Supernova Ia Spectrum | Understanding Dark Energy

[pi.rootpi]

Hi, I have an image of a graphic describing the spectrum of a supernova Ia, the problem is that I don't really know how to read it. I'd like to know if there's any importance in this image that can drive us to think about dark energy (or accelerated expansion).

The explanation of the graph says:
Spectrum of SN 1997ap, after binning by 12.5 °A, placed within a time series of
spectra of “normal” SNe Ia 17,18,19,20,21 (the spectrum of SN 1993O was provided courtesy
of the Cal´an/Tololo Supernova Survey), as they would appear redshifted to z = 0.83. The
spectra show the evolution of spectral features between 7 restframe days before and 2 days
after restframe B-band maximum light. SN 1997ap matches best at 2 ± 2 days before
maximum light. The symbol \oplus{} indicates an atmospheric absorption line and * indicates a region affected by night sky line subtraction residuals. The redshift of z = 0.83 ± 0.005 was
determined from the supernova spectrum itself, since there are no host galaxy lines detected.

Thanks for all!

And here you have the image:

 

[marcus]

I think you are doing the right thing by looking into the details.

It's not just about the mysterious dark energy, or the even more enigmatic alternative mechanisms that might be having a similar effect.

It's about some fairly simple things: the different ways stars explode,
and different ways we measure distance.

Have you read about how Type Ia Supernovae work?

I don't want to start telling you stuff you already know.

How they work is different from other Supernovae and must lead to recognizable differences in the spectrum, so you can tell a SNIa from other kinds.

Also the lightcurve, how the explosion brightness varies over time, it takes a few days to happen. That's different too, I believe.

And do you know why Type Ia SNe are all about the same brightness---so they can serve to tell distance, as a socalled "standard candle". Most likely you do.

Those are all pretty interesting nuts-and-bolts questions. If you want to ask, some others of us will probably try to respond.

About what dark energy actually is, its harder to talk about because so little is known.
Speculation that get too far ahead of established facts and understanding can be kind of frustrating and useless. If not silly

 

[pi.rootpi]

Hi!
Marcus, thank you very much for your help.

I'll tell you what's what i know

1. I know they've used Supernovae Ia to study the accelerated expansion of the Universe.

2. I've been reading mostly about Cosmology Supernovae Project (Saul Perlmutter).

3. Due to me lack of knowledge in the field there are lots of things I don't really understand: the first problem are mathematics, I'm in last year of High School and we haven't seen anything further the derivative and the 3D space. The second lack is on physics, we haven't seen waves so I just have a little idea of what the wavelenght is and so with the spectrum.


So:

1. In which of these lacknesses do you think I should pay more attention?

2. Could I arrive to understand the graph I wrote in the link (I just have 20 days to finish my project)?


So everything you can explain from basic concepts is great to me!

THANKS!

 

[cristo]

I'm a little confused as to whether you want to know the Astrophysics behind type Ia supernovae, or how observations of these showed that the universe was accelerating? If the former, I would say that is a topic in itself since, as marcus eludes to, the evolution of such objects is quite complex.

I would suggest, at least for now, that you restrict yourself to the acceleration of the universe (at least, if you want to get your project done in a couple of weeks) and not the Astrophysics of SNIa.

 

[marcus]

It's a judgment call, but I think Cristo is right and the best idea is keep it simple and go for the essentials. (BTW, SNe is short for "supernovae" the plural of supernova)

What we should try to do in this thread is review the essentials of how SNe data shows accelerated expansion. I'm going to forget that you have a course project, you do what you want about that (open another thread in another forum even). What we have to do here is to say in the simplest clearest way what's going on in those 1998 reports like Perlmutter et al.

A. Type Ia SNe are standard candles.
They all have approximately the same brightness, so measuring their apparent brightness tells you something called "luminosity distance."
Intuitively, dimness translates to a measure of distance. It's not the whole story, other factors play a role, but it's one possible measure.

The central law in cosmology is Hubble's Law which astronomers constantly try to confirm out to larger and larger distances. You check Hubble Law by comparing redshift with distance. To tell the real distance, you need a standard candle. Other standard candles, used earlier, were only good at closer range, they weren't bright enough. So Hubble Law had only been checked at closer range. Perlmutter's team was trying to check the Hubble Law relation of distance and redshift at unprecedented longer range, with a new kind of standard candle. They didn't expect to see acceleration. There were actually two teams working on the same thing.

Cristo, Janus, DH, George, Russ...please correct me if I am oversimplifying or have something wrong.

B. Both teams found that SNe at a give redshift were DIMMER than they expected them to be, at that redshift, using the pre-1998 standard non-accelerating cosmic model. In other words, if you plotted luminosity distance as a function of redshift, the luminosity distance was increasing FASTER than was expected (without including dark energy in the model)

Now the hardest thing to understand in this whole business, in my view, is how that translates into accelerated expansion.
George Jones could probably give a clear simple explanation if he were around. I will think about it and get back to this.
You can get a certain amount just by looking here:
http://en.wikipedia.org/wiki/Dark_energy

And there is a technical explanation, full of math, here:
http://arxiv.org/abs/astro-ph/0303428
That won't help probably. It is a review article by Perlmutter and Brian Schmidt. The key equation is equation (8) on page 6.

It gives the luminosity distance D_L as a function of redshift z.

I know this is too mathy to be of much use, but I'll just get it out anyway. Equation (8) says that D_L is proportional to z + z²(1 - q)/2 + tiny correction term,
where q is a deceleration parameter that is always going to be positive unless there is some dark energy.

If you look on page 6 you see that D_L is actually equal to that, multiplied by the Hubble distance c/H which we know is about 13.8 billion ly.
That's just a constant, and we can drop the tiny correction term. So for practical purposes we could just be sloppy and write our sloppy version of equation #8:

D_L = z + z²(1 - q)/2

where they initially thought q would be positive, a measure of how much all the matter in the universe was slowing expansion by its gravity, and then they were shocked to see D_L was increasing faster, as a function of z, than it ought to. So the only way to fix it was to reduce q, make it negative even! Which you can do only if you have some negative pressure stuff.

Don't let any teacher see the sloppy version, if you copy equation (8) then put in the Hubble distance c/H, or replace the equals sign by a squiggle ~ that means "is proportional to".

I realize this is torture if you don't understand where the math is coming from, and we ought to be able to translate that into words. Perlmutter and Schmidt attempt some explanation. But right now I don't see a good way to put it. I'll think some more about it, and maybe someone else will jump in.

 

[marcus]

OK, no one else happened to be around and put in a word, so here's what I suggest. This way you don't need any equations. You can produce a table using Ned Wright's calculator
http://www.astro.ucla.edu/~wright/CosmoCalc.html

If you put in a typical redshift like z = 0.5, and press the "general" button, it will tell you the luminosity distance in lightyears, actually in Gly (billions of lightyears).

Keep pressing "general" and put in different amounts of dark energy---change the 0.73 to what they thought it was back in 1998, which was zero. You will get something like 8 Gly.
That was what they expected.

Remember luminosity distance measures dimness. The dimmer it looks the farther it is, by that measure.

Well they were surprised to see that the luminosity distance was not 8 Gly, it was NINE Gly. More precisely it was 9.2 Gly.

"Hey, this supernova as a redshift of z = 0.5, so the D_L is supposed to be 8 Gly, but it is dimmer than that, looks like a D_L of 9.2 Gly!"

So let's put in a little dark energy. Instead of 0.0 put in 0.1
well a little better, the model predicts 8.387.
But what we observe is 9.2, so let's try adding more dark energy.

All we are doing is changing what is in the box where it usually says 0.73
This is the Omega_vac box.

Keep z= 0.5 and keep changing Omega_vac, and keep pressing "general"

0.3       8.6
0.4       8.7
0.5       8.9
0.6       9.0
0.73      9.2

They had to add an amount of dark energy to the model corresponding to 0.73 which means an amount 73 percent of the critical energy density (critical happens to be 0.85 nanojoules per cubic meter, but that doesn't matter.) The absolute amounts don't matter as much as that they had to add a certain definite amount to make the model predict the right luminosity distance (the right dimness) for the supernovas that they actually saw.

And they didn't only do this for a single redshift like z = 0.5. They had a whole bunch of data on supernovae of a bunch of different redshifts starting as low as z = 0.1, if I remember correctly.

I just took 0.5 as an example to work with the calculator.
=================

Omega vac means the vacuum energy density expressed as a fraction of critical density. We use critical density as a standard of comparison like "par" in golf. It makes the numbers manageable because they are all simple percentages of par. Don't have to be saying units all the time like joules or kilograms meters etc etc.
=================

If you really want things in metric units. Then our benchmark reference energy , critical energy density, is 0.85 nJ per m^3
and what produces the good fit is a dark energy density which is 73 or 74 percent of critical. So that comes to 0.62 nJ per m^3
for dark energy. That's the amount that if you plug it into the model it will make the model fit several different kinds of data, including the supernova data.

It's good to be skeptical but the evidence continues to build and the ranges of uncertainty of the numbers are narrowing down. Look at this thread.
https://www.physicsforums.com/showthread.php?t=280456
Look at the second paragraph of post #1 with the link to Carroll's blog. Carroll's figure 3 is pretty impressive. Four different kinds of evidence.

 

[pi.rootpi]

Hey! THANKS!
I think I'm beginning to Understand, let me tell you what I've understand and correct me please if I'm wrong.

They were observing a Supernova, and they know the redshift was z=0.5. Due to be a standard candel they thought they know the distance there was and they thought it should be 8Gyr. But when they observed it was farther, it was 9.2 Gyr. And they started to give numbers to the density parameter of vacuum, and they saw that it had to be 0.73 to agree with observation.

Well, now I have more questions

1. Perhaps it's an stupid question but, how did this fact bring them to think about a vacuum energy?

2. You told me in the last post they tried with more posibilities of redshift, it was because they saw the observation was different to the calculation, or because they always try with more than one "z".

THANKS!

 

[marcus]

Hey! THANKS!
I think I'm beginning to Understand, let me tell you what I've understand and correct me please if I'm wrong.

They were observing a Supernova, and they know the redshift was z=0.5. Due to be a standard candel they thought they know the distance there was and they thought it should be 8Gyr. But when they observed it was farther, it was 9.2 Gyr. And they started to give numbers to the density parameter of vacuum, and they saw that it had to be 0.73 to agree with observation.

That is basically right, but I told you an oversimplification. They looked at a lot of SNe at a lot of different redshifts. I don't remember but a whole bunch roughly in the range 0.1 to 0.5. (wild-***-estimates, look in Perlmutter's paper for the truth).

Then they chose 0.73 plus or minus so as to match ALL the data as close as possible. they got a confidence interval range, not an exact number. And in my oversimplified story they were only matching one data point, but in reality they were trying to fit a whole bunch of data points. So it came down to around 0.73.

2. You told me in the last post they tried with more posibilities of redshift, it was because they saw the observation was different to the calculation, or because they always try with more than one "z".

If there is a dark energy, then it should work for ALL size redshifts. The more SNe you observe the better the sample the more confident you can be. They always try with more than one "z". The bigger the sample the better. One measurement can be off, by some mistake or freak accident. Astronomers love data. a lot of their work is actually applied statistics.

1. Perhaps it's an stupid question but, how did this fact bring them to think about a vacuum energy?

Your question #1, how did they think of this?

Well cosmologists have a simple model based on two equations, the socalled Friedmann equations. When you use Wright calculator those two equations are what is "under the hood". Most people cannot solve differential equations in their head and so one IMPLEMENTS the equation model in the form of a calculator, to me it is a cause of happiness, for others it may simply be a convenience.

So the Wright calculator is an embodiment of the standard equation model.
All equation models have a few numbers you have to plug in, called parameters. The numbers like Omega_vacuum and H that you have to plug into the calculator correspond to coefficients, key ratios and stuff you would have to plug into the Friedmann model.

Now the Friedmann equations are derived from Einstein's main equation of General Rel.
Friedmann simplified and boiled down the main GR equation, in 1922.
And Einstein had already put a parameter Lambda into the main GR equation by around 1918.
So it was natural for the 1922 Friedmann equations to carry over Lambda. Anybody would see to do that if they were deriving. You could assume Lambda = 0 and leave it out, or you could put it in.

You can see the Friedmann equations in Wikipedia. Just google "wikipedia friedmann equations". It is good to know the historical origins. Like go to the Lincoln memorial if you are in Washington DC. See it at least once.

I can't say what they were thinking or why they thought to try dark energy to make the data fit. But I can guess.

There was this parameter Lambda sitting around in the Friedmann equations (just like it was in the original GR equation) and one way you write the Friedmann equations has Lambda appear in the form of a vacuum energy. So you probably did not have to be a rocket scientist to get the idea to try making Lambda slightly positive, instead of setting it to zero as had been usually done before 1998.

One good thing about cosmologists is that they instinctively don't just study our universe, they explore all the different versions they can get out of the model they are using, by varying the parameters. So actually they had already studied an accelerated expansion universe called deSitter. They knew about accelerated expansion, it was part of the theory lore that you learned in grad school. Willem de Sitter was a dutchman. You learned about it. You didn't believe that the real universe accelerated, but deSitter's was interesting so you studied that case and maybe did homework problems about it.

So when the 1998 news came out they were probably in some sense mentally prepared, some of them. Several people actually had already predicted a slightly positive Lambda based on their own personal/philosophical grounds. Science is quite funny, but it is a waste of time trying to keep track of how funny it is because there are more interesting issues to learn about.

 

[pi.rootpi]

Hi again!

(This has few to do with the rest but I didn't want to open a new post to ask it)
Oks, now I think that i understand the "oversimplificated" history. Now let me ask you if you see it's good what I'm going to put in my project, or if you would say something else (this part is only a part of the project).

-Dark energy
...*History (Saul Perlmutter and Brian Schmidt)
...* Discovery (All you have explained me about supernovae)
...* What is dark energy?
...>Vacuum energy (Cosmological Constant)
...>Quintessence
...* Opened Universe?Well, I hope it's not bad, but your opinion would be great!

TAHNKS!

 

[pi.rootpi]

Hi! I have another question, it's about the redshift.

If SNe Ia are standard candels, the know the original bright, and they received the final bright, so, why did they try with more than one redshift?

Does the fact that the Universe is expandig change the result we obtain when we do:

z =(lamda observed - lambda original)/lambda original

Or there are more things that play a role when they try to calculate the redshift.

I don't know If I have explained myself really well, but I don't know how to ask it


Thanks!

 

[marcus]

...If SNe Ia are standard candles, they know the original bright, and they received the final bright, so, why did they try with more than one redshift?...

I think there are several reasons why they would want to use as large a sample of SNe observations as was practical and possible to get.

One is the normal errors you get in measuring anything. There is always some spread in the data. No matter how carefully you measure there will be random error in measuring the brightness, and even in measuring the redshift.

Another is that even though there is a reason for all type Ia SNe to be approximately the same brightness, it does not guarantee they will be exactly the same.

So it makes sense for the research team to measure many many SNe and average the results. Hoping that, although each individual measurement is wrong, averaging will make it come out right. The art of doing this properly is called Statistics.

Understanding how to do Statistics correctly is probably more important than knowing how to use a telescope, if you are an astronomer. But you should know both.
====================

Did you read Wikipedia about Type Ia? I hope so. For me probably the most interesting question in this discussion is WHY the Type Ia SNe are all approximately the same brightness.

A binary star. One big and the other small:

A white dwarf that has finished fusion and is in some sense a
dead cinder----made mostly of Carbon, Oxygen and elements of about that weight.
It is not massive enough to have the pressure needed to fuse Carbon etc., so it is dead.

A red giant near the end of its life. It has swollen up and is slowly blowing off its outer layers.

Look! the outer layer of hot gas that the big partner is slowly losing, some of that is falling by gravity onto the little partner and building up the mass of the dwarf.
At some point it will have enough mass to create the internal pressure needed to fuse all that Carbon etc etc which it was unable to fuse earlier. This will happen at a particular mass threshhold. What will happen when that threshold mass is reached?

This is probably an oversimplification of the story. But I hope you have read some about the supernovae mechanisms. There are several different mechanisms causing stars to blow up. You should at least have some idea of how the Ia mechanism works and why it involves the explosion of dwarf stars which are all of about the same mass, and therefore it makes explosions which are all of approximately the same energy.

 

[pi.rootpi]

Hey! Yess, I have read and understood what happens before a Ia Supernova. (all of the degeneration effect created by the electrons -although i don't really understand why do they do it, I've read something about Pauli exclusion principle- and then when the red giant has "send" to the white dwar enough mass (1.44 the mass of the Sun) the carbon reacts due to the temperature and the start explodes (I hope everything I've said it's correct, I've written it more or less like this in my project.

Then my question is (BTW, thanks for your patience and help with me!) what makes the SNe spectrum so special? I mean, I've seen the light curve with the Ni and Co but I don't really get why the fact that the highest point of the luminosity graph is the point when it also will decrease faster, makes them so important.


Thanks and Happy Christmas!

 

[marcus]

... what makes the SNe spectrum so special? I mean, I've seen the light curve with the Ni and Co but I don't really get why the fact that the highest point of the luminosity graph is the point when it also will decrease faster, makes them so important.
...

It is fun talking with you, PiRootPi. You read and think and learn stuff on your own.
You should also connect with Cristo and George Jones and others. If necessary write them PM (not about your school project because our policy is not to help, but about general questions).
A fast-learning person should not rely on just one resource-person.

BTW I am not an expert about Ia SNe but I have the impression that what we see is not the explosion but the radioactive decay of radioactive isotopes after the explosion.

The explosion itself would be a tiny source of Xray. We normally do not see the Xray or gammaray light.

If stuff is too hot it makes a small percentage visible light, it makes a larger percentage of Xray light. The flash of the actual explosion is finished very soon. Most of the energy is not in visible wavelengths. It is small (about the size of a star)

Afterwards there is a big cloud. Hot, from radioactivity. This is what makes the visible light. One reason it has high luminosity is because it is very big, millions of times bigger than the original star and the original explosion.

I could be wrong, or this might be an oversimplification. You should get some other people's ideas. Have to go out to do Holiday errands.