ZwCl 1400.4+0949 Project

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Zw1400.4+0949 Project notes

Redshifts We are using the Hα redshift. Note that we should drop ones with zConf > 0.35 which have bad measures. We should also look at ones which have Z_WARNING set to something other than blank.

Correction of velocities to the rest frame of the CMB:

Kogut et al. 1993 give the motion of the Sun wrt the CMB is V = 369.0+/-2.5 km/s in direction of l = 264.31+/-0.19 degrees and b = 48.05 +/- 0.1 degrees. From NED, we find for the direction of Zw1400.4+0949, this translates to a correction to the observed heliocentric velocity of +260 km/s.

The CMB correction applies to objects beyond the local flow field. For the moment, we won't worry about it for Zw1400.4+0949.

Calculation of distances:

For most galaxies, we use the CMB velocity and divide by the Hubble constant, which we adopt to be 70 km/s/Mpc.

However, for galaxies believed to be a member of the ZwCl 1400.4+0949 cluster, we assign the distance using the mean redshift of the cluster.

Group/cluster membership:

Refer to the discussion in Koranyi & Geller (2002, AJ 123, 100). As in that reference, we adopt the center to be the peak of the ROSAT X-ray emission, RA = 14h02m48s = +09d19'40" = (210.70,9.33). We should look up the ROSAT reference in Price et al. (1991). This is virtually identical to the position for WBL 486 given in NED.

To determine the mean distance and membership, we examine the histogram of CMB velocities for galaxies within 0.68 and 1.36 degrees of the cluster X-ray position. I settle on those regions iteratively, noting that at 83.7 Mpc, 1 Mpc = 41 arcmin = 0.68 degrees.

Radius	Vcmb range	Group	# of galaxies	Vsys	sigma
0.68deg	5600-6600	Zw1400+09	45	5861	241
0.68deg	6600-7600	Background	29	6890	201

Following Koranyi & Geller, we assume objects at 5000 km/s are in the foreground. We use Hubble flow correction to CMB velocities for those objects.

Mass of the cluster: Methods of estimating the masses of groups of galaxies are discussed in a paper by Heisler, Tremaine & Bahcall, 1985, ApJ 298, 8. As mentioned there, most estimates of the mass of groups are based on application of the Virial Theorem. The trick is that, in practical applications, we observe only radial velocities and projected (on the sky) positions, and we have to deal with "interlopers", unrelated objects projected onto the group as it appears to us.

For each object which we designate as a cluster member, we have (a) the line-of-sight velocity relative to the cluster mean and (b) the projected separation from the centroid. Equation (11) of Heisler, Tremaine & Bahcall (1985) can then be used to estimate the mass, since they discuss exactly what correction factors to use to deal with projected quantities.

HI mass:

The HI mass is calculated simply from the HI flux in Jy-km/s and the distance in Mpc.
is given by:
HI mass (solar masses) = 2.36E+06 * Dist² * HI line flux.

Linear diameters:

We can calculate the linear diameter from one of the radii given in the SDSS photometric database. But see the note on HI deficiency, below.

For the angular diameter, we start with the DR7 value petroR90_r, the radius, in arcsec, encompassing 90% of the Petrosian magnitude. You should probably find out what a "Petrosian magnitude" is.

The linear diameter then is calculated from simple geometry, using 2X petroR90_r, and adopting the distance to each galaxy.

Note In round 1, I find 4 galaxies with anomalously low diameters (D < 3 kpc). Check them out below; these clearly demonstrate the pitfalls of SDSS pipeline catalogs.

AGC 238643 1355583+085936 208.9929 8.99333	SDSSNavigate	NED	off center knot in LSB object; petroR90 not good
AGC 249100 1402578+103713 210.7408 10.62028	SDSSNavigate	NED	2 photoObjs in center of late-type barred spiral; replacing 587736477051322652 instead of 587736477051322663 This works and this galaxy appears to get fixed!
AGC 243852 1407045+104245 211.7688 10.71250	SDSSNavigate	NED	Blue knot in LSB object
AGC 243830 1414435+100429 213.6812 10.07472	SDSSNavigate	NED	In the glare of a very bright star.

HI Deficiency:

We will following the thinking in Haynes & Giovanelli (1984) and Solanes et al. (1996). (This needs to be updated to Toribio et al. 2011). The trick is that the diameters we are using are different from the ones employed in those studies, so we should check the calibration of the relation. We have to work a little more on this.

Here is a first crack at looking at how the HI mass varies with linear diameter. It is a log-log plot; the filled blue symbols represent galaxies identified with MKW 12 (sepdeg< 1.36, 5600 < vcmb < 6600) while the red ones show galaxies in the background group in the same sky region (sepdeg< 1.36, 6600 < vcmb < 7600). I need to remove those anomalous points (with bad linear diameters petroR90_r, as discussed above).

Inclinations:

The inclination can be derived from the observed axial ratio b/a where b is the minor axis and a is the major axis. We adopt from SDSS DR7 the observed expAB_r which is the axial ratio in the R-band. The inclination is given by:
cos²i = (r² - p²)/(1 - p²)
where r = b/a, the observed axial ratio, and p = c/a, the intrinsic axial ratio. The intrinsic axial ratio is probably dependent on the morphological type, and we adopt p = 0.2 for types Sbc and earlier, and 0.12 for later types.

Correction of magnitudes for galactic extinction:

NED gives a value of the (B-V) color excess, E(B-V), of 0.031; this comes from the DIRBE sky maps of interstellar dust emission made by the COBE satellite as understood by Schlegel, Finkbeiner and Davis (1998, ApJ 500, 525). We need to know how to apply that to SDSS magnitudes.

Table 6 of Schlegel, Finkbeiner and Davis (1998) gives the exinction A_lambda relative to E(B-V) for the SDSS filters, namely:

Filter	L_eff	A/A_V	A/E(B-V)
Sloan u	3546	1.579	5.155
Sloan g	4925	1.161	3.793
Sloan r	6335	0.843	2.751
Sloan i	7799	0.639	2.086
Sloan z	9294	0.453	1.479

The SDSS correction for E_BminusV = 0.031 therefore is for u,g,r,i,z respectively: 0.160, 0.118, 0.085, 0.065 and 0.046 magnitudes.

Correction of magnitudes for internal extinction:

This is a little messy, because the correction depends on the inclination of the galaxy and the adopted extinction law. I have not been able to find a reference which explains this well for SDSS filters, so I am depending on the (exhaustive) discussion carried out for (Landolt-based) I-band by Giovanelli et al. (1995, Astro J 110, 1059). We use the basic result given in that paper and their formula which gives the internal extinction depending on the observed axial ratio (inclination) and on galaxy luminosity. This is discussed further in Giovanelli et al. (1997, Astro J. 113, 22; here is what they say:

We will use their basic values for I-band and then adopt the same relationships among the other wavelengths as given by Schlegel et al. (1998; see above).

To perform this correction, we have to calculate the Landolt I-band absolute magnitude for each galaxy, starting with the SDSS i-band magnitude and the distance. The SDSS website gives a conversion relation (admittedly for stars, not galaxies)
I = r - 1.2444*(r - i) - 0.382
(See also the ALFALFA U-grad page.) Let's convert using the galactic extinction corrected magnitudes at the r and i bands. Once we calculate the I-band magnitude, we can calculate the I-band absolute magnitude simply.

Schlegel, Finkbeiner and Davis (1998) also give conversions for Milky Way extinction in Landolt I-band (as for Sloan; see the discussion of galactic extinction above). Assuming the same relationship applies in other galaxies as in the MW, we can use their value of Landolt I in their Table 6 :

Filter	L_eff	A/A_V	A/E(B-V)
Landolt I	8090	0.594	1.940

The internal extinction correction at SDSS i band Δm_i then is just (2.086/1.940)*Δm_I. We can similarly calculate the internal extinction corrections for u, g, r, z by scaling to the i band value, using the relations given in Table 6, e.g. Δm_u = (5.155/2.086)*Δm_i, etc.

Correction of magnitudes for K-correction:

Blanton et al (2003), AJ 125, 2348 discuss the K-corrections for SDSS data in great detail; they also provide a library of appropriate IDL code which can be downloaded from Mike's web page. The median redshift of galaxies in the SDSS spectroscopic sample is 0.11, much higher than that of our sample. We expect that the K-correction will be very small. In fact, they state (Section 2.2, p124):

"...We want to emphasize here that, while K-correcting to a fixed-frame bandpass is sometimes necessary in order to achieve a scientific objective, it is not always necessary or appropriate. Because K-corretions are inherently uncertain (the broadband magnitudes do not uniquely determine the SED), they should be avoided or minimized when possible..."

So, since our sample is at such low redshift, I suggest we not apply a K-correction.

We now can calculate the corrected apparent magnitude in each filter band as:
m_corr_f = petromag_f - Δm(galext) - Δm(intext) Whoopee, now we can calculate absolute magnitudes!

Calculation of Absolute Magnitudes:

The absolute magnitude for each filter f is given by the simple expression:
absMag_f = m_corr_f + 5. - 5.* alog10(dist*1.0E+06)
and then the luminosity at that filter is:
luminosity_f = 10.**[0.4(absMag_Sun_f - absMag_f)]

We note the values given for the urgiz colors of the Sun at: SDSS:

Assuming M(V)=+4.82, U-B=+0.195, B-V=+0.650, V-Rc=+0.36, and Rc-Ic=+0.32, the Sun has
    M(g)=   (+/-0.02)
    u-g = +1.43  (+/-0.05)
    g-r = +0.44  (+/-0.02)
    r-i = +0.11  (+/-0.02)
    i-z = +0.03  (+/-0.02)

so, we adopt M(r)= +5.12 - 0.44 = +4.68.

Calculation of stellar masses:

Once we have corrected magnitudes, we can calculate the stellar masses associated with the observed luminosity. We adopt need to adopt a stellar M/L according to the galaxy color. See Bell et al. 2003:

TABLE 7
Stellar Mass-to-Light Ratio as a Function of Color 
(here _f refers to SDSS or 2MASS filter)
Color   a_g     b_g      a_r     b_r      a_i     b_i      a_z     b_z      a_J     b_J      a_H     b_H      a_H     b_H
u-g   -0.221   0.485   -0.099   0.345   -0.053   0.268   -0.105   0.226   -0.128   0.169   -0.209   0.133   -0.260   0.123
u-r   -0.390   0.417   -0.223   0.299   -0.151   0.233   -0.178   0.192   -0.172   0.138   -0.237   0.104   -0.273   0.091
u-i   -0.375   0.359   -0.212   0.257   -0.144   0.201   -0.171   0.165   -0.169   0.119   -0.233   0.090   -0.267   0.077
u-z   -0.400   0.332   -0.232   0.239   -0.161   0.187   -0.179   0.151   -0.163   0.105   -0.205   0.071   -0.232   0.056
g-r   -0.499   1.519   -0.306   1.097   -0.222   0.864   -0.223   0.689   -0.172   0.444   -0.189   0.266   -0.209   0.197
g-i   -0.379   0.914   -0.220   0.661   -0.152   0.518   -0.175   0.421   -0.153   0.283   -0.186   0.179   -0.211   0.137
g-z   -0.367   0.698   -0.215   0.508   -0.153   0.402   -0.171   0.322   -0.097   0.175   -0.117   0.083   -0.138   0.047
r-i   -0.106   1.982   -0.022   1.431    0.006   1.114   -0.052   0.923   -0.079   0.650   -0.148   0.437   -0.186   0.349
r-z   -0.124   1.067   -0.041   0.780   -0.018   0.623   -0.041   0.463   -0.011   0.224   -0.059   0.076   -0.092   0.019
                                                         
Color                                          
B-V   -0.942   1.737   -0.628   1.305   -0.520   1.094   -0.399   0.824   -0.261   0.433   -0.209   0.210   -0.206   0.135
B-R   -0.976   1.111   -0.633   0.816   -0.523   0.683   -0.405   0.518   -0.289   0.297   -0.262   0.180   -0.264   0.138

Notes. Stellar M/L ratios are given by log(M/L) = a_f + b_f x color, 
where the M/L ratio is in solar units. 
If all galaxies are submaximal, then the above zero points a_f should be modified by 
subtracting an IMF dependent constant as follows: 0.15 dex for a Kennicutt or 
Kroupa IMF, and 0.4 dex for a Bottema IMF. Scatter in the above correlations 
is 0.1 dex for all optical M/L ratios, and 0.1-0.2 dex for NIR M/L ratios 
(larger for galaxies with blue optical colors). SDSS filters are in AB magnitudes; 
Johnson BVR and JHK are in Vega magnitudes.

For our purposes, let's stick to the r-band and hence use:
log M/L(rband) = -0.306 + 1.097*(corrmag_g - corrmag_r)
M(stars) = L_r * M/L(rband)

Color-magnitude diagram

Ok, so now we can try to make a color-magnitude plot like the one in Baldry et al. which plots AbsMag_r versus (u - r) color. Note that I use now corrected magnitudes and colors (with corrections for galactic and internal extinction).

Baldry et al present a functional divider between the red and blue sequence given by:
divider= 2.06 - 0.244*dtanh(factor)
which I can include on the plot.

There are a few weird outliers on this diagram, and it is worth taking a look at them so, here they are. See also the SDSS mosaic of their images.

ALFALFA	Too faint/blue?	238636 SDSSNavigate	very low surface brightness faint object
ALFALFA	Too blue?	232563 SDSSNavigate	interacting system
ALFALFA	Too faint?	243859 SDSSNavigate	very low surface brightness faint object
ALFALFA	Too faint?	243835 SDSSNavigate	very diffuse low surface brightness object
DR7 spect	Too blue?	243916 SDSSNavigate	small, compact galaxy
ALFALFA	Too faint?	249095 SDSSNavigate	very low surface brightness faint object
DR7 spect	Too red?	730099 SDSSNavigate	early type galaxy in pair; but watch nearby star
DR7 spect	Too red?	249364 SDSSNavigate	interacting system
DR7 spect & ALFALFA	Too faint?	243852 SDSSNavigate	HII knot in galaxy?
ALFALFA	Too faint?	249109 SDSSNavigate	very diffuse low surface brightness object
ALFALFA	Too faint?	249118 SDSSNavigate	very diffuse low surface brightness blue object
DR7 spect	Too red?	244010 SDSSNavigate	early type in glare of nearby star; color probably contaminated

Starbursts versus AGN:

Sarah is investigating the ratios of emission line equivalent widths for galaxies in our region and how they can be used to discriminate starburst from AGN. The basic method of performing such classification is to examine the location of each galaxy on an "Osterbrock diagram" as discussed in the book "Astrophysics of Gaseous Nebulae and Active Galactic Nuclei" by Donald Osterbrock (and the 2008 new edition of the same by Osterbrock and Ferland; see Chapter 14 especially).

Kauffmann et al (2003 MNRAS, 346, 1055) select AGNs from the SDSS using:
log([OIII]λ5007/Hβ) >= {0.61/[log([NII]λ6583/Hα)-0.05]} + 1.3.

Here is the lineratios plot. There are a few outliers; we should take a look to see if we understand what's up.

These objects have strange lineratios compared to Osterbrock & Ferland 
yratio > 1.4 or < -1
xratio > 1 
 yratio 713708     2.00399804    2.28546691    0.69992298    0.02398900  -0.06   1.47 587736543625871510
 yratio 713771     1.84882700    4.10145998    1.91484499    0.07510300  -0.35   1.41 587736477587734736
 xratio 243884    54.40460205    3.20507312   98.11115265   51.38726425   1.23   0.28 588017726558830607
 yratio 243860     1.30253100    4.78960323    3.74071908    0.00986084  -0.57   2.58 587736542553178754
 yratio 713819     3.76380396    6.83772182    8.32061577    0.27839500  -0.26   1.48 587736478662131825
 yratio 240082     2.03377104    4.15707493    0.00469569    0.20766100  -0.31  -1.65 587736543090311257
 yratio 730130     8.12229824    5.26415014    6.16007423    0.02006800   0.19   2.49 587736478125719660
 yratio 715930     4.19501305    4.44104195    5.93706417    0.16350999  -0.02   1.56 587736540943548456
 yratio 713892     1.32766998    5.30448103    3.52231598    0.05954200  -0.60   1.77 587736478126047320

AGC 713708 208.3308 10.12167 SDSSNavigate NED
AGC 713771 209.6637 11.07639 SDSSNavigate NED
AGC 243884 210.0008 7.76444 SDSSNavigate NED
AGC 243860 210.7525 9.04944 SDSSNavigate NED
AGC 713819 211.2933 11.77111 SDSSNavigate NED
AGC 240082 211.4288 9.51222 SDSSNavigate NED
AGC 730130 212.2192 11.17778 SDSSNavigate NED
AGC 715930 212.9183 7.80222 SDSSNavigate NED
AGC 713892 212.9717 11.20917 SDSSNavigate NED

Star formation rates

The Hα equivalent width (EW) provides a measure of the current rate of massive star formation. A measure of the star formation rate SFR in solar masses per year is given by
SFR(M_solar/yr) = 7.9 x 10^-42 L(Hα)
where L(Hα) is the luminosity in the Hα line in erg/s. Remember the definition of equivalent width:
EW (Angstroms) = ∫ (F_cont - F_λ)/F_cont * dλ

with F_cont = 1 the continuum level unit normalized, F_λ the line profile level, and dλ the sampling in wavelength units (Angstroms). Also remember that EW < 1 for an absorption line and EW > 1 for an emission line.

We should be able to compute the flux of the Hα line from the EW via:
F_line(Hα) = EW(Hα) X F_cont(Hα).
so we need to find F_cont from the SDSS. We can get the value of continuum flux at the line center from the SDSS database, F_cont, in units of 10^-17 ergs/s/cm^2/per Angstrom. We then can calculate the Hα luminosity just by 4πDistance**2/Flux, using the proper units, of course.

There are several additional corrections we need to make: (1) for stellar absorption; (b) for internal extinction and (3) for SDSS aperture (the fibers) for internal extinction to the measured Balmer line equivalent widths. These corrections are discussed by Nakamura et al. (2004, AJ 127, 2511) and in Hopkins et al. (2003, ApJ 599, 971; this is the paper I am using now). I am applying a straight correction for stellar Hα absorption of 1.3 Angstroms; this seems to be an intermediate value and we should probably investigate it further someday. I am not here making a correction for internal extinction, but we could do that using the ratio of Hβ to H&alpha. For the aperture correction, it is conventional practice to use a correction based on scaling from the fiber magnitude to the Petrosian magnitude. There is another discussion in the Appendix to the Hopkins et al. paper, but I am not sure it will apply to this nearby sample. For the moment, I use the fiber-to-Petrosian scaling aperture correction but this too is work for the future.

Rotational velocities

The ALFALFA catalog gives values of the HI line profile width, measured at 50% of the peak, in km/s; the observed full width W50 is related to twice the rotational velocity projected along the l.o.s. To convert this to a disk rotational velocity, we have to first correct for the inclination of the disk, using the inclination we derived above. V_rot = 1/2 * W50/sin(i).

Velocity dispersions

The SDSS dataset includes measures of the velocity dispersion of spectral lines, the parameter l.sigma in SDSS nomenclature. The units of sigma are a bit weird, so that to convert to km/s you have to multiply by the speed of light and then divide by the rest wavelength (l.sigma*300000.0/l.wave). Notice too that they are measured only over the aperture of the optical fibers used: 3 arcseconds.

First, let's use the H-alpha line (rest wavelength 656.281 nm); when we do, we find a few bogus values (sigma = -99999.) which need to be checked out; It turns out they all have problems with their spectra in the region of H-alpha.

AGC 715896 SDSSNavigate no Halpha
AGC 730083 SDSSNavigate no Halpha
AGC 243969 SDSSNavigate no Halpha
AGC 713930 SDSSNavigate no Halpha

We should also take note of the SDSS warning regarding velocity dispersion measurements for low signal-to-noise < 10 and velocity dispersion estimates smaller than about 70 km/s given the typical S/N and the instrumental resolution of the SDSS spectra.

We might also try a stellar absorption line .... haven't yet though.

Dynamical masses

The dynamical mass within some radius R can be defined as M(r2/G.

Tully-Fisher relation

The Tully-Fisher relation is a well known scaling relation between the rotational velocity and optical luminosity. Since we calculate both of those, we can see if our galaxies follow the T-F relation and ask if some are outliers.

Dark Galaxies(!):

There are two objects in the ALFALFA catalog in our box which do not have optical counterparts. They are AGC 238652 and AGC 249137.

AGC 238652 1358170+070848 209.5708 7.1467 Explore ObjID SDSSNavigate SkyView.03 SkyView.10 DSS2red.03 DSS2blu.03 DSS2red.10 DSS2blu.10 NED

AGC 249137 1400571+083333 210.2379 8.55917 Explore ObjID SDSSNavigate SkyView.03 SkyView.10 DSS2red.03 DSS2blu.03 DSS2red.10 DSS2blu.10 NED

Here are quick plots of the distribution of galaxies in the vicinity of the two objects: 238652 and AGC 249137. BTW, the circles here represent the ALFA beams if ALFA were staring at the central object; don't take them too seriously. But remember about sidelobes? What about them?

AGC 238652: In the vicinity of 238362, there are several galaxies within 5 arcminutes and at similar velocities.

 AGC#  Name        RA,Dec          THESE VALUES COME FROM THE AGC database                  separation
  8881 046-018  1357588+070941  120  20 152   160   7084  0    774 206 7051 413  A50J875     4.60
238653          1358088+070921   28  18 177   100   7252-98      0   0    0   0     00 0     2.11
238652 HIdet    1358170+070848    0   0   0     0      0  0     43 209 7317  39  A50J875     0.00
231119 046-025  1358201+071328   80  50 151   300   7390-99     80 209 7283  73  A50J875     4.73

ALFALFA catalog entries:
HI source ID      AGC                  RA,Dec (HI)             no opt id            V21          W21        Flux                  SNR   RMS  Code   gridname  
HI135758.5+070952   8881  046-018  135758.5+ 7 952  -4  10  135758.8+ 7 941    1.1  7051    3   413    5    7.74  0.11    7.49   40.6  2.06   1     1356+07  
HI135817.0+070848 238652           135817.0+ 7 848   0   0  0000 0.0+ 0 0 0    1.1  7317    5    39   10    0.43  0.04    0.45    7.2  2.09   1     1356+07
HI135819.0+071300 231119  046-025  135819.0+ 713 0 -15 -28  135820.1+ 71328    1.2  7283    3    73    7    0.80  0.05    0.72    9.9  2.09   1     1356+07

Here are links to the ALFALFA spectra for these galaxies:UGC 8881, AGC 238652 and AGC 231119.

It is likely that the HI source 238652 is related in some way to the other two objects 231119 and 238653. There may be some kind of interaction going on. We'd need to map with higher resolution to find out. Anyway, this is NOT an isolated "dark galaxy".

AGC 249137: In the vicinity of 249137, there are several galaxies within 5 arcminutes and at similar velocities.

 AGC#  Name        RA,Dec          THESE VALUES COME FROM THE AGC database                  separation
230925 074-035  1400310+083901  110  20 156   160   4593-99    339   0 4363 620  P200255     8.46  
249137 HIdet    1400571+083333    0   0   0     0      0  0     53 225 4702  33  A50J875     0.00
231601 074-038  1401089+083500   53  22 153   120   4876-99    155 226 4864 400  A50J875     3.26

ALFALFA catalog entries:
HI source ID      AGC                  RA,Dec (HI)             no opt id            V21          W21        Flux                  SNR   RMS  Code   gridname  
HI140031.3+083900 230925  074-035  140031.4+ 83852   6  -8  140031.0+ 839 1    1.4  4572    2   180    5    2.62  0.06    2.62   26.3  1.65   1     1356+09
HI140057.0+083341 249137           140057.1+ 83333   0   0  0000 0.0+ 0 0 0    2.5  4702    3    33    6    0.53  0.04    0.54    8.8  2.25   1     1404+09
HI140111.9+083500 231601  074-038  140112.0+ 83452  45  -7  1401 8.9+ 835 0    1.2  4864    8   400   15    1.55  0.11    1.13    7.7  2.26   1     1404+09

Here are links to the ALFALFA spectra for these galaxies: AGC 230925, AGC 249137 and AGC 231601.

It is likely that the HI source 249137 is related in some way to the other two objects 230295 and 231601. There may be some kind of interaction going on. We'd need to map with higher resolution to find out. Anyway, this is NOT an isolated "dark galaxy".