Looking for "New Earth" around Alpha Centauri

"New Earth" is just my favourite way of referring to a hypothetical
planet orbiting around either one of the two principal stars in the
Alpha Centauri system, within their respective *habitable* zones.
So... assuming such a planet does exist, I'd like to know if we could
hope to see it *directly* through a telescope using special techniques
like masking out the glare of the star itself.

Focusing on Alpha Centauri 'A', which is of spectral type G2V -
exactly like the Sun - and whose habitable zone is located at between
1.2 to 1.3 AUs out, is there a projected *magnitude* that an
Earth-sized planet is expected to have? If indeed it exists, at
maximum elongation from the star New Earth would wander a total of 2.7
arc-seconds out and be amply within astrometric resolution limits for
even amateur sized telescopes! Since *resolution* is not an issue and
*masking* out the star itself in a telescope is no problems, then
clearly how bright such a planet is the determining factor for its
detection. I know Hubble has detected objects down to as low as 30th
magnitude, so I'm wondering if New Earth is expected to be of a
magnitude figure brighter than 30th magnitude and if the Hubble was
able to mask out the brilliance of Alpha Centauri 'A', whether or not
theoretically, it would have been able to image the planet directly.

I am also wondering if there's any projections for the expected
magnitude of a Jupiter-sized planet orbiting within the habitable
zones around each star. Why bother with a gas giant orbiting within
the habitable zone? Because New Earth could be one of the *moons* of
such a giant planet!

Any thoughts on the expected magnitudes of such exo-planets, anyone?

Abdul Ahad

"AI" == AA Institute writes:

AI "New Earth" is just my favourite way of referring to a
AI hypothetical planet orbiting around either one of the two
AI principal stars in the Alpha Centauri system, within their
AI respective *habitable* zones. So... assuming such a planet does
AI exist, I'd like to know if we could hope to see it *directly*
AI through a telescope [...]

AI Focusing on Alpha Centauri 'A', which is of spectral type G2V -
AI exactly like the Sun - and whose habitable zone is located at
AI between 1.2 to 1.3 AUs out, is there a projected *magnitude* that
AI an Earth-sized planet is expected to have?

The rough number that I remember is that the contrast between a star
and a terrestrial planet in the optical is something approaching 1
billion. That is, the star is 1 billion times (or about 23
magnitudes) brighter than its planet.

AI If indeed it exists, at maximum elongation from the star New Earth
AI would wander a total of 2.7 arc-seconds out and be amply within
AI astrometric resolution limits for even amateur sized telescopes!
AI Since *resolution* is not an issue

Correct, resolution per se is not the issue, particularly not for
Alpha Centauri.

AI and *masking* out the star itself in a telescope is no problems,

No, masking, to this level of precision, is incredibly difficult. Any
imperfections within the optics of the telescopes can scatter light.
When one is trying to work at the 1 part in 1 billion level of
precision, even small imperfections could end up swamping the expected
signal.

Take a look at the documentation on the Terrestrial Planet Finder
mission, which is going to try to do exactly this.

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(AA Institute) wrote in message

maximum elongation from the star New Earth would wander a total of 2.7
arc-seconds out and be amply within astrometric resolution limits for
even amateur sized telescopes!

Correction - that's a mistake on my part...the max. angular separation
of an Earth-like planet located in a circular orbit within the outer
edge of the habitable zone around Alpha Cen 'A' should be: Arctan
(1.3/272,000 AUs) = 0.986 arc-seconds, not 2.7!

Joseph Lazio wrote in message ...
"AI" == AA Institute writes:

AI "New Earth" is just my favourite way of referring to a
AI hypothetical planet orbiting around either one of the two
AI principal stars in the Alpha Centauri system, within their
AI respective *habitable* zones. So... assuming such a planet does
AI exist, I'd like to know if we could hope to see it *directly*
AI through a telescope [...]

AI Focusing on Alpha Centauri 'A', which is of spectral type G2V -
AI exactly like the Sun - and whose habitable zone is located at
AI between 1.2 to 1.3 AUs out, is there a projected *magnitude* that
AI an Earth-sized planet is expected to have?

The rough number that I remember is that the contrast between a star
and a terrestrial planet in the optical is something approaching 1
billion. That is, the star is 1 billion times (or about 23
magnitudes) brighter than its planet.

NASA factsheets for the Earth give a photometric visual magnitude when
seen from unit distance, a quantity referred to as V(1,0), as -3.86
(=m2). The Sun shines at roughly -26.8 (=m1) from the equivalent unit
distance, hence:-

Brightness ratio, R = 10^0.4*(m2-m1) = 1.5 billion to 1

So I think Earth would be overpowered by the Sun by this amount when
seen from far away. I'm sure there is a way I can relate this to
magnitude... let me do some research on this.


Correct, resolution per se is not the issue, particularly not for
Alpha Centauri.

The habitable zone around Alpha Cen 'A' is wide enough with a maximum
angular radius of 0.986"; that around Alpha Cen 'B' is considerably
tighter at some 0.561". Hence, both within amateur resolution range!

AI and *masking* out the star itself in a telescope is no problems,

No, masking, to this level of precision, is incredibly difficult.

Ahh, so that's the hard part. I wonder if ground based interferometry
arrangements using large telescopes like the Keck along with adaptive
optics, computerised processing, filtering, etc. could manage such a
task.

If Hubble did have such a star occulting disk, then from an orbital
location surely the vacuum of space would have made the scattering
problem quite possibly manageable, and if New Earth shines at 23rd
magnitude and Hubble's limiting magnitude is 30 (extreme end of its
range!), it *just* might have managed to photograph 'something'...?

Abdul Ahad

"AI" == AA Institute writes:

AI Joseph Lazio wrote in message
AI ...

AI "New Earth" is just my favourite way of referring to a
AI hypothetical planet orbiting around either one of the two
AI principal stars in the Alpha Centauri system, within their
AI respective *habitable* zones. So... assuming such a planet does
AI exist, I'd like to know if we could hope to see it *directly*
AI through a telescope [...]

AI Focusing on Alpha Centauri 'A', which is of spectral type G2V -
AI exactly like the Sun - and whose habitable zone is located at
AI between 1.2 to 1.3 AUs out, is there a projected *magnitude* that
AI an Earth-sized planet is expected to have?

The rough number that I remember is that the contrast between a
star and a terrestrial planet in the optical is something
approaching 1 billion. That is, the star is 1 billion times (or
about 23 magnitudes) brighter than its planet.

AI NASA factsheets for the Earth give a photometric visual magnitude
AI when seen from unit distance, a quantity referred to as V(1,0), as
AI -3.86 (=m2). The Sun shines at roughly -26.8 (=m1) from the
AI equivalent unit distance, hence:-

AI Brightness ratio, R = 10^0.4*(m2-m1) = 1.5 billion to 1

AI So I think Earth would be overpowered by the Sun by this amount
AI when seen from far away.

What do you know? My memory is accurate! A brightness ratio of 1
billion to 1 (or 23 magnitudes) is huge.

AI *masking* out the star itself in a telescope is no problems,
No, masking, to this level of precision, is incredibly difficult.

AI Ahh, so that's the hard part. I wonder if ground based
AI interferometry arrangements using large telescopes like the Keck
AI along with adaptive optics, computerised processing, filtering,
AI etc. could manage such a task.

I doubt it. I suspect that there is too much scatter from the
atmosphere.

Let me try to illustrate the difficulty by way of analogy. The Empire
State Building is about 450 meters tall. Suppose you are looking for
something 1 billion times shorter on the ground outside the building.
Then you're looking for something that is only 0.00000045 m high or
0.45 microns in size. By contrast, a human hair is about 50 microns
in size. That is, if you're looking for something 1 billion times
shorter than the Empire State Building on the ground outside the
building, you're looking for something that is 1000 times smaller than
a typical human hair. That's a good analogy to trying to find a
terrestrial planet in the glare from its parent star.

AI If Hubble did have such a star occulting disk, then from an
AI orbital location surely the vacuum of space would have made the
AI scattering problem quite possibly manageable, and if New Earth
AI shines at 23rd magnitude and Hubble's limiting magnitude is 30
AI (..), it *just* might have managed to photograph 'something'...?

Going to space certainly helps the scattering problem as it removes
the atmosphere. Even so the Terrestrial Planet Finder (TPF)
coronagraph mission is a tough problem. If you've read the
documentation, you'll see that there is discussion of a precursor
mission utilizing a 1.8 m telescope (smaller than Hubble) attempting
to detect Jupiter-mass planets (which are bigger so the brightness
contrast is smaller, though still formidable).

--
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In article , Joseph Lazio wrote:
That is, if you're looking for something 1 billion times
shorter than the Empire State Building on the ground outside the
building, you're looking for something that is 1000 times smaller than
a typical human hair. That's a good analogy to trying to find a
terrestrial planet in the glare from its parent star.

It's an analogy, but it's not necessarily a *good* analogy. Where
it breaks down is that your analogue for "observing" (the height of the
objects compared) has only one dimension of measure. But "observing",
using electromagnetic radiation has *two* dimensions you can work on -
the intensity of the radiation you measure from each object and the
wavelength of the radiation you're observing with.
Consider a planet with a surface temperature of 25deg C and a
star of surface temperature of 5000deg C. You observe at two
wavelengths. The first wavelength is the peak wavelength of a black body
at 5000deg C (about a green-orange in the visible spectrum); the second
wavelength is the peak wavelength of a black body at 25deg C, which is
in the medium infrared. In one observation, the star is immensely
brighter than the planet; in the second observation, their luminosities
are much more comparable.

--
Aidan Karley,
Aberdeen, Scotland,
Location: 57°10'11" N, 02°08'43" W (sub-tropical Aberdeen), 0.021233

In article ,
(AA Institute) writes:
I wonder if ground based interferometry
arrangements using large telescopes like the Keck along with adaptive
optics, computerised processing, filtering, etc. could manage such a
task.

There are some attempts along those lines, but:

1. They (at least the ones I know about) work in the infrared, where
the star/planet ratio is smaller.

2. They are attempting to find "Jupiters," not "Earths," so the
planet is a lot brighter.

The work I know about uses a "nulling interferometer," in which two
beams are combined destructively for the central source but not for
surrounding sources. If everything is perfect, the central source
(the star) vanishes, but nearby sources (planets) are not cancelled.
Of course in the real world, there are plenty of things that are not
perfect, and the question is how small the residuals can be.

Typing "nulling interferometer" into an ADS abstract search shows
eight papers in refereed journals and more than forty in conference
proceedings in the last two years, though some of these may refer to
space-based instruments. This is definitely work in progress.

--
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
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In article d,
Aidan Karley writes:
Consider a planet with a surface temperature of 25deg C and a
star of surface temperature of 5000deg C. You observe at two
wavelengths. The first wavelength is the peak wavelength of a black body
at 5000deg C (about a green-orange in the visible spectrum); the second
wavelength is the peak wavelength of a black body at 25deg C, which is
in the medium infrared. In one observation, the star is immensely
brighter than the planet; in the second observation, their luminosities
are much more comparable.

This helps but not as much as you might hope. In the limit of very
long wavelengths, the ratio of brightnesses will be the ratio of
surface area times temperature. The Sun has about 12000 times the
surface area of the Earth, and the temperature ratio is about 20, so
at best the brightness ratio will be 240000. It's bigger than that
at mid-IR wavelengths; you have to go to far-IR to get close to the
limit.

A ratio of 1E6 isn't wonderful, but it's whole lot better than 1E9!
Still, when you realize people work very hard to do 1% photometry
(and with best effort can perhaps reach 0.1%), you can see this is a
hard problem.

--
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
email may be sent to your ISP.)

(Steve Willner) wrote in message ...
In article ,
(AA Institute) writes:
I wonder if ground based interferometry
arrangements using large telescopes like the Keck along with adaptive
optics, computerised processing, filtering, etc. could manage such a
task.

There are some attempts along those lines, but:

1. They (at least the ones I know about) work in the infrared, where
the star/planet ratio is smaller.

2. They are attempting to find "Jupiters," not "Earths," so the
planet is a lot brighter.

I've managed to patch together a basic magnitude model that lets you
project the expected visual (V-band) magnitude for an extrasolar
planet (exoplanet) having Earth- or Jupiter-like photometric
properties, which is located in the habitable zone and shining by the
light reflected from its parent star, as viewed from our vantage point
here on Earth.

In theory, the model should hold accurate for gauging the brightness
of an exoplanet around *any* star, since by the default definition of
a "habitable zone", a planet would experience a total light flux of a
constant planet/star ratio in all cases.

m2 = 5/2 * Log10 R + m1

[where m2 = magnitude of planet, R = star/planet brightness ratio
(Earth = 1,499,684,836, Jupiter = 9,120,108, m1 = apparent visual
magnitude of parent star ]

My article in full, is he-

http://uk.geocities.com/aa_spaceagen...r-planets.html

This model is of course only focussed on what matters most: a planet
located in the *habitable zone* where a "New Earth" must surely exist!
I'd be keen to hear any views/disagreements about my assumptions
underlying this model and the validity of its results.

Thanks
Abdul Ahad

In article ,
(Abdul Ahad) writes:
I've managed to patch together a basic magnitude model that lets you
project the expected visual (V-band) magnitude for an extrasolar
planet (exoplanet) having Earth- or Jupiter-like photometric
properties, which is located in the habitable zone and shining by the
light reflected from its parent star, as viewed from our vantage point
here on Earth.

In theory, the model should hold accurate for gauging the brightness
of an exoplanet around *any* star, since by the default definition of
a "habitable zone", a planet would experience a total light flux of a
constant planet/star ratio in all cases.

The model is basically right, but there are a few complications. The
habitable zone is constant in _bolometric magnitude_, i.e. the total
flux at all wavelengths per unit surface area of the planet. But for
detection, what is important is the magnitude at the particular
wavelength of observation, which varies with the temperature of the
star. Look up "bolometric correction" for details.

A second complication is that in the mid to far infrared, a planet
shines not by reflected light but by thermal emission of its own.
This makes the planet quite a lot brighter than the model would
predict. In the long wavelength regime, the brightness ratio is the
ratio of (surface area * temperature) for the planet and star.

A third complication is that the brightness at particular wavelengths
will be modified by a planet's atmosphere, if it has one.

m2 = 5/2 * Log10 R + m1

[where m2 = magnitude of planet, R = star/planet brightness ratio
(Earth = 1,499,684,836, Jupiter = 9,120,108, m1 = apparent visual
magnitude of parent star ]

You can replace (2.5*log10 R) with a magnitude ratio, 22.9 for Earth,
17.4 for Jupiter. Mathematically the same but perhaps easier to
write.

My article in full, is he-

http://uk.geocities.com/aa_spaceagen...r-planets.html

--
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
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