def F(x):
len_gap_kpc = np.deg2rad(sss.gap_size(
mass, dist=dist, timpact=x))/auni.rad*dist
vel = 1 # kms
len_gap_km = 3.086e16*len_gap_kpc
time_fill_gap = len_gap_km/vel/3.15e7/1e9 # in gyr
return time_fill_gap/x-1
def find_gap_size_depth(mass, dist, maxt=1, **kwargs):
# if gap_fill = True
"""
Arguments:
---------
mass:
subhalos mass in units of 1e7 Msun
dist:
distance of stream in kpc
Returns:
---
(len_gap_deg, depth_gap):
length of gap in degrees
gap depth
"""
# time to fill the gap created by subhalo of the given mass and impact parameter
time = find_gap_fill_time(mass, dist, **kwargs)
# cap time after the impact to the time required to fill the gap
time = min(time,
maxt) # time to fill gap if less than max t (default 0.5 Gyr)
#print ('x',F(0.5),F(0.001),F(10),time,maxt)
print('time', time, mass) # ,maxt)
len_gap_deg = sss.gap_size(mass, dist=dist, timpact=float(time), **
kwargs) / auni.deg
depth_gap = 1 - sss.gap_depth(mass, timpact=time, **kwargs)
return len_gap_deg, depth_gap
def find_gap_size_depth(mass, dist, maxt=1):
def F(x):
len_gap_kpc = np.deg2rad(sss.gap_size(
mass, dist=dist, timpact=x))/auni.rad*dist
vel = 1 # kms
len_gap_km = 3.086e16*len_gap_kpc
time_fill_gap = len_gap_km/vel/3.15e7/1e9 # in gyr
return time_fill_gap/x-1
R = scipy.optimize.root(F, 0.1)
time = R['x'][0]
time = min(time, maxt)
#print ('x',F(0.5),F(0.001),F(10),time,maxt)
print('time', time, mass) # ,maxt)
len_gap_deg = sss.gap_size(mass, dist=dist, timpact=float(time))/auni.deg
depth_gap = 1 - sss.gap_depth(mass, timpact=time)
return len_gap_deg, depth_gap
def predict_gap_depths(mu, distance_kpc, survey, width_pc=20, maglim=None,
timpact=1, gap_fill=True):
"""
Arguments:
---------
mu: real
Surface brightness of the stream in mag/sq.arcsec^2
distance_kpc: real
Distance to the stream in kpc
survey: str
Name of the survey
width_pc: real
The width of the stream in pc
timpact: real
The time of impact in Gyr
gap_fill: bool
If true we take into account the filling of the gaps. I.e. we
use the depth of the gap and the size of the gap up to a point
in time when the gap is supposed to be filled (assuming that it
fills with 1km/s velocity)
Returns:
---
(masses,tdepths,odepths): Tuple of 3 numpy arrays
The array of halo masses
The array of theoretically predicted gap depths
The array of potentially observable gap depths
"""
isoname = 'iso_a12.0_z0.00020.dat'
mockarea = 100
mockfile = 'stream_gap_mock.fits'
width_deg = np.rad2deg(width_pc/distance_kpc/1e3)
mgrid = 10**np.linspace(3., 10, 100)
mgrid7 = mgrid / 1e7
if not gap_fill:
gap_depths = np.array(
[1 - sss.gap_depth(_, timpact=timpact) for _ in mgrid7])
# We do 1-gap_depth() because sss_gap_depth returns the height of
# the gap from zero rather than from 1.
gap_sizes_deg = np.array(
[sss.gap_size(_, dist=distance_kpc * auni.kpc, timpact=timpact) /
auni.deg for _ in mgrid7])
else:
gap_depths = np.zeros(len(mgrid))
gap_sizes_deg = np.zeros(len(mgrid))
for i, curm in enumerate(mgrid7):
gap_sizes_deg[i], gap_depths[i] = find_gap_size_depth(
curm, dist=distance_kpc, maxt=timpact)
if maglim is None:
maglim_g = getMagLimit('g', survey)
maglim_r = getMagLimit('r', survey)
else:
maglim_g, maglim_r = [maglim]*2
dens_stream = snc.nstar_cal(mu, distance_kpc, maglim_g=maglim_g,
maglim_r=maglim_r)
dens_bg = get_mock_density(distance_kpc, isoname, survey,
mockfile=mockfile, mockarea=mockarea,
maglim_g=maglim_g, maglim_r=maglim_r)
print('Background/stream density [stars/sq.deg]', dens_bg, dens_stream)
max_gap_deg = 10 # this the maximum gap length that we consider reasonable
N = len(gap_sizes_deg)
detfracs = np.zeros(N)
for i in range(N):
area = 2 * width_deg * gap_sizes_deg[i]
# twice the width and the length of the gap
nbg = dens_bg * area
nstr = dens_stream * area
print('Nstream', nstr, 'Nbg', nbg)
detfrac = 5 * np.sqrt(nbg + nstr) / nstr
# this is smallest gap depth that we could detect
# we the poisson noise on density is sqrt(nbg+nstr)
# and the stream density (per bin) is nstr
detfracs[i] = detfrac
if gap_sizes_deg[i] > max_gap_deg:
detfracs[i] = np.nan
return (mgrid, gap_depths, detfracs)