# How to calculate galaxy bolometric luminosity?

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I am a bit confused by bolometric corrections. If I have an x-ray luminosity in the 2-10 keV band, how does one convert that to $$L_{bol}$$? From Netzer's book The Physics and Evolution of Active Galactic Nuclei I got these bolometric correction factors:

Optical: $$BC_{5100} = 53 - log(L_{5100})$$

and x-ray: $$log(L_{5100}) = 1.4 imes log(L_X) - 16.8$$

where the bolometric correction for the x-ray luminosity ($$L_X$$) is obtained in two steps, using the equation for the optical BC again. The index $$5100$$ stands for the optical continuum measured at $$5100$$ angstrom. I can't figure out what I have to do with this $$BC_{5100}$$ once I've got it. Multiply by $$L_X$$? The book says "(… ) BCs, that can be used to convert a single-band measurement of $$L$$ into an approximate $$L_{bol}$$."

I'm happy to use correction factors defined elsewhere instead of the ones I quoted. I just want to calculate an estimate for $$L_{bol}$$ for my galaxies.

The bolometric correction is the difference between a bolometric magnitude and the magnitude in some band.

$$BC = M_{ m bol} - M_{5100} = -2.5logleft(frac{L_{ m bol}}{L_{5100}} ight)$$ $$log L_{ m bol} = log L_{5100} - 0.4BC ,$$ $$log L_{ m bol} = log L_{5100} +0.4log L_{5100} - 21.2 ,$$ $$log L_{ m bol} = 1.4(1.4 log L_x -16.8) - 21.2 ,$$ $$log L_{ m bol} = 1.96log L_x -44.72 .$$

## How to calculate luminosity in g-band from absolute AB magnitude and luminosity distance?

How can I calculate the (non-bolometric) luminosity $L$ of a galaxy (or a star for that matter) over a given band from its AB apparent magnitude $m_$ over that band and its luminosity distance $d_L$?

For instance, consider the g-band which typically has a $lambda_ = 467 ext< nm>$ and a $Delta lambda = 100 ext< nm>$. Given this galaxy has an apparent AB magnitude of $m_g = 22.5$ and luminosity distance of $1991 ext< Mpc>$ (i.e. $z = 0.355$ if you are curious), what is its luminosity? I know I shold use the following equation, but I don't know what value to pick for $M_odot$.

I tried 5.12 from a website which is the value of $M_odot$ in g-band but it gives me a different answer compared to when I calculate luminosity using flux:

$L = 4 pi d_^2 f_ u Delta u$

where $f_ u$ is flux density and $Delta u$ is the frequency width of the band (this is an approximation to the integration over frequency, assuming bands are step functions). So, how can I find luminosity using absolute magnitude?

## Luminosity for a black body

In astronomy, luminosity is the total amount of energy emitted by a star, galaxy, or other astronomical object per unit time. It is related to the brightness, which is the luminosity of an object in a given spectral region. In SI units luminosity is measured in joules per second or watts. Values for luminosity are often given in the terms of the luminosity of the Sun, which has a total power output of 3.846×1026 W. The symbol for solar luminosity is L⊙. Luminosity can also be given in terms of magnitude. The absolute bolometric magnitude (Mbol) of an object is a logarithmic measure of its total energy emission.

The Stefan–Boltzmann equation applied to a black body gives the value for luminosity for a black body, an idealized object which is perfectly opaque and non-reflecting.

As far as I know, you need to have photon counts for specific temperatures for the stars that you want to calculate the correction for. This is basically because at a given temperature, there is a photon count we expect to see and a photon count we actually see, the difference is, in part, due to the fact that the detector we use is not sensitive to all wavelengths.

The formula I'm aware of regarding bolometric correction is:

where Ni's are photon counts and T's are temperatures. BC2 is the bolometric correction for the second star.

Though, I'm not sure if you need to, but there are other factors worth metioning. For example, the detector used to find the counts above is likely to not only not be sensitive to all wavelengths but is also likely to unintentionally incorporate a bias - it will not be equally sensitive to all wavelengths. There are also other factors such as - are your photon counts subject to interstellar absorption? Not sure if any of this is relevant.

can the bolometric correction be calculated if all i know of a cepheid variables properties are its period? for example, if the cepheid variable has a period of 3 days i can use a period-luminosity relationship to calculate the luminosity, from here i can then calculate the bolometric magnitude. my question really is this, can i then calculate the bolometric correction required to find the absolute visual magnitude? or is there an easier way to get to the absolute visual magnitude from just the information given.

hopefully some one can point me in the right direction, thanks

(this is a question that has come up in one of the books i am reading, so if it is in the wrong forum i appologies)

For a Cepheid, if you know nothing but the period, you wouldn't be able to use the period-luminosity relationship to get bolometric magnitude or much of anything, including distance. This is because there are "classical cepheids" of Population I with periods of 2 to 40 days and "W-Virginis Stars" which are cepheids of Population II.

For a given period, the W-Virginis stars are about 1.5 to 2.0 magnitudes less than classical cepheids, so you would at least need a spectral analysis to determine if the star is a Pop I or Pop II cepheid. It was on this particular point that the early (1920's I think) measurements to the Andromeda galaxy showed

1.1 million Ly when it is actually

2.2-2.5 million Ly. The first cepheid measurements and period-luminosity relationships were done only on classical cepheids, hence the original error(s).

## How to calculate galaxy bolometric luminosity? - Astronomy

The Astronomy Calculator includes functions that are useful for studying astronomy. Formulae are organized in different tabs to the right as follows: T 2 = (4π • R 3 )/(G•M)
Kepler&aposs Third Law

#### Astronomy Calculators

• Kepler&aposs 3 rd Law formula T² = (4π • R³)/(G • M)
• (M) - mass of the system .
• (T) - period of the orbit .
• (R) - separation distance between the two objects .
• (G) - universal gravity constant
• (α) - angle
• (D) - distance to astronomical object
• (S) - size or diameter of astronomical object
• Change in Magnitude from Flux Ratio
• Flux Ratio from Magnitudes
• Resolving Power of a Telescope
• Magnification of a Telescope
• Mass from Luminosity
• Mass from Acceleration and Radius
• Mass from Speed and Separation
• Mass of extra-solar planet from mass of star, radius of star orbit and radius of exoplanet orbit
• Mass of extra-solar planet from mass and velocity of star and velocity of planet
• Relative Size from Relative Temperature and Luminosity
• Relative Temperature from Relative Size and Luminosity
• Relative Luminosity from Relative Temperature and Size
• Velocity from shift in Wavelength and Unshifted Wavelength
• Wavelength Shift from Wavelength and Speed
• Blackbody Wavelength from Temperature
• Blackbody Temperature from Peak Wavelength
• Photon Energy from Wavelength
• Photon Wavelength from Energy
• Distance from absolute and apparent magnitude
• Radius from Speed and Period
• Speed of Circular Motion
• Hubble Time
• Luminosity from Mass

Related Astro Calculators:

• Hubble&aposs Law
• Kepler&aposs 3 rd Law Calc has Kepler&aposs 3 rd law solved for each parameter.
• Astronomy Calculator contains basic formulas for a college level Introduction to Astronomy
• Exoplanet Calculator contains formulas for studying planets outside of our Solar System.
• Astronomical Distance Calculator provides the distance from the Earth to numerous astronomical bodies (e.g. Sun, Moon, planets, stars, Milky Way&aposs Center and Edge, Andromeda Galaxy)
• Astronomical Distance Travel Time Calculator computes the time to travel to distant parts of space at different velocities.
• Ellipse Calculator
• 3D Vector Calculator:
• Drake Equation Calculator
• Seager Equation Calculator
• Friedman Equation Calculator

### Astronomy Calculator&aposs Creator

Special thanks to Dr. Stephen Spicklemire, Department Chair, Physics &Earth-Space Science , Associate Professor of Physics at the University of Indianapolis. Dr. Spicklemire created this calculator and all of the underlying equations (functions) to help his astronomy students.

"vCalc is awesome for my astronomy students. With vCalc I can give them real problems that would normally require fairly sophisticated reasoning and mathematics, and now they can do the reasoning, because they’re not daunted by the math. It’s great." Dr. Steve Spicklemire

Aren't the radial velocities way off from newtonian/relativistic mechanics and calculated based on a theoretical model about dark matter? I see MOND can be an excellent predictor of star velocites for very specific types of galaxies but it appears to be just a mathematical trick so it really isn't a good explanation for the higher velocities that we see.

What would be an example of a basic formula used to calculate mass without going for significant accuracy?

Luminous mass I believe is measured experimentally through star count, and is a fairly rough estimate. It's only real purpose is to get the order of magnitude right, which is clearly an order of magnitude less than the total mass, so it is an estimate just accurate enough to tell us that there is a lot of mass somewhere else.

Calculating the mass of the galaxy can be done using a solar systems radial velocity:

say a solar system is orbiting the center of a galaxy with radius d. The orbit is circular, but if you draw a sphere around the center of the galaxy, again with radius d so that the solar system is rotating along the edge of the sphere, then the mass contained within the volume of this sphere is :

P = orbital period
G = grav. constant

mass in sphere: M = 4*pi^2*d^3/(GP^2) = d*v^2/G

Most of the mass, especially the "dark mass" will be located within a solar systems orbit, so this is a sufficient approximation.

There's no way to calculate such a thing from first principles: the luminosity of a galaxy depends on how efficiently it managed to form stars out of the matter available to it. Star formation is far too complicated to admit of a first-principles calculation.

But there are empirical relationships between mass and luminosity, which have been used and refined for many years. When trying to understand the large-scale structure of the Universe, we want to know where the mass is, but what we can measure is where the light is. Hence the great interest in mass-luminosity relations. The link you provide in your edit is an example of this work. To find others, a good buzzword to search for is "mass-to-light ratio." For instance, this article might be a good place to start (although I haven't read it).

## How to calculate galaxy bolometric luminosity? - Astronomy

Aims: We aim to study the fraction of stellar radiation absorbed by dust, f abs , in 814 galaxies of different morphological types. The targets constitute the vast majority (93%) of the DustPedia sample, including almost all large (optical diameter larger than 1'), nearby (v ≤ 3000 km s -1 ) galaxies observed with the Herschel Space Observatory.
Methods: For each object, we modelled the spectral energy distribution from the ultraviolet to the sub-millimetre using the dedicated, aperture-matched DustPedia photometry and the Code Investigating GALaxy Evolution (CIGALE). The value of f abs was obtained from the total luminosity emitted by dust and from the bolometric luminosity, which are estimated by the fit.
Results: On average, 19% of the stellar radiation is absorbed by dust in DustPedia galaxies. The fraction rises to 25% if only late-type galaxies are considered. The dependence of f abs on morphology, showing a peak for Sb-Sc galaxies, is weak it reflects a stronger, yet broad, positive correlation with the bolometric luminosity, which is identified for late-type, disk-dominated, high-specific-star-formation rate, gas-rich objects. We find no variation of f abs with inclination, at odds with radiative transfer models of edge-on galaxies. These results call for a self-consistent modelling of the evolution of the dust mass and geometry along the build-up of the stellar content. We also provide template spectral energy distributions in bins of morphology and luminosity and study the variation of f abs with stellar mass and specific star-formation rate. We confirm that the local Universe is missing the high f abs , luminous and actively star-forming objects necessary to explain the energy budget in observations of the extragalactic background light.

## How to calculate galaxy bolometric luminosity? - Astronomy

We present a study of the multi-wavelength properties, from the mid-infrared to the hard X-rays, of a sample of 255 spectroscopically identified X-ray selected type-2 AGN from the XMM-COSMOS survey. Most of them are obscured and the X-ray absorbing column density is determined by either X-ray spectral analyses (for 45% of the sample), or from hardness ratios. Spectral energy distributions (SEDs) are computed for all sources in the sample. The average SEDs in the optical band are dominated by the host-galaxy light, especially at low X-ray luminosities and redshifts. There is also a trend between X-ray and mid-infrared luminosity: the AGN contribution in the infrared is higher at higher X-ray luminosities. We calculate bolometric luminosities, bolometric corrections, stellar masses and star formation rates (SFRs) for these sources using a multi-component modeling to properly disentangle the emission associated to stellar light from that due to black hole accretion. For 90% of the sample we also have the morphological classifications obtained with an upgraded version of the Zurich estimator of structural types (ZEST+). We find that on average type-2 AGN have lower bolometric corrections than type-1 AGN. Moreover, we confirm that the morphologies of AGN host-galaxies indicate that there is a preference for these type-2 AGN to be hosted in bulge-dominated galaxies with stellar masses greater than 10 10 solar masses.

## How to calculate galaxy bolometric luminosity? - Astronomy

Aims: We study the influence of the environment on the evolution of galaxies by investigating the luminosity function (LF) of galaxies of different morphological types and colours at different environmental density levels.
Methods: We construct the LFs separately for galaxies of different morphology (spiral and elliptical) and of different colours (red and blue) using data from the Sloan Digital Sky Survey (SDSS), correcting the luminosities for the intrinsic absorption. We use the global luminosity density field to define different environments, and analyse the environmental dependence of galaxy morphology and colour. The smoothed bootstrap method is used to calculate confidence regions of the derived luminosity functions.
Results: We find a strong environmental dependency for the LF of elliptical galaxies. The LF of spiral galaxies is almost environment independent, suggesting that spiral galaxy formation mechanisms are similar in different environments. Absorption by the intrinsic dust influences the bright-end of the LF of spiral galaxies. After attenuation correction, the brightest spiral galaxies are still about 0.5 mag less luminous than the brightest elliptical galaxies, except in the least dense environment, where spiral galaxies dominate the LF at every luminosity. Despite the extent of the SDSS survey, the influence of single rich superclusters is present in the galactic LF of the densest environment.