Author Topic: A question about size on a galactic scale  (Read 27303 times)

Offline LunarOrbit

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A question about size on a galactic scale
« on: March 08, 2011, 04:49:06 PM »
I'm having a discussion on another forum with someone who quoted a news story saying Betelgeuse is going to give Earth "a second Sun" when it goes supernova (the article is full of crackpot stuff about "the end of the world" in 2012).

I've said it may be bright enough to be seen during daylight, but comparing it to the Sun is a bit of an exaggeration because I can't imagine it would be anything more than a bright star. But he is saying it would be as large in the sky as the Sun.

How large would the supernova have to be (at a distance of 640 light years) in order to have an apparent size of 32 arc minutes in our sky like the Sun? The guy says it would expand to "a few light years in diameter" but even if that's true (and I don't know) it still seems unlikely to me that it would be more than a bright star at that distance.

Astronomy isn't exactly one of my strong points, even though I find it fascinating.
« Last Edit: March 08, 2011, 08:37:40 PM by LunarOrbit »
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Offline Bob B.

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Re: A question about size on a galactic scale
« Reply #1 on: March 08, 2011, 05:59:58 PM »
Betelgeuse will explode as a type II supernova.  To estimate how bright it will be, we can look to another type II supernova for comparison.  SN 1987A exploded in the Large Magellanic Cloud 51.4 kiloparsecs away and had an apparent magnitude of +3.  This equates to an absolute magnitude of -15.5, which is how bright an object appears from a distance of 10 parsecs (32.6 light years).

We can reasonably assume Betelgeuse will have a similar absolute magnitude.  With an absolute magnitude of -15.5 and a distance of 640 light years (196 parsecs), Betelgeuse will have an apparent magnitude of about -12.3.  This is approximately 2/3 as bright as the full moon.  The Sun has an apparent magnitude of -26.74, which is 600,000 times brighter than magnitude -12.3.  Betelgeuse will be a really impressive object in the sky, but clearly no where near as bright as the Sun.

Regarding size, at 640 light years away, Betelgeuse would have to expand to 6 light years across to have the same apparent size as the Sun.  Of course, by the time it expands to something that big, it will have faded in brightness.

Offline LunarOrbit

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Re: A question about size on a galactic scale
« Reply #2 on: March 08, 2011, 06:20:51 PM »
Thank you, Bob!

So is it safe to say that at it's brightest (before it expands and fades) the supernova will still only look like a bright star from that distance?

How long would it take for the supernova to expand to a diameter of 6 light years? It doesn't expand at light speed, right?
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Offline Bob B.

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Re: A question about size on a galactic scale
« Reply #3 on: March 08, 2011, 08:18:02 PM »
How long would it take for the supernova to expand to a diameter of 6 light years? It doesn't expand at light speed, right?

Let’s again use a known supernova as an example to extrapolate from.  

The Crab Nebula was formed from a supernova that exploded in the year 1054, or 957 years ago.  It currently has a diameter of 11 light-years and is expanding at a velocity of about 1,500 km/s.  To reach it’s current size, the average expansion velocity has been 1,723 km/s.  If we assume the velocity has been slowing at a constant rate, then the initial velocity was 1,946 km/s and it has been decelerating 0.466 km/s-year.

Using these numbers, the amount of time needed to reach a diameter of 6 light-years is 491 years.

So is it safe to say that at it's brightest (before it expands and fades) the supernova will still only look like a bright star from that distance?

Naked eye, yes.

The light curve of a type II supernova decays at about 0.008 magnitudes per day (source: http://en.wikipedia.org/wiki/Type_II_supernova).  This means that Betelgeuse will decay to naked eye invisibility (magnitude 6) in about 6.25 years.  Using the numbers above, the nebula will expand to a diameter of 0.08 light-years in that amount of time.  This will give the nebula an apparent diameter of 26 arc-seconds, which is below naked eye resolution.  (Naked eye resolution is about 1 arc-minute.)

In a telescope, however, a disc should be resolvable fairly quickly.  For instance, the nebula should expand to an apparent diameter equal to that of Uranus in less than a year.  Even my 8-inch telescope can easily resolve the disc of Uranus.

(Please note that the Sun has a diameter of 32 arc-minutes – you previously said “arc seconds”.)

« Last Edit: March 09, 2011, 08:15:07 AM by Bob B. »

Offline LunarOrbit

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Re: A question about size on a galactic scale
« Reply #4 on: March 08, 2011, 08:50:42 PM »
Thanks again, Bob. That was very helpful... and I actually understood it. ;)

One of these days I'm going to get myself a telescope and learn how to use it. I remember my next door neighbour showing me Saturn and Halley's comet when I was a kid and I've wanted a telescope of my own ever since.

Quote
Please note that the Sun has a diameter of 32 arc-minutes – you previously said “arc seconds”.

Whoops. Thanks, I've corrected my original post.
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Offline ijuin

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Re: A question about size on a galactic scale
« Reply #5 on: March 09, 2011, 01:43:32 AM »
In a telescope, however, a disc should be resolvable fairly quickly.  For instance, the nebula should expand to an apparent diameter equal to that of Uranus in less than a year.  Even my 8-inch telescope can easily resolve the disc of Uranus.

(Please note that the Sun has a diameter of 32 arc-minutes – you previously said “arc seconds”.)
I'd use some good strong light filters if I were going to look at a naked-eye-visible supernova through a telescope--you are, after all, looking at something with about one million times the apparent brightness of Uranus.

Offline Bob B.

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Re: A question about size on a galactic scale
« Reply #6 on: March 09, 2011, 11:59:56 AM »
One of these days I'm going to get myself a telescope and learn how to use it. I remember my next door neighbour showing me Saturn and Halley's comet when I was a kid and I've wanted a telescope of my own ever since.

It's a good hobby to have.  I rarely get my telescope out anymore unless there's some special event going on, but I observed regularly while living in Alabama during the 90s.  I was a member of the local astronomy club and we had a nice dark sky observing site.  Getting away from city lights is really important unless you only want to observe the moon and planets.  If you have binoculars, that is a good way to get started.  There are quite a few bright objects that can be seen with binoculars and it gives you practice learning you're way around the sky.