# Determining line ratios in planetary nebula

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I know that the line strength ratio tells us how hot the electron plasma in a nebula is, and also give information about the electron densities in the nebula. But how do you compute the line ratios? Say we consider two emission lines (both forbidden) decaying to the ground state. If I have the Einstein A coefficients and the statistical weights, how do I compute the line ratios? Any explanation (preferably with examples) will be highly appreciated.

You need a model for the excitation of the line. But since you say you have two forbidden lines, you can try assuming the density is well below the "critical density" (which is the density at which point the upper levels of the transitions get quenched by collisions instead of waiting as long as it takes for the "forbidden" radiative transition to occur). Then if you are talking about two transitions from the same upper level, the line ratio is simply the ratio of the Einstein A values for the two transitions (note that the Einstein A value normally already includes the statistical weights of the lower levels). If you are talking about two different upper levels, then you need a model for how those upper levels get populated, and the line ratios will be the ratios of the upper level populations times the Einstein A values. It's not always easy to know how the upper levels get populated, so that's why it's hard to give you an answer to your question, it is very context dependent. But the main simplification of using forbidden lines is that you don't have to worry about the photons getting reabsorbed before they get out. (A detail is that line ratios are often given in terms of energy flux ratios, rather than photon ratios, so you'd need to multiply the Einstein A values by the photon energies if the transitions are at very different energies.)

## Determining line ratios in planetary nebula - Astronomy

Images of the elliptical planetary nebula NGC 7009 have been obtained with narrow band filters centred in most of the main optical emission lines. The Hα and [OIII]5007A images reveal an extended, high excitation circular halo around the central elliptical body of the planetary. A [SIII]9069A image shows a localized outer condensation, previously unreported. Bidimensional plasma diagnostics have been obtained. The halo is entirely excited by photons, whereas gas dynamical effects play an important role in determining the shape and excitation of the inner regions. The existence of bow shocks may be inferred from images of forbidden to Balmer line ratios. If the shape of the inner nebula is due to rotation of the planetary nebula nucleus (PNN), the progenitor of NGC 7009 probably was a main sequence star of about 2M sun _, and the mass of the halo is approximately 1M sun _. The inner nebula contains two rings of material, probably related to episodic mass loss events. The rings are not aligned. If this misalignment is due to precession of the PNN, we find a precession period of approximately 30,000 years. If precession is being driven by a companion star, the latter is located

4.5R sun _ from the PNN. No common envelope would be expected at the present stage of evolution of this system.

A Hubble Space Telescope image of the Blinking Planetary Nebula NGC 6826 (with additional processing by Judy Schmidt)

While the Milky Way along the backbone of the constellation Cygnus, the Swan, offers many fine targets for stargazers, the wings of the constellation are also well worth exploring, especially in the months of July through October when the constellation lies near the meridian. In this short tour, let’s tiptoe through the western wing of the Swan and inspect the remarkable Blinking Planetary, NGC 6826, and a few more intriguing deep-sky objects .

Before we get to the Blinking Planetary, let’s look at the brightest star in this part of the sky. It’s δ (delta) Cygni, a 3rd magnitude triple star system about 165 light years away. Such a bright star in a prominent part of the sky deserves a proper name, but most star maps just label it δ Cygni, though some call it Rukh or Al-Fawari. Future generations will surely assign another name to this star. When the wobbling Earth directs its axis towards δ Cygni in a little more than 9,200 years, it will be called, for a time, the North Star.

Location of NGC 6826, the Blinking Planetary, in the western wing of Cygnus, the Swan. The star cluster NGC 6811 is also shown (created with SkyX Serious Astronomer Edition by Software Bisque).

Have a look at the star with your telescope and you’ll see the main 3rd-magnitude component as a blue-white gem. The bone-white 6th-magnitude companion lies about 2.4″ away, which makes it challenging to discern in unsteady sky. You’ll need 75x or so to split this pair in a small telescope. The much fainter red dwarf companion shines at 12th magnitude and is very hard to pick out from the background stars.

OK, now let’s get to the Blinking Planetary. Cataloged as NGC 6826, it’s just southeast of the star iota (ι) Cygni, and just west of a line extended from kappa (κ) to iota (ι) with a length equal to the distance between the two stars. The 9th-magnitude planetary is fairly small, just 25″ in apparent diameter, so it appears nearly star-like at 50x. You can determine if you have indeed found the nebula by increasing magnification to enlarge the disk. At 120x or more, the nebula will reveal an obviously oval shape and a subtle blue-green color. The 10th-magnitude central star of NGC 6826 is quite obvious in a small telescope. This star is generating the nebula as it casts off its outer layers from its blazing hot central core.

The video below shows you the nebula through an image intensifier and gives you an idea of what it looks like at high magnification.

The Blinking Planetary is an object that most dramatically demonstrates the effect of averted vision. Stare directly at this blue-green planetary nebula for several seconds and you see only the central star. Look slightly to the side and the faint nebula around the star appears suddenly. When you switch from straight on to averted vision, the nebula appears to blink on and off. It’s darned impressive. Using a nebula filter (such as a UHC or OIII filter) increases the contrast of the nebula against the background sky, but ruins the blinking effect.

The open star cluster NGC 6811 in Cygnus (credit: Roberto Mura/Wikipedia)

If you’re hungry for more stargazing, look for the lovely little open star cluster NGC 6811. It’s just west of the line between δ Cyg and ι Cyg and much closer to the former. The little cluster is most fascinating for the assortment of shapes it resembles. Some say it looks like a smoke ring, some say it resembles the Liberty Bell, and others see Nefertiti’s headpiece, for example. Crank your telescope up to a moderate magnification around 50-80x and observe the cluster closely and carefully. What shape do you see?

## Exercise 2: Detecting Interstellar Reddening

In this exercise, you will learn how interstellar reddening affects the spectrum of a planetary nebula. Comparing the spectra of several nebulae, you will be able to determine which are more or less affected by interstellar reddening. Combining these results with the galactic latitudes of these planetary nebulae, you will be able to conclude something about the distribution of interstellar dust in our Milky Way Galaxy.

### The Balmer Decrement

In the Bohr model of the hydrogen atom there are many distinct energy levels, between which electrons can transfer if they emit or absorb the proper amount of energy. Upward moves require absorption of energy, while downward ones release energy. Downward electron transitions that end on the second energy level are called the Balmer series, and are important in optical astronomy, since these are the only transitions that involve visible light. The first three of these are called H &alpha, H&beta, and H&gamma, for the transitions from 3-2, 4-2, and 5-2, respectively. When many ionized hydrogen atoms are recombining, as in a planetary nebula where atoms are being ionized and recombining all the time, the captured electrons cascade down through the energy levels, emitting photons of the appropriate wavelengths as they fall. The likelihood of any particular downward jump is dictated by atomic constants, and thus the ratios of all possible transitions can be calculated. This leads to the "Balmer decrement," the well known ratios among the intensities of the Balmer lines, where H&alpha is the strongest line, H&beta is weaker, H&gamma is weaker still, and so on. Under typical conditions in planetary nebulae these ratios are (from Osterbrock, Astrophysics of Planetary Nebulae and Active Galactic Nuclei, University Science Books, 1989):

### The Phenomenon of Interstellar Reddening

Thus, the Balmer decrement, the intensity ratios of Balmer lines in all planetary nebulae, should be roughly the same. However, this is not what is observed. Interstellar reddening produced by micron-sized dust particles selectively dims shorter-wavelength, bluer light more than it does longer-wavelength, redder light, leading to Balmer line ratios that differ systematically from the theoretical predictions. A planetary nebula lying behind a cloud of interstellar dust will be observed to have the intensity ratios H&alpha/H&beta more than 2.86, and H&gamma/H&beta less than 0.47. The more dust, the greater the disparity between the observed and theoretical Balmer decrements. Turning this concept around, from the size of the discrepancy between observed and theoretical Balmer decrements, astronomers can infer the amount of interstellar reddening, and therefore, dust, between us and a given planetary nebula.

### The Milky Way Galaxy and Galactic Coordinates

Our solar system and all of the planetary nebulae in this database reside in the Milky Way Galaxy. The Milky Way is a flattened spiral of stars, gas, and dust, surrounded by a more spheroidal, extended, and much more diffuse region, called the galactic halo. Locations in the Milky Way are conveniently specified by galactic coordinates, similar to latitude and longitude as seen by someone viewing from the center of the Earth. The origin of the galactic coordinate system, though, is not at the center of the Milky Way, but rather, is located at the sun's position, because that's where we are as we view the heavens.

The Browse page of this website lists galactic coordinates for each planetary nebula as "lll.l (sign)bb.b," where lll.l is the galactic longitude in degrees, and bb.b is the galactic latitude in degrees. The plus or minus sign before the galactic latitude indicates whether the object is above or below the galactic plane, respectively.

### The Exercise

Listed below are eight planetary nebulae. For each of them, you will estimate the relative intensities of the H&alpha and H&beta lines and compare them with the theoretical prediction of 2.86 and with each other. Finally, you will be able to come to some conclusions about the distribution of dust in the Milky Way.

## Determining line ratios in planetary nebula - Astronomy

While planetary nebulae have been known for a long time, understanding of what they are had to wait for the advent of spectroscopy in astronomy. In the late 1800's when stellar spectroscopy was first being used people were surprised to find out that PNs had pure emission line spectra, rather than a continuum with absorption lines as was found for stars. The brigthest lines in PN spectra could not initially be identified leading to the hypothesis that an unknown element, named "nebulium" was producing these lines. However more observations showed that various of these unidentified lines varied in strength from object to object in a way that indicated that they came from different elements, and this "nebulium" idea was fairly quickly abandoned.

#### Appearance of the Solar Spectrum

This is what the solar spectrum looks like viewed with a prism, showing the bright continuum and the dark absorption lines from the star. (This image is created from a digital spectrum of a G2V star similar to the Sun, rather than being from an actual prism spectrum. I have seen the solar spectrum by eye using a grating spectrograph and I can vouch that it looked very much like this image. With a prism, which does not have as good a wavelength resolution, many of the fainter lines would be difficult to see at casual inspection.)

#### A Typical Planetary Nebula Spectrum (linear brightness scale)

This spectrum image is made from the observed spectrum of the PN NGC 7027, which is a bright and fairly compact PN in Cygnus. The really bright green line at 5007 Angstroms and the fainter companion line at 4959 Angstroms cause these PNs look green to the eye. When displayed like this you only easily see the one bright green line, and I had to mark the other two barely visible lines in the spectrum with the arrows. You can just barely see a red line, the 6563 Angstrom H alpha line, in the spectrum if you look hard, or if you enlarge the image. (As with the G2V spectrum above, all these spectra are simulated prism spectra based upon modern digital spectra of objects, or are the result of simulations of the nebular emission.)

The line at 5007 Angstroms is often the strongest line in the spectra of PNs, and so it is used in imaging surveys to discover these objects, especially in external galaxies. By taking an image on the spectral line and another image just off the line and subtracting the images, the PNs pop up as bright objects while normal stars subtract out of the difference image. The line is due to doubly ionized oxygen, so the central star has to be rather hot to ionize the oxygen atoms to O +2 . Very "young" PNs that are still getting hotter may not be able to excite this line, and very "old" PNs where the star has cooled off may also not have this line, but a large fraction of them do have this line as the strongest line in the optical spectrum.

#### The Same Planetary Nebula Spectrum, scaled to show faint lines

When the image is displayed with a logarithmic intensity scaling, as above, it becomes clear that there are lots of other lines present, but they are generally much weaker than the strong lines. The human eye sees brightness on a logarithmic scale, so if the spectrum could be made bright enough a person would see the weak lines and the strong lines as shown above.

Some of the lines here could be identified as due to Hydrogen and Helium, while many of the other lines were not initially identified. If you compare this spectrum with the two simulated spectra below you can see that one yellow line is due to He and that there are four lines of the Hydrogen Balmer series present in the NGC 7027 spectrum. If one looks one finds in fact a number of He lines in the spectrum besides the strong yellow line.

#### Simulated Pure Hydrogen Spectrum

This is from a computer calculation of the spectrum of a pure Hydrogen nebula, since I don't have a spectrum of such a thing.

#### Simulated Hydrogen and Helium Only Spectrum

This is from a computer calculation of the spectrum of a nebula with only Hydrogen and Helium, since I don't have a spectrum of such a thing.

You may see it better with the spectra side by side (H above, the NGC 7027 spectrum in the middle, H plus He below):

About 100 years ago the mysterious lines in PN spectra were identified as being collisionally excited "forbidden" lines of the ionized and neutral forms common elements such as oxygen, nitrogen, and carbon. These lines are not actually forbidden, but they only happen in nature under very low density conditions. A PN is a very low density cloud of ionized gas around a central star the star is producing ultraviolet radiation to ionize and excite the gas around it.

The lines seen in the spectra of PNs are of two types: recombination lines formed when an ion and an electron combine, leading to a cascade of the electron down the ground state, and collisionally excited lines from low lying energy levels in atoms or ions. The recombination lines include the H and He lines and many very faint lines of other elements observed in the spectra. However most of the stronger lines observed in PNs are for collisionally excited lines, whch we think are excited by electron collisions in the ionized plasma created by the star. Many of these low lying energy levels at a few electron volts above the ground state cannot radiate very effectively. On Earth the transitions don't take place under normal conditions because another collision takes place before the electron in these levels can radiate light. Even if one has a high vacuum and the gas density in the chamber is low, the gas inside still collides with the walls of the vacuum chamber fairly frequently. In the very low density conditions of these PNs -- densities are estimated to be typically of order 1000 atoms per cubic centimeter, which is equivalent to a pressure of the order of 10 -16 atmospheres. Having no walls to collide with, the ions and atoms in the gas can sit there until the forbidden transition takes place. The emission is very weak, but with a cubic light year or so of the gas even very weak emission can add up to something that is bright enough to observe.

In principle a careful analysis of the spectrum of a PN can provide us information about the temperature and density of the gas, as well as the abundances of the elements. These days this is usually done using a photoionization code to simulate the atomic physics and see what the line strengths are expected to be for different situations, and then adjusting the parameters to match the observed line ratios. Gary Ferland's CLOUDY code is an example of one of these simulation codes (intended for experts only. ).

One of the remaining big puzzles about PNs is that analysis of the recombination lines does not produce results consistent with the analysis of the collisionally excited forbidden lines. The physics of both of these processes are well understood, and actually closely related, so it is hard to understand why the two types of lines seem to indicate very different physical conditions in the nebula.

People have been trying to understand the reason for this for more than 50 years, and no entirely satisfactory solution has been found. There are two general ideas for explaining this, each with its own "camp": one is that there are significant variations in the plasma temperature over the nebula, and the other is that there are small pockets of gas which totally lack hydrogen distributed through the nebula. In either case its difficult to figure out how this state of affairs can be created, so I am not convinced of which of these is likely to be correct.

## Abell 30

Of the approximately 2500 planetary nebulae known in our galaxy, five are seen to contain clumpy hydrogen-deficient material. The best-studied example is Abell 30, a nebula that consists of a large, faint spherical shell, at the centre of which is a highly complex array of knots, in which hydrogen is virtually absent ( figure 1). The long-held theory for the formation of the hydrogen-deficient material in A30 is that its central star experienced a very late thermal pulse (VLTP), long after the ejection of the original nebula, which ejected freshly processed material into the nebula ( Iben 1983)

The planetary nebula Abell 30, in the light of [O ii ]. The left panel is a ground-based image the right is a Hubble Space Telescope image of the central knotty complex. (NASA/ESA/WIYN/X-W Liu)

## Contents

Astronomers use several different methods to describe and approximate metal abundances, depending on the available tools and the object of interest. Some methods include determining the fraction of mass that is attributed to gas versus metals, or measuring the ratios of the number of atoms of two different elements as compared to the ratios found in the Sun.

### Mass fraction Edit

Stellar composition is often simply defined by the parameters X, Y and Z. Here X is the mass fraction of hydrogen, Y is the mass fraction of helium, and Z is the mass fraction of all the remaining chemical elements. Thus

For the surface of the Sun, these parameters are measured to have the following values: [5]

Description Solar value
Hydrogen mass fraction X sun = 0.7381 >=0.7381>
Helium mass fraction Y sun = 0.2485 >=0.2485>
Metallicity Z sun = 0.0134 >=0.0134>

Due to the effects of stellar evolution, neither the initial composition nor the present day bulk composition of the Sun is the same as its present-day surface composition.

### Chemical abundance ratios Edit

The overall stellar metallicity is conventionally defined using the total hydrogen content, since its abundance is considered to be relatively constant in the Universe, or the iron content of the star, which has an abundance that is generally linearly increasing in the Universe. [6] Iron is also relatively easy to measure with spectral observations in the star's spectrum given the large number of iron lines in the star's spectra (even though oxygen is the most abundant heavy element – see metallicities in HII regions below). The abundance ratio is the common logarithm of the ratio of a star's iron abundance compared to that of the Sun and is calculated thus: [7]

where N Fe >> and N H >> are the number of iron and hydrogen atoms per unit of volume respectively. The unit often used for metallicity is the dex, contraction of "decimal exponent". By this formulation, stars with a higher metallicity than the Sun have a positive common logarithm, whereas those more dominated by hydrogen have a corresponding negative value. For example, stars with a [Fe/H] value of +1 have 10 times the metallicity of the Sun (10 1 ) conversely, those with a [Fe/H] value of −1 have 1 ⁄ 10 , while those with a [Fe/H] value of 0 have the same metallicity as the Sun, and so on. [8] Young Population I stars have significantly higher iron-to-hydrogen ratios than older Population II stars. Primordial Population III stars are estimated to have metallicity less than −6, a millionth of the abundance of iron in the Sun. [9] [10] The same notation is used to express variations in abundances between other individual elements as compared to solar proportions. For example, the notation "[O/Fe]" represents the difference in the logarithm of the star's oxygen abundance versus its iron content compared to that of the Sun. In general, a given stellar nucleosynthetic process alters the proportions of only a few elements or isotopes, so a star or gas sample with certain [/Fe] values may well be indicative of an associated, studied nuclear process.

### Photometric colors Edit

Astronomers can estimate metallicities through measured and calibrated systems that correlate photometric measurements and spectroscopic measurements (see also Spectrophotometry). For example, the Johnson UVB filters can be used to detect an ultraviolet (UV) excess in stars, [11] where a smaller UV excess indicates a larger presence of metals that absorb the UV radiation, thereby making the star appear "redder". [12] [13] [14] The UV excess, δ(U−B), is defined as the difference between a star's U and B band magnitudes, compared to the difference between U and B band magnitudes of metal-rich stars in the Hyades cluster. [15] Unfortunately, δ(U−B) is sensitive to both metallicity and temperature: if two stars are equally metal-rich, but one is cooler than the other, they will likely have different δ(U−B) values [15] (see also Blanketing effect [16] [17] ). To help mitigate this degeneracy, a star's B−V color can be used as an indicator for temperature. Furthermore, the UV excess and B−V color can be corrected to relate the δ(U−B) value to iron abundances. [18] [19] [20]

Other photometric systems that can be used to determine metallicities of certain astrophysical objects include the Strӧmgren system, [21] [22] the Geneva system, [23] [24] the Washington system, [25] [26] and the DDO system. [27] [28]

### Stars Edit

At a given mass and age, a metal-poor star will be slightly warmer. Population II stars' metallicities are roughly 1/1000 to 1/10 of the Sun's ([Z/H] = −3.0 to −1.0 ), but the group appears cooler than Population I overall, as heavy Population II stars have long since died. Above 40 solar masses, metallicity influences how a star will die: outside the pair-instability window, lower metallicity stars will collapse directly to a black hole, while higher metallicity stars undergo a Type Ib/c supernova and may leave a neutron star.

#### Relationship between stellar metallicity and planets Edit

A star's metallicity measurement is one parameter that helps determine whether a star may have a giant planet, as there is a direct correlation between metallicity and the presence of a giant planet. Measurements have demonstrated the connection between a star's metallicity and gas giant planets, like Jupiter and Saturn. The more metals in a star and thus its planetary system and proplyd, the more likely the system may have gas giant planets. Current models show that the metallicity along with the correct planetary system temperature and distance from the star are key to planet and planetesimal formation. For two stars that have equal age and mass but different metallicity, the less metallic star is bluer. Among stars of the same color, less metallic stars emit more ultraviolet radiation. The Sun, with 8 planets and 5 known dwarf planets, is used as the reference, with a [Fe/H] of 0.00. [29] [30] [31] [32] [33]

### HII regions Edit

Young, massive and hot stars (typically of spectral types O and B) in H II regions emit UV photons that ionize ground-state hydrogen atoms, knocking electrons and protons free this process is known as photoionization. The free electrons can strike other atoms nearby, exciting bound metallic electrons into a metastable state, which eventually decay back into a ground state, emitting photons with energies that correspond to forbidden lines. Through these transitions, astronomers have developed several observational methods to estimate metal abundances in HII regions, where the stronger the forbidden lines in spectroscopic observations, the higher the metallicity. [34] [35] These methods are dependent on one or more of the following: the variety of asymmetrical densities inside HII regions, the varied temperatures of the embedded stars, and/or the electron density within the ionized region. [36] [37] [38] [39]

Theoretically, to determine the total abundance of a single element in an HII region, all transition lines should be observed and summed. However, this can be observationally difficult due to variation in line strength. [40] [41] Some of the most common forbidden lines used to determine metal abundances in HII regions are from oxygen (e.g. [O II] λ = (3727, 7318, 7324) Å, and [O III] λ = (4363, 4959, 5007) Å), nitrogen (e.g. [NII] λ = (5755, 6548, 6584) Å), and sulfur (e.g. [SII] λ = (6717,6731) Å and [SIII] λ = (6312, 9069, 9531) Å) in the optical spectrum, and the [OIII] λ = (52, 88) μm and [NIII] λ = 57 μm lines in the infrared spectrum. Oxygen has some of the stronger, more abundant lines in HII regions, making it a main target for metallicity estimates within these objects. To calculate metal abundances in HII regions using oxygen flux measurements, astronomers often use the R23 method, in which

R 23 = [ O II ] 3727 Å + [ O III ] 4959 Å + 5007 Å H β , =>]_<3727

where O III 3727 Å + O III 4959 Å + 5007 Å >_<3727

mathrm >> is the sum of the fluxes from oxygen emission lines measured at the rest frame λ = (3727, 4959 and 5007) Å wavelengths, divided by the flux from the Hβ emission line at the rest frame λ = 4861 Å wavelength. [42] This ratio is well defined through models and observational studies, [43] [44] [45] but caution should be taken, as the ratio is often degenerate, providing both a low and high metallicity solution, which can be broken with additional line measurements. [46] Similarly, other strong forbidden line ratios can be used, e.g. for sulfur, where [47]

S 23 = [ S II ] 6716 Å + 6731 Å + [ S III ] 9069 Å + 9532 Å H β . =>]_<6716

Metal abundances within HII regions are typically less than 1%, with the percentage decreasing on average with distance from the Galactic Center. [40] [48] [49] [50] [51]

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In: Astrophysical Journal , Vol. 614, No. 1 I, 10.10.2004, p. 167-185.

Research output : Contribution to journal › Article › peer-review

T1 - The planetary nebula system of M33

N2 - We report the results of a photometric and spectroscopic survey for planetary nebulae (PNs) over the entire body of the Local Group spiral galaxy M33. We use our sample of 152 PNs to show that the bright end of the galaxy's [O III] λ5007 planetary nebula luminosity function (PNLF) has the same sharp cutoff seen in other galaxies. The apparent magnitude of this cutoff, along with the IRAS DIRBE foreground extinction estimate of E(B - V) = 0.041, implies a distance modulus for the galaxy of (m - M )0 = 24.86 -0.11+0.07 (0.94-0.05+0.03 Mpc). Although this value is ∼ 15% larger than the galaxy's Cepheid distance, the discrepancy likely arises from differing assumptions about the system's internal extinction. Our photometry, which extends more than 3 mag down the PNLF. also reveals that the faint end of M33's PNLF is nonmonotonic, with an inflection point ∼ 2 mag below the PNLF's bright limit. We argue that this feature is due to the galaxy's large population of high core mass planetaries and that its amplitude may eventually be a useful diagnostic for studies of stellar populations. Fiber-coupled spectroscopy of 140 of the PN candidates confirms that M33's PN population rotates along with the old disk, with a small asymmetric drift of ∼ 10 km s-1. Remarkably, the population's line-of-sight velocity dispersion varies little over ∼4 optical disk scale lengths, with σrad ∼ 20 km s-1. We show that this is due to a combination of factors, including a decline in the radial component of the velocity ellipsoid at small galactocentric radii and a gradient in the ratio of the vertical to radial velocity dispersion. We use our data to derive the dynamical scale length of M33's disk and the disk's mass-to-light ratio. Our most likely solution suggests that the surface mass density of M33's disk decreases exponentially, but with a scale length that is ∼2.3 times larger than that of the system's IR luminosity. The large scale length also implies that the disk's V-band mass-to-light ratio changes from M/LV ∼ 0.3 in the galaxy's inner regions to M/LV ∼ 2.0 at ∼9 kpc. Models in which the dark matter is distributed in the plane of the galaxy are excluded by our data.

AB - We report the results of a photometric and spectroscopic survey for planetary nebulae (PNs) over the entire body of the Local Group spiral galaxy M33. We use our sample of 152 PNs to show that the bright end of the galaxy's [O III] λ5007 planetary nebula luminosity function (PNLF) has the same sharp cutoff seen in other galaxies. The apparent magnitude of this cutoff, along with the IRAS DIRBE foreground extinction estimate of E(B - V) = 0.041, implies a distance modulus for the galaxy of (m - M )0 = 24.86 -0.11+0.07 (0.94-0.05+0.03 Mpc). Although this value is ∼ 15% larger than the galaxy's Cepheid distance, the discrepancy likely arises from differing assumptions about the system's internal extinction. Our photometry, which extends more than 3 mag down the PNLF. also reveals that the faint end of M33's PNLF is nonmonotonic, with an inflection point ∼ 2 mag below the PNLF's bright limit. We argue that this feature is due to the galaxy's large population of high core mass planetaries and that its amplitude may eventually be a useful diagnostic for studies of stellar populations. Fiber-coupled spectroscopy of 140 of the PN candidates confirms that M33's PN population rotates along with the old disk, with a small asymmetric drift of ∼ 10 km s-1. Remarkably, the population's line-of-sight velocity dispersion varies little over ∼4 optical disk scale lengths, with σrad ∼ 20 km s-1. We show that this is due to a combination of factors, including a decline in the radial component of the velocity ellipsoid at small galactocentric radii and a gradient in the ratio of the vertical to radial velocity dispersion. We use our data to derive the dynamical scale length of M33's disk and the disk's mass-to-light ratio. Our most likely solution suggests that the surface mass density of M33's disk decreases exponentially, but with a scale length that is ∼2.3 times larger than that of the system's IR luminosity. The large scale length also implies that the disk's V-band mass-to-light ratio changes from M/LV ∼ 0.3 in the galaxy's inner regions to M/LV ∼ 2.0 at ∼9 kpc. Models in which the dark matter is distributed in the plane of the galaxy are excluded by our data.

## Abstract

Using the 13.7m radio telescope at Qinhai Station of Purple Mountain Observatory, new observational results have been obtained for 5 planetary nebulae. Among them, the CO(2-1) emission of M1-8 and M3-3 has been detected and the results of observation of their CO(1-0) emission are presented in this paper. For the other objects, i.e., M1-12, M2-43 and NGC 6537, for which previous CO observations failed to detect CO emission, their CO(1-0) emission is here identified for the first time.

## SkyTools 4 Imaging Overview

In understanding my approach towards creating SkyTools 4 Imaging, its worth considering how major professional observatories, such as ESO, use mathematical models of their telescope and instruments to plan their observations. It is useful to know the image scale, what exposure times to use, whether a star will bloom or if the signal will become nonlinear, and how many exposures are required to reach a given Signal to Noise Ratio (SNR).

I have long thought that amateurs could greatly benefit from such a tool, but many of the difficulties in doing so seemed insurmountable. The professional apps tend to focus on one telescope, one instrument, and a specific type of work such as spectroscopy. To be truly useful to the amateur, an app would have to work with any telescope, camera, and filter. Most difficult of all, it would have to handle a range of target objects such as stars, galaxies, and emission nebulae.

Figure 1 – Spectrum of a Sun like star

My previous software product, SkyTools 3, is primarily aimed at visual observers. It does have an imaging capability, but it uses a crude imaging model that suffers from many shortcomings. The model was originally developed by Bradly Schaeffer and it makes many simplifying assumptions, such as filters that must be approximately Gaussian, and it has no means of handling emission line objects, such as HII regions and supernovae.

It was a first step, but only that. In order to be more useful, I would need a much better model, and I would have to invent ways to approximate both the spatial and spectral energy distribution of everything from comets to planetary nebulae.

In the end, SkyTools 4 Imaging took over four years of full-time work and introduces an entirely new imaging system model. It begins with the target object and ends with an accurate prediction of the target object signal, sky signal, system noise, and finally SNR. Any set of observing conditions can be simulated, including the effects of seeing, airmass, twilight, and moonlight.

Spectral-Energy Distribution of the Target Object

Stars and other stellar sources (quasars, minor planets, etc.) are modeled based on the continuum, which can be described by their UBVRI color indices (see Figure 1).

Figure 2 – Spectrum of a typical Planetary Nebula

Reflection nebulae, galaxies, and comets are modeled similarly, using UBVRI colors representative of these objects. For galaxies, the type of galaxy determines the color characteristics.

Planetary nebulae, HII regions and supernova remnants are modeled via their emission line spectrum (see Figure 2). The primary emission lines used in SkyTools are H-Alpha, H-Beta, OIII, NII, and SII. Other lines are included when data is available.

For some objects, (HII regions and supernova remnants in particular) there is no catalog data available for the required emission line strengths. To obtain data for these objects I have scoured the scientific literature. For those that remained without sufficient data I have initiated an observing campaign using narrow band filters to measure the emission.

For a given object, the total energy as well as the energy distribution is modified as it passes through the atmosphere. The degree to which it is modified depends on the airmass, atmospheric conditions (temperature, humidity), and time of year.

The brightness of the sky background depends on the amount of light pollution, moonlight, twilight, altitude of the target, and atmospheric conditions.

Telescope Optics

The area of the telescope objective, minus what may be obstructed by the presence of a secondary mirror, determines how much total energy is collected. The optics also modify the spectral distribution, depending on the optical coatings. In the case of reflecting optics, the time since the mirror was last cleaned has a significant effect.

Figure 3 – Filter Transmission

A filter is modeled by combining the spectral transmission curve of the filter with the energy distribution of the target object, as modified by the atmosphere and optical system (see Figure 3).

Camera Detector

At the final step, the number of photons counted by each pixel is the integral over wavelength of the spectral energy distribution of the light that reaches the detector, combined with the spectral quantum efficiency of the detector. The quantum efficiency tells us how many electrons are produced for each photon detected (see Figure 4).

Figure 4 – Detector Quantum Efficiency

As a result of the previously mentioned steps, the signal in e- (electrons) can be predicted. For extended objects it is predicted on a per pixel basis, along with the signal from the sky background. The signal measured by each pixel in e- is converted to ADU via the camera gain. The SNR can be estimated per pixel based on the signal and the total noise (primarily composed of detector readout noise and sky noise).

For stellar objects the total signal in e- is predicted. The atmospheric conditions and limitations of the telescope optics determine how this signal is spread over the detector, as modeled by a point spread function. The photometric SNR is computed for the total signal and noise over a circular aperture. The peak SNR is computed for the peak signal (peak of the point spread function) and the estimated noise at the peak.

Diffuse objects such as galaxies, nebulae, and comets, are not uniform. For example, a spiral galaxy may consist of a bright central core, spiral arms, and a faint outer halo.

So, when estimating the SNR, it is important to specify what part of the galaxy we are exposing for. Do you wish to merely detect the bright core? Or do you wish to obtain a high-quality (high SNR) image of the spiral arms? The surface brightness corresponding to each part of the galaxy is estimated by a combination of the overall brightness of the galaxy and statistics for galaxy type.

A similar process is used for other diffuse objects, such as reflection nebulae. For comets, the size of the coma and degree of concentration from recent observations are used.

The model has been tested extensively using the many imaging systems available at iTelescope.net.

/>Figure 5 – SkyTools 4 Imaging Graphic: The blue line is the relative imaging quality (IQ) for the object during the night. The quality is highest when at the top of the graphic. The red dashed line is the altitude of the target object. The teal line is the altitude of the moon.

The primary testing was done with Landolt UBVRI standard star fields. I developed an image analysis app that uses the information from the FITS header along with photometry extracted from the image data. The photometry was tested against software from the AAVSO to ensure its accuracy. For each image the actual signal is compared to the signal predicted by the model for the time and conditions of the image.

Interestingly, several additional significant effects were uncovered in testing, such as the age and cleanliness of the mirrors, and the optical transmission of the camera window.

In the end we can compute the SNR for any exposure at any time during the night. But what if the conditions are changing rapidly? E.g. what if the sky brightness is changing during the exposure? Or for an image of a comet at high airmass, the airmass can change quickly as it sets.

Standard SNR calculators implicitly assume that conditions don’t change during the exposure. But the SkyTools Imaging calculator integrates the signal, sky brightness, and other factors, over time. As a result, it can estimate the SNR of an image even when the conditions are changing rapidly during the exposure.

Finally, we can create a model with real world inputs that are based on the properties of the target object, location, weather conditions, airmass, sky brightness, and imaging system. This can be very useful by itself, but we can take it a step further. For any time of night the SNR can be computed for an arbitrary exposure. We can also compute the SNR for the same exposure, but under the ideal conditions at the same location. When we compare the two by dividing the SNR computed for the test exposure by the SNR under ideal conditions, we have an index that can be used to estimate the imaging quality (IQ) at any time. This is extremely useful for planning when to image in each filter.

It has been a long journey, and I faced many apparently insurmountable problems, but I am very happy with the result. I can’t imagine planning my own imaging without it. I use SkyTools 4 Imaging to select targets that are appropriate for an imaging system, determine the number of exposures and sub exposure times required to meet a target SNR, maximize my SNR by planning my images during the best time of the night, and even to select which available telescope is best for a given target.

Greg Crinklaw operates Skyhound and is the developer of SkyTools. He is a life-long amateur astronomer, who is also trained as a professional astronomer, holding a BS, MS in astronomy, and an MS in astrophysics. He also worked for NASA as a Software Engineer on a Mars orbital mission. Greg and his family live in the mountains of Cloudcroft, New Mexico.

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