# Flux vs. Velocity representation of spectra?

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I'm looking for a basic explanation of the flux vs. velocity representation of a spectrum and how it's obtained from the regular flux vs. wavelength representation. A good example of this is in Arav et al 2001 (see here, Fig. 2 and 3).

More specific questions I can ask are:

• How do you convert between wavelength and velocity in these figures (i.e. what phenomenon are we using to make the conversion & what's the equation)?
• What thing has the velocity in question/what does the velocity represent? For example, is it the astrophysical object moving in this direction?

… But any further elaboration is much appreciated. As much as I've seen these (I'm trying to brush up, it's been a while since I've done astro stuff), I can't find any explanation for this; perhaps I don't know the right jargon, but yeah it's difficult to find a simple answer. Thanks in advance for the help.

I think the velocity scale is calculated something like this: $$v_r = cleft( frac{lambda - lambda_0}{lambda_0} ight),$$ where $$lambda$$ is the observed wavelength and $$lambda_0$$ is wavelength of the Mg II line, corrected for the redshift of the quasar ($$z=0.868)$$ it is observed towards. The confusing thing is, for Fig.~3 in the cited paper, that the Mg II feature is actually doublet with lines at rest wavelengths of $$lambda_r =2796.35$$ and $$2803.53$$ Angstroms. Therefore $$lambda_0 = lambda_r (1+z) = 5223.58 { m or} 5236.99 { m Angstroms}$$ corresponding to the thick and thin solid lines on Fig.3 respectively.

In other words, zero on the velocity scale would correspond to a Mg II absorber at the redshift of the quasar (an intrinsic absorber), whereas negative velocities correspond to absorbers at lower redshift, by the velocities indicated.

For a check on this - calculate the velocity of feature "b", which appears to be at about 5221 Angstroms in the observed spectrum for the redder doublet component (the thin solid line in Fig.3). Using the above definition, this would be a velocity of -915 km/s.

Looking at Fig.3, there seems to be a major problem. Feature "b" is at -680 km/s. However, if we look further on at Figs. 4 and 5, we see feature "b" plotted at -850 km/s in the Mg II spectrum, which is much closer, and would perhaps be in exact agreement if feature "b" was actually at 5222 Angstroms (which looks unlikely) or that a 4th, unspecified decimal place had been used in the redshift. e.g. if $$z=0.8676$$ then $$lambda_0 = 5235.87$$ Angstroms, and the velocity of a feature measured at 5221 Angstroms would then be -852 km/s in perfect agreement with Figs. 4 and 5.

Either way, there is major disagreement between Fig. 3 (which I suspect is in error) and Figs. 4 and 5 (which could be reconciled with the above analysis if the redshift was 0.8676).

I'm sorry this is not very conclusive and I certainly wouldn't accept it without someone else verifying that the x-axis of Fig.3 appears to be problematic.

## Spectral Flux

Spectral flux measures the spectral change between two successive frames and is computed as the squared difference between the normalized magnitudes of the spectra of the two successive short-term windows:

where EN i ( k ) = X i ( k ) ∑ l = 1 Wf L X i ( l ) , i.e. EN i ( k ) is the k th normalized DFT coefficient at the i th frame. The spectral flux has been implemented in the following function:

Figure 4.11 presents the histograms of the mean value of the spectral flux sequences of segments from two classes: music and speech. It can be seen that the values of spectral flux are higher for the speech class. This is expected considering that local spectral changes are more frequent in speech signals due to the rapid alternation among phonemes, some of which are quasi-periodic, whereas others are of a noisy nature.

Figure 4.11 . Histograms of the mean value of sequences of spectral flux values, for audio segments from two classes: music and speech.

## Region of Fast Neutrons

The first part of the neutron flux spectrum in thermal reactors, is the region of fast neutrons. All neutrons produced by fission are born as fast neutrons with high kinetic energy.

At first we have to distinguish between fast neutrons and prompt neutrons. The prompt neutrons can be sometimes incorretly confused with the fast neutrons. But there is an essential difference between them. Fast neutrons are neutrons categorized according to the kinetic energy, while prompt neutrons are categorized according to the time of their release.

Most of the neutrons produced in fission are prompt neutrons. Usually more than 99 percent of the fission neutrons are the prompt neutrons, but the exact fraction is dependent on the nuclide to be fissioned and is also dependent on an incident neutron energy (usually increases with energy). For example a fission of 235 U by thermal neutron yields 2.43 neutrons, of which 2.42 neutrons are the prompt neutrons and 0.01585 neutrons (0.01585/2.43=0.0065=ß) are the delayed neutrons.

• Prompt neutrons are emitted directly from fission and they are emitted within very short time of about 10 -14 second.
• Most of the neutrons produced in fission are prompt neutrons – about 99.9%.
• For example a fission of 235 U by thermal neutron yields 2.43 neutrons, of which 2.42 neutrons are prompt neutrons and 0.01585 neutrons are the delayed neutrons.
• The production of prompt neutrons slightly increase with incident neutron energy.
• Almost all prompt fission neutrons have energies between 0.1 MeV and 10 MeV.
• The mean neutron energy is about 2 MeV. The most probable neutron energy is about 0.7 MeV.
• In reactor design the prompt neutron lifetime (PNL) belongs to key neutron-physical characteristics of reactor core.
• Its value depends especially on the type of the moderator and on the energy of the neutrons causing fission.
• In an infinite reactor (without escape) prompt neutron lifetime is the sum of the slowing down time and the diffusion time.
• In LWRs the PNL increases with the fuel burnup.
• The typical prompt neutron lifetime in thermal reactors is on the order of 10 -4 second.
• The typical prompt neutron lifetime in fast reactors is on the order of 10 -7 second.

Basic features of prompt neutron energy spectra are summarized below:

• The neutrons produced by fission are high energy neutrons.
• Almost all fission neutrons have energies between 0.1 MeV and 10 MeV.
• The prompt neutron energy distribution, or spectrum, may be best described by dependence of the fraction of neutrons per MeV on neutron energy.
• The most probable neutron energy is about 0.7 MeV.The mean neutron energy is about 2 MeV.
• These values are for thermal fission of 235 U, but these values vary only slightly for other nuclides.

Prompt neutron fission spectra evaluation is one of the most interesting aspects of evaluation of actinides. Many experimental and theoretical researches have been carried out for the determination of prompt neutron spectra. There are several representations of prompt fission neutron spectra. Two early models of the prompt fission neutron spectrum, which are still used today, are the Maxwellian and Watt spectrum.

The modern spectrum representation of the prompt fission neutron spectrum and average prompt neutron multiplicity is called the Madland-Nix Spectrum (Los Alamos Model). This model is based upon the standard nuclear evaporation theory and utilizes an isospin-dependent optical potential for the inverse process of compound nucleus formation in neutron-rich fission fragments.

Prompt Neutron Energy Spectra – Dependence on fissioning nucleus.
Source: Madland, David G., New Fission-Neutron-Spectrum Representation for ENDF, LA-9285-MS, April 1982. Prompt Neutron Energy Spectra – Dependence on incident neutron energy.
Source: Madland, David G., New Fission-Neutron-Spectrum Representation for ENDF, LA-9285-MS, April 1982. http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/14/718/14718824.pdf

• The presence of delayed neutrons is perhaps most important aspect of the fission process from the viewpoint of reactor control.
• Delayed neutrons are emitted by neutron rich fission fragments that are called the delayed neutron precursors.
• These precursors usually undergo beta decay but a small fraction of them are excited enough to undergo neutron emission.
• The emission of neutron happens orders of magnitude later compared to the emission of the prompt neutrons.
• About 240 n-emitters are known between 8 He and 210 Tl, about 75 of them are in the non-fission region.
• In order to simplify reactor kinetic calculations it is suggested to group together the precursors based on their half-lives.
• Therefore delayed neutrons are traditionally represented by six delayed neutron groups.
• Neutrons can be produced also in (γ, n) reactions (especially in reactors with heavy water moderator) and therefore they are usually referred to as photoneutrons. Photoneutrons are usually treated no differently than regular delayed neutrons in the kinetic calculations.
• The total yield of delayed neutrons per fission, vd, depends on:
• Isotope, that is fissioned.
• Energy of a neutron that induces fission.
• Variation among individual group yields is much greater than variation among group periods.
• In reactor kinetic calculations it is convenient to use relative units usually referred to as delayed neutron fraction (DNF).
• At the steady state condition of criticality, with keff = 1, the delayed neutron fraction is equal to the precursor yield fraction β.
• In LWRs the β decreases with fuel burnup. This is due to isotopic changes in the fuel.
• Delayed neutrons have initial energy between 0.3 and 0.9 MeV with an average energy of 0.4 MeV.
• Depending on the type of the reactor, and their spectrum, the delayed neutrons may be more (in thermal reactors) or less effective than prompt neutrons (in fast reactors). In order to include this effect into the reactor kinetic calculations the effective delayed neutron fraction – βeff must be defined.
• The effective delayed neutron fraction is the product of the average delayed neutron fraction and the importance factor βeff = β . I.
• The weighted delayed generation time is given by τ = ∑iτi . βi / β = 13.05 s, therefore the weighted decay constant λ = 1 / τ ≈ 0.08 s -1 .
• Their presence completely changes the dynamic time response of a reactor to some reactivity change, making it controllable by control systems such as the control rods.

Depending on the type of the reactor, and their spectrum, the delayed neutrons may be more (in thermal reactors) or less effective than prompt neutrons (in fast reactors). In order to include this effect into the reactor kinetic calculations the effective delayed neutron fraction – βeff must be defined.

Delayed neutrons are traditionally represented by six delayed neutron groups, whose yields and decay constants (λ) are obtained from nonlinear least-squares fits to experimental measurements.

Prompt Neutron Energy Spectra – Dependence on fissioning nucleus.
Source: Madland, David G., New Fission-Neutron-Spectrum Representation for ENDF, LA-9285-MS, April 1982.

The vast of the prompt neutrons and even the delayed neutrons are born as fast neutrons (i.e. with kinetic energy higher than > 1 keV). But these two groups of fission neutrons have different energy spectra, therefore they contribute to the fission spectrum differently. Since more than 99 percent of the fission neutrons are the prompt neutrons, it is obvious, that they will dominate the entire spectrum.

Therefore the fast neutron spectrum can be described by following points:

• Almost all fission neutrons have energies between 0.1 MeV and 10 MeV.
• The mean neutron energy is about 2 MeV.
• The most probable neutron energy is about 0.7 MeV.

The fast neutron spectrum can be approximated by the following (normalized to one) distribution:

## 1. Introduction

[2] Turbulence power spectra of the along-channel (u′) and vertical (w′) velocity fluctuations are often used to describe the range of scales in turbulence, in particular the dominant eddy sizes responsible for turbulent transfer as well as the distribution of variance with frequency [ Roth et al., 1989 ]. Likewise, turbulence cospectra, or their integral versions, ogive curves, are used to describe the distribution of the covariance (uw′) across the frequency domain, where uw′ represents a vertical flux of along-channel momentum that is due to turbulent fluctuations.

[4] Given this, measured spectra, cospectra, and ogive curves, when made nondimensional appropriately, are generally supposed to exhibit the relations found by Kaimal et al. [1972] , hereafter referred to as the Kaimal curves [see, e.g., Kristensen and Fitzjarrald, 1984 Roth et al., 1989 Al-Jiboori et al., 2001 ]. Since then, numerous studies performed in marine bottom boundary layers (MBBLs), such as those found in coastal and/or estuarine environments, have used Kaimal curves derived from the ABL for calculating nondimensional turbulence spectra, cospectra, and ogive curves [e.g., Soulsby, 1977 Feddersen and Williams, 2007 ]. Various investigators have used the Kaimal curves in the MBBLs for various purposes including filtering waves from turbulence [ Shaw and Trowbridge, 2001 Feddersen and Williams, 2007 Kirincich et al., 2010 ], comparing the general shape and form to the Kaimal curves [ Soulsby, 1977 Scully et al., 2011 ], analyzing the vertical structure of Reynolds stresses [ Feddersen and Williams, 2007 ], determining turbulent scales in the coastal ocean [ Trowbridge and Elgar, 2003 ], and modeling vorticity flux spectra [ Lien and Sanford, 2000 ]. In all of these cases, however, the Kaimal scaling was assumed to hold. Here, instead, we test the validity of the Kaimal scaling using data acquired in a fairly generic estuarine tidal flow. Turbulence spectra, cospectra, and ogive curves of a well-mixed, tidal flow will be scaled according to Monin-Obukhov similarity theory and compared to the Kaimal curves.

By default all columns in the SED format are optional. To facilitate interoperability of files produced by different packages/tools, the SED format defines an SED Type string which is set with the SED_TYPE header keyword. The SED type defines a minimal set of columns that must be present in the SED. The SED types and their required columns are given in the following list:

• dnde : e_ref , dnde
• e2dnde : e_ref , e2dnde
• flux : e_min , e_max , flux
• eflux : e_min , e_max , eflux
• likelihood : See Likelihood SED .

## TULLY-FISHER RELATION

The luminosity (L) of a spiral galaxy is proportional to its rotational velocity (v) to the fourth power:

The relationship is called the Tully-Fisher relation. By using spectral lines, we can easily determine the rotational velocity, and hence, the luminosity of a galaxy. A similar relation, called the Faber-Jackson relation, holds for the characteristic velocities of the stars in elliptical galaxies and is also measured from the galaxies&rsquo spectra. These methods work for greater distances than methods based on stars because galaxies are much brighter than stars and can be seen to much greater distances than can individual stars. In practice, the Tully-Fisher and Faber-Jackson relations can be used out as far as we can measure the spectral lines of a galaxy. This is out to billions of light-years.

The relationship between stellar orbital speed and brightness becomes apparent when astronomers study galaxies in a given galaxy cluster. The galaxies in a cluster are essentially all at the same distance, and so this is reminiscent of how Henrietta Leavitt observed Cepheids in the Small Magellanic Cloud to discover the period&ndashluminosity relation. Without a nearby calibration, only relative distances can be determined, not absolute distances. The HST Key Project for Cepheids in the Virgo Cluster of galaxies provided a precise local calibrator for the Tully-Fisher and Faber-Jackson relations.

###### TULLY-FISHER RELATION

In this activity, you will study the Tully-Fisher relationship between rotational velocity and intrinsic brightness for a set of spiral galaxies. The method will bear some similarities to the Cepheid distance method in that there is a relationship between luminosity of an object and an easily measurable quantity. In the case of Cepheids, the relationship is between luminosity and period of pulsations. For spiral galaxies, the relationship is between luminosity and rotation speed of the galaxy.

The rotation speed of a galaxy is determined from its spectrum, specifically the 21-cm emission line from neutral hydrogen gas. If a galaxy is rotating, the gas in the part of the galaxy rotating toward us will show a blueshift, while the gas in the part of the galaxy rotating away from us will show a redshift. However, this motion is superimposed on the net motion of the galaxy in space. This motion is almost always much larger than the rotation speed of the galaxy, and it is away from us for all but a few galaxies. So the net effect is that the entire emission line will be redshifted, but the parts rotating away will have a larger redshift than the parts moving toward us. The center of the galaxy will not be rotating toward or away from us.

The emission line from hydrogen in a galaxy looks strange. That is because the entire galaxy contains hydrogen and the entire galaxy is rotating. We see different components of that rotation depending on where we look. For instance, the outer parts are moving almost straight toward us or straight away from us, so we see the entire motion reflected in the redshift there. But if we look toward the center of the galaxy, we see a lot of gas that is traveling across our line of sight, and only a little that is moving toward or away. This effect causes the emission line to be smeared out in a broad plateau. It is the width of this plateau that gives us the rotation speed of the galaxy.

A. Determining the Tully-Fisher Relation

In the first part of this activity, 10 galaxy spectra are available. You should use at least six of them in order to obtain a good determination of the Tully-Fisher Relation.

1. Select a galaxy to plot using the pull-down menu on the screen. A spectrum is usually plotted as intensity vs. wavelength (or frequency), but here we have converted wavelength to velocity using the Doppler formula:

a. Pick a point on the left side of the line. Hover over the point to get its velocity. Record the velocity that you measure in the &ldquovelocity start&rdquo box provided for the galaxy. An example is provided in Figure A.6.3.

c. Measure a corresponding point on the right side of the line. Be as consistent as possible about the height on the line you perform your measurement. Notice that the line is narrower at the top than at the bottom, so if you are not consistent with how you measure the line, it will skew your results slightly. You should carry over your measurement method from one galaxy to the next as best you can. Record the velocity that you measure in the &ldquovelocity stop&rdquo box provided for the galaxy.

Figure credit: NASA/SSU.

B. Using the Tully-Fisher Relation to Estimate the Distance to Galaxies

In this part of the activity, you will use the Tully-Fisher Relation that you created in Part A to determine the distances to three additional galaxies.

1. If you haven't done so already, hit the &ldquonext&rdquo button again. You will be presented with a pull-down, from which you will be able to choose another galaxy to plot. However, this galaxy is one that does not have a known distance (or not as far as you know). You will use the equation you derived in the last part, your Tully-Fisher relation, to determine the absolute magnitude for this and the other galaxies, and hence, their distances.

a. Select a galaxy and measure its rotation speed as you did previously for Part A. Again, you should try your best to measure the rotation using the same part of the emission line as you did before. Measure the velocities at both sides of the line and enter the values in the boxes provided. Enter the rotation velocity in the data table below.

b. Hit the Calculate Magnitude box when you are done. Then hit the equal sign after the relationship for absolute magnitude to be displayed. Enter the absolute magnitude of the galaxy into the table below.

This is the general way that the Tully-Fisher relation is used to measure the distances to galaxies. We have omitted some of the complicating details so that you get a better understanding of how the method works.

Now that you have done the Tully-Fisher activity, you may be interested in seeing the original data (Figure 6.18), published in 1977. R.B. Tully and J.R. Fisher are shown in Figure 6.19.

Figure 6.18 The original data published by Tully and Fisher in 1977. The plot shows the photographic magnitude of the galaxy plotted vs. the rotation speed. Credit: Tully, R.B. and Fisher, J.R. 1977, Astronomy and Astrophysics, 54,3, 661

Figure 6.19: (a) R. Brent Tully and (b) J. Richard Fisher today. R. Brent Tully is an astrophysicist at the Institute for Astronomy in Hawaii. He went to graduate school at the University of Maryland before moving to Hawaii, one of the world&rsquos best places to do astronomical observations at visible wavelengths. J. Richard Fisher is a radio astronomer, working at the National Radio Astronomy Observatory in Charlottesville, Virginia. Dr. Fisher also went to graduate school at the University of Maryland and is an adjunct professor at the University of Virginia. Credits: (a) www.ifa.hawaii.edu/

tully/ (b) www.astro.virginia.edu/people//faculty/jrf2v/

The Faber-Jackson relation (Figure 6.20) was developed in 1976 by astronomers Sandra Faber (Figure 6.21) and Robert E. Jackson. It relates the luminosity of an elliptical galaxy to the spread in velocities observed near the galaxy&rsquos center.

Figure 6.20: Data used in the original Faber-Jackson relation. The plot shows the velocity dispersion vs. the galaxy&rsquos brightness in magnitudes. Credit: Faber, S.M. and Jackson, R.E. 1976, Astrophysical Journal, 204,668

Figure 6.21: Sandra Faber is a professor at the University of California, Santa Cruz, and is a prominent cosmologist who has won many awards for her work, including the Heineman Prize, the Harvard Centennial Medal, and the Franklin Institute&rsquos Bower Award. She is a member of the National Academy of Sciences and was an early leader in the use of the Hubble Space Telescope for cosmological observations. Robert E. Jackson was Faber&rsquos graduate research assistant at UC Santa Cruz, and he helped analyze the data that led to the determination of the relation. Credit: http://astro.ucsc.edu/

The 3-vectors DVELH and DVELB are given in a right-handed coordinate system with the +X axis toward the Vernal Equinox, and +Z axis toward the celestial pole.

The projected velocity towards the celestial object can be computed from: v = dvelb[1]*cos(dec)*cos(ra) + dvelb[2]*cos(dec)*sin(ra) + dvelb[3]*sin(dec)

The algorithm here is taken from FORTRAN program of Stumpff (1980). Stumpf claimed an accuracy of 42 cm/s for the velocity. A comparison with the JPL FORTRAN planetary ephemeris program PLEPH found agreement to within about 65 cm/s between 1986 and 1994. The option in IDL astrolib's baryvel.pro to use the full JPL ephemeris is not implemented in R.

## Line Emission

Instead of using our spectrometer on a light bulb, what if we were to use it to look a tube of gas - for example, hydrogen? We would first need to heat the hydrogen to very high temperatures, or give the atoms of hydrogen energy by running an electric current through the tube. This would cause the gas to glow - to emit radiation. If we looked at the spectrum of light given off by the hydrogen gas with our spectroscope, instead of seeing a continuum of colors, we would just see a few bright lines. Below we see the spectrum, the unique fingerprint of hydrogen.

These bright lines are called emission lines. Remember how we heated the hydrogen to give the atoms energy? By doing that, we excited the electrons in the atom - when the electrons fell back to their ground state, they gave off photons of light at hydrogen's characteristic energies. If we altered the amount or abundance of hydrogen gas we have, we could change the intensity of the lines, that is, their brightness, because more photons would be produced. But we couldn't change their color - no matter how much or how little hydrogen gas was present, the pattern of lines would be the same. Hydrogen's pattern of emission lines is unique to it. The brightness of the emission lines can give us a great deal of information about the abundance of hydrogen present. This is particularly useful in a star, where there are many elements mixed together.

Each element in the periodic table can appear in gaseous form and will each produce a series of bright emission lines unique to that element. The spectrum of hydrogen will not look like the spectrum of helium, or the spectrum of carbon, or of any other element.

We know that the continuum of the electromagnetic spectrum extends from low-energy radio waves, to microwaves, to infrared, to optical light, to ultraviolet, to X and gamma-rays. In the same way, hydrogen's unique spectrum extends over a range, as do the spectra of the other elements. The above spectra are in the optical range of light. Line emission can actually occur at any energy of light (i.e. visible, UV, etc. ) and with any type of atom, however, not all atoms have line emission at all wavelengths. The difference in energy between levels in the atom is not great enough for the emission to be X-rays in atoms of lighter elements, for example.

### Different Graphical Representations of Spectra

Below, you will see the spectrum of the Sun at ultraviolet wavelengths. There are distinct lines (in the top graph) and peaks (in the bottom one) and if you look at the X-axis, you can see what energies they correspond to. For example, we know that helium emits light at a wavelength of 304 angstroms, so if we see a peak at that wavelength, we know that there is helium present.

### Spectra and Astronomy

Spectral information, particularly from energies of light other than optical, can tell us about material around stars. This material may have been pulled from a companion star by a black hole or a neutron star, where it will form an orbiting disk. Around a compact object (black hole, neutron star), the material in this accretion disk is heated to the point that it gives off X-rays, and the material eventually falls onto the black hole or neutron star. It is by looking at the spectrum of X-rays being emitted by that object and its surrounding disk, that we can learn about the nature of these objects.

## What velocity dispersion tells us about galaxy evolution

When astronomers go out and observe galaxies, they make measurements that don’t necessarily have much physical meaning on their own. Consider the most basic “observable” of any astronomical object: flux (usually reported in the oft-maligned magnitude system). Flux is related to the amount of energy being generated by a star (or an entire galaxy), but you can’t actually calculate the luminosity unless you also know how far away the star (or galaxy) is. Once you have luminosity, though, you can compare one object to another directly, and luminosity functions have been a valuable tool for understanding changes in galaxy populations for virtually as long as we’ve known about other galaxies. But is luminosity really the most fundamental property of a galaxy? There is other stuff in galaxies besides stars (which are responsible for much of a galaxy’s luminosity), so opinions are mixed. Some astronomers (like the authors of today’s paper) prefer to use the velocity dispersion of stars as a predictor of galaxy properties instead and have gone out and measured the velocity dispersion of a large number of individual galaxies in order to prove their point.

The stellar velocity dispersion of a galaxy essentially measures the random line-of-sight motion of stars due to a the presence of mass (i.e., the gravitational potential well). Historically, velocity dispersion has played an major role in understanding galaxies and shows up in a number of important scaling relations, including the fundamental plane of elliptical galaxies (which has been used to estimate distances to elliptical galaxies as well as place constraints on their evolution) and the infamous M-sigma relation (which is nicely described in this astrobite). The origin of these scaling relations is still somewhat unclear, but one idea that is gaining momentum is that the mass of a galaxy’s dark matter halo is actually what determines many galaxy properties. Because stellar velocity dispersion probes the depth of the gravitational potential well in which the stars are sitting (which is dominated by dark matter), velocity dispersion also traces the properties of the dark matter halo a paper from earlier this year claims that velocity dispersion is essentially the best metric to use, above other mass tracers like stellar mass or dynamical mass (which is itself determined using the velocity dispersion).

The trouble is that you need a spectrum in order to measure velocity dispersion, since it is calculated from the width of absorption lines. This is a very difficult task, especially for faint objects, and so Rachel Bezanson and her collaborators used other galaxy properties which can be measured using images to infer the velocity dispersions of over 25,000 galaxies from redshift 1.5 down to 0.3 (i.e., back when the Universe was 4 to 10 billion years old). Dividing the galaxies in bins by redshift (i.e., time), they looked at the number density of galaxies as a function of velocity dispersion, which they call the velocity dispersion function (VDF). Figure 1 shows how the VDF changes with redshift for quiescent (or passive, non-star-forming) galaxies and star-forming galaxies.

Figure 1: The evolution of the velocity dispersion function (VDF) for quiescent galaxies (left) and star-forming galaxies (right). The low velocity dispersion end of the quiescent VDF changes noticeably with redshift, but the VDF for star-forming galaxies stays essentially the same. Original figure from Bezanson et al. (2012).

There are a few important results:

For both quiescent and star-forming galaxies, the number of galaxies at the highest end of the VDF changes very little as a function of time, which may suggest that these galaxies (and their dark matter halos) were already in place by redshift

The overall idea is that changes in the VDF are due to two competing processes: transformation and dissipation (see Figure 2). The former, transformation, occurs when a star-forming galaxy stops forming stars (why it does so is a different question!) and starts being counted as a quiescent galaxy. Dissipation refers to gas sinking to the center of a galaxy and causes the gravitational potential well to become deeper, therefore moving the galaxy to a higher velocity dispersion bin. Since these gas motions are more important in star-forming galaxies, the effect of dissipation is seen predominately in the VDF evolution of those galaxies.

Figure 2: The effects of transformation and dissipative processes on the velocity dispersion functions (VDFs) of quiescent galaxies (red) and star-forming galaxies (blue). Original figure from Bezanson et al. (2012).

The authors go on to model the effect of these two processes on the VDF and their results are strikingly similar to the observations (see Figure 8 in their paper!). At some level, however, this is not surprising and only serve to confirm what we already suspected. At late times (low redshift), star formation continues in galaxies with lower velocity dispersion, while the nearly all of galaxies with the highest velocity dispersions are already quiescent. Further, since velocity dispersion correlates with the mass of a galaxy’s supermassive black hole, the fixed high velocity dispersion end of the VDF suggests that the most massive black holes had already formed by redshift

1.5, which is consistent with the fact that those same black holes accreted a significant fraction of their mass 1.5 billion years earlier, at redshift

2. Both of these phenomena are related to the idea of “downsizing” or anti-hierarchical structure formation (basically the opposite of what we expect if galaxy formation is dictated only by gravity). Of course, there are still plenty of challenges left in explaining the underlying physics responsible for all of these observations. Putting together a complete picture of galaxy evolution will require continued efforts to understand the properties of individual galaxies and how those properties change as a function of redshift, which is exactly what Bezanson et al. have done.

## Flux vs. Velocity representation of spectra? - Astronomy

The results of a program of observations of the cataclysmic variable V442 Oph from UV to IR wavelengths are reported. The observations comprise IUE SWP and LWR-camera spectra from October, 1981 UBVr and R photometry at Manastash Ridge Observatory from August, 1980 UBV photometry and IR measurements at Kitt Peak from July, 1981 and Coudespectroscopy at Mt. Wilson from June, 1980, and at Mt Lemmon from July, 1982. Tables of data, plots of H-alpha and He-II radial velocity, sample spectra, light curves, and a log-log diagram of F(lambda) vs lambda are given. Flux-ratio analysis of the IR data indicates a disk with very little optically thin material anad an outer-edge temperature of about 7920 K. The calculated period (3.37 h) and mass-accretion rate (1 x 10 to the -8th solar mass/yr) are compared to those of similar objects, and V442 Oph is found to be similar in this respect to systems like H2252-035. Its lack of a rotational period and the weakness of the optical and UV line emissions, however, are more like the old nova V603 Aql.