Bias effects in galaxy detection

[ngc3314]

Suppose T1 - toy galaxy #1, introduced by ngc3314, with an M_bol=-24, uniformly luminous circular disk, radius 10 kpc - were the surface of a sphere, at a distance of 10 pc from us, emitting all its electromagnetic radiation in the V-band. Would the dark, cloudless/clear, moonless night sky be sufficed with a uniform glow, of apparent magnitude ~2.8?

I'm not sure how much cloud/fog/smog would be needed, or how early in the morning/late in the afternoon (etc), but the Sun's apparent visual magnitude is surely often very close to -24; spreading this much light over the whole sky (both day and night) would - if I understand it correctly - merely make the sky glow like the diffuse light from a nearby large city (in my personal experience, it doesn't take much to drown out the SMC, and M31 is even easier to sink).

One reference point - the typical light of the daytime sky is the redistributed version of (most of the) >25% or so of the light of the Sun which is extinguished[1] by the atmosphere at a typical sea-level site. So an apparent magnitude -24 spread around the sky would be pretty bright, much brighter than the scattered light of the night sky at full Moon. This does get unrealistic - we shod treat the surface brightness itself, since our distance changes so much from different regions of that imaginary disk centered 10 pc away that the mapping gets complicated - the mean distance from each piece of it is pretty large. Surface brightness is the same at mag=18.81 per square arcsecond, but total flux gets strange. Working back from that we get an equivalent magnitude all over that hemisphere of 18.81-10 log (60)-2.5 log (20600) = -9.7. If in the V band, that would be very roughly the brightness of a typical sky when the Moon is up just slightly after first quarter (using the 25% rule from sunlight).

[1]Weasel words because extinction includes actual absorption and scattering, and the mix changes with wavelength as well as overall scaling with secant[2] of the angular distance from zenith.

[2] Slight swindle, secant assumes the Earth and atmosphere are flat.

[Nereid]

Suppose T1 - toy galaxy #1, introduced by ngc3314, with an Mbol=-24, uniformly luminous circular disk, radius 10 kpc - were the surface of a sphere, at a distance of 10 pc from us, emitting all its electromagnetic radiation in the V-band. Would the dark, cloudless/clear, moonless night sky be sufficed with a uniform glow, of apparent magnitude ~2.8?

I'm not sure how much cloud/fog/smog would be needed, or how early in the morning/late in the afternoon (etc), but the Sun's apparent visual magnitude is surely often very close to -24; spreading this much light over the whole sky (both day and night) would - if I understand it correctly - merely make the sky glow like the diffuse light from a nearby large city (in my personal experience, it doesn't take much to drown out the SMC, and M31 is even easier to sink).

One reference point - the typical light of the daytime sky is the redistributed version of (most of the) >25% or so of the light of the Sun which is extinguished[1] by the atmosphere at a typical sea-level site. So an apparent magnitude -24 spread around the sky would be pretty bright, much brighter than the scattered light of the night sky at full Moon. This does get unrealistic - we shod treat the surface brightness itself, since our distance changes so much from different regions of that imaginary disk centered 10 pc away that the mapping gets complicated - the mean distance from each piece of it is pretty large. Surface brightness is the same at mag=18.81 per square arcsecond, but total flux gets strange. Working back from that we get an equivalent magnitude all over that hemisphere of 18.81-10 log (60)-2.5 log (20600) = -9.7. If in the V band, that would be very roughly the brightness of a typical sky when the Moon is up just slightly after first quarter (using the 25% rule from sunlight).

[1]Weasel words because extinction includes actual absorption and scattering, and the mix changes with wavelength as well as overall scaling with secant[2] of the angular distance from zenith.

[2] Slight swindle, secant assumes the Earth and atmosphere are flat.

These last few weeks my internet access has been, um, unpredictable. I had taken to preparing all my responses offline ... but in this case I made an exception.

Of course, the moment I pressed "Post", I realised I had made several, pretty enormous, mistakes!

The toy galaxy, T1, is huge! It has a radius of 10 kpc!!

My musing - in the post quoted by ngc3314 - concerns a completely different toy galaxy, an almost laughably small one: although they both have the same bolometric absolute magnitude (absolute bolometric magnitude?), -24, their surface areas are wildly different. T1's is ~3x10^8 square parsecs, my 'musing' one, ~1.3x10^3 pc^2.

Assuming no absorption between us and the (puny) toy galaxy - and that includes the Earth's atmosphere - the surface brightness would be ~5.3 mag per "^2; a 'Moon's worth' - directly overhead - would shine at an integrated magnitude of ~-10.7.

Anyway, back to doing some real astrophysics, albeit with toy galaxies.

[Nereid]

To keep track of the various toy galaxies, I've started numbering/naming them: Tn (for Toy galaxy, number)

So far there are nine so far (click on the name to get the post in which it was first introduced, in this thread):

Tn..M_bol...r¹...SB²...SED³; note
-- ----- ---- ----- ---------
T1 -24.0 10.0 18.81 unspecified
T2 -24.0 10.0 18.81 [OIII] 5007
T3 -17.7 10.0 25.12 265.0 nm
T4 -22.3 10.0 20.52 666.5 nm
T5 -19.7 10.0 23.12 350.0 nm
T6 -21.9 10.0 20.92 558.3 nm
T7 -21.3 10.0 21.52 460.0 nm
T8 -23.1 10.0 19.72 265, 350, 460, 558.3, 666.5 nm; T3 to T7 combined
T9 -24.0 0.01 05.32 V-band
-- ----- ---- ----- ---------


¹ all the galaxies are uniformly luminous, circular disks (unless otherwise noted); radius (in kpc)
² local, mag per arcsec^2
³ Spectral Energy Density (or Distribution), in shorthand (refer to the originating post for details)

[Nereid]

First, though, let's explore (observe) my toy galaxies galaxy a bit more.

Put all five of the galaxies together. They would have an M_bol of -23.1, and the bolometric SB locally would be 19.7 mag/"^2.

This is T8.

Locally its colours would be, in an idealised, perfect SDSS system:

u-g: 1.6
g-r: 1.6 (T8's absolute r-band magnitude is -22.9 (-22.86 actually), can you see why?)
r-i {meaningless; T8 does not emit in the i-band}
i-z {meaningless; T8 does not emit in the i-band, nor the z-band}

So this galaxy would appear rather red (though perhaps not to the unaided eye of course, even when viewed through the eyepiece of a really big telescope; do you know why?)

If we were to try to approximate this toy galaxy's SED - as measured by those two colours alone - as a blackbody, what temperature would it have? What if we added the NUV emission, at 265.0 nm?

If observed at a distance of z=0.25, its apparent colours would be:
u-g: 2.0
g-r: 1.6
r-i: 0.6
i-z: 0.4

These would shift red-ward, by one colour, at z=0.75.

And blue-ward, also by one colour, at z=0.1.

At other redshifts in our table (0.5, 1, 1.5, and 2) the colours would be rather unnatural; e.g. no flux in the r-band at z=0.5 and z=1 (at z=2, the only band with flux would be the z-band).

Could someone please check my calculations?

[Nereid]

I hope, by now, you - dear reader - will see that Disney&Lang's conclusions are based on evidence that even my (and ngc3314's) toy galaxies shows is silly ridiculous not of this universe.

Take, as a very simple example, the fact that the redshift at which even the SDSS u-band disappears from that wildly successful five-band survey is relatively modest, cosmologically speaking ... and that it's even more dramatic if you restrict yourself - as Disney seems to imply - to the workhorse of astronomical surveys of the 1960s (or thereabouts); namely, photographic plates and Schmidt telescopes.

Let's explore observability, sinking, etc with the HST. What, for example, are the perfect (toy universe) pass-bands routinely used by ACS? What is the sky (in mags per arcsec squared), in those pass/wave-bands? How deep can the HST+ACS go, in survey mode?

[George]

This is T8.

Locally its colours would be, in an idealised, perfect SDSS system:

u-g: 1.6
g-r: 1.6 (T8's absolute r-band magnitude is -22.9 (-22.86 actually), can you see why?)
r-i {meaningless; T8 does not emit in the i-band}
i-z {meaningless; T8 does not emit in the i-band, nor the z-band}

So this galaxy would appear rather red (though perhaps not to the unaided eye of course, even when viewed through the eyepiece of a really big telescope; do you know why?)

[Assuming I understand that the emissions are monochromatic...]

It seems white to me since you have red (T4), green (T6) and blue (T7) emissions, but the blue and green are stronger, similar to sunlight, which is white.

If observed at a distance of z=0.25, its apparent colours would be:
u-g: 2.0
g-r: 1.6
r-i: 0.6
i-z: 0.4

I think this changes it toviolet, red and greenish-yellow. I don't know off-hand what color this result would be.


At z = .5, you have only green and red, which might produce a yellowish color.

At z = .75, you have blue and orange, which should give some sort of greenish color I suspect.

At z = 1, you have green and red, which might give you a yellowish or orangish appearance.

At other redshifts in our table (0.5, 1, 1.5, and 2) the colours would be rather unnatural; e.g. no flux in the r-band at z=0.5 and z=1 (at z=2, the only band with flux would be the z-band).

Wouldn't T3 be red from z=1.5 to almost 2?

[antoniseb]

... Wouldn't T3 be red from z=1.5 to almost 2?

There are UV photons being redshifted into the visible spectrum as well. The whole Lyman series most prominently, but other transitions as well. Once you get beyond Z=1, the Lyman series starts showing up as blue-indigo.

[ngc3314]

Once you get beyond Z=1, the Lyman series starts showing up as blue-indigo.

Well, z>1.6 to get Lyman alpha past the atmospheric cutoff around 3200 A. (Picky, picky).

Continuum starlight, rather than emission lines, is the only important thing in normal galaxies in the emitted UV - there aren't any more strong emission lines until you get to Lyman alpha (which is grotesquely sensitive to internal radiative-transfer effects) for non-AGN.

[George]

There are UV photons being redshifted into the visible spectrum as well. The whole Lyman series most prominently, but other transitions as well. Once you get beyond Z=1, the Lyman series starts showing up as blue-indigo.

I may be in the weeds relative to the path of this thread since I haven't had time to absorb the interesting and educational content this thread provides. As usual, however, I will exercise my amateur privledge and throw out what little I have in my back pack...

If we have a 265 nm emission (T3), then a redshift of 1.5 will produce a red color observation (662 nm). At z = 2, then the observed wavelength becomes 795 nm, which is just past the observable red for many, though some can see this wavelength, reportedly. [I used the simple non-relativistic formula of z+1 = lambda_obs / lambda_emit.]

[George]

Well, z>1.6 to get Lyman alpha past the atmospheric cutoff around 3200 A. (Picky, picky).

Continuum starlight, rather than emission lines, is the only important thing in normal galaxies in the emitted UV - there aren't any more strong emission lines until you get to Lyman alpha (which is grotesquely sensitive to internal radiative-transfer effects) for non-AGN.

Oops, I missed this post. So are the stated wavelengths for the "toys" the emission lines and not an imaginary bulk emission at those wavelengths? [I just knew I had to be in the weeds, or, at best, forbes.]

[Nereid]

Oops, I missed this post. So are the stated wavelengths for the "toys" the emission lines and not an imaginary bulk emission at those wavelengths? [I just knew I had to be in the weeds, or, at best, forbes.]

The toy emission lines are unreal (or, to be a bit more picky, unreal for real galaxies; I'm sure there are atomic transitions at, or near, my toy lines, but no real galaxy emits these, as dominating its SED, even within a band¹).

I intend to introduce a somewhat more satisfactory set of toy lines later, so that we will not ever encounter the rather silly "Locally its colours would be, in an idealised, perfect SDSS system: [...] r-i {meaningless; T8 does not emit in the i-band}; i-z {meaningless; T8 does not emit in the i-band, nor the z-band}".

To recap: the toy astronomy I'm doing so far is only imaging and photometry, and most of it is done using an idealised, perfect SDSS system of pass/wavebands (I hope to introduce something similar, from the Hubble's ACS; maybe later this week?). This is consistent with the Disney and Lang paper ngc3314 introduced, in the OP: that paper is totally blind to spectroscopy (though spectrophotometry is marginally relevant, if only implicitly).

¹ There's some interesting stuff here, that I hope to pursue later, concerning real galaxies; hint: why does Hanny's Voorwerp appear pure blue in the images from SDSS' CAS? If you could see it with your own eyes, what colour would it appear?

[Nereid]

[Assuming I understand that the emissions are monochromatic...]

It seems white to me since you have red (T4), green (T6) and blue (T7) emissions, but the blue and green are stronger, similar to sunlight, which is white.

I think this changes it toviolet, red and greenish-yellow. I don't know off-hand what color this result would be.


At z = .5, you have only green and red, which might produce a yellowish color.

At z = .75, you have blue and orange, which should give some sort of greenish color I suspect.

At z = 1, you have green and red, which might give you a yellowish or orangish appearance.


Wouldn't T3 be red from z=1.5 to almost 2?

Let's explore this a bit more ...

The central wavelengths of the SDSS bands are, approximately:
u 354 nm
g 477 nm
r 623 nm
i 763 nm
z 913 nm

A sufficiently bright light, at each of those wavelengths, would be perceived, by a person with normal vision, as ...?

The SDSS bands overlap somewhat; the transitions occur at approximately:
u/g 395 nm
g/r 550 nm
r/i 689 nm
(no need for the i/z one; humans' eyes are blind to that!)

A sufficiently bright light, at each of those wavelengths, would be perceived, by a person with normal vision, as ...? (This will give us an idea of how perceived colour varies, across each SDSS band).

If you look at a colour (u-g) - colour (g-r) plot, of stars, or galaxies, or quasars, are there many (any?) near (1.6, 1.6)? If so, finding one of those objects will tell us what colour T8 would appear, locally.

At z = 0.25, the region of this colour-colour plot we're interested in is around (2.0, 1.6).

[George]

The toy emission lines are unreal (or, to be a bit more picky, unreal for real galaxies; I'm sure there are atomic transitions at, or near, my toy lines, but no real galaxy emits these, as dominating its SED, even within a band¹).

[my bold] Somehow I missed this description. I prefer laser [monochromatic] toys, especially the size of galaxies.

Visual color, of course, is never determined by emission lines, so I would assume. Color is simply the result of the integration of the visible SED, though more appropriately represented by a photon flux distribution, IMO, since blue peaks in a SED can mislead one into thinking a blue color might be possible.

To recap: the toy astronomy I'm doing so far is only imaging and photometry, and most of it is done using an idealised, perfect SDSS system of pass/wavebands (I hope to introduce something similar, from the Hubble's ACS; maybe later this week?). This is consistent with the Disney and Lang paper ngc3314 introduced, in the OP: that paper is totally blind to spectroscopy (though spectrophotometry is marginally relevant, if only implicitly).

As I feared, I need to get my head around the whole subject matter before I advance my foot-in-mouth disease... Or not...

If spectrometry is no longer a problem, shouldn't the SED be the ideal story teller of any object? Obviously, the filter sets are wonderful if no spectrometry is obtainable, or perhaps, their are greater problems for spectrometry with extended objects. I'm just guessing that SEDs should be the more modern view due to advanced technologies, especially given the Sloan work. [Perhaps they are.]

¹ There's some interesting stuff here, that I hope to pursue later, concerning real galaxies; hint: why does Hanny's Voorwerp appear pure blue in the images from SDSS' CAS? If you could see it with your own eyes, what colour would it appear?

Well, you couldn't have picked a more appropriate, though rarther unique, example, huh ngc3314?

Very few extended objects in the universe exhibit color. The eye's sensitivity range of about 12 orders does not apply to color sensitivity, so we lose the ability to see color for the dimmer objects, especially nebulae. There are exceptions, of course. I have seen the blue ring of the "bright" Eskimo nebula using an 82" telescope.

The other problem is the fact that if we magnify or even travel closer to these objects, we essentially gain no improvement in being able to see color. Surface brightness and size both obey the inverse square law. Traveling half the distance toward the object yields 4x the amount of light but it will appear 4x as large, so if it was grey when you left, it will still look grey. [It took Ken G an embarassing no. of posts to convince me no optical device could alter this circumstance to the point we bet an ice cream Sundae. A freakish technicallity emerged and, well, I owe him a steak, but owes me an ice cream Sundae. ]

[Hopefully I'm on topic.]

[George]

¹ There's some interesting stuff here, that I hope to pursue later, concerning real galaxies; hint: why does Hanny's Voorwerp appear pure blue in the images from SDSS' CAS? If you could see it with your own eyes, what colour would it appear?

I'm curious also about Hanny's Voorwerp possible visual color. It does seem bright.

I think I'm correct in saying that if any region of a nebula has a local surface brightness brighter than around 5 mag. per sq. arcminute (~ 14 mag. per sq. arcsec) then color is possible, and if there is a significant bulge in the visual band of the SED that would allow a specific color to emerge. The Eskimo, for instance, has a surface brightness average of about 6.8 mag (sq. arc. min.)

[ngc3314]

It does seem bright.

Not so much! I'm aware of a couple of people who have seen it visually, all using Jimi Lowrey's personal 1.2m Dob in West Texas. Jimi did detailed enough sketches to tell that unfiltered he was mostly seeing the continuum star-forming regions, while an SDSS g filter brought out the gas. I can't picture a normal human detecting the color (which would, based on the spectrum dominated by redshifted [O III], be distinctly greenish).

Side note: my eyes seem to see [O III] somewhat bluer with age - 30-odd years ago, NGC 7027 was almost emerald green, while more recent observations of planetaries with a friend's 62-cm Dob give them more of a bluish-green tint.

[George]

A sufficiently bright light, at each of those wavelengths, would be perceived, by a person with normal vision, as ...? (This will give us an idea of how perceived colour varies, across each SDSS band).

u 354 nm UV, not visible
477 nm Light blue, or more blue saturated cyan
623 nm Orangish-red
763 nmRed, but many likely can not quite see it, though some can.
913 nm NIR, not visible

The color spectrum chart in Wiki (about half way down the page) is about as accurate as I think it should be. When I first wondered what wavelengths produced each color sensation, I discovered a surprising variation in the color charts. The heliochromolgist took an average of many charts to help establish a likely spectral coloring chart. Wiki's chart seems to match fairly close to that of the heliochromologist, so it's probably wrong.

[Perhaps there are a few major research papers on this. ]

The SDSS bands overlap somewhat; the transitions occur at approximately:
u/g 395 nm
g/r 550 nm

Unfortunately, this is essentially half of the visual color spectrum, from violet to green. (Green lasers are 532nm)

g/r 550 nm
r/i 689 nm

And this is the other half. [Yellow and orange are very narrow bands within the spectrum]

Leave it to astronomers to focus on scientific efficacy, and not side asterochromolgical issues! *wink*

A sufficiently bright light, at each of those wavelengths, would be perceived, by a person with normal vision, as ...? (This will give us an idea of how perceived colour varies, across each SDSS band).

The broad band of these filters, in spite of my spite, should reveal the two typical celestial colors: bluish-white and orange (white doesn't count). I suspect there are few yellow stars out there. The hot ones are bluish-white (never a saturated blue) and the cool ones are orange. [Some (e.g. Grant) see Antares as red, but I see it as orange. What do you see?]

Planck distributions for stars reveal why most are white stars since no one color dominates all that much. Green is all but impossible, though yellow is since green and orangish-red augment the tiny yellow band.

[George]

Not so much! I'm aware of a couple of people who have seen it visually, all using Jimi Lowrey's personal 1.2m Dob in West Texas. Jimi did detailed enough sketches to tell that unfiltered he was mostly seeing the continuum star-forming regions, while an SDSS g filter brought out the gas. I can't picture a normal human detecting the color (which would, based on the spectrum dominated by redshifted [O III], be distinctly greenish).

Well the images y'all produced sure make it look cool regardless! I do not know of many objects that do reveal color, though there are some including a few you have mentioned in the past. 14 mag. per sq. arc sec. is rare for any region of any extended object, no doubt.

Side note: my eyes seem to see [O III] somewhat bluer with age - 30-odd years ago, NGC 7027 was almost emerald green, while more recent observations of planetaries with a friend's 62-cm Dob give them more of a bluish-green tint.

500 nm is almost cyan. Feel better? Also, tornadic dust will favor greater blue scattering, or perhaps residual hot air after a recent football game [or both] are contributing factors.

[Nereid]

To make the toy astronomy more consistent, somewhat more real, and easier to work in, I've re-worked my workhorse (a spreadsheet), and re-designed my (toy) filter set.

In this post, the toy filter set.

There are ten filters in all, and I've given them the following names (in order of increasing wavelength): n1t, n2t, ut, gt, rt, it, zt, IR1t, IR2t, and IR3t (If anyone would like to suggest a better set of names, I'd be happy to adopt it!).

The cutoffs between toy bands are perfectly sharp (no overlaps, unlike the real SDSS ones, for example), and there are no gaps. The long wavelength end of each of the ten bands is as follows (in nm): 192.0, 327.0, 405.5, 533.0, 675.5, 821.8, 985.5, 1185.5, 1452.1, and 1777.8. The lower (short) wavelength cutoff for the n1t band is 114.0 nm.

I'll also be extending the redshift coverage of my toy astronomy, to z=6. Here are the extra entries in the table (following ngc3314); i.e. T1.

z...DL,Mpc ang scale, kpc/"" m_bol Bolometric SB
3.0 25842 . . 7.83 . . . . . 23.06 24.83
4.0 36524 . . 7.08 . . . . . 23.81 25.80
5.0 47594 . . 6.41 . . . . . 24.38 26.59
6.0 58951 . . 5.83 . . . . . 24.85 27.26

Next: revised 'visibility' of T8 (which, automatically, also includes T3 to T7).

[Nereid]

Thanks very much for you comments, George!

Rather than try to comment on my rather muddled earlier colours, I'll use "[t]he color spectrum chart in Wiki (about half way down the page) is about as accurate as I think it should be" to describe the colour ranges of my new toy filters/bands.

As expected, the first two - n1t and n2t - and the last four - zt, IR1t, IR2t, and IR3t - are totally outside the range of human colour vision/perception.

The upper (long) wavelength of the ut band (405.5 nm) falls in the Wiki page's violet (can that colour be reproduced, in anything approaching faithfulness, in this forum?)

The gt band stretches from violet to green (405.5 to 533.0 nm); perhaps we could represent this, as a default, as cyan?

And rt from green to red (533.0 to 675.5 nm); would orange be OK as a default, for this band?

The it band is entirely in the red.

Antares? The last time I really paid attention (rather too many years' ago, I'm sorry to say), it seemed reddish-orange. I do recall - vaguely - noticing that it seemed redder when low down (close to the horizon).

Galaxy colours - if only you could see them (they're generally far too faint, and the SB far too low)! - can be quite different from stars'. For example, there can be light from galaxies almost completely dominated by emission lines. As redshift increases, these move red-ward (and new lines come into view). There are some interesting threads in the Galaxy Zoo forum on this (though they are more about the appearance in the CAS gri->BGR mapped false colours than what you'd see if only your eyes were sensitive enough). Zooites - as they call themselves - found some quite remarkable objects.

[Nereid]

As promised, the 'visibility' of the toy galaxy, T8, in the revised toy filter/bands, at various redshifts.

Recall that T8 has an M_bol of -23.1, and emits all its light in five lines - at restframe wavelengths of 265, 350, 460, 558.3, and 666.5 nm.

Locally, and at z=0.01, T8 would be visible in just four of the toy bands: nt2, ut, gt, and rt (visible in the sense that light emitted by it could, potentially, be detected; whether it would actually be detected depends - obviously - on details of the toy telescope+photometer we use to observe it). Note that the emission at 558.3 and 666.5 nm would both be detected in the rt band.

At z = 0.1, we have five-band visibility: nt2, ut, gt, rt, and it.

Ditto at z = 0.25, also five-band visibility, in a game of 'musical bands': ut, gt, rt, it, and zt.

At z = 0.5, ut and gt remain, but 460 nm moves into the it band, and the other two lines also play musical bands; i.e. they move into the zt and IR1t bands.

Back to five contiguous bands at z = 0.75: gt, rt, it, zt, and IR1t.

A 'drop-out' band re-appears at z = 1: the 350 nm line is in the it band, while the 265 nm one remains in the gt band; otherwise, musical bands again: gt, it, zt, IR1t, IR2t.

By z = 1.5, we see the last appearance of the 666.5 nm line, in the IR3t band, and another drop-out, this time in the it band. The line-up is rt, zt, IR1t, IR2t, and IR3t.

At z = 2, the last of ngc3314's redshifts, the drop-out is in the zt band, and we've lost the 666.5 line: it, IR1t, IR2t, and IR3t.

Only two lines/bands remain at z = 3, 265 nm visible in the IR1t band, and 350 nm in the IR2t band. These move to the IR2t and IR3t bands, respectively, at z = 4.

Finally, at z = 5, just one colour/band remains, IR3t.

At z = 6 T8 has vanished into the infrared, beyond the capabilities of our toy, ten-band, astronomy.

Next: when does T8 become too faint to be detected, in any band? When does its surface brightness drop below 25 (mag/arcsec^2)?

Oh, and does the fact that no one has commented mean that you've all checked my calculations, and found no errors?

[George]

[QUOTE=Nereid;1986733]The upper (long) wavelength of the ut band (405.5 nm) falls in the Wiki page's violet (can that colour be reproduced, in anything approaching faithfulness, in this forum?)
The color html code #AA3BFF should come fairly close. It just so happens that 405 nm is another laser wavelength.

The gt band stretches from violet to green (405.5 to 533.0 nm); perhaps we could represent this, as a default, as cyan?

I fear I'm missing where this is suppose to be going. [I've been a lousy lurker, admittedly.] What is it you (ya'll) are trying to accomplish? Doesn't the SED say it all now that SDSS data is available?

Antares? The last time I really paid attention (rather too many years' ago, I'm sorry to say), it seemed reddish-orange. I do recall - vaguely - noticing that it seemed redder when low down (close to the horizon).

Of course, the extensive scattering effects near the horizon will make most things more red. [It is rare to see a very red Sun, surprisingly, especially at sunrise.]

Here is an interesting image of Antares...
Antares_b.jpg

... just before it entered our atmosphere and exploded, apparently.

[How do we reduce the image size??]

I think I was trying a defocusing technique to avoid over exposure in order to capture its "true" color. It does happen to be the color I see it when defocused through the scope, and at a high altitude.

Again, because stars are close to bb radiators, even strong red emissions get blueshifted into orange because of the semi-strong emissions in the rest of the visible spectrum. T-class stars are certainly an exception due to molecular color "magic".

Galaxy colours - if only you could see them (they're generally far too faint, and the SB far too low)! - can be quite different from stars'.

Yes, but what about the "hot" spots shortly after a million stars are borne from a GMC? And what about the nuclei of quasars or AGN? If I'm right (and I'm never always wrong), all you need is a region > a couple of sq. arcminutes that exceeds about 14 mag. per sq. arcminute to potentially present a color result.

For example, there can be light from galaxies almost completely dominated by emission lines.

I didn't know this. This would mean, I assume, that the shroud of gas around these galaxies has all but elimiated the other portions of the spectrum? If so, they must be quite dim, so even if it was OIII, it would be too dim to be seen and appreciated as green. I hear it is tough being green.

As redshift increases, these move red-ward (and new lines come into view). There are some interesting threads in the Galaxy Zoo forum on this (though they are more about the appearance in the CAS gri->BGR mapped false colours than what you'd see if only your eyes were sensitive enough). Zooites - as they call themselves - found some quite remarkable objects.

False coloring is almost always better. I saw a true color for the "Pillars of Creation" and the result is rather a sickly red and orange columnated blobs. Hester et. al. false coloring allows for excellent revelations of the distinctive primary gases, with the side benefit of looking great.

[Nereid]

I fear I'm missing where this is suppose to be going. [I've been a lousy lurker, admittedly.] What is it you (ya'll) are trying to accomplish? Doesn't the SED say it all now that SDSS data is available?

I can't say what others who are active here are trying to accomplish; however, I would like to demolish as many of the key parts of the Disney and Lang paper as possible, in a way that could be relatively easily - and convincingly - explained without the use of anything other than some simple algebra (and a big pile of definitions).

The toy galaxy ngc3314 introduced, which I gave the name T1, is the key, I think, to developing just such a thing. But it's going to need some work, and I'm inflicting that work on y'all, rather than do it all invisibly.

The colours aspect is an interesting spin-off; it will play a more important role than it has - so far - fairly soon (and you've already touched on several of the main points anyway!).

I think I was trying a defocusing technique to avoid over exposure in order to capture its "true" color. It does happen to be the color I see it when defocused through the scope, and at a high altitude.

I've seen that technique written up - Sky&Telescope?

I didn't know this. This would mean, I assume, that the shroud of gas around these galaxies has all but elimiated the other portions of the spectrum? If so, they must be quite dim, so even if it was OIII, it would be too dim to be seen and appreciated as green. I hear it is tough being green.

Check out the spectrum of SDSS J113902.01+310336.7 (click on the GIF image of the spectrum at the bottom of the page). In this case the continuum is close to zero, and the Balmer lines relatively weak (though why H-beta is almost as strong as H-alpha is a mystery to me). Now move this around (increase and decrease the redshift), so the [OIII]5007/4959+H-beta complex moves into different parts of the colour spectrum ...

SDSS J110116.39+004814.5 is the same sort of thing, but with different relative strengths of the strong emission lines (the two [OIII] lines are more dominant here). To be sure, both these galaxies are small (the Petrosian radius is ~the seeing!), ...

(In case any reader is interested, these are "Green Peas"^WP, a hithertofore unknown class of galaxy discovered by zooites; AFAIK, several hundred have been found).

Now what if a Green Pea (or similar) galaxy has a very strong [OII]3728 line, and a redshift which puts the other major emission lines beyond the red end of human vision?

ETA: added link to Wikipedia entry on Green Peas

[Nereid]

I'm going to standardise my criteria.

In the NDTSS (Nereid Digital Toy Sky Survey), a toy galaxy is detectible, in a toy band (did I really just write that?!? ), if its integrated magnitude is <22.2 in that band AND if its surface brightness (SB) is <25.0 (magnitudes per arcsec squared) in that band.

The next bit is tricky, but crucial; I need a robust way to switch between energy (per second per square centimetre, so it's actually flux) - which is what the Tolman signal is defined in - and magnitudes, which is what astronomers (including toy ones) work in¹. Here's what I've chosen²:

I work in the STMAG system, of monochromatic (apparent) magnitudes per unit wavelength; i.e. I need a way to deal with spectral flux densities, and this is how I've done it. Here's the conversion:



Why?

Well, I need to add energies (actually fluxes), because my toy galaxies are colourful, they emit light in more than one wavelength (if they were monochromatic, I could work entirely in bolometric magnitudes ... which is what I did, up to T7).

Here's an example: T8. This toy galaxy is composed of five toy galaxies combined into one. Each of these five is monochromatic, but each has a different M_bol. What, then, is M_bol of T8? Well, use the above conversion formula (actually a definition) to get the flux densities of each component, add those flux densities, then convert back to magnitudes!

So, -17.7 (M_bol of the 265.0 nm component) is 0.0437 (ignoring units); -19.7 (the 350 nm component) 0.275; -21.3 (460.0 nm) 1.2; -21.9 (558.3 nm) 2.09; and -22.3 (666.5 nm) 3.02. Adding them up, we get 6.6287; putting that back into the formula we find that T8 has an M_bol of -23.15.

Yes, I also need to standarise rounding and precision; generally, magnitudes will be given to one decimal place, and ±0.1 mag will be good enough.

¹ "An ancient and arcane, but compact and by now unchangeable, way of expressing brightnesses of astronomical sources", as one source puts it (follow link in this earlier post in this thread, it's on p10)
² If this is unclear, going to be unwieldly, or is downright wrong, I'd appreciate you, dear reader, saying so (my skin is pretty thick, so you can be as blunt as this forum's civility rules allow).

[ngc3314]

I didn't know this. This would mean, I assume, that the shroud of gas around these galaxies has all but elimiated the other portions of the spectrum? If so, they must be quite dim, so even if it was OIII, it would be too dim to be seen and appreciated as green. I hear it is tough being green.

It can also happen when the stellar population is so young that the great majority of its direct radiation is produced in the UV; most of the (large) fraction of that shortward of the Lyman limit at 912 A is absorbed and reprocessed into emission lines, some of which we see projected against the much weaker continuum in the optical bands. The equivalent widths [1] of emission lines, especially the hydrogen recombination lines, can be seen as measuring the slope of the continuum between their wavelengths as the wavelengths where the radiation is absorbed to ionize the gas.

False coloring is almost always better. I saw a true color for the "Pillars of Creation" and the result is rather a sickly red and orange columnated blobs. Hester et. al. false coloring allows for excellent revelations of the distinctive primary gases, with the side benefit of looking great.

Yeah, despite my rants about the Hester "Hubble palette", using energy-based color balance and the closest visual approximations for strong emission lines, most nebulae just look like assorted hues of crimson. The Hubble palette does a much better job of making changes i line ratios (and thus physical conditions) clear on visual inspection, aside from being visually very striking and sort of appealing.

[1] Equivalent width is a normalized expression of the flux (positive or negative) in a spectral line - the definition is the wavelength span of a stretch of the continuum with the same flux as the spectral line has. For an absroption line, this is the usually the only sensible way to measure its total impact.

[George]

I can't say what others who are active here are trying to accomplish; however, I would like to demolish as many of the key parts of the Disney and Lang paper as possible, in a way that could be relatively easily - and convincingly - explained without the use of anything other than some simple algebra (and a big pile of definitions).

The toy galaxy ngc3314 introduced, which I gave the name T1, is the key, I think, to developing just such a thing. But it's going to need some work, and I'm inflicting that work on y'all, rather than do it all invisibly.

If time allows, I'll try to be of a little more help.

The colours aspect is an interesting spin-off; it will play a more important role than it has - so far - fairly soon (and you've already touched on several of the main points anyway!).

Hornblower just reminded me of Roger Clark's work. He does a great job with visual astronomy.

...must run

[Nereid]

I'm going to standardise my criteria.

In the NDTSS (Nereid Digital Toy Sky Survey), a toy galaxy is detectible, in a toy band (did I really just write that?!? ), if its integrated magnitude is <22.2 in that band AND if its surface brightness (SB) is <25.0 (magnitudes per arcsec squared) in that band.

I missed one: when is an object a point source, and when is it an extended source (i.e. when can we tell, by looking at an image of it, that it's a galaxy, and not a star/quasar)?

Simple: if it's bigger than the FWHM seeing, it's an extended source/galaxy! In the case of the NDTSS, the FWHM seeing is 1.4".

Oh, and for convenience, "local" means "at z = 0.01" (unless otherwise specified).

[Nereid]

The next bit is tricky, but crucial; I need a robust way to switch between energy (per second per square centimetre, so it's actually flux) - which is what the Tolman signal is defined in - and magnitudes, which is what astronomers (including toy ones) work in¹. Here's what I've chosen²:

I work in the STMAG system, of monochromatic (apparent) magnitudes per unit wavelength; i.e. I need a way to deal with spectral flux densities, and this is how I've done it. Here's the conversion:



Why?

Well, I need to add energies (actually fluxes), because my toy galaxies are colourful, they emit light in more than one wavelength (if they were monochromatic, I could work entirely in bolometric magnitudes ... which is what I did, up to T7).

Here's an example: T8. This toy galaxy is composed of five toy galaxies combined into one. Each of these five is monochromatic, but each has a different M_bol. What, then, is M_bol of T8? Well, use the above conversion formula (actually a definition) to get the flux densities of each component, add those flux densities, then convert back to magnitudes!

So, -17.7 (M_bol of the 265.0 nm component) is 0.0437 (ignoring units); -19.7 (the 350 nm component) 0.275; -21.3 (460.0 nm) 1.2; -21.9 (558.3 nm) 2.09; and -22.3 (666.5 nm) 3.02. Adding them up, we get 6.6287; putting that back into the formula we find that T8 has an M_bol of -23.15.

Yes, I also need to standarise rounding and precision; generally, magnitudes will be given to one decimal place, and ±0.1 mag will be good enough.

¹ "An ancient and arcane, but compact and by now unchangeable, way of expressing brightnesses of astronomical sources", as one source puts it (follow link in this earlier post in this thread, it's on p10)
² If this is unclear, going to be unwieldly, or is downright wrong, I'd appreciate you, dear reader, saying so (my skin is pretty thick, so you can be as blunt as this forum's civility rules allow).

There may be circumstances in which the integrated apparent magnitude, across all ten NDTSS bands, is important. So far, however, that's purely cosmetic (testing is done by detection and classification in one or more bands).

As promised, the 'visibility' of the toy galaxy, T8, in the revised toy filter/bands, at various redshifts.

Recall that T8 has an Mbol of -23.1, and emits all its light in five lines - at restframe wavelengths of 265, 350, 460, 558.3, and 666.5 nm.

Locally, and at z=0.01, T8 would be visible in just four of the toy bands: nt2, ut, gt, and rt (visible in the sense that light emitted by it could, potentially, be detected; whether it would actually be detected depends - obviously - on details of the toy telescope+photometer we use to observe it). Note that the emission at 558.3 and 666.5 nm would both be detected in the rt band.

Here's one place I may need to be confident I'm doing integrations correctly.

At z = 0.01, what's observed in the rt band comes from T8's emission at both 558.3 and 666.5 nm (restframe); using the above method, T8 has an apparent rt magnitude of 10.28, which leads to an estimated M_bol of -22.87; its observed SB would be 20 mag/arcsec^2 (in the rt band).

[Nereid]

Hornblower just reminded me of Roger Clark's work. He does a great job with visual astronomy.

That is awesome!

[George]

I missed one: when is an object a point source, and when is it an extended source (i.e. when can we tell, by looking at an image of it, that it's a galaxy, and not a star/quasar)?

If it is reasonably bright, it might appear as an extended object. To test if it is, couldn't we use greater magnification to see whether or not it increases in apparent size?

Simple: if it's bigger than the FWHM seeing, it's an extended source/galaxy! In the case of the NDTSS, the FWHM seeing is 1.4".

I am unclear if this applies so nicely as it seems on paper, however. If the point source is relatively bright, it will appear extended, and the measuring may be a bit tricky for FWHM -- not that I have ever messed with this, admittedly. Just asking.

[parejkoj]

Can I answer?

If it is reasonably bright, it might appear as an extended object. To test if it is, couldn't we use greater magnification to see whether or not it increases in apparent size?

I don't know the cost of the telescope used in the NDTSS, but most surveys that get good signal-to-noise at ~20th magnitude and 1.4" seeing have costs in the tens of millions of dollars. "Changing the magnification" means building another telescope, in a location with better seeing.

Sorry.

Nereid: I haven't seen a proper cost writeup for the NDTSS? What kind of construction costs are you looking at?

I am unclear if this applies so nicely as it seems on paper, however. If the point source is relatively bright, it will appear extended, and the measuring may be a bit tricky for FWHM -- not that I have ever messed with this, admittedly. Just asking.

Stars, being point sources, have a roughly Gaussian light profile. Specifically, a point source has a light profile that is exactly the point spread function (PSF) of the optical system + seeing. Most telescopes over-resolve the PSF, so that the light from a point source falls across several pixels (usually ~2-3 pixels in each direction). If the PSF is well modeled, though a combination of proper understanding of the optics plus measurements of the profiles of known, moderately luminous, unsaturated stars, you can say that anything with a light profile "similar enough" to the PSF is a point source, and thus a star (or quasar). Anything that isn't fit well by the PSF is not a point source.

This becomes very tricky for very faint, very distant sources, where the difference between a PSF fit and a "galaxy-like" fit is statistically indistinguishably. There is a limit in any image where you can't tell the difference between a faint point source and a small, faint galaxy. SDSS III is already working at that limit for its photometric data, and has to use object colors and a map of the density of known stars to help disentangle these. It still sometimes gets it wrong, as when an object is targeted for spectroscopy because it is thought to be a z~0.6 galaxy, but it turns out to be a star. There's a whole paper about correcting some of these systematics, as applied to the SDSS III data.