text stringlengths 128 2.05k |
|---|
Radio-bright AGN (such as core-dominated Seyferts) have lower [MATH] values than samples composed purely of SFGs. We have calculated [MATH] |
for our sample of sBzK galaxies under the two temperature assumptions used above (since we do not measure directly the rest-frame 60- and 100- [MATH] m part of the spectrum). The results are summarised in Table . Unfortunately, our lack of knowledge of the dust temperatures in the sBzK galaxies limits the usefulness of... |
, we find [MATH] is low compared to the star-forming FIR/radio relation, and more similar to the values found in Seyfert samples; for a dust SED with [MATH] |
, we find [MATH] to be entirely consistent with star-forming values. The average temperature of IRAS -bright galaxies in the local Universe is [MATH] |
(Dunne et al. 2000), and galaxies containing an AGN would usually tend to have hotter dust than those without – due to extra heating of dust near the nuclear regions. The [MATH] values we find are only similar to those of Seyferts for the coldest dust temperature assumptions, if we use a dust temperature more appropria... |
; Kuraszkiewicz et al. 2003) the we see from Table that the [MATH] values are then inconsistent with those derived for AGN. This is further evidence that star formation is dominating the radio emission of our sBzK sample. Further investigation of the FIR/radio relationship will be possible with forthcoming Herschel obs... |
Discussion: the SFRs of [MATH] -selected galaxies We now split the samples into bins of redshift and stellar mass [MATH] ), or absolute rest-frame [MATH] mag. The rest-frame |
[MATH] mags are calculated with the photometric redshifts using the best-fitting SED template. These are then converted into [MATH] using the relationship given by the Millennium simulation (de Lucia et al. 2006) in the manner employed by Serjeant et al. (2008) which is effectively using a Salpeter IMF. This is a redsh... |
[MATH] ; the scatter in the relationship used here is of order 0.2-0.3 dex at a given redshift. A more careful measurement will be possible in the future using the results of the Spitzer |
Legacy survey of the UDS, in particular the 3.6–8- [MATH] m data. We have checked that using [MATH] rather than the simpler absolute [MATH] mag does not change the trends discussed in this section. We use [MATH] as this is more directly comparable to other work in the literature. |
6.1 Star-formation history To begin with, we look at the SFRD as a function of redshift for our full sample (i.e. ‘All galaxies’ from Section 3.1 ). The sample was divided into a number of redshift bins and the median SFR for each bin calculated. The volume contained within each bin was calculated using the effective s... |
[MATH] by finding the number of galaxies within each redshift bin in this magnitude range, multiplying that number by 1.2 and adding it to the number of galaxies in that redshift bin at [MATH] . These corrections are small and range from 1.04 at low redshift to 1.13 at [MATH] . The SFRD is estimated by multiplying the ... |
[MATH] -selected sample we are stacking does lose lower [MATH] luminosity sources at higher redshifts. If the radio-derived SFR and [MATH] -band luminosity are correlated then we will have an effective ‘luminosity limit’ to our radio stacks, as a function of redshift, which will mean that we will be missing some fracti... |
mag ( [MATH] ) and the results are shown in Fig. 10 . We stacked in two redshift bins ( [MATH] and [MATH] ) to minimise any redshift-dependent trends. The fits in both cases show [MATH] which, within the uncertainties, is consistent with a linear relationship. |
We will now attempt to correct for the fraction of the radio luminosity density lost from the faint end of the [MATH] -band LF. The deepest wide-area study of the evolution of the [MATH] -band LF is provided by the UDS (Cirasuolo et al. 2008) who present Schechter function fits as a function of redshift. The integrated... |
[MATH] from infinity to some fixed lower luminosity ( [MATH] ) is given by: [EQUATION] where [MATH] is the normalisation, [MATH] is the characteristic luminosity in [MATH] [MATH] is the faint-end slope and |
[MATH] is the incomplete Gamma function. The correction we want to make ( [MATH] ) for each redshift bin is the ratio of [MATH] integrated to the lowest observed luminosity at that redshift – the cut-off luminosity ( [MATH] ), to |
[MATH] integrated to [MATH] , the lowest observed luminosity at [MATH] . We used the evolving [MATH] from Cirasuolo et al. (2008), with a fixed faint-end slope and calculated [MATH] |
for each redshift bin. Thus [EQUATION] The radio SFRD points were corrected by the factor [MATH] and are shown as solid circles on Fig. 11 . The uncorrected values are also shown as open diamonds in Fig. 11 for comparison. |
The radio-derived SFRD is consistent with the multi-wavelength compilation of HB06 out to [MATH] . After this, the radio-derived points appear to drop more steeply than the other data, even after correction for the missing faint end part of the [MATH] -band LF. This is the highest redshift study of star formation in th... |
[MATH] (Kovacs et al. 2006; Ibar et al. 2008) but these studies focus on samples with much higher [MATH] and [MATH] . Our LF corrections may also be underestimated if the faint end slope of the [MATH] -band LF undergoes evolution with redshift. The optical/UV points at [MATH] are also subject to substantial correction ... |
We can also compare the radio-derived SFRD determined using the two SFR relationships discussed earlier. Fig. 11 a shows the conversion of 1,400-MHz luminosity to SFR from Condon (1992) while Fig. 11 b shows that of Bell (2003). Both SFR calibration methods straddle the points from HB06, with Condon’s a little high, an... |
at [MATH] , compared to a correction of 6 [MATH] at [MATH] for Seymour et al. (2008). The lowest redshift point, at [MATH] , has been corrected (to integrated and for clean -to-dirty) by a factor 2.61, as described in § 3.2 . Without this differential correction for the lowest redshift bin, this point would be very low... |
The general agreement between the two SFR estimators and the literature work further supports the mounting evidence that AGN are not strongly contributing to the globally-averaged radio emission of these stacked samples. Overall, at this point, we feel there is nothing to choose between the two SFR conversions and so w... |
6.2 Specific star-formation rates We can also look at the average SFR per unit stellar mass, defined as the SSFR, as a function of stellar mass and redshift. SSFR is often used as a measure of the star-formation efficiency of a galaxy, since it provides information about the fraction of a galaxy’s mass which could be c... |
The results for the full [MATH] -selected sample are shown in Fig. 12 , where Fig. 12 a uses Condon’s SFR and Fig. 12 b uses Bell’s SFR. We see a strong trend of increasing SSFR with redshift for all bins of stellar mass. There is no difference in the evolution of SSFR with redshift for different mass bins out to [MATH... |
points to account for his finding that low-luminosity galaxies are deficient in non-thermal radio flux for a given SFR. Fig. 12 b therefore shows a trend for the lowest mass galaxies to have the highest SSFR in the lowest redshift bin, whereas Fig. 12 a (Condon SFR) does not. |
A large volume of literature on SSFR has been produced since recent advances in deriving robust stellar masses for large galaxy samples through deep and wide [MATH] -band and Spitzer imaging (Feulner et al. 2005, 2007; Caputi et al. 2006; Zheng et al. 2007; Daddi et al. 2007; Elbaz et al. 2007; Iglesias-Paramo et al. 2... |
We will now make a detailed comparison between our results and those in the literature and discuss possible reasons for the differences. |
Fig. 13 shows in more detail the relationship between SSFR and [MATH] . Fig. 13 a uses the Condon SFR and Fig. 13 b uses the Bell SFR. From this we can notice two things. First, most panels show a weak relationship between SSFR and [MATH] , where the steepness of the correlation appears to increase with redshift. Secon... |
We have over-plotted comparisons with other literature where available. The studies by Daddi et al. (2007) of BzK galaxies at [MATH] , and by Elbaz et al. (2007) of sources at [MATH] selected using 24- [MATH] m data in the Great Observatories Origins Deep Survey (GOODS), are over-plotted on the [MATH] and [MATH] panels... |
galaxies from the SDSS by Brinchmann et al. (2004) finds a shallower slope of [MATH] . The Brinchmann et al. trend is overplotted at [MATH] to show that the slope of the relationship we find is intermediate between that at [MATH] and [MATH] |
The rather weak trends of SSFR versus [MATH] found here are at some odds with other findings in the literature. Some studies find that the differences in SSFR at [MATH] over the mass range [MATH] to be a factor [MATH] compared to our differences of a factor [MATH] (Feulner et al. 2005; Caputi et al. 2006; Zheng et al. ... |
[MATH] panel, we find that the change in SSFR over the range [MATH] at [MATH] is a factor [MATH] closer to the values seen at lower redshift in the other studies. |
Most of the surveys reporting these steeper trends have two things in common. First, they are selected in the optical and use [MATH] or Spitzer data to estimate [MATH] . Second, they rely on detections of galaxies in one or more bands, from which the SFR is then directly inferred (e.g. UV, 24 [MATH] m). The rest-frame ... |
[MATH] -band surveys select via stellar mass (for [MATH] , at least). [MATH] -band selection produces greater correlation between SSFR and [MATH] . This selection band bias most strongly affects low-mass galaxies. Elbaz et al. (2007) and Zheng et al. (2007) also noted that optical selection for spectroscopic completene... |
Our sample is based on selection via an extremely deep [MATH] -band survey (where selection is not strongly dependent on current SFR at [MATH] and the current SFR is determined by radio stacking (rather than via a flux-limited radio sample). The weak dependence of SSFR on [MATH] at [MATH] found here – and the similar e... |
In summary, many independent studies find similar trends, with SSFR increasing with redshift and decreasing with stellar mass. However, the strength of these relationships varies considerably and is likely to be due to a complicated combination of sample-selection criteria, particularly wavelength and depth. Many autho... |
Given that our exploration of SFR versus absolute [MATH] mag produced a linear correlation, with [MATH] , it is the conversion of [MATH] mag to stellar mass which introduces the slight non-linearity in SFR versus [MATH] [MATH] ). This, in turn, produces the shallow observed dependence of SSFR on [MATH] . Thus, the conv... |
The upcoming addition of extremely deep [MATH] [MATH] and 3.6–24- [MATH] Spitzer imaging, as well as several thousand more spectroscopic redshifts, the stellar masses and redshifts of the UDS sample will improve markedly. At that time, it will be interesting to test whether these trends remain. |
6.3 Specific star-formation rates in BzK galaxies We have further split the samples of sBzK, pBzK and non-BzK galaxies into bins of redshift and stellar mass to investigate their SSFR trends. This is shown in Fig. 14 with different colours and symbols denoting the different samples and open and filled symbols used to d... |
The pBzK galaxies behave quite differently. Their SSFR drops from [MATH] to [MATH] and then appears to be consistent again with the other samples at very high redshifts. We have already noted changes in pBzK properties at [MATH] from their radio spectral indices (§ 5.1 ), the decrease in their radio flux density and th... |
[MATH] could be due either to low-level SFG contamination or to radio-quiet AGN activity. The radio spectral indices and submm stacking also suggest a change in the dominant pBzK population at |
[MATH] , but our submm and 610-MHz observations are not deep enough to allow us to conclude which of the above scenarios is responsible for the low-level 1,400-MHz emission at [MATH] |
Future analysis of the larger SHADES 1.1-mm AzTEC image, newly acquired Spitzer data, alongside the zUDS spectroscopic programme, should determine the true nature of pBzK galaxies. |
Conclusions We have stacked several [MATH] -selected populations into a deep 1,400-MHz mosaic in order to investigate their star-formation history. There is much dispute over the relative contribution from star formation and AGN to the radio populations at sub-mJy levels and our knowledge is almost non-existent at flux... |
[MATH] -selected galaxies at these flux densities (5–20 [MATH] Jy). We find a strong relationship between stacked radio flux density and apparent [MATH] mag. We also find SFR to be a strong and almost linear function of absolute [MATH] mag and stellar mass. |
Both sBzK and pBzK galaxies are detected robustly in the radio stack. The stacked radio flux density of the sBzK galaxies is roughly constant with redshift, inferring a strong evolution in SFR. |
Our photometric redshifts suggest that a significant fraction [MATH] 30–40 per cent) of galaxies occupying the sBzK and pBzK regions of the BzK diagram lie at [MATH] . The similarity between sBzK and [MATH] pBzK galaxies – in terms of their radio- and submm-derived SFR and SSFR – leads us to suggest that the BzK diagra... |
The pBzK galaxies suffer a dramatic reduction in radio flux density at [MATH] . Their weak radio flux density at [MATH] suggests either a persistent, low-level of contamination by SFGs, or that the radio emission for these objects is powered by radio-quiet AGN. Deeper 610-MHz and submm data are required to determine wh... |
The variation of radio-derived SFR density with redshift agrees well with that determined at other wavelengths, for [MATH] . This suggests that the contribution from AGN-related radio emission is small. At [MATH] , the radio-derived SFR density declines due to our inability to fully sample the [MATH] -band luminosity f... |
We find that the SSFR (SFR/ [MATH] ) is only weakly dependent on stellar mass, with SSFR decreasing as [MATH] increases. The observed correlation of SSFR with stellar mass is consistent with the shallower determinations in the literature, such as Daddi et al. (2007) at [MATH] and Elbaz et al. (2007) at |
[MATH] . It is much less steep than many optical-/UV-based studies and we argue that these differences are largely due to selection biases present in UV- and optically-selected samples. We also find a very strong trend of increasing SSFR with redshift, stronger than reported elsewhere, with a flattening at [MATH] . Thi... |
Comparing the radio-derived SFR conversions from Bell (2003) and Condon (1992), the former provides a better match to the observed trends in SSFR versus stellar mass in the lowest mass bins, and also in reproducing the low-redshift SFRD seen in other wavebands. |
In summary, the UDS has produced a statistically powerful sample of [MATH] -selected galaxies, including several thousand selected by colour to lie at high redshift. Stacking these samples into a deep 1,400-MHz radio image has enabled us to determine their radio properties at flux densities an order of magnitude fainte... |
Acknowledgements We thank the anonymous referee for helpful comments on the paper. We would like to thank Stephen Serjeant for useful discussions. OA would like to ackowledge the support of the Royal Society. SF, AJM, RM and MC acknowledge support from STFC. |
# Source: arxiv 0808.3140 # Title: Direct calculation of the radiative efficiency of an accretion disk around a black hole # Sections: all # Downloaded: 2026-03-02T07:58:32.590949+00:00 |
DIRECT CALCULATION OF THE RADIATIVE EFFICIENCY OF AN ACCRETION DISK AROUND A BLACK HOLE Abstract Numerical simulation of magnetohydrodynamic (MHD) turbulence makes it possible to study accretion dynamics in detail. However, special effort is required to connect inflow dynamics (dependent largely on angular momentum tra... |
[MATH] accreting onto a black hole with spin parameter [MATH] , we find that there is significant dissipation beyond that predicted by the classical Novikov-Thorne model. However, much of it occurs deep in the potential, where photon capture and gravitational redshifting can strongly limit the net photon energy escapin... |
greater than the Novikov-Thorne prediction. If the accreted thermal energy were wholly radiated, the total luminosity of the accretion flow would be [MATH] greater than the Novikov-Thorne value. |
Black holes - magnetohydrodynamics - instabilities - stars:accretion Introduction For the past thirty-five years, it has been the standard view in the astrophysical community that the total amount of energy per unit mass dissipated in the course of accretion onto a black hole is exactly equal to the binding energy of t... |
Although the significance of magnetic forces was no more than a speculation when the zero-stress boundary condition was first criticized, in recent years it has been recognized that they are, in fact, essential to accretion (Balbus & Hawley, 1998 . Stimulated by this recognition, the past decade has seen many numerical... |
(Hawley & Krolik, 2001 2002 ; Armitage et al., 2001 ; Reynolds & Armitage, 2001 ; Armitage & Reynolds, 2003 ; Machida & Matsumoto, 2003 ; De Villiers et al., 2003 ; Krolik et al., 2005 ; Gammie et al., 2004 . Initially these simulations assumed Newtonian dynamics in a pseudo-Newtonian potential; in the middle of this e... |
(Beckwith et al., 2008a In an effort to remedy this situation, we have altered the HARM code in two significant ways. First, we have extended it from 2D (axisymmetric) to 3D. This extension has two major consequences: we can study nonaxisymmetric fluctuations, and are free from 2D artifacts like the “channel solution”;... |
For our first use of this code, we chose to run a simulation that would illustrate how MHD turbulence influences the global energetics of accretion onto a black hole. Its results can be compared directly to those of NT: Time-averages of its data can be matched against the classical model’s steady state. Quantities inte... |
Because we recognize that quantitative results may well depend on a number of parameters (magnetic field configuration and disk thickness, most notably) and because our radiation model does not fully represent any particular physical situation, we emphasize that the numbers we present here are only preliminary samples.... |
The Computation: HARM3D and the Parameters of Our Simulation Quite a number of general relativistic MHD simulation codes have been written already |
(Komissarov, 1999 ; Koide et al., 1999 ; Gammie et al., 2003 ; De Villiers & Hawley, 2003 ; Duez et al., 2005 ; Shibata & Sekiguchi, 2005 ; Anninos et al., 2005 ; Antón et al., 2006 ; Noble et al., 2006 ; Mizuno et al., 2006 ; Anderson et al., 2006 ; Tchekhovskoy et al., 2007 ; Fragile et al., 2007 ; Del Zanna et al., ... |
(Gammie et al., 2003 ; Noble et al., 2006 HARM solves the equations of motion in flux-conservative form, but is restricted to axisymmetry As we have already mentioned, axisymmetric calculations suffer from two major drawbacks: the dominance of “channel solutions”, which are ubiquitous in 2D but unstable in 3D (Balbus &... |
HARM ’s conservative formulation means that it does not lose energy to numerical dissipation; rather, kinetic and magnetic energies lost at the gridscale are captured as heat. At the same time, a conservative formulation permits easy introduction of a formal radiative cooling term. Thus, our new code, called HARM3D , i... |
2.1 Basic Equations We begin the description of HARM3D with an explicit statement of the equations governing our model. Contrasts with Gammie et al. ( 2003 HARM and De Villiers & Hawley ( 2003 GRMHD ) will be highlighted along the way. We use Greek letters for spacetime indices, and Roman letters for spacelike indices.... |
The general relativistic MHD (GRMHD) equations of motion include the continuity equation, [EQUATION] the equations of local energy conservation |
[EQUATION] and Maxwell’s equations [EQUATION] [EQUATION] Here, [MATH] is the rest-mass density, [MATH] is the 4-velocity of the fluid, [MATH] is the Faraday tensor times [MATH] |
[MATH] is the dual of this tensor or the Maxwell tensor times [MATH] , and [MATH] is the 4-current The total stress-energy tensor is the sum of the fluid part, |
[EQUATION] and the electromagnetic part [EQUATION] where [MATH] is the metric, [MATH] is the specific enthalpy, [MATH] is the pressure, [MATH] is the specific internal energy density, [MATH] |
is the magnetic field 4-vector, and [MATH] is twice the magnetic pressure [MATH] Equations ( ) can be expressed in flux conservative form |
[EQUATION] where [MATH] is a vector of “conserved” variables, [MATH] are the fluxes, and [MATH] is a vector of source terms. Explicitly, these are |
[EQUATION] [EQUATION] [EQUATION] where [MATH] is the determinant of the metric, [MATH] is the metric’s affine connection, and [MATH] is our magnetic field |
Note that the source term for the energy equation is non-zero only when the metric is time-dependent (as evidenced by its proportionality to [MATH] ). The equations of motion are closed by an equation of state, |
[MATH] where [MATH] is the adiabatic index, set to [MATH] in this work. The primitive variables, [MATH] , are recovered using an optimized version of the the “2D” algorithm described in |
Noble et al. ( 2006 . The primitive velocity is the flow’s velocity as viewed by a zero angular momentum observer (ZAMO): [EQUATION] |
where [MATH] is the lapse function and [MATH] is the Lorentz factor. 2.2 Initial Data In the initial state of the simulation, the matter is in an axisymmetric hydrostatic torus that orbits the black hole with a specific angular momentum profile slightly shallower than Keplerian and [MATH] The disk is centered about the... |
[MATH] In order to solve the time-independent Euler equations, we must therefore specify [MATH] . Following Chakrabarti ( 1985 and De Villiers et al. ( 2003 we do this by assuming that |
[MATH] , where [MATH] The solution is simplified by setting [MATH] to its Schwarzschild value [MATH] , which is exact when [MATH] but leads to a solution marginally out of equilibrium when [MATH] ; the slight departure from equilibrium insignificantly affects the disk’s evolution because the magnetic field quickly beco... |
[MATH] , where [MATH] and [MATH] With the intention of closely mimicking the initial conditions of simulation KDP of De Villiers et al. ( 2003 , we put the torus pressure maximum at [MATH] and choose an angular momentum distribution parameter [MATH] . The torus inner boundary is |
[MATH] , with [MATH] These parameters yield a disk very similar to that of De Villiers et al., but with a slightly larger [MATH] |
The solution to Euler’s equations provides us with [MATH] and [MATH] The rest-mass density is then calculated from the equations of state— [MATH] and |
[MATH] —and [MATH] [MATH] We suppose that the gas is non-relativistic, choosing [MATH] and [MATH] . Integrating over the volume of the initial gas distribution, we find a total rest-mass of 353. This is [MATH] larger than that in simulation KDP, a shift due to our slightly different choice of [MATH] . Note that the cod... |
The initial magnetic field lies entirely within the torus and follows contours of constant density. The magnitude of the magnetic field is set so that the volume-weighted integrated magnetic pressure is [MATH] times less than the volume-weighted integrated gas pressure. |
The atmosphere surrounding the disk is unmagnetized and static. The atmosphere’s density and pressure are set to their smallest allowed values, which are chosen so that the floor state is in approximate pressure equilibrium: |
[MATH] and [MATH] where [MATH] is the initial maximum value of the rest-mass density in the disk. 2.3 Radiative Cooling A magnetized accretion disk is subject to the magneto-rotational instability (MRI), which transfers angular momentum outward. This transfer taps into the available free energy of differential rotation... |
[EQUATION] where [MATH] is the amount of radiated energy-momentum per unit 4-volume in the coordinate frame. To describe the radiation, we make the simplest assumption: that the emission is isotropic in the fluid’s frame: |
[EQUATION] where the “cooling function” [MATH] is the rate energy is radiated per unit proper time in the fluid frame. The NT assumptions include complete prompt radiation of all locally-dissipated heat. We cannot exactly replicate that in a simulation, for the gas must retain some thermal energy. However, we can arran... |
In different contexts, different definitions of the scale-height [MATH] are sometimes used. For a thin isothermal disk in a Newtonian potential, the density profile is Gaussian, [MATH] , with |
[MATH] , for isothermal sound speed [MATH] . Another common measure of the scale-height is the half-width at half-maximum (HWHM), |
[MATH] . A third is the vertical density moment, [EQUATION] When the profile is Gaussian, [MATH] We prefer the moment definition because it is a direct measure of the characteristic mass-weighted disk thickness, it is robust with respect to fluctuations, and it is closely related to the characteristic scalelengths of h... |
In any event, given this definition, the temperature that should produce a desired aspect ratio [MATH] in Newtonian gravity is [EQUATION] |
In code units, [MATH] In our simulation, we evaluate [MATH] in the disk body using the relativistic orbital frequency [MATH] In a more completely relativistic treatment, [MATH] would be replaced by [MATH] , where |
[MATH] is the Newtonian Keplerian rotation frequency and [MATH] is the relativistic correction factor for the vertical gravity ( (Abramowicz et al., 1997 notation as in (Krolik, 1999a Inside the innermost stable circular orbit (ISCO), we define |
[MATH] as the orbital frequency of a particle with the specific energy and angular momentum of the circular orbit at the ISCO: [EQUATION] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.