime, it (a) hydrogen into helium and helium into carbon.

If it is more (b) it also creates heavier elements, up to
(c) by fusion, and even heavier elements, up to uranium, during a (d) explosion.

When the star ends its life as a planetary nebula or in a supernova explosion, it disperses these elements into the (e) medium.
Thus, over time the interstellar medium contains an (f) proportion of heavier elements than it did originally.

## Star density in- versus out- of the arms of the galactic pattern? - Astronomy

This is awesomely weird. Imagine a bike wheel – each spoke is an “arm.” When the wheel rotates, the arms rotate, right? This is NOTHING like our galaxy. Imagine a beanie hat with a propeller on top. Hold the propeller still, and spin the hat underneath. That’s a little more like it. The hat is the stars, dust, gas, and everything our galaxy is made of. It spins around, passing THROUGH the arms (the propeller) of our galaxy. The arms aren’t made of anything. Whoa, what?

Okay, interested? Confused? Ready for more? Good, because that wasn’t a very accurate description, it was just enough to make you think.

### Arms are Denser Areas

When I said “the arms aren’t made of anything” that’s because they’re just denser areas of the same stuff the whole galaxy is made out of, but as the galaxy spins, the arm is made up of different stars, different dust from one eon to the next. The stars and stuff glide right through the arms, though they may slow down while they’re there.

#### Try this at home:

1. Take a face-on mug shot of your favorite spiral galaxy (how’z about the Milky Way?)
2. Mark your 1000 favorite stars in one arm.
3. Wait 100 million years.
4. Take another photo.
5. Find those 1000 favorite stars, and where the arms are now, compared to before.
6. The arms may have moved a bit, but the stars will have moved a LOT. Some of them will be halfway around the galaxy again, some will only have moved a touch, and still others may have gone around a couple times. The arms will now be made up of different stars, but they’ll still be there.

Okay, obviously you can’t really do this at home for about 10 very good reasons, but you get the idea.

### Stars Travel through the Arms (Traffic Jam)

Think about it another way. Spiral arms are like traffic jams of stars. You know how there’s always a traffic jam at the Renton S-Curves, or by the U District on I-5? If you take either of these routes, you’ll be in the traffic jam for a while, and then once you’re out of the bad area, you can get back up to speed. The traffic jam is still there though? (usually true … we’re talking about I-5 here), but you’re out, it’s someone else’s turn to bite their lip and grumble at traffic.

Same way with stars. The traffic jam is always there, but different people are in it at different times.

There’s a PERFECT animation over at: Traffic Waves.

### Density Wave Motion

Now that we’ve established that spiral arms are density waves (technically a “spiral density wave”), and it’s the stars that move through it, not the arm spinning around like a bike wheel, I’ve got a shocker for you. The arms move too, just at a different speed. That’s called the “pattern speed.”

Watch this video – see how the traffic jam moves around the circle, but the cars move differently?

Now this one – it’s a little easier to see both motions with this spinning galaxy.

### Density Wave Formation

How do the spiral arms get started? Umm… that’s an open question, but I can tell you a couple of useful things.

First – the galaxy rotates differentially. Oops, jargon. The middle rotates at a different speed than the outer edge. Ta-da! Differential rotation. The Sun and Jupiter do this too. A bicycle wheel does not.

This differential rotation is due to Kepler’s laws. objects closer in revolve around the center a lot faster than objects further out.

Second, the likelihood that the galaxy started as one big perfectly even ball of gas is pretty low. There were pockets of lots of gas, and pockets of less stuff. These pockets will spread out and spin into denser areas.

So that’s a pretty easy explanation. There are still some problems we need to solve, but that should give you an idea.

Lastly, a way in which the arms keep themselves dense is due to the gravity of more material in the arm itself: stars speed up as they enter and arm, and then slow down as they leave it – the opposite of a traffic jam.

### The Wind-Up Problem

But how come the arms don’t twist themselves up? Well, that’s one of the problems with the formation hypothesis I just showed you. This is the question that led to the idea of density wave arms in the first place.

It doesn’t twist itself up because the arms are not made of material, they’re just a denser area, there’s no reason for the arm to change.

### Want More?

Check out Voyages to the Stars and Galaxies by Fraknoi, Morrison, and Wolff

## Lecture 27: Spiral Galaxies

The Milky Way & Andromeda are examples of Spiral Galaxies .

Spheroids vary greatly in size.

## Disk Structure

• Open Clusters & loose Associations of stars
• Mix of young & old stars
• Cepheid Stars in young clusters

## Rotation of the Disk

Measure using the Doppler Effect

Stars : Doppler shifts of stellar absorption lines

Ionized Gas : emission lines from HII regions

• Cold H clouds emit a radio emission line at a wavelength of 21-cm
• Can trace nearly the entire disk beyond where the stars have begun to thin out.

## Rotation Curves

The disk rotates about the center of the galaxy

## Rotation Speeds

Inner Parts : Rise from Zero to few 100 km/sec

Outer Parts : Nearly constant at a few 100 km/sec

## Measuring Masses of Galaxies

Star or Gas cloud is held in its orbit by the mass interior to the orbit.

Where: M(R) = mass interior to radius R
Vrot = rotation speed

## Example: Milky Way

Provides us with a way to measure the masses of Galaxies.

## Spiral Arms

Pattern of hot stars, star clusters, gas & dust crossing the disk.

• O&B Stars
• HII Regions (star forming regions)
• Giant Molecular Clouds
• Hydrogen Gas and Dust Clouds

## Sites of Active Star Formation

See O&B Stars and HII Regions strung along the Spiral Arms like "Beads on a String."

Newton's Gravity predicts: Where: M(R) = mass interior to radius R
Vrot = rotation speed This measures the enclosed mass within an orbit. As you go further out, you expect the enclosed mass, M(R), to increase (more of the galaxy is inside your orbit).

Measuring the rotation speeds in spiral galaxies provides us with a good way to measure the masses of spiral galaxies, and measure how that mass is distributed within the galaxies. As we'll see in future lectures, those measurements held some surprises.

## Formation & Evolution

Studies on galaxy formation and evolution, unlike star formation and evolution, are still very young and in the early stages. There are some widespread theories that have gained popularity, however, of galaxy formation and evolution.

### Formation

Galaxies likely are a result of slight differences in density in the early universe. Places with higher density would get matter pulled toward them through gravity, while places with lower density would have matter pulled away from them. These galaxies may have merged and grown to form the large galaxies we see today.

### Evolution

Galaxies can evolve in two ways. They can evolve passively (without outside influence of other galaxies) or, much more commonly through interaction.

#### Passive Evolution

A galaxy's overall color, composition, and appearance will change as stars evolve and interstellar matter gets used up, and recycled through star death. The already red elliptical galaxies will likely get redder and fainter. The blue spiral and irregular galaxies will stay blue as long as gas remains are available for them to reform.

#### Interaction

Galaxies can interact to change in their entire internal structure, which can trigger star formation or causing activity in the galactic nucleus.

### Galactic Interactions

Galaxies can interact with each other gravitationally in many ways. The most common is a near miss, where two galaxies pass each other nearly. The matter in both galaxies is gravitationally pulled together and the two galaxies begin to change structure, even from afar. This likely results in the galaxies returning together to merge. If the merger of galaxies was between a small and large galaxy, it is called galactic cannibalism, and the structure of the larger galaxy is likely to remain mostly unaffected. On the other hand, if the merger is between two galaxies of similar size, it results in a dramatic change in both galaxies (if both were spirals, it will likely end in an elliptical galaxy).

## Are galactic spiral arms traffic jams or do they wind up? The evidence is… polarizing.

You might think spiral arms form because, due to gravity, stars close in to the center of the galaxy orbit faster than stars farther out, so a spiral pattern naturally appears. But there's a problem with this: Over time, this would wind up the arms, destroying the structure. The thinking was that we see so many galaxies with arms that this can't be the way things work.

astronomers came up with an idea called the density wave hypothesis. Spiral arms, according to this, are more like traffic jams of stars and gas in a galaxy. A traffic jam on a road can persist for a long time, even though individual cars move in and out of them. Spiral arms were thought to be the cosmic equivalent, where spiral density waves form due to the complicated physics of the gravity of a galactic disk. Stars move in and out of them, but the wave itself persists. This way, arms don't wind up over time.

While the density wave hypothesis explains a lot of spiral arm structure, recently results have come in that show that it is actually possible that the arms in galaxies really are winding up, eventually getting so tight they fall apart, only to start to reform once again, with the whole process repeating. I explain all that in the July 2019 post, so please give that a read.

So we have two competing ides on how spiral arms form. Which is right?

A new set of observations seem to support the density wave hypothesis: Astronomers looked at magnetic fields in the galaxy NGC 1068, a nearby spiral at a distance of about 44 million light years. The astronomers used SOFIA (the Stratospheric Observatory for Infrared Astronomy), which is quite literally a 2.5-meter telescope sticking out of the side of a 747! Some wavelengths of infrared light are absorbed by water vapor in the atmosphere, making them impossible to see from the ground, but SOFIA flies high enough to get above the vast majority of that gas, allowing it to see the skies at those wavelengths.

To map the magnetic fields in NGC 1068, they exploited an effect of those fields on the dust in the galaxy. This has a few steps to it, so hang tight.

A Hubble image of the nearby spiral galaxy NGC 106, aka M77. Credit: NASA, ESA & A. van der Hoeven

Dust is made up of tiny grains of rocky material (silicates) and long chains of carbon molecules (basically, soot). In the presence of a magnetic field, these grains tend to align their long axes along the magnetic field lines — this is the same thing that happens when you put iron filings on a piece of paper with a bar magnet underneath the filings align themselves with their long axes along the field lines.

When you have great clouds of dust light years across like this where the dust is all aligned, another effect comes into play: polarization. Light from stars hits the dust grains and, because the grains are aligned, the light waves that bounce off get aligned as well. This happens in everyday life when you’re outside on a sunny day, light reflecting off glass or the hoods of cars is polarized, and if you wear polarized glasses they specifically filter that out, reducing glare from reflections.

Astronomers want to actually see and measure that polarization, though, so they use special cameras sensitive to it. Warm dust in galaxies tends to glow at very long wavelengths, which is why these new observations used SOFIA it has a camera on it called HAWC (High-resolution Airborne Wideband Camera/Polarimeter) that measures the polarization of the light from the dust. The way the magnetic fields align in the galaxy affects the way the light is polarized, so they were able to map the direction of the magnetic fields in the arms of the galaxy! And when they did, they got this:

The magnetic fields lines in the galaxy NGC 1068 (swirls) as inferred from SOFAI observations superposed on an image combining observations from Hubble Space Telescope (visible light), NuSTAR (X-rays), and the Sloan Digital Sky Survey (also visible light). The magnetic fields trace the spiral arms. Credit: NASA/SOFIA NASA/JPL-Caltech/Roma Tre Univ.

That image is a combination of different observatory images of NGC 1068 and the magnetic field streamlines added on top (streamlines are magnetic field lines in a fluid that moves, changing the shape of the lines). What it shows is that the magnetic field lines follow the shape of the spiral arms, including specific tracers of spiral structure like gas clouds and stars that also follow the pattern. They also found the field lines follow a symmetric opening or pitch angle, the angle between the spiral arm at any one point and a circle of the same size.

A spiral arm has an opening angle, called the pitch angle, which is how much the arm deviates from a circle. The red arrow indicates the pitch angle of this particular spiral if it were 0° the arm would overlap the grey circle, and the larger the angle the wider flung the arm is. Credit: Morn the Gorn / Wikipedia

That’s important because that’s a natural outcome of the density wave hypothesis! As the wave moves through the galaxy’s disk, the opening angle should stay constant, and the magnetic fields should align with it. So this result supports the density wave idea.

It’s not clear if the winding-up hypothesis would predict this or not. That idea is relatively new, and I didn’t see any papers on it making a prediction for magnetic fields. If this new observation can be explained by spiral arms winding up, it’s up to astronomers to see how that works. To be honest, I don’t really know how much weight to put into the winding-up idea it’s relatively new and I don’t know how seriously it’s being taken just yet. But it’s observations like this one that can make or break a paradigm, so I’ll keep my eyes open in the journals to see if more is being said. Science, after all, isn’t static it changes, grows, learns, drops old ideas, and attacks new ones, all in the name of making sure we have the best possible understanding of the Universe.

## Star density in- versus out- of the arms of the galactic pattern? - Astronomy

We consider the age distributions of open star clusters attributed to three segments of Galactic spiral arms. The smoothed distributions of clusters on the age-Galactocentric angle plane show a great nonuniformity. The time dependence of the formation rate of Galactic disk clusters recovered by taking into account selection effects and dynamical evolution of clusters shows that, on average, the formation rate of open star clusters decreases with time. This is in agreement with the increase in star formation rate into the past, as follows from the study of this process by the method of stellar population synthesis. The present time is the epoch of a current maximum of the cluster formation rate. In addition to the current maximum, there have been at least three more maxima with a period of 300 400 Myr and a duration of no more than 300 Myr. The age distributions are consistent with the pattern of star formation governed by the successive passages of density waves through each examined volume of the Galactic disk. The spiral structure becomes more complex when passing from the inner regions of the Galaxy to its outer regions.